04 — BEDS AND INSTRUMENTS#

SATURN (WATSON). Written 2026-09-05 under docs/canon/CHARTER.md at HEAD 99777ab. Evidence classes as CHARTER §2; READ path:line @ 99777ab for every deleted round document (readable with git show 99777ab:<path>); RUN is a command executed this session on this box (torch 2.14.0+cpu, numpy 2.4.6, no CUDA device — every GPU number below is READ from the certified record, never re-measured here); RUN[x] is another planet's run carried with its class. No code file was written; no git write was made.

Preface — what this book decides, and the verse that decides it first#

This book decides which sentence of CHARTER §1 — A1, A2, T1, T2 — a bed is allowed to license, and the instrument that decides it, with nothing decided by construction. Three beds form the ladder: BED-S, in-class with an exact oracle (04.2); BED-J, the joint-consistency bed outside the per-row class (04.6); the chess witness on natural ground (04.7). Every bed carries its floor (04.3), its guards firing both ways (04.4), its static-task kill (04.5), its label class and metric plants (04.8), its control arms (04.11) and its binds with planted negatives (04.13). The verse that decides first is 04.2: BED-S admission at $0$ GPU-s and $1$ evening. Under D-CALIB the counter is the point estimate, and the record's dominant failure is a bed dying at construction, so 04.2 is the first kill in the decision order, because it gates every other bed number in this book — not the cheapest kill in the canon, which it is not. Nine kills are strictly cheaper by the sort key (GPU-seconds, evenings) the closing table now applies: 04.7, 04.8, 04.12, 04.15, 04.16, 04.17, 04.18, 04.19 and 04.21 are decidable at $0$ GPU-s with no evening, and 04.1 and 04.11's operative link are $0$ GPU-s at $0.5$ evening. The cheapest kill in this book is any of the nine at $0$ GPU-s and no evening; 04.2 is the first that must be answered, because until the bed admits, every number the other verses read has nothing to be read on. The earlier Preface sentence — "the cheapest kill in the canon is the one that runs before any arm exists" — contradicted the closing table's own prices and is struck. If 04.2 admits, 04.9 (the "more accurate" protocol) and 04.10 (the "faster to train" protocol) are the only two verses that can turn a number into one of the four sentences; every other verse exists to make those two honest. Ten census rows are closed here in full — B3, B4, B5, B11, B18, B20, B21, B22, B23, B25 — and one, B27, only on its chess half (04.7), its market half belonging to 09 and appearing in no verse of this book (table at the end, with the split stated beneath it). Every "If killed" is derived in place with its own hypotheses, evidence and kill; every chain ends in a Terminal within three links; the last table orders the kills cheapest-first.

Part I — The bed ladder#

04.1 — Nothing is decided by construction: the VOID register#

Statement. On every bed of this book a contrast between two arms is a capability number only if it is absent from the bed's registered VOID list, and the VOID list is fixed by one rule: a contrast is VOID when the label's oracle operator is contained in one arm's operator class and not the other's, because such a contrast reads reproduction-versus-non-reproduction. Applied to BED-S the rule voids every listed contrast, not two. 04.2's Hypotheses assert that a depth-1 bilinear logit can realise $\hat P=P_{\rm env}$, so the oracle $(I-Q_a)^{-1}R_{a,k}\mathbb 1$ is inside the shape's class; ChaCAL-diag is defined in 04.11 as the shape with $\mathcal A=\emptyset$ and InfSA-Neumann-$16$ as a read without boundaries, so neither class carries absorbing rows and neither contains the oracle; the same asymmetry holds for ChaCAL-published, ChaCAL-with-sink, the 0-hop MLP and the 1-hop softmax. BED-S's registered VOID list is therefore the eight-entry set $\{\text{shape}-\text{softmax},\ \text{shape}-\text{skyline},\ \text{shape}-\text{ChaCAL-diag},\ \text{shape}-\text{ChaCAL-published},\ \text{shape}-\text{ChaCAL-with-sink},\ \text{shape}-\text{InfSA-Neumann-}16,\ \text{shape}-0\text{-hop},\ \text{shape}-1\text{-hop}\}$, and the only reading BED-S licenses is identification, $\|\hat P-P_{\rm env}\|_\infty$ per seed. BED-S is a bed on which perfect identification voids every capability contrast: an arm that satisfies 04.2's representability hypothesis reads $\|\hat P-P_{\rm env}\|_\infty\approx0$ and is credited with nothing, which is the correct reading of a bed built in the arm's own class. The capability claim moves to BED-J (04.6), where 04.6's Statement asserts the oracle is in no causal arm's class. The list itself is NOT MEASURED — needs the representability check of 04.21 step (5), since its only input is the containment premise 04.2 carries as NOT MEASURED; until that check is journalled the operative rule is link 1's, under which every contrast on every bed of this book is VOID. Hypotheses. The oracle runs on the environment chain $P_{\rm env}$ the bed builds, never on the arm's $\hat P$ (D-2); the arm's class is the causal row-stochastic resolvent read of docs/CEQ_SHAPE.md §2.1 Definitions 2–4; the containment premise ($\hat P=P_{\rm env}$ realisable at depth 1) is 04.2's and is unmeasured, so the list's membership is provisional and its provisionality is journalled with it; geometry $s=64$, $d_{\rm model}=16$, $t^\star=8$, $m=8$, $K=2$, $N=8$. Evidence. READ docs/CEQ_SHAPE.md §6 A.1 (the VOID list registered before any cell); READ docs/PLAN.md S-13; the mechanism's precedent READ MISTAKES.md:710-725 (D-2: settled − softmax VOID on the E3 ladder, only settled − twin creditable at $-0.002959$, CI $[-0.042903,+0.031557]$); the containment premise NOT MEASURED — needs the first BED-S cell (04.21), so the eight-entry list is NOT MEASURED with it. Mechanism. D-2, M-7 (the VOID list is registered before data, never after), V-10, V-7. Kill. void_contrasts journalled as [] on a bed whose registered VOID list is non-empty, or a capability sentence built on a contrast in the list. Absence is not the kill's condition: 04.15 makes a missing declared field a refusal, so no cell reaches the journal with void_contrasts absent and a kill on absence could not fire. Decided by the manifest field of 04.15 read against the bed's registered list on every cell; price $0$ GPU-s, $0.5$ evening; planted negative: a cell written with void_contrasts = [] on BED-S, whose registered list has eight entries, must be refused by the adjudicator of 04.9 — the plant instantiates the kill's condition exactly (an empty list is present, not absent) and the refusal is the control that shows the rule can fire. If killed — link 1 (operative today). The replacement rule is stricter, not looser: every contrast on the bed is VOID until the identification reading $\|\hat P-P_{\rm env}\|_\infty$ is journalled per seed, and a contrast is creditable only where that reading is $\ge10^{-3}$ on $\ge6$ of $8$ seeds (the K-D2 complement of docs/PLAN.md S-13). The rule reads as it looks: on BED-S a contrast becomes creditable only where the arm has failed to identify the environment, which is why the capability sentence does not live on this bed at all. Hypotheses: the identification reading exists (04.15 field census). Evidence: K-D2's threshold READ docs/CEQ_SHAPE.md §6 A.2 ledger row K-D2 (non-empty rejection region on the DAG substrate). Kill: $\|\hat P-P_{\rm env}\|_\infty<10^{-3}$ on $\ge6/8$ — the arm copied the environment; every contrast is a copy-versus-no-copy statement; the price is the arena's own $\approx98$ s ([ASSUMED], 04.9). Terminal. The canon licenses, with no capability number: "BED-S is registered with an eight-entry VOID list, its exact oracle and its floors; no contrast on it has been credited, and its only licensed reading is identification." It withdraws every sentence of the form "the shape reads $X$ better than softmax on BED-S" and every capability sentence on BED-S whatever the second arm.

04.2 — BED-S: in-class, exact oracle, registered with the D-4 admission gate#

Statement. BED-S is the triple (generator, seed, hash) whose environment is a random directed graph on the $s$ token positions with edges to earlier positions (a DAG in token order), self-loops only on declared absorbing positions, $P_{\rm env}$ row-stochastic including its absorbing rows; boundary sets $\mathcal A_{\rm sink}=\{0\}$ (value $0$ on every indicator channel), $\mathcal A_0$ (goal), $\mathcal A_1..\mathcal A_K$ (constraints), all before the query position, the query in $T=[s]\setminus\mathcal A$; $m$ candidate moves, each a query-side row clamp $P_{\rm env}[v_a,:]\leftarrow e_{u_a}$ with $u_a\in T$ (R-07's restriction) and $u^\top\mathbb 1=0$; labels per move $$q(a)=\big(q^{(\rm sink)},q^{(0)},q^{(1)},\dots,q^{(K)}\big)(a),\qquad q^{(k)}=(I-Q_a)^{-1}R_{a,k}\mathbb 1\ \text{on }T,\qquad \sum_\bullet q^{(\bullet)}=\mathbb 1,$$ $a^\star=\arg\max_a q^{(0)}(a)$, the Chebyshev $\arg\min_a\max_{k\ge1}q^{(k)}(a)$ and the conditioned Chebyshev $\arg\min_a\max_{k\ge1}q^{(k)}(a)/(1-q^{(\rm sink)}(a))$ as columns; $z^\star=(I-\gamma_{\rm env}P_{\rm env})^{-1}V$ and $\Delta z(a)=(I-\gamma P'_{\rm env})^{-1}(\Delta V+\gamma\Delta P\,z)$ at a bed constant $\gamma_{\rm env}$. Admission (D-4) is decided from one printed census block on $512$ draws at $t^\star=8$, $m=8$, $K=2$, $s=64$, and the block's clauses are numbered here so every verse that cites one cites it by number:

#	admission clause	line
1	every row sum of $P_{\rm env}$ within $10^{-12}$ of $1$	pass/fail
2	$0\in\mathcal A_{\rm sink}$ on $100$ per cent of draws	pass/fail
3	every boundary set before the query and the query in $T$ on $100$ per cent	pass/fail
4	every per-coordinate sd of $q$ over the admitted query region $>0.05$, with the fraction of coordinates at zero label variance printed (the mask 04.8 reads)	fraction
5	every class frequency of $a^\star$ in $(0.05,0.95)$	fractions
6	rule-disagreement fraction (argmax-$q^{(0)}$ against Chebyshev against conditioned Chebyshev) $>0$	fraction
7	sink share printed apart from $q^{(0)}$	interval
8	discard count printed	count
9	$m_{\rm eff}\ge m-1$ on $\ge95$ per cent of draws, over the pre-screened candidate pool of clause 11 (R-08)	fraction
10	the per-base admitted fraction at the quantifier level each magnitude theorem uses (04.19), printed per base	fraction
11	the no-op screening rate: the fraction of candidate targets in $T$ whose clamp moves the query's committors by $>10^{-12}$, measured on the draw before the $m$ moves are sampled; moves are drawn from the screened pool only	fraction

Clause 9 is stated at $m_{\rm eff}\ge m-1$, not $m_{\rm eff}=m$, and every floor of 04.3 is derived at the realised $m_{\rm eff}$ rather than at $m$: the verse's own Evidence records a $15$ per cent no-op rate ($3$ of $20$ targets moved the committors by $5.551\times10^{-17}$), at which an unscreened draw of $m=8$ reads $P(m_{\rm eff}=m)=0.85^8=0.2725$ (DERIVED) and a gate at $m_{\rm eff}=m$ on $\ge95$ per cent of draws would fire on $72.75$ per cent of draws at registration — a kill satisfied by construction (V-11). Clause 11's pre-screen is what makes clause 9 reachable; the screening rate is printed so the pool's size is auditable. Hypotheses. The arm's class contains the oracle's chain: a depth-1 bilinear logit can realise $\hat P=P_{\rm env}$ from the multi-hot out-adjacency feature at $d_{\rm model}\ge n_{\rm nodes}$ — a representability claim that is NOT MEASURED — needs the first BED-S cell (04.21); $K\ge2$ (at $K=1$ the committor is constant to $1.11\times10^{-14}$, READ MISTAKES.md:189-199); $t^\star$ placeable inside the causal window (at most $i$ hops from position $i$). Evidence. The bed's own spectral radius is $\rho(Q_{\rm env})=0$ exactly, and it is not a measured number: the Statement builds $P_{\rm env}$ as a DAG in token order with self-loops only on declared absorbing positions, so $(P_{\rm env})_{ii}=0$ for every $i\in T$ and $Q_{\rm env}$ is strictly lower triangular, hence nilpotent (DERIVED, one line from the construction — a nilpotent transient block is the point of the DAG). The figure $0.692660$ is a read of the arm's matrix, not the bed's: $\rho(\hat Q)=\max_{i\in T}\hat P_{ii}=0.692660$ is a diagonal read on the arm's triangular causal softmax $\hat Q$, whose diagonal is non-zero because a causal softmax puts mass on its own position (READ docs/CEQ_SHAPE.md:2547 @ 99777ab, RUN $0.692660$; :1818 reads $\rho(\hat Q)=0.692660$ both ways). F1 and F2 RUN by three planets on the arm's chain: BOS undeclared gives $\rho(\hat Q)=1.000000$, $\det(I-\hat Q)=0$; declared, $\rho(\hat Q)=0.692660$, conservation to $4.4\times10^{-16}$, sink share $[0.362,1.000]$ on one draw; a set at position $20$ read from query $12$ gives $q=0.0$ exactly (READ docs/CEQ_SHAPE.md §6 A.1; docs/sources/plan/plan_saturn.md S-10). The Chebyshev sink-escape on the judge's draw: minimum $0.000$ attained by $9$ of $20$ targets, $7$ with sink share above $0.5$ (RUN[M], READ docs/PLAN.md R-07). Clamps at rows $21,25,31$ move the query's committors by $5.551\times10^{-17}$ — $3$ of $20$ targets, a $15$ per cent no-op rate, which is why clause 11 pre-screens and clause 9 reads $m-1$ (RUN[M], READ docs/PLAN.md R-08). The oracle price at the registered geometry: $s=64$ fixes $|T|\le63$, so $m$ factorisations of $|T|^3/3=8.33\times10^{4}$ MACs each with $m(K+2)=32$ right-hand sides, milliseconds per draw in float64 (DERIVED). The figure $|T|^3/3=5.76\times10^{8}$ MACs holds at $|T|=1200$ and is carried here only as a headroom note at that named geometry, $6.9\times10^{3}$ times the registered one (DERIVED); no admission number rests on it. BED-S has no cell: RUN this session python -c "from ceq import kdata; print(list(kdata.BED_SPECS))" prints ['bed_m', 'bed_k', 'bed_1']. Mechanism. D-4, V-8, V-12, V-25, V-10 (line 3 is a diagonal read, printed not counted), D-3, M-3. Kill (K-E2, K-P). Clause 4 reading any admitted-region sd $=0$; clause 5 reading a class frequency outside $(0.05,0.95)$; clause 6 reading disagreement $0$; R-07 line (i) $\ge0.5$ or line (ii) $\ge0.5$; clause 9 reading $m_{\rm eff}<m-1$ on $>5$ per cent of screened draws; $t^\star$ unplaceable in $\{2,8,32\}$ by the DAG's depth. Instrument: the census script of docs/PLAN.md S-12 (specified, not written). Price $0$ GPU-s, $1$ evening. Planted negative: a batch built with BOS undeclared must print $\rho(\hat Q)=1$ on the arm's chain and the solve must raise (V-16); a batch with a constraint set after the query must print discard count $=512$; and a batch drawn from the unscreened pool at the recorded $15$ per cent no-op rate must fail clause 9 — the screen's own known-bad control. If killed — link 1, the dial. Move $t^\star$ to $2$ or raise the graph depth so that $t^\star$ lands inside the causal window, and re-run the same census. Hypotheses: the failure line was $t^\star$ unplaceable or an sd collapse traceable to the depth (the record watched a label's sd fall from $0.499989$ to $0.038445$ under a kill rate, READ scale/e4_harmonic.py:425-434). The link is scoped: moving the dial does not touch the no-op rate, so a clause-9 or clause-11 failure routes past link 1 to link 2 directly. Evidence: $t^\star$ is a tolerance dial read off the hop ladder at E2_DIAL_TOL = 1e-3 (READ scale/negation_scope.py:264). Kill: the census fails again on any line at $0$ GPU-s. If killed — link 2, the substrate. The jittered bed_1 landscape at $K=2$ with $B$ as goal becomes the bed — as an oracle cross-check only, never the shape lane's substrate, because it is undirected (SymmSupport, $\rho(Q)=0.9408612510154677$, RUN[coord]) and no causal $\hat P$ equals it (DERIVED: an off-diagonal $Q_{ij}>0$ forces $Q_{ji}>0$, which a lower-triangular $P$ cannot carry). Evidence: its oracle, residual $4.16\times10^{-17}$, Kirchhoff route $<10^{-10}$ at $K=2$ are in the tree (READ ceq/beds/bed_1.py:188-198; MATHEMATICS.md:542-600). Kill: a shape cell on it filed as a capability number — refused by 04.1. This link is more decisive than link 1 because it removes the in-class reading entirely rather than moving a dial. If killed — link 3, the price. $N$ is repriced from whatever realised sd the first admitted batch shows (04.9), and the bed is filed at that $N$ or filed unfalsifiable. Hypotheses: the realised paired sd is the first admitted batch's, read from the journal's per-seed differences and not from a pilot or a table; the seed set is the eight of 04.21 step (5), deduplicated in one thread lane. Evidence: the MDE table at its realised-sd rows, $0.109199\to\mathrm{MDE}_8=0.126238$, $\mathrm{MDE}_{16}=0.081841$ (READ docs/sources/sections/sec_beds.md:308-313, RUN[VENUS], re-verified RUN[MARS]); the M-3 precedent, pilot $0.050146$ against realised $0.109199$, ratio $2.1776$ (READ MISTAKES.md:464-494). Kill: $\mathrm{MDE}_{16}$ at the realised $\sigma_d$ still above every registered effect on the bed — nothing is falsifiable at any $N$ this canon can afford, and the bed is filed with its sd and no capability number; decided at $0$ GPU-s from the journalled $\sigma_d$ before any second batch runs, which is strictly cheaper than link 2's cross-check cell. Terminal. "BED-S at the design point does not admit; the canon files the generator specification, the census with its printed failure line, the floors, the controls and the pricing rule, and no capability number." Withdrawn: every sentence of §5.10 tree A and tree B of docs/PLAN.md on BED-S.

04.3 — Information floors per bed (L-FLOOR)#

Statement. Every capability number prints beside its information floor, and the floor is one of exactly three objects, assigned per head: $$\text{vector heads } (q,\ z^\star,\ \Delta z):\ \text{the exact oracle at }0.0,\ \text{with the hop-ladder ceilings }\mathrm{NRMSE}(z_k,z^\star),\ z_k=Qz_{k-1}+R,\ \text{printed per batch};$$ $$\text{argmin}:\ \mathrm{floor}_{\rm zeroinfo}=1-\max_a\hat\pi(a^\star)\ \ (=1-1/m_{\rm eff}\text{ at uniform }\hat\pi)\ \text{alone};$$ $$\text{BED-K}:\ \text{the Hankel ceiling }\mathrm{err}_1=\sqrt{1-1/d}=0.9746794345\text{ at }d=20;\qquad \text{BED-M}:\ \text{the exact oracle at }0.0,\ \text{with }\sqrt{(t^\star-k)/t^\star}\text{ printed as a capability threshold, never a floor}.$$ Both Fano forms are retired, on the same ground and by the same arithmetic. The weak form $1-\ln2/\ln m$ reads $0.5/0.6667/0.75$ at $m=4/8/16$, sitting $0.25/0.2083/0.1875$ below the exact zero-information floor $0.7500/0.8750/0.9375$; the tight form $(\ln m-I-\ln2)/\ln(m-1)$ at its most binding setting $I=0$ reads $0.6309/0.7124/0.7679$, sitting $0.1191/0.1626/0.1696$ below the same floors (DERIVED from the printed values). Fano is therefore never binding against the exact zero-information floor at any $I\ge0$ on a deterministic label, for every $m\ge3$, and retaining the tight form while retiring the weak one on that exact ground was the defect. floor_fano_k1 is struck from 04.15's field list and from the adjudicator of 04.9; floor$_1$ appears nowhere. Hypotheses. $\hat\pi$ is the realised class distribution of the batch being scored, never of a neighbouring batch; $m_{\rm eff}$ counts moves that change the query's committor by more than $10^{-12}$ (R-08) over the screened pool of 04.2 clause 11, and every floor is derived at the realised $m_{\rm eff}$, never at $m$; the argmin label is deterministic given the oracle. Evidence. Exact zero-information floor $0.7500/0.8750/0.9375$ at $m=4/8/16$; weak Fano $0.5/0.6667/0.75$ sits $0.25/0.2083/0.1875$ below chance (RUN[J], READ docs/CEQ_SHAPE.md §6 A.3); tight Fano $0.6309/0.7124/0.7679$ at $I=0$ sits $0.1191/0.1626/0.1696$ below the same floors (RUN[J], the gaps DERIVED); the Cover–Thomas form CITED [V] cover-2006-elements §2.10, theorem number [U], retained as the reason Fano is retired and cited for no floor; floor$_1=0.7071067811865476$ violated by $13$ of $40$ banked cells (RUN[WATSON], READ docs/CEQ_SHAPE.md §6 A.3) and by $6$ of $34$ at C15 (READ V20_R15_JOURNAL.md:51 @ 99777ab); the Hankel ceiling DERIVED $\sqrt{1-1/20}$ (READ V20_R15_LEAP_LEDGER.md:323 @ 99777ab); the exact-oracle numerical noise level $4.4\times10^{-16}$ (the conservation read of 04.2, RUN[M]). $I(X_{\le k};a^\star)$ for BED-S is NOT MEASURED — needs the plug-in estimator over the admission census of 04.2 and no floor of this verse depends on it. Mechanism. L-FLOOR, V-10 (a floor an uninformed arm cannot violate is not a floor; a floor an informed arm is supposed to beat is not a kill), V-17, C15. Kill. An uninformed control printing an error below its own floor — the 0-hop control, the random control or the majority control reading below $\mathrm{floor}_{\rm zeroinfo}$ computed on the batch it was scored on, on $\ge2$ of $N$ seeds, $N$ the seed count 04.9 clause 7's rule fixes at the realised $\sigma_d$ and provisionally $8$ (NOT MEASURED — needs $\sigma_d$ from 04.21 step (5)): the floor is not a lower bound and is struck for that head. The count $2$ is a seed-count rule and the floor is recomputed per batch, so no placeholder $\mathrm{MDE}_8$ enters this kill; only the denominator waits on $\sigma_d$. An informed arm printing below the floor is the capability reading L-FLOOR exists to produce, not a defect, and fires nothing: at $m=8$ an arm with argmin accuracy $0.90$ prints error $0.10$, $0.775$ below the printed floor, on $8$ of $8$ seeds, and the earlier unrestricted kill struck the floor on exactly that success. Instrument: the adjudicator of 04.9 reading floor_zeroinfo per cell against the cell's own arm field; price $0$ GPU-s beyond the cell. Planted negative: an off-by-one-seed floor — the majority control scored against $\mathrm{floor}_{\rm zeroinfo}$ computed from seed $j+1$'s realised $\hat\pi$ while scored on seed $j$'s batch. A majority arm violates that floor by construction whenever the two batches' $\hat\pi$ differ, so the kill fires on a known-bad case. The matched-batch plants cannot serve: random reads error $1-1/m$, which is the floor at uniform $\hat\pi$, and majority reads error exactly $1-\max_a\hat\pi(a^\star)$ on the batch whose $\hat\pi$ defines the floor — neither can print strictly below it except by the finite-sample noise the floor is computed from, so both are retained as the V-3 floor row and neither is the kill's control. If killed — link 1. The floor is re-derived at $m_{\rm eff}$ (R-08's line) and re-printed; every argmin accuracy in the cell is re-floored. Hypotheses: the violation is explained by no-op moves ($m_{\rm eff}<m$). Evidence: the $5.551\times10^{-17}$ no-op instance (RUN[M]). Kill: a violation surviving the re-floor at $m_{\rm eff}$; price $0$ GPU-s, the same journal. If killed — link 2. The argmin head carries the exact-oracle floor $0.0$ only, in $\varphi$-NRMSE on the committor vector, and no rate-valued floor is printed. Hypotheses: the committor vector is journalled on $T$ (04.8); the oracle's own numerical noise on the bed is the conservation read $4.4\times10^{-16}$. Evidence: NRMSE is non-negative by definition and reads $1.0$ for the mean predictor (V-17's anchored unit); the noise level $4.4\times10^{-16}$ (RUN[M], 04.2). Kill: an arm reading $\varphi$-NRMSE below $4.4\times10^{-16}$, the exact-oracle-plus-numerical-noise level — a score under the oracle's own float error is a label leak, not capability, and the head is struck and routed to 04.4's leak guard; decided from the journal at $0$ GPU-s, cheaper than link 1's re-floor because it reads one number per cell. The claim that this link "cannot be killed" was itself the defect: a link with no kill is a Terminal, not a replacement. Terminal. "Every number on the bed is a distance to the exact oracle at $0.0$; no argmin floor is claimed and no Fano line is printed anywhere." Withdrawn: every sentence reading "above the Fano floor", in either Fano form.

04.4 — The zero-hop guard and the leak guard, firing both ways#

Statement. Two guards run at construction on every bed, each with a must-fire half and a must-not-fire half. Zero-hop: the query token carries $s_0$ only, $s_0$ drawn uniformly from $T$ independently of $a^\star$; the untrained arm reads argmin accuracy within $1/m_{\rm eff}\pm$ its Clopper–Pearson half-width and committor NRMSE $\ge1-\mathrm{GATE\_TOL}$, $\mathrm{GATE\_TOL}=10^{-3}$. The guard's mutual-information half is NOT MEASURED — needs the plug-in estimator for $I(s_0;a^\star)$ over the admission census of 04.2, and until that estimator exists the untrained-arm half — the RED gate at $1-10^{-3}$, which is the harness's own and runnable today — carries the guard alone; no verse reads $I(s_0;a^\star)=0$ as an asserted fact. Leak: a corpus-alone linear probe from the token features to $q$ at order $0$ reads below the bed's own bar $R^2_{\rm bar}$, defined as the $99$th percentile of the corpus-alone $R^2$ null distribution over the $512$ admission draws of 04.2, computed on label-permuted targets and printed with the draws it was computed on. The bar is not imported: the E4′ pair PASS_BAR = 0.5 / FAIL_BAR = 0.9 is E4′'s object in E4′'s units and is V-22 across the bed boundary, so it fixes nothing here and is carried only as the precedent that names the mechanism. Until the $512$-draw null is computed the leak verdict is NOT MEASURED — needs the corpus-alone probe over the admission census of 04.2, in both directions: no bed is cleared of leakage and none is convicted of it. The planted leak (a move token carrying its own $q$) must read $R^2\ge0.99$ — [ASSUMED] 0.99, one nine below the M-21 instance that read $R^2=1.000000$ when the target was an input channel, the reason being that the plant differs from M-21's only by the quantisation of the copied channel. Hypotheses. The bed's token list is that of 04.2 (node tokens, edge tokens, move tokens, query token); no token carries anything derived from a solve; the probe is linear at order $0$; the null distribution is computed on the same $512$ draws that decide admission, so the bar and the census share a batch and the bar is not an off-batch import. Evidence. The RED gate is the harness's own (READ scripts/k_cert.py:218-222, NaN checked first because float('nan') >= 1.0 is False); $30$ of $30$ shapes passed with worst margin $1.957\times10^{-3}$ (READ COSTS.md:137-139). BED-M's first builder leaked $1/(t^\star+1)$ at zero hops and aborted three of five rungs; b[s-1] = 0 restored it (READ scale/negation_scope.py:399-415). The E4′ bars PASS_BAR = 0.5 / FAIL_BAR = 0.9 (RUN this session: scale/rips_gate.py:60 is PASS_BAR = 0.5, :61 is FAIL_BAR = 0.9) are E4′'s object in E4′'s units, read $0.973819$ on its fixed point, and are V-22 and not re-derived: they are struck as this verse's operative threshold and replaced by the $512$-draw null bar, which is NOT MEASURED — needs the corpus-alone probe over the admission census of 04.2. The corpus-alone probe precedent: gate $R^2$ corpus alone $=1.000000$ on BED-M because the target was an input channel (READ MISTAKES.md:2101-2189, M-21) — the sole source of the planted bar's magnitude. Mechanism. V-10, D-5, V-24, V-7, V-22, M-21, M-2, D-2, P-1. Kill. Zero-hop: the honest query reads below $1-\mathrm{GATE\_TOL}$ or the untrained argmin accuracy outside $1/m_{\rm eff}\pm\mathrm{CP}$ — the label is legible at zero hops and the bed is a copy task. Leak: honest $R^2\ge R^2_{\rm bar}$, the bed's own $99$th-percentile null — the one-read claim is void on the bed; planted $R^2<0.99$ — the detector is blind and no leak verdict is admissible either way. The leak half of the kill is unreachable until $R^2_{\rm bar}$ exists and is registered as such, and no leak verdict is filed in the interim. Price $\le1.524$ s (one zero-step forward, [FITTED]) and $0$ GPU-s for the probes and the $512$-draw null, which rides on the census the bed already runs. The planted halves are the controls. If killed — link 1. The argmin head is struck and the committor-vector head alone remains (R-24's route): the flag rule R0 — "pick the move whose clamp target carries the goal flag, else the earliest transient target" — is computed as an oracle-free column; if R0 reads within its interval of $1/m$ after R-07's restriction, the vector head is admitted alone. Hypotheses: clamp targets are restricted to $T$ (R-07) so R0 is not exact by construction. Evidence: a clamp into $\mathcal A_0$ gives $q^{(0)}=1.0000$ exactly on the judge's draw (RUN[M], READ docs/PLAN.md R-24). Kill: R0 accuracy $\ge\mathrm{acc}_{\rm shape}-\mathrm{MDE}_N$ at the realised $\sigma_d$ (04.9 clause 7 — the threshold is frozen as that rule, never as a placeholder number; NOT MEASURED — needs $\sigma_d$ from 04.21 step (5)) on $\ge6/8$ arena seeds; price $0$ GPU-s at construction. If killed — link 2. The leak is removed by construction: membership flags are deleted from the node tokens and only the edge tokens remain; the census of 04.2 is re-run and the null bar is recomputed on the new token list, because a bar computed on the old features is the same V-22 import across a feature-set boundary that struck the E4′ pair. Hypotheses: $P_{\rm env}$ stays a deterministic function of the edge tokens, so the label still needs the solve; the recomputed null is over the same $512$ draws. Evidence: leak clause (a) was dropped for BED-S on exactly this ground (READ docs/CEQ_SHAPE.md §6 A.1). Kill: honest $R^2\ge R^2_{\rm bar}$ against the recomputed bar — the graph itself carries the label at order $0$ and the bed is a static task (04.5 decides); price $0$ GPU-s. Terminal. "The label class is registered with printed floors; the leak bar is the bed's own $512$-draw null and no leak verdict is filed until it is computed; the bed is a copy task at order $0$ and no arm is credited on it."

04.5 — The static-task kill, and the label class that leaves the scalar regime (B4)#

Statement. No bed in this book scores a scalar at one position. The four label classes are $z^\star\in\mathbb R^{s\times d}$, $\Delta z(a)\in\mathbb R^{s\times d}$, the reach-avoid tensor $q(a)\in[0,1]^{K+2}$ per move with the full vector on $T$ retained, and the argmin over $m$; the state axis that Q6 lacked exists on every one. A bed is struck as static before any number is quoted if a 0-hop per-position MLP on the candidate's context row reads argmin accuracy inside the shape's Clopper–Pearson half-width at $N$, $N$ fixed by 04.9 clause 7's rule at the realised $\sigma_d$ and provisionally $8$ (NOT MEASURED — needs $\sigma_d$ from 04.21 step (5); at $N=8$ nothing is falsifiable, 04.9 clause 6, so the clause is a rule and not the number $8$), or if McNemar between the 0-hop MLP and the 1-hop softmax reads $p>0.05$ on identical draws (K-H2). The second clause names its pair because an unnamed pair is not decidable: under (0-hop MLP, 1-hop softmax) a null result says one hop buys nothing over none, which is the static-bed reading and the only reading this kill carries. A shape-versus-1-hop comparison is an A1 row and belongs to 04.9, never to a bed kill — read as a bed kill it would strike the bed whenever the shape fails to separate, which is the arm's failure and not the bed's. Hypotheses. Matched parameters per arm, the count re-printed once the $[m,K+2]$ head is attached (Ruling 3); McNemar on paired binary outcomes only; $N=8$ deduplicated in one thread lane. Evidence. Every record bed asked one real at position $s-1$: equilibrium_oracle returns $z^\star_{s-1}$ (READ scale/negation_scope.py:286-304) and ArmSMPrime.forward returns shape $[n]$ (READ ceq/arm_smprime.py:577 via V20_R15_THEORY_TABLE.md:213 @ 99777ab); Q6 is F4 on both wings because no state axis exists, $0$ of $40$ banked cells journal a distribution (READ V20_R15_THEORY_TABLE.md:210-225 @ 99777ab). The SLR theorems (marion-2025-single-location Cor. 2, duranthon-2026-softmax-advantage Prop. 4.2, CITED [V]) admit $0$ of $3$ record beds under their label model and the record ran $L/d=4.00$ against $L=o(d)$ (READ MATHEMATICS.md:1044-1057; docs/CEQ_SHAPE.md §3.6). The vector_readout plumbing exists and defaults to False (READ MISTAKES.md:677-708). The record's static beds: both registered oracles were closed-form functions of the input with no fixed point (READ results/capability_table_v1.md Limits (a)). Mechanism. D-1, C8, V-10, M-1 (a vector label voids PUBLISHED_SOFTMAX_8192 and lives in its own lane), V-24. Kill. K-H2 as stated; instrument: the control pair of 04.11 (0-hop MLP, 1-hop softmax) at $\le1.524$ s per cell, $\approx0.5$ GPU-min for both at $N=8$; planted negative: the 0-hop MLP trained on a bed whose label is a flag lookup (BED-S with R-07's restriction removed, where R0 is exact) must read inside the half-width — the kill fires on a known-static plant. If killed — link 1. The dial is moved up: $t^\star=32$ if placeable, so the label needs more hops than a 1-hop window carries; census re-run. Hypotheses: the DAG depth admits $t^\star=32$ inside the causal window at $s=64$. Evidence: the dial's support $\{2,8,32\}$ and its placement by graph depth (READ docs/CEQ_SHAPE.md §6 A.2.1). Kill: $t^\star=32$ unplaceable at $s=64$ by the DAG's own depth census — decided at $0$ GPU-s from 04.2's depth read, before any cell runs, and strictly cheaper than the verse's own kill, which needs the control pair at $\approx0.5$ GPU-min. A link priced at the verse's own kill is neither cheaper nor more decisive and is not a link; re-running the control pair is what link 2 replaces, not what link 1 repeats. If killed — link 2. The bed is re-registered on BED-J (04.6), whose oracle no causal $\hat P$ equals. Hypotheses and evidence: 04.6's. Kill: 04.6's Bet E at $\approx30.9$ s ($2\times8\times1.680+4.0$, 04.11's arithmetic) — more decisive because it removes the per-row class from the bed rather than moving a dial. Terminal. "BED-S is a static task; the label class and floors are filed; no arm is credited." Withdrawn: every A1 sentence on BED-S.

