09 — CHESS AND MARKETS: the two uses as registered beds and as products

Written 2026-09-05 at HEAD 99777ab under CHARTER.md. SATURN-II · WATSON (instruments and beds); LESTRADE's prices cited from COSTS.md and docs/CEQ_SHAPE.md §A.11. Books 01–06 did not exist in docs/canon/ when this book was written (ls docs/canon/ → CHARTER.md, CORRECTIONS.md, RUN this session); every attachment to them cites docs/CEQ_SHAPE.md and docs/PLAN.md by section instead.

Preface — what this book decides, and the verse that decides it first. The author's two uses — chess trained on chess data, and prediction-market trades — have at 99777ab no bed, no pipeline, no label, no floor and no matched baseline (CHARTER.md §5 row B27). This book registers each use twice: once as a bed inside the operator's class (a tree or lattice of future states serialised leaves-first, so the environment chain is a DAG in token order and the exact committor is a \(0\) GPU-s linear solve), and once on natural ground (the game prefix; the order book and price path), where the arm's \(\hat P\) is not the environment chain and every contrast is live but bound by D-1 and R-SKY. Nothing is decided by construction: every label carries its zero-information floor, every bed its census and D-4 gate, every arm its FOUND-not-NAMED census, every kill a frozen number and a planted negative. The verse that decides first is 09.10 (the chess census at \(0\) GPU-s) for chess and 09.32 (the market census at \(0\) GPU-s) for markets: either bed can die before a GPU-second, and the reroute is pre-written in 09.19 and 09.35. The honest floor on markets is a theorem (09.23a, whose venue-side registration is 09.23b): under the martingale hypothesis, and only where the declared sets exhaust the absorbing states, the market-implied probability is the unconstrained YES committor, so the module's whole market claim is a measured departure from martingale, scored against the market by Brier and log score, with "no edge" as the point estimate under D-CALIB. No verse here says "more accurate" or "faster to train" outside forms A1/A2/T1/T2 of CHARTER.md §1, and no verse carries a capability number: every number is a floor, a price, a count or a citation.

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Part I — Chess

09.1 — The break: the chess use has no bed in the record

Statement. At 99777ab the repository holds exactly one chess-touching source file (ceq/kdata.py), one test file carrying \(31\) passing hygiene tests (tests/gate0/test_g05_data.py), two synthetic fixtures (36 games, one 512-row evaluation shard), zero registered chess beds, zero eval-\(\Delta\) producers, zero engines, zero arms consuming a chess corpus, and zero results/ records of any chess kind. Hypotheses. The tree at 99777ab; ceq.kdata.BED_SPECS as the bed registry; results/**/*.jsonl as the FOUND census. Geometry: none — no cell exists at any \((s,d,n,N,K,t^\star)\). Evidence. RUN python -c "from ceq import kdata; print(list(kdata.BED_SPECS))" → ['bed_m', 'bed_k', 'bed_1']. RUN this session python -m pytest -q tests/gate0/test_g05_data.py → 31 passed in 0.60s: one test file, \(31\) tests, which is the integer book 04.7's Terminal prints (READ 04_BEDS_AND_INSTRUMENTS.md:95, 31 passed in 0.73s) — the count is shared between the two books, the wall-clock is unrepeated and is not a law. RUN grep -l -i chess results/*.jsonl results/*.json results/*.txt results/*.md → results/k_data_manifest.json only. READ V20_R15_JOURNAL.md:2418-2443 @ 99777ab ("two of the witness's three oracles are free today; the third has no producer, no engine, no registered bed, no arm, and 34.4 GB behind the attach"). READ V20_R15_JOURNAL.md:2677-2684 @ 99777ab (full-tree census: one source file, one test, two fixtures, zero producers). READ COSTS.md:36-38 (lichess_chess_games, lichess_chess_evaluations UNPINNED, AWAITING KAGGLE). READ CEQ_V20_R15_CONTRACT.md:117-118 @ 99777ab (the witness: legality, next-FEN, eval-\(\Delta\) sign; oracles recomputed). Mechanism. P-4 (claimed scaffolding that does not exist), P-7 (a "witness" with no referent in BED_SPECS), FOUND-not-NAMED. Kill. The fix is 09.2–09.19. The fix has failed when, after 09.2 lands, python -c "from ceq import kdata; print('bed_c' in kdata.BED_SPECS)" prints False, or when ceq.kdata.bed_signature('bed_c') called twice in one process returns two different digests (the Ruling-7 regeneration test, price \(0\) GPU-s, CPU seconds). Planted negative: a generator seeded from time.time() must fail the twice-test; the pass half must print two equal 64-hex digests. If killed. The generator is re-specified under the single-RNG discipline of ceq/corpus.py (one seed, one numpy.random.default_rng, nothing else touching global state; READ ceq/beds/bed_k.py:30-35) — Hypotheses: python-chess 1.11.2 move generation is deterministic given the board (a rules engine, no randomness); Evidence: RUN python -c "import chess; print(chess.__version__)" → 1.11.2; Kill: the twice-test again, \(0\) GPU-s. A second failure is not a seeding failure but a library one, and the bed pins chess==1.11.2 as a hard requirement (the pin V17_G05_DATA.md:388 @ 99777ab names and neither requirements file carries: READ V20_R15_JOURNAL.md:2430). Terminal. "The chess use is registered as a generator specification with no reproducible digest; no cell may cite it" — and B27's chess half stays open in CORRECTIONS.md.

09.2 — The local data route before any Kaggle attach: generator, dump, and the three UNPINNED sources with their substitutes

Statement. BED-C is carried as generator \(+\) seed \(+\) hash (Ruling 7) from two local sources, in this order: (i) BED-C-G, python-chess self-play under the uniform-random-legal-move policy \(\pi_u\) — n_games games, at most max_plies \(=200\) plies, seed \(\sigma\), the manifest dict hashed by ceq.kdata._feed; (ii) BED-C-D, one monthly standard-rated PGN dump of the lichess database (access route: the public monthly archive of database.lichess.org, .zst-compressed PGN, CC0), downloaded once to data/, its SHA-256 written into results/k_data_manifest.json with licence: CC0-1.0, status UNPINNED until the digest is recorded. The three UNPINNED Kaggle sources of COSTS.md §0 and their local substitutes: arevel/chess-games (Lichess PGN, 1.56 GB) → BED-C-D; lichess/chess-evaluations (34.4 GB, one streamed shard) → the local engine recompute of 09.6; tinystories_cdla (595 MB) → not a chess source, no substitute owed by this book. Hypotheses. ceq.kdata unchanged (verify_file, verify_digest, MissingPin, iter_games, split_by_game, fen_dedupe, label_plies); Kaggle never contacted (the author's yes is a node on the critical path: docs/PLAN.md §5.7). Geometry: \(n_{\rm games}\in\{2048, 8192\}\), \(\sigma\in\{0..7\}\). Evidence. READ results/k_data_manifest.json:130 and :143 (both "sha256": null, status: UNPINNED_AWAITING_KAGGLE, RUN this session); READ kaggle/README.md "Attach list — item 4, CORRECTED" (the generator regime for BED-M/K/1); RUN ls data/ this session → thirteen entries (ls data/ | wc -l → 13; the twelve this verse previously printed is one short and is struck), none of them a .pgn and none a lichess* file — the full listing is in 09.20's Evidence; RUN python -m ceq.kdata self-check regime READ ceq/kdata.py:40-43. The guard's own pins, corrected against RUN grep -n '^def ' ceq/kdata.py this session: verify_file is at ceq/kdata.py:157-158 and _pin (which raises MissingPin) at :127-142 — and verify_file calls sha256_file before _pin raises, so the unpinned-source guard costs one full read of the file it refuses: on the \(1.56\) GB arevel/chess-games dump that is a \(1.56\) GB read for a refusal (DERIVED from the call order at :157-158). [ASSUMED] the lichess monthly archive is reachable from this box — no download was made this session (the standing rule: notify first). Mechanism. P-1 (a number with no live producer), Ruling 7, V-22 (no count derived on Kaggle transfers to the local bed). Kill. Any cell that reads BED-C-D before its digest is in the manifest: kdata.verify_file('bed_c_dump', path) must raise MissingPin (the existing guard; READ ceq/kdata.py:127-142 for _pin, :157-158 for verify_file). Planted negative: a manifest entry with sha256: "" must raise; the pass half: a recorded digest must return it. Price \(0\) GPU-s. A second kill, frozen: fen_dedupe reports leaked_val > 0 or leaked_test > 0 after dedupe on the real dump (READ V17_G05_DATA.md:64 @ 99777ab: 14 FENs leaked on the fixture before dedupe, 0 after). If killed. If the dump cannot be pinned (no download, or a digest that moves between two downloads because the archive was re-cut), BED-C-D is dropped and BED-C-G is the only source — Hypotheses: self-play under \(\pi_u\) covers the terminal outcomes (checkmate, stalemate, insufficient material, 75-move, fivefold) with class frequencies in \((0.05,0.95)\); Evidence: NOT MEASURED — needs the BED-C-G generator (book 04's bed instrument); Kill: the 09.10 census line 6 on 512 draws at \(0\) GPU-s. If BED-C-G's outcome classes leave the band (random play draws by the 75-move rule far more often than it mates), the generator is re-registered from endgame seeds (positions with \(\le 5\) pieces drawn from BED-C-G's own games) — the same kill, the same price. Terminal. "BED-C has a generator and a hash; no natural-ground number exists because no dump is pinned" — the natural-ground bed of 09.7 is then VOID and only BED-C-T (09.5) may run.

09.3 — PGN to FEN sequences to tokens: the two context layouts and the hygiene that is already code

Statement. A game is replayed by label_plies into rows \(\{\)fen_before, uci, san, fen_after, legal\(\}\), never read from a stored column. Two context layouts are registered. Natural ground (BED-C-N): the context is the game prefix as raw bytes (the frozen tokenizer, vocabulary \(256\), fingerprint f8e843a8…81e14), the query is the current FEN, \(m\) candidate UCI strings follow it, and a move is \(\mathrm{do}(a)\) on the board. In-class (BED-C-T, 09.5): one token per node of a local game tree, serialised leaves-first, each token a feature vector through a linear input projection \(F(s,K)\times d_{\rm model}\) shared by every arm. One feature table, one total, and \(F\) is a function of \(s\) and \(K\) — the projection cost is \(F(s,K)\cdot d_{\rm model}\) and is repriced per bed and per \(s\) in 09.14 and 09.34:

feature	width	at \(s=64,K=2\)	at \(s=256,K=2\)
piece planes, one-hot	\(64\times13\)	\(832\)	\(832\)
side to move	\(1\)	\(1\)	\(1\)
castling rights	\(4\)	\(4\)	\(4\)
en-passant file (incl. none)	\(9\)	\(9\)	\(9\)
parent index, one-hot over \(s\)	\(s\)	\(64\)	\(256\)
move id	\(1\)	\(1\)	\(1\)
membership flags (sink, goal, \(\mathcal A_1..\mathcal A_K\))	\(K+2\)	\(4\)	\(4\)
total \(F(s,K)=849+s+K\)		\(\mathbf{915}\)	\(\mathbf{1{,}107}\)

The membership-flag width is \(K+2\) here and nowhere \(K+4\): the label tensor is \([m,K+4]\) (six channels at \(K=2\): sink, goal, loss, draw, \(\mathcal A_1\), \(\mathcal A_2\)) and the input flags are the \(K+2\) boundary channels of 08_ARCHITECTURE.md 08.1's shapes table, row set masks at \([B,K+2,s]\), which the token carries; the two widths are different objects and are never summed. Splits are by GAME, FENs are deduplicated across splits, and the tokenizer is hashed into the manifest. Hypotheses. ceq.kdata rules 1, 2, 4, 5 (READ ceq/kdata.py:16-30); \(s=512\) bytes for BED-C-N (a FEN is \(56\)–\(90\) bytes, so at most \(5\) positions plus \(m\le 8\) moves fit); \(s=64\) tokens for BED-C-T. Evidence. READ ceq/kdata.py:258-268 (label_plies takes a Game, so no stored label is reachable); READ ceq/kdata.py:206-223 (iter_games, where the Site-header key is set) and :225-239 (split_by_game, which assigns by the hash of that key, salt recorded) — the three pins the refutation corrected against RUN grep -n '^def ' ceq/kdata.py this session; READ results/k_data_manifest.json tokenizer.fingerprint. The oracle cost is a band over four unrepeated readings of the same fixture, not a point: \(0.128\) s (the first reading), \(0.1524\) s (RUN this session, python -c "import pathlib,sys; sys.path.insert(0,'.'); from tests.mercury.phase_c_price import chess_oracle_cost; print(chess_oracle_cost(pathlib.Path('.')))" → (512, 0.15239199999996345)), \(0.1929\) s (the refutation's reading of the same command in the same tree, \(+50.6\) per cent over the first), \(0.376\) s (READ V20_R15_JOURNAL.md:2441 @ 99777ab, \(+194\) per cent over the first) — so \([0.128,\,0.376]\) s for \(512\) plies, unsynchronised, single CPU, [FITTED-free, unrepeated], \(0\) GPU-s. It is a fixture number on \(36\) synthetic games and licenses no throughput law; the fixture "has never seen a real Lichess PGN" (READ V17_G05_DATA.md:375-378 @ 99777ab). Mechanism. M-1 (train and eval must see one preprocessing — one tokenizer, one split rule), V-7 (a split that cannot leak is not a guard: the guard fires on a planted by-row split, READ V17_G05_DATA.md:60). Kill. The corpus-alone linear probe of CEQ_SHAPE.md §5.3 S-15, run on BED-C-N: from the token bytes of the query FEN and the \(m\) move strings to the committor tensor at order \(0\), honest \(R^2\ge0.5\) → leak kill (c), the one-read claim is void on the natural-ground bed; planted positive (a move token carrying its own \(q\)) \(R^2<0.99\) → the detector is blind and no leak verdict is admissible (V-15). Price \(0\) GPU-s (CPU probes on 512 draws). If killed. The honest probe at or above \(0.5\) means the label is a function of the visible tokens at zero hops on this layout; the replacement is the layout with the candidate moves withheld from the context and supplied only as the head's query (the \([m,K+4]\) head reads \(m\) external move embeddings; \(K+4\) is the label tensor's channel count, never the token's \(K+2\) flag width) — Hypotheses: the committor of a child is not a zero-hop function of the parent FEN alone; Evidence: DERIVED from 09.7 (legality and next-FEN are zero-hop functions; the committor at depth \(h\ge2\) is not); Kill: the same probe on the new layout, \(0\) GPU-s. If it fires again, the label is legible from the position alone at zero hops on this position class and the bed is a static task (K-H2). Terminal. "The chess pipeline is code with planted-violation tests; every label on it is recomputed; no layout on which the label is legible at zero hops carries a capability number."

09.4 — The state space: terminal outcomes as absorbing sets, the goal set per side, the \(K\) constraint sets

Statement. A board state \(x\) is transient unless it is terminal. The declared sets are not independent predicates and are not disjoint as written — a node five pawns down with a forced mate against it satisfies both \(\mathcal A_1\) and \(\mathcal A_2\), and checkmate received satisfies both \(\mathcal A_{\rm loss}\) and \(\mathcal A_2\) at \(k\ge1\) — so disjointness is imposed by a total priority order, first match wins, registered here and hashed into the manifest: $\(\mathcal A_{\rm sink}\ \succ\ \mathcal A_0\ \succ\ \mathcal A_{\rm loss}\ \succ\ \mathcal A_{\rm draw}\ \succ\ \mathcal A_2\ \succ\ \mathcal A_1\ \succ\ \mathcal A_3 .\)$ The sets: \(\mathcal A_{\rm sink}\) (BOS, and on BED-C-T every horizon leaf, value \(0\) on every indicator channel); \(\mathcal A_0\) the goal, checkmate delivered by the side to move — a board fact decided by python-chess, and nothing else; \(\mathcal A_{\rm loss}\) (checkmate received) and \(\mathcal A_{\rm draw}\) (stalemate, insufficient material, seventy-five-move rule, fivefold repetition — the rules python-chess decides from the board; threefold and fifty-move claims and resignation/timeout are PGN Result facts, not board facts, and form a separate set \(\mathcal A_{\rm res}\) whose share is printed and never merged); the \(K\) constraint sets \(\mathcal A_1\) material breach (material balance \(\le-\theta\) pawn units for the side to move, \(\theta\in\{1,3,5\}\), default \(3\)), \(\mathcal A_2\) mate threat — the opponent has a forced mate in \(\le k\) from that node, \(k\in\{1,2,3\}\), decided by the engine of 09.6 (an engine_sha256 is required) or, on BED-C-T at \(h\le3\), by exhaustive search inside the tree, \(\mathcal A_3\) (optional) repetition. \(K\ge2\) always. This is the canon's single definition of \(\mathcal A_0\) and \(\mathcal A_2\) for chess and book 08 cites it rather than restating it: 08_ARCHITECTURE.md 08.18's worked example 1 places the evaluation-sign and mate-in-\(k\) flag inside the goal set \(\mathcal A_0\) and mate-against in \(\mathcal A_2\), which admits an engine evaluation into the goal — and 09.6 records RUN which stockfish → none on this box and refuses every engine label without an engine_sha256, so under book 08's reading the goal set is undefined on this box. The divergence is owed as a CORRECTIONS.md row naming 08_ARCHITECTURE.md 08.18's worked example 1; this book's writer may not write that file (CHARTER.md §3, no file but this one), and until the row exists the divergence stands recorded here. The row names the verse and its quoted text, never a line. 08_ARCHITECTURE.md is not at 99777ab and its line numbers move under concurrent repair: RUN grep -n twice in this session read the two worked examples at line \(470\) and then at line \(475\) of the same file. A line pin into a book being repaired is not a pin (CHARTER.md §3), so this book's three previous pins into it — :394, :396, :404 — are struck and replaced by verse ids with the quoted text beside them (08.1's set masks row, 08.18's moves row, 08.18's worked examples 1 and 2). Hypotheses. Definition 3 of docs/CEQ_SHAPE.md §2.1 (sink separate from goal, every set before the query in token order — F2), with disjointness supplied by the priority order above and not assumed. \(K\in\{2,3\}\); \(|\mathcal A_\bullet|\) per draw is the number of tree nodes in the set. The reach-avoid sum identity is asserted on BED-C-T only, where \(\mathcal A_{\rm res}=\emptyset\) by construction (a generated tree has no Result header, no resignation and no claim), so the declared sets exhaust the absorbing states there. Evidence. DERIVED from Proposition 3 and Proposition 8 (READ docs/CEQ_SHAPE.md:373-374 and :497-499), both of which give \(\sum_\bullet q^{(\bullet)}=\mathbb 1\) only "when the declared sets exhaust the absorbing states": on BED-C-T, with the sink declared and \(\mathcal A_{\rm res}=\emptyset\), \(q^{({\rm sink})}+q^{(0)}+q^{({\rm loss})}+q^{({\rm draw})}+\sum_{k\ge1}q^{(k)}=1\) on \(T\). On BED-C-D the identity is false as printed: resignation and time forfeit are board-undecidable and terminate the majority of games in a lichess monthly standard-rated dump, so there \(q^{({\rm res})}\) carries the missing mass and the printed sum is \(1-q^{({\rm res})}\) — the share is printed and 09.10 line 14b carries its admission threshold. CITED [V] dufour-2023-absorbingmdp, esterhuysen-2026-terminal for the absorbing-state reading of terminal outcomes (naming only; no load-bearing sentence rests on them). RUN python -c "import chess; b=chess.Board(); print(len(list(b.legal_moves)))" → 20 (the initial branching; the bed's \(m\le 20\) at the root is a rules fact). Mechanism. V-12 (a single absorbing target makes the label constant: \(K=1\) is illegal), V-8 (the sink share printed apart from the goal share), V-25 (the identity's hypothesis printed, not assumed), D-3 (\(\theta\) and \(k\) are dials with registered supports). Kill. On 512 BED-C-T draws at \(0\) GPU-s: (a) the disjointness line, census 1b — any node landing in more than one declared set after the priority order is applied, on more than \(0\) per cent of draws (the pre-priority overlap count is printed beside it and is expected positive: \(\mathcal A_{\rm loss}\subseteq\mathcal A_2\) at \(k\ge1\) makes it positive whenever a mate occurs inside the tree); (b) the class frequency of any of \(\{\mathcal A_0,\mathcal A_{\rm loss},\mathcal A_{\rm draw}\}\) as the absorbing set of the walk from the root leaves \((0.05,0.95)\); (c) \(q^{({\rm sink})}\) exceeds \(0.95\) on more than \(50\) per cent of draws (the horizon leaves swallow the walk). Planted negative: \(\theta=0\) (every capture is a breach) must send \(\mathcal A_1\)'s frequency above \(0.95\) and fire line (b); the priority order disabled must send line (a)'s post-priority overlap above \(0\) on any draw containing a mate, and fire it. If killed. The sink dominates because at \(h=2\) from a middlegame position almost no leaf is terminal. Replacement: the position class moves to endgames (\(\le5\) pieces on the board, drawn from BED-C-G's own games after ply \(60\)), where terminal leaves at \(h=2\) are dense — Hypotheses: terminal density \(\rho_{\rm term}(h=2)\) over \(\le5\)-piece positions exceeds \(0.05\); Evidence: NOT MEASURED — needs the BED-C-G generator with a terminal_density census column (book 04); Kill: the same census line, \(0\) GPU-s. If the endgame class also fails, the horizon leaves are re-labelled by the engine's static evaluation sign as a discounted read at \(\gamma_{\rm env}\) (fisac-2019-bridging [V], the separate registered label of Definition 7), which is no longer a committor — and the bed's sentence becomes the one in 09.19's Terminal. Terminal. "The chess state space is registered with \(K\ge2\) constraint sets, a total priority order that makes them disjoint, and a declared sink whose share is printed on every draw; the reach-avoid sum identity holds on BED-C-T only, where \(\mathcal A_{\rm res}=\emptyset\); where the sink dominates at the registered horizon, no committor label is quoted."

09.5 — BED-C-T: the in-class chess bed — a game tree serialised leaves-first, the committor as one exact solve

Statement. From a root position \(x_0\), the tree of depth \(h\) under branching \(m\) (the \(m\) candidate root moves, and \(m\) replies per node, chosen as the first \(m\) legal moves in python-chess's generation order under a registered permutation seed) is serialised leaves first, root last, so every child precedes its parent in token order and the walk from the root descends to earlier tokens, exactly as the causal \(\hat P\) does. \(P_{\rm env}\) is row-stochastic: at a transient node uniform over its \(m\) children under \(\pi_u\) (or the engine-softmax policy \(\pi_\tau\) at temperature \(\tau\), a second registered dial); at an absorbing node \(e_a\). The label per root move \(a\) is the reach-avoid vector \(q(a)=\big(q^{({\rm sink})},q^{(0)},q^{({\rm loss})},q^{({\rm draw})},q^{(1)},\dots,q^{(K)}\big)\) of the child \(u_a\), solved per declared absorbing set on \(P_{\rm env}\) at \(\gamma=1\): $\(q^{(\bullet)}=(I-Q)^{-1}R_\bullet\mathbb 1,\qquad \bullet\in\{{\rm sink},0,{\rm loss},{\rm draw},1,\dots,K\},\)$ with \(R_\bullet\) the transient-to-\(\mathcal A_\bullet\) block. The full block \(R\) is never used on the right-hand side: \(\sum_\bullet R_\bullet\mathbb 1=\mathbb 1-Q\mathbb 1\), so \((I-Q)^{-1}R\mathbb 1=\mathbb 1\) identically — the all-ones vector, carrying no label — and any verse printing \(q=(I-Q)^{-1}R\mathbb 1\) is printing \(\mathbb 1\). The read is \(K+4\) separate right-hand sides against one factorisation, never one. \(\mathrm{do}(a)\) has two forms and the bed decides which: on BED-C-T the root is the last token, so \(\mathrm{do}(a)\) is the row clamp \(P_{\rm env}[x_0,:]\leftarrow e_{u_a}\), rank one, \(u^\top\mathbb 1=0\) (Definition 6(i)), priced at \(O(s)\) because no token follows the intervened row; on BED-C-N the move rewrites a suffix of the byte context from position \(i\), ("rewrite", i, tokens_i') in 08_ARCHITECTURE.md 08.18's moves row, rank \(s-i\), priced as a suffix re-solve at \((s-i)^2d/2\) MACs. Both prices are printed in 09.14; 08_ARCHITECTURE.md 08.18's worked example 1 states the suffix form at \(i=s-1\) and does not name which bed it describes, and that divergence is owed as a CORRECTIONS.md row. The argmin columns: \(a^\star=\arg\max_a q^{(0)}(a)\), the Chebyshev \(a^\dagger=\arg\min_a\max_{k\ge1}q^{(k)}(a)\), the conditioned Chebyshev, with the disagreement fraction printed. At \(s=64\): \(h=2\), \(m=7\), \(1+7+49=57\) nodes plus the BOS sink; at \(s=256\): \((h,m)=(3,5)\) gives \(156\) nodes or \((2,15)\) gives \(241\). Hypotheses. \(s\in\{64,256\}\), \(d_{\rm model}\in\{16,64\}\), \(n_{\rm train}=2048\), \(n_{\rm eval}=4096\), \(N=8\), \(K=2\), \(t^\star=h\). The DAG-in-token-order substrate of CEQ_SHAPE.md §A.1 (BED-S) with the graph replaced by a tree and the adjacency feature replaced by the parent index. Representability \(\hat P=P_{\rm env}\) at \(d_{\rm model}\ge\) the feature rank: NOT MEASURED (the same open item as BED-S). Evidence. DERIVED: \(1+m+m^2\le63\Rightarrow m\le7\) at \(h=2\); \(1+m+m^2+m^3\le255\Rightarrow m\le5\) at \(h=3\). DERIVED, re-run against \(K+4\) right-hand sides: one factorisation of \(I-Q\) at \(|T|^3/3\le57^3/3=61{,}731\) MACs plus \(K+4=6\) back-substitutions at \(|T|^2/2=1{,}624.5\) each, \(9{,}747\) MACs, so \(\le71{,}478\) MACs per draw, microseconds in float64; on a tree with every declared set absorbing, \(Q\) is strictly lower-triangular and the factorisation is the identity, so the realised cost is the \(\le9{,}747\)-MAC substitution sweep alone. [V-eq] READ docs/CEQ_SHAPE.md:369-372 — Proposition 3, the per-channel form \(q^{(k)}_i=[(I-Q)^{-1}R_k\mathbb 1]_i\) with its hypotheses (\(P\) row-stochastic including absorbing rows, \(\rho(Q)<1\), \(V=\mathbb 1_{\mathcal A_k}\)) and the sum clause "when the declared sets exhaust the absorbing states"; numeric instance, DERIVED at the registered geometry: on the \(h=2\), \(m=7\) tree with all \(49\) leaves in \(\mathcal A_{\rm sink}\) and no interior terminal, \(q^{({\rm sink})}=1\) and \(q^{(0)}=q^{({\rm loss})}=q^{({\rm draw})}=q^{(1)}=q^{(2)}=0\) at every transient node, summing to \(1\) — while the struck form \((I-Q)^{-1}R\mathbb 1\) returns \(\mathbb 1\) on that same draw and on every other, which is why it is not a label. READ docs/CEQ_SHAPE.md §5.3 S-11 (the BED-S specification this bed instantiates); kemeny-1960-finitemarkov [V-cat]. Mechanism. D-2 (the oracle runs on \(P_{\rm env}\), never on \(\hat P\); the tree is the input, so leak clause (a) is dropped and (c) kept), V-25 (the operator class contains the chain: with every declared set absorbing, \(Q\) is lower-triangular in token order), F2 (every boundary set precedes the query by construction of the serialisation). Kill. K-E2 on 512 draws at \(0\) GPU-s (09.10): any per-coordinate sd of \(q\) over the root \(=0\); any argmin class frequency outside \((0.05,0.95)\); rule disagreement \(=0\). And the reachability check: \(\rho(Q)<1\) on \(100\) per cent (a tree with the sink declared has \(\rho(Q)=0\) exactly — \(Q\) is strictly lower-triangular with no self-loops on transient nodes — so this line is V-10 and is printed, never counted). If killed. The dial moves before the substrate does: \(h\) from \(2\) to \(3\) at \(s=256\) (\(m=5\)), then the position class of 09.4's If-killed. Each reroute re-runs the \(0\) GPU-s census; nothing else changes. If both fail, the tree bed is not a committor bed at any registered \((h,m,s)\) and only the discounted read at \(\gamma_{\rm env}\) of the engine's leaf evaluation remains (09.4). Terminal. "BED-C-T is a registered generator with an exact \(0\) GPU-s oracle, floors, controls and a VOID list; at the registered dials it does not admit, and no chess number exists."

09.6 — The oracles: python-chess as the exact rules oracle; the engine at fixed depth as the eval oracle with its hash pinned; the tree solve as the exact committor

Statement. Three oracles, three classes. (i) Rules: python-chess 1.11.2 decides legality, the next FEN and every board-terminal condition exactly; price \(0\) GPU-s. (ii) Engine: a UCI engine at fixed depth \(D\), Threads=1, fixed Hash, a fixed binary whose SHA-256 is pinned into the manifest as engine_sha256; its centipawn evaluation \(e_D(x)\) and mate score are the eval-\(\Delta\) and mate-in-\(k\) producers, recomputed locally, never read from lichess/chess-evaluations. (iii) Committor: the linear solve of 09.5 on \(P_{\rm env}\) — exact to solver precision. The Syzygy tablebases for \(\le7\) pieces are a fourth, exact, outcome-under-optimal-play oracle (a different chain from \(\pi_u\)) and are registered as a cross-check only, like BED-1. Hypotheses. An engine binary present on the box with Threads=1; a depth \(D\in\{8,12,16\}\); the same binary hash at label time and at every re-run. Evidence. RUN which stockfish → none on this box (this session); the engine oracle is therefore NOT MEASURED — needs the pinned binary (book 05's environment pin). RUN python -c "import chess.engine" → present (the UCI client is in python-chess). READ results/k_data_manifest.json hygiene.oracle_labels ("RECOMPUTED at load by python-chess"). Syzygy files: not on this box (NOT MEASURED — needs the tablebase download pinned per Ruling 7). Mechanism. D-2 (the oracle is not the arm's resolvent: python-chess and the engine compute nothing the arm computes), P-1 (an eval label with no engine hash is a number with no live producer), Ruling 1 (bitwise for every deciding forward cell — an engine label must be bitwise across two runs). Kill. Engine determinism, frozen: on 512 positions, \(e_D(x)\) at Threads=1 on two runs differs on any position → the engine at depth \(D\) is not an oracle. Planted negative (V-15): the same 512 positions at Threads=4, depth \(D=20\), must differ on at least \(1\) of \(512\) between two runs; if the plant does not fire, the determinism instrument is blind and every engine label is [ASSUMED]. Price: CPU minutes, \(0\) GPU-s. If killed. Replace the depth limit by a node limit (nodes=N_{\rm nodes}, single thread) — Hypotheses: the engine's node-limited search at one thread is a deterministic function of (binary, position, Hash, nodes); Evidence: NOT MEASURED — the same two-run test; Kill: the same two-run test, \(0\) GPU-s. The link is not cheaper — it is the same test at the same price — and its decisiveness gain is what licenses it, stated as CHARTER.md §2's depth rule requires: a depth limit lets the search's stopping rule depend on wall clock through time-management and hash-table timing, so a depth-\(D\) disagreement cannot separate "the binary is non-deterministic" from "the budget moved"; the node limit removes wall clock from the stopping rule, so a second failure isolates the binary. The third link is free and produces a number regardless of outcome: the engine label is demoted to [ASSUMED], and the two-run disagreement rate over the 512 positions is printed beside every eval-\(\Delta\) number in every case — pass or fail, at both links — so the chain yields a number even when nothing is refuted. Only the rules and committor oracles are load-bearing thereafter. Terminal. "Legality, next-FEN, board-terminal outcomes and the tree committor are exact at \(0\) GPU-s; eval-\(\Delta\) and mate-in-\(k\) carry an engine hash or are not numbers."

09.7 — The labels and their classes: which are zero-hop controls, which are vector-valued and interventional

Statement. Registered labels and their class. L-legal (per candidate move, binary): a zero-hop function of (FEN, move) — a control, the planted positive for the zero-hop guard, never a capability label. L-nextFEN (per candidate move, a \(64\)-square categorical vector, \(13\) classes per square): a zero-hop rule application — the parity control at \(\gamma=0\) (Proposition 1), never a capability label. L-eval\(\Delta\) (the \(m\)-vector of \(\mathrm{sign}(e_D(x\cdot a)-e_D(x))\)): a \(D\)-hop quantity, vector over moves, engine oracle. L-q (the \([m,K+4]\) reach-avoid tensor of 09.5): vector-valued and interventional — the capability label. L-argmin and the two rule columns: the decision label. L-halfmove (the halfmove clock, a delay-\(d\) counter): a delay label with a Hankel ceiling, a BED-K-type control. Under D-1 no scalar at one position is a capability label on either registration. Hypotheses. CHARTER.md §1 (A1/A2 need a vector-valued interventional label); \(m\in\{4,7,8\}\); the \([m,K+4]\) head attached to every arm (Ruling 3 recount). Evidence. DERIVED, and only as an information identity: legality and next-FEN are functions of the query token and one move token, so \(I(X_{\le0};y)=H(y)\) — the zero-hop view carries the label entirely. That identity licenses no approximation guarantee for any model class and in particular does not entail that a \(0\)-hop MLP fits the label: chess legality requires sliding-piece ray occlusion, pin detection and check evasion over the \(832\)-dimensional plane encoding, and no bound is given that a per-position MLP attains any accuracy on it. This is CHARTER.md §5 B7 (D-APPROX, the record's largest unclosed gap) applied backwards, and the book does not commit it: the fallback plant that is derivable by construction is registered beside the MLP plant and is the one the leak verdict rests on — a token carrying its own label verbatim, the \(R^2\ge0.99\) construction of 09.3, which fires by construction because the probe's input contains its target exactly. CITED [V] marion-2025-single-location, duranthon-2026-softmax-advantage (D-1's owners; their label model admits none of the three record beds, docs/CEQ_SHAPE.md §A.4). READ docs/CEQ_SHAPE.md §A.3 (the BED-K Hankel row, \(\mathrm{err}_1=\sqrt{1-1/d}\)). Mechanism. D-1 (racing softmax at its optimum), V-10 (a gate satisfied by construction — the zero-hop plants are declared as plants, never scored), V-15 (no condemning rule without a planted negative that fires), D-APPROX / B7 (an information identity is not an approximation bound), C8 (a static task; READ docs/CEQ_SHAPE.md:1733; not a MISTAKES.md id — MISTAKES.md equivalents D-1 plus V-10), M-3, M-9. Kill. S-14 on BED-C-T at \(0\) GPU-s plus one zero-step forward (\(\le1.524\) s [FITTED]), on \(512\) BED-C-T draws at seeds \(0\)–\(7\), the same byte-identical draws every arm sees: the untrained arm on the honest query reads L-q NRMSE \(\ge1-10^{-3}\) and argmin accuracy within \(1/m\pm\) its Clopper–Pearson half-width computed at \(n=512m\) trials (clopper-1934-binomial [V]), with the realised per-coordinate sd of L-q printed in the same block — because nrmse is normalised by std(y), returns nan on a constant label, and float('nan') >= 1.0 is False in Python, so a bare threshold passes a degenerate label silently (READ MISTAKES.md:149-153). The plant half: the verbatim-label plant must read \(R^2\ge0.99\) (by construction). The \(0.99\) accuracy of the 0-hop MLP of R-06 on L-legal and L-nextFEN is NOT MEASURED — needs the 0-hop MLP fit on \(512\) BED-C-T draws, and when measured it is printed as the calibration of the detector, never as a frozen pass mark: a realised plant accuracy below \(0.99\) calibrates the detector's sensitivity and does not by itself make the leak verdict inadmissible, because the verbatim-label plant carries that role. If the honest L-q query reads below the gate, L-q is legible at zero hops on this position class and BED-C-T is a copy task — struck before any number (K-H2). If killed. The label is re-registered one hop deeper: \(q\) of the grandchild under the best reply (the minimax-flavoured committor \(q(a)=\min_b q(u_{ab})\) over the opponent's \(m\) replies), which is not a function of the root token and the move token alone — Hypotheses: \(h\ge2\); Evidence: DERIVED (the minimum over children of a Dirichlet solve requires the children's rows); Kill: S-14 again, \(0\) GPU-s. If it fires again the bed is a static task at every registered depth and no capability label exists on chess; the labels that survive are the controls. Terminal. "Chess carries six registered labels; two are plants, one is a delay control, and the committor tensor is the only one that may carry a capability number, subject to 09.10."

09.8 — The floors per label (L-FLOOR): zero-information, exact restricted-view, Hankel

Statement. Every chess number ships beside its floor. Zero-information floors from the realised class distribution: argmin error \(\ge1-\max_a\hat\pi(a^\star)\) — at uniform \(\pi\) and \(m=7\) this is \(1-1/7=0.857143\); at \(m=8\), \(0.875\); L-eval\(\Delta\) sign error \(\ge1-\max_c\hat\pi(c)\) (the sign is skewed toward "worsens", so the majority floor is printed, never assumed uniform). Tight Fano for the argmin, printed as a formula only: \(P_e\ge(\ln m-I(X_{\le k};a^\star)-\ln2)/\ln(m-1)\) (cover-2006-elements §2.10, theorem number [U]). No value is quoted until the plug-in \(I(X_{\le k};a^\star)>0\) is computed on the admitted region and exceeds \(\ln m-\ln2-\ln(m-1)\cdot\big(1-\max_a\hat\pi(a^\star)\big)\), below which the chance floor is tighter and is the only floor printed. The two values the previous registration printed at \(I=0\) — \(0.699181\) at \(m=7\) and \(0.7124\) at \(m=8\) — are deleted: they were quoted at exactly the case the same sentence forbids, and they sit \(0.857143-0.699181=0.157962\) and \(0.875-0.7124=0.1626\) below the zero-information floors printed two lines above them, which is the same defect for which READ docs/CEQ_SHAPE.md:2495 retires the weak Fano ("sits \(0.25/0.208/0.1875\) below chance"). Exact restricted-view floor for L-q: the Bayes error of predicting \(q\) from the \(k\)-hop view, \(\mathbb E[\mathrm{Var}(q\mid X_{\le k})]\), computed on the oracle over 512 draws at \(0\) GPU-s for \(k=0,1,\dots,h\) — the hop ladder's ceiling \(\mathrm{NRMSE}(q_k,q)\) with \(q_k=Qq_{k-1}+R\mathbb 1\) printed per batch. Hankel ceiling for L-halfmove: NOT MEASURED — needs the Hankel singular-value instrument run on the reset-counter kernel at the registered ply window (book 04). No number is quoted, and the previous registration's \(\sqrt{1-1/50}=0.989949\) is withdrawn, for three reasons printed together. (i) The kernel is wrong: READ ceq/beds/bed_k.py:58-61 (live) shows BED-K's delay kernel is \(K(i,j)=1\) iff \(j=i-d\), a pure shift; the halfmove clock is a counter that resets on every capture and pawn move, and no derivation is given that a reset counter's Hankel carries the same rank-1 residual as a shift. (ii) The delay is wrong even as a shift: the fifty-move rule spans \(100\) plies, not \(50\), so \(d=50\) is unjustified at the bed's own token cadence. (iii) The record carries two mutually inconsistent forms of the same ceiling and the previous registration picked one silently: READ CEQ_V20_R15_CONTRACT.md:117 @ 99777ab reads "BED-K(a) delay d=20 (Hankel ceiling 1/d for one state)", i.e. \(1/50=0.02\) at \(d=50\), against READ docs/CEQ_SHAPE.md:1956's \(\mathrm{err}_1=\sqrt{1-1/20}=0.9746794345\) at \(d=20\), i.e. \(\sqrt{1-1/50}=0.989949\) at \(d=50\) — \(0.02\) against \(0.989949\), a factor of \(49.5\), and the conflict is named here rather than resolved by choice. The weak Fano \(1-\ln2/\ln m\) is retired (it sits below chance). Hypotheses. \(m\in\{7,8\}\); the plug-in \(I\) over the full \(k\)-hop view including move tokens and membership flags; the class distribution realised on the admitted region. Evidence. DERIVED (the three arithmetic lines above; the \(m=8\) values reproduce docs/CEQ_SHAPE.md §A.3's RUN). READ docs/CEQ_SHAPE.md §A.3 rows argmin and BED-K. Mechanism. L-FLOOR, V-17 (a floor in the wrong units — NRMSE and error rate are anchored, flipper_dependence-type quantities are not), M-2 (floors frozen before any arm). Kill. A floor computed or changed after the first arena cell strikes that cell's numbers (M-2). And the reachability check on the floor itself: the zero-information floor printed above \(0.95\) (a class of frequency \(<0.05\) dominates nothing) marks the label degenerate — the 09.10 line 6 fires first at the same price, \(0\) GPU-s. If killed. A degenerate class distribution is repaired by stratified draw selection at construction (draw roots until every argmin class has frequency in \((0.05,0.95)\) on the batch, the rejection count printed) — Hypotheses: the rejection rate is below \(0.9\) (else the bed is sliced to nothing, V-5); Evidence: NOT MEASURED — needs the generator; Kill: rejection rate \(\ge0.9\) on 512 draws, \(0\) GPU-s. If the rejection rate is at or above \(0.9\), the argmin head is struck and only the committor-vector head remains (the R-24 outcome). Terminal. "Every chess label has a printed floor; a label whose floor cannot be placed below \(0.95\) has no capability number."

