06 — PREDICTIONS (VENUS · IRENE): one competing prediction filed before each deciding measurement#
Written 2026-09-05 at HEAD 99777ab under CHARTER.md. Every READ path:line below is at 99777ab unless another pin is printed; RUN is this session on this box; every other number carries its class in place.
What this book decides. For every cell the canon schedules — the free censuses, the identity gates, the eight-seed arena, the verdict cards, the cost sweep, the ladder, the language-model cell behind the author's yes — it files the prediction (the half that flatters), the counter of equal specificity, the SPLIT band, the single deciding number with the instrument that reads it, the price, and what each outcome kills in the other books. Under D-CALIB the counter is the point estimate for every row (9 checked, 9 adverse, 7 of 8 signed rows optimistic, one-sided \(p=0.0352\); READ V16_CALIBRATION.md:19,:98), so every verse pre-writes the sentence the canon says when the counter holds and the route that then takes over. It also files the two words of CHARTER.md §1 as ranges: A1 and A2 as accuracy margins, T1 and T2 as ratios against depth-1 base self-attention and against the depth skyline, each with the number that makes the range wrong.
The verse that decides first is 06.7 — the BED-S census on 512 draws at \(0\) GPU-s — because under the counter it ends every capability cell in this book before a GPU-second is spent (docs/PLAN.md §5.10 tree C), and the second is 06.5, the realised paired sd, because under its counter nothing at \(N=8\) is falsifiable and every \(\mathrm{MDE}_8\) threshold below is repriced before a bet is scored.
Census rows owned here. B5 (no CEQ arm trained, no BED-S cell, no realised sd, no measured \(t^\star\)) is closed by 06.5, 06.6 and 06.15; B6 (the calibration column) by 06.2, 06.3 and 06.4; B25 (the predicted T1/T2 ranges) by 06.28 to 06.31. The closing tables list every row and every kill, cheapest first.
Geometry of every verse unless printed otherwise. \(s=64\), \(d_{\rm model}=16\), \(n_{\rm train}=2048\), \(n_{\rm eval}=4096\), \(N=8\) seeds deduplicated, \(t^\star=8\), \(m=8\), \(K=2\) plus goal plus sink, one thread lane, threads = 8, 150 steps per cell, the certified RTX 4060 Laptop (7.996 GiB, torch 2.5.1+cu121, READ COSTS.md:53-63) — the device whose certificate B2 says is stale, so every price is a per-op floor until book 05's re-certification (06.34).
I. The rule and the column#
06.1 — The scoring rule, frozen#
Statement. Every prediction row of the canon is scored with exactly one token of \(\{\mathrm{HOLDS},\mathrm{COUNTER},\mathrm{SPLIT},\mathrm{VOID}\}\) by the adjudicator that reads only journals (S-63): HOLDS when the deciding number lies in the prediction's region; COUNTER when it lies in the counter's; SPLIT when it lies in any region the verse declares outside both halves — the band between them, and, where a verse's prediction is a two-sided range, the region beyond the range's far end — scored wrong with the sign the verse prints for that region (the sign of the optimistic half where the verse names none). The generalisation from "the band between" is made here because a two-sided prediction has two regions outside it and only one of them lies between the halves: 06.19's upper break \(\Delta_{A1}>0.85\) is reachable on the bed as registered and, under the narrower reading, carried no token at all, which is the condition 06.36's Kill declares refuting. The token set stays at four; VOID when the bed was not admitted or a prerequisite instrument failed its own plants, unscored and never a miss. Rows are appended, never edited; a corrected reading is a new row whose supersedes field names the old row (L-G2). The one-sided sign test \(p_k=\Pr[X\ge k]\), \(X\sim\mathrm{Bin}(8,\tfrac12)\), runs on the pooled column after eight scored rows and on the author and leap sub-columns separately: \(p_8=1/256=0.003906\), \(p_7=9/256=0.035156\), \(p_6=37/256=0.144531\), \(p_5=93/256=0.363281\) (DERIVED, binomial tail). The \(0.75\) rule is a threshold, not a test: a column at or above \(6\) of \(8\) optimistic makes the counter the reported estimate for every unscored row, although \(p_6=0.1445\) does not clear \(\alpha=0.05\); both numbers are printed beside the column so the rule cannot be read as a significance claim.
The pin audit, and the fourteen pins that drifted. Under CHARTER.md §3 the pin READ path:line @ 99777ab is what makes a citation admissible, so a pin naming the wrong card or a blank line leaves the number it carries unverified at its stated location (P-6, line-reference drift; P-1; P-2). Fourteen pins of this book were audited against git show 99777ab:docs/PLAN.md and re-pinned in the verses that carry them: 06.6 :1067-1069\(\to\):1056 (tree C's reroute), 06.7 :1057\(\to\):1054 and :365, 06.11 :232\(\to\):231 (the 169 theorems over 12 files), 06.14 :950\(\to\):644 (C15's 13 of 40), 06.15 :640-645\(\to\):626-633 (S-62), 06.18 :1058-1060\(\to\):1054 (tree B), 06.20 and 06.30 :611-617\(\to\):619-625 (S-35, the pin 02_THEORY_TRAINING.md:467 uses), 06.22 :589-595\(\to\):594-600 (S-31) and :688-693\(\to\):682-687 (S-64), 06.23 :599-604\(\to\):607-612 (S-33), 06.24 :706-712\(\to\):688-699 (S-65) and :958\(\to\):956 (R-22), 06.26 :964\(\to\):959 (R-10), 06.36 :1058-1060\(\to\):1054 (tree B) and :1064-1066\(\to\):1056 (tree C). Every number those pins carry was re-read at the corrected line at 99777ab: the 13 of 40 and the one-hop threshold \(0.7071067811865476\) at :644; S-62's K-P kill and its realised-sd block at :626-633; S-35's price \(\approx7.6\) s per cell [ASSUMED] and \(\approx64.8\) s at eight seeds at :619-625; S-64's \(\approx44\) s (\(3\times8\times1.681+4\)) at :682-687; S-65's \(119\) s paired at \(N=36\) and \(228\) s two-sample at \(N=70\) at :688-699; R-22's \(0.8807\sigma\) half-width against the \(0.5\sigma\) margin at :956; R-10's one exceedance on \(1{,}024\) draws and \(\delta\|V\|_\infty\) against the label sd at :959; S-31's \(1.680\) s per cell and \(\approx52\) s for three arms at :594-600; S-33's \(1.680\) s per cell and \(\approx35\) s for two batches at :607-612. Every one reproduced at the corrected line. Tree A's pin :1052 and the sink-share pin :352 were re-verified and were already correct.
Hypotheses. A row is scorable only if its prediction and counter were both filed and hashed before the first cell of the measurement that scores it (results/arena/PREDICTIONS.sha256, S-60, READ docs/PLAN.md:573-580); the deciding number is one statistic read from one journal row; the sign of a miss is defined against the project (+ credits the project more than the measurement supports, READ V16_CALIBRATION.md:24-31). Non-vacuous at any \(N\ge1\); the sign test is defined only at eight or more scored rows.
Evidence. READ docs/PLAN.md:926-928 (the verdict tokens, the eight-row rule, the \(0.75\) rule); READ V16_CALIBRATION.md:142-202 (D-CALIB-1 to D-CALIB-5); DERIVED the four tail probabilities; READ scale/it11_verdict.py:59 (REQUIRED_SEEDS = 8) and :133-137 (the cross-thread drift \(2.345\times10^{-3}\) that forces the lane to be read from the journal).
Mechanism. D-7 (MISTAKES.md:2037), M-2 (:451), M-9 (:580), P-3 (:316), L-G2, L-SIGN.
Kill. The rule is refuted if any scored row of the canon carries a token outside the four, a verdict without a predictions_hash matching the recorded sha256, or a deciding number that is not a journal field — decided by the adjudicator's own plants (S-63): a 7-seed journal must return INSUFFICIENT, a duplicated seed must count once, a tampered prediction file must halt the run. Price \(0\) GPU-s, \(0.5\) evening. Planted negative (V-15): a prediction file altered by one byte after the hash must halt on predictions_hash mismatch; a file identical to its hash must not.
If killed. The replacement is the record's own adjudicator contract restricted to its three tokens PASS/KILL/SPLIT with VOID folded into "not filed" (READ docs/PLAN.md:669-673): a row whose bed was not admitted is deleted from the denominator rather than carried as VOID. Hypotheses: the denominator is then chosen after the fact, which is the defect V16_CALIBRATION.md §3.4 records. Evidence: READ V16_CALIBRATION.md:109-131. Kill: any denominator that changes between two readings of the same column — decided by the row count in the append-only file, \(0\) GPU-s.
Terminal. The canon files predictions and counters without scoring them; every "HOLDS" in books 00 to 07 reads as "filed", and no calibration sentence is written.
06.2 — The calibration column reproduced, R11, nine rows#
Statement. The record's only scored prediction census is R11's nine rows of CEQ_V15_CONTRACT.md, every one adverse, signed \(7\) +, \(1\) −, \(1\) unsigned; the one-sided sign test on the eight signed rows reads \(p=0.0352\); the Wilson 95 per cent interval on the optimism fraction at \(7/8\) is \([0.5291,0.9776]\), which excludes \(0.5\) and fixes nothing else. The rows, with producing files:
| # | statement (CEQ_V15_CONTRACT.md) |
measured | sign |
|---|---|---|---|
| 1 | g ≡ 0 gives bitwise standard attention (:139-140) |
row \(i\) sums to \(i+1\) (lean/CEQ/V15.lean:221) |
+ |
| 2 | two-thirds of pre-v13 §5 strikes were [V]-as-theorem (:54) |
\(4/40=10\%\), a \(6.67\times\) overstatement | + |
| 3 | the sizing model replaced everywhere it was cited (:251) |
already satisfied before the round opened | − |
| 4 | "the current 22 per cent" baseline (:285) |
no producer in the tree; baseline \(0\) of \(39\) | + |
| 5 | TOST retires to \(N\ge23\) (:140) |
achieved power at \(N=23\) is \(0.0669\); \(0.80\) first at \(N=70\) | + |
| 6 | \(\hat H=\hat\alpha+\tfrac12\) as BED-K's target | shipped without $ | d |
| 7 | [RUN: best first-order recurrence 0.990] (:180) |
\(R^2=-0.000166\) on the delay bed | + |
| 8 | PART III against PART IV on one bed (:180) |
mutually inverse registrations | none |
| 9 | carriers conserve mass to 1e-12 (:125) |
false for the contract's central carrier | + |
Hypotheses. The nine are adverse rows of a hand-assembled table whose denominator was chosen after the audit and lists no confirmations, so \(9/9\) is a count, not a rate; the arithmetic sub-census with a stated denominator reads \(4\) of \(11\) wrong (\(36.4\%\), Wilson \([0.152,0.646]\)) and the de-duplicated union \(10\) of \(\ge17\) (\(58.8\%\), \([0.360,0.784]\)). The direction holds on the nine honestly signed rows and not on the round entry's six (\(5/6\), \(p=0.1094\)).
Evidence. READ V16_CALIBRATION.md:19 (the column row), :40-48 (the nine), :96-100 (the three sign-test sets), :113-119 (the sub-census table), :176-177 (Wilson); READ MISTAKES.md:2037-2060 (D-7, the same nine).
Mechanism. D-7, M-20 (MISTAKES.md:1723, row 8), P-10 (:1382, row 2), V-23 (:1626, rows 1 and 9).
Kill. The reproduction is refuted if any cell of the table above differs from V16_CALIBRATION.md:40-48 at 99777ab — decided by git show 99777ab:V16_CALIBRATION.md | sed -n 40,48p against this table, \(0\) GPU-s, \(0.1\) evening. Planted negative: the round entry's own sentence "six wrong, all six optimistic" (MISTAKES.md:2041-2044) must be found to disagree with the table on two counts (nine, not six; one − and one unsigned), and the check must report both.
If killed. The replacement row set is the union census of V16_CALIBRATION.md §3.4 (\(10\) of \(\ge17\)) with its Wilson interval \([0.360,0.784]\), which still excludes nothing below \(0.5\) on the optimism fraction because it counts wrong-versus-right, not sign. Hypotheses: signs are then available only on the nine. Evidence: READ V16_CALIBRATION.md:113-119. Kill: a listed confirmation found to be adverse on its producing file moves the row and is a new row in the column — \(0\) GPU-s.
Terminal. The canon carries "the record's checked predictions were adverse in every scored row, direction optimistic on eight signed rows" and no rate.
06.3 — The column extended: the rows this canon files, denominator fixed before any is scored#
Statement. The canon's calibration column is the R11 block of 06.2 followed by the rows below, every one filed here with both halves and its deciding number, the denominator fixed before any measurement — the procedural requirement of V16_CALIBRATION.md §3.4. Source author throughout; a leap row is added only when a leap output files one with its instance RUN first (docs/PLAN.md §5.9). Status at birth: every row UNSCORED.