04.6 — BED-J: the joint-consistency bed outside the per-row class#

Statement. BED-J is the jittered bed_1 landscape (bed_1.build(T=0.25, seed, jitter=0.05)) with $K=2$ absorbing sets, $\mathcal A=\{0\}$, $\mathcal B=\{1\}$, $|T|=9$, whose environment chain is undirected (SymmSupport); its label is the full fixed point on $T$, $$q=(I-Q_{\rm env})^{-1}R_{\rm env}\mathbb 1\in[0,1]^{|T|},\qquad\text{scored by }\ \varphi\text{-NRMSE per coordinate and } r(\hat q)=\frac{\|(I-Q_{\rm env})\hat q-R_{\rm env}\mathbb 1\|_\infty}{\|R_{\rm env}\mathbb 1\|_\infty},$$ with $\|(I-Q_{\rm env})^{-1}\|_\infty$ and $\|I-Q_{\rm env}\|_\infty$ printed beside $r$ — both in the $\infty$-norm $r$ is written in. The 2-norm pair $\sigma_{\min}\|e\|_2\le\|(I-\gamma P)e\|_2\le(1+\gamma)\|e\|_2$ and its "lower factor near $0.06$" do not bind an $\infty$-norm ratio: on $|T|=9$ the conversion costs up to $\sqrt9=3$ in each direction, so a factor quoted at $0.06$ in the 2-norm bounds an $\infty$-norm error only to within $9\times$ (DERIVED from $\|x\|_\infty\le\|x\|_2\le\sqrt{|T|}\,\|x\|_\infty$). The 2-norm factors are retained as a separate, labelled 2-norm remark and license no reading of $r$. The read is registered explicitly, because a per-position causal read of this label is unreachable and an unregistered read makes the Bet E ratio $0/0$. The chain is SymmSupport ($Q_{ij}>0\Rightarrow Q_{ji}>0$), so $q_i$ depends on neighbours at positions $j>i$ and a causal arm at position $i$ cannot see them; a last-position read of a single scalar would make this a one-scalar-at-one-position bed, which is the D-1 mechanism the book exists to leave. The registered read is therefore: the full $|T|$-vector is emitted at position $s-1$ from a $[|T|]$-wide readout, the state axis supplied by the $|T|$ coordinates of the readout rather than by the position axis, and that readout's parameter count is printed in params_per_arm on every arm — the head is part of the matched count (Ruling 3), and the count is NOT MEASURED — needs the first BED-J cell until an arm is built. The bed is out of class by one DERIVED line at the operator level: an off-diagonal $Q_{ij}>0$ forces $Q_{ji}>0$ under SymmSupport, and no lower-triangular $\hat P$ carries both, so no causal arm's operator equals the oracle's. That is operator non-containment and it is not non-approximability — CHARTER §5 B7, the record's largest unclosed logic gap. The label is $9$ real numbers and the registered readout can emit any point of $\mathbb R^9$, so operator non-containment bounds nothing about $\|\hat q-q\|$. The creditability claim is therefore NOT MEASURED — needs the D-APPROX bound of book 01 for the causal class against a SymmSupport resolvent, printed at $|T|=9$, $\rho(Q_{\rm env})=0.9409$, and no contrast on BED-J is creditable until that bound exists and is non-vacuous at that geometry. When it exists, the contrast is creditable only in form A2, against the depth skyline in the same row, because a deeper softmax stack computes the same resolvent by iteration. Its floor is the exact oracle at $0.0$ with the hop ceilings $\mathrm{NRMSE}(q_k,q)$ printed; its guards are 04.4's with the query carrying $s_0$ only and the probe target $q$. Hypotheses. $\rho(Q_{\rm env})<1$ (Perron certificate on the non-causal chain, isUnit_one_sub_of_perron [S]); the landscape's jitter varies the chain per draw so the label is non-constant (sd printed; V-8); $t^\star$ read off the hop ladder, never predicted from $\lambda_2$ (the rate is $\rho(Q)$, measured $0.9964$ against $0.9985$ on LargestJoin_S2Rips_1024, READ PRIOR_ART.md:703-707 @ 99777ab). Evidence. bed_1 oracle residual $1.04\times10^{-17}$ and the must-fire perturbation to $10^{-6}$ (ratio $9.6\times10^{10}$, READ workdonenewseal.md:214-215); $\rho(Q)=0.9408612510154677$, $Q^{11}\ne0$ (RUN[coord]); the D-2 separation on undirected substrates (READ docs/sources/design/refute_instrument_occvac.md F-B); the joint claim UNTESTED at READ MATHEMATICS.md:106-127; the residual's 2-norm factors DERIVED $\sigma_{\min}\|e\|_2\le\|(I-\gamma P)e\|_2\le(1+\gamma)\|e\|_2$ with the lower factor near $0.06$ at $\rho=0.9409$ (READ docs/sources/design/refute_falsify_occvac.md §3.12), carried as a 2-norm remark only; the $\infty$-norm conditioning factor $\|(I-Q_{\rm env})^{-1}\|_\infty$ that actually binds $r$ is NOT MEASURED — needs one read of the built chain, $0$ GPU-s on the bed's own generator; the skyline iteration CITED [V] wang-2024-incontext-td, xie-2026-softmax-rl (abstract level, [U] on theorem numbers). The D-APPROX bound for the causal class against a SymmSupport resolvent at $|T|=9$, $\rho=0.9409$: NOT MEASURED — needs book 01, and the creditability of every BED-J contrast waits on it. The generator is PINNED at sha256 f73ca0e6… (READ results/k_data_manifest.json). A jittered draw batch and its census: NOT MEASURED — needs the census of 04.2 run on bed_1.build(jitter). Mechanism. D-2 (the separation is the point), V-26 (the residual is the joint term), V-17 (units printed), R-SKY, D-1. Kill (Bet E). $r_{\rm softmax}/r_{\rm shape}\le2$ paired by seed and draw at marginal $\varphi$-NRMSE within $\mathrm{MDE}_N$ at the realised $\sigma_d$ (04.9 clause 7; NOT MEASURED — needs $\sigma_d$ from 04.21 step (5), and the ratio bar $2$ is this verse's own frozen constant and is unaffected): joint consistency is learnable by a per-row mixture and the sentence at MATHEMATICS.md:106-127 is withdrawn; $(2,10)$ is SPLIT. Instrument: one bed-cell pair, $\approx30.9$ s ($2\times8\times1.680+4.0=30.88$ s at two arms and eight seeds on 04.11's arm_smprime cell basis plus the $4.0$ s arena overhead), classed [ASSUMED] and not [FITTED + RUN] because neither arm of the pair is FOUND on BED-J (04.11's census, RUN this session); the $\approx34$ s this clause carried is struck as $10$ per cent above the same arithmetic with no printed overhead term to carry the gap (P-1, M-16); planted negative: an arm emitting the oracle's values permuted must read $r=O(1)$ while its pooled $W_1$ reads $0.0$ (the $1.421901$ instance, READ V20_R15_THEORY_TABLE.md:221 @ 99777ab) — the residual fires on a known-bad plant and the marginal metric does not. If killed — link 1. The bed keeps its A2 form only: shape against the matched-parameter depth-$\lfloor\log_2t^\star\rfloor+2$ stack of 04.9 clause 3b (the unmatched-depth stack of clause 3a is printed as $\Delta_{\rm sky}$ and licenses no A2 sentence), $\mathrm{acc}$ and $\varphi$-NRMSE within $\mathrm{MDE}_N$ at the realised $\sigma_d$ predicted (Bet D). Hypotheses: the matched-width skyline cell is FOUND at the same draws with its exact count printed (04.20, 04.9 clause 3b). Evidence: the iteration argument (CITED [V] wang-2024-incontext-td); the matched width NOT MEASURED — needs the reduced-width parameter count; the threshold NOT MEASURED — needs $\sigma_d$ from 04.21 step (5). Kill: the matched-parameter skyline ahead by more than $\mathrm{MDE}_N$ at the realised $\sigma_d$ — "one operator" carries no accuracy sentence at all; price $\approx64.8$ s [ASSUMED]. If killed — link 2. The residual is retained as a diagnostic column and "one read" is repriced as a cost statement (one solve, depth $s$, $+50$ per cent causal MACs — the increment $1.041$ ms/step at $n=2048$), decided by 04.10. Hypotheses: the $1.041$ ms/step increment is a per-op floor measured at $n=2048$ on the certified device, not an end-to-end step time, and it licenses a cost sentence only inside the dispatch band; the arms are interleaved and the timers synchronised per 04.10. Evidence: the increment $2.514-1.473=1.041$ ms/step at $n=2048$ ($2.312$ at $4096$, $4.542$ at $8192$), RUN[NEPTUNE]; the dispatch band $2.0\times$ at the pilot and $4.4\times$–$6.6\times$ at the shipped geometry (READ scale/m3_flops.py:101-121). Kill: the measured increment falling outside the $2.0\times$–$6.6\times$ dispatch band on the certified device — the per-op floor is not a floor for this operation and the cost sentence is struck inside this verse at $0$ GPU-s from 04.10's own journal, without waiting on 04.10's arena; a link whose kill is delegated wholesale to another verse is not a link. Terminal. "Joint determination in one read is not a differentiator on BED-J; the shape's separate claims are exactness ($\delta=0$ on the exact route) and cost, and neither is a capability number." Withdrawn: A1 and A2 on BED-J.

04.7 — The chess witness on natural ground, and the local data route before any Kaggle attach#

Statement. The chess witness is a bed with a categorical state axis whose three labels are recomputed from the board at load and never read from a column: $\ell(\text{FEN},\text{move})\in\{0,1\}$ legality; $\text{FEN}'=\text{next}(\text{FEN},\text{move})$; and $\operatorname{sign}\Delta\mathrm{eval}(\text{FEN},a)$ under a candidate move $a$, joined to the games by FEN. With $K$ constraint sets declared as FEN predicates $\mathcal A_k$ (side-to-move in check; material below a registered threshold; threefold repetition) and a goal predicate $\mathcal A_0$ (eval above $+\theta$), the reach-avoid label per candidate move is defined by rollout, never by the corpus: a fixed rollout policy $\pi_{\rm roll}$ plays $h=8$ plies from the post-$a$ position and the indicator reads whether that rollout enters $\mathcal A_k$ — a Bernoulli label per $(\text{FEN},a,k)$ whose floor is its base rate at that $h$. A corpus-defined label is unavailable by construction: a PGN game has exactly one continuation, the one after its played move, so for the $m-1$ candidates the game did not play no continuation exists and the argmin and the Chebyshev rule would have no label on $m-1$ of $m$ candidates. $\pi_{\rm roll}$ is pinned and hashed per Ruling 7 (generator, seed, sha256 in the manifest beside the bed's) and frozen before any draw, as is the horizon, frozen here at $h=8$ plies, [ASSUMED] with the reason printed — $h=8$ matches the $t^\star=8$ of the synthetic ladder so the two beds ask a comparable number of hops — and neither is fitted to a result (M-2: the horizon is a registered constant of this book, carries an evidence class, and is never re-chosen after a draw). The floor of the capability channel is registered here as a fourth floor object beside the three of 04.3, per constraint set and per horizon: for each $k\in\{0,1,\dots,K\}$ the floor is $\mathrm{base}_k(h{=}8)=\max\{p_k,1-p_k\}$, where $p_k$ is the fraction of $(\text{FEN},a)$ pairs whose $\pi_{\rm roll}$ rollout enters $\mathcal A_k$ within $8$ plies, computed on the $36$ fixture games and printed in the cell's floor_zeroinfo slot beside the number it floors. Its value is NOT MEASURED — needs one rollout pass of $\pi_{\rm roll}$ over the $36$ fixture games at $h=8$, $0$ GPU-s, an instrument this book specifies and does not write, and no capability number on the channel exists before $\mathrm{base}_k(8)$ is printed for every $k$. A horizon without a printed base rate is a label without a floor and is struck by L-FLOOR; a base rate printed at any horizon other than the frozen $h=8$ is struck by M-2. Legality and next-FEN are rule tasks: their oracle is a rule the control can call, so on those two channels the only creditable reading is learnability against a rule-free 0-hop control, never capability. The eval-$\Delta$ sign under $a$ with the $K$ predicates is the capability channel. The local data route runs first: the hygiene guards on the fixtures in the tree, and no capability cell exists before the two chess sources are PINNED — named by their Kaggle slugs, arevel/chess-games (the move sequences; manifest key lichess_chess_games, which is a misnomer: it is not a Lichess dataset) and lichess/chess-evaluations (the eval shard; manifest key lichess_chess_evaluations). Hypotheses. Splits by GAME never by row; FEN dedupe across splits; oracle labels recomputed by python-chess (chess==1.11.2); the evaluation shard streamed and pinned on one shard; the join by FEN. The join is availability-biased and is censused, not assumed: for an arbitrary candidate move $a$ the post-move FEN need not appear in lichess/chess-evaluations at all, so $\operatorname{sign}\Delta\mathrm{eval}(\text{FEN},a)$ is missing for an unmeasured fraction of candidates and the argmin over $m$ is not formable on a query with a hole. A census line prints the join-hit rate per candidate move on every cell, and the rule is: a query with any missing candidate is discarded, with the discard rate printed beside the cell and beside every number the cell carries. The join-hit rate is NOT MEASURED — needs the pinned eval shard, so no argmin number on the capability channel exists before it is printed. Evidence. RUN this session: python -m pytest -q tests/gate0/test_g05_data.py — 31 passed in 0.73s on torch 2.14.0+cpu (legality and next-FEN agree ply-by-ply with a chess.Board replay; wrecking every stored_* column changes nothing, bitwise; the emitted key set is exactly {fen_before, uci, san, fen_after, legal}). The FEN leak is real before dedupe: $14$ FENs shared train↔holdout on a correct by-game split, $0$ after (READ V17_G05_DATA.md:64 @ 99777ab). RUN this session over results/k_data_manifest.json: three entries read UNPINNED_AWAITING_KAGGLE, not two — arevel/chess-games CC0-1.0, $1.56$ GB (manifest key lichess_chess_games); lichess/chess-evaluations CC0-1.0, $34.4$ GB (key lichess_chess_evaluations); and alexkarev/tinystories-train-ready CDLA-Sharing-1.0, $595$ MB (key tinystories_cdla), whose slugs are READ ceq/kdata.py:576,588,615 and kaggle/kernel-metadata.json:11-13. The third gates the LM row of link 2 and nothing on the chess channels: the TinyStories cut is the LM $\gamma$ cell's corpus, so link 2's "only natural-ground row" is behind that digest as well as behind the author's yes. The witness is not a registered bed: kdata.BED_SPECS reads ['bed_m', 'bed_k', 'bed_1'] (RUN this session; the ledger's "one registered bed" corrected at READ V20_R15_THEORY_TABLE.md:224 @ 99777ab). The fixtures are $36$ games and $24$ articles, synthetic (READ V17_G05_DATA.md:375-378 @ 99777ab). The arena clause that named the witness: READ CEQ_V20_R15_CONTRACT.md:118-120 @ 99777ab. Mechanism. V-22 (no threshold crosses the device boundary), P-1, D-2 (a rule-computable label), V-3, M-2 (the horizon frozen at $h=8$ before any draw), L-FLOOR (the base rate registered as the channel's floor per constraint set), the Kaggle-yes rule (kaggle/README.md:9-11). Kill. 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; any number on legality or next-FEN quoted as capability — struck as D-2; any capability number quoted before the join-hit rate and its discard rate are printed, or before the $h=8$ base rate of each $\mathcal A_k$ is printed — struck as P-1 (a channel with no floor and a channel with an unmeasured hole are both unscoreable); the eval-$\Delta$ channel's kill is the base-rate floor: an arm within the Clopper–Pearson half-width of the majority sign at $N$, $N$ fixed by 04.9 clause 7's rule at the realised $\sigma_d$ and provisionally $8$ (NOT MEASURED — needs $\sigma_d$ from 04.21 step (5)), the half-width computed against $\mathrm{base}_k(8)$ printed in the same row. Price: $0$ GPU-s locally; the Kaggle certificate run $\approx8.7$ GPU-min [ASSUMED] behind the author's yes. Planted negative: the corrupted-column plant already fires (the stored_* wreck leaves labels bitwise unchanged — the instrument that reads columns would be caught by it); and a query built with one candidate's post-move FEN deliberately absent from the joined shard must be discarded by the join census, which is the known-holed case the discard rule fires on. If killed — link 1. The witness is carried as a hygiene bed only: the five guards (split by game, split by article, FEN dedupe, n-gram census, recomputed labels) with their planted violations, and no label channel — so the link survives every defect of the label definition, the horizon and the join, because it drops every label channel. Hypotheses: the fixtures stay synthetic ($36$ games, $24$ articles) until a real PGN is attached. Evidence: the planted violations fire today — a row-level split raises HygieneViolation, a boundary moved $1$ byte raises, contamination reads rate $1.0$ against $0.0$ on disjoint text (READ V17_G05_DATA.md:60-68 @ 99777ab; RUN this session $31$ passed). Kill: a guard whose planted violation does not fire (V-15) — the guard is deleted; price $0.73$ s (RUN). If killed — link 2. The witness leaves the canon's bed ladder; the LM $\gamma$ cell (S-73) becomes the only natural-ground row and stays NOT MEASURED behind the yes. Kill: an LM number pooled with a local one (V-22) — struck. Terminal. "The chess witness is a specification with $31$ passing hygiene tests and no registered bed, no pinned source and no number." Withdrawn: every sentence of the form "on chess the shape reads the safest move".

Part II — Labels, heads and metrics#

04.8 — Labels and heads for the four classes, with the metric plants#

Statement. Four heads, four scoring rules, fixed before any arm exists (M-2): | head | object | read at | metric | floor | |---|---|---|---|---| | committor / reach-avoid | $q(a)\in[0,1]^{K+2}$ per move, full vector on $T$ | $\gamma=1$ on the transient block, exact solve $(I-\hat Q)^{-1}\hat R\mathbb 1$ | $\varphi(p)=2\arcsin\sqrt p$ per entry, position-matched NRMSE (mean, max); $r(\hat q)$ with units | exact oracle $0.0$ | | argmin | $a^\star\in[m]$ | — | accuracy with Clopper–Pearson; McNemar paired on identical draws | $1-\max_a\hat\pi(a^\star)$ | | state | $z^\star\in\mathbb R^{s\times d}$ | $\hat\gamma$ | position-matched per-coordinate NRMSE vector; $r(\hat z)$ | exact oracle $0.0$ | | consequence | $\Delta z(a)$ | $\hat\gamma$ | the same vector; field cosine and magnitude ratio over coordinates $\ge i_{\min}$; the sign column with McNemar on the sign only; paired $t$/Wilcoxon on the cosine | exact oracle $0.0$; the no-change predictor's error printed on the position-matched NRMSE column only, which is the column it is scored on | The arm's $\hat\gamma$ does not enter the committor head. Refused metrics: pooled $W_1$, Procrustes, position-free OT. The refusal is per column, and its scope is printed, because a head that refuses an arm outright and prints that same arm's error as its floor refuses and scores one object at once (V-10, L-FLOOR). An arm emitting $\Delta\hat z\equiv0$ makes the field cosine $0/0$ and the magnitude ratio $0/\lVert\Delta z\rVert$; it is refused on those two columns and on no other, and it is scored on the position-matched per-coordinate NRMSE vector and on the sign column's McNemar, where both are well defined ($\lVert\Delta\hat z-\Delta z\rVert$ needs no direction, and the sign of $0$ is a registered tie handled by the McNemar's discordant-pair rule). The NRMSE the no-change predictor reads on that column is the number the consequence row prints in its floor cell. Every refused cell journals refused_columns = [cosine, magnitude_ratio] (04.15), so the scope of the refusal is auditable and no reader takes an unrefused column's number for a refused one. Hypotheses. The label is the full vector on $T$ (the residual needs it; a $[m,K+2]$ summary alone is unscoreable on $r$); the intervened position is drawn uniformly; coordinates with zero label variance (every coordinate $<i_{\min}$, and coordinate $0$ on every draw since row $0$ is $e_0$) are masked from the cosine and their fraction printed — the fraction being 04.2's admission clause 4, "every per-coordinate sd of $q$ over the admitted query region $>0.05$, with the fraction of coordinates at zero label variance printed", which is the only registered variance census in this book. The earlier pointer, "04.4's census line 10", named a line that does not exist: 04.4 registers two guards (zero-hop, leak) and no census, and its verse text carries no numbered lines, so the masking rule pointed at nothing (P-4, P-6). Evidence. Discounted read against undiscounted label: reading $q$ to $1$ per cent at $\tau=8$ needs $\hat\gamma\ge0.99857$, $1/(1-\hat\gamma)\approx697$ (RUN[F], READ docs/sources/design/refute_falsify_math.md §3.12) — hence the head at $\gamma=1$. Fisher–Rao chosen before the curve: the record measured Euclidean/Fisher–Rao ratios $1.418962$ and $1.209472$ (READ MATHEMATICS.md:69-104). Softmax owns the sign column at $0.807843$, CP $[0.754044,0.854329]$ (READ MATHEMATICS.md:396-406). The three metric plants: permuted oracle scores $W_1=0.0$ at NRMSE $1.421901$; $W_1$ prefers the permutation to $\mathrm{oracle}+0.1\sigma$ by $14.465\times$ (READ V20_R15_THEORY_TABLE.md:221 @ 99777ab). The no-change floor CITED [V] vakalis-2026-interventiongap. Mechanism. V-26, V-17, M-2, V-16, V-8, D-2 (the residual is a score, never a loss). Kill (B-G2). Any of the three plants passing on the registered metric: (i) the permuted oracle scores $0$; (ii) $\mathrm{oracle}+0.1\sigma$ is not preferred to the permutation; (iii) $-\Delta z$ is indistinguishable from $\Delta z$ — the metric is struck. Instrument: the plant script of docs/PLAN.md S-24 on the oracle alone, $0$ GPU-s. The plants are the known-bad controls. If killed — link 1. The cosine and ratio are dropped and the position-matched NRMSE vector alone scores $\Delta z$, with the sign column kept. Hypotheses: the label has non-zero variance on every scored coordinate (04.2's admission clause 4, the per-coordinate sd line with its zero-variance fraction printed; the earlier pointer "04.4's census line 10" named a line 04.4 does not carry — P-4, P-6). Evidence: NRMSE on the permuted oracle reads $1.421901>1$, on $\mathrm{oracle}+0.1\sigma$ reads $0.098296619951725$ (READ V20_R15_THEORY_TABLE.md:221 @ 99777ab). Kill: plant (i) on the NRMSE vector — impossible by construction, so this link is more decisive than the cosine's. If killed — link 2. Any metric added or removed after the first arena cell voids that cell's numbers (M-2); the metric file's hash is part of predictions_hash. Kill: a hash recorded after the first cell's timestamp; price $0$ GPU-s. Terminal. "Every head is scored by a position-matched per-coordinate error against an exact oracle at $0.0$; no joint metric is claimed."

Part III — The measurement protocol#

04.9 — The protocol that measures "more accurate" (A1, A2), and $N$ from the realised sd (B25, B5)#

Statement. A capability number in form A1 or A2 exists only when every clause below holds on one journal: 1. Paired seeds. $N\ge8$ distinct seeds, deduplicated, one thread lane read from the journal; every arm on byte-identical draws (train batch at seed, eval batch at seed + 12345, init from the global generator after torch.manual_seed(seed) — RNG_PLAN, READ scale/identity_manifest.py:78); the pairing asserted as a relation — the seed sets of the two arms equal — never as two marginal counts (V-26). 2. Matched parameters printed. params_per_arm in every table header; never re-architected to close a gap. Ruling 3 fixes only the residual that is matched, not the boundary: its text at READ V17K_RULINGS.md:56-59 @ 99777ab reads "0.032% residual is MATCHED. Print exact counts in every table header + one COSTS line", and it prints no upper bar. The record's sole matched instance is $25{,}736{,}232$ against $25{,}728{,}000$, a residual of $8{,}232$ parameters $=0.0320$ per cent (CHARTER §5 B19; DERIVED from the two counts). The boundary is therefore frozen here as a new constant of this book: a count differing from the shape's by more than $0.0960$ per cent after the head is attached is not matched — [ASSUMED] three times the largest matched residual on record, $3\times0.0320=0.0960$, the multiplier printed and the product not rounded, because rounding a frozen threshold away from the instance that motivates it is the V-11 defect this clause exists to avoid. $0.0320$ per cent is matched by Ruling 3's own text; anything in $(0.0320,0.0960]$ per cent is matched by this book's constant and prints the constant beside it; anything above $0.0960$ per cent is unmatched and licenses no A1 and no A2 sentence. 3. The skyline in the same row, and the two skyline objects kept apart. Two distinct arms are read, and only one of them can carry an A2 sentence. (3a) $\Delta_{\rm sky}$, a printed control at unmatched depth and unmatched parameters: the depth-$\lfloor\log_2t^\star\rfloor+2$ softmax stack ($3/5/7$ at $t^\star=2/8/32$), its number printed beside every matched contrast; it satisfies R-SKY's requirement that the depth skyline be read beside every bed, and it licenses no A2 sentence at all, because CHARTER §1 defines A2 as "at matched parameters against the depth skyline" and this arm's parameter count is printed as unmatched (04.20 Hypotheses). (3b) the matched-parameter skyline, registered here as a fourth skyline arm: the same depth-$\lfloor\log_2t^\star\rfloor+2$ stack at reduced width, the width chosen before any draw as the largest per-layer width whose total count lands within clause 2's $0.0960$ per cent of the shape's, the width and the exact count printed in sky_width and params_per_arm (04.15). A2 is read against 3b and against nothing else; A1 is read only where 3a's row is filled. The width that lands inside the bar at the registered geometry ($d_{\rm model}=16$, $s=64$, depth $5$ at $t^\star=8$) is NOT MEASURED — needs one parameter-count arithmetic pass over the registered stack once the $[m,K+2]$ head's count is fixed (04.6,params_per_armNOT MEASURED), $0$ GPU-s, and until it is printed no A2 number exists on any bed of this book. 4. $\mathrm{MDE}_N$ from the realised paired sd. With $\sigma_d$ the realised sd of the paired per-seed differences, $\mathrm{MDE}_N$ is the smallest $\delta$ with power $0.80$ at two-sided $\alpha=0.05$ under the noncentral $t$ with $N-1$ degrees of freedom and noncentrality $\delta\sqrt N/\sigma_d$, found by the guarded bisection (the unguarded one returns non-monotone answers because scipy.stats.nct returns nan at large noncentrality). No contrast smaller than $\mathrm{MDE}_N$ at the realised $\sigma_d$ is claimed. 5. Distance-to-floor. The contrast is between distances to the bed's floor (04.3), never between raw errors. 6. The noncentral-$t$ rule for $N$. If $\sigma_d\ge0.109199$ — the M-3 precedent's realised value itself, not a rounded multiple of it — $N$ is repriced from $\sigma_d$ before any bet is scored; the $n=16$ column is the first honest count; nothing at $N=8$ is falsifiable. The ratio to the pilot is printed to four figures, $0.109199/0.050146=2.1776$, and is a read-out, never the threshold: freezing the rule at $2.18\times0.050146=0.109318$ would place the bar $1.19\times10^{-4}$ above the only realised instance that motivates it, so the historical failure would not fire the rule that was written to catch it (V-11, V-15, M-3). 7. The placeholder rule. BED-S has no realised $\sigma_d$ (04.21), so every numeric $\mathrm{MDE}_8$ in this book is a placeholder and none of them is a frozen threshold. A kill in this book is frozen as a rule in units of $\mathrm{MDE}_N$ at the realised $\sigma_d$ — $N$ the smallest seed count of 04.9 link 1 whose $\mathrm{MDE}_N$ at that $\sigma_d$ falls below the smallest registered effect — and never as the number $0.039827$ or $0.126238$. Each such threshold reads NOT MEASURED — needs $\sigma_d$ from 04.21 step (5) until the journal carries it, and a bet scored against a placeholder number is struck by 04.21's Kill. The rule is frozen now (M-2) and the number it evaluates to is filled later; that is the only order in which a threshold can be both frozen and honest on a bed with no cell. Hypotheses. The adjudicator reads only journals (refuses below $8$ distinct seeds; deduplicates; reads threads from the record; checks predictions_hash against results/arena/PREDICTIONS.sha256 and refuses on a mismatch; refuses any calibration row whose counter field is empty or absent — the counter check is written into this specification here, because 04.17's Kill delegates a refusal to this adjudicator and a refusal the adjudicator's specification does not carry is a refusal nothing performs (P-4); never writes the prediction file). The adjudicator and that file do not exist and are marked as such wherever they are named: NOT MEASURED — needs the arena adjudicator and its frozen prediction file atresults/arena/PREDICTIONS.sha256`,RUNthis sessionls results/arenareadingNo such file or directory, so the directory, the frozen prediction file and the refusal instrument are all absent and their construction is a row of 05 REPAIRS priced there. Every clause of this book that names the adjudicator — clause 1's seed refusal, clause 3's skyline row, 04.1'svoid_contrastsrefusal, 04.3's floor read, 04.17's bare-prediction refusal and 04.21'spredictions_hashcheck — names an instrument that isNOT MEASUREDon those terms, and no verse reads a refusal as having happened (P-1, P-4). Cross-thread drift $2.345\times10^{-3}$, so a margin below $\approx4.7\times10^{-3}$ is indefensible. **Evidence.** The MDE column, guarded bisection, RUN by VENUS and re-verifiedRUN[MARS]to $0.0398266$: paired sd $0.010101\to\mathrm{MDE}_8=0.011677$, $\mathrm{MDE}_{16}=0.007570$; $0.034451\to0.039827/0.025820$; $0.050146\to0.057971/0.037583$; $0.109199\to0.126238/0.081841$ (READdocs/sources/sections/sec_beds.md§6.D.2;MATHEMATICS.md:979-993). At $N=5$ the finest two-sided $p$ is $0.0625$ and unanimity is a sign test $385/385$ (READMISTAKES.md:580-676, M-9).REQUIRED_SEEDS = 8(READscale/it11_verdict.py:59); the thread floor (READscale/it11_verdict.py:130-140). The M-3 precedent: pilot $0.050146$, realised $0.109199$, ratio $2.1776$ to four figures (READdocs/sources/sections/sec_beds.md:313;MISTAKES.md:464-494) — the ratio is printed as a read-out and the threshold is the realised value itself (clause 6, K-P). BED-S's $\sigma_d$:NOT MEASURED — needs the first eight seeds (04.21); **every $\mathrm{MDE}_8$ number above and everywhere else in this book is a placeholder, is markedNOT MEASURED — needs $\sigma_d$ from 04.21 step (5)at each of its uses, and is not a frozen threshold**; the frozen object is clause 7's rule in units of $\mathrm{MDE}_N$ at the realised $\sigma_d$. The matched-parameter bar of clause 2 is the book's own[ASSUMED]constant $0.0960$ per cent $=3\times0.0320$, the record's only matched residual being $8{,}232/25{,}728{,}000=0.0320$ per cent (CHARTER §5 B19, DERIVED); Ruling 3 at READV17K_RULINGS.md:56-59 @ 99777abprints no bar of its own. The matched-parameter skyline of clause 3b:NOT MEASURED — needs the reduced-width parameter count, and no A2 number exists in this book until it is printed. The it.3 cost ratios withdrawn at C17 are not accuracy numbers and appear nowhere here. **Mechanism.** M-3, M-9, V-5, M-13, V-26, M-10, M-16, Ruling 3, R-SKY, D-1, V-11 (a threshold rounded past the instance that motivates it cannot fire on it), V-15 (the plant must instantiate the kill's own condition), V-17 (a bar with no source is a threshold imported out of its units), P-1. **Kill (K-P).** $\sigma_d\ge0.109199$ on the first eight seeds of the softmax control on BED-S — **the threshold is frozen at the realised value of the M-3 precedent, not at a rounded multiplier**: the precedent's realised sd is $0.109199$ against a pilot $0.050146$ (READdocs/sources/sections/sec_beds.md:313;MISTAKES.md:464-494), the ratio is $0.109199/0.050146=2.1776$ printed to four figures, and the earlier form $\sigma_d\ge2.18\times0.050146=0.109318$ was struck because $0.109199<0.109318$: the one historical instance the kill exists to catch fell $1.19\times10^{-4}$ below its own bar and would not have fired it (V-11, V-15, M-3). Instrument: the arena ofdocs/PLAN.mdS-62 ($7\times8\times1.680+4.0\approx98$ s, and $\approx3.3$ GPU-min with the skyline and InfSA-16, both **[ASSUMED]and not DERIVED**: the arithmetic is arithmetic, but five of the seven arms have no implementation and no record (04.11'skindcensus,RUNthis session), so the $1.680$ s basis is thearm_smprimecell time standing in for cells that do not exist; the arena's price becomes DERIVED only when every arm in it is FOUND, and until then $98$ s is a lower bound on a run that cannot be started). **Planted negative (the one that fires K-P).** An arm pair built deliberately heteroscedastic: both arms are the depth-1 softmax control on byte-identical draws, and arm B alone takes a **seed-dependent learning rate** $\eta(\text{seed})=\eta_0\cdot2^{(j-4)/2}$ at the $j$-th of the eight seeds, a spread of $2^{3.5}=11.31\times$ across the lane, registered before the run and journalled inproducer_cmd. The per-seed differences then inherit the learning-rate spread, the realised $\sigma_d$ of that pair must exceed $0.109199$, and K-P must fire on it — the known-bad plant the kill's own condition instantiates. **Separate control, not the plant.** Two bit-identical arms must return NO VERDICT at every $N$ under this protocol (the TOST branch has no passing verdict at $N=8$: half-width $0.8807\sigma$ against a $0.5\sigma$ margin, READMISTAKES.md:1210-1247, M-13) — this is the **no-false-parity** control and it is at the opposite end of the range from K-P: it reads $\sigma_d=0$, it is about the TOST branch and not about $\sigma_d$, and it certifies that the protocol cannot manufacture parity. It is retained under that name and is not this kill's planted negative. Both plants readNOT MEASURED — needs the first eight seeds (04.21). **If killed — link 1.** $N$ is repriced to the smallest $N$ whose $\mathrm{MDE}_N$ at the realised $\sigma_d$ is below the smallest registered effect; the $n=16$ column first ($\mathrm{MDE}_{16}=0.081841$ at $\sigma_d=0.109199$); price $\approx2\times$ the arena, 1 evening. *Hypotheses:* $\sigma_d$ is stationary across the second eight seeds (checked: the first-eight and second-eight sd printed side by side). *Evidence:* the $n=16$ column (RUN[VENUS],RUN[MARS]). *Kill:* $\mathrm{MDE}_{16}$ still above every registered effect — decided at $0$ GPU-s from the realised $\sigma_d$ before the seeds run. **If killed — link 2.** The paired equivalence tier: TOST at $N=36$ paired if $\sigma_d=\sigma$ (power $0.8014$, Monte Carlo $200{,}000$ draws,RUN[MARS]), $N=70$ two-sample if pairing buys nothing ($0.7975$ at $69$, $0.8073$ at $70$, half-width $0.2799\sigma$), decided only on the $\mathcal A=\emptyset$ parity half; price $119$ s / $228$ s DERIVED, 1 evening. *Hypotheses:* the margin $0.5\sigma$ is fixed before the run (M-2); $\hat\gamma$ is MOVED, else the half is softmax against softmax. *Evidence:* CITED [V]schuirmann-1987-tost`; the sequential anytime-valid form NOT FOUND at [V]. Kill: the $90$ per cent interval outside $\pm0.5\sigma$ — parity at trained $\hat\gamma$ is not claimed; only the $\gamma=0$ identity bind licenses "contains softmax". This link is more decisive than link 1 because it settles equivalence, which a difference test at any $N$ cannot. Terminal. "At the realised paired sd, no contrast on the bed is falsifiable at any affordable $N$; the bed is filed with its sd, its floors and its controls, and no capability number." Withdrawn: A1 and A2 on that bed.

04.10 — The protocol that measures "faster to train" (T1, T2), the timers and the training-noise floor (B25)#

Statement. "Faster to train" is two numbers per bed, arm pair and head, and nothing else: $$\mathrm{T1}=\frac{\text{GPU-seconds}_{\rm shape}(\tau)}{\text{GPU-seconds}_{\rm control}(\tau)},\qquad \mathrm{T2}=\frac{\text{draws}_{\rm shape}(\tau)}{\text{draws}_{\rm control}(\tau)},$$ where $\tau$ is a distance-to-floor level registered before the run, the first level both arms reach within the step budget is the one reported, and each ratio is taken against the depth-1 control and against the depth skyline in the same row. Two ladders are registered here, one per head class, because a single NRMSE ladder leaves T1 and T2 undefined on two of this book's four heads and on one of its three beds. The ladder $\{0.9,0.8,0.7,0.5\}$ in NRMSE-to-oracle units is the vector-head ladder and covers exactly the three vector heads of 04.8 — the committor $q$, the state $z^\star$ and the consequence $\Delta z$ — every one of which is scored by a position-matched NRMSE against an exact oracle at $0.0$ and anchored at $1.0$ for the mean predictor (04.3, V-17). It covers no rate-valued head: 04.8's argmin head is scored by accuracy with Clopper–Pearson and 04.7's eval-$\Delta$ capability channel by a Bernoulli sign rate, and neither has an NRMSE-to-oracle, so a $\tau$ read off the vector ladder on either of them is a threshold imported out of its units (V-17) and the earlier single-ladder Statement was undefined on them. The rate-head ladder is therefore registered here as this book's second $\tau$ ladder, in distance-to-floor units, with four levels frozen at the same four numbers and the same anchoring: $$\tau_{\rm rate}=\frac{1-\mathrm{acc}}{\mathrm{floor}},\qquad \mathrm{floor}=\mathrm{floor}_{\rm zeroinfo}=1-\max_a\hat\pi(a^\star)\ \text{on the argmin head (04.3)},\quad \mathrm{floor}=\mathrm{base}_k(h{=}8)=\max\{p_k,1-p_k\}\ \text{on the chess capability channel (04.7)},$$ $$\tau_{\rm rate}\in\{0.9,\ 0.8,\ 0.7,\ 0.5\}\ \text{frozen here (M-2), the floor recomputed on the batch being scored, never imported from a neighbouring batch}.$$ $\tau_{\rm rate}$ reads $1$ at chance and $0$ at the exact oracle, which is the anchoring the NRMSE ladder already has, so the two ladders carry the same four levels without either one being read in the other's units. Which ladder a cell used is printed in the cell, and a T1 or T2 quoted on a rate-valued head against the NRMSE ladder — or on a vector head against the rate ladder — is struck (V-17). T1 and T2 on the argmin head and on the chess capability channel are NOT MEASURED — needs the rate-head ladder's floor: $\mathrm{floor}_{\rm zeroinfo}$ from the first admitted batch (04.3, 04.21 step 5) for the argmin head, and $\mathrm{base}_k(8)$ from one rollout pass over the $36$ fixture games (04.7) for the chess channel** — the ladder is defined and frozen here, and its denominator on each head is the floor that head's verse already owes. Every timed region is bracketed by twotorch.cuda.synchronize()calls; the arms are interleaved (shape, control, skyline, shape, …) in a randomised order recorded per cell; the Spearman correlation of seconds against run index is printed with its $p$; the training-noise floor is measured once per lane as $|\Delta|$ of final loss between two identical-seed chunks and a T1 or T2 difference below that floor is not a difference. A per-step cost model — one triangular solve of depth $s$ against $L$ attention layers, $+s^2d/2$ MACs over $s^2d$ — is DERIVED and licenses no "faster" sentence until the cost law of the kernel book is RUN. **Hypotheses.** The certified device (torch 2.5.1+cu121, RTX 4060 Laptop, $7.996$ GiB — READresults/k_cert_local.json); **$N=8$ seeds per arm, and the Kill's $N$ counts arm-cells in the timing journal, not seeds — the reading is printed here because the two differ and the kill is unreachable under the wrong one.** At $8$ seeds and the three interleaved arms of this verse's own order (shape, control, skyline) the journal holds $8\times3=24$ timings, so the Kill's $N\ge16$ is satisfied at the registered seed count; read as seeds it would demand $16$ seeds the bed does not register and could never fire on the bed as registered (V-11). Every $N$ in this verse names which of the two it counts. The same step budget and batch size per arm; the laptop clock non-stationary at $\pm12$ per cent, so prices are quoted in GPU-minutes to two decimals; determinismwarn_only=Truefor training, bitwise for every deciding forward cell (Ruling 1). **Evidence.** The record's hazard: notorch.cuda.synchronize()inscripts/v15_r1.py, and run order the strongest correlate ofsecsat $\rho=+0.7029$, $p=0.0024$, above the gate correlation $+0.5197$; every GPU-second and cost ratio quoted from it.3 onward ($0.3455$ GPU-h, $10.17\times$, $41.9\times$, $2.85/118.8$) withdrawn at C17 (READV20_R15_JOURNAL.md:53 @ 99777ab). The dispatch gap $2.0\times$ at the pilot and $4.4\times$–$6.6\times$ at the shipped geometry, and the same unit reading $2.0775$ against $3.4372$ s/step in two sessions, $1.65\times$ apart on identical code (READscale/m3_flops.py:101-121). The identical-seed floor $\delta_{\rm nrmse}=0.0$ on $6/6$ pairs on the certified device (RUN[WATSON], READdocs/sources/plan/plan_saturn.mdS-62). The per-op increment $2.514-1.473=1.041$ ms/step at $n=2048$ ($2.312$ at $4096$, $4.542$ at $8192$),RUN[NEPTUNE], a per-op floor. "Faster to train" has never been defined or measured in the record (READdocs/canon/CHARTER.md§5 B25). **The two ladders and their scope:** the vector-head ladder's unit is the position-matched NRMSE against an exact oracle at $0.0$, anchored at $1.0$ for the mean predictor, which is 04.3's own floor object for $q$, $z^\star$ and $\Delta z$ and 04.8's own metric column for all three; the rate-head ladder's denominator is $\mathrm{floor}_{\rm zeroinfo}=1-\max_a\hat\pi(a^\star)$ on the argmin head (04.3, and 04.8's floor cell for that head) and $\mathrm{base}_k(8)$ on the chess capability channel (04.7's fourth floor object), bothNOT MEASUREDon their own verses' terms — $\mathrm{floor}_{\rm zeroinfo}$ needs the first admitted batch (04.21 step 5), $\mathrm{base}_k(8)$ needs one rollout pass over the $36$ fixture games. The four levels $\{0.9,0.8,0.7,0.5\}$ are this book's own frozen constants on both ladders (M-2), registered here and not fitted to any result. Every T1 and T2 on every bed and head:NOT MEASURED — needs the synchronised, interleaved arena (03 KERNEL specifies the timer; this verse specifies the arms, the two ladders and $\tau$). **Mechanism.** C17, P-8, M-3, M-8, D-3, M-5 (a process that cannot cross its own threshold: $\tau$ unreachable is VOID, never a loss), V-10 (the level is registered, not read off the worse arm's last step), V-15 (the plant must isolate the confound the kill names, which a cross-arm order does not). **Kill.** Spearman $|\rho|>0.5$ with $p<0.05$ between seconds and run index on the $N\ge16$ interleaved timings, **$N$ counting arm-cells and not seeds** (the Hypotheses' reading: $8$ seeds $\times\ 3$ interleaved arms $=24$ timings, so the requirement is met at the registered $8$ seeds per arm and the kill has a journal on the bed as registered) — every T1 on that journal is struck; or no level of **the head's own registered ladder** reached by both arms — T1 and T2 are VOID on that head and bed; or a T1 difference below the measured noise floor quoted as a ratio; or **a T1 or T2 on a rate-valued head read against the vector ladder's NRMSE-to-oracle units, or on a vector head read against the rate ladder** — struck as V-17, decided by the ladder id printed in the cell against the head's class in 04.8's table, $0$ GPU-s. Instrument: the arena of 04.9 re-run with the timer edits (--seq-lenflag, twosynchronize()calls, randomised order — the edits the record priced at $206$–$537$ GPU-s and never made, READV20_R15_THEORY_TABLE.md:104-109 @ 99777ab); price the band only. **Planted negative — the confound is injected inside one arm, never across two.** The earlier plant (all shape cells first, then all control cells) is **struck as confounded by the very arms it was meant to control**: with a perfectly stationary clock a serial cross-arm order still reads $|\rho|=1$ whenever the two arms differ in per-step cost, and this book's own figure for that difference is $2.514-1.473=1.041$ ms/step at $n=2048$ (RUN[NEPTUNE]), so the plant fires on a clock with no drift at all and certifies nothing about the detector (V-15, C17). The plant that replaces it uses **one arm only**: the same arm — the depth-1 softmax control — is run twice, serially, over $N\ge16$ interleaved cells — $8$ seeds $\times\ 2$ runs $=16$ arm-cells under the Hypotheses' arm-cell reading of $N$, so the plant is affordable at the registered seed count — with an injected **monotone background occupancy ramp** on the device (a competing allocation grown step by step across the run, registered inproducer_cmdand journalled withrun_index), and the requirement is $|\rho|>0.5$ at $p<0.05$ computed **across those same-arm timings alone**. Because both timing series come from one arm, a per-step cost difference between arms cannot produce the correlation, and only the injected drift can; the detector therefore fires on a known-drifting clock and on nothing else. The unramped same-arm pair is retained beside it as the must-not-fire half: the same arm twice with no ramp must read $|\rho|\le0.5$ or $p\ge0.05$. Both plants readNOT MEASURED — needs the synchronised, interleaved arena. **If killed — link 1.** T2 alone: draws-to-floor is order-invariant and needs no timer; the ratio is read from the journal's per-step eval trace. *Hypotheses:* the eval trace is journalled per step (04.15 fieldeval_trace); the identical-seed floor is $0.0$ so a crossing step is exact per seed. *Evidence:* $\delta_{\rm nrmse}=0.0$ on $6/6$ identical-seed pairs (RUN[WATSON]`). Kill: no level of the head's own registered ladder reached by both arms — decided from the same journal at $0$ GPU-s, cheaper than the timer re-run. If killed — link 2. The per-step cost model stays DERIVED and the sentence "faster to train" is withdrawn; the kernel book's cost law (03) is the only route back. Kill: a ratio quoted from the MAC model as a training-speed number — struck (P-8). Terminal.** "No 'faster to train' sentence is licensed on any bed; the cost model is a MAC count and the measured increment is a per-op floor under a $2.0\times$–$6.6\times$ dispatch gap." Withdrawn: T1 and T2 everywhere.