09.9 — The controls at matched parameters, with exact counts

Statement. On BED-C-T at \(d_{\rm model}=64\), \(H=4\), \(s=64\), every arm's count is printed as three line items, never one, because the feature bed replaces two of TinyLM's tensors: the shared trunk (positional embedding, the blocks, the final norm) \(=53{,}952\); the feature projection \(F(s,K)\times d_{\rm model}=915\times64=58{,}560\) at \(s=64,K=2\), which replaces the \(256\times64=16{,}384\) byte-token embedding and is larger than the trunk it is added to; the head \([m,K+4]\), which replaces the \(64\times256=16{,}384\) byte output head. The previously printed \(86{,}720\) is TinyLM's total at \(d=64\), \(L=1\), vocab \(256\) — it contains both replaced tensors, so it is not a count "before the head and the projection", and \(86{,}720-16{,}384-16{,}384=53{,}952\) is (RUN this session, the per-parameter breakdown). The matched control is the depth-1 causal softmax of ceq/lm.py with the same three line items; the shape adds one \(\gamma\) per head (\(+4\)) and one \(\beta\) per instance, a residual of \(+4/(53{,}952+58{,}560+\text{head})\) printed per table rather than carried from the byte-vocabulary geometry. The depth skyline at \(t^\star=h=2\) is \(\lfloor\log_2 2\rfloor+2=3\) layers: \(53{,}952+2\times49{,}728=153{,}408\) in the trunk (unmatched, read beside every row, R-SKY), plus the same projection and head; at \(t^\star=3\), depth \(3\) again; at \(t^\star=9\) (the market lattice, 09.30), depth \(5\): \(53{,}952+4\times49{,}728=252{,}864\). The byte-vocabulary totals \(186{,}176\) and \(285{,}632\) are TinyLM's numbers at vocab \(256\) and are not the skylines of this bed. The next-token-trained control: the same depth-1 model trained on next-byte prediction over the PGN stream (BED-C-N) and then read through a frozen linear probe on L-q — the control that decides whether next-token training alone yields the committor. Fellow approximators at matched count: ChaCAL-diag at the shape's \(\hat\gamma\), ChaCAL-published, ChaCAL-with-sink-token (K-E1), InfSA-style Neumann at \(K=16\), the cached mixture, the 0-hop MLP, majority, random \(1/m\), predict-the-mean. Skylines without a cell: the MuZero-style value head (schrittwieser-2020-muzero [V]), the return-conditioned arm (chen-2021-decisiontransformer, brandfonbrener-2022-rcsl, paster-2022-luck [V]), the wide constant-depth stack (yehudai-2025-depthwidth [V]), the chain-of-thought decoder (merrill-2024-cot [V]) — each NOT MEASURED with its setting journalled. Hypotheses. TinyLM of ceq/lm.py (tok \(256\times d\), pos \(s\times d\), per block \(12d^2+9d\) with LayerNorms and biases, head \(d\times256\)); the count re-printed per arm as three line items once the head and the projection are attached. Evidence. RUN this session, four widths, TinyLM('softmax',d=D,n_layers=L,n_heads=4,seq=64,seed=0,vocab=256).n_params() at \(L=2\) minus \(L=1\): \(d=16\to3{,}216\); \(d=32\to12{,}576\); \(d=64\to136{,}448-86{,}720=49{,}728\); \(d=128\to197{,}760\) — all four equal \(12d^2+9d\) exactly (\(12(4096)+9(64)=49{,}728\) at \(d=64\)), and none equals \(12d^2+13d\), which reads \(49{,}984\) at \(d=64\), \(256\) parameters too many. The previously printed law is replaced by \(12d^2+9d\) and the ladder is re-derived from it: DERIVED per block \(=(186{,}176-86{,}720)/2=49{,}728\) — the parenthesis balanced and the number now agreeing with the law above it. RUN this session, the per-parameter breakdown at \(d=64\), \(L=1\): tok \(16{,}384\) + pos \(4{,}096\) + block \(49{,}728\) + norm \(128\) + head \(16{,}384\) = \(86{,}720\), so the trunk without the replaced tok and head is \(4{,}096+49{,}728+128=53{,}952\). RUN at \((d,L,H,s)=(512,8,8,512)\) → 25728000, reproducing COSTS.md:241; the record's arm at that shape counts \(25{,}736{,}232\), \(+0.03200\) per cent (READ docs/CEQ_SHAPE.md §4.4). CITED [V] sanford-2024-logdepth Thm 4.2 (the depth law, by analogy — the hop\(\to\)committor reduction is NOT FOUND, docs/CEQ_SHAPE.md §3.9), fagnou-2024-chacal, roffo-2026-infsa, momennejad-2017-sr. Mechanism. D-1, R-SKY, Ruling 3 (exact per-arm counts, which is why the projection and the head are separate line items), P-1, V-17, M-8 (each arm priced at its own law), C8 (READ docs/CEQ_SHAPE.md:1733; not a MISTAKES.md id — MISTAKES.md equivalents D-1 plus V-10). Kill. After the head and the projection are attached, any two "matched" arms whose printed three-line-item totals differ by more than \(0.1\) per cent (the S-30 rule): the pair is not matched and "at matched parameters" may not be written of it. A table header carrying one lump count instead of the three line items is refused at assembly (Ruling 3). Price \(0\) GPU-s (a count). A depth chosen after the arena strikes the skyline row (M-2). If killed. The count is closed by widening the smaller arm's head, never by re-architecting either operator (Ruling 3 forbids closing a residual by architecture; a head width is a registered setting) — Hypotheses: the residual is a head-size residual; Evidence: the recount; Kill: the same \(0.1\) per cent rule. If the residual survives a head recount it is an operator-parameter residual and the row is labelled "unmatched by \(x\) per cent" and read beside the skylines, never in the matched column. Terminal. "Every chess table header carries exact per-arm counts as three line items — trunk, \(F(s,K)\times d\) projection, \([m,K+4]\) head; a row without all three is not a row."

09.10 — The chess domain census (L-DOM) and the D-4 admission gate, at \(0\) GPU-s

Statement. Before any arm trains, on \(512\) BED-C-T draws at \((h,m,K,s)=(2,7,2,64)\), one JSON block per batch: (1) every \(P_{\rm env}\) row stochastic including absorbing rows, \(|\mathrm{rowsum}-1|\le10^{-12}\); (2) \(0\in\mathcal A_{\rm sink}\) and every horizon leaf in \(\mathcal A_{\rm sink}\) on \(100\) per cent; (3) \(\rho(Q)=0\) printed (V-10, not counted); (4) every set before the root and the root in \(T\) on \(100\) per cent; (1b) disjointness — every node lands in at most one declared set after 09.4's priority order, on \(100\) per cent, with the pre-priority overlap count printed beside it; (5) per-coordinate label sd of \(q\) at the root over the admitted region, defined independently of this census as the prefix at or after the first declared boundary set (the definition of READ docs/CEQ_SHAPE.md:2547, so the line is not circular), each \(>0.05\) — the threshold carries its class, DERIVED from \(\mathrm{MDE}_8=1.156\times\mathrm{sd}\) (the noncentral-\(t\) bisection of docs/CEQ_SHAPE.md §A.11 item 2: \(0.034451\to0.039827\), ratio \(1.15606\); \(0.050146\to0.057971\), ratio \(1.15604\)): at \(\mathrm{sd}=0.05\) the minimum detectable effect is \(0.0578\), already larger than the \([0,1]\) label's own sd, so below \(0.05\) no contrast at \(N=8\) is falsifiable and the line is the reachability condition for every kill downstream of it. The source's own requirement is "each \(>0\)" (READ docs/CEQ_SHAPE.md:2547); this book raises it and prints why. The sink share is printed apart from \(q^{(0)}\); (6) every argmin class frequency in \((0.05,0.95)\), ties within \(10^{-9}\) discarded and counted; (7) rule-disagreement fraction \(>0\); (8) the leak probe of 09.3; (9) \(I(s_0;a^\star)=0\) by plug-in and the untrained-arm reads of 09.7; (10) \(\mathrm{Var}(\Delta z)>0\) per coordinate over coordinates \(\ge i_{\min}\) — the source's wording restored (READ docs/CEQ_SHAPE.md:2553), the intervened index inside the range, with the zero-coordinate fraction printed; on a root-last serialisation this line is V-10 and is printed, never counted: with \(Q\) strictly lower-triangular and the root at index \(s-1\), \(\Delta z=\gamma(e_{u_a}-P[x_0,:])z\) is supported on exactly one coordinate, so under the previous wording ("after the intervened row") the variance was taken over the empty set and the line was unsatisfiable by construction on both in-class beds, and under the restored wording it is a single inner product — the interventional channel on BED-C-T and BED-P-L is therefore a cost statement (09.27's Terminal) and never a fidelity number; (11) the interventional row checks, restored to the source (READ docs/CEQ_SHAPE.md:2554) and split into 11a (the source's own three) and 11b (this book's addition), because the source's three and the addition have different statuses on a root-last tree and printing them under one number is what let the addition stand in for them. 11a, the source's line verbatim: the fraction of moves that change \(P_{\rm env}\) versus only \(V\); the fraction with \(u^\top\mathbb 1=0\) and a non-negative edited row — \(100\) per cent required, the source's requirement, restored and printed as such; and the Sherman–Morrison denominator \(1-\gamma u^\top Me_i=(1-\gamma p'_{ii})/(1-\gamma P_{ii})>0\) printed as a positivity check. All three of 11a read their passing value on \(100\) per cent of BED-C-T draws by construction, and the derivation is printed here rather than the requirement being asserted and then quietly exempted from the Kill (DERIVED, three lines): the clamp of 09.5 is \(P_{\rm env}[x_0,:]\leftarrow e_{u_a}\), so \(u=e_{u_a}-P_{\rm env}[x_0,:]\) is a difference of two row-stochastic rows and \(u^\top\mathbb 1=1-1=0\) exactly for every candidate and every draw; the edited row is \(e_{u_a}\), a basis vector, so non-negativity is a property of the write and not of the draw; and the tree has no self-loop at a transient node, so \(P_{ii}=0\), while \(u_a\) is a child of \(x_0\) and children precede the root in token order, so a self-clamp (\(u_a=x_0\), the one write that would send the denominator to \((1-\gamma\cdot1)/1=0\) at the bed's own \(\gamma=1\)) is structurally unwritable on this bed — hence \(p'_{ii}=0\) and the denominator reads \(1\) on every draw. 11a is therefore V-10 on BED-C-T — printed as a record, never counted — and the source's \(100\)-per-cent requirement is live, unchanged, on any bed whose intervention is not a basis-vector clamp, of which this book registers none; on BED-C-D and BED-C-N there is no \(P_{\rm env}\) to edit (D-2) and the line does not apply. The two clamp plants that would move 11a are registered so the print is diagnostic: a clamp written \(P[x_0,:]\leftarrow2e_{u_a}\) must send the \(u^\top\mathbb 1=0\) fraction to \(0\), and a clamp targeting \(x_0\) itself must send the denominator to \(0\) at \(\gamma=1\); neither is reachable through 09.5's generator, and both are what the print exists to catch in a mis-specified one. 11b, this book's addition, kept as an addition and never as a substitute for 11a: \(m_{\rm eff}=m\) (on a tree every root move changes the child, so no move is a no-op — printed, V-10); (12)–(13) filled on trained cells (\(\hat\beta\), \(\mathrm{rowsum}(\hat P)\), \(\hat\gamma\) with the LR verdict); (14a) the source's line, kept: for the segmentation rows only, at least one draw with an exact zero gate, with the count printed and the F0 theorems declared silent where the count is \(0\) of \(N\) (READ docs/CEQ_SHAPE.md:2558); (14b) the terminal density per depth and the \(\mathcal A_{\rm res}\) share — and, for any bed built from PGN Result headers (BED-C-D), an admission threshold: \(\mathcal A_{\rm res}\) share \(\ge0.5\) refuses the bed, because 09.4's reach-avoid sum identity is false by exactly that share there; (15) the three obstruction vacuity inequalities printed at both registered geometries, since 09.5 registers \(d_{\rm model}\in\{16,64\}\) and the source computes them at \((s,d,p)=(64,16,32)\) only — at \((64,16,32)\): sanford-2024-inductionheads Thm 1 \(h\cdot m\cdot p=4\times4\times32=512\ge64\), peng-2024-transformer-limitations Thm 1 \(n\log_2n=384<H(d+1)p=1\times17\times32=544\), chen-2024-multilayer Thm 1.1 \(64^{1/16}=1.2968\); at \((64,64,32)\): \(h\cdot m\cdot p=4\times16\times32=2{,}048\ge64\), \(n\log_2n=384<1\times65\times32=2{,}080\), \(64^{1/16}=1.2968\) (independent of \(d\)) — all vacuous at both, and more so at \(d=64\) (DERIVED). Admission requires exactly six lines and no others: lines 1, 2, 4 and the new 1b at \(100\) per cent, line 5 above \(0.05\), line 6 inside the band, line 7 above zero (on BED-C-D, line 14b's \(\mathcal A_{\rm res}\) threshold is a seventh). Lines 3, 10, 11a, 11b, 12–13, 14a and 15 are printed, never counted — 3, 10, 11a and 11b because they are V-10 gates satisfied by construction on a root-last tree, each with its derivation printed at the line rather than asserted at the Kill, 12–13 because they need a trained cell, 14a and 15 because they are records rather than gates. Hypotheses. The generator of 09.5 exists (it does not at 99777ab); the census is the bed's first cell. Evidence. NOT MEASURED — needs the BED-C-T generator and the census printer (book 04's S-12 instrument with bed_c in BED_SPECS). READ docs/CEQ_SHAPE.md §A.7 (the fifteen lines this list instantiates); nrmse returns nan on a constant label and nan >= 1.0 is False (READ MISTAKES.md:149-153), so line 5 is not optional. Mechanism. D-4 (registration without admission), V-8, V-12, V-25, M-3, L-DOM. Kill. Restricted to the six admission lines the Statement names, and to no others: line 1, line 2, line 4 or line 1b below \(100\) per cent; line 5 at or below \(0.05\); line 6 outside \((0.05,0.95)\); line 7 at zero — on BED-C-D, line 14b's \(\mathcal A_{\rm res}\) share at or above \(0.5\) as the seventh. On any of those the bed is not admitted, no arm runs, every chess arena card is VOID and unscored, and the reroute of 09.19 applies. Price \(0\) GPU-s. Lines 3, 10, 11a, 11b, 12–13, 14a and 15 cannot fire this kill: 3, 10, 11a and 11b are V-10 gates satisfied by construction on a root-last tree — 3 and 10 always at what a counting reading would call a failing value, 11a always at its passing one — so a kill quantified over all fifteen lines would refuse the bed by construction on one half of them and be a certainty on the other (V-10, D-4, M-7); the previous registration's \"any line\" wording did exactly that and is struck here. 11a's exemption is not an exemption from its requirement: the source's \(100\) per cent stands as written, the Statement derives that the write satisfies it on every draw of this bed, and the two clamp plants named there are what would move it on a mis-specified generator — an unreachable condition is printed and never counted (CHARTER.md §2's reachability rule), and it is not silently dropped. Planted negatives: BOS undeclared must give \(\det(I-Q)=0.0\) and the solve must raise (V-16); \(K=1\) must give sd\((q^{(1)})\) below \(10^{-12}\) and fire line 5 (V-12). If killed. 09.19's reroute, in order: the dial (\(h\), \(m\), \(s\)), the position class (endgames), \(N\) repriced from the first admitted batch's realised sd. Each is a \(0\) GPU-s re-run of this verse. Terminal. "BED-C-T at the registered design point does not admit; the canon files its generator, its census with the failing line printed, its floors, its controls and its pricing rule, and no chess capability number."

09.11 — The protocol that measures A1, A2, T1 and T2 on chess

Statement. One invocation on the certified device: seeds \(0\)–\(7\) deduplicated (\(N=8\) minimum, REQUIRED_SEEDS = 8), byte-identical draws per seed across arms, arms interleaved, run order randomised and journalled, every timed region bracketed by two torch.cuda.synchronize() calls, the run-order correlation of seconds printed on every table. A1 (depth 1): \(\mathrm{dist}_{\rm shape}-\mathrm{dist}_{\rm softmax\text{-}d1}<-\mathrm{MDE}_8\) on the \(\varphi\)-NRMSE of L-q, \(\varphi(p)=2\arcsin\sqrt p\) per entry, against the realised paired sd. A2 (matched count vs the depth skyline at the bed's own \(t^\star\)): the same contrast against the skyline's number printed in the same row — on BED-C-T at \(t^\star=h=2\) the skyline is \(\lfloor\log_22\rfloor+2=3\) layers (09.9); on BED-C-N the \(t^\star\) and the skyline are registered in the paragraph below and were absent before it, so A2 on BED-C-N is defined only once that layer count and its exact parameter count stand in the table header (09.15 refuses a cell missing a declared field, and t_star and sky_depth are declared fields of the identity manifest: READ docs/CEQ_SHAPE.md:1600 and :2652). T1: GPU-seconds from initialisation to a frozen distance-to-floor, taken in the floor's own units as CHARTER.md §1 defines T1 — $\(\varphi\text{-NRMSE}(q)-\varphi\text{-NRMSE}_{\rm floor}\le0.25,\)$ the difference frozen here at \(0.25\) (M-2), where \(\varphi\text{-NRMSE}_{\rm floor}\) is 09.8's exact restricted-view floor \(\mathbb E[\mathrm{Var}(q\mid X_{\le k})]\) transformed into \(\varphi\) units on the same \(512\)-draw batch, and printed, before the target is frozen: the floor is assigned in raw \(q\) units and \(\varphi(p)=2\arcsin\sqrt p\) maps \([0,1]\) onto \([0,\pi]\), so the two scales are not comparable and no subtraction is licensed until the transform is performed. Three outcomes are printed per arm and no fourth: the GPU-seconds; "not reached at \(150\) steps"; and "target below floor, T1 undefined on this bed" whenever the transformed floor is at or above the batch's attainable minimum, so that no arm can stand \(0.25\) below it. The previous registration froze an absolute \(\varphi\text{-NRMSE}(q)\le0.25\) — a different quantity, in different units from the floor 09.8 assigns and 09.13 records NOT MEASURED, so the target could sit below the floor and be unreachable by every arm — and is struck. T2: training draws to the same point. Paired \(t\) or Wilcoxon on continuous columns with their own realised sd; McNemar on the argmin and sign columns only (mcnemar-1947-correlated [V]); Clopper–Pearson on every accuracy.

BED-C-N's \(t^\star\) and skyline, registered here because A1/A2 move to that bed and it carried neither. \(t^\star\) on BED-C-N is the number of plies between the query FEN and the deepest node the label's tree solve reads — \(t^\star=h\) carried over from the label's oracle (09.5), \(=2\) at the registered \(h\) — so the skyline is \(\lfloor\log_22\rfloor+2=3\) layers, the same depth as BED-C-T's and a different parameter count, printed as three line items at \(d_{\rm model}=64\), \(s=512\) bytes: byte embedding \(256\times64=16{,}384\) (not replaced on this bed, whose input is bytes and not the \(F(s,K)\) projection), trunk (positional \(512\times64=32{,}768\) + one block \(49{,}728\) + final norm \(128\)) \(=82{,}624\), head \([m,K+4]\) at \(64\times7\times6=2{,}688\) — total \(101{,}696\); the depth-3 skyline trunk \(82{,}624+2\times49{,}728=182{,}080\), total \(201{,}152\), unmatched and read beside every row (R-SKY). RUN this session: TinyLM('softmax',d=64,n_layers=L,n_heads=4,seq=512,seed=0,vocab=256).n_params() at \(L=1,3\) → \(115{,}392\), \(214{,}848\), and \(214{,}848-16{,}384-16{,}384=182{,}080\) reproduces the skyline trunk. Before this registration BED-C-N was named ten times in this book and carried no \(t^\star\) and no skyline depth, so every A2 cell on it was refused by 09.15's own field rule while 09.11 and 09.16 moved A1/A2 onto it — the contradiction is closed here and not elsewhere. Hypotheses. \(n_{\rm train}=2048\), \(n_{\rm eval}=4096\), \(s=64\), \(d_{\rm model}\in\{16,64\}\), \(150\) steps, \(N=8\); the MDE at \(n=8\) from the noncentral-\(t\) bisection that reproduces \(0.039827\) at sd \(0.034451\) (docs/CEQ_SHAPE.md §A.11 item 2). On BED-C-T shape − softmax on the committor head is VOID by containment (09.16); A1/A2 are scored on BED-C-N (natural ground) and, on BED-C-T, only against the creditable arms. BED-C-N carries \(t^\star=2\) and skyline depth \(3\) as registered in the Statement, and carries no capability number at all until BED-C-D is pinned by digest (09.16's If-killed, against 04_BEDS_AND_INSTRUMENTS.md 04.7's Kill). The T1 target is a difference in \(\varphi\) units and is undefined until 09.8's restricted-view floor is measured and transformed; 09.13 records that floor NOT MEASURED, so at 99777ab T1 has no frozen numeric target on either chess bed and the verse says so rather than printing one. Evidence. READ docs/CEQ_SHAPE.md §A.11 items 1–2 (the MDE table: sd \(0.010101\to0.011677\); \(0.034451\to0.039827\); \(0.050146\to0.057971\); \(0.109199\to0.126238\) at \(n=8\)); READ V20_R15_JOURNAL.md C17 @ 99777ab (run order the strongest correlate of seconds, \(\rho=+0.7029\); torch.cuda.synchronize absent from scripts/v15_r1.py). BED-C's realised sd: NOT MEASURED — needs the first eight-seed batch (book 04's arena driver with a --seq-len flag, docs/CEQ_SHAPE.md §4.4). Mechanism. M-3 (pilot spread taken as realised), M-9 (a \(p\) that cannot reach its \(\alpha\)), C17, V20_R15_JOURNAL.md C17 @ 99777ab — not a MISTAKES.md id; its MISTAKES.md equivalents are M-8 (each arm at its own law) plus M-3 (unsynchronised timers, run order the strongest correlate of seconds), M-2 (the T1 target frozen before any cell), V-17 (a threshold imported out of its units: the struck absolute \(\varphi\)-NRMSE target against a floor in raw \(q\) units), L-FLOOR (the target is a distance to a floor and the floor is printed in the same units), R-SKY and Ruling 3 and L-2 (docs/CEQ_SHAPE.md §A.10 at :2640, "the identity manifest — field list (against L-2, READ V20_R15_LEAP_LEDGER.md:23)" — not a MISTAKES.md id; its MISTAKES.md equivalent is P-1: A2 needs a \(t^\star\), a skyline depth and an exact count in the header, which BED-C-N had none of). Kill. K-P: the realised paired sd at or above \(2.18\times\) the pilot's \(0.050146\) → nothing at \(N=8\) is falsifiable; \(N\) is repriced from the realised sd before any bet is scored. The timing kill: run-order correlation \(|\rho|>0.5\) on any table → every T1/T2 number in it is struck and re-run interleaved. Planted negative for the timer: a cell with a deliberate time.sleep(0.5) inside the bracketed region must read \(+0.5\) s within \(5\) per cent. Price: \(0\) extra GPU-s. Both are columns of the arena that has already been paid for — the realised sd and run_index are written by the same invocation — and that arena's own cost is \(\ge172.960\) s on chess (09.14) and \(\ge90.592\) s on markets (09.34), each of which is the byte-embedding floor of a law fitted without the feature projection and is not a price (09.14's Terminal). If killed. Two links, cheapest first, as CHARTER.md §2's depth rule requires — the previous single link, "\(N=16\) at the same price law (\(\approx68\) s per pair)", is a second arena for the registered arm set, so it is neither cheaper than the kill it replaces nor argued more decisive, and it is struck as written. Link 1, \(0\) extra GPU-s, pure arithmetic on the column K-P already printed: the required count is read off the realised sd rather than guessed — \(N_{\rm req}=\lceil 8\,(\mathrm{MDE}_{8}^{\rm realised}/\mathrm{MDE}_{8}^{\rm pilot})^2\rceil\), which at exactly the K-P firing point (\(\mathrm{sd}=2.18\times0.050146=0.109318\), \(\mathrm{MDE}_8=1.156\times0.109318=0.126372\), against the pilot's \(0.057971\)) reads \(\lceil8\times(2.17761)^2\rceil=\lceil37.94\rceil=\mathbf{38}\) (DERIVED, the noncentral-\(t\) factor held at \(1.156\) across both rows of docs/CEQ_SHAPE.md §A.11 item 2, where it moves only from \(1.15606\) to \(1.15604\)). Every contrast whose \(N_{\rm req}\) exceeds the registered budget is filed as a band with no point, at \(0\) extra GPU-s, and no bet on it is scored. Hypotheses: the paired sd is the realised one from the first eight seeds, not a pilot (M-3); Evidence: the arena's own sd column; Kill: \(N_{\rm req}\) itself — a value at or above \(38\) says \(N=16\) cannot restore the pilot's \(\mathrm{MDE}\) and the second link may not be run. This link is what makes the old one wrong rather than merely expensive: at the K-P firing point \(N=16\) leaves \(\mathrm{MDE}_{16}\approx0.126372/\sqrt2=0.0894\), still \(1.54\times\) the pilot's \(0.057971\), so a second arena at \(N=16\) buys a number that is still not falsifiable — the arithmetic that shows it costs nothing and is now taken first. Link 2, run only when link 1 returns \(N_{\rm req}\le16\), and strictly more decisive: \(N=16\) at \(\approx68\) s per pair (DERIVED \(2\times34\) s on the certified stack, the byte-embedding floor and not a price), which halves the variance of the paired mean rather than restating it — the one thing arithmetic on eight seeds cannot do. If \(N=16\) is run and the contrast is still short of \(\mathrm{MDE}\), the contrast is filed as a band with no point and the bed's sentence is 09.19's, which is the Terminal. Terminal. "A1/A2/T1/T2 on chess are defined and priced; none is measured; the first eight seeds fix \(\mathrm{MDE}_8\) before any of them may be quoted."

09.12 — The bed-side half of B22: the ChaCAL controls carry their diagonal convention and a planted negative on this bed

Statement. Two controls rest on ChaCAL's diagonal convention (docs/CEQ_SHAPE.md §8: one HTML fetch decides them). On BED-C-T both are run with the manifest field diag_convention ∈ {kept, removed} declared, and the convention is verified at the identity level on the bed's own draw before either arm is scored: at \(\gamma=0.9\) on one 512-draw batch, ChaCAL-diag (diagonal kept) must have every transient row of \(\Pi_\gamma\) summing to \(1.000000\) within \(10^{-12}\), and ChaCAL-published (diagonal removed inside the inverse) must have transient row sums strictly below \(1\) on \(100\) per cent of rows — the sub-stochastic signature the record read as \(0.400\)–\(0.765\) at \(s=32\). Hypotheses. Proposition 5(b) (docs/CEQ_SHAPE.md §2.2: \(\Pi_\gamma\) row-stochastic with the diagonal kept, for any row-stochastic \(P\)); the published form [V-fetched] from one HTML render, to be re-read against the PDF (docs/CEQ_SHAPE.md §A.13). Evidence. READ docs/CEQ_SHAPE.md §A.4 rows ChaCAL-diag / ChaCAL-published (RUN[J] row sums \(0.400\) to \(0.765\) for the published form). CITED [V] fagnou-2024-chacal Eq. 5 and Eq. 7. On BED-C-T: NOT MEASURED — needs the untrained forward of both arms on one batch (\(0\) GPU-s on CPU, or one zero-step forward \(\le1.524\) s). Mechanism. V-3 (a control that is one's own construction: the identity half is declared, the rejection half must fail at \(O(1)\)), P-10 (a source's intro cited as its theorem), V-2 (a control that must fail by construction is deleted — "ChaCAL must emit chance" is not run). Kill. ChaCAL-published's transient row sums within \(10^{-6}\) of \(1\) on any row at \(\gamma=0.9\): the two controls are one control and the convention was misread; both arms are struck from the chess table until the PDF is read. Price \(0\) GPU-s. If killed. The PDF is read and the convention field flipped; the two arms are re-run with the corrected diag_convention — Hypotheses: exactly one of the two conventions is ChaCAL's; Evidence: the PDF ([V-eq] once read, with Eq. 5 and one numeric instance); Kill: the same row-sum test. If the PDF leaves the convention ambiguous, both conventions are run as two arms named by their convention, neither named "ChaCAL", and the chess delta against ChaCAL is stated at the identity level only (parity at \(\gamma=0\), Proposition 1). Terminal. "The chess controls that depend on ChaCAL's convention carry the convention in their manifest and a row-sum plant on the bed's own draw; where the convention is unverified, the arms are named by their convention and not by the paper."

09.13 — The first chess cell at \(0\) GPU-s: census, floors, oracle hashes, the label sd on 512 draws

Statement. The first cell writes, before any GPU-second: (a) the 09.10 census block; (b) the 09.8 floors on the realised class distribution; (c) the oracle hashes — python_chess_version = 1.11.2, engine_sha256 (or absent, which refuses every engine label), syzygy_sha256 (or absent); (d) the per-coordinate sd of L-q at the root over 512 draws, and the sd of L-eval\(\Delta\) where an engine exists; (e) the bed digest by bed_signature('bed_c') twice. Hypotheses. BED-C-T generator present; 512 draws at \((2,7,2,64)\); CPU only. Evidence. RUN python -c "import chess; print(chess.__version__)" → 1.11.2; RUN which stockfish → none (engine hash absent on this box); RUN the fixture oracle: \(512\) labelled plies from the \(36\)-game fixture in \([0.128,\,0.376]\) s — a band over four unrepeated readings of the same command in the same tree, never a point (09.3): \(0.128\) s (the first reading), \(0.1524\) s (RUN this session), \(0.1929\) s (the refutation's reading, \(+50.6\) per cent over the first) and \(0.376\) s (READ V20_R15_JOURNAL.md:2441 @ 99777ab, \(+194\) per cent) — [FITTED-free, unrepeated], unsynchronised, single CPU, \(0\) GPU-s. The \(0.128\) s this verse previously quoted as a point is struck: the same command on the same tree does not reproduce at that precision, and the band is a fixture number on \(36\) synthetic games that licenses no throughput law and is quoted in no price. Label sd on 512 draws: NOT MEASURED — needs the generator (book 04). DERIVED cost: \(512\) solves at \(\le61{,}731\) MACs each, under one CPU-second. Mechanism. M-3 (the sd is measured, not piloted), P-1, V-8. Kill. Any per-coordinate sd of \(q^{(0)}\) or \(q^{(k)}\) over the admitted region at or below \(0.05\) → the bed is not admitted (09.10 line 5). The threshold carries the class 09.10 line 5 gives it and this verse restates rather than importing: DERIVED from \(\mathrm{MDE}_8=1.156\times\mathrm{sd}\) (the noncentral-\(t\) bisection of docs/CEQ_SHAPE.md §A.11 item 2: \(0.034451\to0.039827\), ratio \(1.15606\); \(0.050146\to0.057971\), ratio \(1.15604\)), so at \(\mathrm{sd}=0.05\) the minimum detectable effect is \(0.0578\), larger than the \([0,1]\) label's own sd, and below \(0.05\) no contrast at \(N=8\) is falsifiable. The admitted region is defined independently of this census as the prefix at or after the first declared boundary set (READ docs/CEQ_SHAPE.md:2547, whose own requirement is "each \(>0\)" and whose reason for excluding the earlier prefix is that it reads \(q^{(0)}\approx1\) and inflates the sd), so the sd is not computed over a region the sd itself decides. Two unequal digests in (e) → 09.1's kill. If killed. 09.19's reroute; the cell is re-run at \(0\) GPU-s per reroute. Terminal. "The chess bed's first cell is free and decides admission; nothing after it runs until the author reads the block."

09.14 — The first chess GPU cell, priced from the record's laws

Statement. The first GPU cell is one bed-cell pair (shape on the softmax corner \(+\) depth-1 softmax control), \(8\) seeds each, at \(n_{\rm train}=2048\), \(s=64\), \(d_{\rm model}=16\), \(150\) steps: \(\approx34\) s carried (two invocations; \(29.6\) s in one), from \(1.680\) s per shape cell [FITTED + RUN] and \(1.524\) s per softmax cell [FITTED] plus \(4.0\) s fixed. The arena is priced arm by arm at each arm's own law (M-8), never by one multiplier, and the priced-row count equals the registered-kind count of 09.17 — thirteen and thirteen. The struck line read "\(7\times8\times1.680+4.0\approx98\) s; the depth-3 skyline \(\approx3\times1.524\times8\approx36.6\) s": it copies a figure from READ docs/CEQ_SHAPE.md:1952 @ 207e7b9 whose own sentence prices two of this book's arms outside it — "\(7\times8\times1.680+4.0\approx98\) s \(\approx1.6\) GPU-min DERIVED, plus \(\approx64.8\) s for the skyline [ASSUMED] and \(\approx44.9\) s for InfSA-16 DERIVED, so \(\approx3.3\) GPU-min in total" — and 09.17 registers thirteen kinds, not seven. The per-arm column at \(8\) seeds, \(d_{\rm model}=16\), \(s=64\), \(150\) steps:

kind	law per cell	class	\(8\) seeds
bed_c_shape	\(1.680\) s	[FITTED + RUN] READ COSTS.md:73-74	\(13.440\) s
bed_c_softmax_d1	\(1.524\) s	[FITTED] READ COSTS.md:73-74	\(12.192\) s
bed_c_softmax_d3 (skyline)	\(3\times1.524=4.572\) s	[ASSUMED linear in depth]	\(36.576\) s
bed_c_chacal_diag	\(1.680\) s	READ docs/CEQ_SHAPE.md:2509 @ 207e7b9	\(13.440\) s
bed_c_chacal_pub	\(1.680\) s	DERIVED, same MACs, READ :2509	\(13.440\) s
bed_c_chacal_sink	\(1.680\) s	READ :2509	\(13.440\) s
bed_c_neumann16	\(\approx5.1\) s	DERIVED from the \(25.409\) ms hop microbenchmark, READ :2509	\(40.800\) s
bed_c_mlp0	\(\le1.524\) s	[ASSUMED] ceiling, no attention block	\(\le12.192\) s
bed_c_cached	\(1.680\) s	DERIVED, one solve	\(13.440\) s
bed_c_majority	\(0\)	a count, no forward	\(0\)
bed_c_random	\(0\)	a count, no forward	\(0\)
bed_c_mean	\(0\)	a count, no forward	\(0\)
bed_c_nexttoken	NOT MEASURED — needs the BED-C-N cost law at \(s=512\)	the \(s\)-sweep band \(206\)–\(537\) GPU-s (RUN, below)	NOT MEASURED
fixed overhead	\(4.0\) s	[FITTED]	\(4.0\) s
total of the twelve priced rows			\(\mathbf{172.960}\) s

\(172.960\) s \(\approx2.9\) GPU-min against the struck \(\approx98\) s — a \(1.76\times\) understatement, of which \(40.800\) s is InfSA-16 alone, an arm 09.9 lists among the chess fellow approximators and the struck figure priced at \(1.680\) s per cell while its own source prices it at \(\approx5.1\) s. The thirteenth kind, bed_c_nexttoken, carries no number and is not in the total. The feature projection is \(F(s,K)\times d_{\rm model}\) at the one feature table of 09.3, \(F(s,K)=849+s+K=915\) at \(s=64,K=2\), so \(915\times64=58{,}560\) — the previous registration's \(F=832+1+4+9+64+m+K+4\) double-counted \(m\) and used the label tensor's \(K+4\) where the token carries the \(K+2\) boundary flags, and is struck. \(F\) is a function of \(s\), so the projection is repriced per bed and per \(s\) and never carried across a reroute (09.3's one table; DERIVED at \(K=2\), \(d_{\rm model}=64\) for the parameter column and \(d_{\rm model}=16\) for the MAC column, the priced width):

bed and geometry	\(F(s,K)=849+s+K\)	projection params at \(d=64\)	projection MACs/token at \(d=16\)	against the block's \(12d_{\rm model}^2=3{,}072\)	head \([m,K+4]\) at \(d=64\)
BED-C-T, \((h,m,s)=(2,7,64)\), registered	\(915\)	\(58{,}560\)	\(14{,}640\)	\(4.766\times\)	\(64\times7\times6=2{,}688\)
BED-C-T, \((3,5,256)\), 09.19 reroute 1	\(1{,}107\)	\(70{,}848\)	\(17{,}712\)	\(5.766\times\)	\(64\times5\times6=1{,}920\)
BED-C-T, \((2,15,256)\), 09.19 reroute 2	\(1{,}107\)	\(70{,}848\)	\(17{,}712\)	\(5.766\times\)	\(64\times15\times6=5{,}760\)
BED-P-L / BED-P-N, \(s=64\) (09.29b, 09.30)	\(18\), the market table's own width at 09.21's augmented state	\(1{,}152\)	\(288\)	\(+9.375\) per cent	\(64\times7\times5=2{,}240\)

The parent-index one-hot is the only \(s\)-dependent row of 09.3's table, contributing \(64\) at \(s=64\) and \(256\) at \(s=256\), which is the whole of the \(915\to1{,}107\) move; no other row changes with \(s\), and the market bed's \(F=16\) is a different table with no parent index at all. A reroute to \(s=256\) therefore re-prices the projection before it re-runs the census, and a price quoted at \(s=64\) may not be carried to it. Every price table in this verse carries the three line items of 09.9 in its header — trunk \(53{,}952\), projection \(915\times64=58{,}560\), head \([m,K+4]\) at \(d\cdot m(K+4)=64\times7\times6=2{,}688\) (DERIVED) — never one lump count. The projection changes the parameter count identically on every arm. "and does not change the per-token law" is withdrawn, and every chess and market price in this book is re-labelled NOT MEASURED — needs the cost-law refit at the chess feature width (book 03). The \(1.680\) s and \(1.524\) s laws were fitted on BED-M/K, whose input is a byte embedding — a table lookup at \(0\) MACs per token — so they are the byte-embedding floor and not the price of a feature-projected arm. The increment is printed beside them at the priced cell's own width \(d_{\rm model}=16\): the chess projection costs \(F(s,K)\times d_{\rm model}=915\times16=\mathbf{14{,}640}\) MACs per token against the block's dense \(12d_{\rm model}^2=12\times256=3{,}072\), a ratio of \(\mathbf{4.766\times}\) (DERIVED); at the width the refutation filed, \(F=923\), the same arithmetic reads \(14{,}768\) MACs and \(4.81\times\), and the defect is identical at either width — 09.3's corrected \(F(s,K)=849+s+K=915\) moves the size of the increment and not its sign. The market projection at 09.21's augmented \(F=18\) costs \(18\times16=\mathbf{288}\) MACs per token against the same \(3{,}072\), \(+9.375\) per cent (DERIVED), so the market refit is expected to move its law by a factor near \(1.094\) and the chess refit by a factor near \(5.766\); both are NOT MEASURED and neither is assumed. The \(F=16\), \(256\)-MAC, \(1.083\) reading is at the width that omitted running PnL and signed exposure and is struck. Every number in the arena table above, in 09.34, and in the kills table's price column is therefore the byte-embedding floor with its increment named, and none is a price until book 03's refit lands. Both forms of \(\mathrm{do}(a)\) are priced here, as 09.5 requires: on BED-C-T the root is the last token, the clamp \(P_{\rm env}[x_0,:]\leftarrow e_{u_a}\) is rank one, and the displacement is \(O(s)=64\) MACs per candidate, \(448\) MACs for all \(m=7\) candidates at \(s=64\) (DERIVED); on BED-C-N the move rewrites a suffix of the byte context from position \(i\) and the re-solve is rank \(s-i\) at \((s-i)^2d/2\) MACs — at \(i=s-1\) that is \(d_{\rm model}/2=32\) MACs at \(d_{\rm model}=64\), and at \(i=0\) it is \(s^2d/2=512^2\times64/2=8{,}388{,}608\) MACs, a range of \(2.62\times10^5\) across the one index 08_ARCHITECTURE.md 08.18's worked example 1 leaves unnamed (DERIVED). The two prices are not one price and no verse may quote either without naming its bed. BED-C-N at \(s=512\) bytes: NOT MEASURED — the record's throughput law was fitted at \(s=64\) only and the \(s\)-sweep is priced as a band, \(206\)–\(537\) GPU-s. Hypotheses. The certified device (RTX 4060 Laptop, torch 2.5.1+cu121) — which this box no longer runs (torch 2.14.0+cpu, CUDA False, RUN this session; CHARTER.md §5 B1) — so every price here carries "on the certified stack" and none is measurable on the installed one until book 05's pin lands. Evidence. READ COSTS.md:73-74 (the two fitted laws, both on a byte-embedding input), docs/CEQ_SHAPE.md §A.11 item 5 (the price table), READ docs/CEQ_SHAPE.md:1952 @ 207e7b9 (the struck seven-arm figure with the skyline and InfSA-16 priced outside it), READ docs/CEQ_SHAPE.md:2509 @ 207e7b9 (the per-arm law column: ChaCAL-diag/published/sink at \(1.680\) s, InfSA-16 at \(\approx5.1\) s DERIVED from the \(25.409\) ms hop microbenchmark, depth-1 softmax at \(1.524\) s), docs/PLAN.md §5.7. RUN python -c "import sys; sys.path.insert(0,'.'); from tests.mercury.phase_c_price import s_exponent_band; print(s_exponent_band())" → (206.03, 309.05, 537.15) GPU-s. RUN python -c "import torch; print(torch.__version__, torch.cuda.is_available())" → 2.14.0+cpu False. The cost-law refit at the chess feature width: NOT MEASURED — needs book 03's cost-law experiment with synchronised timers and interleaved arms at \(F(s,K)=915\), \(d_{\rm model}=16\). Mechanism. M-8 (each arm at its own law; the solve is an increment, and one multiplier over thirteen kinds is not a price), M-3 (no scaling of a pilot across \(s\)), P-8 (an upper bound stated as a price is refused; these are per-op floors under a \(2.0\times\)–\(6.6\times\) dispatch gap), V-22 (no price crosses the device boundary), P-1 (a figure copied from a source that prices two of its own arms separately), M-3 again (a law fitted on a byte-embedding input carried to a feature-projected one), D-5 (two objects named \(\mathrm{do}(a)\) at two ranks, priced separately). Kill. The measured pair outside the law-versus-measured band \([-1.8,+14.4]\) per cent of \(1.680\) s per cell (the S-20 smoke band): the price is re-labelled the per-op floor it was declared to be and every chess price is re-quoted from the measured cell. Price: the cell itself, \(\approx34\) s on the certified stack. Planted negative (V-15): the same cell run with the projection disabled (a byte-token embedding at \(0\) MACs per token, the geometry the \(1.680\) s law was actually fitted on) must read inside the band, and the same cell at \(s=256\), \(F=1{,}107\) — \(5.766\times\) the block's per-token cost against \(4.766\times\) — must read outside it; a band that does not separate those two ends is blind and no smoke verdict is admissible. If killed. Two links, cheapest first, as CHARTER.md §2's depth rule requires — the previous ordering put a four-point refit at eight seeds, which costs at least \(4\times34\) s, directly behind a \(\approx34\) s kill, and is struck as a chain whose second link is neither cheaper nor argued more decisive. Link 1, \(0\) extra GPU-s: the cell that fired the kill is already paid for, so its eight seeds are re-quoted as a measured point price — the per-cell median seconds with the realised across-seed spread printed beside it — and every chess price in this book is restated from that point instead of from the \(1.680\) s law. Hypotheses: the eight seeds of the fired cell are byte-identical draws under 09.11's protocol, so their spread is a device spread and not a data spread; Evidence: the fired cell's own secs_sync column; Kill: the across-seed spread of that one cell exceeding the band's own width, \(16.2\) per cent of the median (DERIVED, \(+14.4-(-1.8)\)) → the point does not reproduce inside the run that produced it and is not a price either. Price \(0\) extra GPU-s: it is arithmetic on a column already written. Link 2, strictly more decisive and strictly more expensive, which the depth rule permits on the decisiveness half: prices are re-fitted from the first eight chess cells on the certified stack (a new [FITTED] law at the chess feature width, R² printed) — Hypotheses: throughput is linear in \(n\) at fixed \(s\) (the record's exponent \(1.0026\)); Evidence: COSTS.md:74; Kill: R² below \(0.99\) over four points. The decisiveness gain is stated and not assumed: a single smoke cell decides only whether one point sits inside a band around one law, while four fitted points decide the exponent — whether the cost is linear in \(n\) at all at the projected feature width — which no single cell can distinguish from a constant offset, and which is the quantity every price in this book and in 09.34 is quoted from. If the law does not fit, prices are quoted as measured points only, never as a law, which is the Terminal. Terminal. "The first chess GPU cell costs about half a minute on the certified stack and cannot run on the installed one; no chess price in this book is a measurement — every one is the byte-embedding floor of a law fitted without the feature projection, whose per-token cost is \(4.766\times\) the block's at the priced width, and the arena of thirteen registered kinds costs at least \(172.960\) s on that floor rather than the \(\approx98\) s the struck line carried."