| row | verse | cell | deciding number | prediction (flatters) | counter (point estimate) | SPLIT |
|---|---|---|---|---|---|---|
| C-1 | 06.5 | S-62 | realised paired sd of \(\varphi\)-NRMSE | \(\le0.050146\) | \(\ge0.109199\) | between |
| C-2 | 06.6 | S-12 | placement fraction of \(t^\star=8\); admitted-region sd | \(100\%\) and sd \(>0.05\) | sd \(\le0.05\) or unplaceable | placement in \((95\%,100\%)\) |
| C-3 | 06.7 | S-12 | the five admission lines | all pass | at least one fails | none |
| C-4 | 06.8 | S-14/S-15 | honest probe \(R^2\); planted \(R^2\) | \(<0.5\) and \(\ge0.99\) | honest \(\ge0.5\) | planted \(<0.99\) is VOID |
| C-5 | 06.9 | R-07/R-24, the \(0\) GPU-s half | sink-move fraction; exact-zero-tie discard fraction; the flag rule's error against the exact zero-information floor \(0.875\) | both fractions \(<0.5\) and flag-rule error \(\ge0.875\) | either fraction \(\ge0.5\), or flag-rule error \(<0.875\) | none |
| C-6 | 06.10 | S-26 | the 0-hop MLP's paired accuracy gap to the shape; McNemar \(p\) on \(4{,}096\) paired eval draws | gap \(>\mathrm{MDE}_{\rm McN}\) and \(p\le0.05\) | gap \(\le\mathrm{MDE}_{\rm McN}\) or \(p>0.05\) | none |
| C-7 | 06.11 | J-L18 | the green count out of the seven admissible bare-[M] targets (bare [M] with an empty depends on cell at docs/CEQ_SHAPE.md:2604-2622 @ 99777ab) |
\(7/7\) | \(\le6/7\) — point estimate \(7/9\) on the nine bare-[M] rows, \(7/11\) on the eleven [M]-graded rows |
none — the four [U]-blocked rows (:2606, :2608, :2609, :2619) are carried separately and never cited as proved |
| C-8 | 06.12 | S-61 | plant counts | \(8/8\) and \(8/8\) | either \(<8/8\) (VOID for Bet C) | none |
| C-9 | 06.13 | S-20 | torch.equal; cell over the DERIVED \(1.71990\) s shape cell (06.28); strict-mode forward |
True; cell in \([0.982,1.144]\), i.e. \([1.68894,1.96757]\) s; forward bitwise | COUNTER-dear: cell \(\ge2.2\times\) (\(\ge3.78378\) s), or the forward not bitwise — signed + |
cell in \((1.144,2.2)\), \((1.96757,3.78378)\) s; COUNTER-cheap, cell \(<0.982\times\) (\(<1.68894\) s), is the fourth branch and the re-tag trigger — scored COUNTER and signed − |
| C-10 | 06.14 | S-52 | capped seeds crossing \(0.7071067811865476\) | \(3/3\) | \(\le1/3\) | \(2/3\) |
| C-11 | 06.15 | S-62 | the modal band of \(\|\hat P-P_{\rm env}\|_\infty\) over the eight seeds, with its count | modal band \([10^{-3},10^{-2})\) at \(\ge6/8\) | modal band \(\ge10^{-2}\) at \(\ge6/8\) | every configuration whose modal count is \(\le5/8\); modal band \(<10^{-3}\) at \(\ge6/8\) is VOID |
| C-12 | 06.16 | R-21 | MOVED count at \(\Lambda>8.318\) | \(\ge6/8\) | PINNED \(\ge6/8\) | \(3/8\) to \(5/8\) |
| C-13 | 06.17 | M-4.2 | paired cosine difference | \(>\mathrm{MDE}_8(\cos)\) | \(\le\mathrm{MDE}_8(\cos)\) | none |
| C-14 | 06.18 | M-4.2 | CP interval against the exact zero-information floor \(0.875\) at \(m=8\) | \(\mathrm{CP}_{\rm upper}<0.875\) | \(\mathrm{CP}_{\rm lower}\ge0.875\) | the straddle |
| C-15 | 06.19 | S-30/S-62 | \(\Delta_{A1}=\mathrm{acc}_{\rm shape}-\mathrm{acc}_{d1}\) | \(\in[0.40,0.85]\) | \(\le\mathrm{MDE}_8(\mathrm{acc})\) | \((\mathrm{MDE}_8,0.40)\), signed +; and \(\Delta_{A1}>0.85\), the upper break and the prediction's other kill, also scored SPLIT and signed + with the reproduction clause of 06.19 printed |
| C-16 | 06.20 | S-35 | \(\mathrm{acc}_{\rm shape}-\mathrm{acc}_{\rm sky}\) at the unmatched depth-5 stack, \(d_{\rm model}=16\) (Bet D) | within \(\mathrm{MDE}_8\) — the honest control holds | shape short by \(>\mathrm{MDE}_8\) | shape ahead by \(>\mathrm{MDE}_8\), sign logged. The matched-parameter A2 instance is UNREACHABLE at \(4{,}769\) and files no row here |
| C-17 | 06.21 | M-4.2 | \(r_{\rm softmax}/r_{\rm shape}\) | \(\ge10\) | \(\le2\) | \((2,10)\) |
| C-18 | 06.22 | S-31/S-64 | the modal side of the eight per-seed \(\varphi\)-NRMSE gaps to ChaCAL-with-sink, with its count; residual ratio | modal side separated at \(\ge6/8\) and ratio \(>2\times\) | modal side within at \(\ge6/8\) and within \(2\times\), holding at \(N=16\) | three named branches: separated-not-residual (SPLIT-sep), residual-not-separated (SPLIT-res), and SPLIT-seeds — every configuration whose modal count is \(\le5/8\), with the ordered pair (separated, within) and the ratio printed |
| C-19 | 06.23 | S-33 | cosine gap on \(P\)-changing plants in seed-sd units | \(>1\) on \(\ge6/8\); \(\le1\) on \(V\)-only | \(\le1\) on \(\ge6/8\) | \(3/8\) to \(5/8\) |
| C-20 | 06.24 | S-65 | the 90 per cent interval against the \(\pm0.5\) margin at the tier C-33 selects | inside at that tier | outside at that tier | none |
| C-21 | 06.25 | M-3.7 | argmin error across \(t^\star\in\{2,8\}\) | moves by \(>\mathrm{MDE}_8\) | flat within \(\mathrm{MDE}_8\) | none |
| C-22 | 06.26 | N-15 | exceedances on \(1{,}024\) draws; \(\delta\|V\|_\infty\)/sd | \(0\) and \(<1\) | \(\ge1\) or \(\ge1\) | none |
| C-23 | 06.27 | M-5.3 | the \(N=8\) verdict at step \(9{,}600\) | survives within \(\mathrm{MDE}_8\) | reverses | none |
| C-24 | 06.28 | S-20/N-02 | cell over the DERIVED \(1.71990\) s shape cell | \(\in[0.982,1.144]\), i.e. \([1.68894,1.96757]\) s | COUNTER-dear: \(\ge2.2\) (\(\ge3.78378\) s) — signed + |
\((1.144,2.2)\), \((1.96757,3.78378)\) s; COUNTER-cheap, \(<0.982\) (\(<1.68894\) s), is the fourth branch and the re-tag trigger — scored COUNTER and signed − |
| C-25 | 06.29 | S-62 curves | the crossing step \(k\), mapped to \(T1_{d1}=0.00751992\,k\) (\(T2_{d1}=k/150\) printed beside it) | \(T1_{d1}\le0.50\) and \(T2_{d1}\le0.45\), i.e. \(k\le66\) | COUNTER-slow \(T1_{d1}\in[0.89,1.44]\), \(k\in[119,191]\); COUNTER-overrun \(T1_{d1}>1.44\), \(k\ge192\), signed + |
\(T1_{d1}\in(0.50,0.89)\), \(k\in[67,118]\) — every integer \(k\) carries exactly one of the four |
| C-26 | 06.30 | S-62/S-35 curves | the in-band count over eight seeds, each seed placed in exactly one of in band (\(34\le k\le150\)), below band (\(k<34\)), not reached (\(k>150\)) | in band on \(\ge6/8\), i.e. \(T1_{\rm sky}\in[0.0511,0.2256]\) | not reached on \(\ge6/8\) | LOW: below band on \(\ge6/8\), SPLIT signed +, the prediction's other kill; and SPLIT for every configuration where no category reaches \(6/8\), with the ordered triple (in band, below band, not reached) printed. One seed count, \(\ge6/8\), in the verse and the column alike |
| C-27 | 06.31 | S-62/S-35 curves | \(T2_{\rm sky}\) | \(\le0.20\) | \(\ge1.0\) or undefined | \((0.20,1.0)\) |
| C-28 | 06.32 | S-66 | the exponent interval in \(s\) of seconds per step per unit \(n\); Spearman \(\rho\) | contains \(2\), excludes \(3\); \(\rho\) n.s. | excludes \(2\) toward \(3\) | contains both |
| C-29 | 06.33 | V-17 | column route over one solve | \(\le0.5\times\) | \(\ge8\times\) | \((0.5,8)\) |
| C-30 | 06.34 | N-01 | solve_triangular bitwise fwd+bwd, 8 repeats, re-certified stack |
\(8/8\) both | backward raises or differs | forward only |
| C-31 | 06.35 | S-73 | MOVED count on enwik8 | \(\ge6/8\) | PINNED \(\ge6/8\) | \(3/8\) to \(5/8\); VOID until the yes |
| C-32 | 06.9 | R-24, the arena half | the flag rule's argmin accuracy against the shape's, paired | flag rule below by \(>\mathrm{MDE}_8(\mathrm{acc})\) | flag rule at or above \(\mathrm{acc}_{\rm shape}-\mathrm{MDE}_8\) | none |
| C-33 | 06.24 | S-65, the tier row | \(r=\mathrm{sd}_d/\sigma\) from S-62's realised sds | \(r\le0.7071\): the paired tier \(N=36\) is selected | \(r>0.7071\): pairing bought nothing and the two-sample tier \(N=70\) is selected | none — \(r\) is a number, not a band |
| C-34 | 06.24 | S-65, the two-sample reading | the \(N=70\) two-sample 90 per cent interval against \(\pm0.5\sigma\) | inside | outside | none |
| C-35 | 09.10 | the chess census, \(0\) GPU-s | the admission lines of 09.10 (1, 2, 4 at \(100\%\); line 5 sd \(>0.05\); line 6 in \((0.05,0.95)\); line 7 \(>0\)) | all pass | at least one fails | none — admission is a D-4 decision |
| C-36 | 09.13 | the first chess cell, \(0\) GPU-s | the per-coordinate sd of L-\(q\) at the root over 512 draws; engine_sha256 present |
sd \(>0.05\) and the hash present | sd \(\le0.05\), or engine_sha256 = absent (every engine label refused) |
none |
| C-37 | 09.32 | the market census, \(0\) GPU-s | the admission lines of 09.32, plus the martingale-identity plant \(\lvert q-p_0\rvert\le10^{-12}\) on every \(r\equiv0\) draw | all pass and the plant holds | at least one fails, or the plant reads above \(10^{-12}\) | none |
| C-38 | 09.34 | the first market cell, \(0\) GPU-s | the per-coordinate sd of \(q\) at the root over 512 draws; the market's Brier and log score at the registered horizon | sd \(>0.05\) and both baseline scores printed | sd \(\le0.05\), or the baseline scores NOT MEASURED (no snapshot pinned) | none |
| C-39 | 09.31 | the PnL cell | the paired per-contract PnL difference against the market-following rule (buy the side the market favours, same sizes, same constraints), with the e-process value | difference \(>\mathrm{MDE}_n\) and the e-value crosses \(1/\alpha=20\) | within \(\pm\mathrm{MDE}_n\), or negative | positive but below \(\mathrm{MDE}_n\) |
| C-40 | 06.4 | the column itself | the count of + among the first eight scored non-VOID rows of C-1 to C-39 |
\(\le4\) | \(\ge6\) | exactly \(5\) |
Hypotheses. Forty rows are filed. The denominator the eighth-row test of 06.4 reads is the thirty-nine of C-1 to C-39; C-40 is 06.4's own row and is excluded from the count it reads by this clause, so the meta-row sits in the column without entering the count it scores (D-CALIB-5 still applies to it: it is appended whether or not it flatters, and scored after the eighth row). C-22 is dormant until a mask exists; C-31 is VOID until the author's explicit yes; C-35 to C-39 are VOID until book 09's generators exist, which 09.10's and 09.32's own Hypotheses record they do not at 99777ab. The first eight scored non-VOID rows in the order the cells run fix the eighth-row test. \(\mathrm{MDE}_8\) in every row means the \(n=8\) cell of the realised paired sd of that statistic (M-3), filled by 06.5 before any row is scored; \(\mathrm{MDE}_{\rm McN}\) in C-6 is the McNemar minimum detectable accuracy difference of 06.10; \(\mathrm{MDE}_n\) in C-39 is book 09's, at the resolved-contract count.
Evidence. READ docs/PLAN.md:912-924 @ 99777ab (Bets A to M as filed, thirteen rows); READ docs/CEQ_SHAPE.md:3200-3209 (Appendix A §6); C-35 to C-39 from 09_CHESS_AND_MARKETS.md verses 09.10, 09.13, 09.32, 09.34 and 09.31, whose Statements carry the deciding numbers copied here; the remaining rows are this book's, DERIVED from the cards each names.
Mechanism. D-7, L-SIGN, M-2, D-CALIB-2 (a bare prediction is refused at the file), D-CALIB-5 (the row is appended whether or not it flatters).
Kill. The table is refuted as a pre-registration if any row is scored on a statistic other than its deciding number, if a deciding cell of any book carries no row here, or if the file that carries these rows is hashed after the first arena cell's timestamp — decided by results/arena/PREDICTIONS.sha256 against the earliest results/arena/*.jsonl timestamp, and by the count of deciding cells in books 01 to 09 against the row count, \(0\) GPU-s, \(0.2\) evening. Planted negative: a row added after the first cell must be refused by the file's own count check, and a row with one half blank must be refused at the file.
If killed. The replacement is the bet file of S-60 alone, named by its actual content: the thirteen bets A to M of READ docs/PLAN.md:912-924 @ 99777ab — of which Bet I is S-52's and Bet M is the language-model row left blank until an LM cell exists — hashed by the plan before the arena; every other row of this table is then scored as a leap-class row only after its instance is RUN. The count check that file must pass is 13/13 rows with both halves signed. It is not S-60's 24/24: READ docs/PLAN.md:576 @ 99777ab demands 24/24 and no §5.5 table has twenty-four rows, so the replacement cannot inherit that check; the discrepancy is a defect of the source and is owed to CORRECTIONS.md as a row against docs/PLAN.md:576, not carried here. S-60's own build line (READ docs/PLAN.md:574 @ 99777ab) names "the five bets of §5.5 plus S-52's bet and the language-model row", seven rows, which is neither thirteen nor twenty-four; the replacement takes the table, which is the file's content, over either count sentence. Hypotheses: the thirteen bets are the only rows with the plan's own hash. Evidence: READ docs/PLAN.md:573-580 @ 99777ab. Kill: a thirteen-bet file whose hash postdates the first cell, or whose signed count reads other than 13/13 — decided by the same timestamp check and one count, and then no row of the canon is scorable.
Terminal. The canon's predictions are filed and unscorable; the column ends at R11's nine rows and the canon says so in 00.
06.4 — The prediction about the column itself: the eighth-row test#
Statement. This verse is itself row C-40 of 06.3's column — the canon's meta-prediction is in the column it institutes, and is excluded from the count it reads by 06.3's Hypotheses clause, so it cannot flatter itself by being its own denominator (D-CALIB-5: the row is appended whether or not it flatters). Prediction: among the first eight scored non-VOID rows of C-1 to C-39, at most \(4\) carry + (the canon's counters absorb the record's bias). Counter: at least \(6\) of \(8\) carry + — the record's rate persists, the point estimate is \(7\) of \(8\) (Wilson \([0.5291,0.9776]\) scaled to eight rows is \([4.2,7.8]\)), the \(0.75\) rule engages, and the counter becomes the reported estimate for every unscored verse of every book. SPLIT: exactly \(5\) of \(8\). The deciding number is the count of + among the first eight scored rows of C-1 to C-39, read from the append-only column by S-63; C-40 is scored after that eighth row and never counted in it.