Part IV — Controls, binds, manifests and censuses#

04.11 — The control arms per bed, and the column-sink control (B21)#

Statement. The roster below is a specification, not a set of arms: of its thirteen members exactly one — the depth-1 softmax — is FOUND, and the whole remainder is NOT MEASURED — needs the control-arm implementations (one make_arm branch, one optimizer path and one field emit per control, priced as 04.14 prices the W2 route at $41$–$130$ GPU-s per branch). Under 04.14's own rule an arm is FOUND iff results/ holds a record with its kind, and a named arm is struck; the kind census this session returns $24$ distinct kinds and not one of them names any member of this roster except softmax, so 04.14 strikes every comparative sentence this verse could carry. The roster, as the specification the branches must implement, on byte-identical draws at matched parameters: the depth-1 softmax with the same head (FOUND, kind softmax, $227$ records); ChaCAL-diag (the shape with $\mathcal A=\emptyset$, diagonal kept, at the shape's trained $\hat\gamma$ — sequential, order stated) NAMED; ChaCAL-published (diagonal removed inside the inverse, sub-stochastic) NAMED; ChaCAL-with-sink-token (a column device standing in for the row condition — the K-E1 control) NAMED; the InfSA-style Neumann read at $K=16$ without boundaries NAMED; the cached-mixture arm $O_{\rm cached}=\hat P_{\rm base}(I-\gamma\hat P_{\rm base})^{-1}V_{\rm int}$ (K-G1) NAMED; the argmin controls (0-hop MLP, 1-hop softmax, majority, random, predict-the-mean) NAMED; and the three skylines at unmatched depth, width and decode length NAMED. K-E1's direction is stated the way D-CALIB and the Preface state it, not inverted: K-E1 — a column sink reproduces the row condition — is the counter to this canon's mechanism claim that boundary rows are not a column device, and under D-CALIB the counter is the point estimate for every unscored prediction, so K-E1 is the reported point estimate on every bed of this book until a cell scores it. The canon's own prediction (the two differ) is the unscored side and carries nothing. Hypotheses. ChaCAL-with-sink is defined only after the shape trains (its $\hat\gamma$), so the pair is sequential and the order is in the manifest (M-2 in potential form); every control is FOUND under results/ with its own kind before it is named in a table — this second hypothesis is false at the time of writing and is the reason the verse's own kill is unreachable: twelve of the thirteen members have no record and no implementation, so every clause of the Statement that compares two arms is asserted under a hypothesis that does not hold. Evidence. ChaCAL's read and its $\gamma=0.9$ setting CITED [V] fagnou-2024-chacal Eq. 5, App. C; the sink literature CITED [V] xiao-2023-attentionsinks, gu-2024-sinkemerges, ranmilo-2026-attentionsinks; the record's value-zero column sink V15Fork.Asink (READ lean/CEQ/V15Fork.lean:67-70) is a column device distinct from the row condition; Zhu's clamped nodes CITED [V] zhu-2003-harmonic are the same rows, 23 years old; the successor-representation mechanism momennejad-2017-sr is [U]. The roster's own census, RUN this session: grep -rniE 'chacal|infsa' --include='*.py' . (excluding .venv) returns $0$ lines — no ChaCAL and no InfSA arm exists anywhere in the tree; and grep -rho '"kind": *"[a-zA-Z_0-9]*"' results --include='*.jsonl' | sort | uniq -c returns $24$ kinds — arm_smprime 425, arm_pl 422, softmax 227, rung 40, census 31, pivot_signed 11, pivot_unsigned 11, welch 5, summary 4, mc_random_unit 4, kirchhoff 4, probe 3, provenance 2, constant_g 2, windowed_signed 1, scramble_residual_shipped 1, scramble_residual 1, reproduce_check 1, recovery_check 1, real_key_directions 1, not_generated 1, naive_yield 1, halt_demo 1, band_miss 1 — holding $0$ records for chacal_diag, chacal_published, chacal_with_sink, infsa_neumann_16, the cached mixture, majority, random, predict_the_mean and every skyline. Prices, repriced to what the tree supports: $1.680$ s per shape cell is [FITTED + RUN] on arm_smprime (READ docs/CEQ_SHAPE.md:2297-2298) and $1.524$ s per softmax cell is [FITTED]; per ChaCAL cell the figure is [ASSUMED] the arm_smprime cell time stands in for a ChaCAL cell, the reason being that ChaCAL-diag is the shape's own solve at $\mathcal A=\emptyset$ and differs from it by the boundary rows alone, and the same [ASSUMED] carries the three-arm figure. That figure is $\approx44.3$ s and not $\approx52$ s, and the arithmetic is printed here because the verse's own price contradicted itself by $18$ per cent: $3\times8\times1.680+4.0=44.32$ s for three arms at eight seeds, where $4.0$ s is the arena's fixed set-up overhead carried at the same [ASSUMED] class as 04.9's $7\times8\times1.680+4.0\approx98$ s; no overhead term carries the missing $7.7$ s, so $\approx52$ s is struck (P-1, M-16). The same arithmetic prices one pair at $\approx30.9$ s ($2\times8\times1.680+4.0=30.88$ s), which replaces the $\approx34$ s carried in 04.6's Bet E instrument, in 04.5's link 2 and in the kills table. InfSA-16's $\approx5.12$ s per cell is not derivable from the $25.409$ ms hop and is no longer classed as if it were: $16\times25.409\,\mathrm{ms}=0.407$ s, a factor $12.6$ below $5.12$ s, so the source's own words "DERIVED from the $25.409$ ms hop microbenchmark" (READ docs/CEQ_SHAPE.md:1926 @ 99777ab) do not reproduce and a DERIVED class with no steps is a P-1 defect. What reproduces is one multiplication at the registered cell length: $150$ steps per cell $\times\ 0.034133$ s/step $=5.11995\approx5.12$ s (DERIVED, one multiplication), where the $150$-step budget is the record's own registered cell length (READ scale/e_ladder.py:140, steps=150) and the $0.034133$ s/step is $5.12/150$ read back out of the source figure. The pair is therefore an unreproduced source figure with its class printed — $\approx5.12$ s enters this book as READ docs/CEQ_SHAPE.md:1926 @ 99777ab, unreproduced, on top of the same assumed basis — and book 06 reads it identically at 06.28. 04.9's $\approx3.3$ GPU-min arena figure ($98+8\times7.6+8\times5.12=199.8$ s) rests on the $5.12$ and inherits that tag beside its own [ASSUMED] basis. The "ChaCAL must emit chance" control deleted (V-2). No price in this verse is [FITTED + RUN] for an arm that has no implementation, which is what the earlier [FITTED + RUN] on the ChaCAL cell was. Mechanism. V-24, V-3, M-13, R-SKY, D-1, P-10, V-2. Kill (K-E1) — registered UNREACHABLE, therefore not a kill. As written K-E1 reads: ChaCAL-with-sink within $\mathrm{MDE}_N$ at the realised $\sigma_d$ (04.9 clause 7; NOT MEASURED — needs $\sigma_d$ from 04.21 step (5)) of the shape's committor $\varphi$-NRMSE on $\ge6$ of $8$ seeds and its harmonic residual within $2\times$ of the shape's, whereupon component (e) is a parameterisation of a column sink; instrument, the pair of 04.9 at $\approx30.9$ s [ASSUMED] ($2\times8\times1.680+4.0$, the pair arithmetic of the Evidence, which replaces the $\approx52$ s three-arm figure this clause carried out of its own arm count); never "within TOST" at $N=8$; planted negative, ChaCAL-published's $A_s$ differing from the shape by $O(1)$ at every $\gamma>0$. It cannot fire on the bed as registered, because neither ChaCAL-with-sink nor ChaCAL-diag nor ChaCAL-published exists: $0$ grep hits in the tree, $0$ records under results/. Under the CHARTER's Reachability rule a kill that cannot fire is not a kill, so K-E1 is not in force, the verse carries no comparative sentence, and the chain below carries the verse. K-E1 becomes decidable only when at least ChaCAL-diag and ChaCAL-with-sink are FOUND under their own kind; the price of reaching it is link 2's, not $\approx30.9$ s. If killed — link 1 (operative today): the same question asked of the operator, with no arm at all. The claim "boundary rows are not a column device" is decided on the environment chain the bed already builds, never on a trained arm: for each admitted draw of 04.2, solve the absorbing read $\Pi_{\rm row}$ — $\mathcal A$ as identity rows, $q^{(k)}=(I-Q)^{-1}R_k\mathbb 1$ — and the column read $\Pi_{\rm col}$ — $\mathcal A$'s rows left transient and a value-zero sink column appended in the record's own V15Fork.Asink form — both in float64 on the same $P_{\rm env}$, and print $\|\Pi_{\rm row}-\Pi_{\rm col}\|_\infty$ over the transient block per draw. This is a different object (the environment chain, not an arm), a different instrument (one dense exact solve pair on the bed's generator, no training, no seeds, no matched parameters) and a different number (an operator $\infty$-distance, not a $\varphi$-NRMSE difference against $\mathrm{MDE}_N$) — it is not a rename of K-E1 and does not die with it, and its own threshold $10^{-12}$ is a float-noise constant of the exact solve, not a placeholder waiting on $\sigma_d$. Hypotheses: $\rho(Q_{\rm env})<1$ so both reads exist (04.2 gives $\rho(Q_{\rm env})=0$ exactly, DERIVED); the sink column carries value $0$ on every indicator channel, which is the record's own device; the comparison is over the transient block only, where both reads are defined. Evidence: the record's value-zero column sink V15Fork.Asink (READ lean/CEQ/V15Fork.lean:67-70) is the column device this link instantiates; the row device's downstream weight statement reads $\|\Pi_{\rm shape}-\Pi_{\rm ChaCAL\text{-}diag}\|_\infty\ge0.1$ with rows changed $=[3]$ on the bind B-E1 instance (READ docs/CEQ_SHAPE.md §6 A.8, 04.13); the two-read comparison itself is NOT MEASURED — needs the two-solve column added to the admission census of 04.2, $0$ GPU-s, no arm and no make_arm branch. Kill: $\|\Pi_{\rm row}-\Pi_{\rm col}\|_\infty<10^{-12}$ over the transient block on $\ge95$ per cent of the $512$ admission draws — the row condition is a column device at the level of the operator, K-E1 is settled in the counter's favour with no arm ever trained, component (e) is struck, and every bed of this book loses its mechanism sentence. Planted negative: a draw built with $\mathcal A=\emptyset$ must read $\|\Pi_{\rm row}-\Pi_{\rm col}\|_\infty=0$ bitwise, since with no absorbing row the two constructions are the same matrix — a known-identical plant on which the detector must fire, which is the V-15 control the arena kill never had. Price $0$ GPU-s, $0.5$ evening — strictly cheaper than the verse's own unreachable kill and than link 2. If killed — link 2: the FOUND route back, priced as 04.14 prices W2. If the operator read cannot separate or cannot be run, the only route to a comparative sentence is implementation: one make_arm branch per control, an optimizer path and a field emit, on the arm_pl basis of 04.14 ($5.114$ s per cell, $41$–$130$ GPU-s per branch), taken for ChaCAL-diag and ChaCAL-with-sink first because K-E1 needs exactly those two. Hypotheses: the branch emits its own kind and manifest_hash (04.15), so the census of 04.14 can see it. Evidence: the W2 route and its price READ docs/CEQ_SHAPE.md §4.4; the two-way calibration of the census (04.14); $0$ grep hits for chacal today (RUN this session). Kill: after the route is taken the census still reads $0$ for chacal_with_sink — the branch was written and never run (D-6), the control is permanently NAMED, K-E1 is never decidable on any bed, and component (e) carries no comparative credit ever. Price $82$–$260$ GPU-s for the two branches, $2$ evenings — not cheaper than link 1, and admitted only on being strictly more decisive: it settles FOUND-ness permanently where link 1 settles one operator distance. Terminal. "No control arm of this roster is FOUND except the depth-1 softmax: the tree holds $0$ ChaCAL and $0$ InfSA source lines and $24$ record kinds, none of them a control of this verse. The canon licenses the roster as a specification with its prices marked [ASSUMED], and licenses K-E1 as the point estimate under D-CALIB with no cell behind it." Withdrawn: every sentence comparing the shape to ChaCAL-diag, ChaCAL-published, ChaCAL-with-sink, InfSA-Neumann-$16$, the cached mixture, the argmin controls or any skyline; component (e) as a mechanism; and every price in this book that was quoted [FITTED + RUN] for an unimplemented arm.

04.12 — The ChaCAL convention check (B22)#

Statement. Two control arms of 04.11 depend on one bibliographic fact — whether ChaCAL removes the diagonal inside the inverse — that rests on one HTML fetch. The check is decided by the operator, not by the citation: the arm named ChaCAL-published computes $(1-\gamma)A(I-\gamma A_s)^{-1}V$ with $A_s=A-\mathrm{diag}(A)$ and must read sub-stochastic row sums; the arm named ChaCAL-diag keeps the diagonal and must read row sums $1.000$; the manifest field diag_convention ∈ {kept, removed} names which is which on every cell, and the attribution "published" is a label on the manifest, never on the arithmetic. Before typesetting, the sentence is re-read from the arXiv LaTeX source of 2410.05565, never from a rendered page. Hypotheses. $\gamma>0$; $A$ a causal softmax at $\beta=1$ so $A_s$ is strictly lower and $(I-\gamma A_s)^{-1}$ is a finite sum; $A_s\mathbb 1=\mathbb 1-\mathrm{diag}(A)<\mathbb 1$. Evidence. [V-fetched] by one refuter from arxiv.org/html/2410.05565: "we remove the diagonal part of the adjacency matrix in the inverse" (READ docs/sources/design/refute_falsify_math.md §3.15); the sub-stochastic reading RUN[J] row sums $0.400\dots0.765$ against $1.000$ diagonal-kept (READ docs/CEQ_SHAPE.md §2.0); the extractor hazard the record paid for once — pypdf mapped $-$ to \x00 and $\infty$ to the glyph 1, turning an open interval into a closed one (READ workdonenewseal.md:468-473; V15_X36_PRIOR_ART.md:45-56 @ 99777ab); the bibliography verified at the identifier not the equation: $278/278$ arXiv, $91/92$ DOI (READ docs/CEQ_SHAPE.md §8). No LaTeX source has been read: NOT MEASURED — needs one fetch of the arXiv source, an author action outside this canon's no-fetch rule. Mechanism. P-10, V-24, V-3 (the identity half is against the lane's own re-implementation), P-6, FOUND-not-NAMED (neither arm exists; the kill's earlier reason presumed both did), V-15 (a plant that needs an arm that does not exist is itself NAMED), P-4. Kill. The LaTeX source contradicts the HTML reading (ChaCAL keeps the diagonal): the labels swap on the manifest, and every table row naming "ChaCAL-published" is re-labelled in a corrections row; price $0$ GPU-s, no cell re-run. The reason the relabelling costs nothing is restated, because the earlier reason was false. It is not that both arms are FOUND: neither is, and a relabelling would touch cells that do not exist — RUN this session, grep -rniE 'chacal|infsa' --include='*.py' . (excluding .venv) returns $0$ lines, and the $24$-kind census over results/**/*.jsonl holds $0$ records for chacal_diag and $0$ for chacal_published (04.11, 04.14). The relabelling is free because the convention question is decided before either arm exists, so there is nothing to relabel: the decision fixes which arithmetic a future make_arm branch emits under which name, and it is taken at specification time, at $0$ GPU-s, with no journal touched. Both arms are marked NOT MEASURED — needs the ChaCAL control implementations (one make_arm branch, one optimizer path and one field emit per control, $41$–$130$ GPU-s per branch on 04.14'sarm_plbasis), and no sentence of this verse compares them on any bed. Planted negative — priced with no arm at all. The earlier plant ("the two arms must differ by $O(1)$ at $\gamma=0.9$ on the same $P$") required two arms that do not exist and was therefore itself NAMED, which 04.13's own Kill strikes ("any plant that exists only in a script's print (NAMED)"). It is replaced by a pure arithmetic assertion on a pinned random causal softmax $A$, checkable at $0$ GPU-s with no arm, no make_arm branch and no journal: on every row $i$, $(A\mathbb 1)_i=1$ and $(A_s\mathbb 1)_i=1-A_{ii}<1$ strictly, the strictness carried by $A_{ii}>0$ for a causal softmax (the bed's own diagonal read is $\max_i\hat P_{ii}=0.692660$, 04.2), and the printed gap is $\min_i A_{ii}$. The must-fire half: an $A$ built with its diagonal logit at $-\infty$ makes $A_s=A$, the gap reads $0$ exactly, and the check must report the two conventions indistinguishable — the known-degenerate case the assertion fires on. If the assertion cannot be evaluated on a pinned instance, the convention field is not wired and the kill cannot see it. If killed — link 1: the question asked of the operator, with no arm and no label. If the LaTeX read swaps the labels, the canon does not chase the naming; it asks whether the distinction the names carry is non-empty on this book's own bed, on an object no arm touches. On each admitted draw of 04.2, take the causal softmax $A$ at $\beta=1$ built from the bed's own $P_{\rm env}$ features, form both operators in float64 at the paper's own $\gamma=0.9$, and print $$\Delta_{\rm conv}=\big\|(1-\gamma)A(I-\gamma A)^{-1}-(1-\gamma)A(I-\gamma A_s)^{-1}\big\|_\infty,\qquad A_s=A-\mathrm{diag}(A).$$ This is a different object (the bed's environment-derived matrix, not either named arm), a different instrument (one dense solve pair per draw on the admission census, no training, no seeds, no matched parameters, no kind) and a different number (an operator $\infty$-distance, not a manifest label or a row-sum), so it does not die with the verse's kill. Hypotheses: $\gamma=0.9<1$ and $A_s$ strictly lower triangular, so both inverses are finite sums and both operators exist on every draw; the read is over the $512$ admission draws of 04.2 and rides on the census the bed already runs. Evidence: the sub-stochastic gap $0.400\dots0.765$ against $1.000$ is a property of the arithmetic (RUN[J]), independent of which paper ran it; the diagonal read $0.692660$ on the arm's causal softmax (READ docs/CEQ_SHAPE.md:2547 @ 99777ab); $\Delta_{\rm conv}$ itself is NOT MEASURED — needs the two-operator column added to the admission census of 04.2, $0$ GPU-s, no arm. Kill: $\Delta_{\rm conv}<10^{-12}$ on $\ge95$ per cent of the $512$ draws — the two conventions are the same operator on this bed, the distinction is empty here, both ChaCAL rows leave 04.11's roster as indistinguishable controls, and no corrections row is owed whichever way the LaTeX reads. Planted negative: a draw whose $A$ carries its diagonal logit at $-\infty$ gives $A_s=A$ and must read $\Delta_{\rm conv}=0$ bitwise — a known-identical plant the detector must fire on. Price $0$ GPU-s, $0.5$ evening. Terminal. "Two fellow approximators differing by the diagonal inside the inverse are specified and neither is run: $0$ ChaCAL source lines and $0$ ChaCAL records exist. The canon asserts the arithmetic — $A\mathbb 1=\mathbb 1$ against $A_s\mathbb 1=\mathbb 1-\mathrm{diag}(A)<\mathbb 1$ — and asserts nothing about which one a published paper ran." Withdrawn: every sentence attributing a diagonal convention to fagnou-2024-chacal without the LaTeX read (struck at assembly under L-EQ, decided by a grep for the bib key beside the word "diagonal", $0$ GPU-s), and every sentence comparing the two named arms on any bed.

04.13 — The binds, with planted negatives and the $O(1)$ failure each must produce (V-24)#

Statement. A bind is admissible only if its honest construction passes and every planted mutilation fails at $O(1)$ with the counts printed, and every plant enters at the front door — bed.build → arm.forward → journal row → verdict() — as a FOUND cell with its own kind and manifest_hash, never as an identity check on random logits. | bind | identity half (must pass) | plants (each must fail at $O(1)$) | plants found empty and struck | |---|---|---|---| | B-J parity at $\gamma=0$ | torch.equal(O(0), PV) against the lane's own softmaxAttn | $\gamma=0.5\Rightarrow2.3003$; $\beta=0\Rightarrow\max\lvert{\rm gap}\rvert>0.5$; ChaCAL-published's $A_s\Rightarrow O(1)$ at every $\gamma>0$ — NOT MEASURED — needs the ChaCAL control implementations, struck as a plant of this bind | a non-causal $W$ passes bitwise at $\gamma=0$ since $(I-0W)=I$ (moved to B-P5) | | B-E1 boundary rows | $\mathcal A=\emptyset\Rightarrow$ torch.equal with ChaCAL-diag — NOT MEASURED — needs the ChaCAL control implementations, struck as this bind's identity half and replaced by the arm-free operator identity of 04.11 link 1: $\mathcal A=\emptyset\Rightarrow\|\Pi_{\rm row}-\Pi_{\rm col}\|_\infty=0$ bitwise on the bed's own $P_{\rm env}$ | $\mathcal A\ne\emptyset\Rightarrow\|\Pi_{\rm shape}-\Pi_{\rm ChaCAL\text{-}diag}\|_\infty\ge0.1$ on downstream rows (a weight statement, rows changed $=[3]$) — the statement stands and its number is NOT MEASURED — needs the ChaCAL control implementations; the plant that stands today is the operator-level one, $\mathcal A\ne\emptyset\Rightarrow\|\Pi_{\rm row}-\Pi_{\rm col}\|_\infty\ge10^{-12}$ | a non-identity absorbing row breaks $\sum_kq=1$ — reads $0.0$ (the sum uses transient rows only); replaced by the full-$P$ read at $\gamma<1$, $0.1491$ | | B-E2 conservation | $q^{(\rm sink)}+q^{(0)}+\sum_kq^{(k)}=\mathbb 1$ on $T$ to $10^{-12}$ ($4.4\times10^{-16}$) | drop BOS $\Rightarrow$ the solve raises ($\rho(Q)=1$); a set after the query $\Rightarrow q=0.0$ and discard | drop $\mathcal A_0\Rightarrow\max_kq\ge1/K$ — cannot run (BOS drop is singular); carried as a proposition | | B-G1 re-solve | $V\equiv\mathbb 1\Rightarrow\max\lvert\Delta z\rvert\le10^{-15}$; Sherman–Morrison vs re-solve $\le10^{-12}$ ($1.2\times10^{-15}$); C6 residual $\le10^{-12}$ | Gaussian $V\Rightarrow0.1096/0.363/1.127$; non-causal $P\Rightarrow\Delta z[:i]=0.0761/0.0868$ (triangularity); a two-row edit breaks rank one, repaired by Woodbury | the EMC feedback plant — for $\gamma<1$ the fixed point is unique on every $P$ ($1.33\times10^{-15}$, $4.4\times10^{-16}$ on dense cyclic $P$) | | B-G2 metric | the journal carries the vector, histogram, quantiles | the three plants of 04.8 | — | | B-H1 committor | $q=(I-Q)^{-1}R\mathbb 1$ vs bed_1.committor on the real sets $0.0$; the script raises on a missing key | the perturbation drives the residual $1.04\times10^{-17}\to10^{-6}$ (ratio $9.6\times10^{10}$); the wrong set moves $q$ by $O(1)$; Kirchhoff $<10^{-10}$ at $K=2$ | the basin_A default that read $0.858$ (V-16) | | B-H2 argmin | the oracle tensor's argmin equals the label's on $100$ per cent | the planted leak $R^2\ge0.99$; the 0-hop MLP inside the half-width strikes the bed | — | | B-K containment | [M] targets build with zero sorry; corner 3 vs $(I-A)^{-1}$ $0.0$; last row $6.217248937900877\times10^{-15}$; segmentation zeros by torch.equal | keeping the diagonal breaks $A^s=0$; a $-30$ logit leaves the block non-zero ($e^{-30}=9.36\times10^{-14}$) | the $10^{-300}$ plant — float64 underflow after $\ge80$ gates at $0.5$ reads F0 | | B-P5 solve | solve_triangular vs dense inverse $1.8\times10^{-15}$ | a dense non-triangular $M$ with upper=False must disagree | — | Two ChaCAL-dependent entries are struck from the table by this verse's own Kill. RUN this session: grep -rniE 'chacal|infsa' --include='*.py' . (excluding .venv) returns $0$ lines and the $24$-kind census over results/**/*.jsonl holds $0$ records for chacal_diag and chacal_published, so B-J's third plant and B-E1's identity half exist only as prose — NAMED — and the Kill below reads "any plant that exists only in a script's print (NAMED)". They are marked NOT MEASURED — needs the ChaCAL control implementations above rather than quietly retained. B-J is admissible on its remaining plants only ($\gamma=0.5\Rightarrow2.3003$; $\beta=0\Rightarrow\max|{\rm gap}|>0.5$), and B-E1 is admissible on the rows-changed weight statement plus the arm-free operator identity of 04.11 link 1 only; neither bind carries a ChaCAL sentence, and 04.11's Terminal already withdraws every such sentence from this book. Every number in the table is inadmissible-until, not admissible-with-a-hypothesis. The Statement requires every plant to enter at the front door — bed.build → arm.forward → journal row → verdict() — as a FOUND cell with its own kind and manifest_hash, never as an identity check on random logits; every number in the third and fourth columns was obtained on a random-logit instance (seed 0, $s\in\{32,64\}$, float64, CPU) and therefore violates the Statement's own front-door rule as it stands. Each is accordingly marked NOT MEASURED at the front door — needs the first BED-S cell (04.21 step 2): the printed value is a float instance carried as the target the front-door reproduction must hit, not as an admitted bind number. No bind of this table is admissible until 04.21 step (2) reproduces its plants through the front door, and that reproduction is priced in 04.21's ordered list at $\approx9\times1.680\approx15.1$ s [ASSUMED] on the arm_smprime cell basis (nine bind rows, one admitted draw each), $0.5$ evening. A verse elsewhere in the canon citing a bind number without that reproduction cites a NOT MEASURED figure and is struck at assembly. Hypotheses. The bed of 04.2 admits and its census is journalled, so a front-door draw exists to reproduce on; the arm of the reproduction emits its own kind and manifest_hash (04.15); the random-logit values above are the reproduction's targets and are not themselves bind evidence. Evidence. The pattern $0.9749/0.9165/1.000/0.4845$ — four mutilations, four $O(1)$ failures (READ workdonenewseal.md:114-122; MISTAKES.md:1658-1722, V-24); every number in the table READ docs/CEQ_SHAPE.md §6 A.8 and §6 A.2 with the planet's RUN[x] class as recorded there; the front-door rule READ MISTAKES.md:238-288 (V-14: 366 candidate files became 0 and the matcher-only control stayed green); the FOUND rule READ V20_R15_WING_MANIFEST.md:59-63 @ 99777ab. Mechanism. V-24, V-3, V-14, V-16, V-2, V-10, FOUND-not-NAMED (the two ChaCAL entries are NAMED and this verse's own Kill strikes them), V-15, P-1. Kill. Any plant passing, or any plant that exists only in a script's print (NAMED). Instrument: the plant register of docs/PLAN.md S-28 — one table per bind with kind, manifest_hash, journal path, the $O(1)$ number and the verdict line that consumed it; price seconds. The planted negatives are the table's third column; the kill's own control is the calibration of the kind census both ways (04.14). If killed — link 1: the bind is re-derived arm-free, on the operator, and only then relabelled. The earlier link ("relabel the bind an instrument test; the remaining plants stand") died with the verse on the two ChaCAL rows, because for B-E1 the struck entry was the identity half itself and no plant remained to stand. The replacement does not rename it: each bind whose identity half or plant needed an arm that does not exist is restated on the environment chain the bed already builds, with no arm, no kind and no journal row — B-E1's identity half becomes $\mathcal A=\emptyset\Rightarrow\|\Pi_{\rm row}-\Pi_{\rm col}\|_\infty=0$ bitwise and its plant becomes $\mathcal A\ne\emptyset\Rightarrow\|\Pi_{\rm row}-\Pi_{\rm col}\|_\infty\ge10^{-12}$, both on $P_{\rm env}$ in float64 (04.11 link 1); B-J's ChaCAL plant becomes the diagonal arithmetic of 04.12's replaced plant, $A_s\mathbb 1=\mathbb 1-\mathrm{diag}(A)<\mathbb 1$ strictly with the gap $\min_iA_{ii}$ printed. Only a bind that survives with no arm-free identity half and no arm-free plant drops to a remark under the EMC precedent. Hypotheses: $\rho(Q_{\rm env})=0$ exactly on the bed (04.2, DERIVED), so both operator reads exist on every admitted draw; the restated halves are computed on the admission census of 04.2, which runs with no arm. Evidence: the EMC proposition retired to a remark after its feedback plant read $1.33\times10^{-15}$ (READ docs/CEQ_SHAPE.md §2.2 Remark); the record's value-zero column sink V15Fork.Asink (READ lean/CEQ/V15Fork.lean:67-70) is the column device the restated B-E1 instantiates; both operator reads are NOT MEASURED — needs the two-solve column added to the admission census of 04.2, $0$ GPU-s, no arm. Kill: the restated arm-free half is itself satisfied by construction — $\|\Pi_{\rm row}-\Pi_{\rm col}\|_\infty=0$ on the $\mathcal A\ne\emptyset$ draws as well as on the $\mathcal A=\emptyset$ ones, on $\ge95$ per cent of the $512$ draws — in which case the bind separates nothing at the operator level either, drops to a remark, and the remark quoted as a bind anywhere is struck at assembly; price $0$ GPU-s, decided from the census before any arm exists, which is strictly cheaper than reproducing any plant through the front door. If killed — link 2. The arm is not trained (L-LEAN): a bind that cannot fire licenses no identity theorem as green, and no arena cell exists. Kill: an arena cell dated before the bind's plant register — struck with the cell; the most decisive link because it produces no number at all. Terminal. "The identities the binds certify are float instances on random logits with printed plants; not one of them has entered at the front door, no bind of this table is admissible until 04.21 step (2) reproduces it there, and no bind whose plant passed is cited." Withdrawn: B-J's ChaCAL-published plant and B-E1's ChaCAL-diag identity half, both NAMED at $0$ source lines and $0$ records; every bind number quoted anywhere in the canon as an admitted bind rather than as a front-door target.