09.15 — The identity manifest for chess cells

Statement. Every chess cell carries the field list of docs/CEQ_SHAPE.md §A.10 plus: bed = bed_c_t | bed_c_n, policy_env ∈ {uniform, engine_softmax} with tau, tree_depth h, branching m, theta_material, k_mate, position_class ∈ {opening, middlegame, endgame_le5}, pgn_source_sha256 (or generator with seed), python_chess_version, engine_sha256 | absent, engine_depth | engine_nodes, syzygy_sha256 | absent, terminal_density, res_share, feature_dim F, params_per_arm after the head. A cell missing any declared field is refused, not reported absent. Hypotheses. The manifest's drift plant (READ V20_R15_WING_MANIFEST.md:148-152 @ 99777ab, the one-line-drift test). Evidence. READ docs/CEQ_SHAPE.md §A.10 (the base list and the refusal rule). Mechanism. L-2 (docs/CEQ_SHAPE.md §A.10 at :2640, the identity-manifest field list; not a MISTAKES.md id — MISTAKES.md carries \(71\) headings spanning V-1..V-26, P-1..P-11, M-1..M-21 and D-1..D-7 only, RUN grep -cE '^### ' MISTAKES.md → 71 this session — and its MISTAKES.md equivalent is P-1), P-1, V-3 (the manifest's own planted negative). Kill. Flipping any one of policy_env / h / m / theta_material / k_mate / engine_sha256 by one unit fails to move manifest_hash; or an engine label appears in a cell whose engine_sha256 is absent. Price \(0\) GPU-s. If killed. The hash's input set is the field list itself; the missing field is added to the hashed set and the plant re-run — Hypotheses: manifest_hash is a function of the declared field values; Kill: the same flip test. A second failure means the manifest is not hashing what it declares (P-4) and every chess cell journalled under it is struck. Terminal. "No chess cell without its full identity; a cell with an engine label and no engine hash does not exist."

09.16 — The VOID list for chess, registered before any cell

Statement. BED-C-T (in class): shape − softmax-d1 and shape − depth-3 skyline on the committor head are reproduction-versus-non-reproduction contrasts and are VOID as capability numbers; creditable unconditionally are shape − ChaCAL-published, shape − Neumann-16 (exactness), shape − 0-hop MLP and shape − 1-hop softmax on the argmin (K-H2), and \(\|\hat P-P_{\rm env}\|_\infty\) per seed as a learnability reading. Two entries are creditable only conditionally, and the condition is printed in the row: shape − ChaCAL-diag and shape − ChaCAL-with-sink-token (the boundary mechanism, K-E1) are creditable only on seeds whose Ruling-10′ likelihood-ratio verdict on \(\hat\gamma\) reads MOVED, and are VOID on PINNED seeds, where ChaCAL-diag at \(\hat\gamma=0\) is softmax and the contrast collapses onto the VOID shape − softmax-d1 row — READ docs/CEQ_SHAPE.md:2375 @ 207e7b9 (Tree B, the median outcome): "S-31 and S-64 are then void, because ChaCAL at \(\hat\gamma=0\) is softmax." The PINNED/MOVED seed split is printed as two integers out of \(8\) in the same row as the contrast, and under D-CALIB the counter is the point estimate: CHARTER.md §5 B12 records \(\hat\gamma\) predicted PINNED on at least \(6\) of \(8\) seeds, so the point estimate of the creditable half is at most \(2\) of \(8\), and a contrast standing on two seeds carries \(N=2\) and no \(\mathrm{MDE}_8\). The previous registration listed shape − ChaCAL-diag as creditable with no condition and is struck. shape − next-token-trained control is moved off this bed, below. BED-C-N (natural ground): \(t^\star=2\) and skyline depth \(3\) at the counts 09.11 registers; nothing is VOID by containment (\(\hat P\) is not the environment chain), and every scalar-at-one-position contrast is VOID by D-1; only the \([m,K+4]\) tensor, the \(64\)-square next-FEN vector and the \(m\)-vector eval-\(\Delta\) sign carry contrasts. shape − next-token-trained control is registered here and nowhere else, because on BED-C-T the two arms share no input space: 09.9 defines the control as the same depth-1 model trained on next-byte prediction over the PGN stream — vocabulary \(256\) raw bytes at \(s=512\) — while BED-C-T's input is the \(F(s,K)=915\)-dimensional feature projection at \(s=64\) (09.3, 09.14), so the contrast could not be run on the bed that registered it. The transfer route is stated and is the only one licensed: freeze the byte-trained trunk, attach the \([m,K+4]\) head, linear probe only — \(99{,}008\) frozen parameters (byte embedding \(16{,}384\) + positional \(512\times64=32{,}768\) + one block \(49{,}728\) + final norm \(128\)) against \(2{,}688\) trainable (\(64\times7\times6\)), \(101{,}696\) in total, which is the shape's own BED-C-N count (09.11), the byte output head's \(16{,}384\) having been replaced by the probe (DERIVED; RUN this session, \(115{,}392\) at \(L=1\), \(s=512\), \(d=64\)). An unfrozen trunk is a second trained arm and is not this control. Markets — the list 09.33 borrows with bed_p names: the containment rule holds on BED-P-L exactly as on BED-C-T, and the same conditional applies to shape − ChaCAL-diag there. The equilibrium-phase contrast of 09.36 is VOID by D-1 on both market registrations: the phase label at one horizon is a scalar at one position, which 09.7's Statement forbids as a capability label on either registration, so no McNemar contrast on it may license a positive sentence — 09.36 is a definition verse and carries no such contrast. Hypotheses. docs/CEQ_SHAPE.md §A.1's VOID list (the model); the void_contrasts manifest field on every cell, in a commit dated before the first chess arena cell. Evidence. READ docs/CEQ_SHAPE.md §3.8, §A.1 (the BED-S list and its reasoning); MISTAKES.md D-2 (E1's registration comment, the pattern). Mechanism. D-2, M-7 (a pre-registration with a hole), V-10, R-SKY and D-CALIB (a contrast creditable only where the dial moved, with the counter's split printed), M-1 and V-3 and P-4 (a control registered on a bed whose tokenisation it cannot read), P-1 and V-22 and D-4 (a capability number on natural ground behind a digest that does not exist). Kill. K-D2: \(\|\hat P-P_{\rm env}\|_\infty<10^{-3}\) on at least \(6\) of \(8\) seeds → the arm copied the tree and every contrast on BED-C-T against a non-reproducing arm is a copy-versus-no-copy statement, filed as identification, never capability. Price: read off the arena, \(0\) extra GPU-s. If killed. The reading is what it is: identification. The capability question moves to BED-C-N, whose VOID list is the D-1 list — Hypotheses: BED-C-N admits under 09.10 run on natural-ground draws; Evidence: NOT MEASURED; Kill: the same census. And the move is gated, not free: BED-C-N carries no capability number until BED-C-D is pinned by digest under Ruling 7. 04_BEDS_AND_INSTRUMENTS.md 04.7's Kill reads, verbatim: "Any capability number on the witness before the arevel/chess-games and lichess/chess-evaluations sha256 digests are written into results/k_data_manifest.json — struck as P-1". Both digests read "sha256": null (READ results/k_data_manifest.json:130 and :143, RUN this session), ls data/ shows no .pgn and no lichess* file (RUN, 09.2), and 09.37 states that nothing in this book launches, uploads or attaches on Kaggle — so this book leaves both digests unpinned by design, and the escape hatch this If-killed opens is closed by a neighbouring book's kill until they are pinned. BED-C-G is not a substitute for that purpose: 04.7's kill is written against the witness on natural ground, and self-play under \(\pi_u\) is a generator (09.2), not natural ground; this book does not read BED-C-G as natural ground and claims no exemption from 04.7. Whether 04.7's kill wording should name "on natural ground" explicitly, so that BED-C-G's status is decidable from the wording alone, is owed as a CORRECTIONS.md row naming 04.7's Kill; this book's writer may not write that file (CHARTER.md §3), and until the row exists the divergence stands recorded here. If BED-C-N does not admit, or the digests are never pinned, no chess capability number exists (09.19). Terminal. "On the in-class chess bed, the shape may be shown to reproduce its own class; that is a learnability sentence and not a capability sentence — and the natural-ground bed the capability question moves to carries no capability number until both Lichess digests are written into the manifest, which this book leaves unpinned by design, so at 99777ab the chess capability question has no live bed at all."

09.17 — FOUND-not-NAMED for every chess arm

Statement. An arm on chess is FOUND iff results/ holds at least one journalled record whose kind is the arm's registered name. Registered kinds: bed_c_shape, bed_c_softmax_d1, bed_c_softmax_d3, bed_c_chacal_diag, bed_c_chacal_pub, bed_c_chacal_sink, bed_c_neumann16, bed_c_mlp0, bed_c_nexttoken, bed_c_cached, bed_c_majority, bed_c_random, bed_c_mean. The census by kind over results/**/*.jsonl is printed with every table, calibrated on both sides: it must read \(0\) for every name above today and above \(0\) for softmax (the record's \(182\)). Hypotheses. The record's discriminator (READ CEQ_V20_R15_CONTRACT.md:49, :266 @ 99777ab). Evidence. RUN grep -l -i chess results/*.jsonl → no file (every chess kind at \(0\)); READ docs/CEQ_SHAPE.md §4.4 (arm_pl 191, softmax 182, arm_smprime 182, arm_phase 0 — the counter's calibration). Mechanism. FOUND-not-NAMED, V-7 (a search structurally incapable of finding anything), P-4. Kill. Any chess sentence citing an arm whose kind count is \(0\) is struck at assembly. Price \(0\) GPU-s. If killed. The sentence is rewritten to name the arm as NAMED with its route back (one make_arm branch, one optimiser path, one field emit — the W2 precedent at \(41\)–\(130\) GPU-s for eight cells, READ docs/CEQ_SHAPE.md §4.4) and no number. Terminal. "No chess arm exists in the record today; every arm named here is NAMED until its first journalled cell."

09.18 — What "4D chess" adds, and what it does not

Statement. "4D" is a reading, not a board. It adds exactly three things the canon operationalises: (i) \(K\) constraint sets held at once — material breach, mate threat, repetition — as absorbing rows, with the reach-avoid vector read in one solve and the degeneracy lemma stated with its vacuity line printed at this verse's own geometry, because its hypothesis is false there (CHARTER.md §2's skyline rule; V-25). The lemma: if the \(K\) constraint sets exhaust the absorbing states, \(\max_kq^{(k)}\ge1/K\) by pigeonhole. The vacuity line, DERIVED at \(K=2\) on BED-C-T: 09.4 declares \(\mathcal A_{\rm sink}\), \(\mathcal A_0\), \(\mathcal A_{\rm loss}\), \(\mathcal A_{\rm draw}\) and \(\mathcal A_{\rm res}\) alongside the \(K\) constraint sets, so on every draw $\(\sum_{k\ge1}q^{(k)}\ \le\ 1-q^{({\rm sink})}-q^{(0)}-q^{({\rm loss})}-q^{({\rm draw})}\ (-\,q^{({\rm res})}\text{ on BED-C-D}),\)$ and the lemma binds only where that bound reaches \(1\) — that is, only where all four of the other declared coordinates are identically zero on the batch. 09.10's admission line 5 forbids exactly that: it requires the per-coordinate sd of every declared channel of \(q\) to exceed \(0.05\) over the admitted region, and a channel identically zero has sd \(0\), so a batch on which the lemma binds is a batch the bed does not admit. At \(K=2\) the lemma's conclusion would read \(\max_kq^{(k)}\ge0.5\), against a bound that the census keeps strictly below \(1\) and that 09.4's own kill (c) keeps below \(0.05\) whenever the sink swallows the walk. The lemma is therefore recorded as the guard against a mis-declared boundary set — a generator that silently drops the sink, the goal, the loss or the draw set makes its hypothesis true and the conclusion fires — and never as a live constraint on any admitted chess batch; no sentence in this book rests on it; (ii) multiple horizons through \(\gamma\) — \(\gamma=0\) is next-FEN (the next transient state, softmax bitwise), \(0<\gamma<1\) the discounted hitting-time read \(E[\gamma^{\tau-1}\mathbb 1_k]\) at a bed constant \(\gamma_{\rm env}\in\{0.6,0.9\}\), \(\gamma\uparrow1\) the game outcome (the equilibrium phase: which absorbing set the mass flows to); (iii) the safest move as the argmin rule — the one-step safety filter \(a^\dagger=\arg\min_a\max_{k\ge1}q^{(k)}(\mathrm{do}\,a)\) with the goal rule and the conditioned form as columns. It does not add board geometry, a fourth spatial axis, a variant rule set, or any data beyond standard chess games; the record trains on standard chess data and nothing else. Hypotheses. Definition 7 and Proposition 8 (docs/CEQ_SHAPE.md §2.1–2.2); R-20's vocabulary (a one-step filter, never a policy; hsu-2023-safetyfilter, vanmoffaert-2013-chebyshev [V]; the multichain hazard misra-2023-safety-constrained-mdp [V] carried in Limits). Evidence. DERIVED (the three items are Definitions 3, 5 and 7 applied to the state space of 09.4). READ CHARTER.md §0 (the author's clarification: "yes 4d chess exists but we will train on chess data"). Mechanism. P-7 (vocabulary with no referent: "4D" is given its referent here and nowhere else), V-12 (the degeneracy lemma), V-25 (the lemma printed with a hypothesis that is false at this verse's geometry, and its vacuity line now printed at \(K=2\) with the sink, goal, loss and draw sets declared — the defect this repair closes), V-17. Kill. R-20's number: on 512 admitted draws, the one-step filter and the two-step optimum (apply \(a\), re-solve, best reply) disagree on more than \(0.5\) of draws → "safest move" is replaced by "one-step safety filter" in every chess sentence and the sequential problem is filed as future work with the citation. R-07's number: with clamp targets unrestricted, the Chebyshev minimum is attained by a sink-bound move on at least \(0.5\) of draws → the Chebyshev column as written is struck and only the goal rule and the conditioned form are named. Both \(0\) GPU-s. If killed. The conditioned Chebyshev \(\arg\min_a\max_{k\ge1}q^{(k)}(a)/(1-q^{({\rm sink})}(a))\) with clamp targets restricted to transient children (the R-07 construction fix, registered now) — Hypotheses: at least one transient child per root; Kill: the same two lines. If the conditioned form also disagrees with the two-step optimum above \(0.5\), the decision head is withdrawn and only the committor vector is reported. Terminal. "The canon's 4D is \(K\) absorbing rows and one dial \(\gamma\) on standard chess data; a decision rule that disagrees with its own two-step optimum on most draws is not called safest."

09.19 — The chess bed's reroute and its Terminal

Statement. If BED-C-T does not admit at \((h,m,K,s)=(2,7,2,64)\): first the dial moves — \((h,m,s)\to(3,5,256)\), then \((2,15,256)\) — and the census re-runs at \(0\) GPU-s; second the horizon changes — the position class moves to endgames with \(\le5\) pieces, where terminal density at \(h=2\) is highest, and the census re-runs; third \(N\) is repriced from whatever realised paired sd the first admitted batch shows (at the \(2.18\times\) precedent \(\mathrm{MDE}_8=0.126238\) and \(N=16\) is the first honest count). If none admits, BED-C-N is attempted under the same census with the D-1 VOID list; if it does not admit either, the chess use has no bed. Hypotheses. docs/CEQ_SHAPE.md §5.10 tree C (the reroute pattern); Ruling 7 for every rerouted generator. Evidence. DERIVED (the node counts of 09.5); READ docs/CEQ_SHAPE.md §5.10. Mechanism. D-4, D-3 (a dial that does not vary describes nothing — the reroute is recorded, never forced: a \(t^\star\) that cannot be placed is recorded), M-3. Kill. Each reroute has 09.10's kill at \(0\) GPU-s; the chain is three links and ends here. If killed. None — this verse is the reroute. Terminal. "The chess use is registered as two beds with exact oracles, printed floors, matched controls with exact counts, a VOID list and a manifest; at every registered dial the in-class bed did not admit, or the natural-ground bed was a static task; the canon licenses the pipeline, the census with its failing line, and no chess capability number."

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Part II — Prediction markets

09.20 — The break: the market use has no bed, no source, no citation in the record

Statement. At 99777ab the repository holds no market data, no market bed, no market label, no market floor, no market baseline, and docs/references.bib (408 entries) holds no entry on prediction markets, order books, proper scoring rules or price impact. Hypotheses. The tree at 99777ab; docs/references.bib as the citation registry. Evidence. RUN grep -n -i 'prediction.market\|polymarket\|kalshi\|metaculus\|order.book\|brier\|price.impact\|kyle\|almgren' docs/references.bib → no match (this session). RUN ls data/ this session → thirteen entries: CHECKSUMS.sha256, README.md, four COGS .tsv files (cogs_dev, cogs_gen, cogs_test, cogs_train), six SCAN .txt files (scan_addprim_jump_test/train, scan_length_test/train, scan_simple_test/train) and tinystories_20k.txt — no market file and no PGN. The previous registration read "CHECKSUMS.sha256, README.md, COGS and SCAN files only", which drops tinystories_20k.txt, the \(211{,}765\)-line, \(18{,}167{,}706\)-byte file results/k_data_manifest.json names at the tinystories_cdla entry's note (READ that note: "That local file is a different cut (\(211{,}765\) lines, sha256 2767818…, pinned in data/CHECKSUMS.sha256)"), and is struck; the conclusion it carried — no market data in the tree — is unaffected by the correction and stands. The entry count is thirteen and not twelve: RUN ls data/ | wc -l this session → 13, so the twelve this book printed in 09.2 and the twelve the refutation filed are both one short, and thirteen is the number both are corrected to. READ CHARTER.md §5 B27. Mechanism. P-4, P-7, L-EQ (a load-bearing market statement with no [V-eq] source is inadmissible: every theorem this part rests on is one already in the bibliography — durrett-2019-probability, ayer-1955-empirical, wilson-1927-probable, ramdas-2023-game-theoretic, hoeffding-1963-probability — and every market-specific citation is marked owed). Kill. The fix is 09.21–09.36. It has failed when bed_p is absent from kdata.BED_SPECS after 09.25 lands, or when its digest fails the twice-test (09.1's kill, \(0\) GPU-s). If killed. As 09.1. Terminal. "The market use is registered as a generator specification and a set of owed citations; no cell may cite it."

09.21 — The state: order-book snapshots and the price path as the context; a trade as \(\mathrm{do}(a)\)

Statement. The state at decision time \(t\) is the augmented tuple $\(x_t=\big(\text{book}_t,\ \text{path}_{\le t},\ T_{\rm res}-t,\ \Pi_t,\ X_t\big),\)$ where \(\text{book}_t\) is the top-\(\ell\) levels on each side (price, displayed size; \(\ell=10\)), \(\text{path}_{\le t}\) the mid-price path at cadence \(\Delta t\) over the last \(W\) steps, \(T_{\rm res}-t\) the time to resolution, \(\Pi_t\) the running PnL and \(X_t\) the signed exposure, both in units of the size grid \(\mathcal Q\) and never in the currency of any venue (V-17). Candidate trades \(a\in\{\text{hold}\}\cup\{(\text{side},q):\text{side}\in\{\text{YES},\text{NO}\},\ q\in\mathcal Q\}\) with a registered size grid \(\mathcal Q\) (\(|\mathcal Q|=3\), so \(m=7\)). \(\mathrm{do}(a)\) is the intervention of 09.27.

The last two coordinates are registered here, in the state, and were registered nowhere before this repair. 09.26 declares its constraint sets "absorbing on the augmented state \((t,p,\text{PnL},\text{exposure})\)" — \(\mathcal A_1\) is running PnL reaches \(-D_{\max}\) and \(\mathcal A_3\) is position exceeds \(E_{\max}\) — while this verse's state carried neither coordinate, no token layout carried them, no feature list named them and no \(F\) count paid for them, so two of the three declared constraint sets were absorbing on coordinates the bed did not have (M-1, D-3, P-4). The augmented tuple above is the object every committor of 09.26, 09.32 and 09.33 is read on, and no committor in this book is read on the unaugmented tuple.

How the two coordinates are carried, and what they cost. They are two extra scalar features on every token, not two extra tokens: the market feature width therefore moves from \(F=16\) to \(\mathbf{F=18}\) on both market beds, which is the one number the repricing rests on (DERIVED; 09.29b, 09.30 and 09.34 print the repriced projection \(18\times d_{\rm model}\) and the repriced logistic count, and 09.14's per-bed table carries the same width). At \(d_{\rm model}=64\) the projection is \(18\times64=1{,}152\) parameters; at the priced width \(d_{\rm model}=16\) it is \(18\times16=288\) MACs per token against the block's \(12d_{\rm model}^2=3{,}072\), \(+9.375\) per cent (DERIVED, against \(+8.33\) per cent at the unaugmented \(F=16\)). The token budget is printed at both readings so the choice is visible and not implicit. Under the registered per-token reading the positions are \(2\ell+W\le s\), which at \(s=64\) forces \(W\le44\); under the alternative reading, in which \(\Pi_t\) and \(X_t\) are given tokens of their own, it is \(2\ell+W+2\le s\), which at \(s=64\) forces \(\mathbf{W\le42}\). Under either reading the registered \(W=64\) does not fit \(s=64\) — \(20+64=84>64\), and it did not fit before the augmentation either — so \(W=64\) is a dial of the \(s=256\) layout only, and \(W=16\) (\(2\ell+W=36\), or \(38\) with two tokens of their own) is the only \(W\) this book registers at \(s=64\). On BED-P-L, whose tokens are lattice nodes and whose state is \((t,p,r)\), the two coordinates are carried as the root token's two extra features under \(\mathrm{do}(a)\), one value per candidate trade — which is what makes 09.26's drawdown and exposure sets evaluable on the lattice at all, since a lattice node without a PnL coordinate has no set for \(\mathcal A_1\) to be absorbing on. Hypotheses. A binary contract with prices in \([0,1]\); \(\ell=10\); \(W\in\{16,64\}\) with \(W=16\) the only value the \(s=64\) layout admits and \(W=64\) a dial of the \(s=256\) layout alone, by the budget arithmetic above; \(\Delta t\) registered per venue; BED-P-N is registered as a bed by 09.29b, not here: this field named it and gave it no Statement, no \(K\), no \(t^\star\), no skyline, no census and no Kill while four later verses scored on it, which L-VERSE forbids; its layout (\(s=64\) feature tokens at \(F=18\), or \(s=512\) byte tokens with no count) is stated there. Evidence. DERIVED (a registration; the feature width \(F=18\), the projection \(1{,}152\) at \(d=64\), the \(288\) MACs at \(d=16\), \(+9.375\) per cent, and the two budget inequalities \(W\le44\) and \(W\le42\) are the four arithmetic lines above and carry no measurement). Mechanism. D-3 (the size grid and \(W\) are dials with supports), M-1, P-4 (a constraint set absorbing on a coordinate no layout carries is claimed scaffolding — the defect the augmentation closes), D-3 again (\(W=64\) printed as a dial that does not fit the \(s=64\) layout), V-17 (PnL and exposure in size-grid units, never a venue's currency). Kill. A state in which no candidate trade changes the book or the path (\(m_{\rm eff}=1\): every non-hold trade exceeds displayed depth and is refused by 09.26's liquidity set on \(100\) per cent of draws) → the bed's move set is degenerate at that \(\mathcal Q\) and the grid is re-registered. Price \(0\) GPU-s (a census line). A second frozen line on the augmentation, \(0\) GPU-s: the realised sd of \(\Pi_t\) or of \(X_t\) over the \(512\) admitted draws at or below \(10^{-12}\) → the coordinate is constant on the bed, \(\mathcal A_1\) or \(\mathcal A_3\) is absorbing on nothing, and the set is struck from that bed's declaration rather than censused. Planted negative (V-15): a batch generated with the hold-only trade set must send both sds to \(0\) and fire the line; a batch with the full grid must leave both above it. If killed. \(\mathcal Q\) is re-registered as fractions of displayed depth at the best level (\(\{0.1,0.3,0.5\}\times\)depth) — Hypotheses: displayed depth at the best level is positive on the admitted draws; Kill: \(m_{\rm eff}<m\) on more than \(5\) per cent of draws (R-08's rule). Terminal. "The market state is the augmented tuple \((\text{book},\text{path},T_{\rm res}-t,\Pi,X)\) at feature width \(F=18\), and it is the object every market committor in this book is read on; a trade set on which every trade is refused by the liquidity set describes nothing, and a constraint set absorbing on a coordinate no token layout carries is struck rather than censused."

09.22 — Contracts resolving YES/NO (or into buckets) as absorbing sets; the committor as the probability of resolving in one set before another

Statement. \(\mathcal A_{\rm YES}\) and \(\mathcal A_{\rm NO}\) are absorbing; for a multi-outcome contract the buckets \(\mathcal A_{{\rm bucket}\,1},\dots,\mathcal A_{{\rm bucket}\,B}\) are absorbing and disjoint; contracts voided or delisted before resolution enter \(\mathcal A_{\rm sink}\) with value \(0\) and a printed share. The committor \(q^{({\rm YES})}(x)=P_x(\tau_{\rm YES}<\tau_{\rm NO})\) is the resolvent read with absorbing rows (Proposition 3), and on \(T\): \(q^{({\rm sink})}+q^{({\rm YES})}+q^{({\rm NO})}+\sum_{k\ge1}q^{(k)}=1\). The indexing convention, fixed here once for the whole market part, because the argmin rule is load-bearing on it. Outcome sets carry names and never \(k\) indices — \(\mathcal A_{\rm YES}\), \(\mathcal A_{\rm NO}\), \(\mathcal A_{\rm sink}\), and \(\mathcal A_{{\rm bucket}\,b}\) for a multi-outcome contract (the previous registration wrote those buckets \(\mathcal A_1,\dots,\mathcal A_B\), colliding with the constraint indices, and is struck). The numbered sets \(\mathcal A_1,\dots,\mathcal A_K\) are constraint sets only: \(\mathcal A_1\) drawdown, \(\mathcal A_2\) liquidity, \(\mathcal A_3\) exposure at \(K=3\) (09.26). Every sweep written \(k\ge1\) in this book — 09.26's argmin and threshold rules, the sum identity above, 09.32's census lines — therefore ranges over constraint sets and over nothing else. 08_ARCHITECTURE.md 08.18's worked example 2 indexes the same objects incompatibly, verbatim: "\(\mathcal A_0\) = resolves YES, \(\mathcal A_1\) = resolves NO, \(\mathcal A_2\) = drawdown breach, \(\mathcal A_3\) = liquidity breach", and has no exposure set at all. Under that indexing \(a^\dagger=\arg\min_a\max_{k\ge1}q^{(k)}(a)\) minimises the probability that the contract resolves NO — the sweep swallows \(q^{({\rm NO})}\) at \(k=1\) — which is a different rule from the one either book means, and it would rank a trade by how unlikely the market is to settle against a position the rule has not yet chosen. The convention above is this canon's; the divergence is owed as a CORRECTIONS.md row naming 08_ARCHITECTURE.md 08.18's worked example 2, and this book's writer may not write that file (CHARTER.md §3), so until the row exists the divergence stands recorded here. Hypotheses. Definition 3; resolution almost surely (no contract lives forever: the sink absorbs the rest). Evidence. DERIVED from Proposition 3 and 8 (docs/CEQ_SHAPE.md §2.2), classical (kemeny-1960-finitemarkov [V-cat]). Mechanism. V-12 (\(K\ge2\): the goal set alone makes the reach-avoid read a single committor, admitted only with the constraint sets of 09.26), V-8, V-12 and V-17 again on the indexing (two books numbering the same sets differently is a units error in the argmin's sweep, not a notational preference). Kill. On the pinned resolved-contract history, the YES share outside \((0.05,0.95)\), or the sink (void/delist) share above \(0.5\) → the label is degenerate on that venue and the venue is not admitted. Price \(0\) GPU-s. If killed. Stratify by contract category until the YES share is inside the band, the discarded fraction printed (V-5) — Kill: discard fraction \(\ge0.9\). Terminal. "Resolution is an absorbing set; a venue whose resolutions are one-sided carries no committor label."

09.23a — The theorem: under the martingale hypothesis the market-implied probability is the UNCONSTRAINED YES committor

Statement. Let \(p_t\in[0,1]\) be the mid-price, \(\mathcal F_t\)-adapted, and \(\tau=\min(\tau_{\rm YES},\tau_{\rm NO})\) the resolution time with \(p_\tau\in\{0,1\}\). If \((p_t)\) is a martingale, \(\tau<\infty\) a.s., and \(\{\mathcal A_{\rm YES},\mathcal A_{\rm NO}\}\) exhaust the absorbing states — \(q^{({\rm sink})}=0\) and no constraint set of 09.26 absorbing — then $\(q^{({\rm YES})}(x_t)=P(p_\tau=1\mid\mathcal F_t)=E[p_\tau\mid\mathcal F_t]=p_t .\)$ The market-implied probability is the committor under the efficient-market (martingale) hypothesis of the two-set unconstrained contract, and \(p_t\) is the floor every score is taken against. On a finite-horizon lattice with resolution drawn as Bernoulli\((p_T)\) at \(t=T\), the same holds by the tower property: \(q=E[p_T\mid\mathcal F_t]=p_t\). The identity is false whenever the sink or a constraint set carries mass, and neighbouring verses admit both: 09.22's Kill admits a void/delist share up to \(0.5\), and with \(q^{({\rm sink})}=0.5\) the reach-avoid committor \(P_x(\tau_{\rm YES}<\tau_{\rm NO})\le0.5\) while \(p_t\) ranges over \([0,1]\); 09.26 makes drawdown, liquidity and (at \(K=3\)) exposure absorbing on the augmented state, removing further mass. The object this floor scores is therefore the UNCONSTRAINED YES committor channel and never the \([m,K+3]\) constrained tensor — on the augmented state of 09.26 the tensor's YES channel is a different quantity, and 09.24 and 09.33 name the unconstrained channel explicitly. Hypotheses. Bounded martingale (so optional stopping applies without integrability conditions); \(\tau<\infty\) a.s.; \(q^{({\rm sink})}=0\) and no constraint set absorbing — the declared sets exhaust the absorbing states, the exhaustion clause Proposition 3 requires (READ docs/CEQ_SHAPE.md:373-374); no fees, no bid–ask (with a spread the statement holds for any price inside the spread that is a martingale, and the floor is the mid). Evidence. [V-eq] durrett-2019-probability, the optional stopping theorem for bounded martingales (Thm 4.8.5 in the 5th edition, theorem number [U]); hypotheses as stated; one numeric instance DERIVED: the symmetric \(\pm1/G\) walk on \(\{0,1/G,\dots,1\}\), \(G=100\), absorbed at \(\{0,1\}\), started at \(p=0.3\) — gambler's ruin gives \(P(\text{hit }1\text{ before }0)=0.3\) exactly; the lattice instance at \(T=9\), \(p_0=0.3\): \(E[p_9]=0.3\) exactly. Mechanism. L-EQ (a [V-eq] with its theorem, its hypotheses and one numeric instance), V-8 (the sink's mass printed apart, because the identity dies on it), V-12 (the exhaustion clause is a hypothesis, never an assumption), P-10 (a proposition's sum clause quoted with its condition). Kill. The verse is a theorem and no market datum refutes it, so its kill is the instance, not the hypothesis: the \(G=100\), \(p_0=0.3\) gambler's-ruin solve fails to return \(0.3\) to solver precision (\(|q-0.3|>10^{-12}\)), or the \(T=9\) lattice solve fails to return \(E[p_9]=0.3\) to the same precision. Instrument: the 09.25 lattice solve on a two-set chain. Price \(0\) GPU-s, one evening's arithmetic. Planted negative (V-15): the same solve with a sink of mass \(0.5\) declared at every leaf must return \(q^{({\rm YES})}=0.15\), not \(0.3\) — the plant fires exactly on the unexhausted chain, which is the hypothesis this verse now carries and the previous registration omitted; if the plant returns \(0.3\) the solver is ignoring declared absorbing rows and every committor number in this book is inadmissible. If killed. No replacement exists, and the loss is carried here. Optional stopping for a bounded martingale with \(\tau<\infty\) a.s. is a theorem of durrett-2019-probability; a failing instance is an error in the instance or in the solver, not a competing formula, so there is no second formula to pre-derive. What the canon does instead is drop the citation's class: the verse's [V-eq] becomes [V] naming-only, which L-EQ makes inadmissible for a load-bearing statement, and 09.23b then loses its theoretical warrant and must register the market floor empirically — by its own \(3\)-of-\(10\) Wilson bin test on the pinned venue and nothing else. That is a strictly weaker floor and it is named as such. Terminal. "Under the martingale hypothesis and the exhaustion clause, the market-implied probability is the unconstrained YES committor; where the instance fails, the canon has no theorem for the floor and the floor is whatever 09.23b measures on a venue."

09.23b — The floor registration: on this venue at this horizon, \(p_t\) is the floor

Statement. On a pinned venue (09.29) at a registered horizon (one day before resolution, a dial with the support \(\{\)one hour, one day, one week\(\}\)), the mid-price \(p_t\) is registered as the floor every market number in this book is scored against, and the object scored against it is the unconstrained YES committor channel of 09.23a, never the constrained \([m,K+3]\) tensor of 09.26. This is the load-bearing half of the pair: 09.23a is a theorem no market datum can refute, and this verse is the registration a market datum can. Hypotheses. A pinned venue with resolved contracts and at least \(10\) bins of \(n_{\rm bin}\ge50\) at the horizon; time-ordered splits (09.28); the sink and censored shares printed beside every bin (09.22), since a venue whose void share exceeds \(0.5\) is refused before this verse runs. Evidence. The floor's warrant is 09.23a [V-eq]. Every number on a venue: NOT MEASURED — needs the pinned snapshot (09.29); no venue is pinned at 99777ab (RUN ls data/ → no market file, this session). Mechanism. L-FLOOR (every capability number ships beside its information floor, and here the floor is the market itself), D-CALIB (the counter is the point estimate: "no departure"), M-2 (the horizon and the bin count frozen here, before any cell), V-11 (the kill is decidable only on a venue with bins that reach \(n_{\rm bin}\ge50\), and that count is printed). Kill. On the pinned resolved-contract history, bin \(p_t\) at the registered horizon into \(10\) equal-width bins; if the realised YES frequency lies outside the Wilson \(95\) per cent interval (wilson-1927-probable [V]) in at least \(3\) of \(10\) bins with \(n_{\rm bin}\ge50\), the martingale hypothesis is rejected on that venue at that horizon and \(p_t\) is not the floor there. Planted negative: a synthetic series with drift \(+0.05\) per step must fail at least \(3\) bins; if it does not, the bin test is blind and no floor verdict is admissible. Price \(0\) GPU-s given a snapshot. If killed. The floor becomes the isotonic-recalibrated market probability \(\hat p=\mathrm{PAV}(p_t)\) fitted on a disjoint calibration split (ayer-1955-empirical [V], pool-adjacent-violators) — Hypotheses: the calibration split precedes the test split in time (no look-ahead, 09.28); Evidence: DERIVED; Kill: the recalibrated curve fails the same \(3\)-of-\(10\) test on the test split, in which case the floor is the market as-is with its miscalibration printed and no model is scored against a curve it could learn. Terminal. "The market-implied probability is the floor on any venue where the bin test passes; where it fails and recalibration does not repair it, the floor is the market as-is with its miscalibration printed, and the canon licenses no market sentence that does not name which of the three it used."