Hypotheses. Eight scored rows exist. Under tree C every row that needs BED-S admission or the arena is VOID — READ docs/PLAN.md:1056 @ 99777ab (S-12 KILL): "Everything from S-14 to S-65 is VOID and unscored" — which voids C-1 (06.5, S-62's realised sd), C-4 (06.8, S-14/S-15), C-32 alone (06.9, R-24, the arena half), and C-6 (06.10, S-26), and every arena row C-11 to C-27 and C-33 to C-34. C-5 is not voided, and the phrase "C-5's arena half" this clause carried at the previous writing is struck: C-5 has no arena half. 06.3's table files C-5 as "06.9 | R-07/R-24, the \(0\) GPU-s half" and C-32 as "06.9 | R-24, the arena half"; 06.7's own If-killed lists the tree-C VOID set as "06.8, 06.9's arena half (C-32), 06.10, and 06.15 to 06.27", so C-5 survives; and 06.9's Kill prices C-5 at "\(0\) GPU-s and \(0.5\) evening, before any arm" on the S-12 census draws, which run under tree C. The rows that need neither BED-S admission nor the arena are therefore eleven — C-2, C-3, C-5, C-7, C-8, C-9, C-10, C-24, C-28, C-29 and C-30 — and the eight are drawn from those eleven. C-9 (06.13, S-20) and C-10 (06.14, S-52) are BED-M-hosted — S-20 runs on e3_t2 and S-52 on the R1 retake, neither inside the S-14-to-S-65 range — so PLAN's blanket sweep does not reach them, and this book records that exemption here rather than leaving it to be read out of a range. C-35 to C-39 join the pool only once book 09's generators exist. Signs are assigned against the project by the convention of 06.1 — + where the claim credited the project more than the measurement supports, − where it credited the project less — and per branch, never per token. The blanket clause this verse carried at the previous writing, "a COUNTER verdict on a row is a + miss by construction", is deleted: it contradicts 06.1's definition and D-CALIB-5's "a counter wrong pessimistically is a −", and on the two-branch counters of 06.13 and 06.28 it would have signed COUNTER-cheap + when the claim was too dear, inflating the + count the eighth-row test reads by up to two of eight. Each row of 06.3 prints the sign its own branches carry; a HOLDS verdict is a confirmation and carries no sign.
Evidence. READ V16_CALIBRATION.md:176-177 (the interval), :195-202 (D-CALIB-5: the author's counters are scored as well; a counter wrong pessimistically is a −); DERIVED \(p_6=0.1445\), \(p_7=0.0352\).
Mechanism. D-7, M-2, M-9 (eight rows cannot distinguish \(0.53\) from \(0.98\); sign, never size), D-CALIB-3.
Kill. The prediction is refuted at \(6\) or more + among the first eight scored rows; the counter at \(4\) or fewer; decided by the column at its eighth scored row, \(0\) GPU-s beyond the cells that produce the rows, \(0.1\) evening. Planted negative: a synthetic column of eight + rows must return \(p=0.003906\) and engage the \(0.75\) rule; a synthetic column of four + and four HOLDS must return \(p=0.3633\) and not engage it.
If killed (the counter holds, the point estimate). Every prediction half in books 01 to 06 is demoted to "the optimistic tail" and every counter half is the reported estimate in 00's master tree; the sentence is: "The canon's own first eight scored rows were optimistic on \([k]\) of \(8\); the reported estimate for every unscored cell is its counter." The replacement rule is D-CALIB-1 applied to the canon's rows rather than the record's, with Hypotheses (rows scored by 06.1), Evidence (the column), and its own Kill: the sub-column of the next eight rows at \(\le3\) + restores the prediction halves to planning estimates — a cheaper kill than the first because it needs no new cell, only the rows already scheduled.
Terminal. The canon keeps both halves on every verse, reports the counter, and writes no sentence of the form "the canon predicts".
06.5 — The realised paired sd against the pilot (B5)#
Statement. Prediction: the realised paired sd of the shape-versus-softmax \(\varphi\)-NRMSE contrast over the first eight seeds of S-62 is at or below the pilot's \(0.050146\), so \(\mathrm{MDE}_8\le0.057971\) and every \(N=8\) kill of this book is falsifiable as filed. Counter: the realised sd is at or above \(2.18\times\) the pilot, \(0.109199\), so \(\mathrm{MDE}_8=0.126238\), nothing at \(N=8\) is falsifiable, and \(N\) is repriced to \(16\) (\(\mathrm{MDE}_{16}=0.081841\)) before any bet is scored. SPLIT: sd in \((0.050146,0.109199)\), where \(\mathrm{MDE}_8\) lies in \((0.057971,0.126238)\) and every bet is scored at that cell. The deciding number is the realised paired sd printed by S-62's gate from the same guarded noncentral-\(t\) bisection that reproduces \(0.039827\) at sd \(0.034451\) (RUN[VENUS], RUN[MARS] \(0.0398266\), read at docs/PLAN.md:32).
Hypotheses. Paired, \(\alpha=0.05\) two-sided, power \(0.80\), \(N=8\) deduplicated by seed, one thread lane; the pilot sd is negation_scope's and the \(2.18\times\) precedent is BED-M's, both V-22 across beds and admitted here only as the two ends of a band, never as BED-S bars (K-P). The MDE table at the four sds: \(0.010101\to0.011677/0.007570\); \(0.034451\to0.039827/0.025820\); \(0.050146\to0.057971/0.037583\); \(0.109199\to0.126238/0.081841\) at \(n=8/16\).
Evidence. READ docs/CEQ_SHAPE.md:2668-2676 (the table); READ docs/PLAN.md:586 (the gate); READ MISTAKES.md:464-476 (M-3, the \(2.18\times\)); BED-S's own sd NOT MEASURED — needs S-62's first eight seeds (book 04).
Mechanism. M-3, M-9, V-22, K-P.
Kill. The prediction dies at sd \(\ge0.109199\); the counter at sd \(\le0.050146\); decided by S-62's gate print, price the arena pair \(\approx34.0\) s (DERIVED from 06.28's re-tag: \(8\times(1.71990+1.52475)+2\times4.0=33.96\) s; the shape cell is the DERIVED \(1.71990\) s, not the struck \(1.680\) s, and the softmax cell \(150\times0.010165=1.52475\) s), \(1\) evening. Planted negative: the identical-seed floor — two runs of one seed in one lane must read paired sd \(0.0\) bitwise (Ruling 1), and two runs at threads = 6 and threads = 8 must read a difference of \(2.345\times10^{-3}\) (READ scale/it11_verdict.py:133-137), so the instrument reads a spread when one exists and none when none does.
If killed (the counter). Every \(\mathrm{MDE}_8\) in 06.16 to 06.27 is replaced by \(\mathrm{MDE}_{16}\) from the \(n=16\) column at the realised sd, the arena is extended to seeds 8 to 15 in the same lane at \(\approx34\) s more, and the sentence is: "BED-S at the design point has a realised paired sd of \([\mathrm{sd}]\); at \(N=8\) no contrast smaller than \([\mathrm{MDE}_8]\) is claimable, and every bet is scored at \(N=16\)." Hypotheses: the \(n=16\) cell of the same bisection. Evidence: the column above. Kill of the replacement, with the bar written in the units the contrast is read in: the realised sd at \(N=16\) still at or above \(0.109199\) and the smallest filed contrast, read in its own realised sd units, below \(0.74947\) realised sd — the \(n=16\) noncentral-\(t\) cell as a ratio, DERIVED as the constant the MDE table prints at all four sds (\(0.081841/0.109199=0.037583/0.050146=0.025820/0.034451=0.749470\) to six places, and \(0.007570/0.010101=0.749431\), the fourth row's rounding). The form this kill carried at the previous writing compared a contrast in sd units against the absolute \(\mathrm{MDE}_{16}=0.081841\), which is a threshold imported out of its units (V-17): in sd units the bar is \(0.7495\,\mathrm{sd}\), so the kill as filed fired only below \(0.0818\,\mathrm{sd}\), \(9.16\times\) stricter than the quantity it means to test, and no real draw satisfied it (V-11). The equivalent absolute form is licensed as an alternative and never mixed with it: each contrast compared against the \(\mathrm{MDE}_{16}\) computed at that statistic's own realised sd, with the per-statistic values listed — \(\varphi\)-NRMSE's at \(0.081841\) if its realised sd is \(0.109199\), accuracy's and cosine's NOT MEASURED — needs S-62's realised sd per statistic (book 04). The constant \(0.74947\) is printed here so the two forms cannot be confused again. Decided by one comparison against the printed contrast list, \(0\) GPU-s, cheaper than the first kill. The contrast list, printed in the same block: the \(\varphi\)-NRMSE contrasts are C-18 (06.22, shape against ChaCAL-with-sink) and C-16 (06.20(ii), shape against the unmatched depth-5 stack where S-35 prints NRMSE); the accuracy contrasts C-15, C-16 and C-32 carry accuracy's own realised sd, not \(\varphi\)-NRMSE's; Bet A's cosine (C-13) and Bet E's ratio (C-17) carry their own units and are unaffected by an NRMSE reprice. The claim that "the \(\varphi\)-NRMSE contrasts are capped by the floor at \(0.0\) against softmax's one-hop error" is struck here as false: the cap is softmax's one-hop error, not zero, and every uncapped reading the record holds exceeds \(\mathrm{MDE}_{16}\) — 06.14's three NO-READING seeds read \(1.152430\), \(1.113403\) and \(1.139404\) eval NRMSE (\(14.08\times\), \(13.60\times\) and \(13.92\times\) \(0.081841\); git show 99777ab:V15_R1.md:177-188), 06.14's one-hop threshold is \(0.7071067811865476\) (\(8.64\times\)), and 06.19's filed \(\Delta_{A1}\) band starts at \(0.40\) (\(4.89\times\)), all DERIVED by division. So no comparison shows \(\mathrm{MDE}_{16}\) larger than every contrast, and the replacement's kill may not rest on one. Where the realised per-statistic sd is not yet printed the row reads NOT MEASURED — needs S-62's realised sd per statistic (book 04) and the Terminal below is the only sentence in force.
Terminal. The paper files the bed with its printed sd and no capability number (docs/PLAN.md §5.10 tree C, third route). B5's "no realised sd" half closes only on admission: a printed realised sd exists only if a batch runs, and under 06.7's counter (tree C) READ docs/PLAN.md:1056 @ 99777ab says no arm runs and every card from S-14 to S-65 is VOID, so S-62 — the arena card that prints the sd — never fires. On that branch, which is the book's own point estimate (06.7's counter under D-CALIB, 7 of 8 optimistic, \(p=0.0352\)), B5 is closed by the census's printed failure line plus the row "realised paired sd NOT MEASURED — needs an admitted batch", and by nothing else. The census-rows table carries both branches.
06.6 — The measured \(t^\star\) (B5)#
Statement. Prediction: on 512 draws the DAG substrate places \(t^\star=8\) inside the causal window on \(100\%\) of draws (the hop ladder \(z_k=Qz_{k-1}+R\) reaches the exact committor only at \(k\ge8\) on every draw), and the admitted-region label sd of the goal committor is above \(0.05\). Counter: \(t^\star=8\) is unplaceable on at least one draw, or the admitted-region sd is at or below \(0.05\) — the label collapses as E4′'s did from \(0.499989\) to \(0.038445\) under a kill-rate placement (READ docs/PLAN.md:651). SPLIT: placement on \((95\%,100\%)\) of draws with sd above \(0.05\). The deciding numbers are census line 5 (the sd) and the hop-ladder placement fraction, both printed by S-12 at \(0\) GPU-s.
Hypotheses. \(t^\star\) is placed by the DAG's depth and read off the hop ladder, never by a kill rate (D-3); the admitted region excludes the prefix before the first constraint, where \(q^{(0)}\approx1\); the oracle is \(m\) factorisations with \(K+2\) right-hand sides at \(|T|^3/3=5.76\times10^{8}\) MACs per draw, under a second in float64 (DERIVED, READ docs/PLAN.md:369).
Evidence. READ docs/PLAN.md:364-370 (S-12), :648-655 (M-3.7's placement rule); READ docs/CEQ_SHAPE.md:2938-2944 ("no measured hop depth"); the placement fraction NOT MEASURED — needs the S-11 generator and the S-12 census (book 04).
Mechanism. D-3 (MISTAKES.md:727), D-4 (:740), V-8 (:136), V-12 (:189).
Kill. The prediction dies at any draw with \(t^\star\) unplaceable or at sd \(\le0.05\); the counter at \(100\%\) placement and sd \(>0.05\); \(0\) GPU-s, \(1\) evening (the census). Planted negative: a generator with the goal set at depth 2 must print \(t^\star=2\) on \(100\%\) and a constant prefix that the admitted-region rule excludes; a generator with the goal after the query must print \(q=0.0\) and be discarded by census line 4 (F2), so the instrument reads the placement it is given.
If killed (the counter). The route is tree C's first reroute: \(t^\star\) moves to \(2\) or the graph depth is raised so that the causal window bounds \(t^\star\) from above by construction, the census is re-run at \(0\) GPU-s, and the depth skyline of 06.20 is re-fixed to \(\lfloor\log_2t^\star\rfloor+2=3\) before any arena cell (M-2). Hypotheses: the DAG's depth is a registered dial. Evidence: READ docs/PLAN.md:1056 @ 99777ab (tree C's first route owed: "reroute the dial — move \(t^\star\) to 2 or raise the graph depth, since the DAG substrate bounds \(t^\star\) by the causal window"); the pin :1067-1069 this verse carried at filing names the S-20/S-62/R-21 rows of the smaller-deaths table and is corrected here (P-6). Kill of the replacement: sd \(\le0.05\) at \(t^\star=2\) as well — decided by the same \(0\) GPU-s census, and then the substrate reroute (the jittered bed_1 landscape at \(K=2\), oracle cross-check only, never the shape lane's substrate because it is undirected with \(\rho(Q)=0.9409\)) is the only route left.
Terminal. The paper files the generator specification and the census with its printed failure line; "the measured \(t^\star\)" is the line "\(t^\star\) unplaceable at \(s=64\)" and no capability number.
II. Cells before a GPU-second (tree C)#
06.7 — BED-S admission at the design point#
Statement. Prediction: the five admission lines pass on 512 draws — every admitted-region sd \(>0.05\), every argmin class frequency in \((0.05,0.95)\), rule-disagreement fraction \(>0\), lines 1 to 4 at \(100\%\), discard fraction printed. Counter: at least one line fails — the point estimate is the sink share dominating \(q^{(0)}\) (the declared sink read \([0.362,1.000]\) on the one draw run, READ docs/PLAN.md:1054 @ 99777ab, tree B's "the fix's own risk, since the declared sink read \([0.362,1.000]\) on the one draw run"; the census line that prints the sink share apart from \(q^{(0)}\) is line (5) at READ docs/PLAN.md:365 @ 99777ab; the pin :1057 this verse carried at filing is a blank line and is corrected here, P-6), and the bed is not admitted. No SPLIT: admission is a decision the author takes from the printed block (D-4). The deciding number is the census block of S-12.
Hypotheses. \(0\in\mathcal A_{\rm sink}\) declared; every boundary set precedes the query (F1, F2); ties within \(10^{-9}\) discarded and counted; census lines 8 and 9 are the corpus-alone probe of S-15 and \(I(s_0;a^\star)=0\) by plug-in (READ docs/PLAN.md:365 @ 99777ab, the fifteen census lines as built), never the zero-hop read — the zero-hop read is card S-14 (READ docs/PLAN.md:380-386 @ 99777ab), which 06.8 owns and which the census does not carry as a line. The filing sentence named "the zero-hop read" as line 9 and is corrected here (P-6, V-8, D-4: an admission decision may not name a line the census does not have).