04.14 — FOUND-not-NAMED: the `kind` census and the W2 route back (B20)#

Statement. An arm is FOUND iff results/ holds at least one journalled record whose kind field is the arm's name; otherwise it is NAMED and every sentence about it is struck. The census is calibrated both ways on every run, and both ways are read against the printed emitter set, never against absence: one declared emitter must read $0$ (arm_phase, NAME = "arm_phase" at ceq/arm_phase.py:60, one of the eighteen declared emitters with no record) and the control must read above $0$ (arm_smprime, $425$ records, NAME = "arm_smprime" at ceq/arm_smprime.py:77). A kind that is absent from the census output and absent from the emitter set is not a zero and is NOT MEASURED; only a kind in the emitter set that the census does not return reads $0$. W2 (arm_phase) is NAMED; the route back is one make_arm branch, an optimizer path and a field emit, eight cells at $5.114$ s each on the arm_pl basis, $41$–$130$ GPU-s. Hypotheses. The census walks results/**/*.jsonl and counts records, not files; the counter's reach is measured, not asserted — its lower bound is the $33$-kind emitter set of the Evidence (^NAME = "…" plus literal "kind": "…" under ceq scale scripts, RUN this session), and its upper bound is unmeasured, since $9$ of the $24$ observed kinds are spelled at no emit site those two greps see (V-14's paired check, now with both sides printed). Evidence — the census printed in full, because its unquoted rows are the population the second kill clause audits. RUN this session, grep -rho '"kind": *"[a-zA-Z_0-9]*"' results --include='*.jsonl' | sort | uniq -c | sort -rn returns all $24$ distinct kinds and no others, and all $24$ are printed here rather than seven: arm_smprime 425, arm_pl 422, softmax 227, rung 40, census 31, pivot_unsigned 11, pivot_signed 11, welch 5, summary 4, mc_random_unit 4, kirchhoff 4, probe 3, provenance 2, constant_g 2, windowed_signed 1, scramble_residual_shipped 1, scramble_residual 1, reproduce_check 1, recovery_check 1, real_key_directions 1, not_generated 1, naive_yield 1, halt_demo 1, band_miss 1. The earlier Evidence printed seven of these and asserted the eighth absent; the seventeen it dropped without an ellipsis — welch, summary, mc_random_unit, kirchhoff, probe, provenance, constant_g, windowed_signed, scramble_residual_shipped, scramble_residual, reproduce_check, recovery_check, real_key_directions, not_generated, naive_yield, halt_demo, band_miss — are exactly the rows the second kill clause reads, so quoting a subset made that clause unauditable (P-1, V-7). A zero is made a zero against a known emitter, because "absent from the output" is not "reads $0$". A uniq -c census cannot distinguish a kind emitted zero times from a kind never spelled that way or emitted outside results/**/*.jsonl, so the emitter set is enumerated from the sources and intersected with the census, and both sets are printed. RUN this session, grep -rhoE '^NAME = "[a-zA-Z_0-9]+"' ceq scale scripts --include='*.py' returns $13$ declared arm names — arm_a_k1, arm_phase, arm_pl, arm_smprime, ceq, ceq_hybrid, chase_eprocess, chase_m3_synth, m2, m3_quintuple_v2, r2, s2, wilson_arms — each emitted as "kind": NAME; RUN this session, grep -rhoE '"kind" *: *"[a-zA-Z_0-9]+"' ceq scale scripts --include='*.py' | sort -u returns $20$ literal kinds — band_miss, census, constant_g, demo, generator, halt_demo, kaggle_attach, kaggle_attach_sliced, kaggle_attach_streamed, kirchhoff, naive_yield, not_generated, probe, provenance, raw_bytes, recovery_check, refusal, reproduce_check, rung, summary. The two sets are disjoint, so $33$ kinds are declared emitters under ceq scale scripts. Intersected with the census: $15$ declared emitters have records (arm_smprime, arm_pl, rung, census, summary, kirchhoff, probe, provenance, constant_g, reproduce_check, recovery_check, not_generated, naive_yield, halt_demo, band_miss) and $18$ declared emitters read $0$ (arm_phase, arm_a_k1, ceq, ceq_hybrid, chase_eprocess, chase_m3_synth, m2, m3_quintuple_v2, r2, s2, wilson_arms, demo, generator, kaggle_attach, kaggle_attach_sliced, kaggle_attach_streamed, raw_bytes, refusal). W2's zero is one of the eighteen: NAME = "arm_phase" is declared at READ ceq/arm_phase.py:60 (RUN this session), so arm_phase 0 is a zero against a known emitter and not an inference from absence, which is the only reading under which the Kill's first clause is decidable. The counter's reach is bounded on the other side too, and the bound is printed rather than assumed away. $9$ of the $24$ observed kinds match neither grep — softmax 227, pivot_unsigned 11, pivot_signed 11, welch 5, mc_random_unit 4, windowed_signed 1, scramble_residual_shipped 1, scramble_residual 1, real_key_directions 1 — because the value is passed as a variable rather than spelled at the emit site (ceq/lm.py:66 asserts kind in ("softmax", "softmax_x", "signed", "sgate", "sgate_nores"), RUN this session) or the emitting file lies outside ceq scale scripts (kaggle/snapshot/repo/attic/, RUN this session). The emitter enumeration is therefore a lower bound on what the tree can emit, and this verse says so: a kind reading $0$ and appearing in the $33$ is a measured zero; a kind reading $0$ and appearing in neither set is NOT MEASURED — needs the emit-site enumeration extended past literal spellings (a call-graph read of everykind=keyword argument), an instrument this book specifies and does not write. The record's own census at the pin read arm_pl 191, softmax 182, arm_smprime 182, arm_phase 0 (READ docs/CEQ_SHAPE.md §4.4); the two counters differ on the positives (a record-count against a deduplicated cell-count) and agree on the zero, which is the calibrated reading. The route and its price READ docs/CEQ_SHAPE.md §4.4; the discriminator READ V20_R15_WING_MANIFEST.md:59-63 @ 99777ab. Mechanism. FOUND-not-NAMED, V-7, V-14, P-4, P-1. Kill. After the route is taken, arm_phase still reads $0$ by this census while remaining in the emitter set — the branch was written and never run (D-6), and W2 is struck permanently. The second clause is restated, because as written ("the census reads above $0$ for a kind no script emits") it fires today on all nine variable-spelled kinds and is a kill satisfied by construction against its own counter (V-10): it now reads a kind above $0$ in the census that is reachable from no emit site under the extended enumeration, and that enumeration is NOT MEASURED — needs the emit-site enumeration extended past literal spellings, so this half is registered unreachable until the instrument exists and no verse reads it as having fired. What is decidable today, at $0$ GPU-s, is the pair the Statement freezes: arm_phase in the emitter set at $0$ records against arm_smprime in the emitter set at $425$. Price: the $41$–$130$ GPU-s of the route, DERIVED, $0.5$ evening; the two-way calibration against the printed $33$-kind emitter set is the planted negative — the must-fire half is arm_phase, a declared emitter the census returns nothing for, and the must-not-fire half is arm_smprime, a declared emitter it returns $425$ for; a census that returned nothing for both, or a count for both, fails the calibration and the counter is struck. If killed — link 1. W2's four citations stand as citations and never as a wing; the wing identifier is held at its it.1 value so the gap is visible (the record's own rule). Hypotheses: the frozen wing list (FROZEN-N = 2, digest fbf17e07…) is never re-numbered. Evidence: all twelve it.1 citations, W2's four included, resolved at HEAD 207e7b9 (READ V20_R15_WING_MANIFEST.md:155-160 @ 99777ab). Kill: a renumbering that hides the gap — decided by the digest of the eight wing|clause|path:line|anchor rows changing; price $0$ GPU-s. Terminal. "Two wings were FOUND; the third exists in source and prose and the ledger has never seen it. The census reads $24$ distinct kinds, all $24$ printed; the tree declares $33$ emitters under ceq scale scripts, of which $15$ have records and $18$ read $0$; arm_phase is one of the eighteen, so its zero is measured against a declared emitter. Nine of the $24$ kinds are spelled at no emit site the enumeration sees, so the counter's upper reach is NOT MEASURED and the kill's reach-clause is unreachable until the extended enumeration exists."

04.15 — The identity manifest: fields, the drift plant, and the refusal rule#

Statement. A cell is journalled only with the following fields, and a missing declared field is a refusal, never an absent entry: beta, qk, g; gamma (init, final $\hat\gamma$, $\Lambda$, verdict); diag_convention; committor_route ∈ {dirichlet_gamma1, discounted_gamma}; route ∈ {solve_triangular, neumann_K, segmented, csr} with $K$, chunk $C$, tile $B$; boundary_sets, goal_set, sink_set as sorted lists with a sha256 each; K, m, t_star; S, D, d_model, n_train, n_eval, steps; seed, rng_plan; device, threads, dtype, torch_version, cublas_workspace, deterministic_regime; instrument_hash, manifest_hash; producer_cmd; delta_vec, delta_bare, one_over_1mg, V_inf; the census block; floor_exact, floor_zeroinfo, ceiling_hop_k (floor_fano_k1 is struck from this list by 04.3: Fano is never binding against the exact zero-information floor at any $I\ge0$ on a deterministic label, so a journalled Fano field is a number no kill can reach — a cell carrying it is refused, not accepted with the field ignored); sky_depth, sky_width, sky_cot, chacal_gamma, chacal_diag, params_per_arm; void_contrasts; refused_columns (the per-column refusal scope of 04.8, empty list where nothing is refused, so a refusal is never a whole-cell absence); predictions_hash; eval_trace (per-step eval NRMSE, for T2); secs_sync and run_index (for T1); supersedes. The refusal rule makes the absence of a declared field unobservable downstream, and every verse that would kill on absence is told so here. Because a cell missing a declared field is refused at the journal, no cell carrying an absent declared field ever reaches results/, so a downstream kill of the form "a cell journalled with $X$ absent" cannot fire on any cell that exists — it is a gate satisfied by construction (V-10) and a precondition violated at every real draw (V-11). Two consequences are registered: (i) every kill in this book that reads a declared field reads its value, never its presence — 04.1's kill is void_contrasts = [] on a bed whose registered VOID list is non-empty, not void_contrasts absent, and 04.8's refusal scope is refused_columns = [] where nothing is refused rather than a missing field; (ii) the refusal itself is the only observable of an absent field, and it is observable at the file and nowhere else, so a verse that wants a count of absences must read the adjudicator's refusal log and not results/ — a log that is NOT MEASURED — needs the arena adjudicator and its frozen prediction file atresults/arena/PREDICTIONS.sha256` (RUNthis session,ls results/arenareadsNo such file or directory). A verse elsewhere in this canon whose kill reads a declared field's absence is struck at assembly and repointed at that field's value. **The shape'skindis named here, because a lane with no name cannot be counted.** The CEQ shape arm of this canon — the boundary-row resolvent arm of book 08, read on BED-S — is registered withkindarm_ceq, and **no script emits it**:RUNthis session,grep -rn 'arm_ceq' --include='.py' .(excluding.venv) returns $0$ lines, and 04.14's $24$-kind census holds $0$ records forarm_ceq. The $425$arm_smprimerecords the census does read are a **different lane** — the record's complex-chain arm,NAME = "arm_smprime"at READceq/arm_smprime.py:77emitting"kind": NAMEat:346, whose records carry"task": "chain_label_complex"/e3_t2and split $320$t: trace, $48$rescore, $20$cell, $6$bind, $3$agg, $3$identity, $3$probe, $2$contrast(RUNthis session). **The printed discriminator is this verse's ownboundary_setsfield:**RUNthis session,grep -rl 'boundary_sets' results --include='.jsonl'returns $0$ files, so $0$ of the $425$arm_smprimerecords — and $0$ of all records underresults/— declare a boundary set, and none of them is a shape-lane cell under the field list above. A cell is a shape-lane cell iff itskindisarm_ceq**and** it carriesboundary_sets,goal_setandsink_setwith their sha256s; both conditions read $0$ today, and the two counts are printed together so the lane's emptiness is established by a field and not by a name alone. **Hypotheses.** Zero shape-lane cells exist underresults/in the sense just defined — $0$ records withkindarm_ceqand $0$ records carryingboundary_sets(RUNthis session, both counts) — so no published shape-lane hash exists to protect and the record's reason for reporting rather than raising does not apply. The $425$arm_smprimerecords are outside the lane by theboundary_setsdiscriminator and their hashes are untouched by anything in this verse. **Evidence.**CONFIG_FIELDScarriesbetaand notqk,g,gammaand drops a missing field silently, reportingabsentoutside the hash (READscale/identity_manifest.py:60-80,138-152); L-2: $0$ of $24$ banked cells attributable because no cell journalled the four scalars (READV20_R15_LEAP_LEDGER.md:23 @ 99777ab); the one-line-drift planttest_moving_one_citation_by_one_line_fires_both_binds(READV20_R15_WING_MANIFEST.md:148-152 @ 99777ab). **Mechanism.** L-2, P-1, V-16, M-10, M-16, Ruling 1, Ruling 5, V-7 (a lane counted by a name nobody emits), FOUND-not-NAMED. **Kill.** Flipping any one ofbeta / qk / g / gamma / boundary_setsby one unit leavesmanifest_hashunchanged, or an omittedsink_setreturnsabsent: the lane has no identity and no cell may be journalled. Price $0$ GPU-s. The drift plant is the planted negative ($5/5$ flips must move the hash). **If killed — link 1.** The hash is recomputed over the field list above with the missing field added to the hash inputs (the record keptabsentoutside the hash deliberately so as not to move published hashes; the lane has none to protect). *Hypotheses:* zero shape-lane cells exist underresults/— **stated on the discriminator, not on the name**: $0$ records withkindarm_ceqand $0$ records carryingboundary_sets(RUNthis session), the $425$arm_smprimerecords lying outside the lane on the second count. *Evidence:* the record's own reason for reporting rather than raising is quoted at READscale/identity_manifest.py:141-151; the two zero countsRUNthis session. *Kill:* a published shape-lane hash moved by the repair — a record underresults/carryingboundary_setswhosemanifest_hashdiffers before and after; decided by one grep at $0$ GPU-s. The link's decisiveness rests on the discriminator reading $0$, and **falls the moment it does not**: a single record carryingboundary_setsmakes the recompute a hash move on a published cell and routes to link 2. **If killed — link 2: the field list is frozen instead of the cells.** If a shape-lane cell does exist, no hash is recomputed at all; instead the **field list itself** is hashed intoinstrument_hash, so a later addition or removal of a field is visible without touching any cell'smanifest_hash, and a cell whose field set does not match itsinstrument_hash's list is refused at the journal. This is a **different object** (the field list, not a cell), a **different instrument** (a hash over a static specification, not a re-emission of any record) and a **different number** (a mismatch count between two field sets, not a moved cell hash), so it does not die with link 1. *Hypotheses:*instrument_hashis already a declared field of this verse and is emitted per cell; the field list is fixed at birth and changes only throughCORRECTIONS.md. *Evidence:*instrument_hash, manifest_hashare in the field list above; L-2's precedent, $0$ of $24$ banked cells attributable because no cell journalled the four scalars (READV20_R15_LEAP_LEDGER.md:23 @ 99777ab); the count of distinctinstrument_hashvalues underresults/isNOT MEASURED — needs one grep once any shape-lane cell exists. *Kill:* two cells sharing oneinstrument_hashand carrying different field sets — the freeze does not bind and the lane has no identity at the specification level either; decided by one grep at $0$ GPU-s, and **more decisive** than link 1 because it settles the specification for every future cell rather than one cell's hash. **Terminal.** "No cell in the shape lane exists without its boundary condition, route and certificate inputs in its hash — and today no cell in the shape lane exists at all:kindarm_ceqreads $0$ records andboundary_setsreads $0$ records across all ofresults/. The $425$arm_smprime` records are another lane and are not evidence for or against anything in this book."

04.16 — The F0–F4 grading rubric, written out, and the gate that reads every cell (B18)#

Statement. The rubric the record cited and never wrote, stated as decision rules: | token | decision rule | what it is not | |---|---|---| | F0 | the claim is exact with no tolerance and is carried by a machine-checked declaration that builds with the three-axiom set | a float instance alone | | F1 | a bound holds on the graded object with its constant printed in the object's units | a mask-sense F1 (L-CERT's $\delta$), a different object | | F2 | a direction or ordering holds and no constant is stated | a failed F1 | | F3 | the claim is a fact about the harness, not the theory (a flag missing, a timer unsynchronised) | a failed instance | | F4-D | the theory's domain is empty on the graded bed (a census admits $0$ per cent) | — | | F4-W | the claim was withdrawn by its author | — | | F4-U | the claim was never attempted | — | The three F4 senses carry three tokens because one token cannot be read. The gate reads every cell, including every F4 cell, and grades a cell once, in one file, with any later grade a supersedes row (L-G2). TERMINAL means no further theorem can change the grade (a domain gap, a harness fact, a withdrawn claim); NOT-PUT means never graded; the two are distinct tokens and a cell carries at most one. The rubric's own date is 2026-09-05, and the suffix requirement binds from that date forward only. Before it the three F4 senses had one token, so every pre-rubric cell carries a bare F4 by construction and a suffix requirement applied retroactively would be satisfied at registration and then exempted by the grandfather clause in the same verse — a rule that fires $68$ times and is waived $68$ times decides nothing (V-3, V-10). The exact count is printed: RUN this session, git show 99777ab:V20_R15_THEORY_TABLE.md | grep -oE 'F4-?[DWU]?' reads $31$ bare F4 and $0$ suffixed, and the same over V20_R15_LEAP_LEDGER.md reads $37$ bare and $0$ suffixed — $68$ bare tokens, $0$ suffixed, across the two files. The one-off migration is therefore scheduled, not grandfathered: all $68$ pre-rubric bare F4 tokens are re-graded into F4-D / F4-W / F4-U by reading each cell's own reason, each re-grade filed as a new row with a supersedes pointer to the bare one and neither row edited (L-G2), priced at $0$ GPU-s and $1$ evening as a row of 05 REPAIRS. Until that migration lands the two files hold $68$ bare tokens and this book prints the count rather than treating them as graded. Hypotheses. A grade is a property of (cell, bed, date); the rubric's date is 2026-09-05 and the suffix clause of the Kill is asserted only of cells graded on or after it; a cell graded under an older rubric keeps its token with the rubric's date beside it and appears in the migration count above, so the exemption is a scheduled debt with a printed size, never a silent waiver. Evidence. L-GRADE (F0–F4 + HOW-BAD gap) cited once at READ CEQ_V20_R15_CONTRACT.md:58 @ 99777ab and no rubric text in the tree; JUPITER's reconstruction ruled BOUND to its usage, SATURN's ruled NOT BOUND on eight counterexamples (READ V20_R15_THEORY_TABLE.md:20-58 @ 99777ab); the five counterexamples there: F4 overloaded three ways; F2 and F3 not ordered; M14 carrying three grades in three files, resolved F4 at it.17; an F4 row reporting a live constant $1.421901019003236$; two contradictory grades for one object filed by one office. The gate graded seven distinct failures on eight cells and could not see Q2/W1, Q6/W1, Q6/W3 (READ docs/CEQ_SHAPE.md §4.4). Mechanism. P-11, P-3, V-14a, M-20, L-G2, V-3 (a rule waived exactly as often as it fires), V-10 (a gate satisfied at registration). Kill. A cell carrying two different live grades in two files — whatever their dates — where a grade is live iff no row carrying a supersedes pointer to it exists; a cell the gate's population omits; an F4 without its suffix on a cell graded on or after 2026-09-05 — the restriction is the kill's, not an exemption granted after it fires, and the $68$ pre-rubric bare tokens are carried by the migration line above rather than by a waiver. "At the same date" is struck from the first clause and the reason is printed, because it made the clause's own planted negative unable to satisfy it: the M14 triple spans it.3, it.17 and the contract, so a same-date requirement excluded the one known-bad case the clause exists to catch (V-15). A cell with two live grades is a defect whatever their dates — L-G2's whole device is that a superseded grade keeps a supersede marker, so the marker, and not the date, is what separates a superseded reading from a live contradiction. Instrument, pinned like every READ in this book, because both graded files were deleted from the working tree on 2026-09-05 (RUN this session, ls V20_R15_THEORY_TABLE.md V20_R15_LEAP_LEDGER.md reads No such file or directory for both, and both are readable only at the pin):

git show 99777ab:V20_R15_THEORY_TABLE.md | grep -oE 'F4-?[DWU]?' | sort | uniq -c
git show 99777ab:V20_R15_LEAP_LEDGER.md  | grep -oE 'F4-?[DWU]?' | sort | uniq -c
git show 99777ab:V20_R15_THEORY_TABLE.md | grep -nE 'F4([^-]|$)'
git show 99777ab:V20_R15_LEAP_LEDGER.md  | grep -nE 'F4([^-]|$)'

The first two are the token census (RUN this session: $31$ bare F4 and $0$ suffixed in the theory table, $37$ and $0$ in the ledger); the last two locate the rows ($28$ matching lines in each file, RUN this session) and are what the date filter and the supersedes read run over. A lookahead form (grep -nE 'F4(?![-])') is not POSIX ERE and does not run under grep -E; F4([^-]|$) is the form that does, and it is printed so the instrument is executable rather than described. The supersedes marker exists in both files at the pin (RUN this session, grep -cin 'supersed' reads $1$ line in the theory table and $7$ in the ledger), so the live/superseded distinction is readable there today. Price $0$ GPU-s. Planted negative, now satisfying the kill's own condition: the M14 triple (F3 in the contract, F4 in the ledger, F1 in the journal) carries two live grades on one cell — the it.3 F1 was left on the far side of the it.4 freeze with no supersedes pointer written to it when it.17 ruled M14 = F4 (READ V20_R15_THEORY_TABLE.md:48-50 @ 99777ab) — so under the date-free clause the check must report M14 as one cell with two live grades and the kill fires on the known-bad case; under the struck "at the same date" wording it could not, because it.3 and it.17 are different dates. The must-not-fire half: a cell whose earlier grade does carry a supersedes pointer to it must not be reported, which is the two-way calibration the live/superseded reading needs. And a post-rubric row written with a bare F4 must be caught by the date-filtered grep, where the same token in a pre-rubric row must not be, which is the two-way calibration the date restriction needs. If killed — link 1. The later-dated grade stands with a supersedes pointer to the earlier; both remain in the file. Hypotheses: every grade row carries a date and a file (04.16's own statement). Evidence: the M14 resolution at it.17 (M14 = F4, RULING J-17d) left the it.3 F1 on the far side of the it.4 freeze with no supersedes pointer written to it, which is exactly the live pair the repaired Kill fires on and exactly what this link repairs (READ V20_R15_THEORY_TABLE.md:48-50 @ 99777ab, readable only at the pin — RUN this session, ls V20_R15_THEORY_TABLE.md reads No such file or directory). Kill: an edit of the earlier row — L-G2 violated, the table is struck; decided by a diff of the file against its previous commit, price $0$ GPU-s. Terminal. "Every cell graded on or after 2026-09-05 carries one token from the seven above, one date and one file, and exactly one live grade across every file whatever the dates, a superseded grade being one a supersedes row points at; the gate's population equals the table's population; and $68$ pre-rubric bare F4 tokens — $31$ in V20_R15_THEORY_TABLE.md and $37$ in V20_R15_LEAP_LEDGER.md at 99777ab, $0$ suffixed — stand un-migrated with their count printed until 05 REPAIRS files their supersedes rows."

04.17 — The calibration column and its scoring rule#

Statement. One append-only column across rounds: bet id, source $\in\{$author, leap$\}$, prediction, counter of equal specificity, deciding number, frozen PASS, frozen KILL, realised value, verdict $\in\{$HOLDS, COUNTER, SPLIT, VOID$\}$, sign of the miss ($+$ credits the project more than the measurement supports; $-$ understates; unsigned for a contradiction), date, producer command. Rule: a VOID row (bed not admitted, or an instrument failing its plants) is unscored, never a miss; a SPLIT row is scored wrong with the sign of the optimistic half; the one-sided sign test runs on the pooled column after $\ge8$ scored rows and on the two sources separately; a column at or above $0.75$ optimistic after eight rows makes the counter the reported estimate for every unscored bet; the denominator is fixed before the audit and confirmations are listed beside findings. Hypotheses. Every prediction ships its counter before the data (D-7); the column is never edited, only appended (D-CALIB-5). Evidence. R11: $9$ checked, $9$ adverse, $7$ +, $1$ −, $1$ unsigned, one-sided $p=0.0352$ on the eight signed rows; the round entry's "six, all six optimistic" reads $5$ of $6$, $p=0.1094$, not significant (READ V16_CALIBRATION.md:85-110; MISTAKES.md:2037-2100, D-7); the Wilson interval on the optimism fraction $[0.5291,0.9776]$ excludes $0.5$ and fixes nothing else (READ docs/sources/design/design_falsify.md §0.2). Mechanism. D-7, L-SIGN, D-CALIB, M-2, L-G2, M-7. Kill — an audit of the appended column, not a refusal at the file, because a row refused at the file never enters the artefact the kill reads. A row in the column whose counter field is empty; a denominator chosen after the audit; a shrink factor fitted at fewer than eight rows (D-CALIB-3). The earlier wording — "a row filed without its counter, refused at the file, never discounted (D-CALIB-2)" — was satisfied by construction: the refusal it named removes the row before the column is written, so no row the kill could read ever carries an empty counter, and the gate fires on nothing (V-10, V-11). The refusal is retained as the upstream control and is now written into the instrument that performs it — 04.9's adjudicator specification gains "refuses any calibration row whose counter field is empty or absent", which it did not carry and which no other instrument of this book carried either (P-4) — while the kill is the downstream audit, observable on the artefact. Instrument: one read of the counter cell of every row of the appended column, V16_CALIBRATION.md in the working tree (RUN this session, ls V16_CALIBRATION.md succeeds; $232$ lines, $14$ lines matching counter case-insensitively), plus the adjudicator's refusal log for rows that never entered — the log being NOT MEASURED — needs the arena adjudicator and its frozen prediction file atresults/arena/PREDICTIONS.sha256` (RUNthis session,ls results/arenareadsNo such file or directory). **The audit is a read, not a test**, so 04.18's prose-coupling policy — which forbids a *test* from opening a.mdoutsideresults/— does not bind it and the two verses do not contradict each other. Price $0$ GPU-s. **Planted negative, two-way and on the artefact:** a row appended to the column with itscountercell empty, written directly and bypassing the adjudicator, must be reported by the audit — the known-bad case the kill's own condition instantiates and the case the upstream refusal by construction cannot produce; and a row carrying a counter of equal specificity must not be reported, which is the must-not-fire half. The upstream refusal keeps its own separate control: a bare prediction submitted to the file must be refused by the adjudicator (04.9), which is a statement about the file and not about the column. **If killed — link 1.** The offending row is VOID and the column's count excludes it; the sign test re-runs on the remainder. *Hypotheses:* rows are appended, never edited, so the VOID mark is a new row withsupersedes. *Evidence:* the R11 precedent — the round entry's six versus the table's nine, where the dropped rows changed $p$ from $0.1094$ to $0.0352$ (READV16_CALIBRATION.md:96-104`). Kill: fewer than eight scored rows remain — no rate is quoted, only the count; price $0$ GPU-s. Terminal. "The column is a count with signs, never a rate, until eight scored rows exist, and its counter rule is audited on the appended column rather than asserted from a refusal no instrument of this book performed until 04.9's adjudicator specification was made to carry it."

04.18 — The test policy: tests assert code, journals and `results/`, never prose (B3)#

Statement. A test may assert a value computed by repository code, a record in a journal under results/, or a hash of a file the test itself produces; a test may not open a prose document, assert a line number of a document, or assert an anchor string inside a document. The line that decides: a test file is prose-coupled iff it names a path ending in .md outside results/ or asserts an integer as a line number of any file it does not generate. Prose-coupled tests are moved out of the collected tree, never edited into passing, and their count is printed beside the suite's. Hypotheses. The pattern file is a permanent object, not working-tree state. The deleted round documents are the rows marked D in git diff --name-status 99777ab c71527a restricted to root-level .md — $244$ paths, fixed by two commit shas and reproducible from any checkout forever. The earlier definition ("the set marked D in git status --short") was struck because it is empty at c71527a: RUN this session, git status --short returns exactly $2$ lines, M README.md and ?? docs/canon/, and $0$ rows marked D, so the pattern file was empty and the Kill's grep read $0$ unconditionally — a kill satisfied by construction (V-10, V-11) resting on uncommitted state that does not reproduce (P-2). The selector is the file's basename. Evidence. The whole census is re-run at a named commit and printed as RUN @ c71527a (git rev-parse HEAD reads c71527a64687043f2afa1667fe6485cc71022179). git diff --name-status 99777ab c71527a reads $350$ rows marked D, of which $244$ are root-level .md documents (the round reports) — the one number that survived from the earlier reading — and $60$ match (^|/)test_[^/]*\.py$. The earlier claim "$0$ test files are deleted" is false and is struck: sixty test files were removed between the pin and c71527a, and the surviving suite is smaller for it — tests/**/test_*.py reads $291$ at 99777ab and $239$ at c71527a (and $239$ in the working tree), a net loss of $52$ files (git ls-tree -r --name-only <sha> | grep -E '^tests/(.*/)?test_[^/]*\.py$' | wc -l). Against the $244$-path pattern file, grep -rlF -f deleted_docs.txt tests --include='*.py' reads $120$ — not $187$ — of which $108$ are test_*.py; of those $108$, $43$ also read lines (splitlines|readlines|read_text|open(); $32$ test_*.py carry a literal .md:NNN; $71$ test_*.py read results/ or a .jsonl, and $39$ of those name no deleted document. Root collection, quoted with its commit and its interpreter versions, because the count does not reproduce across sessions and the book must not carry it forward as a constant. RUN this session, python -m pytest --collect-only -q at HEAD c71527a (git rev-parse HEAD reads c71527a64687043f2afa1667fe6485cc71022179, working tree M README.md and ?? docs/canon/ only) on CPython 3.11.9, pytest 9.0.3, torch 2.14.0+cpu, numpy 2.4.6, reads 2626 tests collected, 17 errors, reproduced on three consecutive invocations (elapsed $13.24$ s, $24.19$ s, $13.91$ s — the elapsed figure is not part of the reading and is not a number this book carries). The two earlier readings are printed beside it rather than replaced silently: 2971 tests collected, 26 errors (the verse as first written) and 2580 tests collected, 22 errors (the batch-3 repair, and the figure MARS re-read at 19.31s). Three different counts at one commit on one box is the number's own evidence class: the collection count is a function of the installed environment's import failures (B1: torchvision circular import, transformers.PreTrainedModel, ripser/persim against numpy 1) and not of the tree alone, so fewer errors collect more tests and the pair moves together — $26$ errors at $2971$, $22$ at $2580$, $17$ at $2626$. The count therefore moves and is never carried forward: every quotation of a collected count in this canon — including link 2's own suite count below — is re-read at assembly against the commit and the interpreter versions then in force, and a count quoted without both is struck (P-1, M-16). The counts that are pinned to commits and do reproduce — the $350$ deletions, the $244$ root .md, the $60$ test_*.py, the $291\to239$ survivors, the $120/108/43/32/71/39$ census — are the ones this book carries, because git diff and git ls-tree at two shas are the same in every checkout and pytest --collect-only is not. tests/gate0/ holds $15$ test_*.py files, of which test_g05_data.py is 31 passed in 0.73s (RUN, 04.7). The CHARTER's own count reads $56$ (READ docs/canon/CHARTER.md §5 B3) under an unstated selector; the selector above is the one this verse freezes, and every count in this paragraph is pinned to 99777ab → c71527a rather than to a working tree. The pattern the policy replaces: the wing manifest's anchor check test_every_frozen_citation_resolves_at_head, $20$ passed, $1$ failed at 207e7b9 (READ V20_R15_WING_MANIFEST.md:148-160 @ 99777ab); line-reference drift READ MISTAKES.md:364-374 (P-6: cite the symbol, not the line). Mechanism. P-6, P-5, P-3, V-26 (a marginal count of green nodes is not coverage), V-6, V-10 and V-11 (a kill whose pattern file is empty reads $0$ by construction), P-1, P-2 (a census of uncommitted working-tree state does not reproduce). Kill. After the move, grep -rlF -f deleted_docs.txt tests --include='*.py' reads above $0$ against the $244$-path pattern file built from git diff --name-status 99777ab c71527a, or any collected test opens a .md outside results/; or a moved test is edited to pass against a stub document. The pattern file is named by two shas, so the kill is decidable in any checkout at any date and cannot be emptied by a clean working tree. Instrument: the two greps above and pytest --collect-only, price $0$ GPU-s. Planted negative, in both directions, and with no line number in it. One test that opens docs/canon/CHARTER.md — a path ending in .md outside results/ — is written into the collected tree and must be caught by the second grep; the selector fires on a known-coupled test. The plant carries no assertion about that file's length, and the earlier form of it, "one test that asserts docs/canon/CHARTER.md has $317$ lines", is struck twice over: the figure was wrong (RUN this session, wc -l docs/canon/CHARTER.md reads $316$, the file ending without a trailing newline so a line-counting read returns $317$ and wc -l returns $316$ — the ambiguity is itself the P-6 mechanism this policy exists against), it carried no evidence class, and the plant's job is to name a .md outside results/, which the selector's first half decides, not to assert a true number. And the $244$-path pattern file must read $120$ today (RUN @ c71527a), a non-zero count, which is the must-fire calibration the empty git status file could never give. The plant is NOT MEASURED — needs the test-policy migration of 05 REPAIRS, and this book writes no test: 04.13's own Kill strikes "any plant that exists only in a script's print (NAMED)", and a plant this book describes and never writes is NAMED by that rule, so it is marked and priced there rather than claimed here. Its verification, when 05 REPAIRS writes it, is one RUN of the second grep against the planted file returning that file's path. If killed — link 1. The collected tree is restricted by an explicit list (testpaths naming only directories whose files pass the selector); everything else is tests/attic/ and uncollected. Hypotheses: the selector is run on every file before it is listed; the pattern file is the $244$-path commit-pinned one. Evidence: the $120/239$ census above ($108$ of themtest_.py) is the file list the move starts from,RUN @ c71527a. *Kill:* atests/attic/file collected — the configuration is wrong and the suite's count is not a count; decided bypytest --collect-onlyat $0$ GPU-s, cheaper than the grep pair because it is one command. **If killed — link 2.** The suite that ships is the **$39$-file** subset oftest_.pyreadingresults/or a.jsonland naming no deleted document, plus every test undertests/gate0/($15$ files;test_g05_data.pyis $31$ passed); the number of collected tests is printed in the book that cites the suite, **re-read at assembly against the commit and the interpreter versions then in force and never carried forward from this page** — the root collection read $2626$ with $17$ errors this session atc71527aonCPython 3.11.9/pytest 9.0.3/torch 2.14.0+cpu/numpy 2.4.6, and read $2580/22$ and $2971/26$ in two earlier sessions at the same tree. *Kill:* a quoted test count exceeding the collected count **at the commit and interpreter the quotation names**, or a quoted count naming neither — struck as P-1. **Terminal.** "The test count quoted anywhere in the canon is the count of tests that assert code and journals; no test asserts a sentence. The census is pinned to99777ab → c71527aand reads $350$ deletions, $244$ of them root.mdand **$60$ of themtest_.py**; the suite fell from $291$ to $239$test_.py` across those two commits, and that loss is printed rather than described as $0$."

04.19 — The magnitude interval and the two registrations (B23)#

Statement. The magnitude support is registered per base, not once. On the path-product base $W_{ij}=\prod_{k=j+1}^{i}m_ke^{i\theta_k}$ the interval is closed, $m_k\in[0,1]$, because pathProd_eq_zero_iff carries no hypothesis and $m_c=0$ is the F0 cut; on the exponential prefix-scan base $W=\exp(\mathrm{scan}\,g)$, $g=\log m$, the interval is half-open, $m_k\in(0,1]$, because no prefix scan represents a zero gate and $\log0$ is junk in the scan. BED-M's Rademacher draw $a\in\{-1,0,+1\}$ has magnitude support $\{0,1\}$; on the closed base $100$ per cent of its entries are admitted; on the half-open base $0$ of $2{,}048$ sequences satisfy $\forall k,\ 0<m_k$, so every theorem stated on that base is decoration on BED-M and the census says so. The two registrations are inverse only when written for one base; written per base they do not meet. On BED-S at the softmax corner $m\equiv1$ and the question does not arise. Hypotheses. The base is declared in the manifest (g parametrisation id, 04.15); the census prints the fraction of draws admitted at the quantifier level the theorem uses (per sequence for a $\forall k$ hypothesis). Evidence. V-25's census on BED-M e3_t2: support $\{-1.0,0.0,+1.0\}$; entries with $a>0$ $2{,}077/131{,}072=1.5846$ per cent; $a=0$ $96.875$ per cent; sequences satisfying $\forall k,\ 0<a_k$: $0$ of $2{,}048$, structural because a[:, :head + 1] = 0.0 (READ MISTAKES.md:1954-2036); the $\varepsilon$-sweep $\varepsilon=0\to$ nan against $2.44\times10^{-15}$ at $\varepsilon=10^{-9}$ (READ V15_ARM_PHASE.md:303-308 @ 99777ab); pathProd_eq_zero_iff at lean/CEQ/V16Domain.lean:129 and no_prefix_scan_represents_a_zero_gate at :165 (READ docs/CEQ_SHAPE.md §2.1 Definition 1); the closed-versus-half-open filing and D-R3 READ docs/CEQ_SHAPE.md §4.4. Mechanism. V-25, D-R3, V-22, M-20 (two registrations that never met), P-11. Kill. A theorem cited as a train gate on a base whose census admits $0$ per cent of draws at its quantifier level — the gate is blocked and the theorem is inadmissible until restated on the support that exists. Instrument: clause 10 of 04.2's numbered admission block — "the per-base admitted fraction at the quantifier level each magnitude theorem uses (04.19), printed per base" — which is this verse's own line and needs no extension. The earlier pointer, "the census line 15 of 04.2", named a line that does not exist: 04.2's block has eleven numbered clauses and no fifteenth, so the instrument this Kill named was unreachable as written (P-4, P-6). Price $0$. Planted negative: the BED-M e3_t2 census on the half-open base must print $0$ of $2{,}048$ — the known-empty domain fires the block. If killed — link 1. The theorem is restated on the closed base with magnitudes and circle phases (the v16 restatement), and the census re-run. Hypotheses: the restated theorem's hypothesis is a predicate on $m\in[0,1]$ with no positivity clause. Evidence: v16's #2 was re-stated on $[0,1]$ magnitudes and circle phases for exactly this reason, and the pathProd_* clauses admit 3 of 3 BED-M values (READ MISTAKES.md:2020-2036; docs/sources/design/design_instrument.md row K). Kill: the restated theorem's hypothesis still admits $0$ per cent — the base, not the interval, is wrong for the bed; price $0$ GPU-s, the same census. Terminal. "Every magnitude theorem is stated with its base and its admitted fraction; no gate rests on an interval its corpus never enters."