09.24 — Brier and log score against the market; the near-efficiency counter under D-CALIB

Statement. Per resolved contract \(i\) with outcome \(y_i\in\{0,1\}\) and a model probability \(\hat q_i\) at the registered horizon — \(\hat q_i\) is the model's UNCONSTRAINED YES committor channel of 09.23a, never a channel of the constrained \([m,K+3]\) tensor of 09.26, because the floor \(p_t\) is the unconstrained committor and a constrained channel scored against it is a units error (V-17) —: \(\mathrm{Brier}=\frac1n\sum_i(\hat q_i-y_i)^2\), \(\mathrm{Log}=-\frac1n\sum_i[y_i\ln\hat q_i+(1-y_i)\ln(1-\hat q_i)]\) with \(\hat q\) clipped to \([10^{-3},1-10^{-3}]\) before the log; the skill is the paired difference \(\mathrm{Brier}(p)-\mathrm{Brier}(\hat q)\) per contract, its realised sd across contracts fixing \(\mathrm{MDE}_{n}\). Prediction (the flattering half): skill \(>\mathrm{MDE}_n\). Counter (the point estimate under D-CALIB): skill within \(\pm\mathrm{MDE}_n\) — liquid markets are near-efficient at the registered horizon and the module is a calibrated reader. SPLIT: skill positive but below \(\mathrm{MDE}_n\). Hypotheses. \(n\) resolved contracts on one venue, one horizon, one time-ordered split; the model never sees post-horizon data (09.28); Brier and log are proper scoring rules (the citation is owed — not in references.bib; the propriety of the squared and logarithmic scores is textbook and no load-bearing sentence rests on the citation). Evidence. DERIVED (the definitions). Every number: NOT MEASURED — needs a pinned venue history (09.29). Mechanism. D-7 / L-SIGN (the counter of equal specificity beside the prediction), M-3 (the sd is realised over contracts, never piloted), M-9 (\(n\) must make the finest \(p\) reach \(\alpha\)). Kill. For the module's market sentence: skill \(\le\mathrm{MDE}_n\) at the registered \(n\) and horizon → the counter holds. For the instrument: the market's own Brier on the same split above \(0.25\) (worse than the constant \(1/2\)) marks the split or the horizon mis-registered and the cell is VOID. Price \(0\) GPU-s given a trained model; the model's cell is priced in 09.34. If killed. The horizon is moved (one week, one day, one hour before resolution — a registered support, D-3) and the skill re-scored per horizon with its own \(\mathrm{MDE}\); a skill that appears only at one horizon and not its neighbours is reported as a band with the sign of the miss. If no horizon shows skill above \(\mathrm{MDE}_n\), the sentence of 09.31's Terminal is the market sentence. Terminal. "No edge over the market-implied probability is licensed; the module is registered as a calibrated reader, and the trader sentence requires a pinned venue, \(n\) resolved contracts with its realised sd, and an e-value crossing \(20\) — none of which exists at 99777ab." The previous Terminal read "No edge over the market-implied probability at \(n\) contracts and \(N\) seeds", which states a measured negative on a venue this book records as never pinned (09.29's Terminal: "No venue is pinned; every real-market number in this book is NOT MEASURED"), against an \(n\) that has no value anywhere in this book, and beside an Evidence field that reads "Every number: NOT MEASURED — needs a pinned venue history (09.29)"; it is struck as P-1, P-7 and V-22, and the sentence above is a licensing sentence and not a result.

09.25 — BED-P-L: the in-class market bed — a binomial lattice serialised leaves-first, the committor exact, the departure from martingale planted

Statement. A recombining lattice of \((t,p)\) nodes, \(t=0..T\), \(p\) on the grid \(\{0,1/G,\dots,1\}\), is serialised leaves-first (time \(T\) first, the root \((0,p_0)\) last), so the walk descends in token order. \(P_{\rm env}\): from \((t,p)\) to \((t+1,p\pm1/G)\) with probabilities \(\tfrac12(1\pm\mu(p,r))\), where \(r\in\{0,1\}\) is a hidden regime token carried by every node (the informed-flow regime; \(\mu(p,0)=0\) is the martingale regime, \(\mu(p,1)=\mu_1\in\{0.1,0.2\}\) a registered drift), and \(p\in\{0,1\}\) absorbing — declared for completeness only, and unreachable at the registered geometry, which is printed here and never counted (V-11): the walk moves \(\pm1/G\) per step, so the maximum excursion over \(T\) steps is \(T/G=0.09\) at \(T=9\) and \(0.21\) at \(T=21\) at \(G=100\), and \(\{0,1\}\) is reachable only from \(p_0\le T/G\) or \(p_0\ge1-T/G\); the registered start support is \(p_0\in\{0.3,0.5\}\) (09.23a's instance value and the leaf plant's), and \(0.09<0.3<0.91\) and \(0.21<0.3<0.79\) hold at both \(T\), so no draw at the registered geometry is absorbed at a price boundary and every absorption on BED-P-L is at the leaf Bernoulli at \(t=T\) (DERIVED). A census line counting price-boundary absorption would therefore read \(0\) on every draw by arithmetic and is not written; the boundary rows stay declared so that the lattice's \(P_{\rm env}\) is row-stochastic on them (09.32 line 1) and so that a start moved into \(p_0\le0.09\) by a reroute changes the bed rather than silently breaking it. The gambler's-ruin instance of 09.23a is a different chain from BED-P-L and is not this bed's absorption behaviour: it is the unbounded-time symmetric walk absorbed at \(\{0,1\}\), where absorption at the boundary is certain, whereas BED-P-L runs \(T\le21\) steps and absorbs at the leaf — the identity the lattice supplies to 09.23a is the tower property \(q^{({\rm YES})}(0,p_0)=E[p_T]=p_0\), which this verse's Evidence derives and which holds with no boundary absorption at all. At \(t=T\) the leaf resolves YES with probability \(p_T\) (a two-state absorbing pair per leaf) or, in the constrained version, the leaf is a sink. The label per candidate trade \(a\) is the reach-avoid tensor \(q(a)\in[0,1]^{K+3}\) of 09.26 at the root under \(\mathrm{do}(a)\); the committor \(q^{({\rm YES})}\) is exact by one solve; under \(r=0\) it equals \(p_0\) (09.23a's instance) and under \(r=1\) it does not — the planted departure from martingale exists by construction and is a plant, so that the bed can score whether an arm reads it, never whether markets have it. The word "edge" is not used of it and is used nowhere in this book except on 09.39's withdrawal list and inside the licensing Terminals of 09.24 and 09.31, where it names what is not licensed: this Statement previously read "the edge exists by construction and is a plant", which put a word the book withdraws inside a Statement about a bed property, with no bed, floor, \(N\) or matched count beside it (CHARTER.md §1; P-7, V-17, R-SKY), and that wording is struck. The object is a planted departure from martingale of exact size \(\mu_1T/G\), and that is its only name. At \(s=64\): \(T=9\), \((T+1)(T+2)/2=55\) nodes plus the sink; at \(s=256\): \(T=21\), \(253\) nodes. Hypotheses. \(G=100\); \(T\in\{9,21\}\); the start support \(p_0\in\{0.3,0.5\}\), registered here because the price-boundary reachability inequality above is stated at it and a start outside it changes which absorbing states the bed has; \(K=2\); \(m=7\); the regime is a token feature (so leak clause (a) is dropped as for BED-S: the chain is the input) and the label is never in the tokens (clause (c) kept). Evidence. DERIVED: \((T+1)(T+2)/2\le63\Rightarrow T\le9\) (\(55\) nodes); \(\le255\Rightarrow T\le21\) (\(253\)). DERIVED: with \(r=0\) everywhere, the Dirichlet solve returns \(q^{({\rm YES})}(0,p_0)=p_0\) to solver precision (the tower property on the lattice). DERIVED, the drift plant's exact displacement: transitions \((t,p)\to(t+1,p\pm1/G)\) with probability \(\tfrac12(1\pm\mu)\) give \(E[\Delta p]=\mu/G\) per step, so on the \(r=1\) draws \(q^{({\rm YES})}(0,p_0)=E[p_T]=p_0+\mu_1T/G\) exactly while the walk is unabsorbed, \(=0.018\) at \((\mu_1,T,G)=(0.2,9,100)\). A rejection threshold of \(0.05\) therefore cannot fire at the registered design point: \(0.018<0.05\) on every draw, so the fraction exceeding it is \(0/512\) and the kill would be a certainty rather than a decision. The previous registration froze \(0.05\) against this arithmetic and is struck; the threshold below is frozen from it. The market chain over price levels alone is cyclic (up then down) and is not a DAG in token order; the time index is what makes the lattice in-class, exactly as the tree does for chess. Mechanism. D-2 (the oracle runs on \(P_{\rm env}\); the contrast against softmax is VOID by containment), V-25 (the class overlap is the lattice's DAG-in-time), V-24 (the martingale regime is the identity plant: \(q=p_0\) must hold to \(10^{-12}\); the drift regime is the rejection region, whose threshold is derived from the plant's own displacement and never imported, below), V-11 twice (a threshold larger than the displacement it tests is a precondition failed at every real draw; and a declared absorbing set that no draw at the registered geometry can reach — the price boundary \(\{0,1\}\), printed with its inequality and never counted), M-2 (the threshold is frozen as a formula in \((\mu_1,T,G)\) so that moving a dial moves the threshold with it), M-9 (a rejection line the design point cannot reach is a \(p\) that cannot reach its \(\alpha\)), P-7, V-17 and R-SKY (the struck word "edge" in a Statement about a bed property, with no bed, floor, \(N\) or matched count beside it, on this book's own withdrawal list). Kill. The rejection half, frozen from the plant's arithmetic rather than against it, and conditioned on the informed regime: at the registered design point \((\mu_1,T,G)=(0.2,9,100)\), \(|q^{({\rm YES})}-p_0|>\theta_{\rm rej}\) with \(\theta_{\rm rej}=\mu_1T/(2G)=0.009\) — half the derived displacement — on fewer than \(0.5\) of the \(r=1\) draws among the \(512\), with the realised \(r=1\) count printed beside the fraction as an integer out of \(512\) (09.32 line 14) → the planted departure is invisible at this \(T\) and the bed cannot score a reader of the departure. The conditioning is not decoration: under \(r=0\) the martingale plant gives \(q^{({\rm YES})}=p_0\) to \(10^{-12}\) exactly, so an unconditioned fraction is bounded above by the realised \(r=1\) share, which 09.32 line 14 admits anywhere in \((0.05,0.95)\) — at a realised share of \(0.40\) an unconditioned kill fires at \(0.40<0.50\) for every \(\mu_1\), which is V-11 and D-3, not a measurement. Price \(0\) GPU-s. Planted negative (V-15): a batch generated with \(\mu_1=0\) on the \(r=1\) nodes must send the conditioned fraction to \(0\) and fire the kill; if it does not, the rejection instrument is blind. If killed. The dial reroute \(T\to21\) at \(\mu_1=0.2\) is deleted: it is the same kill, by the same instrument, on the same object, with the threshold formula scaling with \(T\) exactly as the displacement does (\(\theta_{\rm rej}=\mu_1T/(2G)\) against \(\mu_1T/G\), the ratio \(2\) at every \(T\)), so it dies with the verse and is a V-9 defect rather than a replacement. The replacement changes the object the plant lives in. The leaf-miscalibration plant. The departure is moved out of the transition block \(Q\) and into the boundary value vector \(V\): the leaf at \(t=T\) resolves YES with probability \(g(p_T)=p_T+\kappa\,p_T(1-p_T)\), a registered miscalibration map with \(\kappa\in\{0.2,0.4\}\) (and \(g(0)=0\), \(g(1)=1\), \(g\) increasing on \([0,1]\), so \(g\) is a probability), while the transitions stay a pure martingale, \(\mu\equiv0\) on every node. Hypotheses: \(r\) is retired as a dial on this link, \(\kappa\) replaces it, \(G=100\), \(T=9\), \(p_0=0.5\), the walk unabsorbed over \(T\) steps. Evidence, DERIVED in three steps: \(q^{({\rm YES})}(0,p_0)=E[g(p_T)]=E[p_T]+\kappa E[p_T(1-p_T)]\); \(E[p_T]=p_0\) and \(E[p_T(1-p_T)]=p_0(1-p_0)-\mathrm{Var}(p_T)\) with \(\mathrm{Var}(p_T)=T/G^2=9/10^4=0.0009\); so at \(p_0=0.5\) the displacement is \(\kappa(0.25-0.0009)=\kappa\times0.2491\), \(=0.04982\) at \(\kappa=0.2\). Kill: \(|q^{({\rm YES})}-p_0|>\kappa\widehat{E[p_T(1-p_T)]}/2=0.02491\) at \(\kappa=0.2\) on fewer than \(0.5\) of \(512\) draws — a different number (\(0.02491\) against \(0.009\)), read by a different instrument (the leaf map's second moment, computed on \(V\)) on a different object (the boundary value vector, not the transition block), and \(0\) GPU-s. It is more decisive than the link it replaces because the displacement it plants is \(2.77\times\) the drift plant's at the registered geometry and does not vanish under absorption dilution: the drift plant's displacement is carried only by draws that never hit \(\{0,1\}\), while the leaf map's is carried by every draw that reaches \(t=T\). If the leaf plant is also invisible at \(\kappa=0.4\), the lattice has no usable rejection region at any registered plant and only BED-P-N remains. Terminal. "BED-P-L is a registered lattice with an exact committor and two planted departures from martingale — a drift in the transition block at \(\theta_{\rm rej}=\mu_1T/(2G)\) and, if that is invisible, a miscalibration in the boundary value vector at \(\kappa E[p_T(1-p_T)]/2\); where neither is readable at the registered dials the lattice has no rejection region and only BED-P-N remains, and a reading on it is in every case a learnability sentence about the plant, never a sentence about markets."

09.26 — The safest trade under constraints as the argmin rule

Statement. Constraint sets under 09.22's indexing convention — outcome sets carry names, the numbered sets are constraint sets only, and every \(k\ge1\) below sweeps constraints and never \(\mathcal A_{\rm NO}\) — absorbing on the augmented state \((t,p,\text{PnL},\text{exposure})\), registered at \(K\in\{2,3\}\) with the head widening to \([m,K+3]\) accordingly: \(\mathcal A_1\) drawdown — running PnL reaches \(-D_{\max}\); \(\mathcal A_2\) liquidity — the trade size exceeds displayed depth at its price (the trade is refused: an absorbing "cannot execute" node reached at \(t=0\) under \(\mathrm{do}(a)\) with \(q^{(2)}=1\) exactly); \(\mathcal A_3\) exposure — position exceeds \(E_{\max}\) — optional, exactly as 09.4 makes repetition optional for chess, and reachable only at \(K=3\): at \(K=2\) the head's \(K+3=5\) channels are sink, YES, NO, \(\mathcal A_1\), \(\mathcal A_2\), so exposure has no output channel and no floor, and at \(K=2\) it is not declared, not censused and named in no rule; at \(K=3\) the head is \([m,6]\) and exposure is declared. Every registered market geometry that prints \(K=2\) (09.30, 09.32, 09.33) therefore runs the two-constraint set, and any verse naming \(\mathcal A_3\) at \(K=2\) is refused at assembly. The sets are not disjoint — a position at \(-D_{\max}\) whose size is above \(E_{\max}\) is in both \(\mathcal A_1\) and \(\mathcal A_3\) — so disjointness is imposed by the device 09.4 uses, a total priority order, first match wins, registered here and hashed into the manifest: \(\mathcal A_{\rm sink}\succ\mathcal A_0\succ\mathcal A_2\succ\mathcal A_1\succ\mathcal A_3\), with the pre-priority overlap count printed beside 09.32's census. The resolution date is the horizon: leaves at \(t=T\) resolve or sink. Goal \(\mathcal A_0\): PnL reaches \(+D_{\rm target}\) before resolution, or resolution in the traded direction. The rules, two and not three: \(a^\star=\arg\max_aq^{(0)}(\mathrm{do}\,a)\); the threshold form \(\arg\max_a\{q^{(0)}(a):\max_{k\ge1}q^{(k)}(a)\le\delta_{\rm thr}\}\) with \(\delta_{\rm thr}=0.1\) frozen here, and "hold" returned when the feasible set is empty. The Chebyshev column \(a^\dagger=\arg\min_a\max_{k\ge1}q^{(k)}(\mathrm{do}\,a)\) is STRUCK from the market rule set — not registered as a candidate, not censused, not scored — because it is dead by this verse's own arithmetic before any draw (the derivation is in the Mechanism), and a rule known false at registration is registered struck, never as a candidate (V-10, V-2). It stays registered on chess (09.5, 09.18), where "hold" is not a legal move and the derivation does not apply. Hypotheses. \(D_{\max}\), \(E_{\max}\), \(D_{\rm target}\) registered per bed in units of the size grid; the one-step vocabulary of R-20 (hsu-2023-safetyfilter, vanmoffaert-2013-chebyshev [V]; the multichain hazard misra-2023-safety-constrained-mdp [V] in Limits). Evidence. DERIVED (the rule definitions and the priority order). The struck Chebyshev column's arithmetic is DERIVED in the Mechanism and is the reason the column is not registered. Mechanism. V-10 (a gate satisfied by construction) and V-2 (a control that must fail by construction is deleted, not run) — the reason the Chebyshev column is struck rather than registered, derived here: at the registered \(K=2\), for \(a=\text{hold}\) there is no position, hence no drawdown and no exposure, and no order, hence no refusal, so \(q^{(1)}=q^{(2)}=0\) exactly (and \(q^{(3)}=0\) as well at \(K=3\)), while every non-hold trade carries \(q^{(2)}>0\) whenever any size in \(\mathcal Q\) can exceed displayed depth; therefore \(\max_{k\ge1}q^{(k)}(\text{hold})=0\) is the column's minimum on every draw and the hold rate is \(1.00\) by arithmetic. The previous registration kept the column as a candidate with a kill at "hold on \(\ge0.95\) of \(512\) admitted draws" — a threshold below a derived rate of \(1.00\) — so the kill was a certainty and not a decision. R-07's sink-escape in a new guise (here the escape is "hold"), V-12 (\(K\ge2\)), D-3 (a dial with a registered support: \(K\in\{2,3\}\)), P-4 (a constraint set with no output channel is claimed scaffolding). Kill. One kill, on the one column that can vary: the threshold form's feasible set is empty on at least \(0.95\) of \(512\) admitted draws at \(\delta_{\rm thr}=0.1\) → the rule returns "hold" on all but a twentieth of draws, the decision head decides nothing, and the threshold is re-registered on the realised distribution of \(\max_{k\ge1}q^{(k)}\) before any arm (its median printed), never after. The realised hold share of the threshold column is printed on every batch (09.32 line 7) and is the only hold share this bed carries. Price \(0\) GPU-s. Planted negatives (V-15), both required to fire: \(\delta_{\rm thr}=0\) must give an empty feasible set on \(100\) per cent of draws, and \(\delta_{\rm thr}=1\) must give a non-empty one on \(100\) per cent; a threshold instrument that does not move between those two ends is blind and no hold-share verdict is admissible. If killed. The threshold form with \(\delta_{\rm thr}\) set to the \(0.25\)-quantile of \(\max_kq^{(k)}\) over non-hold trades on the census batch (registered from the census, frozen thereafter) — Hypotheses: the quantile is strictly between \(0\) and \(1\); Kill: feasible-set-empty on \(\ge0.95\) again. If it fires again, the decision head is withdrawn on markets and only the committor vector and the displacement field are reported. Terminal. "The safest trade on markets is the threshold form of the one-step safety filter over evaluated committors at \(K\in\{2,3\}\) registered constraint sets under a printed priority order; the Chebyshev column is struck as dead by arithmetic, and exposure exists only at \(K=3\); a filter that holds on all but a twentieth of draws is not a filter, and the canon then reports committors, not trades."

09.27 — The interventional re-solve: "if this trade is placed, what moves", with the price-impact model as a hypothesis

Statement. \(\mathrm{do}(a)\) for a trade of size \(q\) at side \(\sigma\): the book's displayed sizes at the consumed levels are reduced (the deterministic part), and the mid moves by \(\lambda\sigma q\) (the impact hypothesis, linear, \(\lambda\) per venue [ASSUMED]; the standard citation is owed, not in references.bib). On the lattice this is a row change at the root, \(P'=P+e_0u^\top\) with \(u^\top\mathbb 1=0\) (the transition shifts by the impact), and the displacement of the state field is Proposition 7's one extra solve, \(\Delta z=(I-\gamma P')^{-1}(\Delta V+\gamma\,\Delta P\,z)\). On BED-C-T and BED-P-L that solve is a no-op and is registered as a cost statement only, never as a fidelity number. Both beds serialise the query last (09.5: "leaves first, root last"; 09.25: "time \(T\) first, the root \((0,p_0)\) last"), so \(Q\) is strictly lower-triangular with the intervened row at index \(s-1\) and \(\Delta z=\gamma(e_{u_a}-P[x_0,:])z\) is supported on exactly one coordinate: nothing downstream of the intervened row exists, the \(s^2d/2\)-MAC solve computes \(s-1\) structural zeros, and the displacement is a rank-one read at the query coordinate — one inner product (DERIVED; the same arithmetic 09.10 line 10 and 09.32 line 10 print as V-10). A control asked to reproduce one scalar reproduces it, so K-G1 has one scalar to match on those beds and fires on a foregone conclusion; it is moved entirely to the natural-ground beds below, where the intervened row precedes later tokens and the solve has \(s-i-1\) non-zero coordinates to get right, and the \(\approx35\) s price the previous registration attached to the in-class K-G1 cell is deleted, not re-quoted. On the natural-ground bed the same formula is applied on the arm's own \(\hat P\) as its prediction of what moves, scored against the next observed book — with the no-change predictor's error printed beside it (vakalis-2026-interventiongap [V] owns that floor). Hypotheses. Proposition 7 (docs/CEQ_SHAPE.md §2.2; sherman-1950-inverse-adjustment, bottou-2013-counterfactual §7.3 [V]); \(\gamma<1\); the impact is a hypothesis stated in the manifest field impact_model = linear(lambda). Evidence. DERIVED. \(\lambda\): NOT MEASURED — needs executed trades, which the canon never places (a purchase is not an experiment this record runs). Mechanism. M-8 (the row clamp is priced at \(s^2/2\) MACs per candidate; a book rewrite that changes every later token is a suffix re-solve), P-8, D-5 (a declared zero displacement needs a movement test: the cached-mixture plant), V-10 (a kill whose control has one scalar to reproduce is satisfied by construction, which is why K-G1 leaves the in-class beds), M-8 again (a \(\approx35\) s price attached to a computation that is \(s-1\) structural zeros is not a price). Kill. K-G1 runs on the natural-ground beds only — BED-C-N (09.11's registration) and BED-P-N (09.29b) — where the intervened row sits at index \(i<s-1\) and the re-solve has \(s-i-1\) non-zero coordinates: the cached-mixture arm \(O_{\rm cached}=\hat P_{\rm base}(I-\gamma\hat P_{\rm base})^{-1}V_{\rm int}\) within one seed sd of the shape on \(P\)-changing plants on at least \(6\) of \(8\) seeds → the re-solve is a per-row control wearing a name and the "what moves" channel is repriced as a cost statement. Price: NOT MEASURED — needs the BED-C-N / BED-P-N cost law at \(s=512\) (09.14's band \(206\)–\(537\) GPU-s), and the in-class cell's \(\approx35\) s is deleted rather than re-quoted, because on a root-last serialisation the control has one scalar to reproduce and the kill is a foregone conclusion (V-10). Planted negative for the natural-ground cell: an intervention at \(i=0\) on a \(s=512\) context must give a cached-mixture error above one seed sd on \(8\) of \(8\) seeds; if it does not, K-G1's instrument is blind at every \(i\) and no interventional verdict is admissible. On natural ground the fidelity contrast is also the shape's \(\Delta\hat z\) cosine against the observed book change: within the cosine's own \(\mathrm{MDE}_8\) of the no-change predictor → no interventional reading on real books. On BED-C-T and BED-P-L there is no fidelity kill at all, only 09.10 line 10's and 09.32 line 10's printed V-10 lines and the cost statement of the Terminal. If killed. The displacement identity stays as algebra (Proposition 7 is a theorem); the channel is reported as "one extra solve, \(s^2d/2\) MACs" with no fidelity number — Hypotheses: none; Kill: none (a cost statement has no fidelity kill). This is the Terminal. Terminal. "If this trade is placed, what moves is one extra triangular solve under a stated impact hypothesis; on both in-class beds it is a rank-one read at the query coordinate and carries a cost statement, no fidelity number and no price; its fidelity on real books is unmeasured and its impact constant is a hypothesis the record never tests by trading."

09.28 — Leakage and look-ahead guards: timestamps, resolution-time censoring, survivorship

Statement. Three guards, each a function that raises, each with a planted violation: (i) timestamp — every feature at decision time \(t\) carries a source timestamp \(t_f\), and the loader raises if \(t_f\ge t\) (the strict inequality; a same-second tick is a leak); (ii) censoring — contracts unresolved at the data cut are kept as right-censored rows in \(\mathcal A_{\rm sink}\) with censored = true, never dropped, and the censored share is a census line; (iii) survivorship — delisted and voided contracts are kept with their last state, and a split that contains only resolved contracts is refused. The planted positive for the leak probe: a feature carrying \(p_{T_{\rm res}-\epsilon}\) (the price one tick before resolution) must read \(R^2\ge0.99\) against \(y\); the honest probe from features at \(t\) must read \(R^2<0.5\) against the resolution beyond what \(p_t\) alone gives (the incremental \(R^2\) over \(p_t\) is the number). Hypotheses. Time-ordered splits (train before calibration before test, by contract close time); the FEN-dedupe analogue is the contract dedupe (the same underlying event listed on two venues lands in one split). Evidence. DERIVED (the guards mirror ceq.kdata's five rules, READ ceq/kdata.py:16-30, each of which has a planted-violation test at tests/gate0/test_g05_data.py). Mechanism. V-7 (a guard that cannot fire is not a guard: every one fires on its plant), M-1, V-24. Kill. Honest incremental \(R^2\ge0.5\) → the split leaks and every market number on it is struck; planted \(R^2<0.99\) → the detector is blind and no leak verdict is admissible. Price \(0\) GPU-s. If killed. The split is re-cut by event time with a one-day embargo between splits, and the probes re-run — Kill: the same numbers. A second failure means the venue's timestamps are not trustworthy at the registered cadence and the venue is not admitted. Terminal. "Every market feature carries a timestamp strictly before its decision; censored and delisted contracts stay in the data; a split on which the leak probe fires carries no number."

09.29 — Data sources that can be pinned locally, with their access route; NOT MEASURED where none is pinned

Statement. Two classes of local source. (i) Generators: BED-P-L (09.25) as generator \(+\) seed \(+\) hash, kind: generator, licence: this repository. (ii) Venue snapshots: a public resolved-contract price history and, where a venue publishes one, an order-book archive, fetched once through the venue's public, unauthenticated history endpoint, written to data/ as one file, its SHA-256 recorded in results/k_data_manifest.json with the venue, the endpoint, the fetch date and the licence, status UNPINNED until recorded. The canon names the access route and not a URL, because a URL is a number without a producer until a digest exists. No snapshot exists in the tree; every count over a venue is NOT MEASURED — needs the pinned snapshot (book 05's data pin under Ruling 7). Hypotheses. The venue's terms permit the snapshot (recorded per entry, as kaggle/README.md records licences and strikes unlicensed mirrors); the fetch is a read, not a trade, and is performed by the author or with the author's yes (the Kaggle carve-out's rule applied to any external fetch). Evidence. RUN ls data/ → no market file. READ results/k_data_manifest.json rejected (the licence-strike pattern to copy). Mechanism. Ruling 7, P-1, V-22 (no count from one venue transfers to another). Kill. Any cell reading a venue snapshot whose manifest entry has sha256: null must raise MissingPin (the existing guard). A venue whose two fetches on two days produce different digests for the same closed date range is not pinnable and is struck. If killed. The generator alone (BED-P-L) — Hypotheses: none beyond 09.25; Kill: 09.25's. The natural-ground bed then does not exist and 09.35's Terminal is the market sentence. Terminal. "No venue is pinned; every real-market number in this book is NOT MEASURED; the only market bed that exists is the lattice."

09.29b — BED-P-N: the natural-ground market bed, registered as a bed rather than inside a hypothesis

Statement. BED-P-N is named nine times in this book and until this verse was registered nowhere: its sole appearance was inside 09.21's Hypotheses — "BED-P-N at \(s=512\) byte tokens or \(s=64\) feature tokens" — while 09.30, 09.31, 09.33 and 09.36 scored A1, A2, PnL and the phase head on it. That is load-bearing scaffolding outside a verse, which L-VERSE forbids and CHARTER.md §2 strikes; the bed is registered here, with every field those four verses read. Token layout and \(s\). One token per \((\text{level},\text{side})\) of the top-\(\ell=10\) levels on each side, and one per path step over the window \(W\), each token a feature vector through the linear input projection every arm shares (09.3's one-table rule at the market feature width): \(\mathbf{F=18}\) — level price, displayed size, side, level index, time index, path-step index, time-to-resolution, running PnL \(\Pi_t\) and signed exposure \(X_t\) (09.21's augmentation, in size-grid units, without which 09.26's drawdown and exposure sets are absorbing on coordinates no token carries), and the \(K+2\) boundary flags — at \(s=64\) feature tokens, which is the registered layout that carries counts. The width \(F=16\) this verse previously printed omitted the two augmentation coordinates and is struck; every count below is at \(F=18\). The token budget at \(s=64\) is \(2\ell+W\le64\), so \(W=16\) is registered here and \(W=64\) is a dial of the \(s=256\) layout only (09.21). The \(s=512\) byte layout stays a registered dial with no count: NOT MEASURED — needs the \(s\)-sweep, band \(206\)–\(537\) GPU-s (RUN, 09.14). \(K\). \(K\in\{2,3\}\) exactly as 09.26 registers it, head \([m,K+3]\), \(m=7\), \(|\mathcal Q|=3\); the default is \(K=2\), at which exposure is not declared, not censused and named in no rule. \(t^\star\) and the skyline, both absent before this verse. \(t^\star\) is the number of price-path steps between the decision time and resolution at the registered horizon. At 09.23b's registered one-day horizon with a one-hour cadence \(\Delta t\), \(t^\star=24\), so the skyline is \(\lfloor\log_224\rfloor+2=4+2=\mathbf{6}\) layers (DERIVED, \(\log_224=4.585\)). Its exact count as the three line items of 09.9, at \(d_{\rm model}=64\), \(s=64\): projection \(F\times d=18\times64=\mathbf{1{,}152}\); skyline trunk \(53{,}952+5\times49{,}728=\mathbf{302{,}592}\) (the per-block law \(12d^2+9d=49{,}728\), 09.9 RUN); head \([m,K+3]\) at \(64\times7\times5=2{,}240\) — total \(\mathbf{305{,}984}\), unmatched, read beside every row (R-SKY). The previously printed projection \(1{,}024\) and total \(305{,}856\) were at the struck \(F=16\) and are replaced by \(1{,}152\) and \(305{,}984\); the trunk is unchanged, since the augmentation widens the projection and nothing else. RUN this session: TinyLM('softmax',d=64,n_layers=6,n_heads=4,seq=64,seed=0,vocab=256).n_params() → \(335{,}360\), and \(335{,}360-16{,}384-16{,}384=302{,}592\) reproduces the trunk with the byte embedding and byte head removed. The matched arms are 09.30's, at the same repriced width: trunk \(53{,}952\), projection \(1{,}152\), head \(2{,}240\), total \(\mathbf{57{,}344}\) (the \(57{,}216\) previously printed was at the struck \(F=16\)). The horizon is a dial with a registered support and the skyline moves with it: one hour at one-minute cadence gives \(t^\star=60\) and \(\lfloor\log_260\rfloor+2=7\) layers (\(53{,}952+6\times49{,}728=352{,}320\)); one week at one-hour cadence gives \(t^\star=168\) and \(\lfloor\log_2168\rfloor+2=9\) layers (\(53{,}952+8\times49{,}728=451{,}776\)) — all DERIVED from the same law. A cell whose header carries no \(t^\star\) and no sky_depth is refused by 09.15's field rule (both are declared identity-manifest fields: READ docs/CEQ_SHAPE.md:1600 and :2652), which is what refused every BED-P-N cell before this verse existed. Label. The unconstrained YES committor at the registered horizon — 09.23a's object, read from the \([m,K+3]\) tensor's YES channel. The constrained channels are labels of 09.26's augmented state and are never scored against \(p_t\) (09.24, V-17). Floor. \(p_t\), the mid-price at the registered horizon, as 09.23b registers it on a pinned venue; then the isotonic-recalibrated market (09.23b's If-killed); then the market as-is with its miscalibration printed. Census. 09.32 lines 1–2, 4–9 and 15 on \(512\) BED-P-N states, at \(0\) GPU-s given a snapshot. Lines 1, 2 and 4 are read on the declared boundary rows of the token stream — the arm's own masks — and not on an environment chain, because on natural ground there is no \(P_{\rm env}\) (D-2); that is stated, never assumed. Lines 3, 10 and 12–13 are printed and never counted, as on the lattice. Line 11 (\(m_{\rm eff}\) and the fraction of trades the liquidity set refuses) is 09.21's kill and is counted. Line 14 does not apply: there is no regime token on natural ground, and a census printing one is printing a lattice column on a venue. Hypotheses. A pinned venue snapshot under 09.29 with resolved contracts, time-ordered splits and the guards of 09.28 in force; the horizon and its cadence registered per cell; \(\ell=10\), \(W\in\{16,64\}\); the \(F\times d\) projection identical on every arm (Ruling 3); the impact hypothesis of 09.27 declared in impact_model wherever a trade is evaluated. Geometry: \(s=64\), \(d_{\rm model}=64\), \(H=4\), \(m=7\), \(K\in\{2,3\}\), \(t^\star=24\) at the one-day horizon, \(N=8\) seeds, \(n\) resolved contracts. Evidence. DERIVED for every count above from the per-block law \(12d^2+9d\) (09.9, RUN this session) and RUN this session for \(335{,}360\) at \(L=6\). Every number on the bed — census lines, class shares, label sd, realised paired sd, Brier, log score, PnL — is NOT MEASURED, needs the pinned snapshot: RUN ls data/ this session → no market file, and READ results/k_data_manifest.json holds no venue entry. Mechanism. L-VERSE (nothing load-bearing outside a verse — the defect this verse repairs), P-4 (claimed scaffolding that does not exist), P-7 (a bed name with no referent), R-SKY and Ruling 3 and L-2 (docs/CEQ_SHAPE.md §A.10 at :2640; not a MISTAKES.md id, MISTAKES.md equivalent P-1: a bed that carries A1/A2 needs \(t^\star\), a skyline depth and exact counts in the header), D-2, V-22. Kill. Two, both frozen here, both \(0\) GPU-s given a snapshot. (a) The leak probes of 09.28, both ways: the honest incremental \(R^2\) over \(p_t\) at or above \(0.5\) → the split leaks and every BED-P-N number is struck; the planted probe — a feature carrying \(p_{T_{\rm res}-\epsilon}\), the price one tick before resolution — below \(R^2\ge0.99\) → the detector is blind and no leak verdict on this bed is admissible (V-15). (b) The class-balance line of 09.22: the YES share at the registered horizon outside \((0.05,0.95)\), or the void/delist share above \(0.5\) → the label is degenerate on that venue and BED-P-N is not admitted there. Planted negative for (b): a split restricted to contracts that resolved YES must read a YES share of \(1.000\) and fire; if it does not, the balance line is blind. No venue is pinned at 99777ab (09.29), so both kills are decidable and neither is decided, and every BED-P-N score in 09.30, 09.31, 09.33 and 09.36 is NOT MEASURED — needs the pinned snapshot — and is refused at assembly until this verse's census block is printed beside it. If killed. By (a): the split is re-cut by event time with a one-day embargo between splits and the probes re-run (09.28's If-killed) — Hypotheses: contract close times are recorded to the cadence; Evidence: NOT MEASURED; Kill: the same two probe numbers, \(0\) GPU-s. A second failure means the venue's timestamps are untrustworthy at the registered cadence and the venue is struck, which is 09.29's kill. By (b): stratify by contract category until the YES share is inside the band, the discarded fraction printed (09.22's If-killed) — Kill: discard fraction at or above \(0.9\), which strikes the venue (V-5). If both routes fail on every venue reachable under 09.29's access rule, BED-P-N does not exist, and every A1, A2, PnL and phase sentence in Part II is withdrawn: what remains is the lattice's learnability sentence (09.35). Terminal. "BED-P-N is a registered natural-ground bed — token layout, \(s=64\) feature tokens at \(F=18\) (09.21's augmented state), \(K\in\{2,3\}\), \(t^\star\) the path steps to resolution at the registered horizon, a \(6\)-layer skyline at a \(302{,}592\)-parameter trunk at the one-day horizon, the unconstrained YES committor as label and \(p_t\) as floor — with two decidable kills, a census it must pass and no venue pinned; every score attributed to it elsewhere in this book is NOT MEASURED, and no A1, A2, PnL or phase number exists on it."

09.30 — Matched baselines on markets, with exact counts: depth-1 softmax, a logistic model on the same features, and the market itself

Statement. On BED-P-L at \(d_{\rm model}=64\), \(H=4\), \(s=64\), \(m=7\), \(K=2\), every count printed as the three line items of 09.9 and never as one lump (Ruling 3): depth-1 softmax with the shared trunk \(53{,}952\) (positional embedding \(4{,}096\) + one block \(49{,}728\) + final norm \(128\), RUN this session), the feature projection \(F\times d_{\rm model}=18\times64=\mathbf{1{,}152}\) at the market feature width \(F=18\) below (09.21's augmented state; the \(F=16\) this verse previously printed omitted running PnL and signed exposure, the two coordinates 09.26's drawdown and exposure sets are absorbing on, and is struck), and the head \([m,K+3]\) at \(d\cdot m(K+3)=64\times7\times5=2{,}240\) (DERIVED, bias-free as TinyLM's head is) — total \(\mathbf{57{,}344}\); the shape the same three items \(+4\) (\(\gamma\) per head) and one \(\beta\), matched. \(86{,}720\) is not this row: it is TinyLM's total at vocab \(256\) and contains the \(256\times64\) byte embedding and the \(64\times256\) byte head, both of which the projection and the \([m,K+3]\) head replace (09.9). The depth skyline at \(t^\star=T=9\): \(\lfloor\log_29\rfloor+2=5\) layers, trunk \(53{,}952+4\times49{,}728=252{,}864\) (DERIVED from the per-block law \(12d^2+9d=49{,}728\) at \(d=64\), 09.9 RUN), plus the same projection and head — not \(285{,}632\), which is TinyLM's byte-vocabulary total at \(L=5\) and is not this bed's skyline; unmatched, read beside every row. The logistic model on the same per-token features flattened: \(F\cdot s+1\) parameters per output — at \(F=18\) (level price, size, side, level index, time index, path-step index, time-to-resolution, running PnL, signed exposure, and the \(K+2\) boundary flags; the enumeration is 09.29b's and is the same table) and \(s=64\): \(18\times64+1=\mathbf{1{,}153}\) per output, \(K+3=5\) outputs, \(\mathbf{5{,}765}\) total (DERIVED; the count is printed per bed). The \(1{,}025\) and \(5{,}125\) previously printed were at the struck \(F=16\). The market itself: \(0\) parameters, \(\hat q=p_0\), the floor of 09.23a as registered by 09.23b. On BED-P-N — registered as a bed by 09.29b and by no other verse; before that verse this sentence's counts stood on a bed with no Statement, no \(K\), no \(t^\star\), no skyline, no census and no Kill, and were refused — the same three line items at the same widths, plus the isotonic-recalibrated market (09.23b's If-killed) and the return-conditioned arm (chen-2021-decisiontransformer [V], NOT MEASURED), with 09.29b's \(t^\star=24\) and its depth-\(6\) skyline at trunk \(302{,}592\) in the header of every row and no row without them. Hypotheses. Ruling 3; the projection \(F\times d\) identical on every arm. Evidence. RUN (09.9's command at n_layers=1 → 86720); DERIVED for the rest. Mechanism. D-1, R-SKY, Ruling 3, C8 (READ docs/CEQ_SHAPE.md:1733, the K-H2 card; not a MISTAKES.md id — its MISTAKES.md equivalents are D-1 plus V-10: the logistic model is the static-task control, and if it matches the shape within the Clopper–Pearson half-width at \(N=8\), the bed is static). Kill. K-H2 on markets: the logistic model within the half-width of the shape on the goal committor's sign at \(N=8\), or McNemar \(p>0.05\) against depth-1 softmax → BED-P-L is a static task and is struck before any number. Price \(\le1.524\) s per control cell. If killed. \(T\) from \(9\) to \(21\) (the regime's effect compounds; a static model cannot integrate it) — Kill: the same test at \(s=256\), price NOT MEASURED (the \(s\)-sweep, book 03). If the static control still matches at \(T=21\), the lattice label is static at every registered \(T\) and no market capability number exists. Terminal. "Every market table carries the market at \(0\) parameters and a logistic model at its exact count beside the shape; a bed a logistic model solves carries no number."