Evidence. READ docs/PLAN.md:343-347 (the gate), :364-370 (S-12); READ docs/CEQ_SHAPE.md:2543-2560 (the fifteen lines); READ docs/sources/design/design_falsify.md:391 (rank 1 of the death order, the record's dominant failure).
Mechanism. D-4, V-8, V-12, V-10 (MISTAKES.md:168, line 3 is a gate printed, never counted as evidence).
Kill. The prediction dies on any failing line; the counter on all five passing; \(0\) GPU-s, \(1\) evening. Planted negative: BOS undeclared must make the solve raise at \(\rho(Q)=1\) (V-16), never return a number; a constraint placed after the query must read \(q=0.0\) exactly and be discarded; the census must print both counts.
If killed (the counter). Tree C is the paper: "BED-S at the design point does not admit; the paper files the generator specification, the census with its printed failure line, the floors, the controls and the pricing rule, and no capability number." Every cell from S-14 to S-65 is VOID and unscored, which is the cards on BED-S: 06.8, 06.9's arena half (C-32), 06.10, and 06.15 to 06.27 file VOID, not COUNTER. It is not every verse in that numeric span: 06.11 (J-L18, a Lean build), 06.12 (S-61's synthetic plants), 06.13 (S-20 on BED-M's e3_t2) and 06.14 (S-52, the R1 retake) are hosted outside the S-14-to-S-65 range and still run, exactly as 06.4's tree-C pool records; PLAN's blanket sentence is a sentence about BED-S cards and is read here as one. The replacement route is 06.6's chain in order — the \(t^\star\) reroute, then the substrate reroute as oracle cross-check, then the \(N\) reprice — each at \(0\) GPU-s until a batch admits. Hypotheses, Evidence and Kill as in 06.6.
Terminal. No BED-S sentence; the canon's capability verses in 01, 02 and 04 carry their Terminal sentences; the identities, the certificate discipline and the census instrument survive as the paper's contribution.
06.8 — The zero-hop guard and the leak guard, both ways#
Statement. Prediction: the corpus-alone linear probe from token features to \(q\) at order 0 reads \(R^2<0.5\) on the admitted draws, the planted leak (a move token carrying its own \(q\)) reads \(R^2\ge0.99\), and the untrained arm reads the argmin at \(1/m=0.125\) within its Clopper–Pearson half-width with committor NRMSE \(\ge1-10^{-3}\). Counter: the honest probe reads \(R^2\ge0.5\) — the label is legible at zero hops, the one-read claim is void on this bed and the bed is a copy task. A planted probe below \(0.99\) is not a SPLIT but a VOID: the detector is blind and no leak verdict is admissible. Deciding numbers: the two \(R^2\) values (S-15) and the zero-step forward's accuracy and NRMSE (S-14).
Hypotheses. \(s_0\) drawn uniformly from \(T\) independently of \(a^\star\); \(I(s_0;a^\star)=0\) by plug-in with its sampling error; the strictly-local feature set of E4′ (degree, ball sizes to radius 5, absorbing-endpoint flags) re-derived for BED-S before use (V-22); \(\mathrm{GATE\_TOL}=10^{-3}\) (READ COSTS.md:137).
Evidence. READ docs/PLAN.md:380-393 (S-14, S-15); precedent: BED-M's first builder leaked \(1/(t^\star+1)\) at zero hops and aborted three of five rungs (READ scale/negation_scope.py:399-415).
Mechanism. M-21 (MISTAKES.md:2101), V-24 (:1658), V-7 (:117), V-10, D-5 (:755).
Kill. The prediction dies at honest \(R^2\ge0.5\) or an untrained read below \(1-10^{-3}\) on the committor; the counter at honest \(<0.5\) with planted \(\ge0.99\); \(0\) GPU-s for the probes plus one zero-step forward \(\le1.524\) s, \(1.5\) evenings. The planted negative is the guard's own construction: the planted leak must fire and the honest query must not, both counts printed.
If killed (the counter). The one-read sentence is withdrawn on BED-S and the label is re-registered with the leaking feature removed from the token set (the move token carries its index only, never its \(q\)), the probe re-run at \(0\) GPU-s. Hypotheses: the leak is in a named feature. Evidence: the probe's coefficient table. Kill of the replacement: honest \(R^2\ge0.5\) persists with every move-side feature removed — decided by the same probe, and then the bed is a static task and 06.10's Terminal applies.
Terminal. BED-S is struck before any number; the canon keeps the guard as an instrument with its planted positive and negative and says which feature leaked.
06.9 — The sink-escape and the flag-lookup attacks#
Statement. R-24 is filed as two rows because its two halves are decidable at different times and the arena half is circular with 06.19 (each would be the other's precondition: R-24's paired reading needs \(\mathrm{acc}_{\rm shape}\) and \(\mathrm{MDE}_8\), both S-62 outputs, and 06.19's Hypotheses require this verse to have held first — D-4, M-7, D-3). Row C-5, the \(0\) GPU-s half. Prediction: on the unrestricted bed the fraction of draws whose Chebyshev-safest move is the sink is below \(0.5\) and the exact-zero-tie discard fraction is below \(0.5\) (R-07); and the closed-form clamp-target membership rule reads an argmin error at or above the exact zero-information floor \(0.875\) at \(m=8\) on the realised class distribution, computed at construction on the census draws — the membership flags carry nothing the argmin needs. Counter: the sink-move fraction is at or above \(0.5\) — the Chebyshev rule is minimised by falling off the prompt and the column is struck — or the flag rule's error reads below \(0.875\), so a closed form on the membership flags beats chance before any arm exists and BED-S's argmin head is struck at \(0\) GPU-s. No SPLIT. Row C-32, the arena half. Prediction: the flag rule's paired argmin accuracy is below the shape's by more than \(\mathrm{MDE}_8(\mathrm{acc})\); counter: at or above \(\mathrm{acc}_{\rm shape}-\mathrm{MDE}_8\). This row is read after 06.19's cell, never before it, and 06.19's Hypotheses depend on the \(0\) GPU-s half alone. Deciding numbers: the two fractions and the flag rule's construction error against \(0.875\) (C-5, \(0\) GPU-s, before any arm); the paired accuracy difference (C-32, inside the arena).
Hypotheses. BOS is a value-zero sink set apart from the goal; the Chebyshev column is \(\arg\min_a\max_{k\ge1}q^{(k)}\); the flag rule is a closed form on the membership flags the zero-hop view carries.
Evidence. READ docs/PLAN.md:942-944 (R-07, R-24, firing numbers frozen), :415-436; the fractions NOT MEASURED — needs the S-11 generator (book 04).
Mechanism. V-12, V-8, V-10, V-5 (MISTAKES.md:98), D-5, M-21.
Kill. C-5: the prediction dies at either fraction \(\ge0.5\), or at the flag rule's construction error below \(0.875\); the counter at both fractions \(<0.5\) and the error at or above \(0.875\); \(0\) GPU-s and \(0.5\) evening, before any arm. C-32: the prediction dies at the flag rule inside \(\mathrm{MDE}_8(\mathrm{acc})\) of the shape on \(\ge6/8\); the counter at the flag rule below by more; inside the arena, read after 06.19's cell. Planted negative: a bed with the goal set inside a constraint set must read sink-move fraction \(1.0\) (every move falls off) and the flag rule at the floor; a bed whose move token carries the target's membership flag directly must read the flag rule's error at \(0.0\) and fire C-5's kill at \(0\) GPU-s; the instrument reports both counts.
If killed (the counter). R-07's route: the goal rule \(a^\star=\arg\max_aq^{(0)}\) and the conditioned Chebyshev column (restricted to moves with \(q^{({\rm sink})}\) below the goal share) with the restriction in the specification; R-24's route: the committor-vector head alone carries BED-S, the argmin is reported as a derived column with the flag rule's accuracy printed beside it, and Bet B (06.18) is VOID. Hypotheses: the vector head's floor is the exact oracle at \(0.0\). Evidence: READ docs/PLAN.md:1070-1073. Kill of the replacement: the conditioned column's disagreement fraction against the goal rule reads \(0\) — then only one rule may be named — decided by census line 7, \(0\) GPU-s.
Terminal. The safest-move sentence is one rule over an evaluated committor vector, a one-step filter and never a policy (R-20, misra-2023-safety-constrained-mdp [V]); no argmin number.
06.10 — The static-task kill (K-H2)#
Statement. The kill is read on McNemar at the eval draw count, never on a seed-level equivalence at \(N=8\). Prediction: the 0-hop per-position MLP's paired argmin accuracy is below the shape's by more than \(\mathrm{MDE}_{\rm McN}\), and McNemar on identical draws against the 1-hop softmax reads \(p\le0.05\). Counter: the gap is at or below \(\mathrm{MDE}_{\rm McN}\), or \(p>0.05\) — BED-S is a third static task and every capability sentence on it is struck before a number is quoted. No SPLIT. Deciding numbers: the paired accuracy gap against \(\mathrm{MDE}_{\rm McN}\) and the McNemar \(p\) (S-26). \(\mathrm{MDE}_{\rm McN}\) is fixed here: on \(n_{\rm eval}=4096\) paired draws, McNemar's normal form rejects at \(\lvert b-c\rvert/\sqrt{b+c}>1.96\) and reaches power \(0.80\) at \(\lvert b-c\rvert/\sqrt{b+c}\ge1.96+0.8416=2.8016\), so the minimum detectable accuracy difference is \(\mathrm{MDE}_{\rm McN}=2.8016\sqrt{d/4096}=0.04378\sqrt d\) with \(d\) the realised discordant-pair fraction — \(0.01384\) at \(d=0.10\) and \(0.03095\) at \(d=0.50\) (DERIVED). A non-rejection therefore carries a detectable-effect size and may fire tree C; a non-rejection with no printed \(\mathrm{MDE}_{\rm McN}\) may not.
Hypotheses. Matched at the recounted parameter count: \(4{,}769\) is the pre-head count of READ CEQ_V20_R15_CONTRACT.md:119 @ 99777ab, and the post-head count with the \([m,K+2]\) readout attached is NOT MEASURED — needs book 04's recount (READ docs/PLAN.md:314 @ 99777ab: "recounted, never assumed"). Ruling 3's \(0.032\) per cent is not the tolerance at this scale: it was set on the LM pair \(25{,}736{,}232\) against \(25{,}728{,}000\), a residual of \(8{,}232\) parameters, and \(0.032\% \times 4{,}769 = 1.53\) parameters, which no integer \(d_{\rm model}\) reaches (06.20). The match is stated as an absolute parameter gap with both integers printed, or the row says NOT MEASURED. Byte-identical draws; the identity half (oracle argmin equals label argmin on \(100\%\)) declared V-3. The seed-level two-one-sided reading is not run at \(N=8\): at a \(0.5\) margin the two-sample half-width is \(0.8807\sigma\) and the paired half-width \(t_{.95,7}/\sqrt8=1.894579/2.828427=0.669835\,\mathrm{sd}_d\) (both DERIVED, READ MISTAKES.md:1216-1219 @ 99777ab for the two-sample figure, whose own sentence names it two-sample; 06.24 prints the pair of numbers with each design named), so the interval is wider than the window at either design; the two-sample form first drops below \(0.5\) at \(N=23\) and reaches power \(0.80\) at \(N=70\) (same source), and the paired form at \(N=13\) and \(N=36\) respectively (06.24). No non-rejection at \(N=8\) seeds may fire tree C (M-13).
Evidence. READ docs/PLAN.md:501-507 (S-26), :941 (R-06); the C8 correction of the journal (git show 99777ab:V20_R15_JOURNAL.md, the "static task" row).
Mechanism. C8, V-10, V-24, V-3 (MISTAKES.md:72).
Kill. The prediction dies at a gap \(\le\mathrm{MDE}_{\rm McN}\) or \(p>0.05\); the counter at a gap \(>\mathrm{MDE}_{\rm McN}\) with \(p\le0.05\); \(\approx0.5\) GPU-min (two control arms at \(\le1.524\) s per cell, eight seeds each), \(1\) evening. Planted negative: the 0-hop MLP on a bed whose label is a flag lookup (the R-24 plant of 06.9) must read a gap below \(\mathrm{MDE}_{\rm McN}\) with \(p>0.05\) and fire the kill; on a \(t^\star=8\) label with the flags removed it must read at the exact zero-information floor \(0.875\) error with \(p\le0.05\); both \(\mathrm{MDE}_{\rm McN}\) and the realised \(d\) are printed with each.
If killed (the counter). Tree C's sentence with the cause named: "BED-S at the design point is decidable at zero hops by a per-position MLP; the bed is registered with its floors and no capability number." The replacement bed is book 04's joint-consistency bed outside the per-row class, whose label is the full vector on \(T\) and whose 0-hop control is the per-position MLP on the vector — Hypotheses: a vector label voids the per-row shortcut only if the harmonic residual of the per-row read is \(O(1)\); Evidence: READ MATHEMATICS.md:106-127 (the untested joint-determination claim); Kill: the per-row MLP's residual within \(2\times\) the shape's (06.21's counter) — decided inside one pair, \(\approx34\) s, more decisive than the accuracy comparison because it reads the mechanism, not a rate.
Terminal. No capability sentence on any per-row-decidable bed; the canon licenses the identities and the controls.
06.11 — The Lean set (Bet K)#
Statement. The prediction is filed on the seven admissible bare-[M] targets of docs/CEQ_SHAPE.md §A.8.2 — the bare-[M] rows that carry no depends on entry — and not on ten, and not on the eight this verse counted at its previous writing. The section's own heading is the rule: "A.8.2 Lean targets, restated (P0.1; grades [M]/[S]/[D]; every [M] resting on a [U] Mathlib name is [S] until lake build is green — P-11)" (READ docs/CEQ_SHAPE.md:2600 @ 99777ab). Under that rule any prediction filed over a set containing a [U]-dependent row is refuted at its own Evidence pin before a build runs, and its counter is satisfied by construction (P-11: a contract may not cite its own [M]-tagged theorem as settled; V-10: a gate whose outcome is fixed by construction; L-LEAN).
The denominator, recounted from the source, is nine and not eight. The section carries nine bare-[M] rows: gamma_zero_is_softmax (:2604), bos_row_is_absorbing (:2605), later_boundary_unreachable (:2606), softmax_corner_not_nilpotent (:2607), cut_makes_segment_head_absorbing (:2610), displacement_identity (:2611), committor_is_resolvent_read (a) (:2618), (b-causal) isUnit_one_sub_transient_causal (:2619), lowerTriangular_ne_symmSupport (:2622), all READ docs/CEQ_SHAPE.md @ 99777ab. (a) and (b-causal) are two declarations, not one target: they are separate rows with different statements — (a) q = Q*ᵥq + r, IsUnit (1 − Q) ⇒ q = (1−Q)⁻¹ *ᵥ r; (b-causal) for lower-triangular Q with Q i i < 1 on T, IsUnit (1 − Q) — different depends on entries (none; lower_triangular_isUnit) and different shipped refusals (none; bos_undeclared_singular). Merging them is what produced the count of eight, and it is corrected here.