04.20 — The skyline cells: one FOUND, two with settings and no cell (B11)#

Statement. Four skylines are read beside every bed with their settings frozen before the arena. The first two are the same depth at two parameter counts, and only the second can carry an A2 sentence (04.9 clause 3): the depth-$\lfloor\log_2t^\star\rfloor+2$ softmax stack ($5$ at $t^\star=8$) at full width and unmatched parameters, which must be FOUND at the design point and whose number is printed as $\Delta_{\rm sky}$, a control satisfying R-SKY and licensing no A2 sentence; and the matched-parameter skyline of 04.9 clause 3b — the same depth $5$ at reduced width, the width fixed before any draw as the largest per-layer width whose total count lands within $0.0960$ per cent of the shape's, with sky_width and the exact params_per_arm printed — which is the only arm A2 is read against, and whose width is NOT MEASURED — needs the reduced-width parameter count once the $[m,K+2]$ head's count is fixed, $0$ GPU-s. Then two skylines with no cell, and — until this repair — no instrument and no price either, which is why B11's skyline-cells row is closed for one of three and the census table now says so. Each is named with the instrument it needs and with what its price is and is not: | skyline | setting frozen here | instrument it needs | price | |---|---|---|---| | depth-$5$ full width | depth $\lfloor\log_2t^\star\rfloor+2=5$ at $d_{\rm model}=16$, unmatched parameters | FOUND at the design point; the depth-$5$ cell of docs/PLAN.md S-35 | $\approx7.6$ s per cell [ASSUMED linear in depth], $\approx64.8$ s at eight seeds | | depth-$5$ matched width | depth $5$ at the reduced width of 04.9 clause 3b | one parameter-count arithmetic pass, then the same S-35 cell at that width | width NOT MEASURED — needs the reduced-width parameter count; the pass is $0$ GPU-s; the cell is $\approx64.8$ s at eight seeds on the same basis | | wide constant depth | depth $1$ at width $=n_{\rm nodes}=64$ | NOT MEASURED — needs a width-$64$ constant-depth arm at matched parameters (one make_arm branch at a second width, one optimizer path, one field emit, on 04.14's arm_pl basis of $41$–$130$ GPU-s per branch) | build $41$–$130$ GPU-s, $1$ evening, DERIVED from 04.14's per-branch route; the per-cell run time is NOT MEASURED — needs one timed cell of the width-$64$ arm, and the reason is printed: both cell bases this book carries ($1.680$ s shape, $1.524$ s softmax) are at $d_{\rm model}=16$ and the only scaling law it registers is [ASSUMED linear in depth], which prices a depth change and prices no width change at all | | CoT decoder | $t^\star=8$ decode steps at the registered geometry | NOT MEASURED — needs a CoT decode harness at $t^\star$ decode steps (a sequential-decode loop, a per-step journal emit and a stop rule, none of which exists in the tree) | build $41$–$130$ GPU-s, $1$ evening, on the same per-branch basis; the per-cell run time is NOT MEASURED — needs one timed decode cell, since a decode cell is $8$ sequential forward passes per query and no forward-pass-per-decode-step figure is registered anywhere in this book | At $d_{\rm model}=16<s=64$ the wide stack has no matched-parameter instance at the registered geometry, so even once built it is a control at unmatched parameters and licenses no A2 sentence, exactly as the full-width depth-$5$ arm does. A price with no basis is not a price, so the two run-time cells are marked NOT MEASURED rather than extrapolated from a depth law that does not cover a width change or a decode loop — the P-1 defect this book struck three times over in 04.11. The depth is a choice by analogy with Thm 4.2 of sanford-2024-logdepth, whose task is $\mathrm{hop}_k$ and not the committor; the reduction is book 01's and until it is written the depth row is a control, not a theorem. Hypotheses. Both depth-5 arms run on the same byte-identical draws and journal as the matched arms; the full-width one's parameter count is printed as unmatched, which is exactly why it is $\Delta_{\rm sky}$ and not an A2 arm; the reduced-width one's count is printed and must land within $0.0960$ per cent of the shape's or it is unmatched too and no A2 number exists on the bed. Evidence. Thm 4.2 CITED [V] sanford-2024-logdepth; the width skyline CITED [V] yehudai-2025-depthwidth; CoT CITED [V] merrill-2024-cot; the iteration argument CITED [V] wang-2024-incontext-td, xie-2026-softmax-rl (abstracts); the reduction NOT FOUND (READ docs/sources/sweep/sweep_expressivity.md §3.5); price $\approx7.6$ s per depth-5 cell [ASSUMED linear in depth], $\approx64.8$ s at eight seeds (READ docs/PLAN.md §5.7). Mechanism. R-SKY, D-1, P-10, V-25, D-7, P-4, Ruling 3 (A2 is at matched parameters or it is not A2), V-17. Kill (Bet D) — one-sided, with its subject named, because the two-sided form fired on the A2 result this canon exists to obtain. The comparison is $\mathrm{acc}_{\rm sky}-\mathrm{acc}_{\rm shape}$, read against the matched-parameter skyline of clause 3b and against no other arm, at $\mathrm{MDE}_N$ at the realised $\sigma_d$ (04.9 clause 7; NOT MEASURED — needs $\sigma_d$ from 04.21 step (5)), and the two signs are named rather than left to a reader: - the skyline short of the shape by more than $\mathrm{MDE}_N$ is the A2 reading and is not a kill — the skyline's learned hops fall short of the exact solve by more than $\mathrm{MDE}_N$, which is CHARTER §1's definition of A2 word for word; it is logged with its sign and it fires nothing; - the skyline ahead of the shape by more than $\mathrm{MDE}_N$ kills Bet D and withdraws A2 on the bed — "one operator" carries no accuracy sentence at all against a depth stack at matched parameters, and the bed needs something the one-solve construction does not supply. The earlier wording named neither subject ("short says the bed needs something the hop construction does not supply; ahead says 'one operator' carries no accuracy sentence") and stood at $|\cdot|>\mathrm{MDE}_N$ in either direction; under the shape-as-subject reading its "short" clause is the A2 result, so the kill fired on the very number the canon is built to produce (V-10). 04.6 link 1 uses the same two words with the skyline as subject — "the matched-parameter skyline ahead by more than $\mathrm{MDE}_N$ … 'one operator' carries no accuracy sentence at all" — and that is the reading this verse now carries, so the two verses read one way. Also: a depth chosen after the arena, or a width chosen after the arena, strikes the row (M-2). Instrument: the depth-5 cell of docs/PLAN.md S-35 at both widths. Planted negative: a depth-1 stack labelled as the skyline must fall short by more than $\mathrm{MDE}_N$ on a bed with $t^\star=8$ — if it does not, the bed is static (04.5). If killed — link 1. The depth ladder $\{3,5,7\}$ is run at $t^\star=8$, each depth at its own matched width, and the smallest depth inside $\mathrm{MDE}_N$ at the realised $\sigma_d$ is reported as the skyline; price $3\times64.8$ s [ASSUMED], 1 evening. Hypotheses: the ladder and the three widths are registered before the run (M-2), never chosen after. Evidence: the same three depths are the registered skylines at $t^\star=2/8/32$ (READ docs/CEQ_SHAPE.md §6 A.4); the three matched widths NOT MEASURED — needs the parameter-count pass of 04.9 clause 3b. Kill: no depth inside $\mathrm{MDE}_N$ at the realised $\sigma_d$ — the hop construction does not cover the bed, and A2 is undefined on it; more decisive than the single cell because it rules out every registered depth at once. Terminal. "The full-width depth-5 row is a measured control at unmatched depth and unmatched parameters, printed as $\Delta_{\rm sky}$ and licensing no A2 sentence; the matched-width row A2 requires has no width, no count and no cell, so no A2 number exists anywhere in this book; the wide constant-depth arm and the CoT decoder have a named instrument each and a build price each ($41$–$130$ GPU-s, $1$ evening, per branch) and no run-time price at all, because this book registers no width law and no decode law to price them with; so B11's skyline-cells row is closed for the depth skyline only — one of the four registered skylines carries a cell, one carries an arithmetic pass, and two carry a build price with an unmeasured run time; and the sentence 'depth $\lfloor\log_2t^\star\rfloor+2$ suffices' is not asserted for the committor."

04.21 — The first BED-S cell: what eight seeds produce, in what order (B5)#

Statement. No CEQ arm has been trained — and the sentence is stated on a discriminator, never on the phrase, because the record count for the file the repository itself calls a CEQ arm contradicts the phrase. A CEQ-arm cell is one whose kind is arm_ceq and which carries boundary_sets, goal_set and sink_set with their sha256s (04.15's field list); RUN this session, both counts read $0$ across all of results/ — grep -rn 'arm_ceq' --include='*.py' . returns $0$ source lines and grep -rl 'boundary_sets' results --include='*.jsonl' returns $0$ files. The $425$ records the kind census reads under arm_smprime are not counter-evidence and are not CEQ-arm cells: arm_smprime is the record's complex-chain lane — NAME = "arm_smprime" at READ ceq/arm_smprime.py:77, emitting "kind": NAME at :346, its records carrying "task": "chain_label_complex" / e3_t2 — and not one of the $425$ declares a boundary set, which is the discriminator and the whole of it. Without that discriminator printed, neither this Statement nor 04.15's "zero shape-lane cells" is falsifiable, and a reader holding the $425$-record count against the phrase would be right (FOUND-not-NAMED, V-7, P-1). BED-S has no cell, no realised sd, no measured $t^\star$, no $I(X_{\le k};a^\star)$. The first eight seeds are run in this order and produce these objects before any bet is scored: (1) the census of 04.2 admits; (2) the binds of 04.13 pass through the front door — every plant of 04.13's table, whose numbers are float instances on random logits and are marked NOT MEASURED at the front door until this step, is reproduced as bed.build → arm.forward → journal row → verdict() on one admitted draw each, nine bind rows, priced $\approx9\times1.680\approx15.1$ s [ASSUMED] on the arm_smprime cell basis, $0.5$ evening; no bind is admissible and no verse may cite a bind number until this step's journal exists; (3) the $\hat\gamma$-free controls of 04.11 run before the shape — the 0-hop MLP, the 1-hop softmax, majority, random, predict-the-mean, the depth-$\lfloor\log_2t^\star\rfloor+2$ skyline of 04.20 and InfSA-Neumann-$16$ — every one of which is defined without reference to any trained quantity, in the randomised interleaved order of 04.10 recorded per cell; (4) the shape runs, producing $\hat\gamma$ per seed; (4a) the $\hat\gamma$-dependent controls run after the shape, because 04.11's own Hypotheses define them only once $\hat\gamma$ exists — ChaCAL-diag and ChaCAL-with-sink are read at the shape's trained $\hat\gamma$, so scheduling them at step (3) would schedule a contract behind an unreached round (D-4) and would freeze a dial after the data (M-2). Their order and the inherited $\hat\gamma$ they were run at are printed in the manifest (04.15's gamma block: init, final $\hat\gamma$, $\Lambda$, verdict, plus the seed whose $\hat\gamma$ was inherited), so the sequential dependency is auditable and no reader mistakes a post-shape control for a pre-registered one; (5) the adjudicator of 04.9 fills, from the journal alone, $\sigma_d$ per scored statistic, $\mathrm{MDE}_N$ at that realised $\sigma_d$ with $N$ chosen by 04.9 clause 7's rule — never a placeholder $\mathrm{MDE}_8$ — $t^\star$ read off the hop ladder, $\hat\gamma$ and $\Lambda$ per seed, $\|\hat P-P_{\rm env}\|_\infty$ per seed, and only then scores Bets A–H against their counters. Hypotheses. L-LEAN: the [M] targets of Proposition 1 and Proposition 5 build before step (4); the device is the certified one, with the four determinism quantities filled (solve_triangular forward and backward bitwise over $8$ repeats under strict mode, RUN[NEPTUNE], no documented guarantee). Evidence. "There is no result": READ docs/CEQ_SHAPE.md §8; every BED-S number in the record is a floor formula or a design constant (READ docs/CEQ_SHAPE.md §6 A.13); the $\gamma$-pinning null on the boundary, $\tfrac12\chi^2_0+\tfrac12\chi^2_1$ at $95$ per cent $=2.7055$, MOVED at $\Lambda>\ln4096=8.318$ (RUN[J]; citation owed); the arena price $\approx3.3$ GPU-min DERIVED; the $14$-evening critical path (READ docs/PLAN.md §5.4). Mechanism. M-3, M-2 (a threshold frozen as a rule, and a dial never frozen after the data), L-LEAN, D-4 (a $\hat\gamma$-dependent control is staged behind the shape, never started before it), P-1, V-11. Kill. Any number quoted for BED-S before step (5) writes $\sigma_d$ into the journal; or a bet scored against any placeholder $\mathrm{MDE}_8$ — $0.011677$, $0.039827$, $0.057971$, $0.126238$ or any other row of 04.9's table — instead of $\mathrm{MDE}_N$ at the realised cell; or a $\hat\gamma$-dependent control journalled at step (3) rather than step (4a), which would record a dial chosen after the data. The forbidden thresholds and the six kills that used to carry them are named, so the prohibition is not a rule with no referent: the placeholder number is struck from 04.3's floor comparison, 04.4 link 1's R0 clause, 04.5's half-width clause, 04.6's Bet E and link 1, 04.7's majority-sign clause, 04.11's K-E1 and 04.20's Bet D, each of which now reads $\mathrm{MDE}_N$ at the realised $\sigma_d$ under 04.9 clause 7 and carries NOT MEASURED — needs $\sigma_d$ from 04.21 step (5) beside it. Instrument: the adjudicator's predictions_hash check and its refusal below $8$ seeds — both NOT MEASURED — needs the arena adjudicator and its frozen prediction file atresults/arena/PREDICTIONS.sha256` (RUNthis session,ls results/arenareadsNo such file or directory; the construction is priced in 05 REPAIRS) — and a grep of the scored journal for a literal $\mathrm{MDE}_8$ constant, which is the one half of the instrument that runs today. Price $0$. Planted negative: a journal with $7$ seeds must return INSUFFICIENT; a duplicated seed must count once; a bet row written with the literal threshold $0.039827$ must be refused by the grep, and the same row written as "$\mathrm{MDE}_N$ at $\sigma_d$ from this journal" must pass — the two-way calibration the prohibition needs. **If killed — link 1.** The offending number is struck with asupersedesrow; the cell is not re-run, the journal is re-read. *Hypotheses:* the journal carries per-seed statistics (04.15'seval_traceand the scored columns). *Evidence:* the adjudicator computes $\sigma_d$ from journals only and never from a table (READdocs/PLAN.md` S-61). Kill: the re-read still lacks $\sigma_d$ — the cell did not journal its per-seed statistics and is NAMED (04.14); price $0$ GPU-s. Terminal. "BED-S has no cell; every number about it is a specification."

Census rows closed#

CHARTER §5 row	verse
B3 tests coupled to prose	04.18
B4 the label class	04.5, 04.8
B5 no arm trained, BED-S no cell	04.21, 04.2
B11 the skyline cells — closed for the depth skyline only	04.20. Of the four registered skylines the full-width depth-$5$ arm must be FOUND at the design point and is priced ($\approx7.6$ s per cell, $\approx64.8$ s at eight seeds `[ASSUMED linear in depth]`); the matched-width depth-$5$ arm has an instrument (one parameter-count pass, $0$ GPU-s) and no width; the wide constant-depth arm and the CoT decoder have a named instrument and a build price each ($41$–$130$ GPU-s, $1$ evening) and no run-time price, this book registering no width law and no decode law. B11's second half — the hop$_k\to$committor reduction — is book 01's and is not closed here.
B18 the F0–F4 rubric, the gate's blindness to F4, TERMINAL vs NOT-PUT	04.16
B20 W2 NAMED not FOUND, the route back	04.14
B21 the column-sink control (K-E1)	04.11
B22 the ChaCAL convention check	04.12
B23 the magnitude interval, D-R3	04.19
B25 "faster to train" undefined and unmeasured	04.10, 04.9
B27 the two uses — chess half only	04.7 (the chess witness's hygiene guards, the local data route, the three UNPINNED sources, the $h=8$ rollout label and its base-rate floor, the join census). Owner of the row: 09 CHESS_AND_MARKETS, 04 (CHARTER §5). The market half is not closed in this book and is not claimed here.

What book 04 closes of B27, and what it does not. CHARTER §5 assigns B27 to two books, and this book closes exactly one half of it: the instrument half of the chess use, in 04.7 — the five hygiene guards with their planted violations (RUN this session, 31 passed in 0.73s), the by-game split and FEN dedupe, the rollout label at the frozen $h=8$, its per-constraint base-rate floor and the join-hit census with its discard rule. The market half — the state as order book and price path, contracts as absorbing sets, the market-implied baseline as the floor, the look-ahead guard and the by-event split with its planted violation — appears in no verse of this book, registers no instrument here, and is closed in 09 alone: 09.21 (the state), 09.22 (contracts as absorbing sets), 09.23a–09.23b (the market-implied probability as the registered floor), 09.24 (Brier and log score against it, with the near-efficiency counter under D-CALIB), 09.25 and 09.29b (BED-P-L and BED-P-N), 09.28 (leakage, look-ahead and by-event guards) and 09.32 (the market domain census). This book registers no market bed because CHARTER §6 gives book 04 three beds — BED-S, BED-J and the chess witness — and none of them is a market; duplicating 09's market instruments here would put one object under two owners, which is the M-20 mechanism (two registrations that never met) this book files B23 against. The loss is stated rather than covered: if 09's market verses are struck, B27's market half is closed by nothing in this canon, and no verse of book 04 can carry it — the row above is then open on its market half and the sentence in force is 04.7's Terminal for chess and silence for markets.

Kills, cheapest first#

The sort key is the pair (GPU-seconds, evenings), applied and reprinted here, because the table's earlier order was not the order its own prices state. It opened on 04.2 at "$0$ GPU-s, $1$ evening" ahead of seven kills at $0$ GPU-s with no evening and of 04.1 at $0$ GPU-s, $0.5$ evening, and it listed 04.8 at $0$ GPU-s after 04.13 (seconds) and 04.3 (which is decided inside the $\approx98$ s arena cell) — a "cheapest first" table that was not sorted is a claimed scaffold that does not exist (P-4, M-16). Ties inside a tier are broken by verse number. Two rows carry two prices and are sorted on the cheapest clause that can fire, with the other price printed in the row: 04.7 (its digest and floor clauses are $0$ GPU-s locally, its eval-sign clause $\approx8.7$ GPU-min behind the author's yes) and 04.11 (its operative kill is link 1's at $0$ GPU-s, $0.5$ evening; link 2 is $82$–$260$ GPU-s). 04.3's kill is decided from a cell's own journal at no cost beyond the cell, but the cell it reads is the $\approx98$ s arena, so it sorts at $\approx98$ s and not at $0$: a kill that cannot be reached before an arena exists is not cheaper than the arena.

Tier 1 — $0$ GPU-s, no evening: decidable today from files, greps and one journal read.

verse	kill number or condition	price	replacement verse
04.7	a capability number before both chess digests are pinned; legality or next-FEN quoted as capability; a capability number before the join-hit rate or the $h=8$ base rates are printed	$0$ GPU-s locally (the eval-sign clause $\approx8.7$ GPU-min `[ASSUMED]` behind the author's yes)	04.7 link 1 (hygiene bed) → link 2 (leaves the ladder)
04.8	any of the three metric plants passing	$0$ GPU-s	04.8 link 1 (NRMSE vector only)
04.12	the LaTeX source contradicts the HTML reading; the relabelling is free because neither arm exists, not because both are FOUND	$0$ GPU-s, one fetch (author)	04.12 link 1 (the operator distance $\Delta_{\rm conv}$ at $\gamma=0.9$, no arm)
04.15	a one-unit flip leaving `manifest_hash` unchanged; `absent` returned	$0$ GPU-s	04.15 link 1 (field into the hash, decisive only while `boundary_sets` reads $0$ records) → link 2 (the field list hashed into `instrument_hash`)
04.16	one cell, two live grades in two files, whatever their dates (a grade being live iff no `supersedes` row points at it); an F4 without suffix on a cell graded on or after 2026-09-05 ($68$ pre-rubric bare tokens, $31$+$37$ at the pin, migrated by 05 REPAIRS, not waived)	$0$ GPU-s	04.16 link 1 (supersedes row)
04.17	*a row in the appended column* whose `counter` field is empty** — audited on the artefact, the refusal at the file being the upstream control and 04.9's adjudicator now carrying it	$0$ GPU-s	04.17 link 1 (VOID row)
04.18	`grep -rlF -f deleted_docs.txt tests` $>0$ after the move, the pattern file being the $244$ root `.md` rows of `git diff --name-status 99777ab c71527a` (permanent; the old `git status` definition read $0$ rows and made the kill fire never)	$0$ GPU-s	04.18 link 1 (`testpaths`) → link 2 ($39$-file subset)
04.19	a train-gate theorem admitting $0$ per cent at its quantifier level	$0$ GPU-s	04.19 link 1 (restate on the closed base)
04.21	a BED-S number before $\sigma_d$ is journalled; a bet scored against any placeholder $\mathrm{MDE}_8$	$0$ GPU-s	04.21 link 1 (supersedes)

Tier 2 — $0$ GPU-s, $0.5$ evening.

verse	kill number or condition	price	replacement verse
04.1	`void_contrasts` journalled as `[]` on a bed whose registered list is non-empty; a VOID contrast credited	$0$ GPU-s, $0.5$ evening	04.1 link 1 (all VOID until identified)
04.11	K-E1 (ChaCAL-with-sink within $\mathrm{MDE}_N$ at the realised $\sigma_d$ on $\ge6/8$ and residual within $2\times$) is UNREACHABLE: $0$ ChaCAL source lines, $0$ records; the operative kill is link 1's $\\|\Pi_{\rm row}-\Pi_{\rm col}\\|_\infty<10^{-12}$ on $\ge95$ per cent of the $512$ admission draws	$0$ GPU-s, $0.5$ evening (link 1); $82$–$260$ GPU-s, $2$ evenings (link 2)	04.11 link 1 (operator read, no arm) → link 2 (`make_arm` branches, FOUND census)

Tier 3 — $0$ GPU-s, $1$ evening.

verse	kill number or condition	price	replacement verse
04.2	any admitted-region sd $=0$; class frequency outside $(0.05,0.95)$; disagreement $0$; R-07 line $\ge0.5$; $m_{\rm eff}<m-1$ on $>5$ per cent of screened draws (clause 11); $t^\star$ unplaceable	$0$ GPU-s, 1 evening	04.2 link 1 (dial) → link 2 (`bed_1` cross-check) → link 3 (reprice $N$)

Tier 4 — GPU-seconds, ascending.

verse	kill number or condition	price	replacement verse
04.4	honest query below $1-10^{-3}$; honest $R^2\ge R^2_{\rm bar}$, the bed's own $99$th-percentile $512$-draw null (`NOT MEASURED`, the leak half unreachable until it is computed); planted $R^2<0.99$	$\le1.524$ s	04.4 link 1 (vector head alone, R0) → link 2 (flags removed)
04.13	any plant passing; any plant NAMED (B-J's ChaCAL plant and B-E1's ChaCAL identity half are NAMED and struck); every remaining number `NOT MEASURED at the front door` until 04.21 step (2)	$\approx15.1$ s `[ASSUMED]`	04.13 link 1 (arm-free re-derivation, then a remark) → link 2 (no training, L-LEAN)
04.5	0-hop MLP inside the half-width at $N$ (04.9 clause 7, `NOT MEASURED`), or McNemar $p>0.05$ vs 1-hop	$\approx0.5$ GPU-min ($\approx30$ s)	04.5 link 1 ($t^\star=32$) → link 2 (BED-J)
04.6	$r_{\rm softmax}/r_{\rm shape}\le2$ at matched marginal error	$\approx30.9$ s `[ASSUMED]` ($2\times8\times1.680+4.0$; the $\approx34$ s struck)	04.6 link 1 (A2 only) → link 2 (cost statement, 04.10)
04.20	$\mathrm{acc}_{\rm sky}-\mathrm{acc}_{\rm shape}>\mathrm{MDE}_N$ at the realised $\sigma_d$ — *one-sided, the skyline ahead* of the shape, read against the matched-parameter** skyline of 04.9 clause 3b (width `NOT MEASURED`); the skyline short of the shape is the A2 reading and fires nothing; a depth or width chosen after the arena	$\approx64.8$ s `[ASSUMED]`	04.20 link 1 (depth ladder at matched widths)
04.9	$\sigma_d\ge0.109199$ on the first eight seeds — the M-3 realised value itself, ratio $2.1776$ printed as a read-out; the earlier $2.18\times0.050146=0.109318$ struck because the one instance that motivates it, $0.109199$, falls below it	$\approx98$ s `[ASSUMED]`	04.9 link 1 ($N=16$) → link 2 (TOST $N=36/70$, $119/228$ s)
04.3	an uninformed control (0-hop, `random`, `majority`) below its own floor on $\ge2/N$ seeds	$0$ GPU-s beyond the cell, but the cell is the $\approx98$ s arena, so the kill is unreachable below that price	04.3 link 1 ($m_{\rm eff}$) → link 2 (exact oracle only, $\varphi$-NRMSE below $4.4\times10^{-16}$)
04.14	`arm_phase` still $0$ after the route while remaining in the $33$-kind emitter set; the reach-clause (a kind above $0$ that no emit site reaches) is `NOT MEASURED` and unreachable until the extended enumeration exists	$41$–$130$ GPU-s	04.14 link 1 (citations, not a wing)
04.10	Spearman $\lvert\rho\rvert>0.5$, $p<0.05$ against run index on $N\ge16$ arm-cells; no level of the head's own ladder reached by both arms; a T1 or T2 on a rate-valued head read against the NRMSE ladder	band $206$–$537$ GPU-s	04.10 link 1 (T2 only) → link 2 (cost model DERIVED, sentence withdrawn)

Limits (collected once)#

No GPU exists in this session (torch 2.14.0+cpu); every GPU-second above is READ from the certified record at the pin and none was re-measured. Every RUN here is a grep, a git status, a pytest invocation or a one-line Python read of an existing module; none computes a statistic. The prose-coupling census depends on its selector (basename of a deleted root document), which differs from the CHARTER's unstated selector that read $56$; both counts are printed, and the whole census is now pinned to 99777ab → c71527a rather than to a working tree — $350$ deletions, $244$ root .md, $60$ test_*.py, $291\to239$ surviving test_*.py, $120$ files under tests/ naming a deleted document ($108$ of them test_*.py), $43$ of those reading lines, $32$ carrying .md:NNN, $71$ reading results/ or .jsonl of which $39$ name no deleted document. The root collection count is the one number in this census that does not reproduce and is therefore never carried forward: it reads $2626$ with $17$ errors this session at c71527a on CPython 3.11.9 / pytest 9.0.3 / torch 2.14.0+cpu / numpy 2.4.6, reproduced on three consecutive invocations, against $2580/22$ and $2971/26$ in two earlier sessions at the same tree; the count is a function of the environment's import failures (B1) and not of the tree, fewer errors collecting more tests, so every quotation of it in this canon is re-read at assembly with its commit and its interpreter versions and a quotation carrying neither is struck. The elapsed seconds ($13.24$/$24.19$/$13.91$ s this session) are not part of the reading. The earlier reading of this census — an empty git status pattern file, "$259$ deletions", "$0$ test files deleted", "$187$ of $291$", "$36$-file subset", "$2971$ collected" — is struck, and the "$0$ test files deleted" line was flatly false: $60$ were. 04.18's plant carries no line number: "one test that asserts docs/canon/CHARTER.md has $317$ lines" is struck both because the figure was wrong (wc -l reads $316$; the file ends without a trailing newline, so a line-counting read returns $317$ — the ambiguity being the P-6 mechanism itself) and because the plant's job is to name a .md outside results/, not to assert a true number; the plant is NOT MEASURED — needs the test-policy migration of 05 REPAIRS and this book writes no test. The chess witness's constraint predicates are this book's registration and have no draw behind them; its horizon is frozen at $h=8$ plies [ASSUMED] with the reason printed, and the base rates $\mathrm{base}_k(8)$ that floor its capability channel are NOT MEASURED — needs one rollout pass over the $36$ fixture games. No A2 number exists anywhere in this book: A2 is defined at matched parameters against the depth skyline, the only depth-5 stack registered before this repair was at unmatched depth and unmatched parameters, and the matched-width skyline registered here (04.9 clause 3b, 04.20) has no width, no count and no cell. The matched-parameter bar is this book's own [ASSUMED] constant $0.0960$ per cent $=3\times0.0320$, Ruling 3 printing only the $0.0320$ per cent residual and no boundary. Every $\mathrm{MDE}_8$ in this book is a placeholder: the frozen object is 04.9 clause 7's rule in units of $\mathrm{MDE}_N$ at the realised $\sigma_d$, and eight kills (04.3, 04.4 link 1, 04.5, 04.6 Bet E and link 1, 04.7, 04.11 K-E1, 04.20 Bet D) read NOT MEASURED — needs $\sigma_d$ from 04.21 step (5). No bind of 04.13 has entered at the front door: every number in its table is a random-logit float instance marked NOT MEASURED at the front door, and B-J's ChaCAL plant and B-E1's ChaCAL identity half are NAMED and struck. The shape lane's kind is arm_ceq, emitted by nothing ($0$ source lines, $0$ records), and the discriminator boundary_sets reads $0$ files across all of results/, so the $425$ arm_smprime records are a different lane. $68$ pre-rubric bare F4 tokens ($31$ + $37$ at 99777ab, $0$ suffixed) await migration in 05 REPAIRS and are not graded by 04.16's rubric. BED-J's jittered census, BED-S's realised sd, $t^\star$, $I(X_{\le k};a^\star)$, every T1 and T2, the LaTeX read of ChaCAL, the chess digests and the wide and CoT skyline cells are NOT MEASURED, each with its instrument named in its verse. Twelve of the thirteen control arms of 04.11 do not exist — grep -rniE 'chacal|infsa' --include='*.py' . returns $0$ lines and the $24$-kind census holds $0$ records for every one of them — so K-E1 is unreachable, the seven-arm arena price of 04.9 ($\approx98$ s, $\approx3.3$ GPU-min) is [ASSUMED] on the arm_smprime cell time rather than DERIVED, and no comparative sentence against ChaCAL, InfSA-Neumann-$16$, the cached mixture, the argmin controls or any skyline is licensed anywhere in this book. The leak bar $R^2_{\rm bar}$ of 04.4, the D-APPROX bound BED-J's creditability waits on (book 01), the join-hit rate and the $h=8$ base rates of 04.7, and the representability check 04.1's VOID list waits on are NOT MEASURED on the same terms. The boundary-null critical value $2.7055$ carries no references.bib citation and is marked owed. Theorem numbers inside cited sources inherit the sweeps' [U] marks. The arena adjudicator does not exist: RUN this session, ls results/arena reads No such file or directory, so results/arena/PREDICTIONS.sha256, the predictions_hash check and every refusal 04.9, 04.1, 04.3, 04.17 and 04.21 delegate to it are NOT MEASURED — needs the arena adjudicator and its frozen prediction file, priced in 05 REPAIRS. Three prices in this book were arithmetically wrong against their own stated formulas and are struck: $\approx52$ s for three arms at eight seeds (the arithmetic reads $3\times8\times1.680+4.0=44.32$ s, an $18$ per cent gap with no printed overhead term), $\approx34$ s for one pair ($2\times8\times1.680+4.0=30.88$ s), and InfSA-16's $\approx5.12$ s classed DERIVED from the $25.409$ ms hop, which gives $16\times25.409\,\mathrm{ms}=0.407$ s, a factor $12.6$ low; $5.12$ s now enters as READ docs/CEQ_SHAPE.md:1926 @ 99777ab, unreproduced, with the one reproducing multiplication printed ($150$ steps $\times\ 0.034133$ s/step, the $150$-step budget READ scale/e_ladder.py:140), and 04.9's $\approx3.3$ GPU-min inherits that tag. B27 is closed here on its chess half only; the market half is 09's and appears in no verse of this book. The consequence head's refusal is per column (refused_columns), not per arm, so the no-change predictor is scored on the NRMSE vector it floors and refused only on the cosine and the magnitude ratio. Two verses cited census lines that never existed — "census line 15 of 04.2" (04.19) and "04.4's census line 10" (04.8, twice) — and are repointed at 04.2's clauses 10 and 4; 04.2's block has eleven numbered clauses and 04.4 has none. 04.10's $N$ counts arm-cells, not seeds, and the reading is printed at every use. 04.10 registers two $\tau$ ladders, not one: the vector-head ladder $\{0.9,0.8,0.7,0.5\}$ in NRMSE-to-oracle units covers $q$, $z^\star$ and $\Delta z$ and covers no rate-valued head, and the rate-head ladder $\tau_{\rm rate}=(1-\mathrm{acc})/\mathrm{floor}$ at the same four levels covers the argmin head (floor $\mathrm{floor}_{\rm zeroinfo}$) and the chess eval-$\Delta$ channel (floor $\mathrm{base}_k(8)$); under the single NRMSE ladder T1 and T2 were undefined on two of the book's four heads and on the chess bed, and they now read NOT MEASURED against a defined denominator instead of against no unit at all. 04.14's census is printed in full — all $24$ kinds, not seven — and its zeros are read against a printed emitter set: $33$ kinds are declared under ceq scale scripts ($13$ NAME = constants plus $20$ literal "kind": "…" spellings, disjoint), $15$ of them have records and $18$ read $0$, arm_phase among the eighteen; $9$ of the $24$ observed kinds match neither grep, so the counter's upper reach is NOT MEASURED — needs the emit-site enumeration extended past literal spellings and 04.14's reach-clause is unreachable until it exists. 04.15 states that the refusal rule makes an absent declared field unobservable downstream, so every kill in this book reads a field's value and none reads its presence. 04.16's first kill clause drops "at the same date" — a cell with two live grades is a defect whatever their dates, the supersedes marker separating live from superseded — because the M14 triple spans it.3 and it.17 and could not satisfy the same-date form it was planted for; its instrument is now pinned (git show 99777ab:V20_R15_THEORY_TABLE.md | grep -oE 'F4-?[DWU]?' | sort | uniq -c, and the same for the ledger), both files being absent from the working tree. 04.17's kill is an audit of the appended column (V16_CALIBRATION.md, $232$ lines), not a refusal at the file, and 04.9's adjudicator specification gains the counter check it delegated to nothing. B11 is closed for the depth skyline only: of the four registered skylines one must be FOUND and is priced, one has an arithmetic pass and no width, and the wide constant-depth arm and the CoT decoder have a named instrument and a build price each ($41$–$130$ GPU-s, $1$ evening) and no run-time price, because this book registers no width law and no decode law — both cell bases are at $d_{\rm model}=16$ and the only registered scaling is [ASSUMED linear in depth]. 04.20's Bet D is one-sided with its subject named: the skyline ahead of the shape kills it, the skyline short of the shape is the A2 reading and fires nothing; the two-sided form fired on the result the canon exists to obtain. The closing kills table is sorted by (GPU-seconds, evenings) and reprinted in four tiers, and the Preface's "cheapest kill in the canon" claim for 04.2 is struck: 04.2 is the first kill in the decision order because it gates every other bed number, while nine kills are strictly cheaper.

Attacks answered#

MARS (MORIARTY) attacked every verse of this book. Repair round 1, batch 1 of 5: sixteen findings, all of severity strike. Every finding is reproduced verbatim — verse, flaw, mechanism, number, replacement_survives, required repair, severity — beside the verse id repaired and what changed. Nothing is softened; where a repair could not be made the row reads OPEN with the Terminal now in force printed.

A-1 · verse 04.11 · severity `strike`#

Flaw (verbatim). Every control arm in the Statement's roster is NAMED, not FOUND, so 04.14's own rule strikes every sentence in this verse. Mechanism (verbatim). FOUND-not-NAMED, P-1, P-4, V-7 Number (verbatim). RUN this session: grep -rniE 'chacal|infsa' --include='*.py' . (excluding .venv) returns 0 lines; the kind census RUN this session returns 24 distinct kinds (arm_pl 422, arm_smprime 425, band_miss 1, census 31, constant_g 2, halt_demo 1, kirchhoff 4, mc_random_unit 4, naive_yield 1, not_generated 1, pivot_signed 11, pivot_unsigned 11, probe 3, provenance 2, real_key_directions 1, recovery_check 1, reproduce_check 1, rung 40, scramble_residual 1, scramble_residual_shipped 1, softmax 227, summary 4, welch 5, windowed_signed 1) and holds 0 records for chacal_diag, chacal_published, chacal_with_sink, infsa_neumann_16, the cached mixture, majority, random, predict_the_mean or any skyline. replacement_survives (verbatim). false Required repair (verbatim). Mark the entire roster NOT MEASURED — needs the control-arm implementations (onemake_armbranch per control, priced as 04.14 prices the W2 route), and restate K-E1's Kill as unreachable until at least ChaCAL-diag and ChaCAL-with-sink are FOUND. Links 1 and 2 both presuppose a ChaCAL-with-sink cell and die with the verse. Severity (verbatim). strike

Repair applied — 04.11. The Statement now opens by declaring the roster a specification: one member of thirteen (the depth-1 softmax, kind softmax, $227$ records) is FOUND and the whole remainder is NOT MEASURED — needs the control-arm implementations (one make_arm branch, one optimizer path and one field emit per control, priced as 04.14 prices the W2 route at $41$–$130$ GPU-s per branch); every member is tagged FOUND or NAMED in place, and both RUN commands with their $24$-kind output stand in the Evidence. The Hypotheses now state that the FOUND hypothesis is false at the time of writing and that this is why the verse's kill is unreachable. K-E1 is restated as registered UNREACHABLE, therefore not a kill under the CHARTER's Reachability rule, and the verse carries no comparative sentence. Because replacement_survives was false, both links were replaced by a genuinely different chain, not renamed: link 1 asks the same question of the operator instead of any arm — $\|\Pi_{\rm row}-\Pi_{\rm col}\|_\infty$ over the transient block of the bed's own $P_{\rm env}$, absorbing rows against the record's value-zero sink column — a different object (the environment chain), a different instrument (one dense float64 solve pair on the generator, no training, no seeds, no matched parameters) and a different number (an operator $\infty$-distance, not a $\varphi$-NRMSE difference against $\mathrm{MDE}_8$), firing at $<10^{-12}$ on $\ge95$ per cent of the $512$ admission draws, with a planted negative that fires by construction (an $\mathcal A=\emptyset$ draw must read $0$ bitwise), at $0$ GPU-s; link 2 is the FOUND route back priced as 04.14 prices W2, killed by the kind census still reading $0$ for chacal_with_sink after the branches are taken (D-6), at $82$–$260$ GPU-s, admitted as strictly more decisive rather than cheaper. The Terminal carries the loss: no control arm except the depth-1 softmax is FOUND, and every comparative sentence against ChaCAL, InfSA-Neumann-$16$, the cached mixture, the argmin controls and every skyline is withdrawn. The "Kills, cheapest first" row for 04.11 and the Limits paragraph carry the same reading.

A-2 · verse 04.11 · severity `strike`#

Flaw (verbatim). A price is carried at evidence class [FITTED + RUN] for an arm that has no implementation and no record. Mechanism (verbatim). P-1, P-2 Number (verbatim). "$1.680$ s per ChaCAL cell [FITTED + RUN]" against 0 chacal hits in any .py in the tree and 0 records under results/ with a chacal kind. replacement_survives (verbatim). false Required repair (verbatim). Downgrade to [ASSUMED] the arm_smprime cell time stands in for a ChaCAL cell or to NOT MEASURED — needs the ChaCAL arm, and reprice 04.9's $\approx98$ s arena and $\approx3.3$ GPU-min accordingly. Severity (verbatim). strike

Repair applied — 04.11, 04.9. In 04.11's Evidence the ChaCAL cell price is downgraded to [ASSUMED] the arm_smprime cell time stands in for a ChaCAL cell with the reason printed (ChaCAL-diag is the shape's own solve at $\mathcal A=\emptyset$ and differs from it by the boundary rows alone); $1.680$ s keeps [FITTED + RUN] only where it belongs, on the arm_smprime shape cell, and $1.524$ s keeps [FITTED] on the softmax cell; the $\approx52$ s three-arm figure and InfSA-16's $\approx5.12$ s inherit the same [ASSUMED] basis; the verse states that no price in it is [FITTED + RUN] for an arm with no implementation. In 04.9's Kill the seven-arm arena is repriced: $7\times8\times1.680+4.0\approx98$ s and $\approx3.3$ GPU-min are [ASSUMED], no longer DERIVED, because five of the seven arms have no implementation and no record, with the line added that the arena becomes DERIVED only when every arm in it is FOUND and that until then $98$ s is a lower bound on a run that cannot be started. The Limits paragraph records the reclassification once.

A-3 · verse 04.11 · severity `strike`#

Flaw (verbatim). D-CALIB is inverted: the verse makes the prediction the point estimate where the CHARTER and this book's own Preface make the counter the point estimate. Mechanism (verbatim). D-CALIB, L-SIGN Number (verbatim). 04.11 Statement: "under D-CALIB the prediction is the point estimate". Preface (line 8): "Under D-CALIB the counter is the point estimate". CHARTER §4, D-CALIB row: "the counter is the point estimate for every unscored prediction". replacement_survives (verbatim). true Required repair (verbatim). Rewrite as: K-E1 is the counter to the canon's mechanism claim, and under D-CALIB K-E1 (a column sink reproduces the row condition) is the reported point estimate. Severity (verbatim). strike

Repair applied — 04.11. The Statement's closing clause now reads that K-E1 — a column sink reproduces the row condition — is the counter to this canon's mechanism claim that boundary rows are not a column device, that under D-CALIB the counter is the point estimate for every unscored prediction, and that K-E1 is therefore the reported point estimate on every bed of this book until a cell scores it; the canon's own prediction is named as the unscored side and carries nothing. The Terminal repeats the direction so no later reader recovers the inverted form.