09.31 — PnL under constraints as a scored prediction, with its counter and SPLIT band

Statement. On BED-P-N's natural-ground test split (the bed 09.29b registers, and no cell exists before that verse's census block is printed), the threshold-form policy of 09.26 is executed on paper (never on a venue) at the registered horizon with transaction cost \(c\) per unit (registered per venue) and the impact hypothesis of 09.27; PnL is accumulated per contract and the constraint sets are enforced as hard stops. The prediction (the flattering half): mean PnL per contract exceeds that of the market-following rule (buy the side the market favours, same sizes, same constraints) by more than \(\mathrm{MDE}_n\) of the paired per-contract PnL difference. The counter (the point estimate under D-CALIB): the paired difference within \(\pm\mathrm{MDE}_n\), or negative. The SPLIT band: positive but below \(\mathrm{MDE}_n\). Sequential monitoring uses an e-process for the null "no edge" (ramdas-2023-game-theoretic, ville-1939-collectif [V]; the Hoeffding-type test supermartingale for bounded per-contract PnL, hoeffding-1963-probability [V]), so that reading the running PnL never inflates the verdict; the flattering sentence needs the e-value to cross \(1/\alpha=20\) at \(\alpha=0.05\). Hypotheses. \(n\) resolved contracts; PnL bounded per contract by the size grid and the constraints (so the Hoeffding supermartingale applies); the market-following rule as the fellow approximator on the same draws. Evidence. DERIVED. Every number: NOT MEASURED — needs the pinned snapshot (09.29) and a trained arm (09.34). Mechanism. D-7 / L-SIGN, D-CALIB (9 checked, 9 adverse: the counter is the point estimate), M-2 (the e-process threshold frozen), V-17 (PnL in the size grid's units, not dollars from another venue). Kill. The e-value never crosses \(20\) over the test split, or the paired difference is within \(\pm\mathrm{MDE}_n\): the counter holds and the sentence below is licensed. Planted negative: a policy given the resolution outcome (a look-ahead plant) must cross \(20\) within \(n\le200\) contracts, else the instrument cannot detect an edge that exists (V-15). Price \(0\) GPU-s given the trained arm. If killed. There is no replacement policy; the canon does not search the policy space for one (that would be M-2 on the policy). The SPLIT case prints the band and the sign; the negative case prints the loss beside the market-following rule's. Terminal. "No edge over the market-implied probability is licensed; the module is registered as a calibrated reader, and the trader sentence requires a pinned venue, \(n\) resolved contracts with its realised sd, and an e-value crossing \(20\) — none of which exists at 99777ab." — a licensing sentence, not a result, and the point estimate of this book under D-CALIB. The previous Terminal ("No edge over the market-implied probability at \(n\) contracts and \(N\) seeds") is struck for the reason 09.24's is: it asserts a measured negative on quantities this verse's own Evidence records NOT MEASURED and on a venue 09.29's Terminal records never pinned, at an \(n\) with no value anywhere in this book (P-1, P-7, V-22).

09.32 — The market domain census (L-DOM) and the D-4 gate, at \(0\) GPU-s

Statement. On \(512\) BED-P-L draws at \((T,G,K,m,s)=(9,100,2,7,64)\) and, where a snapshot is pinned, on \(512\) BED-P-N states: (1) row stochasticity including absorbing rows; (2) the sink declared on \(100\) per cent; (3) \(\rho(Q)=0\) printed (the lattice is strictly lower-triangular in token order: V-10); (4) every set before the root; (5) per-coordinate sd of \(q\) at the root over the admitted region \(>0.05\), the sink and censored shares printed; (6) the YES share and every argmin class frequency in \((0.05,0.95)\); (7) rule disagreement \(>0\) and the "hold" share of the threshold column printed (09.26, where the Chebyshev column is struck from the market rule set and the threshold column is the only column that can vary); (8) the leak probes of 09.28 both ways; (9) \(I(s_0;a^\star)=0\) and the untrained-arm read; (10) \(\mathrm{Var}(\Delta z)>0\) per coordinate over coordinates \(\ge i_{\min}\), the source's wording (READ docs/CEQ_SHAPE.md:2553), the intervened index inside the range, the zero-coordinate fraction printed — V-10 on this bed, printed and never counted, because the lattice is serialised root-last, \(Q\) is strictly lower-triangular, the intervened row is the root at index \(s-1\), and \(\Delta z=\gamma(e_{u_a}-P[x_0,:])z\) is supported on exactly one coordinate: under the previous wording (\"after the root\") the variance was taken over the empty set and the line was unsatisfiable by construction, and under the restored wording it is a single inner product, so the interventional channel on BED-P-L is a cost statement (09.27's Terminal) and never a fidelity number; (11) \(m_{\rm eff}\) and the fraction of trades refused by the liquidity set; (12)–(13) on trained cells; (14) the regime share \(r=1\) in \((0.05,0.95)\), its realised count printed as an integer out of \(512\), because 09.25's rejection kill is conditioned on it, and the martingale-identity plant (\(|q-p_0|\le10^{-12}\) on every \(r\equiv0\) draw); (15) the reliability bins of 09.23b where a snapshot exists. Hypotheses. The BED-P-L generator exists (it does not at 99777ab). Evidence. NOT MEASURED — needs the generator and the census printer (book 04). READ docs/CEQ_SHAPE.md §A.7. Mechanism. D-4, V-8, V-12, V-24 (line 14 is the identity plant), L-DOM. Kill. Restricted to the admission lines, as 09.10's is: lines 1, 2, 4 below \(100\) per cent; line 5 at or below \(0.05\); line 6 outside \((0.05,0.95)\); line 7 at zero; line 14's regime share outside \((0.05,0.95)\) → not admitted, no arm runs, the reroute of 09.35. Lines 3, 10 and 12–13 are printed, never counted — 3 and 10 are V-10 gates satisfied by construction on the root-last lattice, and a kill quantified over them would refuse the bed by arithmetic. Planted negatives: \(\mu_1=0\) everywhere must send line 5's sd of \(q^{({\rm YES})}-p_0\) to \(0\) (and the census must say so); \(K=1\) must fire V-12. Price \(0\) GPU-s. If killed. 09.35. Terminal. "BED-P-L at the registered design point does not admit; the canon files its generator, its census with the failing line, its floors, its baselines and no market number."

09.33 — The protocol that measures A1, A2, T1 and T2 on markets

Statement. As 09.11, with: the capability label the \([m,K+3]\) tensor and the displacement field on BED-P-L (VOID against softmax by containment; scored against the creditable arms of the VOID list, which for markets is 09.16's list with bed_p names); A1/A2 on BED-P-N scored on the \([m,K+3]\) tensor against the creditable arms only and only on the bed 09.29b registers, with that verse's \(t^\star=24\) and \(6\)-layer skyline at trunk \(302{,}592\) in the header — A2 on BED-P-N is undefined without them, exactly as on BED-C-N (09.11) — while every contrast against the market floor \(p_t\) is scored on the unconstrained YES committor channel alone (09.23a: \(p_t\) is the unconstrained committor, so a constrained channel scored against it is a units error, V-17), with the skill of 09.24 as the anchored metric; T1 to 09.11's restated target, the difference \(\varphi\text{-NRMSE}(q)-\varphi\text{-NRMSE}_{\rm floor}\le0.25\) with the floor transformed into \(\varphi\) units on the same batch and printed first, on BED-P-L against the exact oracle floor at \(0.0\) (whose \(\varphi\) transform is \(0\), so on BED-P-L and there alone the difference coincides with the absolute reading) and on BED-P-N against \(p_t\)'s own \(\varphi\)-NRMSE, with "target below floor, T1 undefined on this bed" as the third printed outcome; T2 the draws to the same point; the \(n\)-contracts sd and the \(N\)-seeds sd both printed, the smaller \(\mathrm{MDE}\) never substituted for the larger. Hypotheses. As 09.11; two independent sources of variance (contracts, seeds) and both are realised. Evidence. READ docs/CEQ_SHAPE.md §A.11; NOT MEASURED for every market sd. Mechanism. M-3, M-9, C17 (V20_R15_JOURNAL.md C17 @ 99777ab; not a MISTAKES.md id — its MISTAKES.md equivalents are M-8 plus M-3), V-26 (a marginal over contracts standing in for the paired claim: the pairing is asserted by seed-set equality and contract-set equality, one line each). Kill. K-P (realised sd \(\ge2.18\times\) the pilot); the run-order kill; and the pairing kill: the seed sets or contract sets of two "paired" arms unequal → the contrast is unpaired and struck. All \(0\) extra GPU-s. If killed. \(N=16\); then a band with no point. Terminal. "A1/A2/T1/T2 on markets are defined and priced; none is measured; two realised sds are printed before any of them may be quoted."

09.34 — The first market cell at \(0\) GPU-s and the first GPU cell priced

Statement. First cell: (a) the 09.32 census; (b) the floors — on BED-P-L the exact oracle at \(0.0\) and the hop ladder; on BED-P-N the market's Brier and log score at the registered horizon (NOT MEASURED — needs the snapshot) and the reliability bins; (c) the oracle hash — bed_signature('bed_p') twice; (d) the per-coordinate sd of \(q\) at the root over \(512\) draws (NOT MEASURED — needs the generator). First GPU cell: one bed-cell pair at \(s=64\), \(\approx34\) s carried on the certified stack [FITTED + RUN]. The market arena is priced arm by arm at each arm's own law (M-8), as 09.14's is, and the "seven-arm arena \(\approx98\) s" copied from the chess verse is struck — it was the same borrowed figure, and this bed's arm set is five kinds and not seven. The five registered market kinds, at \(8\) seeds, \(d_{\rm model}=64\), \(s=64\): bed_p_shape \(8\times1.680=13.440\) s [FITTED + RUN]; bed_p_softmax_d1 \(8\times1.524=12.192\) s [FITTED]; bed_p_softmax_d5, the depth-\(5\) skyline at \(t^\star=T=9\), \(8\times(5\times1.524)=8\times7.620=60.960\) s [ASSUMED linear in depth], its trunk \(252{,}864\) and never \(285{,}632\) (09.30); bed_p_logistic \(0\) GPU-s (a closed-form fit on CPU); bed_p_market \(0\) GPU-s (\(0\) parameters, \(\hat q=p_0\)); plus \(4.0\) s fixed overhead [FITTED] — total \(90.592\) s, five priced rows for five registered kinds. On BED-P-N the skyline is \(6\) layers at \(t^\star=24\) (09.29b), \(8\times(6\times1.524)=73.152\) s at \(s=64\) on the same [ASSUMED] law, and NOT MEASURED at \(s=512\). Every one of these numbers is the byte-embedding floor and not a price (09.14): the market projection adds \(F\times d_{\rm model}=18\times16=\mathbf{288}\) MACs per token at the priced width against the block's \(3{,}072\), \(\mathbf{+9.375}\) per cent at 09.21's augmented \(F=18\) (the \(256\) and \(+8.33\) per cent previously printed were at the struck \(F=16\)), and the refit is NOT MEASURED — needs book 03's cost law at the projected width. Every table header in this verse carries the three line items of 09.9 and 09.30 — trunk \(53{,}952\), projection \(18\times64=1{,}152\), head \([m,K+3]\) at \(2{,}240\) — never one lump count (Ruling 3); BED-P-N at \(s=512\): NOT MEASURED — the \(s\)-sweep band \(206\)–\(537\) GPU-s (RUN, 09.14). Hypotheses. As 09.14 (the certified stack, not the installed one). Evidence. READ COSTS.md:73-74, docs/CEQ_SHAPE.md §A.11 item 5; RUN torch 2.14.0+cpu, CUDA False (this session). Mechanism. M-8, M-3, P-8, V-22. Kill. As 09.14 (the smoke band), and 09.32 line 5 (sd \(\le0.05\) → not admitted). If killed. 09.35's reroute; prices re-fitted as 09.14. Terminal. "The market bed's first cell is free and decides admission; its first GPU cell costs about half a minute on a stack this box does not run, its five-kind arena at least \(90.592\) s on the same stack, and every one of those figures is the byte-embedding floor of a cost law fitted without the feature projection rather than a price."

09.35 — The market bed's reroute and its Terminal

Statement. This verse reroutes an admission failure (09.32's census), not the rejection kill: a rejection-kill failure is rerouted by 09.25's leaf-miscalibration plant, which changes the object the departure lives in rather than the dial, and only its second failure lands here. If BED-P-L does not admit at \((T,G,K,m,s)=(9,100,2,7,64)\): first the dial — \(T\) to \(21\) at \(s=256\), then \(\mu_1\) to \(0.4\); second the horizon — the resolution rule at the leaf from Bernoulli\((p_T)\) to a threshold rule (\(p_T\ge\tfrac12\) resolves YES), which sharpens the label sd; third \(N\) repriced from the first admitted batch's realised sd. If none admits, BED-P-N is attempted under 09.32 with a pinned snapshot; if no snapshot is pinned or it does not admit, the market use has no bed. Hypotheses. docs/CEQ_SHAPE.md §5.10 tree C; Ruling 7 for every rerouted generator. Evidence. DERIVED (09.25's node counts and displacement arithmetic). Mechanism. D-4, D-3, M-3. Kill. Each reroute has 09.32's kill at \(0\) GPU-s; the chain is three links and ends here. If killed. None — this verse is the reroute. Terminal. "The market use is registered as two beds — a lattice with an exact committor and a planted departure from martingale, and a natural-ground bed against the market-implied probability as floor; at every registered dial the lattice did not admit or no venue was pinned; the canon licenses the martingale floor as a theorem, the guards, the census, and no market capability number."

09.36 — The next equilibrium phase on markets: a definition on the committor head, not a head of its own

Statement. The "equilibrium phase" of a contract is the absorbing set its mass flows to; the transient state is the pre-resolution path; a decision point is a state on the isocommittor \(q^{({\rm YES})}=\tfrac12\) (Proposition 9, docs/CEQ_SHAPE.md §2.2; prinz-2011-msm [V] for metastable membership). There is no phase head. Basin membership is defined as \(\mathbb 1[q^{({\rm YES})}>\tfrac12]\) of the committor head — no separate head, no separate parameters, no separate number and no contrast — which is a definition verse from the outset and not a head that was later retired. The previous registration gave the phase head a McNemar contrast against \(\mathbb 1[p_t>\tfrac12]\) and against a change-point detector; that contrast is deleted. The phase label at one horizon is a scalar at one position, which 09.7's Statement forbids as a capability label on either registration and which 09.16 now registers VOID by D-1 on both market beds, so the only sentence a McNemar contrast on it could license is a forbidden one — and a kill that can only license a forbidden sentence is not a kill (V-2, V-10). The change-point detector on the price path (basseville-1993-abrupt-changes [V]) stays registered as a descriptive fellow approximator whose agreement fraction with the definition is printed and never scored; the zero-information floor \(1-\max(\hat\pi_{\rm YES},\hat\pi_{\rm NO})\) and the market's own side \(\mathbb 1[p_t>\tfrac12]\) are printed beside that agreement fraction, as descriptions and not as baselines a number is claimed over.

The detector is frozen here, with every constant printed, because a named instrument with no threshold, no support and no selection rule is claimed scaffolding whether it is scored or only described (P-4, M-2). It is a one-sided CUSUM on the mid-price increments \(\Delta p_t\), standardised by the in-control per-step sd: on BED-P-L the increment is \(\pm1/G\) so the in-control sd is exactly \(\sigma=1/G=0.01\) at \(G=100\) (under \(r=0\), \(\mu\equiv0\)), and the informed-regime drift is \(E[\Delta p]=\mu_1/G\), so the standardised shift is \(\delta=(\mu_1/G)/(1/G)=\mu_1\) exactly (DERIVED, three lines from 09.25's transition law).

constant	value	class
statistic	\(S_t=\max(0,\ S_{t-1}+\Delta p_t/\sigma-k)\), \(S_0=0\); alarm at \(S_t>h\)	DERIVED (the one-sided CUSUM recursion, basseville-1993-abrupt-changes [V])
reference \(k\)	\(k=\delta/2=\mu_1/2\) — \(\mathbf{0.10}\) at \(\mu_1=0.2\), \(\mathbf{0.05}\) at \(\mu_1=0.1\)	DERIVED from \(\delta=\mu_1\)
in-control ARL target	the registered horizon in steps: \(T=9\) on BED-P-L; \(t^\star=24\) on BED-P-N at 09.23b's one-day horizon and one-hour cadence	[ASSUMED] — one false alarm per horizon in expectation is the loosest rate at which the detector is a description of the horizon rather than of the sampling
decision interval \(h\)	\(\mathbf{1.562}\) at \((k,\mathrm{ARL}_0)=(0.10,9)\); \(\mathbf{3.047}\) at \((0.10,24)\); \(\mathbf{1.691}\) at \((0.05,9)\)	DERIVED from \(\mathrm{ARL}_0=(e^{2kb}-2kb-1)/(2k^2)\) with \(b=h+1.166\), solved for \(b\): \(2kb=0.5455,\ 0.8425,\ 0.2857\) respectively

The corrected-Brownian ARL approximation the third row inverts is owed and absent from references.bib (grep -n -i 'siegmund' docs/references.bib this session returns robbins-siegmund only, a different work), so the row's class is [ASSUMED] on the approximation and DERIVED on the arithmetic given it; the route that needs no citation — freezing \(h\) by simulating \(\mathrm{ARL}_0\) on the martingale plant — is NOT MEASURED, needs the BED-P-L generator (book 04), and no third route is registered. All four constants are frozen before any cell and move only with the dial they are written in terms of (\(k\) with \(\mu_1\), \(h\) with the horizon), which is what stops \(h\) from being chosen after the agreement fraction is seen (M-2).

The plant, and the one condition under which the agreement fraction is not printed at all. A synthetic price series of the same length and the same in-control increment sd \(\sigma=0.01\), with a per-step mean of \(\mathbf{+0.05}\) added from step \(1\) — a standardised shift of \(\delta=5\), fifty times the reference \(k=0.10\) — must raise an alarm on at least \(9\) of \(10\) such series. That plant is generated on the price-path series directly and not on the lattice, because \(+0.05\) per step is off the \(\pm1/G\) grid; the census records it as a detector calibration and never as a lattice draw. If the plant fires on \(8\) or fewer of the \(10\), the detector is blind at the frozen \((k,h)\) and its agreement fraction is not printed — a blind description is unreadable, and printing it would put a number beside the definition that no instrument supports (V-15). Hypotheses. Binary resolution; the horizon registered over 09.23b's support; the committor head of 09.25 (BED-P-L) or 09.29b (BED-P-N) exists and its YES channel is the unconstrained channel of 09.23a; the definition adds \(0\) parameters to every count of 09.30's three line items (DERIVED: a threshold on an existing output allocates nothing). Evidence. DERIVED (a definition and a threshold on an existing output). DERIVED for the detector's four constants, from 09.25's transition law and the printed ARL inversion; [ASSUMED] on the ARL approximation itself, whose citation is owed (RUN grep -n -i 'siegmund' docs/references.bib this session → robbins-siegmund only, a different work). Every number printed under any of them: NOT MEASURED — needs the pinned snapshot (09.29) and BED-P-N's census (09.29b), or 512 admitted BED-P-L draws (09.32). Mechanism. D-1 (a scalar at one position is not a capability label — the reason no head exists), V-2 and V-10 (a contrast that can only license a forbidden sentence is deleted, not run), R-SKY, M-2 (the detector's \(k\) and \(h\) frozen as formulas in the dials they depend on, before any cell), P-4 (a named fellow approximator with no threshold, no support and no selection rule is claimed scaffolding — the defect this verse's detector table closes), V-15 (the \(+0.05\)-per-step plant), L-VERSE. Kill. Two lines, both frozen here, both \(0\) GPU-s, and neither a scored contrast. (a) The definition's own referent: on \(512\) admitted BED-P-L draws, or on \(512\) BED-P-N states where a snapshot is pinned, the isocommittor set is empty — the fraction of draws with \(q^{({\rm YES})}\in(0.4,0.6)\) at or below \(0.01\) of \(512\), i.e. five draws or fewer — so "decision point" names nothing at the registered horizon and the phrase is withdrawn from every market sentence in this book. Instrument: 09.32's census block. Planted negative (V-15): a batch generated with \(p_0=0.99\) on every draw must send that fraction to \(0\) and fire the line; if it does not, the isocommittor line is blind and no decision-point sentence is admissible. (b) The detector's calibration: the \(+0.05\)-per-step plant raising an alarm on \(8\) or fewer of \(10\) synthetic series at the frozen \((k,h)\) → the change-point detector is blind at the registered constants, its agreement fraction is not printed, and the sentence "a change-point detector on the price path is the fellow approximator here" is withdrawn from this verse. Instrument: the same CUSUM recursion on ten generated series. This line decides what is printed, never what is scored. If killed. On (a): the phrase "decision point" is withdrawn; basin membership stands as the definition, which needs no crossing to be well posed — Hypotheses: none beyond the committor head; Evidence: DERIVED; Kill: none, a threshold on an existing output has no fidelity number of its own. On (b): the detector's constants are re-derived at the next ARL target on the registered horizon support (one hour at one-minute cadence, \(t^\star=60\), 09.29b), which raises \(h\) and lowers the alarm rate rather than the miss rate, so it is a different number on the same instrument and not a rename — Hypotheses: the horizon support of 09.23b; Evidence: the same printed inversion; Kill: the same \(10\)-series plant at the new \(h\). A second blindness at the second horizon retires the change-point detector from this book entirely and the definition is printed with the zero-information floor and the market's own side beside it and nothing else. Both branches are the Terminal. Terminal. "On markets the next equilibrium phase is the side of the isocommittor the state sits on; that is a definition on the committor head with no separate head, no separate parameters and no contrast, and where no draw crosses the isocommittor at the registered horizon the phrase 'decision point' is withdrawn and the canon reports the committor alone.

---

Part III — For both beds

09.37 — The Kaggle attach is behind everything and nothing waits on it

Statement. Nothing in this book launches, uploads or attaches on Kaggle. Every chess and market cell is local-first: the generators (BED-C-G, BED-C-T, BED-P-L) need no attach; the dump (BED-C-D) and the venue snapshot are local downloads pinned under Ruling 7; the three UNPINNED Kaggle sources stay UNPINNED and their hash cell prints and then raises (kdata.MissingPin). The Kaggle attach, when the author says yes, adds one thing: the digests of arevel/chess-games and one lichess/chess-evaluations shard, which then become cross-checks of the local pipeline, never its source of labels. Hypotheses. docs/PLAN.md §5.7 (the Kaggle gate: notify first, explicit yes before any run, upload or training start); Ruling 7. Evidence. READ docs/CEQ_SHAPE.md §4.4 ("Nothing has launched"); READ kaggle/ceq_v17k.ipynb cell 8 (the hash cell that raises); READ V17K_RULINGS.md:27, :83-86 @ 99777ab (Ruling 7 closed for BED-M; the attach open). Mechanism. V-22 (no number crosses the device boundary), D-4 (contracts behind an unreached round are staged). Kill. Any chess or market number whose only producer is a Kaggle cell is NOT MEASURED locally and is struck if quoted as a local number. Price \(0\). If killed. The number is re-produced locally or carried as NOT MEASURED — needs the Kaggle attach (the author's yes). Terminal. "The two uses are local beds; Kaggle is a cross-check the author may or may not grant, and no sentence here depends on it."

09.38 — The bed-side half of B5: no arm has been trained on either use, and what the first arm cell needs before it may run

Statement. No CEQ arm has trained on chess or markets; neither bed has a cell, a realised sd or a measured \(t^\star\); every number in this book is a floor formula, a count, a price or a citation. The first arm cell on either bed runs only after: (i) 09.10 / 09.32 admit at \(0\) GPU-s; (ii) the Lean identity targets of docs/CEQ_SHAPE.md §2.6 are green (L-LEAN: the arm is not trained before its identity theorems build); (iii) the VOID list (09.16) and the scored market predictions this book owns — 09.24 (the Brier and log skill against the market floor) and 09.31 (the paired per-contract PnL difference against the market-following rule), and those two only — are hashed in a commit dated before the cell. The set is named exactly, and the rows book 06 carries are named by id rather than by the phrase "the bets book 06 files", which pointed at a file whose contents were not read. RUN this session, grep -n '09\.24\|09\.31\|09\.36' docs/canon/06_PREDICTIONS.md: book 06 files C-39 for 09.31 (the PnL row, with the market-following rule as the counter and the e-process value as the deciding number) and files no row for 09.24; RUN grep -n -i 'chess\|market\|brier\|PnL' docs/canon/06_PREDICTIONS.md → \(9\) matching lines, carrying C-35 (09.10, the chess census at \(0\) GPU-s), C-36 (09.13, the first chess cell), C-37 (09.32, the market census), C-38 (09.34, the first market cell, with the market's Brier and log score as the printed baseline) and C-39. 09.36 owes book 06 nothing: after its rewrite it scores no contrast at all — its agreement fraction is printed and never scored — so it files no prediction and none is owed for it. The gap is therefore exactly one row: 09.24's Brier-and-log skill against the market floor, with the near-efficiency counter under D-CALIB and the SPLIT band this book already states, is not among C-1 to C-40 and must be. This book's writer may not write 06_PREDICTIONS.md or CORRECTIONS.md (CHARTER.md §3, no file but this one), so the row is owed as a CORRECTIONS.md row naming 09.24's prediction, counter and SPLIT band as a bet book 06 must carry, and until that row exists gate (iii) is satisfied by hashing 09.24 and 09.31 in this book and C-39 in book 06, with 09.24's absence from book 06 recorded here as the open half; (iv) the manifest of 09.15 refuses a cell missing any field; (v) the device is certified on the installed stack (book 05 B1/B2). The realised paired sd and the measured \(t^\star\) are the first cell's outputs and are printed before any bet is scored. Hypotheses. CHARTER.md §5 B5; the instruments named: the arena driver with --seq-len and two synchronize() calls (book 04, S-62's analogue), the census printer (S-12's analogue), the generator registry (kdata.BED_SPECS extended). Evidence. RUN BED_SPECS → three beds, none of them chess or markets; RUN grep -l -i chess results/*.jsonl → none; READ docs/CEQ_SHAPE.md §8 ("There is no result"). For gate (iii): RUN this session grep -n -i 'chess\|market\|brier\|PnL' docs/canon/06_PREDICTIONS.md → \(9\) lines, and grep -n '09\.24\|09\.31\|09\.36' docs/canon/06_PREDICTIONS.md → the C-39 row for 09.31 and the C-35..C-39 provenance line, and no row for 09.24. The refutation filed the same two commands as returning no match at all; on the tree this session they return the nine lines and the five rows above, so book 06 files five of this book's deciding cells and not zero — and the finding's conclusion survives its own number, because the row 09.38 needs, 09.24's, is the one row still absent. Mechanism. L-LEAN, M-3, D-4, FOUND-not-NAMED, P-11 (an [M] target cited as settled). Kill. A chess or market cell journalled before (i)–(v) are green is struck at assembly, its numbers unquotable. Price \(0\) GPU-s (a date comparison on the journal). If killed. The cell is re-run after the gate, with supersedes pointing at the struck cell (L-G2: journals never move). Terminal. "B5's bed-side half is closed by registration, not by measurement: the two beds exist as specifications with exact oracles and free first cells, and the sentence 'no arm has been trained' stands until a FOUND record exists."

What the book licenses with no capability number

This section is not a verse, and it was one until this repair round. 09.39 carried the Kill "None reachable: a leaf sentence that claims nothing measurable cannot be refuted by a number", and CHARTER.md §6 makes that grounds for deletion before birth: "a verse that no kill can reach is deleted before birth." Its content is a summary of the Terminals of 09.1–09.38 and carries nothing load-bearing that is not already in 09.19, 09.35 and 09.37, so it is demoted out of the verse grammar rather than deleted — the summary survives, the fields do not, and nothing here may be cited as a verse or as the ground of another verse's claim (L-VERSE).

With every kill above fired and every replacement dead, the canon licenses, per bed:

Chess — a pipeline whose labels are recomputed from the rules; a tree bed whose committor is an exact free solve; floors for six labels; controls with exact counts as three line items; a conditional VOID list whose ChaCAL entries are creditable only on MOVED seeds; a manifest that refuses a cell missing a declared field; BED-C-N registered with \(t^\star=2\), a \(3\)-layer skyline and a \(182{,}080\)-parameter skyline trunk; and the reading of "4D" as \(K\) absorbing rows and one dial \(\gamma\). Withdrawn on chess: every capability number, since the in-class bed's contrasts against softmax are VOID by containment and the natural-ground bed carries no capability number until both Lichess digests are pinned, which this book leaves unpinned by design (09.16).

Markets — the martingale theorem making the market-implied probability the unconstrained YES committor and the floor, under its exhaustion clause (09.23a), with its venue-side registration (09.23b); three leak guards that raise; a lattice bed with an exact committor and two planted departures, one in the transition block and one in the boundary value vector; BED-P-N registered as a bed with \(t^\star\), a skyline and two decidable kills (09.29b); the safest trade as the threshold form of a one-step filter, the Chebyshev column struck as dead by arithmetic; the interventional re-solve as algebra under a stated impact hypothesis, a cost statement on the in-class beds and a fidelity contrast only on natural ground; the equilibrium phase as a definition on the committor head; and the sentence "No edge over the market-implied probability is licensed; the module is registered as a calibrated reader, and the trader sentence requires a pinned venue, \(n\) resolved contracts with its realised sd, and an e-value crossing \(20\) — none of which exists at 99777ab."

What is withdrawn on both: every sentence carrying "more accurate", "faster to train", "beats", "edge", "wins", or a capability number on either use; every T1 number, since T1's target is a difference against a floor that is NOT MEASURED on both chess beds; and every price, since each is the byte-embedding floor of a cost law fitted without the feature projection (09.14).

A contradiction between this summary and another book's definition or number is not refuted here: it is the critic's fifth question (CHARTER.md §7) and its row goes to CORRECTIONS.md.

---

Census rows closed

row	what is broken	closing verse(s)
B27	the two uses have no bed, no pipeline, no label, no floor, no matched baseline; the chess witness is behind three UNPINNED Kaggle sources and was never run	chess: 09.1 (the break), 09.2 (local route and the three sources with substitutes), 09.3 (pipeline), 09.4–09.5 (state and bed), 09.6 (oracles), 09.7–09.8 (labels and floors), 09.9 (matched baselines, exact counts), 09.10 (census/gate), 09.19 (reroute, Terminal); markets: 09.20 (the break), 09.21–09.22 (state and absorbing sets), 09.23a (the floor as a theorem) and 09.23b (the floor registered on a venue), 09.24 (scores and counter), 09.25 (bed), 09.26 (safest trade), 09.27 (re-solve), 09.28 (guards), 09.29 (sources), 09.29b (BED-P-N registered as a bed), 09.30 (baselines), 09.31 (PnL as a scored prediction), 09.32 (census/gate), 09.35 (reroute, Terminal); both: 09.37 (Kaggle)
B5, bed-side half	no CEQ arm trained; no cell, no realised sd, no measured \(t^\star\)	09.38, with 09.11 and 09.33 (the protocol that produces the sd), 09.13 and 09.34 (the free first cells and the priced first GPU cells)
B22, bed-side half	ChaCAL's diagonal convention rests on one HTML fetch and decides two controls	09.12 (the convention as a manifest field with a row-sum plant on the bed's own draw; the arms named by convention if the PDF is ambiguous)

Kills, cheapest first

verse	kill number (frozen)	price	replacement verse or route
09.1 / 09.20	bed_c / bed_p absent from BED_SPECS, or two regenerations differ	\(0\) GPU-s, CPU seconds	single-RNG re-specification (09.1 If-killed); then the pin chess==1.11.2
09.17	any arm kind with \(0\) records cited in a sentence	\(0\)	the sentence names the arm NAMED with its route back
09.15	a one-unit flip of a declared field leaves manifest_hash unchanged	\(0\)	the field enters the hashed set; second failure strikes every cell
09.2 / 09.29	MissingPin must raise on an unpinned source; leaked_val>0 after dedupe	\(0\)	generator-only route (09.2 / 09.29 If-killed)
09.4	outcome class frequency outside \((0.05,0.95)\); sink share \(>0.95\) on \(>50\) per cent	\(0\)	endgame class; then the discounted leaf read at \(\gamma_{\rm env}\)
09.5 / 09.10	K-E2: any root sd of \(q\) \(=0\) (admission: \(\le0.05\)); class outside band; disagreement \(0\)	\(0\)	09.19: dial \((h,m,s)\), then endgames, then \(N\)
09.25	\(\lvert q-p_0\rvert>\theta_{\rm rej}=\mu_1T/(2G)=0.009\) on \(<0.5\) of the \(r=1\) draws at \((\mu_1,T,G)=(0.2,9,100)\), the realised \(r=1\) count printed	\(0\)	the leaf-miscalibration plant \(g(p)=p+\kappa p(1-p)\) on \(V\), threshold \(\kappa E[p_T(1-p_T)]/2=0.02491\) at \(\kappa=0.2\); then 09.35
09.32	any admission line failing (1, 2, 4, 5, 6, 7, 14); lines 3, 10, 12–13 printed, never counted	\(0\)	09.35: \(T=21\) at \(s=256\), then the threshold leaf rule, then \(N\)
09.8	zero-information floor above \(0.95\)	\(0\)	stratified draw selection; rejection \(\ge0.9\) strikes the argmin head
09.3 / 09.28	honest probe \(R^2\ge0.5\); planted probe \(<0.99\)	\(0\)	moves withheld from the context (chess); one-day embargo re-cut (markets)
09.18	one-step vs two-step disagreement \(>0.5\); Chebyshev sink-escape \(\ge0.5\)	\(0\)	conditioned Chebyshev with transient targets; then the committor vector alone
09.26	feasible set empty on \(\ge0.95\) of draws at \(\delta_{\rm thr}=0.1\) (the Chebyshev column is struck, not killed: its hold rate is \(1.00\) by arithmetic)	\(0\)	threshold at the census \(0.25\)-quantile; then committors only
09.23a	the \(G=100\), \(p_0=0.3\) gambler's-ruin instance fails to return \(0.3\) to \(10^{-12}\); the sink-mass-\(0.5\) plant must return \(0.15\)	\(0\)	none — the [V-eq] drops to [V], L-EQ makes it inadmissible, and 09.23b registers the floor empirically
09.23b	reliability outside Wilson \(95\) per cent in \(\ge3\) of \(10\) bins (\(n_{\rm bin}\ge50\))	\(0\) (given a snapshot)	isotonic-recalibrated market as the floor; then the market as-is with miscalibration printed
09.22	YES share outside \((0.05,0.95)\); void share \(>0.5\)	\(0\)	stratify by category; discard \(\ge0.9\) strikes the venue
09.21	\(m_{\rm eff}=1\) on \(100\) per cent; and the realised sd of \(\Pi_t\) or \(X_t\) at or below \(10^{-12}\) over \(512\) admitted draws (the hold-only plant must fire it, the full grid must not)	\(0\)	size grid as fractions of depth; a constraint set absorbing on a constant coordinate is struck from that bed's declaration
09.6	engine eval differs on any of 512 positions across two Threads=1 runs; the Threads=4 plant must fire	CPU minutes	node-limited search; then engine labels [ASSUMED] with the disagreement rate printed
09.12	ChaCAL-published transient row sums within \(10^{-6}\) of \(1\) at \(\gamma=0.9\)	\(0\) / one zero-step forward	the PDF read and the convention flipped; then arms named by convention
09.7	S-14: honest \(q\) query below the gate; L-legal / L-nextFEN plants must fire	\(\le1.524\) s	grandchild minimax committor; then the labels that survive are controls
09.9 / 09.30	matched counts differ by \(>0.1\) per cent after the head	\(0\)	widen the smaller head; then "unmatched by \(x\) per cent" beside the skylines
09.30	K-H2: logistic within the CP half-width, or McNemar \(p>0.05\) vs depth-1	\(\le1.524\) s per control	\(T=21\) at \(s=256\) (NOT MEASURED); then no market number
09.14 / 09.34	the pair outside \([-1.8,+14.4]\) per cent of \(1.680\) s per cell; the disabled-projection plant must read inside the band and the \(s=256\), \(F=1{,}107\) plant outside it	\(\approx34\) s, and NOT MEASURED as a price — the byte-embedding floor of a law fitted without the \(+14{,}640\) MACs-per-token projection	link 1, \(0\) extra GPU-s: the fired cell re-quoted as a measured point price, killed by an across-seed spread above the band's own \(16.2\) per cent width; link 2, more decisive and more expensive: the four-point refit at the chess feature width (book 03), which decides the exponent a single cell cannot; then points only
09.14	the thirteen-kind arena priced arm by arm at \(\ge172.960\) s against the struck \(\approx98\) s (\(1.76\times\)); a table whose priced-row count differs from 09.17's registered-kind count	\(0\) (arithmetic)	the per-arm column of 09.14, one row per kind, bed_c_nexttoken NOT MEASURED
09.27	K-G1 on the natural-ground beds only: cached mixture within one seed sd on \(P\)-changing plants on \(\ge6/8\); the \(i=0\) plant must fire on \(8/8\). On BED-C-T and BED-P-L there is no fidelity kill — the displacement is rank one at the query coordinate	NOT MEASURED — needs the BED-C-N / BED-P-N cost law; the in-class \(\approx35\) s is deleted	the displacement as algebra and a cost statement (Terminal)
09.16	K-D2: \(\lVert\hat P-P_{\rm env}\rVert_\infty<10^{-3}\) on \(\ge6/8\)	read off the arena	identification reading; the capability question moves to natural ground
09.11 / 09.33	K-P: realised sd \(\ge2.18\times0.050146\); run-order \(\lvert\rho\rvert>0.5\); unequal seed/contract sets. T1's target is the difference \(\varphi\text{-NRMSE}(q)-\varphi\text{-NRMSE}_{\rm floor}\le0.25\), and \"target below floor, T1 undefined on this bed\" is a third printed outcome	\(0\) extra GPU-s — the sd and run_index are columns of an arena already paid at \(\ge172.960\) s on chess and \(\ge90.592\) s on markets, neither of which is a price	link 1, \(0\) extra GPU-s: \(N_{\rm req}=\lceil8(\mathrm{MDE}^{\rm realised}_8/\mathrm{MDE}^{\rm pilot}_8)^2\rceil\), which reads \(38\) at the K-P firing point, and a band with no point wherever \(N_{\rm req}\) exceeds the budget — this is what shows \(N=16\) leaves \(\mathrm{MDE}_{16}\approx0.0894\), still \(1.54\times\) the pilot; link 2, only where \(N_{\rm req}\le16\): \(N=16\) (\(\approx68\) s per pair, the byte-embedding floor); then a band with no point
09.24	skill \(\le\mathrm{MDE}_n\); market Brier \(>0.25\) voids the cell	\(0\) given a trained arm	horizon moved over its support; then 09.31's Terminal
09.36	(a) the isocommittor set empty: \(q^{({\rm YES})}\in(0.4,0.6)\) on \(\le0.01\) of \(512\) draws; the \(p_0=0.99\) plant must fire. (b) the change-point detector blind at its frozen constants — CUSUM on standardised mid-price increments, \(k=\mu_1/2=0.10\) at \(\mu_1=0.2\), \(h=1.562\) at \(\mathrm{ARL}_0=T=9\) and \(h=3.047\) at \(\mathrm{ARL}_0=24\), and the \(+0.05\)-per-step plant firing on \(8\) or fewer of \(10\) series. The McNemar contrast is deleted — a scalar at one position is VOID by D-1 (09.16)	\(0\)	(a) \"decision point\" withdrawn; basin membership stands as the definition (Terminal). (b) the constants re-derived at the next horizon on the registered support (\(t^\star=60\)), then the detector retired from the book
09.31	e-value never crosses \(20\); paired PnL within \(\pm\mathrm{MDE}_n\); the look-ahead plant must cross within \(200\)	\(0\) given a trained arm and a pinned venue, neither of which exists	none: "No edge over the market-implied probability is licensed; the module is registered as a calibrated reader, and the trader sentence requires a pinned venue, \(n\) resolved contracts with its realised sd, and an e-value crossing \(20\) — none of which exists at 99777ab."
09.38	a cell journalled before the five gates are green	\(0\)	re-run after the gate with supersedes
09.37	a Kaggle-only number quoted as local	\(0\)	re-produced locally or NOT MEASURED
09.29b	the 09.28 leak probes both ways (honest incremental \(R^2\ge0.5\); planted \(<0.99\)); the 09.22 class-balance line (YES share outside \((0.05,0.95)\) or void share \(>0.5\)); the YES-only plant must read \(1.000\)	\(0\) given a snapshot; none is pinned	embargo re-cut; then stratify by category; then BED-P-N does not exist and Part II's A1/A2/PnL/phase sentences are withdrawn
09.19 / 09.35	— (leaves)	—	CORRECTIONS.md

Limits, collected once. Every price in this book is on the certified stack (torch 2.5.1+cu121, RTX 4060 Laptop) and this box runs torch 2.14.0+cpu with CUDA False (RUN this session), so no price here is measurable until book 05's environment pin lands. Every RUN number is a count, a version, a fixture timing or a parameter count; none is a statistic. No chess or market generator exists at 99777ab; every census line, label sd, \(t^\star\), realised sd and floor on realised data is NOT MEASURED and names its instrument. No engine binary and no tablebase is on this box; every engine label is absent until an engine_sha256 exists. No venue snapshot is pinned; every real-market number is NOT MEASURED. The impact constant \(\lambda\), the proper-scoring-rule citation and the price-impact citation are owed and absent from references.bib; the optional-stopping theorem number in durrett-2019-probability is [U]. The depth skylines are chosen by analogy with sanford-2024-logdepth Thm 4.2, whose task is not the committor. The FEN-feature representability at \(d_{\rm model}\ge\) the feature rank is unmeasured, as it is for BED-S. The chess fixture on which the only oracle timing exists has 36 synthetic games and has never seen a real Lichess PGN. T1 has no numeric target on any bed of this book: its target is a difference against 09.8's exact restricted-view floor transformed into \(\varphi\) units, and that floor is NOT MEASURED, so "target below floor, T1 undefined on this bed" is a live outcome and not a formality. No number in this book is a price: the \(1.680\) s and \(1.524\) s laws were fitted on a byte-embedding input, the chess feature projection adds \(14{,}640\) MACs per token against a block's \(3{,}072\) at the priced width (\(4.766\times\), and \(17{,}712\) at \(5.766\times\) at the \(s=256\) reroute geometry) and the market projection \(288\) (\(+9.375\) per cent at 09.21's augmented \(F=18\)), and the refit at either width is NOT MEASURED — needs book 03. Line pins into 08_ARCHITECTURE.md are not pins: that book is not at 99777ab and its lines moved from \(470\) to \(475\) between two grep -n runs in this session, so this book cites it by verse id with the quoted text and its three earlier line pins are struck. Four CORRECTIONS.md rows are owed and none can be written from here (CHARTER.md §3): 08.18's worked example 1 against 09.4's single definition of \(\mathcal A_0\) and \(\mathcal A_2\); 08.18's worked example 2 against 09.22's indexing convention, under which its numbering makes the safest-trade argmin minimise the probability of resolving NO; 04.7's Kill wording, so that BED-C-G's status as generator rather than natural ground is decidable from the wording alone; and 09.24's Brier-and-log skill against the market floor as a bet 06_PREDICTIONS.md must carry — RUN this session, book 06 files C-35 to C-39 for 09.10, 09.13, 09.32, 09.34 and 09.31 and files no row for 09.24, so 09.38's gate (iii) is satisfied on one of the two scored market predictions this book owns and open on the other. Three ids used in Mechanism fields are not MISTAKES.md ids and now say so at every site: MISTAKES.md carries \(71\) headings spanning V-1..V-26, P-1..P-11, M-1..M-21 and D-1..D-7 only (RUN grep -cE '^### ' MISTAKES.md → 71 this session), while C8 lives at docs/CEQ_SHAPE.md:1733 (equivalents D-1 plus V-10), C17 in V20_R15_JOURNAL.md @ 99777ab (equivalents M-8 plus M-3) and L-2 at docs/CEQ_SHAPE.md:2640 (equivalent P-1); each citation now carries its source and its map, and no Mechanism field points at a register that does not hold the id. No code file was written, no git write was made, no external fetch was made, and Kaggle was not contacted.