Two of the nine are [U]-blocked by the heading's own rule, so the admissible set is seven. The depends on column reads lower_triangular_isUnit for :2606 later_boundary_unreachable and for :2619 (b-causal), and lower_triangular_isUnit, diag_one_sub_smul_pos is itself graded "[M]→[S] until Matrix.det_of_lowerTriangular [U] is confirmed" (:2608). The seven that carry no depends on entry are gamma_zero_is_softmax, bos_row_is_absorbing, softmax_corner_not_nilpotent, cut_makes_segment_head_absorbing, displacement_identity, committor_is_resolvent_read (a), and lowerTriangular_ne_symmSupport.
Prediction: those seven elaborate under lake build with exit \(0\), zero sorry, zero sorryAx, and the axiom set \(\{\)propext, Classical.choice, Quot.sound\(\}\) only: \(7/7\). Counter: at most \(6/7\). The four [U]-blocked rows are carried separately and are never cited as proved: the two bare-[M] rows blocked through their dependency, later_boundary_unreachable (:2606) and (b-causal) isUnit_one_sub_transient_causal (:2619); and the two rows the source itself grades conditionally, lower_triangular_isUnit, diag_one_sub_smul_pos (:2608, blocked on Matrix.det_of_lowerTriangular [U]) and resolvent_fromBlocks, segmentation_blockdiag (:2609, blocked on inv_fromBlocks_zero₂₁_of_isUnit_iff [U]). The counter's point estimate is therefore \(7/9\) on the nine bare-[M] rows and \(7/11\) on the eleven rows the section grades [M] or [M]→[S], with all four blocked names listed — never \(8/10\) with two, and never \(8/8\) on a set of eight, both of which this verse printed before and both of which name a denominator the source does not have (L-SIGN: a counter that names fewer blocked rows than the source demotes is not of equal specificity). No SPLIT. Deciding number: the green count out of the seven admissible bare-[M] targets (J-L18), with the four blocked rows' status printed beside it.
Hypotheses. Lean leanprover/lean4:v4.7.0 as the record's toolchain; the census file gives per theorem the fraction of the corpus satisfying its hypotheses, and a \(0\%\) line demotes the theorem to decoration on that bed (L-DOM); a [U]-blocked row becomes scorable in the seven only when its Mathlib name is confirmed, which is a separate row, filed then and not now; "admissible" is decided by one column of one table — a bare-[M] grade and an empty depends on cell at :2604-2622 — so the denominator is read, never chosen.
Evidence. READ docs/PLAN.md:228-235 @ 99777ab (J-L18); :1007-1033 (§5.8); READ docs/CEQ_SHAPE.md:2600 @ 99777ab (the heading's [U]-demotion rule, quoted above), :2604-2626 @ 99777ab (the target list with grades and the depends on column: nine bare [M], two [M]→[S], and the two lower_triangular_isUnit dependencies at :2606 and :2619); the record's 169 theorems over 12 files at READ docs/PLAN.md:231 @ 99777ab (the *measure* line; the pin :232 this verse carried at filing is J-L18's PASS/KILL line and is corrected here, P-6).
Mechanism. P-11 (MISTAKES.md:1597), L-LEAN, L-DOM, V-25 (:1954), V-10, V-9 (the count of eight was the count of ten renamed, and is struck here rather than moved again).
Kill. The prediction dies at any of the seven admissible bare-[M] targets not building; the counter at \(7/7\); \(0\) GPU-s (CPU minutes), \(1\) evening. Planted negative: a target with a deliberately wrong hypothesis (\(\gamma=\tfrac12\) in gamma_zero_is_softmax) must fail to elaborate, and gamma_half_is_not_softmax must build as its refusal — the gate reads red on the wrong statement and green on its negation. Second planted negative, for the denominator itself: later_boundary_unreachable must be absent from the seven the harness builds, and a harness that builds it and reports \(8/8\) must be refused at the depends on column, so the admissible set is known to be read from the table rather than asserted.
If killed (the counter). The demoted row carries [S] with its numeric instance (RUN[coord] \(1.7763568394002505\times10^{-15}\) for the solve, \(0.0\) for corner 3), the "machine-checked" sentence of component (k) is narrowed to the rows that build, and — L-LEAN — no arm trains until parity and the unit are green. The unit is not in the seven: parity is gamma_zero_is_softmax (:2604, bare [M], no dependency) and the unit is lower_triangular_isUnit (:2608), which the source grades [M]→[S] until Matrix.det_of_lowerTriangular [U] is confirmed, so L-LEAN blocks the arena on a row this verse does not predict and cannot predict. Hypotheses: parity carries no depends on entry (:2604), and the unit's greenness is gated on one Mathlib confirmation, filed as its own row. Evidence: READ docs/CEQ_SHAPE.md:2604, :2608 @ 99777ab. Kill of the replacement: parity red, or Matrix.det_of_lowerTriangular not confirmed after the search — decided by the same build plus one grep of Mathlib, and then S-20 is blocked and every arena row is VOID (not COUNTER) for one evening per repair.
Terminal. The paper cites every float instance as RUN and no theorem as proved beyond the rows that build; the arena waits.
06.12 — The \(\gamma\) instrument's own plants (S-61)#
Statement. Prediction: the likelihood-ratio instrument reads PINNED on \(8/8\) synthetic seeds at \(\gamma_{\rm env}=0\) and MOVED on \(8/8\) at \(\gamma_{\rm env}=0.6\), under the boundary null \(\tfrac12\chi^2_0+\tfrac12\chi^2_1\) with 95 per cent point \(2.705543\), MOVED at \(\Lambda>\ln4096=8.318\). Counter: either count below \(8/8\) — the instrument cannot decide Bet C, and row C-12 is VOID until repaired. No SPLIT. Deciding number: the two plant counts.
Hypotheses. \(\gamma\) trained on \([0,1)\) so \(\gamma=0\) is a boundary; the held-out set \(n_{\rm eval}=4096\) declared before training; the \(|\hat\gamma|<0.05\) rule deleted (M-20).
Evidence. READ docs/PLAN.md:327-334 (S-61); the quantile RUN[J], RUN[MARS], RUN[MERCURY] at :329; the citation for the boundary null is owed, and the search that shows it is printed in full so a reader can repeat it. RUN this session, exact commands and their outputs: grep -c 'chernoff' docs/references.bib reads \(0\); grep -c 'self-liang' docs/references.bib reads \(0\); the widened grep -niEc 'chernoff|self.?liang|chibar|chi-bar' docs/references.bib reads \(0\). The two candidate keys searched are the key strings chernoff-1954-boundary and self-liang-1987-boundary, and neither exists in the bibliography. The theorem is named here so a reader can supply the reference without guessing what is missing: the asymptotic null distribution of the likelihood-ratio statistic when the tested parameter lies on the boundary of the parameter space is the half–half mixture \(\tfrac12\chi^2_0+\tfrac12\chi^2_1\), whose \(95\) per cent point is \(2.705543\) — the result the record attributes to no source, classically Chernoff (1954) and Self and Liang (1987, boundary case 5), both NOT FOUND at [V-eq] in this tree. What the absence blocks, named: the PINNED half of every \(\gamma\) verdict — \(\Lambda\le2.705543\) in this verse, in 06.16 (Bet C's counter) and in 06.35 — because the threshold is the mixture's quantile and nothing else in the tree derives it; the PINNED plant count of this verse's own \(8/8\) at \(\gamma_{\rm env}=0\) rests on it as well. It does not block the MOVED threshold: \(\ln 4096=8.317766\) is read off the declared held-out set size \(n_{\rm eval}=4096\) and stands without the null. Until the reference is supplied at [V-eq] with its hypotheses and one numeric instance, the PINNED threshold carries the class NOT FOUND at [V-eq] — the boundary-null quantile is owed (L-EQ, P-10), and a PINNED verdict quoted without that class is refused at the journal.
Mechanism. Ruling 10′, V-9, M-2, M-20, V-24, V-17.
Kill. The prediction dies at either plant below \(8/8\); the counter at both \(8/8\); seconds, \(1\) evening. The plants are the planted negative and positive: a \(\gamma_{\rm env}=0\) generator must not be read MOVED, a \(0.6\) generator must not be read PINNED.
If killed (the counter). The replacement instrument is the ablation alone — \((I-\hat\gamma\hat P)^{-1}\to I\) at trained weights, MOVED iff NRMSE moves by more than one seed sd — with Hypotheses (seed sd from the same lane), Evidence (READ docs/PLAN.md:697) and Kill (the ablation on the \(\gamma_{\rm env}=0\) plant reading a move above one seed sd — decided at \(\le17.4\) s, cheaper than the LR plants because it needs no held-out likelihood).
Terminal. Bet C is VOID; the horizon dial is a definition (Proposition 9) and no pinning sentence is written.
06.13 — Parity, the price band and strict mode (S-20)#
Statement. Prediction: torch.equal(O(0), PV) reads True against the lane's own softmax routine (ceq/lm.py:5, :66), the four plants read \(O(1)\) (\(\gamma=0.5\): \(2.3002850040264393\) at \(s=64\); \(\beta=0\): gap \(>0.5\); ChaCAL-published's \(A_s\): \(O(1)\) at every \(\gamma>0\); a dense non-triangular \(M\): disagrees with the dense inverse), the ChaCAL-diag cell at \(\gamma=0.9\) lands inside \([-1.8,+14.4]\) per cent of the DERIVED \(1.71990\) s shape cell (06.28), and the forward repeats bitwise over 8 repeats under use_deterministic_algorithms(True). Counter, in two named branches that together with the prediction band and the SPLIT band exhaust \([0,\infty)\): COUNTER-dear, the cell at or above \(2.2\times\) the DERIVED cell (\(\ge3.78378\) s; the dispatch gap of \(2.0\times\)–\(6.6\times\) realised as the cell), or the strict-mode forward not bitwise, signed +; COUNTER-cheap, the cell below \(0.982\times\) the DERIVED cell (\(<1.68894\) s), signed −. SPLIT: the cell in \((1.144,2.2)\times\) the DERIVED cell, \((1.96757,3.78378)\) s, with the identity and the plants passing. Deciding numbers: torch.equal; the cell wall-clock over the DERIVED \(1.71990\) s; the strict-mode forward repeat.
The band's centre is the re-tagged cell, not \(1.680\) s. The \(1.680\) s per shape cell of READ docs/PLAN.md:594-600 @ 99777ab carries the [FITTED + RUN] tag 06.28 strikes, and \(1.680/150=0.011200\) s is the superseded step \(0.011206\) s to five places, so a band centred on it is a band centred on the struck constant under the struck tag (M-8, P-3, M-2). The centre is therefore the DERIVED \(150\times0.011466=1.71990\) s (06.28), and every endpoint below is recomputed from it.
The fourth branch, and why the partition had a hole without it. The prediction band is \([-1.8,+14.4]\) per cent of \(1.71990\) s, i.e. a multiplier in \([0.982,1.144]\) and an interval \([1.68894,1.96757]\) s; the SPLIT band is \((1.144,2.2)\), i.e. \((1.96757,3.78378)\) s; the counter as filed began at \(2.2\). The interval \([0,0.982)\) — a cell cheaper than the DERIVED cell by more than \(1.8\) per cent — therefore fell in no branch, and 06.36's own Kill declares the tree refuted when "a scored outcome has no branch" (M-7, a pre-registration with a hole; D-7; M-20). The same hole stood in 06.28 and in rows C-9 and C-24 of 06.3. It is closed here in the direction the canon most wants, so the optimistic outcome carries a verdict rather than escaping one: a cell below \(0.982\times\) the DERIVED cell (\(<1.68894\) s, frozen here) is COUNTER-cheap, scored COUNTER, and its sentence is "the DERIVED cell over-predicts the measurement by \([\cdot]\) per cent; every price in this book is re-derived from N-02's producer before any GPU-minute is quoted, with the sign of the miss printed — the derivation was too dear, not too cheap."
The signs of the two counter branches are corrected here, and they run the other way from the previous writing. 06.1 defines the sign of a miss against the project — + credits the project more than the measurement supports (READ V16_CALIBRATION.md:24-31) — and the object scored is the claim, not the outcome. A cell dearer than the claim means the claim was too cheap and credited the project more than the measurement supports: COUNTER-dear is +. A cell cheaper than the claim means the claim was too dear and credited the project less: COUNTER-cheap is −. The parenthesis printed before — "a cell cheaper than the law flatters every price in this book" — scored the outcome rather than the claim and is deleted; it inverted both signs, and because C-9 and C-24 both sit in 06.4's tree-C pool the inversion moved up to two of the eight signs the eighth-row test reads, in the direction that inflates the + count. The re-tag COUNTER-cheap triggers is the same one COUNTER-dear triggers, and the two branches differ only in the sign the column records.
The backward half is removed from this verse's prediction, and why. The verse as filed predicted solve_triangular bitwise forward and backward under use_deterministic_algorithms(True) and cited the device certificate for it. The certificate does not carry that: it records the gradient bitwise with the determinism flag off and the gradient not executable with the flag on, on an arm that is not the one the sentence names. results/k_cert_local.json (arm arm_smprime, git ab5b485) reads determinism.flag_off.gradient \(=\{\)bitwise: true, max_abs: 0.0, repeats: 8\(\}\) and determinism.flag_on.gradient \(=\{\)executable: false, error: "RuntimeError: cumsum_cuda_kernel does not have a deterministic implementation"\(\}\), with the file's own note that arm_smprime reduces with CUMPROD and cumsum is measured only as the contrast. Citing flag_off for a flag_on claim is V-16, an instrument that cannot measure reporting a pass. The strict-mode backward is therefore not predicted here; it is 06.34's cell on the re-certified stack, and the record's own sentence for it — "solve_triangular ran bitwise forward and backward over 8 repeats under strict mode on this card with no torch-documented guarantee" (READ docs/CEQ_SHAPE.md:2680 @ 99777ab, RUN[NEPTUNE]) — is an undocumented single-producer reading, which is exactly B13, and is filed as NOT MEASURED — needs N-01 on the re-certified stack (06.34).
Hypotheses. The cuBLAS workspace exported before process start; synchronize() bracketing; BED-M e3_t2 as the host; no capability number is read (BED-M is contained, D-2).
Evidence. READ docs/PLAN.md:459-465; RUN[coord] at docs/CEQ_SHAPE.md:356-360; the determinism block split by flag, READ results/k_cert_local.json (arm arm_smprime, git ab5b485, \(n=512\), reduction length \(64\)): flag_off.forward, .hop and .gradient all bitwise: true, max_abs: 0.0, repeats: 8 — flag off; flag_on.forward and .hop bitwise: true, max_abs: 0.0, repeats: 8, and flag_on.gradient executable: false with error: "RuntimeError: cumsum_cuda_kernel does not have a deterministic implementation" — so the strict-mode forward claim of this verse is cited at flag_on.forward and the strict-mode backward is cited nowhere, because it does not execute for this arm; the record's solve_triangular strict-mode forward-and-backward sentence is pinned to its own producer, READ docs/CEQ_SHAPE.md:2680 @ 99777ab (RUN[NEPTUNE], undocumented, B13), and is not used as evidence here; the re-certified value NOT MEASURED — needs N-01 (06.34); the \(2.2\times\) is the record's own re-tagging threshold (READ docs/PLAN.md:463).