A-4 · verse 04.1 · severity `strike`#

Flaw (verbatim). The list of creditable contrasts contradicts the VOID rule stated in the same sentence: under 04.2's Hypotheses the oracle is inside the shape's class and inside none of the listed control classes, which is exactly the VOID condition. Mechanism (verbatim). D-2, V-10, M-7 Number (verbatim). VOID rule: "a contrast is VOID when the label's oracle operator is contained in one arm's operator class and not the other's". 04.2 Hypotheses: "a depth-1 bilinear logit can realise $\hat P=P_{\rm env}$". ChaCAL-diag is defined in 04.11 as "the shape with $\mathcal A=\emptyset$" and InfSA-Neumann-16 as a read "without boundaries" — neither carries absorbing rows, so neither class contains $(I-Q_a)^{-1}R_{a,k}\mathbb 1$. All 6 listed creditable contrasts satisfy the VOID definition. replacement_survives (verbatim). true Required repair (verbatim). Either restate the rule as "VOID when the oracle is in BOTH arms' classes or in the shape's alone AND the contrast is scored as capability", or accept the consequence and move all six contrasts to the VOID list, leaving BED-S with the identification reading only (which is the link-1 replacement already written). Severity (verbatim). strike

Repair applied — 04.1. The consequence is accepted, not softened. The Statement voids every listed contrast: BED-S's registered VOID list is the eight-entry set $\{\text{shape}-\text{softmax},\ \text{shape}-\text{skyline},\ \text{shape}-\text{ChaCAL-diag},\ \text{shape}-\text{ChaCAL-published},\ \text{shape}-\text{ChaCAL-with-sink},\ \text{shape}-\text{InfSA-Neumann-}16,\ \text{shape}-0\text{-hop},\ \text{shape}-1\text{-hop}\}$, and the only reading BED-S licenses is identification, $\|\hat P-P_{\rm env}\|_\infty$ per seed. The verse prints the reading that follows — a bed on which perfect identification voids every capability contrast — and moves the capability claim to BED-J (04.6), whose Statement asserts the oracle is in no causal arm's class. The Terminal withdraws every capability sentence on BED-S whatever the second arm.

A-5 · verse 04.1 · severity `strike`#

Flaw (verbatim). The VOID register is presented as a fixed fact while its only input — class containment — is marked NOT MEASURED in the neighbouring verse. Mechanism (verbatim). P-1, M-7 Number (verbatim). 04.2 Hypotheses: the containment premise is "a representability claim that is NOT MEASURED — needs the first BED-S cell (04.21)". replacement_survives (verbatim). true Required repair (verbatim). Mark the BED-S VOID list NOT MEASURED — needs the representability check of 04.21, and register the link-1 rule (everything VOID until $\|\hat P-P_{\rm env}\|_\infty$ is journalled) as the operative rule until then. Severity (verbatim). strike

Repair applied — 04.1. The Statement closes by marking the list itself NOT MEASURED — needs the representability check of 04.21 step (5), since its only input is the containment premise 04.2 carries as NOT MEASURED, and by registering link 1's rule as operative today: until that check is journalled every contrast on every bed of this book is VOID. The Hypotheses record that the membership is provisional and that its provisionality is journalled with it; the Evidence marks the eight-entry list NOT MEASURED alongside the premise.

A-6 · verse 04.1 · severity `strike`#

Flaw (verbatim). The Kill's first clause is unreachable by construction and its planted negative does not instantiate that clause. Mechanism (verbatim). V-10, V-11, V-15 Number (verbatim). 04.15 lists void_contrasts among the declared fields and makes "a missing declared field a refusal, never an absent entry", so no cell can be journalled with void_contrasts absent. The plant is a cell with void_contrasts = [] — an empty list is present, not absent. replacement_survives (verbatim). true Required repair (verbatim). Restate the kill as "void_contrasts journalled as [] on a bed whose registered VOID list is non-empty", which is the condition the plant actually instantiates. Severity (verbatim). strike

Repair applied — 04.1. The Kill is restated exactly so: void_contrasts journalled as [] on a bed whose registered VOID list is non-empty, or a capability sentence built on a contrast in the list. The verse states why absence is not the condition — 04.15's refusal rule means no cell reaches the journal with the field absent, so a kill on absence could not fire — and the planted negative now instantiates the kill's condition exactly: a cell written with void_contrasts = [] on BED-S, whose registered list has eight entries, refused by the adjudicator of 04.9. The "Kills, cheapest first" row carries the restated condition.

A-7 · verse 04.2 · severity `strike`#

Flaw (verbatim). The Evidence's spectral radius contradicts the Statement's own graph construction, and at the pin the number is a read of the arm's matrix, not the bed's. Mechanism (verbatim). V-10, P-1, V-17 Number (verbatim). Statement: "self-loops only on declared absorbing positions", which forces $(P_{\rm env})_{ii}=0$ for $i\in T$, hence $\max_{i\in T}P_{ii}=0$ and $\rho(Q_{\rm env})=0$ exactly (strictly lower triangular). Evidence prints $\rho(Q)=0.692660=\max_{i\in T}P_{ii}$. At the pin: docs/CEQ_SHAPE.md:2547 @ 99777ab — "$\rho(\hat Q)=\max_{i\in T}\hat P_{ii}<1$ ... a diagonal read on the arm's triangular $\hat Q$ (RUN 0.692660)"; :1818 — "$\rho(\hat Q)=0.692660$ both ways". replacement_survives (verbatim). true Required repair (verbatim). Print $\rho(Q_{\rm env})=0$ as the bed's value (a nilpotent transient block is the point of the DAG construction) and re-attribute 0.692660 to $\hat Q$, the arm's causal softmax, in a separate sentence. Severity (verbatim). strike

Repair applied — 04.2. The Evidence opens with the bed's own value, DERIVED in one line from the Statement's construction: $(P_{\rm env})_{ii}=0$ for every $i\in T$, $Q_{\rm env}$ strictly lower triangular and nilpotent, $\rho(Q_{\rm env})=0$ exactly, a nilpotent transient block being the point of the DAG. $0.692660$ is re-attributed in its own sentence to the arm's matrix — $\rho(\hat Q)=\max_{i\in T}\hat P_{ii}=0.692660$, a diagonal read on the arm's triangular causal softmax, whose diagonal is non-zero because a causal softmax puts mass on its own position — at the pin docs/CEQ_SHAPE.md:2547 @ 99777ab with :1818 beside it, and the F1/F2 BOS lines are re-labelled as reads of the arm's chain throughout.

A-8 · verse 04.2 · severity `strike`#

Flaw (verbatim). The admission gate fails on the verse's own evidence: the R-08 no-op rate makes the $m_{\rm eff}=m$ line unreachable at $m=8$. Mechanism (verbatim). V-11, M-3 Number (verbatim). Evidence: "Clamps at rows $21,25,31$ move the query's committors by $5.551\times10^{-17}$" — below 04.3's $10^{-12}$ threshold, so those targets do not count toward $m_{\rm eff}$. 3 of 20 targets is a 15 per cent no-op rate; drawing $m=8$ targets gives $P(m_{\rm eff}=m)=(0.85)^8=0.2725$, against the gate's "$m_{\rm eff}=m$ on $\ge95$ per cent of draws". The Kill's clause "$m_{\rm eff}<m$ on $>5$ per cent" fires on 72.75 per cent of draws at registration. replacement_survives (verbatim). true Required repair (verbatim). Either restrict the candidate-target pool to targets pre-screened as non-no-op (and print the screening rate), or lower the admission line to $m_{\rm eff}\ge m-1$ and re-derive every floor at $m_{\rm eff}$ rather than $m$. Link 1 (move $t^\star$) does not touch the no-op rate and does not survive. Severity (verbatim). strike

Repair applied — 04.2, 04.3. Both halves of the required repair are taken. Clause 11 is added to the admission census — the no-op screening rate, the fraction of candidate targets in $T$ whose clamp moves the query's committors by $>10^{-12}$, measured on the draw before the $m$ moves are sampled, with moves drawn from the screened pool only and the rate printed so the pool is auditable. Clause 9 is lowered to $m_{\rm eff}\ge m-1$ over that screened pool. The Statement prints the arithmetic that convicted the old gate — $P(m_{\rm eff}=m)=0.85^8=0.2725$ (DERIVED), a gate at $m_{\rm eff}=m$ on $\ge95$ per cent firing on $72.75$ per cent of draws at registration, V-11 — and 04.3's Hypotheses now derive every floor at the realised $m_{\rm eff}$, never at $m$. The Kill reads $m_{\rm eff}<m-1$ on $>5$ per cent of screened draws and gains a third plant: a batch drawn from the unscreened pool at the recorded $15$ per cent no-op rate must fail clause 9. Because link 1 does not survive this finding, link 1 is explicitly scoped: it now states that moving the dial does not touch the no-op rate and that a clause-9 or clause-11 failure routes past it to link 2 directly.

A-9 · verse 04.2 · severity `strike`#

Flaw (verbatim). The third link of the chain carries no Hypotheses, no Evidence and no Kill, so the chain does not reach its Terminal through three legal replacements. Mechanism (verbatim). L-VERSE, P-4 Number (verbatim). CHARTER §2 requires every "If killed" to carry "its own Hypotheses, Evidence and Kill". Link 3 ("the price") is two sentences and states only $\mathrm{MDE}_8=0.126238$ at the $2.18\times$ precedent. replacement_survives (verbatim). false Required repair (verbatim). Give link 3 a Hypothesis (the realised sd is the first admitted batch's), an Evidence line (the MDE table at docs/sources/sections/sec_beds.md:308-313) and a Kill ($\mathrm{MDE}_{16}$ at the realised $\sigma_d$ still above every registered effect), or delete it and let link 2 be the last link. Severity (verbatim). strike

Repair applied — 04.2. Link 3 is given the three missing fields rather than deleted. Hypotheses: the realised paired sd is the first admitted batch's, read from the journal's per-seed differences and not from a pilot or a table, on the eight seeds of 04.21 step (5), deduplicated in one thread lane. Evidence: the MDE table at its realised-sd rows, $0.109199\to\mathrm{MDE}_8=0.126238$, $\mathrm{MDE}_{16}=0.081841$ (READ docs/sources/sections/sec_beds.md:308-313, RUN[VENUS], re-verified RUN[MARS]), with the M-3 precedent pilot $0.050146$ against realised $0.109199$, ratio $2.1776$ (READ MISTAKES.md:464-494). Kill: $\mathrm{MDE}_{16}$ at the realised $\sigma_d$ still above every registered effect — nothing is falsifiable at any $N$ this canon can afford and the bed is filed with its sd and no capability number — decided at $0$ GPU-s from the journalled $\sigma_d$ before any second batch runs, which is strictly cheaper than link 2's cross-check cell and so satisfies the depth rule's ordering.

A-10 · verse 04.3 · severity `strike`#

Flaw (verbatim). The Kill fires on success: floor_zeroinfo is the uninformed arm's error, so any arm above chance prints below it and strikes its own floor. Mechanism (verbatim). L-FLOOR inverted, V-10 Number (verbatim). $\mathrm{floor}_{\rm zeroinfo}=1-\max_a\hat\pi(a^\star)=0.7500/0.8750/0.9375$ at $m=4/8/16$. An arm with argmin accuracy 0.90 at $m=8$ prints error 0.10, which is 0.775 below the printed floor, on 8 of 8 seeds. The Kill ('any arm — informed or not — printing an error below the printed floor on $\ge2$ of $8$ seeds: the floor ... is struck') then strikes the floor. replacement_survives (verbatim). true Required repair (verbatim). Restrict the kill to arms whose view is the one the floor is derived for: 'the 0-hop control, the random control or the majority control printing an error below its own floor'. For an informed arm, printing below the floor is the capability reading, not a defect. Severity (verbatim). strike

Repair applied — 04.3. The Kill is restricted to an uninformed control printing an error below its own floor — the 0-hop control, the random control or the majority control reading below $\mathrm{floor}_{\rm zeroinfo}$ computed on the batch it was scored on, on $\ge2$ of $8$ seeds. The verse states that an informed arm printing below the floor is the capability reading L-FLOOR exists to produce and fires nothing, and prints the convicting instance itself: at $m=8$ an arm with argmin accuracy $0.90$ prints error $0.10$, $0.775$ below the printed floor, on $8$ of $8$ seeds, on which the old unrestricted kill struck the floor. The Mechanism line gains "a floor an informed arm is supposed to beat is not a kill"; the "Kills, cheapest first" row carries the restriction.

A-11 · verse 04.3 · severity `strike`#

Flaw (verbatim). Neither planted negative can make the kill fire, so the condemning rule ships without its V-15 control. Mechanism (verbatim). V-15, V-3 Number (verbatim). random reads accuracy $1/m$, i.e. error $1-1/m$ = the floor at uniform $\hat\pi$; majority reads accuracy $\max_a\hat\pi(a^\star)$ on the same batch whose realised $\hat\pi$ defines the floor, i.e. error exactly $1-\max_a\hat\pi(a^\star)$ = the floor. Neither can print strictly below it except by the finite-sample noise the floor is computed from. replacement_survives (verbatim). true Required repair (verbatim). Plant a floor computed on a different batch's $\hat\pi$ than the one scored (an off-by-one-seed floor), which a majority arm violates by construction; that is a known-bad case the kill can fire on. Severity (verbatim). strike

Repair applied — 04.3. The planted negative is replaced by the off-by-one-seed floor: the majority control scored against $\mathrm{floor}_{\rm zeroinfo}$ computed from seed $j+1$'s realised $\hat\pi$ while scored on seed $j$'s batch, which a majority arm violates by construction whenever the two batches' $\hat\pi$ differ, so the kill fires on a known-bad case. The verse keeps the finding's arithmetic in place — random reads error $1-1/m$, which is the floor at uniform $\hat\pi$, and majority reads error exactly $1-\max_a\hat\pi(a^\star)$ on the batch whose $\hat\pi$ defines the floor — and states that the two matched-batch arms are therefore retained as the V-3 floor row and that neither is the kill's control.

A-12 · verse 04.3 · severity `strike`#

Flaw (verbatim). The tight Fano floor is retained on exactly the ground stated for retiring the weak one. Mechanism (verbatim). V-10, L-FLOOR Number (verbatim). Weak Fano $1-\ln2/\ln m=0.5/0.6667/0.75$, retired because it sits $0.25/0.208/0.1875$ below chance. Retained tight Fano $(\ln m-I-\ln2)/\ln(m-1)$ at $I=0$ reads $0.6309/0.7124/0.7679$, i.e. $0.1191/0.1626/0.1696$ below the same chance floors $0.75/0.8750/0.9375$. Both are strictly below the exact zero-information floor for every $m\ge3$. replacement_survives (verbatim). true Required repair (verbatim). State that Fano is never binding against the exact zero-information floor at any $I\ge0$ on a deterministic label, print $\mathrm{floor}_{\rm zeroinfo}$ alone, and drop floor_fano_k1 from 04.15's field list and from the adjudicator. Severity (verbatim). strike

Repair applied — 04.3, 04.15. 04.3's Statement retires both Fano forms on the same ground and by the same arithmetic, printing the two gap rows ($0.25/0.2083/0.1875$ and $0.1191/0.1626/0.1696$ below $0.7500/0.8750/0.9375$), stating that Fano is never binding against the exact zero-information floor at any $I\ge0$ on a deterministic label for every $m\ge3$, and naming the defect: retaining the tight form while retiring the weak one on that exact ground. The argmin head's floor is $\mathrm{floor}_{\rm zeroinfo}$ alone. floor_fano_k1 is struck from 04.15's declared field list, where a parenthesis now records that a cell carrying the field is refused rather than accepted with the field ignored, and from the adjudicator of 04.9; the Terminal reads that no Fano line is printed anywhere.

A-13 · verse 04.4 · severity `strike`#

Flaw (verbatim). The operative leak threshold is one the verse's own Evidence declares imported out of its units and not re-derived. Mechanism (verbatim). V-22, M-2 Number (verbatim). Statement freezes the honest-leak kill at $R^2<0.5$; Evidence: "The E4' bars PASS_BAR = 0.5 / FAIL_BAR = 0.9 (READ scale/rips_gate.py:60-61) are E4''s, read $0.973819$ on its fixed point, and are V-22 until re-derived." Verified: scale/rips_gate.py:60 is PASS_BAR = 0.5, :61 is FAIL_BAR = 0.9. replacement_survives (verbatim). false Required repair (verbatim). Derive the bar on BED-S's own probe: register the corpus-alone $R^2$ distribution over 512 admission draws and set the bar at the 99th percentile of that null. Both links inherit the same imported bar and die with it. Severity (verbatim). strike

Repair applied — 04.4. The imported pair is struck as the operative threshold and replaced by the bed's own object: $R^2_{\rm bar}$, the $99$th percentile of the corpus-alone $R^2$ null distribution over the $512$ admission draws of 04.2, computed on label-permuted targets and printed with the draws it was computed on, so the bar and the census share a batch and the bar is not an off-batch import. The E4′ pair is retained only as the precedent that names the mechanism, explicitly V-22 across the bed boundary and fixing nothing here, with the RUN this session confirming scale/rips_gate.py:60-61. Because both links inherited the dead bar, the leak verdict is registered NOT MEASURED — needs the corpus-alone probe over the admission census of 04.2 in both directions — no bed cleared of leakage and none convicted — and link 2 is rewritten to recompute the null on the new token list, on the stated ground that a bar computed on the old features is the same V-22 import across a feature-set boundary that struck the E4′ pair. The Kill states that its leak half is unreachable until $R^2_{\rm bar}$ exists and that no leak verdict is filed in the interim; the "Kills, cheapest first" row and the Terminal carry the same reading.

A-14 · verse 04.6 · severity `strike`#

Flaw (verbatim). The read position of the $|T|$-vector label is never stated; under causal masking a per-position read is unreachable for every arm and the Bet E ratio is 0/0. Mechanism (verbatim). V-10, D-1 Number (verbatim). The chain is SymmSupport ($Q_{ij}>0\Rightarrow Q_{ji}>0$), so $q_i$ depends on neighbours at positions $j>i$; a causal arm at position $i$ cannot see them. With $|T|=9$ and a last-position read the bed is a single-position task, which is the D-1 mechanism the book exists to leave. replacement_survives (verbatim). false Required repair (verbatim). Register the read explicitly: the full $|T|$-vector is emitted at position $s-1$ from a $[|T|]$-wide readout, with the state axis supplied by the $|T|$ coordinates rather than by the position axis; print the parameter count of that readout in params_per_arm. Both links inherit the ambiguity. Severity (verbatim). strike

Repair applied — 04.6. The read is registered in the Statement, in the required form: the full $|T|$-vector is emitted at position $s-1$ from a $[|T|]$-wide readout, the state axis supplied by the $|T|$ coordinates of the readout rather than by the position axis, and that readout's parameter count is printed in params_per_arm on every arm as part of the matched count (Ruling 3), marked NOT MEASURED — needs the first BED-J cell until an arm is built. The verse prints the two readings the registration closes off — a per-position causal read is unreachable under SymmSupport because $q_i$ depends on neighbours at $j>i$, and a last-position scalar read would return the bed to the D-1 single-position shape the book exists to leave — so both links inherit a registered read instead of the ambiguity, and the Bet E ratio has a denominator.

A-15 · verse 04.6 · severity `strike`#

Flaw (verbatim). Exact operator-level non-representation is read as non-approximability with no D-APPROX bound, which is CHARTER §5 B7, the record's largest unclosed logic gap. Mechanism (verbatim). B7 (D-APPROX), P-10, V-25 Number (verbatim). "an off-diagonal $Q_{ij}>0$ forces $Q_{ji}>0$ under SymmSupport, and no lower-triangular $\hat P$ carries both; so no arm reproduces the oracle and every contrast is creditable". The label is 9 real numbers; a causal readout can emit any point of $\mathbb R^9$, so operator non-containment bounds nothing about $\|\hat q-q\|$. replacement_survives (verbatim). false Required repair (verbatim). Import book 01's approximation bound for the causal class against a SymmSupport resolvent, printed at $|T|=9$, $\rho(Q)=0.9409$, and gate creditability on that bound being non-vacuous; until it exists, mark the creditability claim NOT MEASURED — needs the D-APPROX bound of book 01. Severity (verbatim). strike

Repair applied — 04.6. The Statement separates the two readings in terms: the DERIVED line establishes operator non-containment and not non-approximability — CHARTER §5 B7 — because the label is $9$ real numbers and the registered readout can emit any point of $\mathbb R^9$, so operator non-containment bounds nothing about $\|\hat q-q\|$. The creditability claim is marked NOT MEASURED — needs the D-APPROX bound of book 01 for the causal class against a SymmSupport resolvent, printed at $|T|=9$, $\rho(Q_{\rm env})=0.9409$, and no contrast on BED-J is creditable until that bound exists and is non-vacuous at that geometry; when it exists the contrast is creditable only in form A2, against the depth skyline in the same row, because a deeper softmax stack computes the same resolvent by iteration. The Evidence carries the same NOT MEASURED line pointing at book 01.

A-16 · verse 04.7 · severity `strike`#

Flaw (verbatim). The reach-avoid label is undefined for every candidate move that is not the move actually played, so the argmin and the Chebyshev rule have no label on $m-1$ of $m$ candidates. Mechanism (verbatim). V-10, D-2 Number (verbatim). "the indicator that the game's own continuation enters $\mathcal A_k$ within $h$ plies after $a$" — a PGN game has exactly one continuation, the one after its played move. For a candidate $a$ not played, no continuation exists in the corpus. replacement_survives (verbatim). false Required repair (verbatim). Define the label by rollout rather than by the corpus: a fixed-depth engine or a fixed policy plays $h$ plies from the post-$a$ position and the indicator is read from that rollout, with the rollout policy pinned and hashed per Ruling 7. Link 1 (hygiene bed only) survives because it drops every label channel; link 2 survives trivially. Severity (verbatim). strike

Repair applied — 04.7. The reach-avoid label is redefined by rollout, never by the corpus: a fixed rollout policy $\pi_{\rm roll}$ plays $h=8$ plies from the post-$a$ position and the indicator reads whether that rollout enters $\mathcal A_k$ — a Bernoulli label per $(\text{FEN},a,k)$ whose floor is its base rate at that $h$. The verse prints the reason the corpus definition is unavailable by construction — a PGN game has exactly one continuation, so for the $m-1$ candidates the game did not play no continuation exists and the argmin and the Chebyshev rule would have no label — and pins $\pi_{\rm roll}$ and $h=8$ per Ruling 7 (generator, seed, sha256 in the manifest beside the bed's), frozen before any draw (M-2), both [ASSUMED] registrations of this book with the reason printed ($h=8$ matches the $t^\star=8$ of the synthetic ladder) and neither fitted to a result. The base rate of each $\mathcal A_k$ at $h=8$ over the $36$ fixture games is NOT MEASURED — needs one rollout pass over the fixtures, $0$ GPU-s, and the Kill strikes any capability number quoted before it is printed. Link 1 is stated to survive every defect of the label definition, the horizon and the join because it drops every label channel.

What this batch did not close#

Nothing in this batch is left OPEN: all sixteen findings are strike and all sixteen are repaired above. Two are repaired by subtraction rather than by a number, and the loss is carried in the Terminals rather than hidden. 04.11 has no control arm to run and K-E1 is unreachable until two make_arm branches exist, so this book licenses no comparison against ChaCAL, InfSA-Neumann-$16$, the cached mixture, the argmin controls or any skyline, and its seven-arm arena price is [ASSUMED]. 04.6 credits no contrast at all until book 01's D-APPROX bound is printed and non-vacuous at $|T|=9$, $\rho(Q_{\rm env})=0.9409$. Four replacements were rewritten rather than renamed after replacement_survives: false — 04.11's chain (the operator read at $0$ GPU-s, then the FOUND route at $82$–$260$ GPU-s), 04.2's link 3 (given its own Hypotheses, Evidence and Kill), 04.4's link 2 (the null recomputed on the new token list) and 04.6's read registration, which both links now inherit — and one link was scoped rather than replaced, 04.2's link 1, which states that it does not touch the no-op rate and routes a clause-9 or clause-11 failure past itself to link 2.

Repair round 1, batch 2 of 5: sixteen findings, all of severity strike. Every finding is reproduced verbatim — verse, flaw, mechanism, number, replacement_survives, required repair, severity — beside the verse id repaired and what changed. Nothing is softened; where a replacement died with its verse a genuinely different one is derived, on a different object, with a different instrument and a different number, and where none could be derived the row reads OPEN with the Terminal now in force printed.

A-17 · verse 04.7 · severity `strike`#

Flaw (verbatim). The horizon $h$ that fixes the label and its base-rate floor is never given a value or an evidence class anywhere in the book. Mechanism (verbatim). P-1, M-2 Number (verbatim). $h$ appears once, in "within $h$ plies after $a$", with no number; the Limits section says only that the predicates and $h$ "have no draw behind them". The floor of the capability channel is "its base rate", which is a function of $h$. replacement_survives (verbatim). true Required repair (verbatim). Freeze $h$ before any draw (M-2), print the base rate of each $\mathcal A_k$ at that $h$ over the 36 fixture games, and register the base rate as the floor per constraint set. Severity (verbatim). strike

Repair applied — 04.7. The horizon is frozen in the Statement at $h=8$ plies with its evidence class printed, [ASSUMED] and the reason given ($h=8$ matches the $t^\star=8$ of the synthetic ladder so the two beds ask a comparable number of hops), under M-2 as a registered constant of this book that is never re-chosen after a draw; M-2 and L-FLOOR are added to the Mechanism line. The base rate is registered as a fourth floor object beside the three of 04.3, per constraint set and per horizon: for each $k\in\{0,1,\dots,K\}$ the floor is $\mathrm{base}_k(h{=}8)=\max\{p_k,1-p_k\}$ with $p_k$ the fraction of $(\text{FEN},a)$ pairs whose $\pi_{\rm roll}$ rollout enters $\mathcal A_k$ within $8$ plies over the $36$ fixture games, printed in the cell's floor_zeroinfo slot beside the number it floors. Its value cannot be printed here without writing a rollout instrument, which the author's standing rule forbids, so it reads NOT MEASURED — needs one rollout pass of $\pi_{\rm roll}$ over the $36$ fixture games at $h=8$, $0$ GPU-s, and the verse adds two decidable clauses: a horizon without a printed base rate is a label without a floor and is struck by L-FLOOR; a base rate printed at any horizon other than $h=8$ is struck by M-2. The eval-$\Delta$ kill now names $\mathrm{base}_k(8)$ as the quantity its Clopper–Pearson half-width is taken against. The Limits paragraph replaces "the predicates and $h$ have no draw behind them" with the frozen $h=8$ and the outstanding base rates.

A-18 · verse 04.9 · severity `strike`#

Flaw (verbatim). The frozen kill threshold is rounded strictly above the only realised instance that motivates it, so the historical failure does not fire it. Mechanism (verbatim). V-11, V-15, M-3 Number (verbatim). Kill: "$\sigma_d\ge2.18\times0.050146=0.109318$". The M-3 precedent's realised sd is $0.109199$ (READ docs/sources/sections/sec_beds.md:313; MISTAKES.md:464-494), and $0.109199<0.109318$. The ratio is $0.109199/0.050146=2.1776$, rounded up to $2.18$. replacement_survives (verbatim). true Required repair (verbatim). Freeze the threshold at the realised value $\sigma_d\ge0.109199$, not at the rounded multiplier, and print the ratio to four figures ($2.1776$). Severity (verbatim). strike

Repair applied — 04.9. K-P is frozen at $\sigma_d\ge0.109199$, the M-3 precedent's realised value itself, with both pins printed (READ docs/sources/sections/sec_beds.md:313; MISTAKES.md:464-494). The ratio $0.109199/0.050146=2.1776$ is printed to four figures as a read-out and never as the threshold, and the struck form is kept visible in the verse with the arithmetic that condemns it: $0.109199<0.109318$, so the one historical instance the kill exists to catch fell $1.19\times10^{-4}$ below its own bar and would not have fired it (V-11, V-15, M-3). Clause 6 of the Statement — the noncentral-$t$ repricing rule — is restated on the same value rather than on $2.18\times$ the pilot. The Evidence line carries the four-figure ratio and the two pins; V-11, V-15, V-17 and P-1 are added to the Mechanism line; the "Kills, cheapest first" row for 04.9 reads $0.109199$ with the struck $0.109318$ named beside it.

A-19 · verse 04.9 · severity `strike`#

Flaw (verbatim). The planted negative does not fire the verse's kill; it demonstrates a different property. Mechanism (verbatim). V-15 Number (verbatim). K-P fires on $\sigma_d\ge0.109318$. Two bit-identical arms give $\sigma_d=0$ and return NO VERDICT — the opposite end of the range. The M-13 half-width figure quoted ($0.8807\sigma$ against a $0.5\sigma$ margin) is about TOST, not about $\sigma_d$. replacement_survives (verbatim). true Required repair (verbatim). Plant an arm pair whose per-seed difference is deliberately heteroscedastic (one arm at a seed-dependent learning rate), whose realised $\sigma_d$ exceeds $0.109199$ and makes K-P fire; keep the bit-identical pair as the separate no-false-parity control it is. Severity (verbatim). strike

Repair applied — 04.9. K-P's planted negative is now an arm pair that instantiates K-P's own condition: both arms are the depth-1 softmax control on byte-identical draws, and arm B alone takes a seed-dependent learning rate $\eta(\text{seed})=\eta_0\cdot2^{(j-4)/2}$ at the $j$-th of the eight seeds — a spread of $2^{3.5}=11.31\times$ across the lane, registered before the run and journalled in producer_cmd — so the per-seed differences inherit the spread, the realised $\sigma_d$ of the pair must exceed $0.109199$, and K-P must fire on it. The bit-identical pair is retained under its own name as the no-false-parity control, with the verse stating in terms that it sits at the opposite end of the range ($\sigma_d=0$), that the M-13 half-width $0.8807\sigma$ against a $0.5\sigma$ margin is about the TOST branch and not about $\sigma_d$, and that it is therefore not this kill's planted negative. Both plants read NOT MEASURED — needs the first eight seeds (04.21). V-15 is added to the Mechanism line.

A-20 · verse 04.9 · severity `strike`#

Flaw (verbatim). The matched-parameter bar carries no evidence class and no source; the CHARTER fixes only the residual that is matched, not the boundary. Mechanism (verbatim). P-1, Ruling 3 Number (verbatim). Clause 2: "a count differing from the shape's by more than $0.1$ per cent after the head is attached is not matched; $0.032$ per cent is matched". CHARTER §1 and §5 B19 fix only $25{,}736{,}232$ vs $25{,}728{,}000$, a $0.0320$ per cent residual; $0.1$ appears in neither. replacement_survives (verbatim). true Required repair (verbatim). Either cite Ruling 3's own bar at V17K_RULINGS.md:56-59 @ 99777ab with its number, or mark $0.1$ per cent [ASSUMED] three times the largest matched residual on record and freeze it here as a new constant. Severity (verbatim). strike

Repair applied — 04.9. Both halves of the required repair are done, and the first shows why the second is needed. Ruling 3 is quoted at its pin — READ V17K_RULINGS.md:56-59 @ 99777ab, "0.032% residual is MATCHED. Print exact counts in every table header + one COSTS line" (RUN this session, git show 99777ab:V17K_RULINGS.md) — and it prints no upper bar at all, so the citation cannot supply one. The record's sole matched instance is therefore stated with its arithmetic: $25{,}736{,}232$ against $25{,}728{,}000$ is a residual of $8{,}232$ parameters $=0.0320$ per cent (CHARTER §5 B19, DERIVED from the two counts). The boundary is then frozen in clause 2 as a new constant of this book at $0.0960$ per cent, marked [ASSUMED] three times the largest matched residual on record, $3\times0.0320=0.0960$, with the multiplier printed and the product not rounded to $0.1$, because rounding a frozen threshold away from the instance that motivates it is the identical V-11 defect A-18 convicts in the same verse. The three bands are stated: $0.0320$ per cent matched by Ruling 3's own text; $(0.0320,0.0960]$ per cent matched by this book's constant, which is printed beside the number; above $0.0960$ per cent unmatched, licensing no A1 and no A2 sentence. The Evidence and the Limits paragraph carry the constant and its derivation once.

A-21 · verse 04.9 · severity `strike`#

Flaw (verbatim). A2 is operationalised against an arm at unmatched depth and unmatched parameter count, which is not the CHARTER's A2. Mechanism (verbatim). Ruling 3, R-SKY, V-17 Number (verbatim). Clause 3: "The depth-$\lfloor\log_2t^\star\rfloor+2$ softmax stack ($3/5/7$ at $t^\star=2/8/32$) at unmatched depth"; 04.20 Hypotheses: "its parameter count is printed as unmatched". CHARTER §1: "(A2) at matched parameters against the depth skyline". replacement_survives (verbatim). true Required repair (verbatim). Register a second skyline arm at depth 5 and reduced width so its parameter count lands within the matched bar, and read A2 against that arm; keep the unmatched depth-5 stack as $\Delta_{\rm sky}$, a printed control that licenses no A2 sentence. Severity (verbatim). strike

Repair applied — 04.9, 04.20, 04.6. Clause 3 is split into two named arms and the A2 licence is moved off the unmatched one. 3a is the depth-$\lfloor\log_2t^\star\rfloor+2$ stack at full width and unmatched parameters, printed beside every matched contrast as $\Delta_{\rm sky}$; it satisfies R-SKY's requirement that the depth skyline be read beside every bed and the verse states in terms that it licenses no A2 sentence at all, because CHARTER §1 defines A2 at matched parameters and 04.20's own Hypotheses print this arm's count as unmatched. 3b is a fourth skyline arm registered here: the same depth $5$ at reduced width, the width fixed before any draw as the largest per-layer width whose total count lands within clause 2's $0.0960$ per cent of the shape's, with sky_width and the exact params_per_arm printed (04.15). A2 is read against 3b and against nothing else; A1 is read only where 3a's row is filled. The width itself reads NOT MEASURED — needs one parameter-count arithmetic pass over the registered stack once the $[m,K+2]$ head's count is fixed, $0$ GPU-s, and the consequence is carried rather than hidden: until it is printed, no A2 number exists on any bed of this book. 04.20's Statement now registers four skylines and its Hypotheses distinguish the two counts; its Bet D is read against 3b; its link 1 runs the depth ladder $\{3,5,7\}$ each at its own matched width; its Terminal states that no A2 number exists anywhere in this book. 04.6 link 1 inherits the same reading. Ruling 3 and V-17 are added to 04.20's Mechanism line, and the Limits paragraph carries the loss once.

A-22 · verse 04.10 · severity `strike`#

Flaw (verbatim). The planted negative is confounded by the very arms it is meant to control, so it fires on a stationary clock and certifies nothing. Mechanism (verbatim). V-15, C17 Number (verbatim). Plant: "a deliberately serial run order (all shape cells first, then all control cells) must reproduce a significant $\rho$". With a perfectly stationary clock, a serial order still produces $|\rho|=1$ whenever the two arms differ in per-step cost; the book's own figure for that difference is $2.514-1.473=1.041$ ms/step at $n=2048$ (RUN[NEPTUNE]). replacement_survives (verbatim). true Required repair (verbatim). Plant the confound inside one arm: run the same arm twice, serially, with an injected monotone load (a background occupancy ramp), and require $|\rho|>0.5$ at $p<0.05$ across those same-arm timings only. Severity (verbatim). strike

Repair applied — 04.10. The cross-arm serial plant is struck with the arithmetic that condemns it printed in place: with a stationary clock a serial cross-arm order still reads $|\rho|=1$ whenever the two arms differ in per-step cost, and this book's own figure for that difference is $2.514-1.473=1.041$ ms/step at $n=2048$ (RUN[NEPTUNE]), so the plant fires on a clock with no drift at all. The replacement injects the confound inside one arm: the same arm — the depth-1 softmax control — is run twice, serially, over $N\ge16$ interleaved cells with a monotone background occupancy ramp registered in producer_cmd and journalled with run_index, and the requirement is $|\rho|>0.5$ at $p<0.05$ computed across those same-arm timings alone, so a per-step cost difference between arms cannot produce the correlation and only the injected drift can. The unramped same-arm pair is retained beside it as the must-not-fire half ($|\rho|\le0.5$ or $p\ge0.05$). Both plants read NOT MEASURED — needs the synchronised, interleaved arena. V-15 is added to the Mechanism line.

A-23 · verse 04.12 · severity `strike`#

Flaw (verbatim). The Kill's stated reason for costing nothing is false: neither arm is FOUND, so a relabelling does touch cells that do not exist. Mechanism (verbatim). FOUND-not-NAMED, P-4 Number (verbatim). Kill: "no cell re-run, because both arms are FOUND regardless of which is called published". RUN this session: 0 chacal occurrences in any .py in the tree; 0 records under results/ with a chacal kind (24-kind census). Link 1's Hypotheses repeat the same false premise. replacement_survives (verbatim). false Required repair (verbatim). Restate: the convention question is decided before either arm exists, so the relabelling is free because there is nothing to relabel; then mark both arms NOT MEASURED — needs the ChaCAL control implementations. Severity (verbatim). strike

Repair applied — 04.12. The Kill's reason is replaced, not softened: it states that the earlier reason was false, prints the counts that make it false (RUN this session, $0$ chacal source lines and $0$ records for chacal_diag and chacal_published in the $24$-kind census), and restates the true one — the convention question is decided before either arm exists, so the relabelling is free because there is nothing to relabel; the decision fixes which arithmetic a future make_arm branch emits under which name and is taken at specification time, at $0$ GPU-s, with no journal touched. Both arms are marked NOT MEASURED — needs the ChaCAL control implementations (one make_arm branch, one optimizer path and one field emit per control, $41$–$130$ GPU-s per branch on 04.14'sarm_plbasis) and no sentence of the verse compares them on any bed. Because replacement_survives was false — link 1's Hypotheses repeated the same false premise — link 1 is re-derived rather than renamed: it drops both arms and asks whether the distinction the names carry is non-empty on this book's own bed, printing $\Delta_{\rm conv}=\|(1-\gamma)A(I-\gamma A)^{-1}-(1-\gamma)A(I-\gamma A_s)^{-1}\|_\infty$ at $\gamma=0.9$ on the causal softmax built from the bed's own $P_{\rm env}$ features, over the $512$ admission draws of 04.2. That is a different object (the environment-derived matrix, not either named arm), a different instrument (one dense solve pair per draw riding on the census the bed already runs, no training, no seeds, no kind) and a different number (an operator $\infty$-distance, not a manifest label), with its own Hypotheses, Evidence, Kill ($\Delta_{\rm conv}<10^{-12}$ on $\ge95$ per cent of draws: the conventions are one operator here, both ChaCAL rows leave 04.11's roster, and no corrections row is owed whichever way the LaTeX reads) and planted negative (an $A$ with its diagonal logit at $-\infty$ gives $A_s=A$ and must read $\Delta_{\rm conv}=0$ bitwise). FOUND-not-NAMED, V-15 and P-4 are added to the Mechanism line; the Terminal now says the two arms are specified and neither is run, and withdraws the attribution sentences the old link 1 carried as its kill.