---

Attacks answered

MARS's refutation of this book, repair round 1, batch 1 of 3. Every finding is reproduced verbatim in its five filed fields — verse, flaw, mechanism, number, severity — beside the repair applied and the verse ids that carry it. Nothing is softened; a finding that reads more gently here than when filed is itself a defect. Where a finding names a repair this book already carried when the batch opened, the row says so and names the residue the batch found and closed; where a finding could not be repaired, the row reads OPEN with the Terminal sentence now in force.

A-1

Verse. 09.5 Flaw. The committor solve as written returns the all-ones vector, not the reach-avoid tensor: with the full transient-to-absorbing block \(R\), \((I-Q)^{-1}R\mathbb 1=\mathbb 1\) identically, because \((I-Q)^{-1}R\) is the row-stochastic absorption matrix. Mechanism. P-10, V-25, L-EQ Number. docs/CEQ_SHAPE.md:369-372 Proposition 3 gives \(q^{(k)}_i=[(I-Q)^{-1}R_k\mathbb 1]_i\) with the PER-CHANNEL block \(R_k\); summing over channels gives \(\sum_k R_k\mathbb 1=\mathbb 1-Q\mathbb 1\) and hence \((I-Q)^{-1}R\mathbb 1=\mathbb 1\) exactly. The book prints \(q=(I-Q)^{-1}R\mathbb 1\) (09.5 Statement, line 48). Replacement survives. false Required repair. Replace the Statement's formula with \(q^{(\bullet)}=(I-Q)^{-1}R_\bullet\mathbb 1\) per declared absorbing set, cite docs/CEQ_SHAPE.md:369-372 as [V-eq] with the numeric instance, and re-run the DERIVED MAC count against \(K+4\) right-hand sides rather than one. Every verse that reads L-q (09.7, 09.8, 09.10 line 5, 09.11, 09.13, 09.16) inherits the corrected object. Severity. strike Repair applied. 09.5 — carried when this batch opened, and verified against it: the Statement prints \(q^{(\bullet)}=(I-Q)^{-1}R_\bullet\mathbb 1\) per declared set, states that \(\sum_\bullet R_\bullet\mathbb 1=\mathbb 1-Q\mathbb 1\) so the full-block form returns \(\mathbb 1\) and is not a label, cites docs/CEQ_SHAPE.md:369-372 as [V-eq] with the \(h=2\), \(m=7\) numeric instance, and re-derives the cost against \(K+4=6\) right-hand sides (one factorisation at \(\le61{,}731\) MACs plus six back-substitutions at \(1{,}624.5\) each, \(\le71{,}478\) total, realised \(\le9{,}747\)). The dependent verses read the per-channel object: 09.7's L-q is the \([m,K+4]\) tensor, 09.10 line 5 is the per-coordinate sd of that tensor, 09.11, 09.13 and 09.16 score it. No residue found.

A-2

Verse. 09.10 (line 10), 09.32 (line 10), 09.27 Flaw. Census line 10 is unsatisfiable by construction on both in-class beds: the serialisation is leaves-first with the root LAST, and the intervened row IS the root, so there are zero coordinates after it and the variance is taken over the empty set. Mechanism. V-10, V-11, V-16 Number. 09.5 line 48: 'serialised leaves first, root last'; 09.25 line 234: 'time \(T\) first, the root \((0,p_0)\) last'. Source line docs/CEQ_SHAPE.md:2553 reads 'Var(Delta z) > 0 per coordinate over coordinates >= i_min' (inclusive of the intervened index); the book rewrote it to 'after the intervened row'. On a strictly lower-triangular \(Q\) with the root at index \(s-1\), \(\Delta z\) is supported on exactly one coordinate. Replacement survives. false Required repair. Restore the source's '\(\ge i_{\min}\)' wording so the intervened coordinate is inside the range, and add the printed statement that on a root-last serialisation \(\Delta z=\gamma(e_{u_a}-P[x_0,:])z\) is a single inner product, so the interventional channel on BED-C-T and BED-P-L is a cost statement (09.27's Terminal) and never a fidelity number. Severity. strike Repair applied. 09.10 line 10 — carried when this batch opened. 09.32 line 10 — repaired in this batch: it still read "\(\mathrm{Var}(\Delta z)>0\) after the root", the identical defect on the lattice, and now restores the source's "\(\ge i_{\min}\)" with the pin docs/CEQ_SHAPE.md:2553, prints the single-inner-product derivation \(\Delta z=\gamma(e_{u_a}-P[x_0,:])z\) at root index \(s-1\), and marks the line V-10, printed and never counted, with the interventional channel on BED-P-L a cost statement. 09.27's Terminal already states the cost sentence and is unchanged.

A-3

Verse. 09.10 Flaw. The Kill and the Statement's admission clause contradict each other; under the Kill's reading the bed dies by construction, under the Statement's it cannot. Mechanism. V-10, D-4, M-7 Number. 09.10 Statement: 'Admission requires lines 1, 2, 4 at 100 per cent, line 5 above 0.05, line 6 inside the band, line 7 above zero' (six lines). 09.10 Kill: 'Any line at its failing value on the 512 draws: the bed is not admitted' (fifteen lines). Lines 3 and 11 are declared V-10 in the same Statement and therefore always at a 'failing' value. Replacement survives. false Required repair. Restrict the Kill to the six admission lines named in the Statement, and print lines 3, 10, 11, 12-13, 15 as 'printed, never counted' exactly as the Statement already labels 3 and 11. Severity. strike Repair applied. 09.10 Kill — repaired in this batch. The Statement's six-line admission clause was carried when the batch opened, but the Kill still read "Any line at its failing value on the 512 draws"; it is now restricted to lines 1, 2, 4 and 1b at \(100\) per cent, line 5 above \(0.05\), line 6 inside the band and line 7 above zero, with line 14b as the seventh on BED-C-D only, and prints that lines 3, 10, 11, 12–13, 14a and 15 cannot fire it, with the V-10 reason and the struck wording named. 09.32's Kill carried the same defect and is repaired to match in this batch: admission lines 1, 2, 4, 5, 6, 7 and 14; lines 3, 10 and 12–13 printed, never counted.

A-4

Verse. 09.9 Flaw. The matched-control count is false for the arm described: 86,720 includes a 256-way output head and a 256-token input embedding, both of which the \([m,K+4]\) head and the \(F\times d\) feature projection replace. Mechanism. Ruling 3, P-1, V-17 Number. RUN this session, python -c "from ceq.lm import TinyLM; print([(n,p.numel()) for n,p in TinyLM('softmax',d=64,n_layers=1,n_heads=4,seq=64,seed=0,vocab=256).named_parameters()])" → tok 16,384 + pos 4,096 + block 49,728 + norm 128 + head 16,384 = 86,720. The count 'before the head and the projection' is \(86{,}720-16{,}384-16{,}384=53{,}952\). The depth-3 skyline is then \(53{,}952+2\times49{,}728=153{,}408\), not 186,176; depth-5 is 252,864, not 285,632. Replacement survives. false Required repair. Print 53,952 as the shared trunk, 153,408 and 252,864 as the skylines, and state the \(F\times d\) projection and the \([m,K+4]\) head as separate line items in every table header (09.9, 09.14, 09.30, 09.34), since Ruling 3 requires exact per-arm counts and the projection at \(F=923\), \(d=64\) is 59,072 parameters — larger than the trunk it is added to. Severity. strike Repair applied. 09.9 — carried when this batch opened and re-verified by RUN this session: TinyLM('softmax',d=64,n_layers=L,n_heads=4,seq=64,seed=0,vocab=256).n_params() at \(L=1,2,3,5\) → \(86{,}720\), \(136{,}448\), \(186{,}176\), \(285{,}632\), and the \(L=1\) per-parameter breakdown reproduces tok \(16{,}384\) + pos \(4{,}096\) + block \(49{,}728\) + norm \(128\) + head \(16{,}384\). Three residues repaired in this batch. 09.30 still printed "\(86{,}720\) before the head and projection" and the depth-5 skyline as "\(285{,}632\)"; it now prints trunk \(53{,}952\), projection \(16\times64=1{,}024\), head \([m,K+3]\) at \(64\times7\times5=2{,}240\) (DERIVED), total \(57{,}216\), and the depth-5 trunk \(252{,}864\), with \(86{,}720\) and \(285{,}632\) named as TinyLM's byte-vocabulary totals that are not this bed's rows. 09.14 carried a fourth and distinct arithmetic error that the finding's own \(F=923\) inherits: its \(F=832+1+4+9+64+m+K+4\) double-counts \(m\) and uses the label tensor's \(K+4\) where 09.3's token carries the \(K+2\) boundary flags; 09.14 now prints the one feature table's \(F(s,K)=849+s+K=915\) and the projection \(915\times64=58{,}560\), so the projection is larger than the trunk it is added to — \(58{,}560\) against \(53{,}952\), the finding's point, at the corrected width rather than at \(923\). 09.34 now carries the three line items in its header and the \(252{,}864\) trunk.

A-5

Verse. 09.9 Flaw. The per-block parameter law printed in the Hypotheses contradicts the book's own RUN difference by 256 parameters at \(d=64\). Mechanism. P-1, V-17 Number. Hypotheses state 'per block \(12d^2+13d\)' = \(12(4096)+13(64)=49{,}984\) at \(d=64\). RUN this session: \(L=2\) minus \(L=1\) = \(136{,}448-86{,}720=49{,}728=12d^2+9d\). Verified at four widths: \(d=16\) → 3,216; \(d=32\) → 12,576; \(d=64\) → 49,728; \(d=128\) → 197,760, all equal to \(12d^2+9d\). Replacement survives. false Required repair. Replace \(12d^2+13d\) by \(12d^2+9d\) in the Hypotheses and re-derive the depth ladder from it; the DERIVED line '\((186{,}176-86{,}720)/2=49{,}728\)' already carries the right number and must not be left contradicting the law above it. Fix the unbalanced parenthesis in the same line. Severity. strike Repair applied. 09.9 — carried when this batch opened: the Hypotheses read "per block \(12d^2+9d\)", the Evidence prints the four-width RUN with \(12d^2+13d\) named as \(256\) parameters too many at \(d=64\), and the DERIVED line reads \((186{,}176-86{,}720)/2=49{,}728\) with its parenthesis balanced. Re-verified by RUN this session (\(136{,}448-86{,}720=49{,}728\)). The depth ladder is re-derived from \(12d^2+9d\) in 09.9, and in this batch also in 09.30 (\(53{,}952+4\times49{,}728=252{,}864\)) and 09.34. No residue found in 09.9.

A-6

Verse. 09.25 Flaw. The rejection kill fires on 100 per cent of draws at the registered design point: the verse's own DERIVED expected displacement is below the frozen threshold, so the planted departure is invisible by arithmetic before any generator exists. Mechanism. V-24, V-11, M-2 Number. Statement: transitions \((t,p)\to(t+1,p\pm1/G)\) with probability \(\tfrac12(1\pm\mu)\), so \(E[\Delta p]=\mu/G\) per step and \(q^{({\rm YES})}(0,p_0)=E[p_T]=p_0+\mu_1T/G\) exactly. At \((\mu_1,T,G)=(0.2,9,100)\) the If-killed block itself prints \(0.018\). The Kill threshold is \(|q-p_0|>0.05\). \(0.018<0.05\) on every draw, so the fraction exceeding it is \(0/512\), not 'fewer than \(0.5\)'. Replacement survives. false Required repair. Freeze the threshold from the arithmetic, not against it: either set the rejection line at \(|q-p_0|>\mu_1T/(2G)\) (half the derived displacement) or register the design point at \((\mu_1,T)=(0.4,21)\) where \(0.084>0.05\). The first replacement link (\(T=21\), \(\mu_1=0.2\), \(0.042\)) must be deleted, since it also reads below \(0.05\) and dies with the verse (V-9). Severity. strike Repair applied. 09.25 — repaired in this batch. The \(0.05\) constant is struck from the verse. The rejection line is frozen from the arithmetic as \(\theta_{\rm rej}=\mu_1T/(2G)=0.009\) at the registered \((\mu_1,T,G)=(0.2,9,100)\), half the derived displacement; the Evidence prints the displacement derivation (\(E[\Delta p]=\mu/G\) per step, \(q^{({\rm YES})}(0,p_0)=p_0+\mu_1T/G=0.018\)) beside the sentence that a \(0.05\) line gives \(0/512\) and is a certainty rather than a decision, and names the previous registration struck. The Mechanism adds V-11, M-2 and M-9 for the threshold's reachability. The \(T=21\), \(\mu_1=0.2\) replacement link is deleted, with the V-9 reason printed: the threshold formula scales with \(T\) exactly as the displacement does (ratio \(2\) at every \(T\)), so the link died with the verse it replaced. The genuinely different replacement derived in its place is the leaf-miscalibration plant — the departure moves out of the transition block \(Q\) into the boundary value vector \(V\), the leaf resolving YES with \(g(p_T)=p_T+\kappa p_T(1-p_T)\) under a pure martingale transition (\(\mu\equiv0\)), with the three-step DERIVED displacement \(\kappa\,(p_0(1-p_0)-\mathrm{Var}(p_T))=\kappa\times0.2491=0.04982\) at \(\kappa=0.2\), \(p_0=0.5\), \(\mathrm{Var}(p_T)=T/G^2=0.0009\), and its kill frozen at \(0.02491\): a different number, a different instrument (the leaf map's second moment computed on \(V\)), a different object (the boundary value vector, not the transition block).

A-7

Verse. 09.25 Flaw. The kill's 'on at least \(0.5\) of draws' is bounded above by the informed-regime share, which the census admits anywhere in \((0.05,0.95)\); at any realised share below \(0.5\) the kill fires whatever \(\mu_1\) is. Mechanism. V-11, M-9, D-3 Number. 09.32 line 14 requires 'the regime share \(r=1\) in \((0.05,0.95)\)'. Under \(r=0\), \(q^{({\rm YES})}=p_0\) exactly (the verse's own martingale plant, \(|q-p_0|\le10^{-12}\)). So \(\Pr[|q-p_0|>0.05]\le\Pr[r=1]\), and at a realised share of, say, \(0.40\) the kill fires at \(0.40<0.50\) for every \(\mu_1\). Replacement survives. false Required repair. State the kill conditionally on the informed regime: '\(|q-p_0|>0.05\) on fewer than \(0.5\) of the \(r=1\) draws', with the realised \(r=1\) count printed beside it, or pin the regime share to \(0.5\) exactly in the generator and print it as a design constant. Severity. strike Repair applied. 09.25 — repaired in this batch by the first branch. The kill now reads "on fewer than \(0.5\) of the \(r=1\) draws among the \(512\), with the realised \(r=1\) count printed beside the fraction as an integer out of \(512\)", and the verse prints the finding's own bound: under \(r=0\) the martingale plant gives \(q=p_0\) to \(10^{-12}\), so an unconditioned fraction is bounded above by the realised \(r=1\) share, and at a realised \(0.40\) an unconditioned kill fires for every \(\mu_1\) — V-11 and D-3, not a measurement. 09.32 line 14 is amended in the same batch to print the realised \(r=1\) count as an integer out of \(512\), because 09.25's kill is conditioned on it.

A-8

Verse. 09.23 Flaw. The identity \(q^{({\rm YES})}=p_t\) is false whenever the sink or any constraint set carries mass, and both are admitted by neighbouring verses; the Hypotheses omit the exhaustion condition the identity needs. Mechanism. V-8, V-12, V-17 Number. 09.22's Kill admits a sink (void/delist) share up to \(0.5\) and prints the identity \(q^{({\rm sink})}+q^{({\rm YES})}+q^{({\rm NO})}+\sum_{k\ge1}q^{(k)}=1\). With \(q^{({\rm sink})}=0.5\) the committor \(P_x(\tau_{\rm YES}<\tau_{\rm NO})\le0.5\) while \(p_t\) ranges over \([0,1]\). 09.26 additionally makes drawdown, liquidity and exposure absorbing on the augmented state, removing further mass. Proposition 3 (docs/CEQ_SHAPE.md:373-374) states the sum identity only 'when the declared sets exhaust the absorbing states'. Replacement survives. false Required repair. Add to the Hypotheses: \(q^{({\rm sink})}=0\) and no constraint set absorbing, i.e. the identity holds only for the unconstrained two-set contract. State separately that on the augmented state of 09.26 the object scored against \(p_t\) is the UNCONSTRAINED YES committor, and re-word 09.24 and 09.33 so the model probability \(\hat q\) scored by Brier is that same unconstrained channel and not the \([m,K+3]\) tensor. Severity. strike Repair applied. 09.23a — repaired in this batch. The Statement carries the exhaustion clause inside the "if", the Hypotheses read "\(q^{({\rm sink})}=0\) and no constraint set absorbing — the declared sets exhaust the absorbing states, the exhaustion clause Proposition 3 requires (READ docs/CEQ_SHAPE.md:373-374)", and the Statement prints the finding's counterexample in arithmetic: at \(q^{({\rm sink})}=0.5\) the committor is at most \(0.5\) while \(p_t\) ranges over \([0,1]\), and 09.26's sets remove further mass on the augmented state. The object scored against \(p_t\) is named the unconstrained YES committor channel. 09.24 is re-worded so that \(\hat q_i\) is that channel and never a channel of the constrained \([m,K+3]\) tensor, with V-17 named; 09.33 is re-worded so the \([m,K+3]\) tensor is scored against the creditable arms only and every contrast against the market floor is scored on the unconstrained channel alone.

A-9

Verse. 09.23 Flaw. The Kill cannot refute the Statement; the verse says so itself. A theorem whose only registered kill tests a hypothesis it names is unfalsifiable as a verse. Mechanism. L-VERSE, M-2 Number. 09.23 Kill, verbatim: 'The hypothesis is tested, not the theorem'. CHARTER §2 requires 'the single decidable number or condition that refutes the statement'. Optional stopping for a bounded martingale with \(\tau<\infty\) a.s. is a theorem of durrett-2019-probability; no market datum can refute it. Replacement survives. true Required repair. Split the verse. Verse (a): the theorem, Evidence [V-eq] with the \(G=100\), \(p_0=0.3\) gambler's-ruin instance, Kill 'the numeric instance fails to reproduce \(0.3\) to solver precision', \(0\) GPU-s. Verse (b): the FLOOR REGISTRATION, whose Statement is 'on this venue at this horizon \(p_t\) is the floor', whose Kill is the existing \(3\)-of-\(10\) Wilson bin test, and whose If-killed is the isotonic route. Only (b) is load-bearing on a venue. Severity. strike Repair applied. 09.23 is split in this batch, exactly as filed. 09.23a carries the theorem with [V-eq] durrett-2019-probability and the \(G=100\), \(p_0=0.3\) gambler's-ruin instance; its Kill is that instance failing to return \(0.3\) to \(10^{-12}\), at \(0\) GPU-s, with a planted negative that fires on the unexhausted chain — the same solve with a sink of mass \(0.5\) must return \(0.15\). Its If-killed states that no replacement exists and carries the loss honestly: the [V-eq] drops to [V] naming-only, L-EQ makes that inadmissible for a load-bearing statement, and 09.23b must then register the floor empirically by its bin test alone, a strictly weaker floor named as such. 09.23b is the floor registration on a venue at a horizon, whose Kill is the \(3\)-of-\(10\) Wilson bin test with its drift plant and whose If-killed is the isotonic route. Every cross-reference is re-pointed in the same batch: the Preface, 09.25's instance, 09.30's floor and its isotonic control, 09.32 line 15, the census-rows table, and the kills table, which now carries a row for each half.

A-10

Verse. 09.26 Flaw. The Chebyshev rule is dead by the verse's own arithmetic before any draw, so its Kill is a certainty rather than a decision; a rule known false at registration must be registered struck, not as a candidate. Mechanism. V-10, V-2 Number. 09.26 Evidence, verbatim: 'for \(a=\text{hold}\), \(q^{(1)}=q^{(2)}=q^{(3)}=0\) exactly ... so the Chebyshev column is minimised by "hold" on every draw'. The Kill fires at '\(\ge0.95\) of 512 admitted draws'; the derived rate is \(1.00\). Replacement survives. true Required repair. Strike the Chebyshev column from the market rule set in the Statement, keep the goal rule and the threshold form, and move the 'hold dominates' derivation into the Mechanism as the reason the column is not registered. The census line 09.32(7) then prints the hold share of the THRESHOLD column, which is the only column that can vary. Severity. strike Repair applied. 09.26 — repaired in this batch. The Statement registers two rules, the goal rule and the threshold form, and prints the Chebyshev column as STRUCK from the market rule set — not registered as a candidate, not censused, not scored — noting that it stays registered on chess (09.5, 09.18), where "hold" is not a legal move and the derivation does not apply. The "hold dominates" derivation moves into the Mechanism as the reason the column is not registered, re-derived at the registered \(K\), together with the sentence that the previous kill at \(\ge0.95\) sat below a derived rate of \(1.00\) and was therefore a certainty. The Kill is now the threshold form's alone, with two planted negatives that must both fire (\(\delta_{\rm thr}=0\) empty on \(100\) per cent; \(\delta_{\rm thr}=1\) non-empty on \(100\) per cent). 09.32 line 7 is amended in the same batch to print the hold share of the threshold column, the only column that can vary.

A-11

Verse. 09.26 Flaw. Three constraint sets are registered but every registered market geometry sets \(K=2\) and every head is \([m,K+3]\), so the third set has no output channel and no floor. Mechanism. V-12, D-3, P-4 Number. 09.26 declares \(\mathcal A_1\) drawdown, \(\mathcal A_2\) liquidity, \(\mathcal A_3\) exposure. 09.30 head '\([m,K+3]\)' with '\(K+3=5\) outputs'; 09.32 geometry '\((T,G,K,m,s)=(9,100,2,7,64)\)'; 09.33 head '\([m,K+3]\)'. At \(K=2\) the channels are sink, YES, NO plus two constraints — \(\mathcal A_3\) is unreachable. Replacement survives. false Required repair. Either mark \(\mathcal A_3\) optional as 09.4 does for chess repetition and register \(K\in\{2,3\}\) with the head widening to \([m,K+3]\) accordingly, or delete exposure from the Statement. Whichever is chosen, the degeneracy sentence must be re-derived at the registered \(K\) (\(q^{(1)}=q^{(2)}=0\) for hold, not three). Severity. strike Repair applied. 09.26 — repaired in this batch by the first branch. \(\mathcal A_3\) exposure is marked optional and reachable only at \(K=3\), exactly as 09.4 marks repetition optional for chess; \(K\in\{2,3\}\) is registered as a dial with a support (D-3) and the head widens to \([m,K+3]\) accordingly — \([m,5]\) at \(K=2\), \([m,6]\) at \(K=3\). The Statement prints that at \(K=2\) exposure has no output channel and no floor, is not declared, not censused and named in no rule, and that any verse naming \(\mathcal A_3\) at \(K=2\) is refused at assembly. The degeneracy sentence is re-derived at the registered \(K\): \(q^{(1)}=q^{(2)}=0\) for hold, with \(q^{(3)}=0\) added only at \(K=3\).

A-12

Verse. 09.4 Flaw. The absorbing sets are asserted disjoint and are not; no priority rule breaks the overlap and no census line tests it, so the reach-avoid sum identity the verse derives can fail on a real draw. Mechanism. V-8, V-12, V-25 Number. \(\mathcal A_1\) = 'material balance \(\le-\theta\) pawn units' and \(\mathcal A_2\) = 'the opponent has a forced mate in \(\le k\)' are independent state predicates: a node down five pawns with a forced mate against is in both. \(\mathcal A_{\rm loss}\) (checkmate received) is contained in \(\mathcal A_2\) at \(k\ge1\) under the same reading. 09.10's fifteen census lines contain no disjointness check. Replacement survives. false Required repair. Add a total priority order to the Statement (\(\mathcal A_{\rm sink}\succ\mathcal A_0\succ\mathcal A_{\rm loss}\succ\mathcal A_{\rm draw}\succ\mathcal A_2\succ\mathcal A_1\succ\mathcal A_3\), first match wins) and add census line 1b: every node lands in at most one declared set on 100 per cent of draws, with the pre-priority overlap count printed. The same repair is owed to 09.26 for drawdown against exposure. Severity. strike Repair applied. 09.4 and 09.10 line 1b — carried when this batch opened: the Statement prints the total priority order \(\mathcal A_{\rm sink}\succ\mathcal A_0\succ\mathcal A_{\rm loss}\succ\mathcal A_{\rm draw}\succ\mathcal A_2\succ\mathcal A_1\succ\mathcal A_3\), first match wins, hashed into the manifest, with both overlaps the finding names printed as the reason; 09.10 carries census line 1b with the pre-priority overlap count beside it, and this batch's repair to 09.10's Kill (A-3) counts 1b among the admission lines. The half the finding owes to 09.26 was not carried, and is repaired in this batch: 09.26 now prints the overlap (\(\mathcal A_1\) against \(\mathcal A_3\), a position at \(-D_{\max}\) whose size exceeds \(E_{\max}\)) and the total priority order \(\mathcal A_{\rm sink}\succ\mathcal A_0\succ\mathcal A_2\succ\mathcal A_1\succ\mathcal A_3\), first match wins, hashed into the manifest, with the pre-priority overlap count printed beside 09.32's census.

A-13

Verse. 09.4 Flaw. The reach-avoid identity is DERIVED from Proposition 8 while the verse declares a further absorbing set outside the sum, so the identity is false wherever that set carries mass — which on the natural-ground bed is the majority of terminations. Mechanism. V-8, V-25, P-10 Number. Proposition 8 (docs/CEQ_SHAPE.md:497-499) and Proposition 3 (:373-374) give \(\sum_\bullet q^{(\bullet)}=\mathbb 1\) only 'when the declared sets exhaust the absorbing states'. 09.4 declares \(\mathcal A_{\rm res}\) (resignation, timeout, threefold and fifty-move CLAIMS) as a set 'whose share is printed and never merged' and omits it from the printed sum. On BED-C-D (a lichess monthly standard-rated dump) resignation and time forfeit are board-undecidable and terminate the majority of games; on BED-C-T \(\mathcal A_{\rm res}\) is unreachable (V-11) and the identity is vacuously safe. Replacement survives. false Required repair. Either include \(q^{({\rm res})}\) in the printed sum identity, or state in the Hypotheses that the identity holds on BED-C-T only, where \(\mathcal A_{\rm res}=\emptyset\) by construction, and add to 09.10 line 14 an admission threshold on the \(\mathcal A_{\rm res}\) share for any bed built from PGN Result headers. Severity. strike Repair applied. 09.4 and 09.10 line 14b — carried when this batch opened, by the second branch: the Hypotheses assert the sum identity on BED-C-T only, where \(\mathcal A_{\rm res}=\emptyset\) by construction, the Evidence prints that on BED-C-D the identity is false as printed and the sum is \(1-q^{({\rm res})}\), and 09.10 line 14b carries the admission threshold "\(\mathcal A_{\rm res}\) share \(\ge0.5\) refuses the bed" for any bed built from PGN Result headers. This batch's repair to 09.10's Kill (A-3) names line 14b explicitly as the seventh admission line on BED-C-D, which the struck "any line" wording left ambiguous. No other residue found.

A-14

Verse. 09.8 Flaw. The tight Fano values are quoted exactly at \(I=0\), the case the same sentence forbids and the case for which the source retires the weak Fano; both printed values sit below the chance floor printed two lines above them. Mechanism. V-10, V-17, L-FLOOR Number. 09.8 prints 'at \(m=7\), \(I=0\): \(0.699181\); at \(m=8\): \(0.7124\)' under the clause 'used only where \(I(X_{\le k};a^\star)>0\)'. The zero-information floors in the same verse are \(1-1/7=0.857143\) and \(0.875\). \(0.857143-0.699181=0.157962\) and \(0.875-0.7124=0.1626\) below chance. docs/CEQ_SHAPE.md:2495 retires the weak Fano precisely because it 'sits \(0.25/0.208/0.1875\) below chance'. Replacement survives. false Required repair. Delete the two \(I=0\) numerals and print the tight Fano as a formula only, with the sentence 'no value is quoted until the plug-in \(I(X_{\le k};a^\star)>0\) is computed on the admitted region and exceeds \(\ln m-\ln 2-\ln(m-1)\cdot(1-\max_a\hat\pi(a^\star))\), below which the chance floor is tighter and is the only floor printed'. Severity. strike Repair applied. 09.8 — carried when this batch opened: the tight Fano is printed as a formula only, the required sentence is present with its threshold \(\ln m-\ln2-\ln(m-1)\cdot(1-\max_a\hat\pi(a^\star))\), and the two numerals survive only inside the deletion record, which names them deleted, prints both differences below chance (\(0.157962\) and \(0.1626\)) and pins docs/CEQ_SHAPE.md:2495 as the precedent that retires a floor below chance. No Fano value at \(I=0\) is quoted as a floor anywhere in the verse. No residue found.

A-15

Verse. 09.8 Flaw. The Hankel ceiling is imported from a pure-delay kernel and applied to a reset counter, and the record's own contract states the same ceiling in a different form. Mechanism. V-17, P-10, L-EQ Number. READ ceq/beds/bed_k.py:58-61 (live): the BED-K delay kernel is \(K(i,j)=1\) iff \(j=i-d\) — a shift. The halfmove clock is a counter that RESETS on every capture and pawn move; no derivation is given that its Hankel has the same rank-1 residual. The 50-move rule spans 100 plies, not 50, so \(d=50\) is unjustified even as a shift. And READ CEQ_V20_R15_CONTRACT.md:117 @ 99777ab states 'BED-K(a) delay d=20 (Hankel ceiling 1/d for one state)' — \(1/50=0.02\), against docs/CEQ_SHAPE.md:1956's \(\sqrt{1-1/20}\), so the record carries two mutually inconsistent forms and the book picks one silently. Replacement survives. false Required repair. Mark L-halfmove NOT MEASURED — needs the Hankel singular-value instrument on the reset-counter kernel, print the two record forms side by side with the conflict named, and withhold any halfmove number until the residual is computed on the bed's own draw at the registered ply window. Severity. strike Repair applied. 09.8 — carried when this batch opened: L-halfmove reads "NOT MEASURED — needs the Hankel singular-value instrument run on the reset-counter kernel at the registered ply window", \(\sqrt{1-1/50}=0.989949\) is withdrawn, and the three reasons are printed together — the shift-versus-reset-counter mismatch pinned to ceq/beds/bed_k.py:58-61, the \(100\)-ply span against \(d=50\), and the two record forms side by side (\(0.02\) from CEQ_V20_R15_CONTRACT.md:117 @ 99777ab against \(0.989949\) from docs/CEQ_SHAPE.md:1956, a factor of \(49.5\)), with the conflict named rather than resolved by choice. No halfmove number survives in the verse. No residue found.

A-16

Verse. 09.7 Flaw. The planted positives are asserted from a mutual-information identity, which licenses no approximation guarantee for the stated model class; this is the record's own largest unclosed gap applied backwards. Mechanism. D-APPROX (CHARTER §5 B7), V-15, P-10 Number. 09.7 Evidence: 'DERIVED: legality and next-FEN are functions of the query token and one move token, so \(I(X_{\le0};y)=H(y)\)'. The Kill then freezes 'the 0-hop MLP of R-06 must read above \(0.99\) accuracy'. \(I=H(y)\) is an information identity; chess legality requires sliding-piece ray occlusion, pin detection and check evasion over an 832-dim plane encoding, and no bound is given that a per-position MLP attains \(0.99\). By the verse's own V-15 clause, a plant that does not fire makes every leak verdict inadmissible, so the whole S-14 gate is undecidable in the plausible case. Replacement survives. false Required repair. Demote the \(0.99\) threshold to NOT MEASURED — needs the 0-hop MLP fit on 512 BED-C-T draws, print the realised plant accuracy as the calibration of the detector rather than as a frozen pass mark, and add the fallback plant that IS derivable: a token carrying its own label verbatim (the R² \(\ge0.99\) construction 09.3 already uses), which fires by construction. Severity. strike Repair applied. 09.7 — carried when this batch opened: the Evidence states the identity is "only as an information identity", licensing no approximation guarantee for any model class, and names D-APPROX / B7 applied backwards with the ray-occlusion, pin and check-evasion argument printed; the \(0.99\) MLP threshold reads "NOT MEASURED — needs the 0-hop MLP fit on \(512\) BED-C-T draws" and is printed as the calibration of the detector, never as a frozen pass mark; the derivable fallback plant — a token carrying its own label verbatim, the \(R^2\ge0.99\) construction of 09.3, which fires by construction because the probe's input contains its target exactly — is registered and is what the leak verdict rests on. The Mechanism carries D-APPROX / B7 and V-15. No residue found.

What this batch changed, by verse. 09.10 (Kill restricted to the six admission lines, with the seventh on BED-C-D); 09.14 (the feature width corrected to \(F(s,K)=849+s+K=915\), the projection \(58{,}560\), the three line items); 09.23 split into 09.23a (the theorem, with the exhaustion hypothesis, an instance kill, a sink-mass plant, and no replacement) and 09.23b (the floor registered on a venue, with the bin-test kill and the isotonic route); 09.24 and 09.33 (the object scored against the market floor is the unconstrained YES committor channel); 09.25 (the rejection threshold frozen from the arithmetic at \(\theta_{\rm rej}=\mu_1T/(2G)=0.009\), conditioned on the \(r=1\) draws, the \(T=21\) link deleted, the leaf-miscalibration plant on \(V\) derived in its place at \(0.02491\)); 09.26 (the Chebyshev column struck, \(\mathcal A_3\) optional and reachable only at \(K=3\), the priority order added, one kill with two plants); 09.30 (trunk \(53{,}952\), projection \(1{,}024\), head \(2{,}240\), skyline trunk \(252{,}864\)); 09.32 (line 7 the threshold column, line 10 restored to \(\ge i_{\min}\) and marked V-10, line 14 the realised \(r=1\) count, the Kill restricted to the admission lines); 09.34 (the three line items and the \(252{,}864\) trunk); 09.35 (the reroute scoped to admission failures, with the rejection-kill reroute pointed at 09.25's new link); and the kills table, which gains a 09.23a row, splits 09.25 from 09.32, and re-states 09.26's single kill. Open findings: none in this batch — every finding filed above is repaired in the book, and no verse was deleted to escape one.

---

MARS's refutation of this book, repair round 1, batch 2 of 3. The same rule governs these rows: every finding verbatim in its five filed fields beside the repair applied, nothing softened, no verse deleted to escape a finding.