Mechanism. V-24, V-3, M-8 (MISTAKES.md:544), P-8 (:387), V-16 (:828), D-2.
Kill. The prediction dies at torch.equal False, any plant passing, the cell \(\ge2.2\times\) (COUNTER-dear, frozen here at \(\ge3.78378\) s), the cell \(<0.982\times\) (COUNTER-cheap, frozen here at \(<1.68894\) s), or the strict-mode forward reading max_abs > 0 over 8 repeats; the counter at all four passing inside the band. A strict-mode backward raise does not decide this verse — it is the expected reading for a cumsum/cumprod reduction and is 06.34's number on the re-certified stack; \(\approx1.72\) s for one cell and \(\approx17.76\) s for eight seeds (DERIVED, \(8\times1.71990+4.0\) fixed, re-derived from 06.28's re-tag; the \(\approx1.7\) s and \(\approx17.4\) s printed before were \(1.680\) s per cell and carried the struck tag), \(1\) evening. Planted negative: the struck plant — a non-causal \(W\) — must pass at \(\gamma=0\) (\(I-0\cdot W=I\)) and is recorded as struck, so the battery is known to contain one plant that cannot fire and does not count it.
If killed (the counter). Two routes by cause. Cell out of band: every [FITTED + RUN] price in this book is re-tagged the P-8 floor it was declared to be and re-measured by N-02's producer before any GPU-minute is quoted; the T1 ranges of 06.29 and 06.30 carry the measured per-step ratio in place of the DERIVED \(1.1280\) (06.28). Strict-mode forward not bitwise: Ruling 1's warn_only=True lane runs, the sentence "the first gated wing whose training step runs strict" is deleted — it rested on docs/CEQ_SHAPE.md:2680's single undocumented producer, not on the certificate — and every deciding forward cell is bitwise by replay in one lane or the cell is refused. Hypotheses: the forward is bitwise regardless (observed true at results/k_cert_local.json). Evidence: READ docs/CEQ_SHAPE.md:2970-2975. Kill of the replacement: the forward not bitwise over 8 repeats on the re-certified stack — 06.34's cell, seconds, more decisive because it is bitwise or not.
Terminal. The containment sentence survives only as the Lean row (gamma_zero_is_softmax [M]); every price is a band; no determinism sentence about training.
06.14 — The capped seeds (Bet I)#
Statement. Prediction: arm_pl on e3_t2 at the three NO-READING seeds 2, 3, 7 (\(1.152430\), \(1.113403\), \(1.139404\) eval NRMSE uncapped; \(\hat a_{\max}\) \(20.3090\), \(49.6613\), \(285.0719\)) with the magnitude capped at \(1.0\) crosses the one-hop threshold \(0.7071067811865476\) on \(3/3\): divergence was the cause. Counter: at most \(1/3\) crosses — the split is not the cap's and the mechanism stays unresolved, the Q3/W3 cell TERMINAL as graded. SPLIT: \(2/3\). Deciding number: the crossing count.
Hypotheses. Same thread lane and flag regime as the retake journal; synchronize() bracketing; randomised order; the threshold is a capability threshold and never a floor — \(13\) of \(40\) banked cells sit below it (C15, READ docs/PLAN.md:644 @ 99777ab — the M-3.7 line that prints the one-hop threshold and the 13 of 40; the pin :950 this verse carried at filing names the R-16/K-D2 row and is corrected here, P-6).
Evidence. git show 99777ab:V15_R1.md:177-188 (the seed table; seeds 0, 1, 4, 5, 6 crossed at \(0.634002\)–\(0.662021\)); READ workdonenewseal.md:143-147; READ docs/PLAN.md:522-528 (S-52).
Mechanism. M-6 (MISTAKES.md:518), D-6 (:1050), P-3, C17.
Kill. The prediction dies at \(\le2/3\); the counter at \(\ge2/3\); \(\approx9.65\) s (\(3\times1.884+4.0\)), \(0.5\) evening. Planted negative: seed 0 re-run under the cap must still cross (the cap is inert where \(\hat a_{\max}=1.4107\)), so a cap that changed the crossing seeds would be detected.
If killed (the counter). The account of R1 keeps "3 of 8 NO READING, mechanism unresolved" and the canon's book 02 verse on divergence under the corner descent (B12) loses its cheapest evidence and stands on the \(\hat\gamma\) trajectory alone. Hypotheses: the R1 seeds are a different arm (arm_pl) from the shape. Evidence: the three uncapped rows. Kill of the replacement: none needed — a stale question dies cheaply either way and the shape's sentences are untouched (READ docs/PLAN.md:527).
Terminal. The record's negatives section carries the three seeds with both readings; no sentence about divergence as a cause.
III. The arena#
06.15 — Identification, not copy (K-D2; B5)#
Statement. Prediction: \(\|\hat P-P_{\rm env}\|_\infty\in[10^{-3},10^{-2})\) on at least 6 of 8 seeds — the trained arm identifies the environment chain without copying it, the first trained CEQ arm the record holds (B5). Counter: \(\ge10^{-2}\) on at least 6 of 8 — the arm did not learn the chain at 150 steps and every capability reading on BED-S is a learnability negative. VOID (not SPLIT): \(<10^{-3}\) on at least 6 of 8 — the arm copied the environment and every contrast is a copy-versus-no-copy statement, filed as identification only.
The scoring rule is the modal band with its count, because "at least 6 of 8" on three bands is not a partition. Three bands each requiring \(\ge6/8\) leaves reachable seed splits with no token and lets one clause name two bands at once: the split \((3,3,2)\) — three seeds identified, three counter, two VOID — reaches \(6/8\) in no band and would have been scored by none, while \((5,3,0)\) and \((3,5,0)\) each sit in the filed SPLIT window "\(3/8\) to \(5/8\)" for two bands simultaneously (M-7, a pre-registration with a hole; D-7; M-9). The rule frozen here: the eight per-seed sup-norms are binned into the three bands, the modal band and its count are printed, and the token is the modal band's — HOLDS if the modal band is \([10^{-3},10^{-2})\) at a count \(\ge6/8\), COUNTER if the modal band is \(\ge10^{-2}\) at \(\ge6/8\), VOID if the modal band is \(<10^{-3}\) at \(\ge6/8\). Every other configuration is SPLIT, including every tie for the mode, and a SPLIT row prints all three counts as an ordered triple \((\,\text{identified},\text{counter},\text{VOID}\,)\) so the reading is recoverable from the row. Exactly one token is reachable per outcome, and the eight seeds always produce one: \((3,3,2)\) is SPLIT with its triple printed, \((5,3,0)\) is SPLIT, \((6,2,0)\) is HOLDS. This is row C-11 of 06.3 as it stands, and verse and column now say the same thing. Deciding number: the per-seed sup-norm, sorted, from S-62, binned as above with the modal count printed.
Hypotheses. Adjacency rows as multi-hot node features so \(\hat P=P_{\rm env}\) is representable at \(d_{\rm model}\ge n_{\rm nodes}\); the DAG substrate, on which the D-2 separation holds (lowerTriangular_ne_symmSupport); the VOID-contrast list in every cell's manifest.
Evidence. READ docs/PLAN.md:371-379 (S-13), :626-633 @ 99777ab (S-62, whose KILL line is K-P and whose measure block carries the K-D2 statistic; the pin :640-645 this verse carried at filing names the S-51 tail and S-50 and is corrected here, P-6); READ docs/CEQ_SHAPE.md:1191-1197 (the FOUND-not-NAMED census, arm_phase \(0\)); RUN this session, grep -rhoE '"kind": *"[A-Za-z0-9_]+"' results --include='*.jsonl' | sort | uniq -c reads arm_smprime 425, arm_pl 422, softmax 227, arm_phase absent — no record with the shape's kind exists, so the shape is NAMED today and becomes FOUND at the first S-62 row.
Mechanism. D-2 (MISTAKES.md:710), M-7 (:529), V-10, FOUND-not-NAMED.
Kill. The prediction dies at a modal band of \(\ge10^{-2}\) on \(\ge6/8\), at a modal band of \(<10^{-3}\) on \(\ge6/8\), or at no band reaching \(6/8\) (SPLIT, scored wrong with the sign of the optimistic half by 06.1); the counter at the identified band modal on \(\ge6/8\); inside the arena's \(\approx98\) s, \(1\) evening. Planted negative: an arm initialised at \(\hat P=P_{\rm env}\) (the copy plant) must read \(<10^{-3}\) on \(8/8\) and be filed VOID; an arm with \(d_{\rm model}<n_{\rm nodes}\) must read \(\ge10^{-2}\) on \(8/8\), so the band has a floor and a ceiling that both fire.
If killed (the counter). The sentence: "At 150 steps the arm reads \(\|\hat P-P_{\rm env}\|_\infty=[x]\) on \([k]\) of 8 seeds; no BED-S number is a capability number; the reading is filed as learnability." The replacement route is the ladder (06.27) on the identification metric alone — Hypotheses: the metric is monotone in steps; Evidence: READ docs/PLAN.md:775-780; Kill: \(\ge10^{-2}\) at step \(9{,}600\) on \(\ge6/8\), decided at \(32\)–\(36\) min per pair, more decisive because it exhausts the budget the record ever spent on one pair.
Terminal. B5 is closed by the row's existence: a FOUND record with the shape's kind, its manifest and its sup-norm; the canon licenses "trained and not identified" and withdraws every capability contrast on BED-S.
06.16 — The horizon dial (Bet C)#
Statement. Prediction: \(\hat\gamma\) MOVED (\(\Lambda>8.318\)) on at least 6 of 8 seeds and the ablation \((I-\hat\gamma\hat P)^{-1}\to I\) moves NRMSE by more than one seed sd. Counter: PINNED (\(\Lambda\le2.7055\)) on at least 6 of 8 — softmax wearing a name on this bed; the corner descent of B12 realised. SPLIT: \(3/8\) to \(5/8\) MOVED, or interval verdicts. Mirror kill: \(\hat\gamma>0.99\) on at least 6 of 8 prints \(1/(1-\hat\gamma)>100\) beside every \(\delta\) and the certificate is vacuous on the \(z\)/\(\Delta z\) channel. Deciding number: \(\Lambda\) per seed on the declared held-out set (R-21).
Hypotheses. 06.12's plants both \(8/8\); \(\gamma\in[0,1)\) one learnable scalar per head; the committor head reads at \(\gamma=1\) on \(\hat Q\) and is untouched by the verdict.
Evidence. READ docs/PLAN.md:914 (Bet C), :694-699 (R-21), :1056-1058 (tree B's "PINNED on at least 6 of 8"); the record's precedent — no \(\gamma\) beat \(0\) on the hop-2 sweep, \(4/4\) blind predictions held (READ docs/sources/design/design_falsify.md:392); R1's \(\hat a_{\max}\) up to \(285.0719\) on 3 of 8 seeds (06.14).
Mechanism. Ruling 10′, V-9, M-20, V-17, B12.
Kill. The prediction dies at PINNED on \(\ge6/8\) or the ablation moving less than one seed sd; the counter at MOVED on \(\ge6/8\) with the ablation moving more; \(0\) GPU-s (a journal read) plus the ablation \(\le17.4\) s, \(1\) evening. Planted negative: 06.12's \(\gamma_{\rm env}=0\) generator inside the arena harness must read PINNED \(8/8\).
If killed (the counter). The horizon-dial sentence retires to a definition; ChaCAL-with-sink at \(\hat\gamma=0\) is softmax, so 06.22 and 06.24 are VOID; the LM claim of 06.35 is retired before it is made; regime N at \(\gamma=1\) (corner 3, exact without a dial) and the constant-value plant are kept. The replacement is book 02's pre-written fixed-\(\gamma\) regime: \(\gamma\) frozen at the bed constant \(\gamma_{\rm env}\) for the \(z\)/\(\Delta z\) channel and the committor head at \(\gamma=1\), so the read is exact without descent — Hypotheses: \(\gamma_{\rm env}\) registered before training (M-2); Evidence: READ docs/CEQ_SHAPE.md:336-342 (Definition 7's discounted read at a bed constant); Kill: at fixed \(\gamma_{\rm env}=0.6\) the paired \(\varphi\)-NRMSE against ChaCAL-diag at the same fixed \(\gamma\) is within \(\mathrm{MDE}_8\) (the dial did nothing that the fixed value does not) — decided inside one pair, \(\approx34\) s, more decisive because no likelihood is involved.
Terminal. \(\gamma\) is a bed-side dial; the equilibrium sentence is withdrawn; the exact solve at \(\gamma=1\) on the transient block is the only read the canon licenses as "next state toward equilibrium".
06.17 — The consequence field (Bet A)#
Statement. Prediction: \(\cos_{\rm shape}-\cos_{\rm softmax}>\mathrm{MDE}_8(\cos)\) on the paired test over byte-identical draws, the cosine's own realised sd. Counter: within \(\mathrm{MDE}_8(\cos)\) — a per-row mixture learns the displacement coordinate by coordinate as well as the joint read. No SPLIT: two-sided on the sign of the miss. Deciding number: the paired cosine difference against the cosine's realised sd (M-4.2).
Hypotheses. Coordinates with label variance \(0\) masked and their fraction printed; an arm emitting \(\Delta\hat z\equiv0\) is refused, not scored (V-16); the intervened position drawn uniformly; the no-change predictor's error printed beside every \(\Delta z\) number (vakalis-2026-interventiongap [V]).
Evidence. READ docs/PLAN.md:910 (Bet A), :700-704; softmax owns the sign column at \(0.807843\) (READ MATHEMATICS.md:396-406, seed 0 only); the cosine's sd NOT MEASURED — needs S-62 (book 04).
Mechanism. D-1 (MISTAKES.md:677), V-26 (:2190), V-17, V-16.
Kill. The prediction dies at a difference \(\le\mathrm{MDE}_8(\cos)\); the counter at \(>\); inside the pair \(\approx34\) s, \(0.5\) evening. Planted negative (B-G2): the permuted oracle must not score \(0\); \(-\Delta z\) must be distinguished from \(\Delta z\); oracle + 0.1σ must be preferred to the permutation — three plants the metric must fail at \(O(1)\).
If killed (the counter). "Consequence as a field" retires to a label class: the canon keeps \(\Delta z=(I-\gamma P')^{-1}(\Delta V+\gamma\Delta P z)\) as algebra (Proposition 7, displacement_identity [M]) and the channel as a cost statement (one extra solve). Hypotheses: the identity holds on every draw (\(V\equiv\mathbf 1\Rightarrow\Delta z\le10^{-15}\)). Evidence: READ docs/CEQ_SHAPE.md:456-476. Kill of the replacement: the C6 identity residual above \(10^{-12}\) on any draw of the cell — decided at seconds, bitwise-class.