A-24 · verse 04.12 · severity `strike`#

Flaw (verbatim). The planted negative requires arms that do not exist, so the plant is NAMED — which 04.13's own Kill strikes. Mechanism (verbatim). V-15, FOUND-not-NAMED Number (verbatim). Plant: "the two arms must differ by $O(1)$ at $\gamma=0.9$ on the same $P$". 04.13's Kill: "Any plant passing, or any plant that exists only in a script's print (NAMED)." 0 chacal hits in the tree. replacement_survives (verbatim). true Required repair (verbatim). Price the plant with the arms it needs, or restate the convention check as a pure arithmetic assertion on a random $A$ ($A_s\mathbb 1=\mathbb 1-\mathrm{diag}(A)<\mathbb 1$), which is checkable at $0$ GPU-s with no arm. Severity (verbatim). strike

Repair applied — 04.12. The second branch is taken. The old plant is named as NAMED and struck against 04.13's own Kill ("any plant that exists only in a script's print"), and is replaced by a pure arithmetic assertion on a pinned random causal softmax $A$, checkable at $0$ GPU-s with no arm, no make_arm branch and no journal: on every row $i$, $(A\mathbb 1)_i=1$ and $(A_s\mathbb 1)_i=1-A_{ii}<1$ strictly, the strictness carried by $A_{ii}>0$ for a causal softmax — the bed's own diagonal read is $\max_i\hat P_{ii}=0.692660$ (04.2) — with the gap $\min_iA_{ii}$ printed. Its must-fire half is a known-degenerate case: an $A$ built with its diagonal logit at $-\infty$ makes $A_s=A$, the gap reads $0$ exactly, and the check must report the two conventions indistinguishable. If the assertion cannot be evaluated on a pinned instance, the convention field is not wired and the kill cannot see it.

A-25 · verse 04.13 · severity `strike`#

Flaw (verbatim). The verse's own Kill fires on its own table: two bind rows require a ChaCAL arm that has no implementation and no record, so their plants cannot have entered at the front door. Mechanism (verbatim). V-14, FOUND-not-NAMED, V-15 Number (verbatim). B-J's third plant: "ChaCAL-published's $A_s\Rightarrow O(1)$ at every $\gamma>0$". B-E1's identity half: "$\mathcal A=\emptyset\Rightarrow$ torch.equal with ChaCAL-diag". RUN this session: 0 chacal occurrences in any .py; the Kill reads "any plant that exists only in a script's print (NAMED)". replacement_survives (verbatim). false Required repair (verbatim). Mark the two ChaCAL-dependent rows NOT MEASURED — needs the ChaCAL control implementations and state that B-J and B-E1 are admissible on their remaining plants only ($\gamma=0.5\Rightarrow2.3003$; $\beta=0\Rightarrow\max|{\rm gap}|>0.5$; the rows-changed weight statement). Severity (verbatim). strike

Repair applied — 04.13. Both entries are marked in the table itself: B-J's third plant reads NOT MEASURED — needs the ChaCAL control implementations, struck as a plant of that bind; B-E1's identity half reads the same and is struck as this bind's identity half. The verse then states the counts that convict them (RUN this session: $0$ chacal source lines, $0$ records for chacal_diag and chacal_published in the $24$-kind census), names them NAMED against its own Kill, and states that B-J is admissible on its remaining plants only ($\gamma=0.5\Rightarrow2.3003$; $\beta=0\Rightarrow\max|{\rm gap}|>0.5$) and B-E1 on the rows-changed weight statement plus an arm-free identity half only. Because replacement_survives was false — link 1's "the remaining plants stand" left B-E1 with no identity half at all — the chain is re-derived: B-E1's identity half becomes the arm-free operator identity of 04.11 link 1, $\mathcal A=\emptyset\Rightarrow\|\Pi_{\rm row}-\Pi_{\rm col}\|_\infty=0$ bitwise on the bed's own $P_{\rm env}$, with plant $\mathcal A\ne\emptyset\Rightarrow\|\Pi_{\rm row}-\Pi_{\rm col}\|_\infty\ge10^{-12}$, and B-J's ChaCAL plant becomes 04.12's replaced diagonal arithmetic, $A_s\mathbb 1=\mathbb 1-\mathrm{diag}(A)<\mathbb 1$ strictly with the gap printed — a different object (the environment chain and a pinned softmax, not any arm), a different instrument (a dense solve pair on the admission census, no make_arm branch) and a different number (an operator $\infty$-distance and a row-sum gap, not a torch.equal against an arm). Link 1 now drops a bind to a remark only when it has no arm-free half and no arm-free plant, and carries its own kill (the restated arm-free half satisfied by construction on $\ge95$ per cent of the $512$ draws) at $0$ GPU-s. FOUND-not-NAMED, V-15 and P-1 are added to the Mechanism line; the Terminal withdraws both ChaCAL entries by name.

A-26 · verse 04.13 · severity `strike`#

Flaw (verbatim). The Hypotheses concede that every number in the table violates the Statement's own front-door rule, and no verse prices the reproduction that would repair it. Mechanism (verbatim). V-14, P-1 Number (verbatim). Statement: "every plant enters at the front door — bed.build → arm.forward → journal row → verdict() — as a FOUND cell with its own kind and manifest_hash, never as an identity check on random logits". Hypotheses: "Each plant's number was obtained on a random-logit instance (seed 0, $s\in\{32,64\}$, float64, CPU)". replacement_survives (verbatim). true Required repair (verbatim). Mark every number in the bind table NOT MEASURED at the front door — needs the first BED-S cell (04.21 step 2), and add the front-door reproduction to 04.21's ordered list with its price, so the bind table is inadmissible-until rather than admissible-with-a-hypothesis. Severity (verbatim). strike

Repair applied — 04.13, 04.21. The table is restated as inadmissible-until, not admissible-with-a-hypothesis: the verse prints the contradiction in terms — every number in the third and fourth columns was obtained on a random-logit instance and therefore violates the Statement's own front-door rule — and marks each NOT MEASURED at the front door — needs the first BED-S cell (04.21 step 2), the printed value being the target the reproduction must hit rather than an admitted bind number. No bind of the table is admissible until 04.21 step (2) reproduces its plants through the front door, and a verse elsewhere in the canon citing a bind number without that reproduction cites a NOT MEASURED figure and is struck at assembly. The Hypotheses no longer concede the violation as a standing condition; they now assert only that an admitted draw exists to reproduce on, that the reproducing arm emits its own kind and manifest_hash (04.15), and that the random-logit values are targets and not bind evidence. 04.21's step (2) is expanded to carry the reproduction with its price — nine bind rows, one admitted draw each, $\approx9\times1.680\approx15.1$ s [ASSUMED] on the arm_smprime cell basis, $0.5$ evening — and states that no verse may cite a bind number until that journal exists. The "Kills, cheapest first" row for 04.13 and the Terminal both carry the reading, and the Limits paragraph records once that no bind has entered at the front door.

A-27 · verse 04.15 · severity `strike`#

Flaw (verbatim). The Hypotheses and link 1 assert the shape lane has no stored cells, but the book never names the shape's kind, and the census it cites reads 425 records for the arm whose file the book treats as the shape. Mechanism (verbatim). P-1, V-7, FOUND-not-NAMED Number (verbatim). Link 1 Hypotheses: "zero shape-lane cells exist under results/ (04.14's census reads no shape kind)". RUN this session: arm_smprime 425 under results/; ceq/arm_smprime.py:346 emits "kind": NAME. The string arm_smprime never appears in 04_BEDS_AND_INSTRUMENTS.md; the only arm kinds named are arm_phase and arm_pl. replacement_survives (verbatim). false Required repair (verbatim). Name the shape's kind in this verse. If it is arm_smprime, the claim 'zero shape-lane cells exist' is false and link 1's decisiveness argument ('a published hash moved by the repair — impossible in a lane with no published cell') fails; if the shape's kind is new and unemitted, say so and mark the 425 arm_smprime records as a different lane with the discriminator printed. Severity (verbatim). strike

Repair applied — 04.15. The second branch is the true one and it is stated with its evidence. The shape's kind is named in the verse as arm_ceq, and it is unemitted: RUN this session, grep -rn 'arm_ceq' --include='*.py' . (excluding .venv) returns $0$ lines and 04.14's $24$-kind census holds $0$ records for it. The $425$ arm_smprime records are marked a different lane with their provenance printed — NAME = "arm_smprime" at READ ceq/arm_smprime.py:77 emitting "kind": NAME at :346, records carrying "task": "chain_label_complex" / e3_t2 and splitting $320$ t: trace, $48$ rescore, $20$ cell, $6$ bind, $3$ agg, $3$ identity, $3$ probe, $2$ contrast (RUN this session). The discriminator is printed and it is this verse's own field: grep -rl 'boundary_sets' results --include='*.jsonl' returns $0$ files (RUN this session), so $0$ of the $425$ and $0$ of all records under results/ declare a boundary set; a cell is a shape-lane cell iff its kind is arm_ceq and it carries boundary_sets, goal_set and sink_set with their sha256s, and both counts read $0$. Because replacement_survives was false, link 1 is restated on the discriminator rather than on the name, its kill sharpened to "a record under results/ carrying boundary_sets whose manifest_hash differs before and after", and the verse states in terms that its decisiveness falls the moment the discriminator is non-zero — and a genuinely different link 2 is derived for that case: the field list itself is hashed into instrument_hash so that a later addition or removal of a field is visible without touching any cell's manifest_hash, killed by two cells sharing one instrument_hash and carrying different field sets, at $0$ GPU-s. That is a different object (the specification, not a cell), a different instrument (a hash over a static list, not a re-emission) and a different number (a field-set mismatch, not a moved cell hash). V-7 and FOUND-not-NAMED are added to the Mechanism line; the Terminal prints both zero counts and states that the $425$ arm_smprime records are evidence for nothing in this book.

A-28 · verse 04.16 · severity `strike`#

Flaw (verbatim). The kill clause "an F4 without its suffix" is satisfied 68 times at registration and then exempted 68 times by the verse's own grandfather Hypothesis. Mechanism (verbatim). V-3, V-10 Number (verbatim). RUN this session: git show 99777ab:V20_R15_THEORY_TABLE.md | grep -oE 'F4-?[DWU]?' reads 31 bare F4 and 0 suffixed; the same over V20_R15_LEAP_LEDGER.md reads 37 bare and 0 suffixed. Hypotheses: "a cell graded under an older rubric keeps its token with the rubric's date beside it." replacement_survives (verbatim). true Required repair (verbatim). Restrict the kill to cells graded on or after the rubric's own date, and add a one-off migration line: the 68 pre-rubric bare F4 tokens are re-graded into -D/-W/-U with a supersedes row each, priced at $0$ GPU-s in 05 REPAIRS. Severity (verbatim). strike

Repair applied — 04.16. The kill clause is restricted in the Kill itself — "an F4 without its suffix on a cell graded on or after 2026-09-05" — with the instrument's grep filtered to rows whose date field is on or after the rubric's own date, so the rule is no longer satisfied at registration and then waived in the same verse. The counts are printed: RUN this session, $31$ bare F4 and $0$ suffixed in V20_R15_THEORY_TABLE.md and $37$ bare and $0$ suffixed in V20_R15_LEAP_LEDGER.md at 99777ab — $68$ bare, $0$ suffixed. The one-off migration is scheduled rather than grandfathered: all $68$ tokens are re-graded into F4-D / F4-W / F4-U by each cell's own reason, each filed as a new row with a supersedes pointer and neither row edited (L-G2), priced at $0$ GPU-s and $1$ evening as a row of 05 REPAIRS. The Hypotheses now state that the exemption is a scheduled debt with a printed size, never a silent waiver; the planted negative is calibrated both ways (a post-rubric bare F4 must be caught by the filtered grep and a pre-rubric one must not); V-3 and V-10 are added to the Mechanism line; the Terminal and the "Kills, cheapest first" row carry the $68$ un-migrated tokens by name.

A-29 · verse 04.18 · severity `strike`#

Flaw (verbatim). The RUN census is uncommitted working-tree state that does not reproduce, and the kill's pattern file is now empty, making the kill read 0 by construction. Mechanism (verbatim). V-11, V-10, P-1, P-2 Number (verbatim). RUN this session: git status --short returns 2 lines (M README.md, ?? docs/canon/) and 0 lines marked D, against the verse's "$259$ deletions, of which $244$ are root-level .md documents". The Hypotheses define the pattern file as "the set marked D in git status --short", which is now empty, so grep -rlF -f deleted_docs.txt tests --include='*.py' reads $0$ unconditionally. git diff --name-status 99777ab HEAD reads 350 D, of which 244 are root-level .md — the one number that survives. replacement_survives (verbatim). false Required repair (verbatim). Redefine the pattern file as the D rows of git diff --name-status 99777ab c71527a restricted to root .md (244 paths), which is permanent, and re-run every count against it. Both links inherit the empty-pattern-file defect. Severity (verbatim). strike

Repair applied — 04.18. The pattern file is redefined in the Hypotheses as the rows marked D in git diff --name-status 99777ab c71527a restricted to root-level .md — $244$ paths fixed by two commit shas and reproducible from any checkout forever — and the struck definition is kept visible with the arithmetic that condemns it: RUN this session, git status --short returns exactly $2$ lines (M README.md, ?? docs/canon/) and $0$ rows marked D, so the old pattern file was empty and the Kill's grep read $0$ unconditionally, a kill satisfied by construction resting on state that does not reproduce (V-10, V-11, P-2). The Kill now names the two shas so it is decidable in any checkout and cannot be emptied by a clean tree, and it carries a two-way plant: a coupled test must be caught, and the $244$-path file must read $120$ today, a non-zero must-fire calibration the empty file could never give. Both links inherit the repaired file — link 1's file list is the $120/239$ census, link 2's subset is recounted at $39$ files — and V-10, V-11, P-1 and P-2 are added to the Mechanism line. The Limits paragraph names the struck numbers ($259$, $187/291$, $36$, $2971$) so no reader recovers them.

A-30 · verse 04.18 · severity `strike`#

Flaw (verbatim). The claim that no test files were deleted is false at HEAD, and every derived count in the Evidence is a stale working-tree number. Mechanism (verbatim). P-1, P-2, V-26 Number (verbatim). RUN this session: of the 350 D rows in git diff --name-status 99777ab HEAD, 60 match (^|/)test_[^/]*\.py$, against the verse's "$0$ test files are deleted". tests/**/test_*.py at 99777ab is 291; at HEAD it is 239. grep -rlF -f <the 244 deleted root docs> tests --include='*.py' reads 120, against the verse's 187. replacement_survives (verbatim). false Required repair (verbatim). Re-run the whole census at a named commit and print it as RUN @ <sha>: 244 deleted root documents, 239 surviving tests/**/test_*.py, 120 naming at least one deleted document, and the sub-counts for line-reading and literal .md:NNN. Severity (verbatim). strike

Repair applied — 04.18. The whole census is re-run and printed as RUN @ c71527a (git rev-parse HEAD reads c71527a64687043f2afa1667fe6485cc71022179): $350$ rows marked D, of which $244$ are root-level .md and $60$ match (^|/)test_[^/]*\.py$. The claim "$0$ test files are deleted" is stated as false and struck in the verse, with the loss printed rather than described: tests/**/test_*.py reads $291$ at 99777ab and $239$ at c71527a (and $239$ in the working tree), a net loss of $52$ files. Against the $244$-path pattern file, grep -rlF -f deleted_docs.txt tests --include='*.py' reads $120$, not $187$, of which $108$ are test_*.py; of those $108$, $43$ also read lines; $32$ test_*.py carry a literal .md:NNN; $71$ test_*.py read results/ or a .jsonl and $39$ of those name no deleted document. Root collection is re-run to 2580 tests collected, 22 errors in 16.43s, replacing 2971 tests collected, 26 errors in 13.52s; tests/gate0/ holds $15$ test_*.py, of which test_g05_data.py is $31$ passed. Link 2's subset is $39$ files, not $36$; the Terminal carries the $60$ deleted test files and the $291\to239$ fall; the Limits paragraph names every struck number once.

A-31 · verse 04.21 · severity `strike`#

Flaw (verbatim). The verse's Kill forbids the threshold six other verses of this book freeze their kills at. Mechanism (verbatim). M-2, P-1, V-11 Number (verbatim). 04.21 Kill: "a bet scored against the placeholder $\mathrm{MDE}_8=0.039827$ instead of the realised cell". 04.9 Evidence: "BED-S's $\sigma_d$: NOT MEASURED — needs the first eight seeds (04.21); every $\mathrm{MDE}_8$ above is a placeholder until then." Kills frozen at $\mathrm{MDE}_8$: 04.3 ($\ge2/8$ against printed floors), 04.5, 04.6 (Bet E, marginal $\varphi$-NRMSE within $\mathrm{MDE}_8$), 04.7, 04.11 (K-E1, within $\mathrm{MDE}_8$ on $\ge6/8$), 04.20 (Bet D, $>\mathrm{MDE}_8$). replacement_survives (verbatim). true Required repair (verbatim). Mark every $\mathrm{MDE}_8$ threshold in the book NOT MEASURED — needs $\sigma_d$ from 04.21 step (5) and restate the six kills in units of $\mathrm{MDE}_N$ at the realised $\sigma_d$, so a threshold is frozen as a rule rather than as a placeholder number. Severity (verbatim). strike

Repair applied — 04.9, 04.3, 04.4, 04.5, 04.6, 04.7, 04.11, 04.20, 04.21. A new clause 7, the placeholder rule, is added to 04.9's Statement: BED-S has no realised $\sigma_d$, so every numeric $\mathrm{MDE}_8$ in this book is a placeholder and none of them is a frozen threshold; a kill is frozen as a rule in units of $\mathrm{MDE}_N$ at the realised $\sigma_d$, with $N$ the smallest seed count of 04.9 link 1 whose $\mathrm{MDE}_N$ falls below the smallest registered effect, and never as the number $0.039827$ or $0.126238$. The rule is frozen now (M-2) and the number it evaluates to is filled later, which is the only order in which a threshold can be both frozen and honest on a bed with no cell. Every affected kill is restated and each carries NOT MEASURED — needs $\sigma_d$ from 04.21 step (5) at its own site: 04.3 (the $\ge2$-of-$N$ floor clause, with the note that the count $2$ is a seed-count rule and only the denominator waits on $\sigma_d$), 04.4 link 1 (R0 accuracy), 04.5 (the Clopper–Pearson half-width at $N$), 04.6 Bet E and link 1, 04.7 (the majority-sign half-width at $N$, against $\mathrm{base}_k(8)$), 04.11 K-E1, 04.20 Bet D and link 1. 04.21's own Kill is widened from the single number $0.039827$ to any placeholder $\mathrm{MDE}_8$ row, names the eight kills that used to carry one so the prohibition has a referent, adds a grep of the scored journal for a literal $\mathrm{MDE}_8$ constant to its instrument, and carries a two-way plant (a row written with the literal $0.039827$ must be refused; the same row written as "$\mathrm{MDE}_N$ at $\sigma_d$ from this journal" must pass). The "Kills, cheapest first" table and the Limits paragraph carry the same reading.

A-32 · verse 04.21 · severity `strike`#

Flaw (verbatim). The ordered run sequence puts the controls before the shape, while two of those controls are defined in 04.11 only after the shape has trained. Mechanism (verbatim). M-2, D-4 Number (verbatim). 04.21 step (3): "the controls of 04.11 run before the shape (order stated)". 04.11 Hypotheses: "ChaCAL-with-sink is defined only after the shape trains (its $\hat\gamma$), so the pair is sequential"; ChaCAL-diag is likewise "at the shape's trained $\hat\gamma$". replacement_survives (verbatim). true Required repair (verbatim). Split step (3): the $\hat\gamma$-free controls (0-hop MLP, 1-hop softmax, majority, random, predict-the-mean, the depth-5 skyline, InfSA-16) run before the shape; the $\hat\gamma$-dependent ChaCAL arms run after, with the order and the inherited $\hat\gamma$ printed in the manifest. Severity (verbatim). strike

Repair applied — 04.21. Step (3) is split. (3) the $\hat\gamma$-free controls — the 0-hop MLP, the 1-hop softmax, majority, random, predict-the-mean, the depth-$\lfloor\log_2t^\star\rfloor+2$ skyline of 04.20 and InfSA-Neumann-$16$, every one defined without reference to any trained quantity — run before the shape, in the randomised interleaved order of 04.10 recorded per cell. (4) the shape runs, producing $\hat\gamma$ per seed. (4a) the $\hat\gamma$-dependent controls run after the shape, because 04.11's own Hypotheses define ChaCAL-diag and ChaCAL-with-sink only at the shape's trained $\hat\gamma$; scheduling them at step (3) would start a contract behind an unreached round (D-4) and would freeze a dial after the data (M-2). Their order and the inherited $\hat\gamma$ are printed in the manifest — 04.15's gamma block (init, final $\hat\gamma$, $\Lambda$, verdict) plus the seed whose $\hat\gamma$ was inherited — so the sequential dependency is auditable and no reader mistakes a post-shape control for a pre-registered one. The Kill gains a third clause: a $\hat\gamma$-dependent control journalled at step (3) rather than step (4a) is struck, because it records a dial chosen after the data. D-4 and M-2 are restated on the Mechanism line with what each now covers.

What batch 2 did not close#

Nothing in this batch is left OPEN: all sixteen findings are strike and all sixteen are repaired above. Five are repaired by subtraction, and the loss sits in the Terminals and in Limits rather than in a softened sentence. No A2 number exists anywhere in this book (A-21): the only depth-5 stack registered before this repair was at unmatched depth and unmatched parameters, so it is now $\Delta_{\rm sky}$, a printed control, and the matched-width skyline A2 requires has no width, no count and no cell. No bind of 04.13 has entered at the front door (A-26), so no verse of this canon may cite a bind number until 04.21 step (2) exists. Neither ChaCAL arm exists (A-23, A-24, A-25), so 04.12 runs nothing, two entries leave 04.13's table, and both verses were re-derived to work on the operator with no arm. The shape lane is empty on a discriminator, not on a name (A-27): kind arm_ceq reads $0$ records and boundary_sets reads $0$ files, and the $425$ arm_smprime records are another lane. Sixty test files were deleted between 99777ab and c71527a (A-30), against a verse that claimed $0$, and the whole prose-coupling census is re-run at the named commit. Five replacements were rewritten rather than renamed after replacement_survives: false — 04.12's link 1 (the operator distance $\Delta_{\rm conv}$ at $\gamma=0.9$, no arm), 04.13's link 1 (arm-free identity halves and plants on $P_{\rm env}$ and on a pinned softmax), 04.15's link 1 restated on the boundary_sets discriminator with a genuinely different link 2 (the field list hashed into instrument_hash), and 04.18's two links, both re-based on a commit-pinned pattern file that cannot be emptied by a clean working tree. Three constants are frozen here as this book's own, each with its evidence class and its arithmetic printed: $h=8$ plies [ASSUMED] (04.7), the matched-parameter bar $0.0960$ per cent $=3\times0.0320$ [ASSUMED] (04.9 clause 2), and K-P at the realised $\sigma_d\ge0.109199$ rather than at a rounded multiplier (04.9 clause 6, A-18).

Repair round 1, batch 3 of 5: sixteen findings — two of severity strike, fourteen of severity repair. Every finding is reproduced verbatim — verse, flaw, mechanism, number, replacement_survives, required repair, severity — beside the verse id repaired and what changed. Seven of the fourteen repair findings name defects that batches 1 and 2 had already struck; for those the row prints the finding verbatim, the required repair verbatim, and the exact text now in force, so the reader can check the repair against the finding rather than take a claim of prior repair on trust. Nothing is softened.

A-33 · verse 04.21 · severity `strike`#

Flaw (verbatim). The Statement "No CEQ arm has been trained" is contradicted by the record count under results/ for the arm whose file the repository calls a CEQ arm, and the book never names the discriminator. Mechanism (verbatim). FOUND-not-NAMED, V-7, P-1 Number (verbatim). RUN this session: arm_smprime 425 records under results/; the emitting file is ceq/arm_smprime.py:346 ("kind": NAME). The string arm_smprime appears 0 times in 04_BEDS_AND_INSTRUMENTS.md. replacement_survives (verbatim). true Required repair (verbatim). State the discriminator in the verse: which kind counts as a CEQ arm with boundary rows, and why the 425 arm_smprime records do not. Without it, 'no CEQ arm has been trained' and 04.15's 'zero shape-lane cells' are both unfalsifiable. Severity (verbatim). strike

Repair applied — 04.21. The Statement now carries the discriminator in its own first clause rather than delegating it: a CEQ-arm cell is one whose kind is arm_ceq and which carries boundary_sets, goal_set and sink_set with their sha256s (04.15's field list), and RUN this session both counts read $0$ across all of results/ — grep -rn 'arm_ceq' --include='*.py' . returns $0$ source lines, grep -rl 'boundary_sets' results --include='*.jsonl' returns $0$ files. The $425$ arm_smprime records are named in the verse, with the file and line the finding names — NAME = "arm_smprime" at READ ceq/arm_smprime.py:77 emitting "kind": NAME at :346, records carrying "task": "chain_label_complex" / e3_t2 — and the reason they are not counter-evidence is printed as a fact about them and not as a definition: not one of the $425$ declares a boundary set. The verse states in terms that a reader holding the $425$-record count against the phrase "no CEQ arm has been trained" would be right without the discriminator, so the sentence is now falsifiable by one grep in either direction. The finding's last clause — "the string arm_smprime appears 0 times in 04_BEDS_AND_INSTRUMENTS.md" — was true when filed and was answered in part by batch 2's A-27 repair to 04.15, which introduced the same discriminator there; this batch puts it in 04.21, the verse whose Statement carries the sentence.

A-34 · verse Census rows closed (table) · severity `strike`#

Flaw (verbatim). B27 is assigned to book 04 by the CHARTER and is not closed; the market half of the author's two uses appears nowhere in the book. Mechanism (verbatim). L-DOM, B27 Number (verbatim). CHARTER §5 B27 owning book: "09 CHESS_AND_MARKETS, 04". The census table lists ten rows and does not name B27. RUN this session: grep -ci market 04_BEDS_AND_INSTRUMENTS.md reads 0. replacement_survives (verbatim). false Required repair (verbatim). Add a verse registering the prediction-market bed as an instrument (state as order book and price path, contracts as absorbing sets, the market-implied baseline as the floor, the look-ahead guard and the by-event split with its planted violation), or add a B27 row to the census table naming 09 as the owner and stating exactly which half of B27 book 04 closes (the chess witness's hygiene guards, 04.7). Severity (verbatim). strike

Repair applied — Census rows closed, Preface. The second of the two routes the required repair licenses is taken, and the reason is stated rather than assumed: CHARTER §6 gives book 04 three beds — BED-S, BED-J and the chess witness — and none of them is a market, while CHARTER §6 gives book 09 the market use in full; registering a market bed here would put one object under two owners, which is the M-20 mechanism (two registrations that never met) this book files B23 against, and would risk two books contradicting each other on one bed's floor. A B27 row is added to the census table reading "the two uses — chess half only", closed by 04.7 and naming the owner as "09 CHESS_AND_MARKETS, 04" per CHARTER §5. A paragraph beneath the table states exactly what this book closes (04.7's five hygiene guards with their planted violations, RUN 31 passed in 0.73s; the by-game split and FEN dedupe; the $h=8$ rollout label; its per-constraint base-rate floor; the join-hit census with its discard rule) and exactly what it does not: the market half — the state as order book and price path, contracts as absorbing sets, the market-implied baseline as the floor, the look-ahead guard and the by-event split with its planted violation — appears in no verse of this book, and is closed in 09 alone, at 09.21, 09.22, 09.23a, 09.23b, 09.24, 09.25, 09.28, 09.29b and 09.32, each named. The Preface's "Ten census rows are closed here" is corrected to ten in full plus B27 on its chess half. Because replacement_survives reads false and a census table is not a verse and carries no If-killed chain, the loss is carried by the row itself: the paragraph states that if 09's market verses are struck, B27's market half is closed by nothing in this canon and no verse of book 04 can carry it, the row is then open on that half, and the sentence in force is 04.7's Terminal for chess and silence for markets.

A-35 · verse 04.11 · severity `repair`#

Flaw (verbatim). The verse's own price arithmetic contradicts itself by 18 per cent inside one verse. Mechanism (verbatim). P-1, M-16 Number (verbatim). Evidence: "$\approx52$ s for three arms at eight seeds"; link 1: "$\approx44$ s ($3\times8\times1.681+4$ DERIVED)" for three arms at eight seeds. $3\times8\times1.680+4.0=44.3$ s. The Kill instrument's "$\approx34$ s" for one pair is $2\times8\times1.680+4.0=30.9$ s. replacement_survives (verbatim). true Required repair (verbatim). Replace 52 with 44.3 and 34 with 30.9, or print the missing overhead term that carries 52 and 34 and give it an evidence class. Severity (verbatim). repair

Repair applied — 04.11, 04.6, 04.5, Kills table. The first route is taken: no overhead term exists that carries $52$ or $34$, so both are struck and the arithmetic is printed at every site. 04.11's Evidence now reads $3\times8\times1.680+4.0=44.32$ s for three arms at eight seeds, with the $4.0$ s named as the arena's fixed set-up overhead carried at the same [ASSUMED] class as 04.9's $7\times8\times1.680+4.0\approx98$ s, and states that no overhead term carries the missing $7.7$ s. The pair price is printed as $2\times8\times1.680+4.0=30.88\approx30.9$ s and replaces $\approx34$ s in 04.6's Bet E instrument, in 04.5's link 2 and in the "Kills, cheapest first" row for 04.6. 04.11's K-E1 clause, which cited the three-arm $\approx52$ s for a two-arm pair, is repriced to $\approx30.9$ s with the arithmetic beside it, and its closing sentence ("the price of reaching it is link 2's, not …") carries the corrected figure. 04.6's Bet E instrument is additionally reclassed from [FITTED + RUN] to [ASSUMED], on A-2's ground: neither arm of that pair is FOUND on BED-J. Limits records the three struck prices once.

A-36 · verse 04.11 · severity `repair`#

Flaw (verbatim). A DERIVED price is printed with no steps and is wrong by 12.6x under the only derivation the verse states. Mechanism (verbatim). P-1 (CHARTER §2: DERIVED (steps)) Number (verbatim). "InfSA-16 $\approx5.12$ s per cell DERIVED from the $25.409$ ms hop": $16\times25.409\,\mathrm{ms}=0.407$ s, a factor $12.6$ below $5.12$. Book 06 supplies the missing factor ("InfSA-16's step is $0.034133$ s", 06_PREDICTIONS.md:349): $150\times0.034133=5.12$ s. 04.9's $\approx3.3$ GPU-min arena price rests on the 5.12 figure. replacement_survives (verbatim). true Required repair (verbatim). Print the derivation in this verse: 150 steps per cell x 0.034133 s/step = 5.12 s, and give the 150-step budget its own evidence class. Severity (verbatim). repair

Repair applied — 04.11. The derivation is printed and the class is corrected. The verse now states that $16\times25.409\,\mathrm{ms}=0.407$ s, a factor $12.6$ below $5.12$ s, so the source's own words "DERIVED from the $25.409$ ms hop microbenchmark" (READ docs/CEQ_SHAPE.md:1926 @ 99777ab) do not reproduce and a DERIVED class with no steps is a P-1 defect. The one multiplication that does reproduce is printed: $150$ steps per cell $\times\ 0.034133$ s/step $=5.11995\approx5.12$ s (DERIVED, one multiplication). The $150$-step budget carries its own evidence class, READ scale/e_ladder.py:140 (steps=150), the record's registered cell length; the $0.034133$ s/step is $5.12/150$ read back out of the source figure and is named as such, so the pair is not passed off as an independent measurement. The $\approx5.12$ s therefore enters this book as READ docs/CEQ_SHAPE.md:1926 @ 99777ab, unreproduced, on top of the [ASSUMED] cell basis of A-2, which is how book 06 reads it at 06.28 — the two books now agree on the class as well as the number. 04.9's $\approx3.3$ GPU-min is shown to rest on it, with its arithmetic printed ($98+8\times7.6+8\times5.12=199.8$ s), and inherits the tag. Limits records the reclassification once.

A-37 · verse 04.2 · severity `repair`#

Flaw (verbatim). The oracle price is DERIVED at a geometry 19x larger in $|T|$ than the geometry the bed registers. Mechanism (verbatim). V-17 Number (verbatim). Hypotheses fix $s=64$, so $|T|\le63$. Evidence: "$|T|^3/3=5.76\times10^{8}$ MACs at $|T|=1200$". At $|T|=63$, $|T|^3/3=8.33\times10^{4}$ MACs — $6.9\times10^{3}$ times smaller. replacement_survives (verbatim). true Required repair (verbatim). Reprint the price at the registered geometry ($8.33\times10^4$ MACs, $m(K+2)=32$ right-hand sides) and keep the $|T|=1200$ figure only as a headroom note with its own geometry named. Severity (verbatim). repair

Repair applied — 04.2 (already in force from an earlier batch; verified against this finding). 04.2's Evidence reads, verbatim in the book: "The oracle price at the registered geometry: $s=64$ fixes $|T|\le63$, so $m$ factorisations of $|T|^3/3=8.33\times10^{4}$ MACs each with $m(K+2)=32$ right-hand sides, milliseconds per draw in float64 (DERIVED). The figure $|T|^3/3=5.76\times10^{8}$ MACs holds at $|T|=1200$ and is carried here only as a headroom note at that named geometry, $6.9\times10^{3}$ times the registered one (DERIVED); no admission number rests on it." Both halves of the required repair are met — $8.33\times10^4$ MACs and $m(K+2)=32$ right-hand sides at the registered geometry, and $|T|=1200$ retained only as a headroom note with its geometry named — and the arithmetic checks: $63^3/3=83{,}349=8.33\times10^4$, $8\times4=32$, $(5.76\times10^{8})/(8.33\times10^{4})=6.9\times10^{3}$. No further edit was owed and none was made; the finding is answered by the text quoted, not by an assertion that it was answered.

A-38 · verse 04.2 · severity `repair`#

Flaw (verbatim). Two other verses cite census lines that do not exist in this verse's admission block. Mechanism (verbatim). P-4, P-6 Number (verbatim). 04.2's admission block prints 9 clauses (row sums; $0\in\mathcal A_{\rm sink}$; sets before query; sd $>0.05$; class frequency; disagreement; sink share; discard count; $m_{\rm eff}$). 04.19's Kill instrument names "the census line 15 of 04.2"; 04.8's Hypotheses name "04.4's census line 10" and 04.4 registers two guards and no census at all. replacement_survives (verbatim). true Required repair (verbatim). Number the nine admission clauses explicitly in 04.2 and repoint 04.19 and 04.8 at the numbered lines, or add the missing clauses (per-base admitted fraction; per-coordinate label variance) so the cited numbers exist. Severity (verbatim). repair

Repair applied — 04.19, 04.8; 04.2 verified. Both halves of the required repair are now in force, one from an earlier batch and one from this one. 04.2's block is numbered and carries eleven clauses, the two the finding names among them: clause 4 is the per-coordinate sd line, "every per-coordinate sd of $q$ over the admitted query region $>0.05$, with the fraction of coordinates at zero label variance printed (the mask 04.8 reads)", and clause 10 is "the per-base admitted fraction at the quantifier level each magnitude theorem uses (04.19), printed per base". This batch repoints the two citing verses. 04.19's Kill instrument now names clause 10 and states in the verse that the earlier pointer "the census line 15 of 04.2" named a line that does not exist, the block having eleven numbered clauses and no fifteenth, so the instrument that Kill named was unreachable as written (P-4, P-6). 04.8's Hypotheses and its link 1's Hypotheses now name 04.2's admission clause 4 — the only registered variance census in this book — and each states that the earlier pointer "04.4's census line 10" named a line 04.4 does not carry, 04.4 registering two guards and no census and carrying no numbered lines. Limits names both dangling pointers once.

A-39 · verse 04.4 · severity `repair`#

Flaw (verbatim). The planted-leak bar carries no evidence class and no derivation. Mechanism (verbatim). P-1, M-2 Number (verbatim). "the planted leak (a move token carrying its own $q$) reads $R^2\ge0.99$" — 0.99 appears nowhere in the Evidence, which cites only $R^2=1.000000$ from a different bed (M-21, MISTAKES.md:2101-2189) and 0.9 from rips_gate.py:61. replacement_survives (verbatim). true Required repair (verbatim). Set the planted bar to the measured value on BED-S's own plant, or state [ASSUMED] 0.99, one nine below the M-21 instance with the reason printed. Severity (verbatim). repair

Repair applied — 04.4 (already in force from an earlier batch; verified against this finding). BED-S has no plant and no cell, so the first route is unavailable and the second is taken. 04.4's Statement reads, verbatim in the book: "The planted leak (a move token carrying its own $q$) must read $R^2\ge0.99$ — [ASSUMED] 0.99, one nine below the M-21 instance that read $R^2=1.000000$ when the target was an input channel, the reason being that the plant differs from M-21's only by the quantisation of the copied channel." The Evidence carries the M-21 source (READ MISTAKES.md:2101-2189) as "the sole source of the planted bar's magnitude", and the rips_gate.py:61 pair PASS_BAR = 0.5 / FAIL_BAR = 0.9 is separately struck as V-22 across the bed boundary and retained only as the precedent that names the mechanism. The class, the value and the reason are all printed; no further edit was owed and none was made.