A-17

Verse. 09.11 Flaw. T1's target is an absolute \(\varphi\)-NRMSE value called a distance-to-floor, in different units from the floor the verse assigns, and the floor is NOT MEASURED — so the target may sit below it and be unreachable by any arm. Mechanism. M-2, V-17, L-FLOOR Number. 09.11: 'T1: GPU-seconds from initialisation to a frozen distance-to-floor, \(\varphi\)-NRMSE\((q)\le0.25\)'. CHARTER §1 defines T1 as time 'to a fixed distance-to-floor'. 09.8's floor for L-q is \(\mathbb E[\mathrm{Var}(q\mid X_{\le k})]\) in raw \(q\) units, and 09.13 records it NOT MEASURED. \(\varphi(p)=2\arcsin\sqrt p\) maps \([0,1]\to[0,\pi]\), so the two scales are not comparable and no subtraction is performed. Replacement survives. false Required repair. Restate T1 as 'GPU-seconds to \(\varphi\text{-NRMSE}(q)-\varphi\text{-NRMSE}_{\rm floor}\le0.25\)', require the restricted-view floor to be transformed into \(\varphi\) units on the same batch before the target is frozen, and print 'target below floor, T1 undefined on this bed' as an explicit outcome beside 'not reached at 150 steps'. Severity. strike Repair applied. 09.11 — repaired in this batch, exactly as filed. The absolute target is struck and named struck inside the verse. T1 now reads \(\varphi\text{-NRMSE}(q)-\varphi\text{-NRMSE}_{\rm floor}\le0.25\), the difference frozen at \(0.25\) (M-2), with 09.8's exact restricted-view floor \(\mathbb E[\mathrm{Var}(q\mid X_{\le k})]\) required to be transformed into \(\varphi\) units on the same \(512\)-draw batch and printed before the target is frozen, and the reason printed beside it (\(\varphi\) maps \([0,1]\) onto \([0,\pi]\), so no subtraction is licensed across the two scales). Three outcomes and no fourth are printed per arm: the GPU-seconds, "not reached at \(150\) steps", and "target below floor, T1 undefined on this bed". The Mechanism gains V-17 and L-FLOOR; the Hypotheses state that at 99777ab T1 has no frozen numeric target on either chess bed, because 09.13 records the floor NOT MEASURED. 09.33 is amended in the same batch to the same target, with the note that on BED-P-L alone the exact oracle floor is \(0.0\) and its \(\varphi\) transform is \(0\), so the difference coincides with the absolute reading there and nowhere else; the kills-table row for 09.11 / 09.33 carries the difference form and the third outcome; and Limits records that T1 has no numeric target anywhere in this book.

A-18

Verse. 09.11, 09.16 Flaw. A1 and A2 are moved to a bed that has no \(t^\star\), hence no depth skyline, hence no A2 as CHARTER §1 defines it, and whose cells the book's own manifest rule then refuses. Mechanism. R-SKY, Ruling 3, L-2 Number. \(t^\star\) appears in the book at exactly two places: 09.5 Hypotheses '\(t^\star=h\)' (BED-C-T) and 09.30 '\(t^\star=T=9\)' (BED-P-L). BED-C-N is named nine times and never carries a \(t^\star\) or a skyline depth. 09.11 states 'A1/A2 are scored on BED-C-N'; 09.16 states 'the capability question moves entirely to BED-C-N'. docs/CEQ_SHAPE.md:2650 makes t_star a required identity-manifest field, and 09.15 refuses any cell missing a declared field. Replacement survives. false Required repair. Register BED-C-N's \(t^\star\) explicitly — the number of plies between the query FEN and the deepest node the label's tree solve reads, i.e. \(t^\star=h\) carried over from the label's oracle — print \(\lfloor\log_2 h\rfloor+2\) as its skyline with the exact count, and state in 09.11 that A2 on BED-C-N is defined only once that number is in the header. Severity. strike Repair applied. 09.11 — repaired in this batch, exactly as filed. BED-C-N's \(t^\star\) is registered as the number of plies between the query FEN and the deepest node the label's tree solve reads, \(t^\star=h=2\) carried over from the label's oracle (09.5); the skyline is \(\lfloor\log_22\rfloor+2=3\) layers, printed with its exact count as three line items at \(d_{\rm model}=64\), \(s=512\): byte embedding \(16{,}384\) (not replaced on this bed), trunk \(32{,}768+49{,}728+128=82{,}624\), head \([m,K+4]=2{,}688\), total \(101{,}696\); skyline trunk \(82{,}624+2\times49{,}728=182{,}080\), total \(201{,}152\) — RUN this session, TinyLM('softmax',d=64,n_layers=L,n_heads=4,seq=512,seed=0,vocab=256).n_params() at \(L=1,3\) → \(115{,}392\), \(214{,}848\), and \(214{,}848-16{,}384-16{,}384=182{,}080\). 09.11 states that A2 on BED-C-N is defined only once that layer count and its exact parameter count stand in the header, and names the field rule that refused every such cell before this batch. The finding's manifest pin is corrected in the same batch: t_star is a declared identity-manifest field at READ docs/CEQ_SHAPE.md:1600 and :2652, not :2650 (RUN grep -n t_star docs/CEQ_SHAPE.md this session); the correction strengthens the finding rather than weakening it, since :1600 declares sky_depth in the same list. 09.16's BED-C-N clause carries the registered \(t^\star\) and skyline; 09.29b does the same for BED-P-N (A-19).

A-19

Verse. 09.33, 09.30, 09.21 Flaw. The only market bed that can carry a capability number exists nowhere as a verse: it is introduced inside a Hypotheses field and then carries A1, A2, PnL and the phase head. Mechanism. L-VERSE, P-4, P-7 Number. BED-P-N appears seven times in the book. Its sole registration is 09.21 Hypotheses: 'BED-P-N at \(s=512\) byte tokens or \(s=64\) feature tokens'. It has no Statement, no \(K\), no \(t^\star\), no skyline, no census geometry, no VOID list of its own, no generator and no Kill. 09.30, 09.31, 09.33 and 09.36 all score on it. CHARTER §2: nothing load-bearing outside a verse. Replacement survives. false Required repair. Add a verse 09.29b registering BED-P-N as a bed: token layout, \(s\), \(K\), \(t^\star\) and its skyline depth with the exact count, the label (the unconstrained YES committor at the registered horizon), the floor (\(p_t\)), the census it must pass (09.32 lines 1-2, 4-9, 15), its Kill (the 09.28 leak probes plus the 09.22 class-balance line) and its Terminal. Until it exists, delete every BED-P-N score from 09.30, 09.31, 09.33 and 09.36. Severity. strike Repair applied. 09.29b is written in this batch, with every field the finding names. Token layout: one token per \((\text{level},\text{side})\) of the top-\(\ell=10\) levels and one per path step over \(W\), through the shared projection at \(F=16\), \(s=64\) feature tokens as the counting layout and \(s=512\) bytes as a dial with no count. \(K\in\{2,3\}\), head \([m,K+3]\), \(m=7\). \(t^\star\) is the price-path steps between the decision time and resolution at the registered horizon: \(24\) at the one-day horizon and one-hour cadence, skyline \(\lfloor\log_224\rfloor+2=6\) layers, exact count trunk \(53{,}952+5\times49{,}728=302{,}592\), projection \(1{,}024\), head \(2{,}240\), total \(305{,}856\) — RUN this session, \(335{,}360\) at \(L=6\), \(s=64\), \(d=64\), and \(335{,}360-16{,}384-16{,}384=302{,}592\); the other two registered horizons give \(7\) and \(9\) layers at \(352{,}320\) and \(451{,}776\). Label: the unconstrained YES committor at the registered horizon (09.23a's object). Floor: \(p_t\) (09.23b), then isotonic, then the market as-is. Census: 09.32 lines 1–2, 4–9 and 15, with lines 1, 2 and 4 read on the token stream's declared boundary rows and not on an environment chain (there is none on natural ground), line 11 counted, line 14 inapplicable. Kill: the 09.28 leak probes both ways plus the 09.22 class-balance line, with a YES-only plant that must read \(1.000\). If-killed and Terminal both written. The scores are gated rather than merely deleted: 09.30, 09.31, 09.33 and 09.36 now cite 09.29b, each states that before that verse its BED-P-N counts stood on a bed with no Statement and were refused, and every BED-P-N number remains NOT MEASURED — needs the pinned snapshot — refused at assembly until 09.29b's census block is printed beside it. The finding's occurrence count is corrected upward: grep -c BED-P-N reads eight at the time of filing and nine after 09.21's field was re-pointed, not seven. 09.21's Hypotheses no longer registers the bed and says so.

A-20

Verse. 09.14 Flaw. The seven-arm arena price copies a figure from a source that prices two of the book's own arms separately, and the book registers thirteen arm kinds, not seven. Mechanism. M-8, P-8, P-1 Number. 09.14: 'The seven-arm arena at eight seeds: \(7\times8\times1.680+4.0\approx98\) s'. The source line docs/CEQ_SHAPE.md:1952 reads '\(7\times8\times1.680+4.0\approx98\) s \(\approx1.6\) GPU-min DERIVED, plus \(\approx64.8\) s for the skyline [ASSUMED] and \(\approx44.9\) s for InfSA-16 DERIVED, so \(\approx3.3\) GPU-min in total'. 09.9 lists InfSA-style Neumann at \(K=16\) among the chess fellow approximators, and docs/CEQ_SHAPE.md:2509 prices it at \(\approx5.1\) s per cell, not \(1.680\) s. 09.17 registers thirteen kinds. Replacement survives. false Required repair. Price the arena arm by arm at each arm's own law (M-8): eleven arms at \(\le1.680\) s, InfSA-16 at \(\approx5.1\) s, the skyline at \(1.524\) s per layer per seed, and print the total as the sum with the per-arm column visible. The registered kind count and the priced arm count must be the same integer. Severity. strike Repair applied. 09.14 — repaired in this batch. The \(\approx98\) s line and the \(\approx36.6\) s skyline line are struck and named struck, with the source's own full sentence quoted from READ docs/CEQ_SHAPE.md:1952 @ 207e7b9 so the reader sees the two arms it prices outside the figure. In their place stands a thirteen-row per-arm column for 09.17's thirteen registered kinds, each at its own law with its own class: shape \(1.680\) s; softmax-d1 \(1.524\) s; the depth-\(3\) skyline \(3\times1.524=4.572\) s per cell; the three ChaCAL arms \(1.680\) s each (READ docs/CEQ_SHAPE.md:2509); InfSA-16 \(\approx5.1\) s (READ :2509, DERIVED from the \(25.409\) ms hop microbenchmark); the \(0\)-hop MLP \(\le1.524\) s [ASSUMED] ceiling; the cached mixture \(1.680\) s; majority, random and predict-the-mean at \(0\); bed_c_nexttoken NOT MEASURED — needs the BED-C-N cost law at \(s=512\); plus \(4.0\) s fixed. Total \(172.960\) s over the twelve priced rows, printed as the sum, against the struck \(\approx98\) s — a \(1.76\times\) understatement, of which \(40.800\) s is InfSA-16 alone. Thirteen registered kinds, thirteen rows; the thirteenth carries NOT MEASURED with its instrument and is named as absent from the total, since inventing a number for it would be the defect this finding files. A kills-table row is added for the arena arithmetic, and 09.34's borrowed "\(\approx98\) s" is re-priced arm by arm in the same batch to \(90.592\) s over five market kinds.

A-21

Verse. 09.14 Flaw. The claim that the feature projection does not change the per-token law is refuted by the verse's own \(F\): the projection is roughly five times the transformer block's per-token cost at the registered width. Mechanism. M-8, P-8, M-3 Number. 09.14 states \(F=832+1+4+9+64+m+K+4\), which at \((m,K)=(7,2)\) is \(923\). At \(d_{\rm model}=16\) the projection costs \(923\times16=14{,}768\) MACs per token; the block's dense cost is \(12d^2=3{,}072\) MACs per token. Ratio \(4.81\times\). The \(1.680\) s and \(1.524\) s laws were fitted on BED-M/K, whose input is a byte embedding (a table lookup, \(0\) MACs). Replacement survives. false Required repair. Withdraw 'does not change the per-token law', re-label every chess and market price NOT MEASURED — needs the cost-law refit at the chess feature width (book 03), and keep the \(1.680/1.524\) s numbers only as the byte-embedding floor with the \(+14{,}768\) MACs-per-token increment printed beside them. Severity. strike Repair applied. 09.14 — repaired in this batch, exactly as filed. "does not change the per-token law" is withdrawn and quoted as withdrawn. Every chess and market price in this book is re-labelled NOT MEASURED — needs the cost-law refit at the chess feature width (book 03), and the \(1.680\) s and \(1.524\) s numbers are kept only as the byte-embedding floor, with the reason printed: both laws were fitted on BED-M/K, whose input is a table lookup at \(0\) MACs per token. The increment is printed beside them at the priced cell's own width \(d_{\rm model}=16\) — \(F(s,K)\times d_{\rm model}=915\times16=14{,}640\) MACs per token against the block's \(12d^2=3{,}072\), ratio \(\mathbf{4.766\times}\) — and the finding's own arithmetic at \(F=923\) (\(14{,}768\) MACs, \(4.81\times\)) is printed beside it, because 09.3's corrected width (\(F=849+s+K=915\), batch 1's A-4) changes the size of the increment and not its sign: the defect stands at either width and is not weakened by the correction. The market increment is printed too — \(16\times16=256\) MACs against \(3{,}072\), \(+8.33\) per cent — so the expected refit factors are named (\(\approx5.766\) on chess, \(\approx1.083\) on markets) and neither is assumed. 09.14's Terminal, 09.34's Terminal, the kills-table price column and Limits all now state that no number in this book is a price.

A-22

Verse. 09.16 Flaw. A contrast is registered creditable that a judged section of docs/CEQ_SHAPE.md rules VOID under the outcome the record's own counter predicts. Mechanism. D-2, M-7, R-SKY Number. 09.16 lists 'shape − ChaCAL-diag' as creditable with no condition. docs/CEQ_SHAPE.md:2375 (Tree B, the median outcome): 'S-31 and S-64 are then void, because ChaCAL at \(\hat\gamma=0\) is softmax.' CHARTER §5 B12 records the counter that \(\hat\gamma\) is predicted PINNED on at least 6 of 8 seeds, and under D-CALIB the counter is the point estimate. Replacement survives. false Required repair. Condition the entry: 'shape − ChaCAL-diag, creditable only on seeds where the LR verdict on \(\hat\gamma\) reads MOVED; VOID on PINNED seeds, where ChaCAL-diag is softmax'. Print the PINNED/MOVED seed split in the same row. Severity. strike Repair applied. 09.16 — repaired in this batch, and more severely than filed. The unconditional entry is struck and named struck. shape − ChaCAL-diag is creditable only on seeds whose Ruling-10′ likelihood-ratio verdict on \(\hat\gamma\) reads MOVED and is VOID on PINNED seeds, with the reason quoted verbatim from READ docs/CEQ_SHAPE.md:2375 @ 207e7b9. shape − ChaCAL-with-sink-token is conditioned identically, because the source line the finding cites voids S-31 and S-64 — the sink-token contrasts — and conditioning only the row the finding names would leave the same defect standing in the row beside it. The PINNED/MOVED split is printed as two integers out of \(8\) in the same row, with the point estimate under D-CALIB beside it: CHARTER.md §5 B12 predicts PINNED on at least \(6\) of \(8\), so the creditable half is at most \(2\) of \(8\), and a contrast standing on two seeds carries \(N=2\) and no \(\mathrm{MDE}_8\). The Mechanism gains D-CALIB and R-SKY.

A-23

Verse. 09.16 Flaw. A control registered creditable on the in-class bed cannot be run on it: the control is defined on the other bed's tokenisation. Mechanism. M-1, V-3, P-4 Number. 09.16 lists 'shape − next-token-trained control' among BED-C-T's creditable contrasts. 09.9 defines that control as 'the same depth-1 model trained on next-byte prediction over the PGN stream (BED-C-N)' — vocabulary 256 raw bytes at \(s=512\). BED-C-T's input is a \(923\)-dimensional feature projection at \(s=64\) (09.3, 09.14). The two arms share no input space. Replacement survives. false Required repair. Move 'shape − next-token-trained control' to BED-C-N's creditable list, where the tokenisations agree, and state the transfer route explicitly (freeze the byte-trained trunk, attach the \([m,K+4]\) head, linear probe only) with its own parameter count printed. Severity. strike Repair applied. 09.16 — repaired in this batch, exactly as filed. shape − next-token-trained control is removed from BED-C-T's creditable list and registered on BED-C-N and nowhere else, with the reason printed: the two arms share no input space on BED-C-T, whose input is the \(F(s,K)=915\)-dimensional projection at \(s=64\) while the control reads \(256\) raw bytes at \(s=512\). The transfer route is stated as the only one licensed — freeze the byte-trained trunk, attach the \([m,K+4]\) head, linear probe only — with its own count printed: \(99{,}008\) frozen (byte embedding \(16{,}384\) + positional \(32{,}768\) + one block \(49{,}728\) + final norm \(128\)) against \(2{,}688\) trainable, \(101{,}696\) in total, the byte output head's \(16{,}384\) replaced by the probe (DERIVED; RUN this session \(115{,}392\) at \(L=1\), \(s=512\), \(d=64\)), and the sentence that an unfrozen trunk is a second trained arm and not this control. The finding's \(923\) is the pre-batch-1 width; the corrected \(915\) is used, and the mismatch is unchanged by the correction, since \(s=64\) feature tokens and \(s=512\) bytes share no input space at any \(F\).

A-24

Verse. 09.36 Flaw. The phase head's label is a scalar at one position, which two other verses of this book declare VOID under D-1 on both registrations, yet this verse gives it a contrast that could license a positive sentence. Mechanism. D-1, V-10, R-SKY Number. 09.7 Statement, last sentence: 'Under D-1 no scalar at one position is a capability label on either registration.' 09.16, BED-C-N clause: 'every scalar-at-one-position contrast is VOID by D-1'. 09.36's Mechanism concedes the same ('the phase label at one horizon is a scalar at one position') and then registers a McNemar contrast against \(\mathbb 1[p_t>\tfrac12]\) and against a change-point detector. Replacement survives. true Required repair. Register the phase contrast VOID by D-1 in 09.16's market list, and restate 09.36 as a definition verse from the outset: basin membership is \(\mathbb 1[q>\tfrac12]\) of the committor head, no separate head, no separate number — which is exactly the verse's own If-killed. Delete the McNemar kill, which can only license a forbidden sentence. Severity. strike Repair applied. 09.16 and 09.36 — repaired in this batch, exactly as filed. 09.16 gains a Markets clause registering the equilibrium-phase contrast of 09.36 VOID by D-1 on both market registrations, naming 09.7's Statement as the rule it violates. 09.36 is rewritten as a definition verse from its title down: there is no phase head, basin membership is defined as \(\mathbb 1[q^{({\rm YES})}>\tfrac12]\) of the committor head, no separate head, no separate parameters (DERIVED: a threshold on an existing output allocates \(0\)), no separate number and no contrast. The McNemar kill is deleted, with the reason printed — the only sentence it could license is a forbidden one, and a kill that can license only a forbidden sentence is not a kill (V-2, V-10). The change-point detector stays as a descriptive fellow approximator whose agreement fraction is printed and never scored, with the zero-information floor and \(\mathbb 1[p_t>\tfrac12]\) printed as descriptions and not as baselines a number is claimed over. The verse keeps one reachable kill that is not a capability contrast: the isocommittor set empty — \(q^{({\rm YES})}\in(0.4,0.6)\) on at most \(0.01\) of \(512\) draws — which withdraws the phrase "decision point", with a \(p_0=0.99\) plant that must fire. The kills-table row is replaced accordingly.

A-25

Verse. 09.24, 09.31 Flaw. The Terminal states a measured negative on quantities the book records as never measured and on a venue the book records as never pinned. Mechanism. P-1, P-7, V-22 Number. Terminal (twice, and again in the kills table): 'No edge over the market-implied probability at \(n\) contracts and \(N\) seeds'. 09.29 Terminal: 'No venue is pinned; every real-market number in this book is NOT MEASURED; the only market bed that exists is the lattice.' 09.24 Evidence: 'Every number: NOT MEASURED — needs a pinned venue history (09.29).' \(n\) has no value anywhere in the book. Replacement survives. false Required repair. Rewrite the Terminal as a licensing sentence rather than a result: 'No edge over the market-implied probability is licensed; the module is registered as a calibrated reader, and the trader sentence requires a pinned venue, \(n\) resolved contracts with its realised sd, and an e-value crossing \(20\) — none of which exists at 99777ab.' The same edit is owed in the kills table row for 09.31. Severity. strike Repair applied. 09.24, 09.31 and the kills table — repaired in this batch, with the filed sentence verbatim. Both Terminals now read: "No edge over the market-implied probability is licensed; the module is registered as a calibrated reader, and the trader sentence requires a pinned venue, \(n\) resolved contracts with its realised sd, and an e-value crossing \(20\) — none of which exists at 99777ab." Each verse prints the struck sentence beside it and the reason it was struck (a measured negative against an Evidence field reading NOT MEASURED, on a venue 09.29's Terminal records never pinned, at an \(n\) with no value anywhere in this book — P-1, P-7, V-22). The kills-table row for 09.31 carries the new sentence and re-labels its price "given a trained arm and a pinned venue, neither of which exists". The demoted closing section (A-26) carries the same sentence, so the struck wording survives nowhere in the book except quoted as struck.

A-26

Verse. 09.39 Flaw. The verse declares that no kill can reach it, which CHARTER §6 makes grounds for deletion before birth. Mechanism. L-VERSE Number. 09.39 Kill, verbatim: 'None reachable: a leaf sentence that claims nothing measurable cannot be refuted by a number.' CHARTER §6, Length: 'a verse that no kill can reach is deleted before birth.' Replacement survives. true Required repair. Demote 09.39 from a verse to a closing section headed 'What the book licenses with no capability number', outside the verse grammar, since its content is a summary of Terminals and carries nothing load-bearing that is not already in 09.19, 09.35 and 09.37. Severity. strike Repair applied. Repaired in this batch, exactly as filed. 09.39 is demoted to the closing section ## What the book licenses with no capability number, outside the verse grammar: no Statement, no Hypotheses, no Kill, no If-killed, no Terminal. The section opens by quoting the struck Kill and CHARTER.md §6's sentence, states that its content duplicates 09.19, 09.35 and 09.37, and states that nothing in it may be cited as a verse or as the ground of another verse's claim (L-VERSE). The summary is kept and brought up to this batch — the conditional VOID list, BED-C-N's registered \(t^\star\) and skyline, BED-P-N's registration, the struck Chebyshev column, the interventional re-solve as a cost statement in class and a fidelity contrast only on natural ground, the phase as a definition, the licensing sentence of A-25, and the withdrawal of every T1 number and every price. The kills table's leaf row now reads 09.19 / 09.35 and no longer names a verse that does not exist.

A-27

Verse. 09.27 Flaw. The interventional re-solve is a no-op on both in-class beds: the intervened row is the last token, so nothing downstream of it exists and Proposition 7's extra solve degenerates to one inner product. Mechanism. V-10, D-5, M-8 Number. 09.5: the root is last in token order and \(\mathrm{do}(a)\) clamps \(P_{\rm env}[x_0,:]\). 09.27: 'On the lattice this is a row change at the root.' With \(Q\) strictly lower-triangular and \(x_0\) at index \(s-1\), \(\Delta z=\gamma(e_{u_a}-P[x_0,:])z\) is supported on a single coordinate; the \(s^2d/2\)-MAC solve computes \(s-1\) zeros. K-G1's cached-mixture control therefore has one scalar to reproduce and fires at \(\approx35\) s spent on a foregone conclusion. Replacement survives. true Required repair. State in the Statement that on BED-C-T and BED-P-L the displacement is a rank-one read at the query coordinate and is registered as a cost statement only (09.27's own Terminal), and move the fidelity contrast and K-G1 entirely to the natural-ground beds, where the intervened row precedes later tokens. Delete the \(\approx35\) s price for the in-class K-G1 cell. Severity. strike Repair applied. 09.27 — repaired in this batch, exactly as filed. The Statement now prints that on BED-C-T and BED-P-L the displacement is a rank-one read at the query coordinate — both beds serialise the query last, \(Q\) is strictly lower-triangular, the intervened row sits at index \(s-1\), \(\Delta z=\gamma(e_{u_a}-P[x_0,:])z\) is supported on exactly one coordinate, and the \(s^2d/2\)-MAC solve computes \(s-1\) structural zeros — and is registered as a cost statement only, never a fidelity number. K-G1 is moved entirely to the natural-ground beds (BED-C-N of 09.11, BED-P-N of 09.29b), where the intervened row sits at \(i<s-1\) and the re-solve has \(s-i-1\) non-zero coordinates, with a new planted negative there: an intervention at \(i=0\) on an \(s=512\) context must exceed one seed sd on \(8\) of \(8\) seeds, else the instrument is blind at every \(i\). The \(\approx35\) s in-class price is deleted, not re-quoted, in the Statement, in the Kill and in the kills table, and the natural-ground price reads NOT MEASURED — needs the BED-C-N / BED-P-N cost law. The verse states explicitly that on BED-C-T and BED-P-L there is no fidelity kill at all, and the Terminal and Mechanism carry the same.

A-28

Verse. 09.16, 09.11 (BED-C-N route) against book 04.7 Flaw. The book's only chess capability escape hatch lands on the bed that a neighbouring canon book kills outright until two digests are pinned, and this book leaves both unpinned by design. Mechanism. P-1, V-22, D-4 Number. 04_BEDS_AND_INSTRUMENTS.md:95 Kill: 'Any capability number on the witness before both Lichess sha256 digests are written into results/k_data_manifest.json — struck as P-1'. 09.29/09.2: no dump is pinned (RUN ls data/ this session → no .pgn, no lichess*); results/k_data_manifest.json:130 and :143 both read "sha256": null. 09.37: 'Nothing in this book launches, uploads or attaches on Kaggle.' Replacement survives. false Required repair. State in 09.16's If-killed that BED-C-N carries no capability number until BED-C-D is pinned by digest under Ruling 7, and that the local self-play generator BED-C-G is NOT a substitute for that purpose because 04.7's kill is written against the witness on natural ground. If the intent is that BED-C-G games are the natural ground, say so and file a correction against 04.7's kill wording in CORRECTIONS.md. Severity. strike Repair applied. 09.16's If-killed — repaired in this batch, by the first branch. It now states that the move to BED-C-N is gated, not free: BED-C-N carries no capability number until BED-C-D is pinned by digest under Ruling 7. 04.7's Kill is quoted verbatim from 04_BEDS_AND_INSTRUMENTS.md; both digests are shown "sha256": null (READ results/k_data_manifest.json:130 and :143, RUN this session), ls data/ shows no .pgn and no lichess* file, and 09.37's sentence is cited — so the verse states that this book leaves both unpinned by design and the escape hatch is closed by a neighbouring book's kill, rather than routing round it. BED-C-G is stated NOT to be a substitute, because 04.7's kill is written against the witness on natural ground and self-play under \(\pi_u\) is a generator (09.2); this book claims no exemption. The wording question — whether 04.7's Kill should name "on natural ground" explicitly, so that BED-C-G's status is decidable from the wording alone — is recorded as owed as a CORRECTIONS.md row naming 04.7's Kill, which this book's writer may not write (CHARTER.md §3), and is listed in Limits with the other two owed rows. 09.11's Hypotheses and 09.16's Terminal both carry the gate, so the sentence "at 99777ab the chess capability question has no live bed at all" now stands in the book. The finding's line pin is corrected: 04.7's Kill is not at 04_BEDS_AND_INSTRUMENTS.md:95 (which is 04.6's \(q\) formula, RUN sed -n 95p this session) but inside verse 04.7; the quoted text is unchanged and the finding stands.

A-29

Verse. 09.4 against 08_ARCHITECTURE.md Flaw. The two books place the same chess predicate in opposite sets: mate-in-\(k\) is the goal in book 08 and a constraint in book 09. Mechanism. V-12, V-8 Number. 08_ARCHITECTURE.md:395: '\(\mathcal A_0\) = positions whose evaluation-sign or mate-in-\(k\) flag marks the side-to-move's winning class, \(\mathcal A_1\) = material-loss positions, \(\mathcal A_2\) = mate-against positions'. 09.4: '\(\mathcal A_0\) the goal, the side-to-move's win set (checkmate delivered) ... \(\mathcal A_2\) mate threat (the opponent has a forced mate in \(\le k\))'. Book 08 additionally admits an ENGINE evaluation sign into the goal set; 09.6 records which stockfish → none on this box and refuses every engine label without an engine_sha256. Replacement survives. false Required repair. One definition, in 09.4, cited by 08 rather than restated: \(\mathcal A_0\) = checkmate delivered (a board fact, python-chess), \(\mathcal A_2\) = mate-against within \(k\) (engine or exhaustive tree search, engine hash required). File the divergence as a CORRECTIONS.md row naming 08's worked example 1. Severity. strike Repair applied. 09.4 — the single definition was carried when this batch opened and is verified against the finding: \(\mathcal A_0\) is "checkmate delivered by the side to move — a board fact decided by python-chess, and nothing else"; \(\mathcal A_2\) is "mate threat — the opponent has a forced mate in \(\le k\) from that node, decided by the engine of 09.6 (an engine_sha256 is required) or, on BED-C-T at \(h\le3\), by exhaustive search inside the tree"; the verse states that book 08 cites this definition rather than restating it, prints that book 08's reading admits an engine evaluation into the goal and therefore leaves the goal set undefined on a box with no engine (RUN which stockfish → none), and records the divergence as owed as a CORRECTIONS.md row naming 08.18's worked example 1. One residue is repaired in this batch: the pin. The finding cites 08_ARCHITECTURE.md:395 and the book cited :404; both are wrong, and a line pin into that file is unstable in principle — 08_ARCHITECTURE.md is not at 99777ab and its worked examples moved from line \(470\) to line \(475\) between two grep -n runs in this session, so a line pin into a book under concurrent repair is not a pin (CHARTER.md §3). All four of this book's line pins into 08 (:394, :396, :404, :470) are struck and replaced by verse ids with the quoted text beside them — 08.1's set masks row, 08.18's moves row, 08.18's worked examples 1 and 2 — and the reason is printed in 09.4 and listed in Limits.

A-30

Verse. 09.5 against 08_ARCHITECTURE.md Flaw. The two books give \(\mathrm{do}(a)\) different ranks and different prices for the same chess move. Mechanism. M-8, P-8, D-5 Number. 08_ARCHITECTURE.md:395: 'a move is ("rewrite", s-1, next-FEN tokens) — rank \(s-i\), priced as a suffix re-solve'. 09.5: '\(\mathrm{do}(a)\) is the row clamp \(P_{\rm env}[x_0,:]\leftarrow e_{u_a}\), rank one, \(u^\top\mathbb 1=0\)'. 09.27 prices the clamp at \(s^2/2\) MACs per candidate; a suffix re-solve at \(x_0=s-1\) costs \(O(1)\) rows but at any earlier \(i\) costs \((s-i)^2d/2\). Replacement survives. false Required repair. State both objects and when each applies: on BED-C-T the root is the last token and the clamp is rank one at \(O(s)\); on BED-C-N the move rewrites a suffix of the byte context and is a suffix re-solve of rank \(s-i\). Print both prices in 09.14 and reconcile 08's worked example to name the bed it is describing. Severity. strike Repair applied. 09.5 — the two-object statement was carried when this batch opened: the clamp on BED-C-T (root last, rank one, \(O(s)\)) and the suffix re-solve on BED-C-N (rank \(s-i\), \((s-i)^2d/2\) MACs), with the divergence recorded as owed. The half the finding owes to 09.14 was not carried and is repaired in this batch: 09.14 now prints both prices — on BED-C-T \(O(s)=64\) MACs per candidate and \(448\) MACs for all \(m=7\) candidates at \(s=64\); on BED-C-N \(d_{\rm model}/2=32\) MACs at the worked example's own \(i=s-1\) and \(s^2d/2=512^2\times64/2=8{,}388{,}608\) MACs at \(i=0\), a range of \(2.62\times10^5\) across the one index the worked example leaves unnamed — with the rule that no verse may quote either price without naming its bed. Reconciling 08's worked example is not in this book's power; it is owed as a CORRECTIONS.md row (CHARTER.md §3), listed in Limits with the other owed rows, and the pin correction of A-29 applies to this finding's :395 as well.

A-31

Verse. 09.22, 09.26 against 08_ARCHITECTURE.md Flaw. The two books index the market absorbing sets incompatibly, and under book 08's indexing the safest-trade argmin minimises the probability that the contract resolves NO. Mechanism. V-12, V-17 Number. 08_ARCHITECTURE.md:395: '\(\mathcal A_0\) = resolves YES, \(\mathcal A_1\) = resolves NO, \(\mathcal A_2\) = drawdown breach, \(\mathcal A_3\) = liquidity breach'. 09.22/09.26: YES and NO are named \(\mathcal A_{\rm YES}\), \(\mathcal A_{\rm NO}\) and left unnumbered; \(\mathcal A_1\) = drawdown, \(\mathcal A_2\) = liquidity, \(\mathcal A_3\) = exposure. The rule \(a^\dagger=\arg\min_a\max_{k\ge1}q^{(k)}\) sweeps \(k\ge1\), so under 08's indexing it includes \(q^{({\rm NO})}\); book 08 has no exposure set at all. Replacement survives. false Required repair. Fix the indexing once in 09.22: the outcome sets carry names, never \(k\) indices, and \(k\ge1\) ranges over constraint sets only. Restate 08's worked example 2 to the same convention and file the divergence in CORRECTIONS.md, since the argmin rule is load-bearing in both books. Severity. strike Repair applied. 09.22 — repaired in this batch, exactly as filed. The indexing convention is fixed once, for the whole market part, in 09.22's Statement: outcome sets carry names and never \(k\) indices (\(\mathcal A_{\rm YES}\), \(\mathcal A_{\rm NO}\), \(\mathcal A_{\rm sink}\), and \(\mathcal A_{{\rm bucket}\,b}\) for multi-outcome contracts — the previous registration wrote those buckets \(\mathcal A_1,\dots,\mathcal A_B\), colliding with the constraint indices, and is struck), and the numbered sets are constraint sets only, so every sweep written \(k\ge1\) in this book ranges over constraints and over nothing else. 08.18's worked example 2 is quoted verbatim and the consequence is printed rather than paraphrased: under that indexing \(a^\dagger=\arg\min_a\max_{k\ge1}q^{(k)}(a)\) minimises the probability that the contract resolves NO, because the sweep swallows \(q^{({\rm NO})}\) at \(k=1\). 09.26's Statement now opens by inheriting the convention and states that \(k\ge1\) there sweeps constraints and never \(\mathcal A_{\rm NO}\). Restating 08's worked example 2 is not in this book's power; the divergence is owed as a CORRECTIONS.md row naming 08.18's worked example 2, recorded in 09.22 and listed in Limits, with A-29's pin correction applied to this finding's :395.

A-32

Verse. 09.10 (line 5), 09.13 Flaw. The admission threshold on the label sd is a new constant with no evidence class, raised from the source's condition, and it is computed over a region that the same line defines. Mechanism. P-1, M-2, V-10 Number. docs/CEQ_SHAPE.md:2547 (A.7 line 5) requires the per-coordinate label sd 'each \(> 0\)'. 09.10 line 5 requires 'each \(>0.05\)' and 09.13's Kill fires 'at or below \(0.05\)'. No DERIVED, RUN, CITED or ASSUMED class is attached to \(0.05\) anywhere in the book. The sd is taken 'over the admitted region', and admission is decided by that sd. Replacement survives. true Required repair. Give \(0.05\) a class: either [ASSUMED] with the reason (below this the MDE at \(N=8\) exceeds the label's range) or DERIVED from \(\mathrm{MDE}_8=1.156\times\mathrm{sd}\), and define the admitted region independently of the census — the prefix at or after the first declared boundary set, as docs/CEQ_SHAPE.md:2547 defines it — so the line is not circular. Severity. repair Repair applied. 09.10 line 5 — carried when this batch opened, by the DERIVED branch: the threshold reads "the threshold carries its class, DERIVED from \(\mathrm{MDE}_8=1.156\times\mathrm{sd}\)" with the noncentral-\(t\) bisection printed (\(0.034451\to0.039827\), ratio \(1.15606\); \(0.050146\to0.057971\), ratio \(1.15604\)) and the reason that at \(\mathrm{sd}=0.05\) the minimum detectable effect is \(0.0578\), larger than the \([0,1]\) label's own sd, so below \(0.05\) no contrast at \(N=8\) is falsifiable; the admitted region is defined independently of the census as "the prefix at or after the first declared boundary set", pinned to READ docs/CEQ_SHAPE.md:2547, with the source's own "each \(>0\)" printed and this book's raise printed beside it. 09.13's residue is repaired in this batch: its Kill cited 09.10 line 5 and carried the bare constant, and now restates the DERIVED class, the bisection numbers, the \(\mathrm{MDE}_8=0.0578\) consequence and the independent definition of the admitted region with the same pin, so the constant carries its class at both sites and neither imports it from the other.

What this batch changed, by verse. 09.4 (the four line pins into 08_ARCHITECTURE.md struck and replaced by verse ids, with the instability shown by two grep -n runs); 09.11 (T1 restated as a difference in \(\varphi\) units with the transformed floor and the third printed outcome; BED-C-N's \(t^\star=2\), skyline depth \(3\) and exact counts \(101{,}696\) / \(182{,}080\) / \(201{,}152\) registered; Hypotheses and Mechanism re-stated); 09.13 (the \(0.05\) threshold's DERIVED class and the independent admitted region restated at the second site); 09.14 (the thirteen-kind per-arm price column totalling \(172.960\) s, the struck \(\approx98\) s named, "does not change the per-token law" withdrawn, every price re-labelled the byte-embedding floor with the \(14{,}640\) and \(256\) MACs-per-token increments, both \(\mathrm{do}(a)\) prices printed); 09.16 (ChaCAL-diag and ChaCAL-with-sink conditioned on the MOVED verdict with the PINNED/MOVED split printed; the next-token control moved to BED-C-N with its frozen and trainable counts; the market clause registering the phase contrast VOID by D-1; the If-killed gated on BED-C-D's digests against 04.7's Kill; the Terminal); 09.21 (its Hypotheses no longer registers BED-P-N); 09.22 (the indexing convention fixed once, the bucket collision struck, 08.18's worked example 2 quoted with its consequence); 09.24 and 09.31 (the Terminal rewritten as a licensing sentence, the struck wording printed); 09.26 (the convention inherited in its opening clause); 09.27 (the in-class displacement stated rank one, K-G1 moved to natural ground with a new plant, the \(\approx35\) s deleted); 09.29b written (BED-P-N registered as a bed with layout, \(s\), \(K\), \(t^\star=24\), a \(6\)-layer skyline at trunk \(302{,}592\), the label, the floor, the census, two kills, an If-killed and a Terminal); 09.30, 09.31, 09.33 and 09.36 (BED-P-N scores gated on 09.29b); 09.33 (T1's difference form, A2 gated on 09.29b's header fields); 09.34 (the market arena priced arm by arm at \(90.592\) s over five kinds, the borrowed \(\approx98\) s struck, the byte-embedding-floor label); 09.36 rewritten as a definition verse with the McNemar kill deleted and an isocommittor-emptiness kill in its place; 09.39 demoted to the closing section ## What the book licenses with no capability number; the census-rows table (09.29b added); the kills table (rows for 09.29b and the arena arithmetic added; rows for 09.11 / 09.33, 09.14 / 09.34, 09.27, 09.31 and 09.36 restated; the leaf row no longer naming 09.39); and Limits (T1 without a target, no number a price, unstable pins into 08, three owed CORRECTIONS.md rows). Open findings: none in this batch — every finding filed above is repaired in the book, and no verse was deleted to escape one.

---

MARS's refutation of this book, repair round 1, batch 3 of 3. The same rule governs these rows: every finding verbatim in its five filed fields beside the repair applied, nothing softened, no verse deleted to escape a finding. Where a finding's own number does not reproduce on the tree this session, the reproduction is printed beside it and the finding's conclusion is carried or refused on that reproduction, never quietly dropped.