Terminal. The displacement is an identity and a price; no fidelity sentence against softmax.
06.18 — The argmin floor (Bet B)#
Statement. The deciding floor of this verse is the exact zero-information floor \(\mathrm{floor}_0=1-\max_a\hat\pi(a^\star)\), \(0.875\) at the realised class distribution when it is uniform at \(m=8\) — not the tight restricted-view Fano. Prediction: \(\mathrm{CP}_{\rm upper}(\mathrm{err}_{\rm shape})<0.875\) at \(N=8\). Counter: \(\mathrm{CP}_{\rm lower}\ge0.875\) — the joint read is no better than knowing nothing about the query. SPLIT: the straddle \(\mathrm{CP}_{\rm lower}<0.875\le\mathrm{CP}_{\rm upper}\) (the R1 precedent straddled \(0.7071\) with \([0.617075,1.041227]\)). Deciding number: the Clopper–Pearson interval against \(0.875\) at the realised \(\hat\pi\).
Why the Fano row is not the floor here, stated in the verse it used to decide. The tight restricted-view bound \((\ln m-I(X_{\le1};a^\star)-\ln2)/\ln(m-1)\) is admissible in its source only where \(I(X_{\le k};a^\star)>0\) (READ docs/CEQ_SHAPE.md:2491 @ 99777ab). This bed's own Hypotheses register \(I(s_0;a^\star)=0\) by plug-in (06.7, 06.8), so the instance the verse evaluated — \(0.7124=(\ln 8-\ln 2)/\ln 7\) at \(m=8\), \(I=0\) — is the one instance the source excludes: L-DOM, a theorem read outside its domain census, which the source's census makes decoration and not a floor. It is also \(0.1626\) looser than the floor the bed actually has, so deciding against it would license a capability sentence at an error rate the zero-information floor already forbids. The Fano number is therefore printed as a row and never as the deciding number, and it is printed only where the plug-in \(I\) over the one-hop view reads strictly positive with its sampling error; where \(I\) reads \(0\) the row prints "\(I=0\): Fano decoration, not a floor (L-DOM)" in place of a value. Book 04 records the same conclusion at the journal: floor_fano_k1 is struck from the mandatory field list and a cell carrying it is refused (READ 04_BEDS_AND_INSTRUMENTS.md:233).
Hypotheses. \(\mathrm{floor}_0\) computed at the realised class distribution on the census draws, not assumed uniform; \(0.875\) is its value at uniform \(m=8\) and the row prints the realised value beside it; the weak Fano \(0.6667\) retired (\(0.208\) below chance); R-08's \(m_{\rm eff}\) correction applied to \(\hat\pi\) before \(\mathrm{floor}_0\) is read; the plug-in \(I\) with its sampling error printed whenever the Fano row is printed at all.
Evidence. READ docs/PLAN.md:911, :2487-2499 of docs/CEQ_SHAPE.md (A.3); RUN of the three floors at docs/CEQ_SHAPE.md:2491, which is also the line carrying the restriction "used only where \(I(X_{\le k};a^\star)>0\)"; READ 04_BEDS_AND_INSTRUMENTS.md:233 (floor_fano_k1 struck from the journal's field list); the realised \(\hat\pi\) NOT MEASURED — needs the S-12 census (book 04).
Mechanism. L-FLOOR, L-DOM, V-10, V-25, M-2, V-17, P-10.
Kill. The prediction dies at \(\mathrm{CP}_{\rm upper}\ge0.875\); the counter at \(\mathrm{CP}_{\rm lower}<0.875\) with the upper below; inside the pair, \(0.5\) evening. Planted negative: the random arm reads \(1/m\) and majority reads \(\max_a\hat\pi(a^\star)\) by construction (declared V-3) and both must sit on the zero-information floor row within their intervals; a floor that random beats is not a floor. Second plant, for the Fano row itself: on a generator whose one-hop view carries the membership flags (06.9's flag plant, \(I>0\) by construction) the Fano row must print a value strictly below \(0.875\) and the plug-in \(I\) strictly above \(0\); on the registered bed it must print the decoration line and no value — so the row is known to be printed only inside its domain.
If killed (the counter). The argmin is repriced to \(N=16\) (\(\approx68\) s) before any argmin sentence, and the reading at \(N=8\) is filed as "no better than knowing nothing about the query licenses" with \(\mathrm{floor}_0\) printed and the Fano row printed only if \(I>0\). Hypotheses: the straddle at \(N=8\) is the median outcome (tree B). Evidence: READ docs/PLAN.md:1054 @ 99777ab (tree B's sentence, "the median outcome"; the pin :1058-1060 this verse carried at filing names the smaller-deaths heading and its table header and is corrected here, P-6). Kill of the replacement: the \(N=16\) interval still straddling or above — decided by one more batch of eight seeds, \(\approx34\) s, and then 06.9's committor-vector-only route.
Terminal. The argmin column is derived and floored only by the exact zero-information floor \(0.875\); the Fano row is decoration at \(I=0\) and is printed as such; the committor vector with the exact oracle at \(0.0\) is the only head with a floor the bed itself supplies.
06.19 — A1 on the argmin: the shape against depth-1 base self-attention at matched parameters#
Statement. The canon's licensed form A1 (CHARTER.md §1) on BED-S is the argmin contrast shape − 1-hop softmax (creditable by S-13; the committor-head contrast is VOID). Prediction: \(\Delta_{A1}=\mathrm{acc}_{\rm shape}-\mathrm{acc}_{d1}\in[0.40,0.85]\) with \(\mathrm{acc}_{\rm shape}\ge0.90\) and \(\mathrm{acc}_{d1}\le0.50\), the depth-5 skyline's accuracy printed in the same row. Counter: \(\Delta_{A1}\le\mathrm{MDE}_8(\mathrm{acc})\) — either \(\mathrm{acc}_{d1}\ge0.85\) because the one-hop view carries the move tokens and membership flags (R-24's lookup) or \(\mathrm{acc}_{\rm shape}\le0.50\) because 06.16's counter holds and the shape reads one hop. SPLIT: \(\Delta_{A1}\in(\mathrm{MDE}_8(\mathrm{acc}),0.40)\).
The range is two-sided and both ends kill. The sentence this verse carried at filing — "\(\mathrm{acc}_{d1}>0.50\) (the lower end fails) or \(\mathrm{acc}_{\rm shape}<0.90\) (the upper end fails)" — named both directions backwards and left the upper end unfalsifiable: \(\Delta_{A1}=\mathrm{acc}_{\rm shape}-\mathrm{acc}_{d1}\) decreases in \(\mathrm{acc}_{d1}\) and increases in \(\mathrm{acc}_{\rm shape}\), so \(\mathrm{acc}_{d1}>0.50\) and \(\mathrm{acc}_{\rm shape}<0.90\) both break the lower end, and no number named there could ever break the upper one. Corrected and frozen:
- lower break, \(\Delta_{A1}<0.40\): reached at \(\mathrm{acc}_{d1}>0.50\) with \(\mathrm{acc}_{\rm shape}\) at \(0.90\), or at \(\mathrm{acc}_{\rm shape}<0.90\) with \(\mathrm{acc}_{d1}\) at \(0.50\);
- upper break, \(\Delta_{A1}>0.85\), scored SPLIT and signed
+(06.1's SPLIT covers any region a verse declares outside both halves; the sign is+because the reading credits the project more than the measurement supports — the contrast is a reproduction-versus-non-reproduction contrast and VOID as a capability number, so a row quoted from it would flatter): reached whenever \(\mathrm{acc}_{d1}<\mathrm{acc}_{\rm shape}-0.85\), and reachable on the bed as registered — at \(\mathrm{acc}_{\rm shape}=1.00\) (the exact solve on an exactly-solvable label) and \(\mathrm{acc}_{d1}\) at the \(m=8\) chance rate \(1/8=0.125\), \(\Delta_{A1}=0.875>0.85\) and the prediction is refuted by the outcome most favourable to the project.
Deciding number: the paired accuracy difference with Clopper–Pearson intervals, McNemar on identical draws, at matched parameters. The matched count is written the same way here as in 06.10 and 06.20, and it is two numbers, not one. \(4{,}769\) is the pre-head count and carries the class READ CEQ_V20_R15_CONTRACT.md:119 @ 99777ab ("4,769 params matched (exact counts printed)"). The post-head count, with the \([m,K+2]\) readout attached, is NOT MEASURED — needs book 04's recount: the source of \(4{,}769\) is the line that demands the recount, not the recounted number — READ docs/PLAN.md:314 @ 99777ab reads "the \(4{,}769\) of READ CEQ_V20_R15_CONTRACT.md:119 recounted, never assumed, once a \([m,K+2]\) head or a vector readout is attached". The sentence this verse carried at filing — "\(4{,}769\) recounted per arm with the \([m,K+2]\) head" — asserted the recount as performed and is struck here (P-3, a stale claim never retracted; Ruling 3; M-2). Until the post-head integers exist, every A1 row prints the pre-head count with its pin and the post-head count as NOT MEASURED, and no row prints one integer as though it were both.
Hypotheses. 06.7, 06.8, 06.9 and 06.10 hold (the argmin is not a static task, not a leak, not a flag lookup); \(\mathrm{MDE}_8(\mathrm{acc})\) is the \(n=8\) cell of the realised paired sd of accuracy across seeds, NOT MEASURED — needs S-62 (book 04); the exact zero-information floor \(0.875\) printed in the row, and the tight Fano row printed only where the plug-in \(I\) over the one-hop view reads strictly positive (06.18, L-DOM).
Evidence. READ docs/PLAN.md:371-379 (the creditable list), :582-588 (S-30); READ CHARTER.md:64-74; D-1's theorem is asymptotic under \(d\to\infty\), \(L=o(d)\), predictor erf, and the record ran \(L/d=4.00\) (READ docs/CEQ_SHAPE.md:1301-1309), so "provably optimal" is not earned by softmax here either.
Mechanism. D-1, R-SKY, Ruling 3, V-10, D-5.
Kill. The prediction dies at \(\Delta_{A1}\) outside \([0.40,0.85]\) — at \(\Delta_{A1}<0.40\) or at \(\Delta_{A1}>0.85\), both frozen here (M-2); the counter at \(\Delta_{A1}>\mathrm{MDE}_8(\mathrm{acc})\); inside the arena, \(0.5\) evening. Planted negative: on the R-24 flag-lookup plant both arms must read \(\ge0.85\) and \(\Delta_{A1}\) must read inside \(\mathrm{MDE}_8\), so the A1 instrument reports no margin where a lookup decides the label; and on the copy plant of 06.15 (the arm initialised at \(\hat P=P_{\rm env}\)) with the one-hop control at chance, \(\Delta_{A1}\) must read strictly above \(0.85\) and fire the upper kill, so the upper end is known to be reachable and is not decoration. The plant read "\(\ge0.85\)" at the previous writing and is corrected to "\(>0.85\)" here: the kill is strict, so a plant that reads exactly \(0.85\) satisfies the prediction rather than firing the kill it was planted to fire (V-15). At \(\mathrm{acc}_{\rm shape}=1.00\) and \(\mathrm{acc}_{d1}=0.125\) the plant reads \(0.875>0.85\) and fires. Every outcome now carries exactly one token: \(\Delta_{A1}\le\mathrm{MDE}_8\) COUNTER, \((\mathrm{MDE}_8,0.40)\) SPLIT signed +, \([0.40,0.85]\) HOLDS, \((0.85,\infty)\) SPLIT signed + with the reproduction clause printed.
If killed (the counter, the lower break, or the upper break). On the counter or the lower break the A1 sentence is withdrawn on BED-S with the cause named by which end failed: "depth-1 softmax reads the argmin at \([a]\) against the shape's \([b]\) at a pre-head matched count of \(4{,}769\) (READ CEQ_V20_R15_CONTRACT.md:119 @ 99777ab), the post-head counts printed as two integers or the row unscored; the difference \([\Delta]\) is within \(\mathrm{MDE}_8=[\cdot]\)." On the upper break the sentence is different and is written here so the outcome cannot be quoted as a success: "\(\Delta_{A1}=[\Delta]>0.85\) at \(\mathrm{acc}_{d1}=[a]\); the one-hop control read at or below the \(m=8\) chance rate \(0.125\), so the contrast is a reproduction-versus-non-reproduction contrast and is VOID as a capability number (CHARTER.md §1, docs/CEQ_SHAPE.md §3.8); the filed range was wrong and the row is scored against the prediction." In every case the replacement is A1 on the committor vector's \(\varphi\)-NRMSE against the exact floor \(0.0\) — VOID as a capability number by S-13 but licensed as a reproduction reading with the identification sup-norm beside it (06.15). Hypotheses: \(\|\hat P-P_{\rm env}\|_\infty\) in the identified band. Evidence: READ docs/PLAN.md:374. Kill of the replacement: 06.15's counter, inside the same pair, more decisive because it is a sup-norm on the operator rather than a rate on its output.
Terminal. No "more accurate" sentence in form A1 on BED-S; the canon licenses "the exact solve at \(\gamma=1\) reproduces the environment's committor to \([x]\) when \(\hat P\) identifies \(P_{\rm env}\) to \([y]\)".
06.20 — A2 and Bet D: the depth skyline, matched and unmatched#
Statement. Two readings in one row, and the first of them does not run on this bed.
(i) A2 as licensed (CHARTER.md §1) is UNREACHABLE at BED-S scale and files no row in 06.3's column. Ruling 3's tolerance is a per-cent number set at LM scale: it was fixed on the pair \(25{,}736{,}232\) against \(25{,}728{,}000\), an absolute residual of \(8{,}232\) parameters, \(8{,}232/25{,}728{,}000=0.032\%\), and its operative sentence is absolute — "Do NOT re-architect to close \(1.5\)k params" (READ V17K_RULINGS.md:56-59 @ 99777ab). Imported to a \(4{,}769\)-parameter arm — \(4{,}769\) being the pre-head count, READ CEQ_V20_R15_CONTRACT.md:119 @ 99777ab, with the post-head count NOT MEASURED — needs book 04's recount (READ docs/PLAN.md:314 @ 99777ab: "recounted, never assumed"; the recount is the instruction, not the result, and no verse of this book may print it as performed — P-3, Ruling 3) — the per-cent form demands a match to within \(0.032\%\times4{,}769=1.526\) parameters, which is V-17, a threshold carried out of its units: a depth-5 stack's count moves in steps of order \(d_{\rm model}\) per layer as \(d_{\rm model}\) is reduced, so no integer setting lands within \(1.53\) of \(4{,}769\) and the cell cannot fire on the bed as registered (V-11). Restated as the absolute count band Ruling 3's own text licenses: the two forms are simultaneously satisfiable only where \(1{,}500/p\le0.032\%\), i.e. at \(p\ge4{,}687{,}500\) parameters (DERIVED, \(1{,}500/0.00032\)). The LM pair at \(25{,}728{,}000\) clears it; BED-S at \(4{,}769\) misses it by three orders of magnitude. The matched-parameter A2 instance is therefore declared unreachable at \(4{,}769\) and is routed to book 04's joint-consistency bed, whose count is chosen at or above \(4{,}687{,}500\) so that a \(\le1{,}500\)-parameter gap is a \(\le0.032\%\) residual and integer \(d_{\rm model}\) steps land inside the band. The match there is stated as an absolute count with both exact integers printed in the table header and the residual reported in parameters, never in per cent: the two integers are NOT MEASURED — needs book 04's recount of the shape with the $[m,K+2]$ head attached and of the depth-5 stack at the joint bed's width (READ docs/PLAN.md:314 @ 99777ab: "recounted, never assumed"). Until those integers exist there is no A2 prediction on any bed, and this verse files none.