A-40 · verse 04.4 · severity `repair`#

Flaw (verbatim). The zero-hop guard's own statistic has no instrument and is marked NOT MEASURED in a neighbouring verse. Mechanism (verbatim). P-1 Number (verbatim). Statement requires "the plug-in $I(s_0;a^\star)=0$ up to its printed sampling error"; 04.3's Evidence: "$I(X_{\le k};a^\star)$ for BED-S is NOT MEASURED — needs the census of 04.2", and 04.21 lists $I(X_{\le k};a^\star)$ among the objects BED-S does not have. replacement_survives (verbatim). true Required repair (verbatim). Mark the mutual-information half of the zero-hop guard NOT MEASURED — needs the plug-in estimator over the admission census and let the untrained-arm half (the RED gate at $1-10^{-3}$) carry the guard until then. Severity (verbatim). repair

Repair applied — 04.4 (already in force from an earlier batch; verified against this finding). 04.4's Statement reads, verbatim in the book: "The guard's mutual-information half is NOT MEASURED — needs the plug-in estimator for $I(s_0;a^\star)$ over the admission census of 04.2, and until that estimator exists the untrained-arm half — the RED gate at $1-10^{-3}$, which is the harness's own and runnable today — carries the guard alone; no verse reads $I(s_0;a^\star)=0$ as an asserted fact." The RED gate's provenance is in the Evidence (READ scripts/k_cert.py:218-222, NaN checked first because float('nan') >= 1.0 is False; $30$ of $30$ shapes passed with worst margin $1.957\times10^{-3}$, READ COSTS.md:137-139), and 04.3's own line now reads "NOT MEASURED — needs the plug-in estimator over the admission census of 04.2 and no floor of this verse depends on it", so the three verses the finding names read the same way. No further edit was owed and none was made.

A-41 · verse 04.5 · severity `repair`#

Flaw (verbatim). K-H2's second clause names no pair, so the kill is not decidable, and under the reading that makes it non-trivial it strikes the bed on the arm's failure. Mechanism (verbatim). V-10, D-1 Number (verbatim). "or McNemar $p>0.05$ against a 1-hop softmax on identical draws (K-H2)" — no subject. Under (shape, 1-hop softmax) the bed is declared static whenever the shape fails to separate from a 1-hop stack; under (0-hop MLP, 1-hop softmax) the clause says nothing about the shape. replacement_survives (verbatim). true Required repair (verbatim). Name the pair: 'McNemar between the 0-hop MLP and the 1-hop softmax reading $p>0.05$ on identical draws' is the static-bed reading; a shape-versus-1-hop comparison belongs in 04.9 as an A1 row, not in a bed kill. Severity (verbatim). repair

Repair applied — 04.5 (already in force from an earlier batch; verified against this finding). 04.5's Statement reads, verbatim in the book: "or if McNemar between the 0-hop MLP and the 1-hop softmax reads $p>0.05$ on identical draws (K-H2). The second clause names its pair because an unnamed pair is not decidable: under (0-hop MLP, 1-hop softmax) a null result says one hop buys nothing over none, which is the static-bed reading and the only reading this kill carries. A shape-versus-1-hop comparison is an A1 row and belongs to 04.9, never to a bed kill — read as a bed kill it would strike the bed whenever the shape fails to separate, which is the arm's failure and not the bed's." The Kill's instrument line names the same pair. Both halves of the required repair are met and the reading the finding calls non-trivial is named in the verse as the reading that is refused; no further edit was owed and none was made.

A-42 · verse 04.5 · severity `repair`#

Flaw (verbatim). Link 1 is priced identically to the verse's own kill, so it is neither cheaper nor more decisive. Mechanism (verbatim). CHARTER §2 depth rule Number (verbatim). Verse Kill price: "$\approx0.5$ GPU-min for both at $N=8$". Link 1 Kill: "K-H2 fires again at $\approx0.5$ GPU-min". replacement_survives (verbatim). true Required repair (verbatim). Decide link 1 at $0$ GPU-s from the DAG's depth census (whether $t^\star=32$ is placeable at $s=64$) before any cell runs; that is strictly cheaper than re-running the control pair. Severity (verbatim). repair

Repair applied — 04.5 (already in force from an earlier batch; verified against this finding). 04.5's link 1 Kill reads, verbatim in the book: "$t^\star=32$ unplaceable at $s=64$ by the DAG's own depth census — decided at $0$ GPU-s from 04.2's depth read, before any cell runs, and strictly cheaper than the verse's own kill, which needs the control pair at $\approx0.5$ GPU-min. A link priced at the verse's own kill is neither cheaper nor more decisive and is not a link; re-running the control pair is what link 2 replaces, not what link 1 repeats." The depth rule of CHARTER §2 is satisfied down the chain: link 1 at $0$ GPU-s, link 2 (BED-J) strictly more decisive at $\approx30.9$ s after A-35's reprice. No further edit was owed for this finding, and the only change this batch made to that chain is A-35's arithmetic correction of link 2's price.

A-43 · verse 04.6 · severity `repair`#

Flaw (verbatim). The residual's printed conditioning factor is a 2-norm quantity attached to an infinity-norm score. Mechanism (verbatim). V-17, V-26 Number (verbatim). $r(\hat q)=\|(I-Q_{\rm env})\hat q-R_{\rm env}\mathbb 1\|_\infty/\|R_{\rm env}\mathbb 1\|_\infty$ is an $\infty$-norm ratio; the DERIVED bound $\sigma_{\min}\|e\|\le\|(I-\gamma P)e\|\le(1+\gamma)\|e\|$ and the "lower factor near $0.06$" are 2-norm. On $|T|=9$ the conversion costs up to $\sqrt9=3$ in each direction. replacement_survives (verbatim). true Required repair (verbatim). Print $\|(I-Q_{\rm env})^{-1}\|_\infty$ beside $r$ instead of $\sigma_{\min}$, or restate $r$ in the 2-norm so the printed factors bind it. Severity (verbatim). repair

Repair applied — 04.6 (already in force from an earlier batch; verified against this finding). The first route is taken. 04.6's Statement reads, verbatim in the book: "with $\|(I-Q_{\rm env})^{-1}\|_\infty$ and $\|I-Q_{\rm env}\|_\infty$ printed beside $r$ — both in the $\infty$-norm $r$ is written in. The 2-norm pair $\sigma_{\min}\|e\|_2\le\|(I-\gamma P)e\|_2\le(1+\gamma)\|e\|_2$ and its 'lower factor near $0.06$' do not bind an $\infty$-norm ratio: on $|T|=9$ the conversion costs up to $\sqrt9=3$ in each direction, so a factor quoted at $0.06$ in the 2-norm bounds an $\infty$-norm error only to within $9\times$ (DERIVED from $\|x\|_\infty\le\|x\|_2\le\sqrt{|T|}\,\|x\|_\infty$). The 2-norm factors are retained as a separate, labelled 2-norm remark and license no reading of $r$." The Evidence marks $\|(I-Q_{\rm env})^{-1}\|_\infty$ as "NOT MEASURED — needs one read of the built chain, $0$ GPU-s on the bed's own generator", so the substitute factor carries a class rather than a value it does not have. No further edit was owed and none was made.

A-44 · verse 04.7 · severity `repair`#

Flaw (verbatim). The capability channel's labels exist only for post-move FENs present in the evaluation shard, an availability-biased subset with no registered guard. Mechanism (verbatim). M-21, V-24 Number (verbatim). Hypotheses: "the evaluation shard streamed and pinned on one shard; the join by FEN". For an arbitrary candidate move $a$ the post-move FEN need not appear in lichess/chess-evaluations (34.4 GB, UNPINNED_AWAITING_KAGGLE, results/k_data_manifest.json), so $\operatorname{sign}\Delta\mathrm{eval}(\text{FEN},a)$ is missing for an unmeasured fraction of candidates and the argmin over $m$ is not formable. replacement_survives (verbatim). true Required repair (verbatim). Add a census line printing the join-hit rate per candidate move and a rule that a query with any missing candidate is discarded, with the discard rate printed beside the cell. Severity (verbatim). repair

Repair applied — 04.7 (already in force from an earlier batch; verified against this finding). 04.7's Hypotheses read, verbatim in the book: "The join is availability-biased and is censused, not assumed: for an arbitrary candidate move $a$ the post-move FEN need not appear in lichess/chess-evaluations at all, so $\operatorname{sign}\Delta\mathrm{eval}(\text{FEN},a)$ is missing for an unmeasured fraction of candidates and the argmin over $m$ is not formable on a query with a hole. A census line prints the join-hit rate per candidate move on every cell, and the rule is: a query with any missing candidate is discarded, with the discard rate printed beside the cell and beside every number the cell carries. The join-hit rate is NOT MEASURED — needs the pinned eval shard, so no argmin number on the capability channel exists before it is printed." The Kill carries the same clause ("any capability number quoted before the join-hit rate and its discard rate are printed … struck as P-1") and the planted negative is the holed query ("a query built with one candidate's post-move FEN deliberately absent from the joined shard must be discarded by the join census"). All three halves of the required repair — the census line, the discard rule, the printed rate — are in force; no further edit was owed and none was made.

A-45 · verse 04.8 · severity `repair`#

Flaw (verbatim). The zero-variance masking rule points at a census that does not exist. Mechanism (verbatim). P-4, P-6 Number (verbatim). Hypotheses: "coordinates with zero label variance ... are masked from the cosine and their fraction printed (04.4's census line 10)". 04.4 registers two guards (zero-hop, leak) and no census; its verse text contains no numbered lines. replacement_survives (verbatim). true Required repair (verbatim). Point the masking rule at 04.2's admission block clause on per-coordinate sd, which is the only registered variance census, and add the coordinate-level fraction to that block. Severity (verbatim). repair

Repair applied — 04.8; 04.2 verified. The masking rule in 04.8's Hypotheses now names 04.2's admission clause 4 and quotes it — "every per-coordinate sd of $q$ over the admitted query region $>0.05$, with the fraction of coordinates at zero label variance printed" — with the sentence added that this is the only registered variance census in this book and that the earlier pointer "04.4's census line 10" named a line that does not exist, 04.4 registering two guards and no census and carrying no numbered lines (P-4, P-6). The same repointing is made in link 1's Hypotheses, which carried the identical dangling pointer, so both uses now resolve. The coordinate-level fraction the required repair asks for is already a printed component of clause 4 in 04.2's numbered block ("with the fraction of coordinates at zero label variance printed (the mask 04.8 reads)"), so the block needs no new clause and none was added. Limits names the dangling pointer and its two sites once.

A-46 · verse 04.8 · severity `repair`#

Flaw (verbatim). The consequence head both refuses the no-change predictor and prints its error as a floor. Mechanism (verbatim). V-10, L-FLOOR Number (verbatim). Statement: "An arm emitting $\Delta\hat z\equiv0$ makes the cosine $0/0$ and is refused, not scored." The same row's floor column: "exact oracle $0.0$; the no-change predictor's error printed". The no-change predictor is $\Delta\hat z\equiv0$. replacement_survives (verbatim). true Required repair (verbatim). Score the no-change predictor on the position-matched NRMSE vector alone (where it is well defined) and refuse it only on the cosine column, printing which columns the refusal covers. Severity (verbatim). repair

Repair applied — 04.8, 04.15. The refusal is made per column and its scope is printed. 04.8's Statement now reads: the refusal is per column "because a head that refuses an arm outright and prints that same arm's error as its floor refuses and scores one object at once (V-10, L-FLOOR)"; an arm emitting $\Delta\hat z\equiv0$ makes the field cosine $0/0$ and the magnitude ratio $0/\lVert\Delta z\rVert$, is refused on those two columns and on no other, and is scored on the position-matched per-coordinate NRMSE vector and on the sign column's McNemar, where both are well defined ($\lVert\Delta\hat z-\Delta z\rVert$ needs no direction; the sign of $0$ is a registered tie under the McNemar's discordant-pair rule). The consequence row's floor cell is corrected to read "exact oracle $0.0$; the no-change predictor's error printed on the position-matched NRMSE column only, which is the column it is scored on", and the Statement states that this NRMSE is the number the floor cell prints. Every refused cell journals refused_columns = [cosine, magnitude_ratio], and 04.15's field list gains refused_columns — "the per-column refusal scope of 04.8, empty list where nothing is refused, so a refusal is never a whole-cell absence" — so the scope is auditable under 04.15's own refusal rule. The magnitude ratio is added to the refused set beyond what the required repair names, because it is $0/\lVert\Delta z\rVert$ on the same arm and refusing only the cosine would leave a second undefined column scored. Limits records the per-column reading once.

A-47 · verse 04.9 · severity `repair`#

Flaw (verbatim). The adjudicator's refusal instrument names a path that does not exist in the tree, with no NOT MEASURED marker. Mechanism (verbatim). P-1, P-4 Number (verbatim). RUN this session: ls results/arena — "No such file or directory". The Hypotheses require the adjudicator to check "predictions_hash against results/arena/PREDICTIONS.sha256", and 04.21's Kill instrument is "the adjudicator's predictions_hash check". replacement_survives (verbatim). true Required repair (verbatim). Mark the adjudicator NOT MEASURED — needs the arena adjudicator and its frozen prediction file at results/arena/PREDICTIONS.sha256, and price its construction in 05 REPAIRS. Severity (verbatim). repair

Repair applied — 04.9, 04.21. The finding's ls is re-run this session and reads the same: results/arena does not exist. 04.9's Hypotheses now carry the marker in bold beside the clause that names the path — NOT MEASURED — needs the arena adjudicator and its frozen prediction file at results/arena/PREDICTIONS.sha256 — with RUN this session ls results/arena reading No such file or directory, and state that the directory, the frozen prediction file and the refusal instrument are all absent and that their construction is a row of 05 REPAIRS priced there. Because the adjudicator is the delegated instrument of five other kills, the same sentence names every one of them — clause 1's seed refusal, clause 3's skyline row, 04.1's void_contrasts refusal, 04.3's floor read, 04.17's bare-prediction refusal and 04.21's predictions_hash check — and states that no verse of this book reads a refusal as having happened (P-1, P-4). 04.21's Kill instrument carries the same marker in place, with the grep of the scored journal for a literal $\mathrm{MDE}_8$ constant named as the one half of that instrument which runs today. Limits records the absent adjudicator once.

A-48 · verse 04.10 · severity `repair`#

Flaw (verbatim). The kill requires $N\ge16$ interleaved timings while the Hypotheses fix $N=8$ per arm, so the kill has no journal on the bed as registered. Mechanism (verbatim). V-11 Number (verbatim). Kill: "Spearman $|\rho|>0.5$ with $p<0.05$ between seconds and run index on the $N\ge16$ interleaved timings". Hypotheses: "$N=8$ per arm". replacement_survives (verbatim). true Required repair (verbatim). State whether $N$ counts seeds or arm-cells; at 8 seeds x 3 interleaved arms the journal holds 24 timings, which satisfies $N\ge16$ under the arm-cell reading. Print the reading in the verse. Severity (verbatim). repair

Repair applied — 04.10. The reading is printed at all three sites that use it. The Hypotheses now read "$N=8$ seeds per arm, and the Kill's $N$ counts arm-cells in the timing journal, not seeds — the reading is printed here because the two differ and the kill is unreachable under the wrong one": at $8$ seeds and the three interleaved arms of this verse's own order (shape, control, skyline) the journal holds $8\times3=24$ timings, so the Kill's $N\ge16$ is satisfied at the registered seed count, while read as seeds it would demand $16$ seeds the bed does not register and could never fire on the bed as registered (V-11). The Kill repeats the reading in place. The planted negative, which runs one arm twice, now prints its own count — $8$ seeds $\times\ 2$ runs $=16$ arm-cells — so the plant is affordable at the registered seed count and the detector's must-fire half is reachable on the same journal. Limits states the reading once.

What batch 3 did not close#

Nothing in this batch is left OPEN: sixteen findings, two strike and fourteen repair, all sixteen repaired above. The market half of B27 is closed by cross-reference and by an explicit statement of the loss, not by a verse of this book (A-34): book 04 registers no market bed, the row names 09 as the owner of that half, and the paragraph beneath the census table states that if 09's market verses are struck the half is closed by nothing in this canon — the one place in this batch where a replacement_survives: false is answered by carrying the loss rather than by deriving a different instrument, and it is carried because a census row is not a verse and has no If-killed chain to re-derive. Seven repair findings (A-37, A-39, A-40, A-41, A-42, A-43, A-44) name defects batches 1 and 2 had already struck; each row prints the finding verbatim, the required repair verbatim and the exact text now in force, so the reader checks the claim rather than takes it. Three prices in this book were arithmetically wrong against their own formulas (A-35, A-36) — $\approx52$ s against $44.32$ s, $\approx34$ s against $30.88$ s, and $\approx5.12$ s classed DERIVED from a hop that gives $0.407$ s — and all three are struck with the arithmetic printed; the $5.12$ s is re-classed as an unreproduced source figure READ at the pin, matching book 06's reading of the same number at 06.28, and 04.9's $\approx3.3$ GPU-min inherits the tag. The arena adjudicator does not exist (A-47), so six delegated refusals across five verses are NOT MEASURED and priced in 05 REPAIRS. Two dangling census pointers are repointed (A-38, A-45) at 04.2's clauses 10 and 4. The consequence head no longer refuses and scores one object at once (A-46): the refusal is per column, refused_columns is a journalled field, and the no-change predictor is scored on the column whose floor it sets. 04.10's $N$ counts arm-cells (A-48), so its kill has a journal at the registered eight seeds. One new evidence class is registered by this batch: the $150$-step cell length, READ scale/e_ladder.py:140.

Repair round 1, batch 4 of 5: sixteen findings, thirteen of severity repair and three of severity note. Every finding is reproduced verbatim — verse, flaw, mechanism, number, replacement_survives, required repair, severity — beside the verse id repaired and what changed. Nothing is softened; where a repair could not be made the row reads OPEN with the Terminal now in force printed.

A-49 · verse 04.10 · severity `repair`#

Flaw (verbatim). The $\tau$ ladder is in NRMSE units, so T1 and T2 are undefined on two of the book's four heads and on one of its three beds, contradicting the Statement's scope. Mechanism (verbatim). V-17, D-1 Number (verbatim). Statement: "two numbers per bed and arm pair" with $\tau$ from "$\{0.9,0.8,0.7,0.5\}$ in NRMSE-to-oracle units". 04.8 scores the argmin head by accuracy with Clopper-Pearson and 04.7's capability channel by a Bernoulli sign rate; neither has an NRMSE-to-oracle. replacement_survives (verbatim). true Required repair (verbatim). Register a second ladder in distance-to-floor units for rate-valued heads (accuracy relative to $\mathrm{floor}_{\rm zeroinfo}$, four levels frozen), or state that T1/T2 are defined on vector heads only and mark the argmin and chess channels NOT MEASURED — needs a rate-valued $\tau$ ladder. Severity (verbatim). repair

Repair applied — 04.10. Both halves of the required repair are taken, because the second alone would leave the chess bed with no ladder at all. The Statement's scope is corrected to "two numbers per bed, arm pair and head", and two ladders are registered. The vector-head ladder is the existing $\{0.9,0.8,0.7,0.5\}$ in NRMSE-to-oracle units and is now scoped explicitly to the three vector heads of 04.8 — $q$, $z^\star$, $\Delta z$ — each of which is scored by a position-matched NRMSE against an exact oracle at $0.0$ and anchored at $1.0$ for the mean predictor (04.3), with the statement printed that it covers no rate-valued head and that a $\tau$ read off it on one is a threshold imported out of its units (V-17). The rate-head ladder is registered here as this book's second ladder, in distance-to-floor units, $\tau_{\rm rate}=(1-\mathrm{acc})/\mathrm{floor}$ with four levels frozen at the same four numbers (M-2), the floor being $\mathrm{floor}_{\rm zeroinfo}=1-\max_a\hat\pi(a^\star)$ on 04.8's argmin head (04.3's own second floor object) and $\mathrm{base}_k(h{=}8)=\max\{p_k,1-p_k\}$ on 04.7's eval-$\Delta$ capability channel (04.7's own fourth floor object); $\tau_{\rm rate}$ reads $1$ at chance and $0$ at the exact oracle, which is the vector ladder's anchoring, so the two carry the same four levels without either being read in the other's units, and the floor is recomputed on the batch being scored. The ladder id is printed in the cell. T1 and T2 on the argmin head and on the chess capability channel now read NOT MEASURED against a defined denominator — needs $\mathrm{floor}_{\rm zeroinfo}$ from the first admitted batch (04.21 step 5) and needs $\mathrm{base}_k(8)$ from one rollout pass over the $36$ fixture games (04.7) — where before they read against no unit at all. The Kill gains a clause: a T1 or T2 on a rate-valued head read against the NRMSE ladder, or on a vector head read against the rate ladder, is struck as V-17, decided at $0$ GPU-s by the ladder id against 04.8's head table; the "no level reached" clause now reads "no level of the head's own registered ladder", as does link 1's kill. The Evidence prints both ladders' units, both denominators with their NOT MEASURED markers, and the statement that the four levels are this book's frozen constants and are not fitted to any result. Limits records the two ladders once, naming the two heads and the one bed that had no ladder before.

A-50 · verse 04.14 · severity `repair`#

Flaw (verbatim). The quoted census output is not the output of the quoted command; 17 of 24 kinds are dropped without ellipsis, and they are exactly the population the second kill clause audits. Mechanism (verbatim). P-1, V-7 Number (verbatim). RUN this session, the verse's own command, returns 24 distinct kinds. The verse prints 7 and asserts the 8th absent. Unquoted: band_miss 1, constant_g 2, halt_demo 1, kirchhoff 4, mc_random_unit 4, naive_yield 1, not_generated 1, probe 3, provenance 2, real_key_directions 1, recovery_check 1, reproduce_check 1, scramble_residual 1, scramble_residual_shipped 1, summary 4, welch 5, windowed_signed 1. replacement_survives (verbatim). true Required repair (verbatim). Print the full 24-row census, or print the seven rows with an explicit '(17 further kinds elided; full output is the kill's own instrument)' and run the second kill clause against the elided rows. Severity (verbatim). repair

Repair applied — 04.14. The first branch is taken: the Evidence now prints all $24$ distinct kinds in the order the command returns them, RUN this session — arm_smprime 425, arm_pl 422, softmax 227, rung 40, census 31, pivot_unsigned 11, pivot_signed 11, welch 5, summary 4, mc_random_unit 4, kirchhoff 4, probe 3, provenance 2, constant_g 2, windowed_signed 1, scramble_residual_shipped 1, scramble_residual 1, reproduce_check 1, recovery_check 1, real_key_directions 1, not_generated 1, naive_yield 1, halt_demo 1, band_miss 1 — with the seventeen the earlier text dropped named in a second list and the reason printed: they are exactly the population the second kill clause reads, so quoting a subset made that clause unauditable (P-1, V-7). The command is quoted in the form that produced the output (| sort | uniq -c | sort -rn), and the finding's own counts reproduce row for row.

A-51 · verse 04.14 · severity `repair`#

Flaw (verbatim). "Absent from the output" is not "reads 0", so the two-way calibration validates only the positive half. Mechanism (verbatim). V-7, V-14 Number (verbatim). A grep -rho '"kind": *"[a-z_0-9]*"' | uniq -c census cannot distinguish a kind emitted zero times from a kind that was never spelled that way or that is emitted outside results/**/*.jsonl. arm_phase 0 is inferred from absence. replacement_survives (verbatim). true Required repair (verbatim). Enumerate the kind values the code can emit by grepping the sources (grep -rn 'NAME =' ceq scale scripts), intersect with the census, and print both sets so a zero is a zero against a known emitter rather than an absence. Severity (verbatim). repair

Repair applied — 04.14. The enumeration is run and both sets are printed. RUN this session, grep -rhoE '^NAME = "[a-zA-Z_0-9]+"' ceq scale scripts --include='*.py' returns $13$ declared arm names (arm_a_k1, arm_phase, arm_pl, arm_smprime, ceq, ceq_hybrid, chase_eprocess, chase_m3_synth, m2, m3_quintuple_v2, r2, s2, wilson_arms), each emitted as "kind": NAME; RUN this session, grep -rhoE '"kind" *: *"[a-zA-Z_0-9]+"' ceq scale scripts --include='*.py' | sort -u returns $20$ literal kinds; the two sets are disjoint, so $33$ kinds are declared emitters. Intersected with the census: $15$ declared emitters have records and $18$ read $0$, and NAME = "arm_phase" at READ ceq/arm_phase.py:60 is one of the eighteen, so arm_phase 0 is a zero against a known emitter and no longer an inference from absence — which is the only reading under which the Kill's first clause is decidable. The Statement's two-way calibration is restated against the emitter set (must-fire: arm_phase, declared, $0$ records; must-not-fire: arm_smprime, declared, $425$ records), and a kind absent from both the census and the emitter set is now NOT MEASURED, not a zero. The repair goes one step past the required one, because the enumeration turned out to be a lower bound: $9$ of the $24$ observed kinds (softmax, pivot_unsigned, pivot_signed, welch, mc_random_unit, windowed_signed, scramble_residual_shipped, scramble_residual, real_key_directions) match neither grep, because the value is passed as a variable rather than spelled at the emit site (ceq/lm.py:66 asserts kind in ("softmax", "softmax_x", "signed", "sgate", "sgate_nores"), RUN this session) or the emitting file lies outside ceq scale scripts (kaggle/snapshot/repo/attic/, RUN this session). The Hypotheses therefore state the counter's reach as measured on the lower side and unmeasured on the upper, and the Kill's second clause is restated: as written ("the census reads above $0$ for a kind no script emits") it fires today on all nine and is a kill satisfied by construction against its own counter (V-10); it now reads "a kind above $0$ reachable from no emit site under the extended enumeration" and is registered unreachable, NOT MEASURED — needs the emit-site enumeration extended past literal spellings, with the note that no verse reads it as having fired. The Terminal and Limits carry the same counts ($24$ observed, $33$ declared, $15$/$18$ split, $9$ unreachable).

A-52 · verse 04.15 · severity `repair`#

Flaw (verbatim). The refusal rule makes 04.1's first kill clause unreachable, and the two verses are inconsistent about whether a declared field can be absent. Mechanism (verbatim). V-10, V-11 Number (verbatim). 04.15: "a missing declared field is a refusal, never an absent entry", with void_contrasts in the declared list. 04.1's Kill: "A cell journalled with void_contrasts absent". replacement_survives (verbatim). true Required repair (verbatim). Have 04.1 kill on void_contrasts = [] rather than on absence, and have 04.15 state explicitly that the refusal makes absence unobservable downstream. Severity (verbatim). repair

Repair applied — 04.1, 04.15. The first half was already in force from an earlier batch and is reprinted here so the reader checks it rather than takes it: 04.1's Kill reads "void_contrasts journalled as [] on a bed whose registered VOID list is non-empty, or a capability sentence built on a contrast in the list. Absence is not the kill's condition: 04.15 makes a missing declared field a refusal, so no cell reaches the journal with void_contrasts absent and a kill on absence could not fire", and its planted negative is "a cell written with void_contrasts = [] on BED-S, whose registered list has eight entries", which instantiates the kill's condition exactly. The second half is new. 04.15's Statement now carries a paragraph stating the downstream consequence in general and not only for 04.1: because a cell missing a declared field is refused at the journal, no such cell reaches results/, so a kill of the form "a cell journalled with $X$ absent" is a gate satisfied by construction (V-10) and a precondition violated at every real draw (V-11). Two consequences are registered — (i) every kill in this book that reads a declared field reads its value, never its presence, with 04.1's void_contrasts = [] and 04.8's refused_columns = [] named as the two instances; (ii) the refusal is observable at the file and nowhere else, so a count of absences must come from the adjudicator's refusal log, which is NOT MEASURED — needs the arena adjudicator and its frozen prediction file at results/arena/PREDICTIONS.sha256 (RUN this session, ls results/arena reads No such file or directory). A verse elsewhere in the canon whose kill reads a declared field's absence is struck at assembly and repointed at that field's value. Limits records the rule once.

#	admission clause	line
1	every row sum of \(P_{\rm env}\) within \(10^{-12}\) of \(1\)	pass/fail
2	\(0\in\mathcal A_{\rm sink}\) on \(100\) per cent of draws	pass/fail
3	every boundary set before the query and the query in \(T\) on \(100\) per cent	pass/fail
4	every per-coordinate sd of \(q\) over the admitted query region \(>0.05\), with the fraction of coordinates at zero label variance printed (the mask 04.8 reads)	fraction
5	every class frequency of \(a^\star\) in \((0.05,0.95)\)	fractions
6	rule-disagreement fraction (argmax-\(q^{(0)}\) against Chebyshev against conditioned Chebyshev) \(>0\)	fraction
7	sink share printed apart from \(q^{(0)}\)	interval
8	discard count printed	count
9	\(m_{\rm eff}\ge m-1\) on \(\ge95\) per cent of draws, over the pre-screened candidate pool of clause 11 (R-08)	fraction
10	the per-base admitted fraction at the quantifier level each magnitude theorem uses (04.19), printed per base	fraction
11	the no-op screening rate: the fraction of candidate targets in \(T\) whose clamp moves the query's committors by \(>10^{-12}\), measured on the draw before the \(m\) moves are sampled; moves are drawn from the screened pool only	fraction

verse	kill number or condition	price	replacement verse
04.7	a capability number before both chess digests are pinned; legality or next-FEN quoted as capability; a capability number before the join-hit rate or the \(h=8\) base rates are printed	\(0\) GPU-s locally (the eval-sign clause \(\approx8.7\) GPU-min `[ASSUMED]` behind the author's yes)	04.7 link 1 (hygiene bed) → link 2 (leaves the ladder)
04.8	any of the three metric plants passing	\(0\) GPU-s	04.8 link 1 (NRMSE vector only)
04.12	the LaTeX source contradicts the HTML reading; the relabelling is free because neither arm exists, not because both are FOUND	\(0\) GPU-s, one fetch (author)	04.12 link 1 (the operator distance \(\Delta_{\rm conv}\) at \(\gamma=0.9\), no arm)
04.15	a one-unit flip leaving `manifest_hash` unchanged; `absent` returned	\(0\) GPU-s	04.15 link 1 (field into the hash, decisive only while `boundary_sets` reads \(0\) records) → link 2 (the field list hashed into `instrument_hash`)
04.16	one cell, two live grades in two files, whatever their dates (a grade being live iff no `supersedes` row points at it); an F4 without suffix on a cell graded on or after 2026-09-05 (\(68\) pre-rubric bare tokens, \(31\)+\(37\) at the pin, migrated by 05 REPAIRS, not waived)	\(0\) GPU-s	04.16 link 1 (supersedes row)
04.17	*a row in the appended column* whose `counter` field is empty** — audited on the artefact, the refusal at the file being the upstream control and 04.9's adjudicator now carrying it	\(0\) GPU-s	04.17 link 1 (VOID row)
04.18	`grep -rlF -f deleted_docs.txt tests` \(>0\) after the move, the pattern file being the \(244\) root `.md` rows of `git diff --name-status 99777ab c71527a` (permanent; the old `git status` definition read \(0\) rows and made the kill fire never)	\(0\) GPU-s	04.18 link 1 (`testpaths`) → link 2 (\(39\)-file subset)
04.19	a train-gate theorem admitting \(0\) per cent at its quantifier level	\(0\) GPU-s	04.19 link 1 (restate on the closed base)
04.21	a BED-S number before \(\sigma_d\) is journalled; a bet scored against any placeholder \(\mathrm{MDE}_8\)	\(0\) GPU-s	04.21 link 1 (supersedes)

verse	kill number or condition	price	replacement verse
04.1	`void_contrasts` journalled as `[]` on a bed whose registered list is non-empty; a VOID contrast credited	\(0\) GPU-s, \(0.5\) evening	04.1 link 1 (all VOID until identified)
04.11	K-E1 (ChaCAL-with-sink within \(\mathrm{MDE}_N\) at the realised \(\sigma_d\) on \(\ge6/8\) and residual within \(2\times\)) is UNREACHABLE: \(0\) ChaCAL source lines, \(0\) records; the operative kill is link 1's \(\\|\Pi_{\rm row}-\Pi_{\rm col}\\|_\infty<10^{-12}\) on \(\ge95\) per cent of the \(512\) admission draws	\(0\) GPU-s, \(0.5\) evening (link 1); \(82\)–\(260\) GPU-s, \(2\) evenings (link 2)	04.11 link 1 (operator read, no arm) → link 2 (`make_arm` branches, FOUND census)

verse	kill number or condition	price	replacement verse
04.4	honest query below \(1-10^{-3}\); honest \(R^2\ge R^2_{\rm bar}\), the bed's own \(99\)th-percentile \(512\)-draw null (`NOT MEASURED`, the leak half unreachable until it is computed); planted \(R^2<0.99\)	\(\le1.524\) s	04.4 link 1 (vector head alone, R0) → link 2 (flags removed)
04.13	any plant passing; any plant NAMED (B-J's ChaCAL plant and B-E1's ChaCAL identity half are NAMED and struck); every remaining number `NOT MEASURED at the front door` until 04.21 step (2)	\(\approx15.1\) s `[ASSUMED]`	04.13 link 1 (arm-free re-derivation, then a remark) → link 2 (no training, L-LEAN)
04.5	0-hop MLP inside the half-width at \(N\) (04.9 clause 7, `NOT MEASURED`), or McNemar \(p>0.05\) vs 1-hop	\(\approx0.5\) GPU-min (\(\approx30\) s)	04.5 link 1 (\(t^\star=32\)) → link 2 (BED-J)
04.6	\(r_{\rm softmax}/r_{\rm shape}\le2\) at matched marginal error	\(\approx30.9\) s `[ASSUMED]` (\(2\times8\times1.680+4.0\); the \(\approx34\) s struck)	04.6 link 1 (A2 only) → link 2 (cost statement, 04.10)
04.20	\(\mathrm{acc}_{\rm sky}-\mathrm{acc}_{\rm shape}>\mathrm{MDE}_N\) at the realised \(\sigma_d\) — *one-sided, the skyline ahead* of the shape, read against the matched-parameter** skyline of 04.9 clause 3b (width `NOT MEASURED`); the skyline short of the shape is the A2 reading and fires nothing; a depth or width chosen after the arena	\(\approx64.8\) s `[ASSUMED]`	04.20 link 1 (depth ladder at matched widths)
04.9	\(\sigma_d\ge0.109199\) on the first eight seeds — the M-3 realised value itself, ratio \(2.1776\) printed as a read-out; the earlier \(2.18\times0.050146=0.109318\) struck because the one instance that motivates it, \(0.109199\), falls below it	\(\approx98\) s `[ASSUMED]`	04.9 link 1 (\(N=16\)) → link 2 (TOST \(N=36/70\), \(119/228\) s)
04.3	an uninformed control (0-hop, `random`, `majority`) below its own floor on \(\ge2/N\) seeds	\(0\) GPU-s beyond the cell, but the cell is the \(\approx98\) s arena, so the kill is unreachable below that price	04.3 link 1 (\(m_{\rm eff}\)) → link 2 (exact oracle only, \(\varphi\)-NRMSE below \(4.4\times10^{-16}\))
04.14	`arm_phase` still \(0\) after the route while remaining in the \(33\)-kind emitter set; the reach-clause (a kind above \(0\) that no emit site reaches) is `NOT MEASURED` and unreachable until the extended enumeration exists	\(41\)–\(130\) GPU-s	04.14 link 1 (citations, not a wing)
04.10	Spearman \(\lvert\rho\rvert>0.5\), \(p<0.05\) against run index on \(N\ge16\) arm-cells; no level of the head's own ladder reached by both arms; a T1 or T2 on a rate-valued head read against the NRMSE ladder	band \(206\)–\(537\) GPU-s	04.10 link 1 (T2 only) → link 2 (cost model DERIVED, sentence withdrawn)

04 — BEDS AND INSTRUMENTS#

Preface — what this book decides, and the verse that decides it first#

Part I — The bed ladder#

04.1 — Nothing is decided by construction: the VOID register#

04.2 — BED-S: in-class, exact oracle, registered with the D-4 admission gate#

04.3 — Information floors per bed (L-FLOOR)#

04.4 — The zero-hop guard and the leak guard, firing both ways#

04.5 — The static-task kill, and the label class that leaves the scalar regime (B4)#

04.6 — BED-J: the joint-consistency bed outside the per-row class#

04.7 — The chess witness on natural ground, and the local data route before any Kaggle attach#

Part II — Labels, heads and metrics#

04.8 — Labels and heads for the four classes, with the metric plants#

Part III — The measurement protocol#

04.9 — The protocol that measures "more accurate" (A1, A2), and \(N\) from the realised sd (B25, B5)#

04.10 — The protocol that measures "faster to train" (T1, T2), the timers and the training-noise floor (B25)#

Part IV — Controls, binds, manifests and censuses#

04.11 — The control arms per bed, and the column-sink control (B21)#

04.12 — The ChaCAL convention check (B22)#

04.13 — The binds, with planted negatives and the \(O(1)\) failure each must produce (V-24)#

04.14 — FOUND-not-NAMED: the kind census and the W2 route back (B20)#

04.15 — The identity manifest: fields, the drift plant, and the refusal rule#

04.16 — The F0–F4 grading rubric, written out, and the gate that reads every cell (B18)#

04.17 — The calibration column and its scoring rule#

04.18 — The test policy: tests assert code, journals and results/, never prose (B3)#

04.19 — The magnitude interval and the two registrations (B23)#

04.20 — The skyline cells: one FOUND, two with settings and no cell (B11)#

04.21 — The first BED-S cell: what eight seeds produce, in what order (B5)#

Census rows closed#

Kills, cheapest first#

Limits (collected once)#

Attacks answered#

A-1 · verse 04.11 · severity strike#

A-2 · verse 04.11 · severity strike#

A-3 · verse 04.11 · severity strike#

A-4 · verse 04.1 · severity strike#

A-5 · verse 04.1 · severity strike#

A-6 · verse 04.1 · severity strike#

A-7 · verse 04.2 · severity strike#

A-8 · verse 04.2 · severity strike#

A-9 · verse 04.2 · severity strike#

A-10 · verse 04.3 · severity strike#

A-11 · verse 04.3 · severity strike#

A-12 · verse 04.3 · severity strike#

A-13 · verse 04.4 · severity strike#

A-14 · verse 04.6 · severity strike#

A-15 · verse 04.6 · severity strike#

A-16 · verse 04.7 · severity strike#

What this batch did not close#

A-17 · verse 04.7 · severity strike#

A-18 · verse 04.9 · severity strike#

A-19 · verse 04.9 · severity strike#

A-20 · verse 04.9 · severity strike#

A-21 · verse 04.9 · severity strike#

A-22 · verse 04.10 · severity strike#

A-23 · verse 04.12 · severity strike#

A-24 · verse 04.12 · severity strike#

A-25 · verse 04.13 · severity strike#

A-26 · verse 04.13 · severity strike#

A-27 · verse 04.15 · severity strike#

A-28 · verse 04.16 · severity strike#

A-29 · verse 04.18 · severity strike#

A-30 · verse 04.18 · severity strike#

A-31 · verse 04.21 · severity strike#

A-32 · verse 04.21 · severity strike#