A-33

Verse. 09.10 (line 11), 09.10 (line 14), 09.10 (line 15) Flaw. Three census lines silently drop or restate requirements the source makes mandatory, including two 100-per-cent checks on the intervention. Mechanism. L-DOM, V-25, M-7 Number. docs/CEQ_SHAPE.md:2554 (A.7 line 11) requires 'fraction with \(u^\top\mathbb 1=0\) and a non-negative edited row (100 % required)' and the printed Sherman-Morrison denominator check; 09.10 line 11 replaces the whole line with '\(m_{\rm eff}=m\) ... printed, V-10'. A.7 line 14 requires the exact-zero-gate segmentation count; 09.10 line 14 replaces it with terminal density and the \(\mathcal A_{\rm res}\) share. A.7 line 15's vacuity inequalities are computed at \((s,d,p)=(64,16,32)\); 09.10 line 15 says 'unchanged' while 09.5 registers \(d_{\rm model}\in\{16,64\}\). Replacement survives. true Required repair. Restore the \(u^\top\mathbb 1=0\) and non-negative-edited-row 100-per-cent requirement and the Sherman-Morrison positivity print to line 11, keeping \(m_{\rm eff}\) as an addition; keep A.7's line 14 as line 14a and the terminal-density/\(\mathcal A_{\rm res}\) block as 14b; and recompute the three vacuity inequalities at \((s,d)=(64,64)\) and print both geometries. Severity. repair Repair applied. Lines 14a/14b and line 15 were carried when this batch opened and are re-verified here: 14a keeps A.7's exact-zero-gate segmentation count with the F0 theorems declared silent where the count is \(0\) of \(N\) (pin docs/CEQ_SHAPE.md:2558), 14b carries the terminal density, the \(\mathcal A_{\rm res}\) share and BED-C-D's \(\ge0.5\) refusal threshold, and line 15 prints all three inequalities at both registered geometries — at \((64,16,32)\): \(4\times4\times32=512\ge64\), \(384<1\times17\times32=544\), \(64^{1/16}=1.2968\); at \((64,64,32)\): \(4\times16\times32=2{,}048\ge64\), \(384<1\times65\times32=2{,}080\), \(64^{1/16}=1.2968\) (independent of \(d\)) — all vacuous at both and more so at \(d=64\) (DERIVED, arithmetic re-checked this session). Line 11's residue is repaired in this batch, and it is the half the carried text left standing: the line printed "\(100\) per cent required" while the Statement and the Kill both exempted line 11 wholesale from counting with a reason — "11's \(m_{\rm eff}\)" — that covered only this book's addition and not the source's two checks, so a mandatory requirement stood beside its own unexplained exemption. Line 11 is now split into 11a (the source's three: the change-\(P\)-versus-change-\(V\) fraction, the \(u^\top\mathbb 1=0\) and non-negative-edited-row \(100\)-per-cent requirement restored verbatim, and the Sherman–Morrison positivity print) and 11b (this book's addition, \(m_{\rm eff}=m\)), with a three-line DERIVED block showing why each of 11a reads its passing value on \(100\) per cent of BED-C-T draws: \(u=e_{u_a}-P_{\rm env}[x_0,:]\) is a difference of two row-stochastic rows so \(u^\top\mathbb 1=0\) exactly; the edited row is the basis vector \(e_{u_a}\) so non-negativity is a property of the write; and children precede the root in token order so a self-clamp — the one write that sends the denominator to \((1-\gamma\cdot1)/1=0\) at the bed's own \(\gamma=1\) — is structurally unwritable, leaving \(p'_{ii}=P_{ii}=0\) and the denominator at \(1\). 11a is therefore V-10 on this bed, printed and never counted, with the source's \(100\) per cent stated live and unchanged on any bed whose intervention is not a basis-vector clamp; the two clamp plants that would move it (\(P[x_0,:]\leftarrow2e_{u_a}\); a clamp targeting \(x_0\)) are registered so the print is diagnostic. The Statement's and the Kill's exemption lists now read "3, 10, 11a, 11b, 12–13, 14a and 15" with the reason given per line, and the Kill prints that 11a's exemption is not an exemption from its requirement.

A-34

Verse. 09.3, 09.2 Flaw. Three live READ pins point at the wrong functions. Mechanism. P-1, L-2 Number. RUN grep -n '^def ' ceq/kdata.py this session: split_by_game is at :225, not the cited :192-215 (which spans tokenizer_fingerprint:182 and iter_games:206); the Site-header key is set in iter_games:220, not in split_by_game, whose docstring says only 'by the hash of the key'. label_plies is at :258-287, not the cited :245-275 (which starts inside check_game_split:241). verify_file is at :157-158, not the cited :118-131 (which spans HashedLineReader.hexdigest:123 and _pin:127). Replacement survives. true Required repair. Repin: READ ceq/kdata.py:206-223 for the Site key, :225-239 for split_by_game, :258-268 for label_plies, :127-142 for the MissingPin guard and :157-158 for verify_file. Note in 09.2 that verify_file hashes the whole file before _pin raises, so the guard costs one full read of a 1.56 GB dump. Severity. repair Repair applied. Carried when this batch opened, and re-verified against the tree this session rather than accepted: RUN grep -n '^def \|^class ' ceq/kdata.py → _pin:127, verify_digest:144, verify_file:157, tokenizer_fingerprint:182, iter_games:206, split_by_game:225, check_game_split:241, label_plies:258. RUN sed -n '157,159p;218,222p;225,232p' ceq/kdata.py this session confirms each pin at its claimed content: :157-158 is def verify_file and its one-line body return verify_digest(name, sha256_file(path), manifest); the Site-header key is yielded at :221, inside the cited :206-223; and split_by_game's docstring at :226-231 reads "Assignment is by the hash of the key, not by position". 09.3 carries all five repins and 09.2 carries the two guard pins with the DERIVED consequence the finding names — verify_file calls sha256_file before _pin raises, so the unpinned-source guard costs one full read of the file it refuses, \(1.56\) GB on the arevel/chess-games dump. No residue found; every kdata.py pin in the book is now one of :16-30, :40-43, :127-142, :157-158, :206-223, :225-239, :258-268, and each was read this session.

A-35

Verse. 09.3, 09.13 Flaw. The one wall-clock RUN number the chess pipeline carries does not reproduce at the precision it is quoted to. Mechanism. M-3, P-1, C17 Number. 09.3 and 09.13 cite '512 labelled plies from the 36-game fixture in \(0.128\) s on CPU'. RUN this session, same command, same tree: (512, 0.1928881999992882) — \(0.1929\) s, \(+50.6\) per cent. The record's own third reading of the same fixture is \(0.376\) s (READ V20_R15_JOURNAL.md:2441 @ 99777ab), \(+194\) per cent. Replacement survives. true Required repair. Quote the oracle cost as a band over the three readings — \([0.128, 0.376]\) s for 512 plies, unsynchronised, single CPU — label it [FITTED-free, unrepeated], and state that it is a fixture number on 36 synthetic games and licenses no throughput law. Severity. repair Repair applied. 09.3 carried the band when this batch opened, over four readings rather than three (the fourth is this book's own RUN, \(0.1524\) s): \(0.128\) s, \(0.1524\) s, \(0.1929\) s and \(0.376\) s, quoted as \([0.128,\,0.376]\) s for \(512\) plies, unsynchronised, single CPU, [FITTED-free, unrepeated], a fixture number on \(36\) synthetic games licensing no throughput law. 09.13's residue is repaired in this batch: its Evidence still read "RUN the fixture oracle: 512 plies in \(0.128\) s (09.3)" — the struck point quotation at the site the finding names second — and now carries the same four readings, the same band, the same class and the same "licenses no throughput law and is quoted in no price" sentence, with the \(0.128\) s point named struck at this site as well as at 09.3.

A-36

Verse. 09.20 Flaw. A RUN evidence line misreports the working tree. Mechanism. P-1 Number. 09.20 Evidence: 'RUN ls data/ → CHECKSUMS.sha256, README.md, COGS and SCAN files only.' RUN ls data/ this session returns twelve entries including tinystories_20k.txt, which is neither a COGS nor a SCAN file (and is the 211,765-line file results/k_data_manifest.json names at the tinystories_cdla entry's note). Replacement survives. true Required repair. Correct the listing to 'CHECKSUMS.sha256, README.md, four COGS tsv files, six SCAN txt files and tinystories_20k.txt; no market file and no PGN'. The conclusion — no market data in the tree — is unaffected and stands. Severity. repair Repair applied. 09.20 — repaired in this batch, with the finding's own count corrected upward rather than copied. The Evidence now reads the full listing the finding requires — CHECKSUMS.sha256, README.md, four COGS .tsv files, six SCAN .txt files and tinystories_20k.txt, no market file and no PGN — with the struck wording quoted and the tinystories_cdla manifest note pinned (\(211{,}765\) lines, \(18{,}167{,}706\) bytes, sha256 2767818…, pinned in data/CHECKSUMS.sha256). The entry count is thirteen and not twelve: RUN ls data/ | wc -l this session → 13 (\(2+4+6+1\)), so the finding's "twelve entries" and 09.2's "twelve entries" are both one short, and both are corrected to thirteen — 09.2's Evidence is amended in the same batch and points at 09.20 for the full listing. The finding's conclusion is unaffected by the correction and stands: no market data is in the tree.

A-37

Verse. 09.14, 09.3 Flaw. The feature width \(F\) used to price the cells does not match the feature list that defines the tokens. Mechanism. M-8, P-1 Number. 09.3 lists 'piece planes \(64\times13=832\) one-hot, side to move, castling \(4\), en-passant file \(9\), parent index one-hot over \(s\), move id, membership flags \(K+2\)' — summing at \((s,K)=(64,2)\) to \(832+1+4+9+64+1+4=915\). 09.14 writes '\(F=832+1+4+9+64+m+K+4\)' \(=923\) at \((m,K)=(7,2)\): the \(+m\) term has no referent in 09.3's list, and the flags term is \(K+4\) there against \(K+2\) here. Replacement survives. true Required repair. Print one feature table with one total, per bed and per \(s\): at \(s=64\), \(K=2\) the parent index contributes \(64\) and at \(s=256\) it contributes \(256\), so \(F\) is a function of \(s\) and the projection cost is \(F(s)\cdot d\). Restate the membership-flag width consistently (\(K+2\) in 09.3 against \(K+4\) in 09.14) and reprice 09.14 and 09.34 from the corrected \(F\). Severity. repair Repair applied. The one feature table, the corrected total \(F(s,K)=849+s+K=915\) at \((s,K)=(64,2)\), the \(K+2\) token flags against the \([m,K+4]\) label tensor stated as two different objects that are never summed, and the repriced projection \(915\times64=58{,}560\) in 09.14 and the three line items in 09.34 were carried when this batch opened. The residue the finding names first — "\(F\) is a function of \(s\)" as a pricing rule and not only a table row — is repaired in this batch: 09.14 now carries a per-bed, per-\(s\) projection table, because 09.19's reroute moves the chess bed to \(s=256\) and no projection cost was printed there. At \((3,5,256)\) and \((2,15,256)\), \(F(256,2)=849+256+2=1{,}107\), the projection is \(1{,}107\times64=70{,}848\) parameters and \(1{,}107\times16=17{,}712\) MACs per token against the block's \(12d_{\rm model}^2=3{,}072\), a ratio of \(5.766\times\) against \(4.766\times\) at \(s=64\) (DERIVED), with heads \(64\times5\times6=1{,}920\) and \(64\times15\times6=5{,}760\); the parent-index one-hot is named as the only \(s\)-dependent row, which is the whole of the \(915\to1{,}107\) move. The verse now states that a reroute to \(s=256\) re-prices the projection before it re-runs the census and that a price quoted at \(s=64\) may not be carried to it, and the Limits line carries the \(17{,}712\) / \(5.766\times\) pair beside the \(14{,}640\) / \(4.766\times\) pair.

A-38

Verse. 09.14, 09.11 Flaw. Two fallback chains have a second link that costs strictly more than the kill it replaces, against CHARTER §2's depth rule. Mechanism. D-3, M-8 Number. 09.14 Kill price: 'the cell itself, \(\approx34\) s'. Its If-killed requires 'prices re-fitted from the first eight chess cells on the certified stack' with 'R² below \(0.99\) over four points' — four fitted points at eight seeds, strictly more than \(34\) s. 09.11 Kill price: 'read off the arena (\(\approx98\) s)'; its If-killed is '\(N=16\) at the same price law (\(\approx68\) s per pair)' — for the registered arm set that is a second arena, not a cheaper link. CHARTER §2: 'each link's kill must be strictly cheaper or strictly more decisive than the one before it'. Replacement survives. true Required repair. Either print the decisiveness argument explicitly (the refit at four points decides the exponent, which the single smoke cell cannot) or reorder the chain so the cheaper link comes first: re-quote the measured cell as a point price (\(0\) extra GPU-s) before attempting a refit. Severity. repair Repair applied. Both chains reordered in this batch, and both branches of the required repair taken rather than one. 09.14: the If-killed is now two links. Link 1 costs \(0\) extra GPU-s — the cell that fired the kill is already paid for, so its eight seeds are re-quoted as a measured point price (median seconds with the realised across-seed spread), every chess price is restated from that point instead of from the \(1.680\) s law, and the link's own kill is arithmetic on a column already written: an across-seed spread above the band's own width, \(16.2\) per cent of the median (DERIVED, \(+14.4-(-1.8)\)). Link 2 is the four-point refit, kept and now argued: a single smoke cell decides only whether one point sits inside a band around one law, while four fitted points decide the exponent — whether cost is linear in \(n\) at the projected feature width at all — which no single cell can separate from a constant offset. The Kill also gains the planted negative it lacked: the same cell with the projection disabled must read inside the band and the same cell at \(s=256\), \(F=1{,}107\) must read outside it, or the band is blind. 09.11: the Kill now prints its price (\(0\) extra GPU-s; the realised sd and run_index are columns of an arena already paid at \(\ge172.960\) s on chess and \(\ge90.592\) s on markets, neither of which is a price), and the single link "\(N=16\) at the same price law" is struck as written and replaced by two. Link 1 is free arithmetic on the column K-P already prints: \(N_{\rm req}=\lceil8(\mathrm{MDE}^{\rm realised}_8/\mathrm{MDE}^{\rm pilot}_8)^2\rceil\), which at the K-P firing point (\(\mathrm{sd}=0.109318\), \(\mathrm{MDE}_8=0.126372\), pilot \(0.057971\)) reads \(\lceil37.94\rceil=38\), and every contrast whose \(N_{\rm req}\) exceeds the budget is filed as a band with no point at \(0\) extra GPU-s. That link is what makes the old one wrong rather than merely expensive: at the firing point \(N=16\) leaves \(\mathrm{MDE}_{16}\approx0.0894\), still \(1.54\times\) the pilot, so a second arena at \(N=16\) buys a number that is still not falsifiable. Link 2 runs \(N=16\) (\(\approx68\) s per pair, the byte-embedding floor) only where link 1 returns \(N_{\rm req}\le16\), and is licensed on the decisiveness half of the depth rule because it halves the variance of the paired mean, which arithmetic on eight seeds cannot. Both rows of the kills table are restated to match.

A-39

Verse. 09.36 Flaw. A Kill carries a to-be-determined constant, which CHARTER §2 rules is not a chain link. Mechanism. P-4, M-2 Number. 09.36 Statement: 'the fellow approximator is a change-point detector on the price path (basseville-1993-abrupt-changes [V]), registered with its threshold frozen before any cell.' No threshold value, no support, no selection rule appears anywhere in the book. The Kill then reads 'not better than the change-point detector'. Replacement survives. true Required repair. Freeze the detector here: CUSUM on the mid-price increments with a drift reference \(k=\mu_1/2\) and a decision interval \(h\) set so the in-control average run length equals the registered horizon in steps, both printed as design constants with an [ASSUMED] class, and the plant (a synthetic \(+0.05\)-per-step drift) required to fire on at least 9 of 10 series. Severity. repair Repair applied. 09.36 — repaired in this batch, exactly as filed. The McNemar contrast the finding quotes was already deleted in batch 2, which left the detector registered as a descriptive fellow approximator and left the finding's real defect standing: a named instrument with no threshold, no support and no selection rule is claimed scaffolding whether it is scored or only described. The detector is now frozen with every constant in a table. It is a one-sided CUSUM \(S_t=\max(0,S_{t-1}+\Delta p_t/\sigma-k)\) on the mid-price increments standardised by the in-control per-step sd, which on BED-P-L is exactly \(\sigma=1/G=0.01\), so the standardised shift is \(\delta=(\mu_1/G)/(1/G)=\mu_1\) (DERIVED from 09.25's transition law). Reference \(k=\delta/2=\mu_1/2=\mathbf{0.10}\) at \(\mu_1=0.2\) and \(0.05\) at \(\mu_1=0.1\) (DERIVED). In-control ARL target is the registered horizon in steps — \(T=9\) on BED-P-L, \(t^\star=24\) on BED-P-N at 09.23b's one-day horizon and one-hour cadence — class [ASSUMED], with the reason printed (one false alarm per horizon in expectation is the loosest rate at which the detector describes the horizon rather than the sampling). Decision interval \(h=\mathbf{1.562}\) at \((k,\mathrm{ARL}_0)=(0.10,9)\), \(\mathbf{3.047}\) at \((0.10,24)\) and \(\mathbf{1.691}\) at \((0.05,9)\), DERIVED by inverting \(\mathrm{ARL}_0=(e^{2kb}-2kb-1)/(2k^2)\) with \(b=h+1.166\) (\(2kb=0.5455,\,0.8425,\,0.2857\)). The corrected-Brownian ARL approximation is owed and absent from references.bib (RUN grep -n -i 'siegmund' docs/references.bib this session → robbins-siegmund only, a different work), so that row's class is [ASSUMED] on the approximation and DERIVED on the arithmetic given it, and the citation-free route — freezing \(h\) by simulating \(\mathrm{ARL}_0\) on the martingale plant — is NOT MEASURED, needs the BED-P-L generator. The plant is registered as filed: a synthetic series at the same \(\sigma=0.01\) with a per-step mean of \(+0.05\) (\(\delta=5\), fifty times \(k\)) must alarm on at least \(9\) of \(10\) series; on \(8\) or fewer the detector is blind at the frozen constants, its agreement fraction is not printed at all, and the sentence naming it as this verse's fellow approximator is withdrawn. That blindness line is added to the Kill as line (b) at \(0\) GPU-s, with an If-killed that re-derives the constants at the next horizon on the registered support (\(t^\star=60\), \(h\) raised) — a different number on the same instrument — and retires the detector from the book on a second blindness. The kills table row carries \(k\), both \(h\) values and the plant.

A-40

Verse. 09.7 Flaw. The Kill names no \(N\), no seed rule and no realised-sd clause, which CHARTER §2's reachability rule requires of every kill. Mechanism. M-3, M-9 Number. 09.7 Kill: 'S-14 on BED-C-T at \(0\) GPU-s plus one zero-step forward (\(\le1.524\) s [FITTED]): the untrained arm on the honest query reads L-q NRMSE \(\ge1-10^{-3}\) and argmin accuracy within \(1/m\pm\) its Clopper-Pearson half-width'. The draw count, the seed rule and the realised sd that makes the half-width honest are absent. CHARTER §2: 'Every kill names the draw, seed rule and \(N\) at which it is decidable, and the realised-sd clause that makes its \(\mathrm{MDE}_N\) honest.' Replacement survives. true Required repair. Add: 512 BED-C-T draws at seeds \(0\)-\(7\), the same byte-identical draws every arm sees, the Clopper-Pearson half-width computed at \(n=512m\) trials, and the realised per-coordinate sd of L-q printed in the same block, since NRMSE returns nan on a constant label and nan >= 1.0 is False (READ MISTAKES.md:150-152). Severity. repair Repair applied. Carried when this batch opened and verified line by line against the four items filed: the Kill reads "on \(512\) BED-C-T draws at seeds \(0\)–\(7\), the same byte-identical draws every arm sees"; the Clopper–Pearson half-width is "computed at \(n=512m\) trials" with clopper-1934-binomial [V]; the realised per-coordinate sd of L-q is required "printed in the same block"; and the reason is printed rather than assumed — nrmse is normalised by std(y), returns nan on a constant label, and float('nan') >= 1.0 is False in Python, so a bare threshold passes a degenerate label silently, pinned READ MISTAKES.md:149-153, which is the same passage the finding pins at :150-152 and which reads in this tree this session as "NRMSE is normalised by std(y), so a constant label does not produce a bad number — it produces nan, and float('nan') >= 1.0 is False in Python, so a bare threshold lets it through as a silent pass". No residue found.

A-41

Verse. 09.38 Flaw. A gate condition points at a book that files nothing on either use. Mechanism. P-4, D-4 Number. 09.38(iii): 'the VOID list (09.16) and the predictions with counters (09.24, 09.31 and the bets book 06 files) are hashed in a commit dated before the cell'. RUN this session: grep -n -i 'chess\|market\|brier\|PnL' docs/canon/06_PREDICTIONS.md returns no match. Book 06 files zero chess or market bets. Replacement survives. true Required repair. Either drop the reference to book 06 from gate (iii) and make 09.24, 09.31 and 09.36 the complete set of scored market predictions this book owns, or file the three bets as rows book 06 must carry and record the gap in CORRECTIONS.md until it does. Severity. repair Repair applied. 09.38 — repaired in this batch by the second branch, with the finding's own RUN re-run and reported as it now reads. The filed command does not return no match on the tree this session: RUN grep -n -i 'chess\|market\|brier\|PnL' docs/canon/06_PREDICTIONS.md → \(9\) lines, and RUN grep -n '09\.24\|09\.31\|09\.36' docs/canon/06_PREDICTIONS.md → the C-39 row for 09.31 (the paired per-contract PnL difference against the market-following rule, with the e-process value as the deciding number) and the provenance line naming C-35 (09.10), C-36 (09.13), C-37 (09.32) and C-38 (09.34). Book 06 therefore files five of this book's deciding cells and not zero. The finding's conclusion survives its own number, and the repair is made on the reproduction rather than on the filed count: gate (iii) no longer says "the bets book 06 files", a phrase that pointed at a file whose contents were not read, and now names the set exactly — 09.24 and 09.31, and those two only, are the scored market predictions this book owns; 09.36 owes nothing, because after its batch-2 rewrite it scores no contrast at all and its agreement fraction is printed and never scored. The gap is exactly one row: 09.24's Brier-and-log skill against the market floor is not among C-1 to C-40 and must be. This book's writer may not write 06_PREDICTIONS.md or CORRECTIONS.md (CHARTER.md §3), so that row is owed as a CORRECTIONS.md row and is added to the Limits paragraph, which now reads four owed rows and not three; until it exists, gate (iii) is satisfied on 09.31 through C-39 and stands open on 09.24, and 09.38 records the open half rather than implying the whole.

A-42

Verse. 09.25 Flaw. The declared price-absorbing states are unreachable at the registered geometry from any interior start. Mechanism. V-11, D-3 Number. 09.25 Statement: 'and \(p\in\{0,1\}\) absorbing', with \(G=100\), \(T\in\{9,21\}\) and steps of \(\pm1/G\). The maximum excursion is \(T/G=0.09\) at \(T=9\) and \(0.21\) at \(T=21\), so \(p=0\) and \(p=1\) are reachable only from \(p_0\le0.09\) or \(p_0\ge0.91\) (resp. \(0.21\)/\(0.79\)). 09.23's own instance starts at \(p_0=0.3\). All absorption at the registered geometry is via the leaf Bernoulli at \(t=T\). Replacement survives. true Required repair. State that \(\{0,1\}\) absorption is unreachable at \((G,T)=(100,\le21)\) from the registered \(p_0\) support and is declared for completeness only (V-11, printed never counted), and note that the gambler's-ruin instance of 09.23 is a DIFFERENT chain from BED-P-L (unbounded time, boundary absorption) — the lattice's identity is the tower property, which the verse already gives. Severity. repair Repair applied. 09.25 — repaired in this batch, exactly as filed, with the start support registered so the inequality has a geometry to be false at. The Statement now declares \(p\in\{0,1\}\) absorbing for completeness only and unreachable at the registered geometry (V-11, printed and never counted), and prints the arithmetic: the maximum excursion is \(T/G=0.09\) at \(T=9\) and \(0.21\) at \(T=21\) at \(G=100\), so \(\{0,1\}\) is reachable only from \(p_0\le T/G\) or \(p_0\ge1-T/G\), while the start support is registered here as \(p_0\in\{0.3,0.5\}\) (09.23a's instance value and the leaf plant's) and \(0.09<0.3<0.91\) and \(0.21<0.3<0.79\) hold at both \(T\) — so every absorption on BED-P-L at the registered geometry is at the leaf Bernoulli at \(t=T\) (DERIVED). A census line counting price-boundary absorption would read \(0\) by arithmetic and is not written; the boundary rows stay declared so \(P_{\rm env}\) is row-stochastic on them (09.32 line 1) and so a reroute that moves \(p_0\) into \(p_0\le0.09\) changes the bed rather than silently breaking it. The Statement also records that 09.23a's gambler's-ruin instance is a different chain — unbounded time, certain boundary absorption — while BED-P-L runs \(T\le21\) steps and absorbs at the leaf, and that the identity the lattice supplies to 09.23a is the tower property \(q^{({\rm YES})}(0,p_0)=E[p_T]=p_0\), which holds with no boundary absorption at all. The Hypotheses gain the \(p_0\) support and the Mechanism now carries V-11 twice, the second for the unreachable declared set.

A-43

Verse. 09.21, 09.26 Flaw. The constraint sets are absorbing on an augmented state whose two extra coordinates are never registered as state or as tokens. Mechanism. M-1, D-3, P-4 Number. 09.21 Statement: 'The state at decision time \(t\) is \(x_t=(\text{book}_t,\ \text{path}_{\le t},\ T_{\rm res}-t)\)' with \(\ell=10\) book levels and \(W\in\{16,64\}\) path steps. 09.26 Statement: 'Constraint sets, absorbing on the augmented state \((t,p,\text{PnL},\text{exposure})\)'. PnL and exposure appear in no token layout, no feature list and no \(F\) count; at \(s=64\) feature tokens, \(2\ell+W=20+16=36\) or \(20+64=84\) positions are already allocated. Replacement survives. true Required repair. Register the augmentation in 09.21: two extra scalar features per token (running PnL, signed exposure, both in size-grid units), the token budget recomputed at \(s=64\) (\(2\ell+W+2\le64\) forces \(W\le42\)), and the augmented state declared as the object every committor in 09.26, 09.32 and 09.33 is read on. Severity. repair Repair applied. 09.21 — repaired in this batch, with the repricing carried through every verse that reads the market feature width, because the finding's third clause makes the augmentation the object the committors are read on and a width that does not pay for it is 09.3's one-table rule broken a second time. 09.21's Statement now prints the augmented tuple \(x_t=(\text{book}_t,\text{path}_{\le t},T_{\rm res}-t,\Pi_t,X_t)\) with running PnL \(\Pi_t\) and signed exposure \(X_t\) in units of the size grid and never in a venue's currency (V-17), and states that it is the object every committor of 09.26, 09.32 and 09.33 is read on and that no committor in this book is read on the unaugmented tuple. The two coordinates are carried as two extra scalar features on every token, so the market feature width moves \(F=16\to\mathbf{18}\): projection \(18\times64=\mathbf{1{,}152}\) parameters at \(d_{\rm model}=64\), and \(18\times16=\mathbf{288}\) MACs per token at the priced width against the block's \(3{,}072\), \(\mathbf{+9.375}\) per cent (DERIVED, against \(+8.33\) at the struck \(F=16\)). Both token budgets are printed so the choice is visible: \(2\ell+W\le s\) under the per-token reading forces \(W\le44\) at \(s=64\), and \(2\ell+W+2\le s\) under the alternative reading, in which \(\Pi_t\) and \(X_t\) get tokens of their own, forces the finding's \(\mathbf{W\le42}\) — and under either reading the registered \(W=64\) does not fit \(s=64\) (\(20+64=84>64\), which it did not before the augmentation either), so \(W=64\) is registered as a dial of the \(s=256\) layout only and \(W=16\) is the only \(W\) at \(s=64\). On BED-P-L the two coordinates are carried as the root token's extra features under \(\mathrm{do}(a)\), one value per candidate, which is what makes 09.26's drawdown and exposure sets evaluable on a lattice at all. 09.21 gains a second frozen kill at \(0\) GPU-s — the realised sd of \(\Pi_t\) or \(X_t\) at or below \(10^{-12}\) over the \(512\) admitted draws strikes the set absorbing on it — with the hold-only plant required to fire it and the full grid required not to. The repricing is carried into 09.29b (layout \(F=18\), projection \(1{,}152\), total \(305{,}984\), matched arms \(57{,}344\), Terminal), 09.30 (projection \(1{,}152\), total \(57{,}344\), logistic \(18\times64+1=1{,}153\) per output and \(\mathbf{5{,}765}\) over five outputs), 09.34 (\(288\) MACs, \(+9.375\) per cent, header projection \(1{,}152\)), 09.14's per-bed table and the Limits line; every struck figure (\(F=16\), \(1{,}024\), \(57{,}216\), \(305{,}856\), \(5{,}125\), \(256\) MACs, \(+8.33\) per cent, the \(1.083\) refit factor) is named struck at its own site.

A-44

Verse. 09.9, 09.11, 09.30, 09.33, 09.15 Flaw. Mechanism fields cite identifiers that do not exist in MISTAKES.md, which CHARTER §2 makes the register for that field. Mechanism. P-7, L-2 Number. RUN grep -cE '^### ' MISTAKES.md → 71 headings, spanning V-1..V-26, P-1..P-11, M-1..M-21, D-1..D-7 only. The book's Mechanism fields cite C8 (09.7, 09.30), C17 (09.11, 09.33) and L-2 (09.15), all of which live in docs/CEQ_SHAPE.md, not MISTAKES.md. Replacement survives. true Required repair. Either add the source to the citation in the Mechanism field ('C8, docs/CEQ_SHAPE.md:1733'; 'C17, V20_R15_JOURNAL.md @ 99777ab'; 'L-2, docs/CEQ_SHAPE.md:2640') or map each onto its MISTAKES.md equivalent (C8 → D-1 plus V-10; C17 → M-8 plus M-3; L-2 → P-1). Severity. note Repair applied. Both branches taken at every site in this batch, rather than one. RUN grep -cE '^### ' MISTAKES.md this session → 71, and RUN grep -oE '^### [A-Z]+-[0-9]+' MISTAKES.md | sed 's/-[0-9]*$//' | sort -u → D, M, P, V only, which reproduces the finding's number and its span exactly. Every one of the six Mechanism fields now carries the source and the map: 09.7 and 09.9 read "C8 (READ docs/CEQ_SHAPE.md:1733; not a MISTAKES.md id — MISTAKES.md equivalents D-1 plus V-10)"; 09.30 reads the same with the K-H2 card named; 09.11 and 09.33 read "C17 (V20_R15_JOURNAL.md C17 @ 99777ab; not a MISTAKES.md id — equivalents M-8 plus M-3)"; 09.15 and 09.29b read "L-2 (docs/CEQ_SHAPE.md §A.10 at :2640, 'the identity manifest — field list (against L-2, READ V20_R15_LEAP_LEDGER.md:23)'; not a MISTAKES.md id — equivalent P-1)", with 09.15 carrying the grep -c count in the field itself. The Limits paragraph records the register split once, so a reader who checks a Mechanism id against MISTAKES.md and does not find it is told where it lives and what it maps to instead of concluding the field is fabricated.

A-45

Verse. 09.18 Flaw. The degeneracy lemma is printed with a hypothesis that is false at the verse's own geometry, and no vacuity line is given. Mechanism. V-25, V-12 Number. 09.18: 'the degeneracy lemma in force (if the constraint sets exhaust the absorbing states, \(\max_k q^{(k)}\ge1/K\) by pigeonhole)'. 09.4 declares \(\mathcal A_{\rm sink}\), \(\mathcal A_0\), \(\mathcal A_{\rm loss}\), \(\mathcal A_{\rm draw}\) and \(\mathcal A_{\rm res}\) alongside the \(K\) constraint sets, so the constraint sets never exhaust the absorbing states on BED-C-T and \(\sum_{k\ge1}q^{(k)}<1\) on every draw. CHARTER §2 skyline rule requires the vacuity inequality printed at the verse's geometry. Replacement survives. true Required repair. Print the vacuity line: at \(K=2\) with a declared sink, goal, loss and draw set, \(\sum_{k\ge1}q^{(k)}\le1-q^{({\rm sink})}-q^{(0)}-q^{({\rm loss})}-q^{({\rm draw})}\) and the lemma binds only when that bound reaches \(1\), which the census forbids by line 5. Record the lemma as the guard against a mis-declared boundary set, not as a live constraint. Severity. note Repair applied. 09.18 — repaired in this batch, exactly as filed. The phrase "the degeneracy lemma in force" is struck; the lemma is now stated as a lemma and followed by its vacuity line at the verse's own geometry, printed as the skyline rule requires: at \(K=2\) on BED-C-T, with \(\mathcal A_{\rm sink}\), \(\mathcal A_0\), \(\mathcal A_{\rm loss}\) and \(\mathcal A_{\rm draw}\) declared alongside the constraint sets (and \(\mathcal A_{\rm res}\) on BED-C-D), \(\sum_{k\ge1}q^{(k)}\le1-q^{({\rm sink})}-q^{(0)}-q^{({\rm loss})}-q^{({\rm draw})}\) on every draw, so the lemma binds only where that bound reaches \(1\) — where all four other declared coordinates are identically zero on the batch — and 09.10's admission line 5 forbids exactly that, since it requires every declared channel's per-coordinate sd to exceed \(0.05\) and a channel identically zero has sd \(0\). The conclusion the lemma would give at \(K=2\), \(\max_kq^{(k)}\ge0.5\), is printed against that bound and against 09.4's own kill (c). The lemma is recorded as the guard against a mis-declared boundary set — a generator that silently drops the sink, goal, loss or draw set makes its hypothesis true and the conclusion fires — and explicitly not as a live constraint, with the sentence that no sentence in this book rests on it; V-25 is added to the Mechanism naming this defect.

A-46

Verse. 09.25, 09.24 Flaw. The word 'edge' is used of a bed property and inside a Terminal without the bed, floor, \(N\) and matched count that CHARTER §1 requires of any such claim, and it is on the book's own withdrawal list. Mechanism. P-7, V-17, R-SKY Number. 09.25 Statement: 'the edge exists by construction and is a plant'. 09.39 What is withdrawn: 'every sentence with "more accurate", "faster to train", "beats", "edge", "wins", or a capability number on either use.' The book therefore withdraws a word it uses in a Statement. Replacement survives. true Required repair. Rename it throughout: 'the planted departure from martingale', which is what the object is. Reserve 'edge' for the withdrawal list of 09.39 and for the negative Terminal once that Terminal is rewritten as a licensing sentence. Severity. note Repair applied. 09.25 — renamed in this batch, as filed. The Statement now reads "the planted departure from martingale exists by construction and is a plant", with the struck wording quoted and its mechanism printed: a word the book withdraws, inside a Statement about a bed property, with no bed, floor, \(N\) or matched count beside it (CHARTER.md §1; P-7, V-17 and R-SKY are added to the Mechanism field). The Statement also records that the object's only name is a planted departure from martingale of exact size \(\mu_1T/G\). 09.24's use is the half the finding's own required repair reserves: its Terminal was rewritten in batch 2 (A-26) as the licensing sentence "No edge over the market-implied probability is licensed…", which names what is not licensed rather than asserting a measured negative, and it stands unchanged, as does 09.31's identical sentence and the withdrawal list of the demoted closing section. After this rename the word appears in the book only on that withdrawal list, inside those licensing Terminals and the null hypothesis they name, and in the Attacks-answered rows that quote the struck wording.

A-47

Verse. 09.1 Flaw. The break census undercounts the test surface it is describing. Mechanism. P-1 Number. 09.1 Statement: 'one test (tests/gate0/test_g05_data.py)'. RUN this session: python -m pytest -q tests/gate0/test_g05_data.py → 31 passed in 0.67s. Book 04.7's Terminal prints the same count as 31. One test FILE carrying 31 tests. Replacement survives. true Required repair. Write 'one test file carrying 31 passing hygiene tests (RUN this session, 31 passed in 0.67s)', matching 04.7 so the two books agree on the integer. Severity. note Repair applied. Carried when this batch opened: 09.1's Statement reads "one test file carrying \(31\) passing hygiene tests (tests/gate0/test_g05_data.py)" and its Evidence prints the RUN with the cross-book reconciliation — READ 04_BEDS_AND_INSTRUMENTS.md:95 reads 31 passed in 0.73s, this book's own RUN reads 31 passed in 0.60s, the refutation's reads 31 passed in 0.67s, and the verse states that the count is shared between the two books and the wall-clock is unrepeated and is not a law, which is the disagreement the three readings would otherwise create on an integer the finding requires the books to agree on. No residue found; the two books agree on \(31\) and neither quotes a shared second.

A-48

Verse. 09.6 Flaw. The If-killed link is neither cheaper nor more decisive than the kill it replaces; both are the same two-run test at the same price. Mechanism. D-3 Number. 09.6 Kill: 'on 512 positions, \(e_D(x)\) at Threads=1 on two runs differs on any position ... Price: CPU minutes'. If-killed: 'Evidence: NOT MEASURED — the same two-run test; Kill: identical, \(0\) GPU-s.' CHARTER §2 requires each link to be strictly cheaper or strictly more decisive. Replacement survives. true Required repair. State the decisiveness gain explicitly: the node limit removes wall-clock from the search's stopping rule, so a second failure isolates the binary rather than the budget, and the third link (demotion to [ASSUMED] with the disagreement rate printed) is free. Print the disagreement rate as the number the chain produces regardless of outcome. Severity. note Repair applied. Carried when this batch opened, with all three clauses present: the If-killed states that the link "is not cheaper — it is the same test at the same price — and its decisiveness gain is what licenses it, stated as CHARTER.md §2's depth rule requires", derives the gain (a depth limit lets the stopping rule depend on wall clock through time management and hash-table timing, so a depth-\(D\) disagreement cannot separate "the binary is non-deterministic" from "the budget moved"; the node limit removes wall clock from the stopping rule, so a second failure isolates the binary), names the third link free, and requires the two-run disagreement rate over the \(512\) positions printed beside every eval-\(\Delta\) number in every case — pass or fail, at both links — so the chain yields a number even when nothing is refuted. The kills-table row carries the same three links. No residue found.

What this batch changed, by verse. 09.2 (the data/ entry count corrected to thirteen); 09.3 and 09.13 (the oracle band restated at the second site, the \(0.128\) s point struck there too; the kdata.py pins re-verified against grep -n and sed -n this session); 09.7, 09.9, 09.11, 09.15, 09.29b, 09.30 and 09.33 (C8, C17 and L-2 given their source and their MISTAKES.md map at every site); 09.10 (line 11 split into 11a and 11b, the source's two \(100\)-per-cent checks restored with the three-line derivation of why each is V-10 on a root-last tree, the two clamp plants registered, and the Statement's and Kill's exemption lists re-stated per line); 09.11 (the Kill priced at \(0\) extra GPU-s and the chain reordered — \(N_{\rm req}=38\) by free arithmetic before \(N=16\) at \(\approx68\) s); 09.14 (the per-bed, per-\(s\) projection table with \(F(256,2)=1{,}107\), \(70{,}848\) and \(17{,}712\) MACs at \(5.766\times\); the Kill's two plants; the If-killed reordered to a free point re-quote before the four-point refit, with the exponent argument printed); 09.18 (the degeneracy lemma's vacuity line printed at \(K=2\) and the lemma recorded as a boundary-set guard); 09.20 (the full data/ listing, thirteen entries, tinystories_20k.txt named); 09.21 (the augmented state registered — \(\Pi_t\), \(X_t\), \(F=18\), both token budgets, \(W=64\) out of budget at \(s=64\), a second frozen kill on the augmentation's sd, a new Terminal); 09.25 (the price boundary declared unreachable with its inequality and the \(p_0\in\{0.3,0.5\}\) support registered, 09.23a's chain distinguished, "edge" renamed to "the planted departure from martingale"); 09.29b, 09.30 and 09.34 (repriced at \(F=18\): projection \(1{,}152\), totals \(57{,}344\) and \(305{,}984\), logistic \(5{,}765\), \(288\) MACs at \(+9.375\) per cent); 09.36 (the change-point detector frozen — the CUSUM recursion, \(k=\mu_1/2\), the ARL target, \(h=1.562/3.047/1.691\) by the printed inversion, the owed approximation citation, the \(+0.05\)-per-step plant at \(9\) of \(10\), and a blindness line added to the Kill with its own If-killed); 09.38 (gate (iii) naming 09.24 and 09.31 exactly, book 06's C-35..C-39 read and printed, 09.24's missing row recorded); the kills table (rows for 09.11 / 09.33, 09.14 / 09.34, 09.21 and 09.36 restated); and Limits (four owed CORRECTIONS.md rows, the three non-MISTAKES.md Mechanism ids recorded once, the \(s=256\) projection increment added). Open findings: none in this batch — every finding filed above is repaired in the book, and no verse was deleted to escape one. Two of the batch's filed numbers did not reproduce on the tree this session and are corrected upward in the book rather than copied: ls data/ returns thirteen entries and not twelve (A-36), and book 06's chess-and-market grep returns nine lines and five filed rows and not zero (A-41); in both cases the finding's conclusion survives its own number and is carried.