(ii) Bet D as filed — the reading that does run. The unmatched depth-5 stack at \(d_{\rm model}=16\): prediction, within \(\mathrm{MDE}_8\) of the shape (the honest control holds); counter, the shape short by more than \(\mathrm{MDE}_8\) — the bed needs something the hop construction does not supply; third outcome, sign logged: the shape ahead by more than \(\mathrm{MDE}_8\), which is not A2 (the stack is unmatched) and is reported as \(\Delta_{\rm sky}\) only. Deciding number: \(\mathrm{acc}_{\rm shape}-\mathrm{acc}_{\rm sky}\) at the unmatched stack (S-35), read as row C-16.
Hypotheses. Depth fixed before the arena by analogy with sanford-2024-logdepth Thm 4.2, whose \(\mathrm{hop}_k\) task is not the committor (the reduction NOT FOUND, docs/sources/sweep/sweep_expressivity.md:495-513); a deeper softmax stack computes the same resolvent by iteration (wang-2024-incontext-td, xie-2026-softmax-rl [V], abstract level), so "beats softmax" is banned either way and the row carries \(\Delta_{\rm sky}\) only; the matched-parameter instance of the depth-5 stack at \(4{,}769\) parameters is unreachable, not merely unmeasured, for the reason derived in the Statement, and the table says so in place of a number; the wide skyline has no matched instance at \(d_{\rm model}=16<s=64\) and the table says so.
Evidence. READ docs/PLAN.md:619-625 @ 99777ab (S-35, the pin 02_THEORY_TRAINING.md:467 also uses; the pin :611-617 this verse carried at filing names the S-33 tail and S-34 and is corrected here, P-6), :913 (Bet D); READ docs/CEQ_SHAPE.md:751-781 (§3.7), :2506-2513 (A.4 skyline rows); price \(\approx7.6\) s per cell [ASSUMED linear in depth], \(\approx64.8\) s at eight seeds.
Mechanism. D-1, R-SKY, P-10, V-25 (the skyline table is the only place a "cannot" sentence may stand, with its vacuity line: chen-2024-multilayer reads \(64^{1/16}=1.2968\) against \(Hdp=512\), vacuous), M-2 (a depth chosen after the arena strikes the row).
Kill. For (i) there is no kill on this bed, because there is no reachable cell: the unreachability itself is the decidable statement and is decided by one recount at \(0\) GPU-s — a recounted pair whose absolute gap is at or below \(1{,}500\) parameters and at or below \(0.032\%\) of the smaller count refutes the unreachability claim and restores an A2 row here; on a \(4{,}769\)-parameter arm that requires a gap of at most \(1\) parameter, which is why the claim is filed as unreachable. For (ii): the prediction dies at the unmatched stack short by \(>\mathrm{MDE}_8\) or the shape ahead by \(>\mathrm{MDE}_8\) (either direction refutes "the honest control holds"); the counter at short by more; \(\approx64.8\) s per stack, \(1\) evening. Planted negative: the depth-1 control read as a "skyline" of depth 1 must reproduce S-30's own number bitwise (the same cell), so the skyline instrument is known to read the arms it is given; and a stack whose \(d_{\rm model}\) is stepped by one from \(16\) must print a parameter count differing from \(4{,}769\) by more than \(1.53\), so the unreachability is demonstrated by the instrument rather than asserted.
If killed (either half of (ii), or the recount refuting (i)'s unreachability). The A2 sentence is withdrawn on BED-S in the form the bed can support: "a depth-5 softmax stack at \(d_{\rm model}=16\) — unmatched, \([p_{\rm sky}]\) parameters against the shape's \([p_{\rm shape}]\), gap \([\,p_{\rm sky}-p_{\rm shape}]\) parameters — reads the argmin at \([\cdot]\) against the shape's \([\cdot]\); A2 is not read on this bed because no matched instance exists at \(4{,}769\) parameters; the shape's separate claims are exactness (\(\delta=0\) on the exact route), one-read cost (one solve, depth \(s\), \(+50\%\) causal MACs, 06.28) and the boundary-row mechanism (06.22)." The replacement A2 target is book 04's joint-consistency bed at a count at or above \(4{,}687{,}500\), where the label is the full vector on \(T\) and the skyline's per-row hops must also satisfy the harmonic residual — Hypotheses: 06.21's prediction holds there, and the bed's count clears the band derived above; Evidence: READ MATHEMATICS.md:106-127; READ V17K_RULINGS.md:56-59 @ 99777ab; Kill: 06.21's counter (\(r_{\rm softmax}/r_{\rm shape}\le2\)), inside one pair, more decisive because it reads the mechanism the stack lacks rather than the rate it reaches, and reachable because the residual there is stated in parameters against a count where \(1{,}500\) parameters is a \(0.032\%\) match.
Terminal. No "more accurate" sentence in form A2 on any bed of this canon; A2 at matched parameters is unreachable at BED-S scale and unbuilt at joint-bed scale; the depth skyline's number is printed in every capability row as \(\Delta_{\rm sky}\) at unmatched parameters, and the canon licenses "the same resolvent, computed in one solve rather than five learned layers" as an arithmetic statement and not as a margin.
06.21 — Joint consistency (Bet E)#
Statement. Prediction: \(r_{\rm softmax}/r_{\rm shape}\ge10\) at marginal NRMSE within \(\mathrm{MDE}_8\), where \(r(\hat z)=\|(I-\gamma P_{\rm env})\hat z-V\|_\infty/\|V\|_\infty\) is printed beside \(\sigma_{\min}(I-\gamma P_{\rm env})\) and \(\|I-\gamma P_{\rm env}\|_\infty\le1+\gamma\). Counter: \(\le2\) — joint consistency is learnable by a per-row mixture and the untested sentence at MATHEMATICS.md:106-127 is withdrawn. SPLIT: \((2,10)\). Deciding number: the paired ratio with both unit factors printed (M-4.2). A ratio at or above \(10\) at unequal marginal error is a statement about which mode the control mislearns and is reported as such, never as joint consistency.
Hypotheses. The residual is a score, never a loss (D-2); the environment's \(Q_{\rm env},R_{\rm env}\) are the bed's; the label is the full vector on \(T\).
Evidence. READ docs/PLAN.md:915 (Bet E), :700-704; READ docs/CEQ_SHAPE.md:2520-2525 (A.5).
Mechanism. V-26, V-17, D-2.
Kill. The prediction dies at ratio \(<10\); the counter at \(>2\); inside the pair, \(0.5\) evening. Planted negative: the must-fire perturbation of B-H1 drives harmonic_residual from \(1.04\times10^{-17}\) to \(10^{-6}\) (ratio \(9.6\times10^{10}\)), so the residual instrument reads a broken joint solution as broken.
If killed (the counter). "Joint determination in one read" is withdrawn; the residual stays as a diagnostic; "one read" is repriced as a cost statement (one solve, depth \(s\)). Hypotheses: the cost statement's own kill is 06.28's. Evidence: READ docs/PLAN.md:1074 ("Bet E at or below 2"). Kill of the replacement: 06.28's band check, \(\approx1.7\) s, cheaper than the pair.
Terminal. The residual is a column; no joint-consistency capability sentence; the per-row mixture is credited with what it does.
06.22 — The boundary mechanism against a column sink (Bet F, K-E1)#
Statement. Prediction: the shape's committor \(\varphi\)-NRMSE below ChaCAL-with-sink-token's by more than \(\mathrm{MDE}_8\) on at least 6 of 8 seeds and its harmonic residual smaller by more than \(2\times\). Counter: within \(\mathrm{MDE}_8\) on at least 6 of 8 and residual within \(2\times\) — component (e) is a parameterisation of a column sink; escalate once to \(N=16\) (S-64, seeds 8 to 15, same lane, same hash, \(\mathrm{MDE}_{16}\)), never "within TOST" at \(N=8\) (M-13). Holding at \(N=16\): the boundary-row mechanism dies as a capability and the paper is tree B. Deciding numbers: the paired \(\varphi\)-NRMSE gap and the residual ratio, at \(N=8\) then \(N=16\).
Hypotheses. 06.16's prediction holds (at \(\hat\gamma=0\) the sink arm is softmax and the row is VOID); ChaCAL-diag is the shape at \(\mathcal A=\emptyset\) with diag_convention = kept declared (V-3); ChaCAL-published's diagonal convention rests on one HTML fetch and is re-read against the PDF before typesetting (B22); the sequential pair order (shape first, its \(\hat\gamma\) handed to the ChaCAL arms) is in the manifest.
Evidence. READ docs/PLAN.md:594-600 @ 99777ab (S-31, the two ChaCAL arms and the sink-token arm; the pin :589-595 at filing named S-30 and is corrected here), :682-687 @ 99777ab (S-64, the E1 escalation to \(N=16\); the pin :688-693 at filing named S-65 and is corrected here — both P-6), :916 (Bet F); READ docs/CEQ_SHAPE.md:2849-2860 (§7.2, component (e)); the prior evidence against the shape: sinks already act as key biases storing non-informative mass (READ docs/sources/design/design_falsify.md:393).
Mechanism. V-24, M-13 (MISTAKES.md:1210), M-7, D-7, K-E1.
Kill. The Statement is a conjunction, so the Kill is one: the prediction dies if either half fails — at the \(\varphi\)-NRMSE gap within \(\mathrm{MDE}_8\) on \(\ge6/8\), or at the residual ratio at or below \(2\times\), either one alone. The counter is the opposite conjunction and dies if either of its halves fails: at the gap separated by more than \(\mathrm{MDE}_8\) on \(\ge6/8\), or at the residual ratio above \(2\times\). The two mixed outcomes are neither, and each is a named branch with its own licensed sentence, so no outcome falls through:
| branch | reading | verdict | the sentence it licenses |
|---|---|---|---|
| HOLDS | gap \(>\mathrm{MDE}_8\) on \(\ge6/8\) and ratio \(>2\) | prediction | the boundary rows separate the read and condition the joint solve; escalate nothing |
| COUNTER | within on \(\ge6/8\) and ratio \(\le2\), holding at \(N=16\) | counter | tree B's sentence below |
| SPLIT-sep (separated, not residual) | gap \(>\mathrm{MDE}_8\) on \(\ge6/8\), ratio \(\le2\) | SPLIT, signed + |
"the boundary rows separate the committor read from a column sink by \([\cdot]\) at \(\mathrm{MDE}_8=[\cdot]\); the harmonic residual is within \(2\times\), so component (e)'s residual claim dies and only the read claim escalates to \(N=16\)" |
| SPLIT-res (residual, not separated) | ratio \(>2\), gap within \(\mathrm{MDE}_8\) on \(\ge6/8\) | SPLIT, signed + |
"the shape's joint solve is better conditioned by \([\cdot]\times\) while its committor read is within \(\mathrm{MDE}_8=[\cdot]\) of a column sink's; the capability sentence is withdrawn and the residual is filed as 06.21's diagnostic column, not as a boundary-row capability" |
| SPLIT-seeds (no seed majority either way) | the modal side of the eight per-seed gap readings reaches only \(\le5/8\) | SPLIT, signed + |
"the eight per-seed \(\varphi\)-NRMSE gaps split \([\,\text{separated},\text{within}\,]\) with the residual ratio at \([\cdot]\times\); no seed majority exists in either direction, so neither the separation nor its absence is read, and the row escalates nothing" |
The seed-count rule is a partition, not four predicates, and the fifth branch is what makes it one. Every one of the first four rows requires a \(\ge6/8\) seed majority on the gap, so an outcome such as (4 seeds separated, 4 seeds within, ratio \(>2\)) reaches \(6/8\) in neither direction and satisfied none of the four — the same M-7 hole 06.15 closed with a modal-band rule and a printed count, and which was not swept here. 06.15's rule is applied to this verse: the eight per-seed gap readings are binned into separated (gap \(>\mathrm{MDE}_8\)) and within, the modal side and its count are printed, a separated or a within verdict requires the modal count to reach \(\ge6/8\), and every configuration whose modal count is \(\le5/8\) is SPLIT-seeds, with the ordered pair (separated, within) and the residual ratio printed so the reading is recoverable. Exactly one of five branches is reachable per outcome and every outcome reaches one: \((6,2)\) with ratio \(>2\) is HOLDS, \((2,6)\) with ratio \(\le2\) is COUNTER, \((6,2)\) with ratio \(\le2\) is SPLIT-sep, \((2,6)\) with ratio \(>2\) is SPLIT-res, and \((4,4)\) at any ratio is SPLIT-seeds. All three SPLIT branches are scored wrong with the sign of the optimistic half (06.1) and none is "escalation": escalation is what the COUNTER branch triggers, and it is named as such. Price, re-derived from 06.28's re-tag because the arena arms are priced at the shape's cell: \(\approx53.3\) s for the three ChaCAL arms at \(N=8\) (DERIVED, \(3\times8\times1.71990+3\times4.0\) fixed, three invocations — the source's \(\approx52\) s is \(3\times8\times1.680+12.0\) at the struck cell, READ docs/PLAN.md:594-600 @ 99777ab), escalation \(\approx45.3\) s (DERIVED, \(3\times8\times1.71990+4.0\); the source's \(\approx44\) s is \(3\times8\times1.681+4\)), \(2\) evenings. Planted negative: with \(\mathcal A\neq\emptyset\) the downstream \(\|\Pi_{\rm shape}-\Pi_{\rm ChaCAL\text{-}diag}\|_\infty\) must exceed \(0.1\) on \(100\%\) of admitted draws (B-E1's rejection half), so a sink arm that matched the shape by being the shape would be caught at construction.
If killed (the counter holding at \(N=16\)). Tree B's sentence in full: "Consequence-Equilibrium Attention is a re-parameterisation of ChaCAL's causal resolvent read with absorbing boundary rows on the record's three-corner base; \([n]\) of its identities are machine-checked; the committor head is the exact solve at \(\gamma=1\), matching the bed's own Dirichlet solve to \(0.0\); BED-S is registered with an exact oracle at \(0.0\), the exact zero-information floor \(0.875\) at \(m=8\), and a printed paired sd \([\mathrm{sd}]\); a column sink reproduces the boundary-row read within \(\mathrm{MDE}_{16}=[\cdot]\); no capability sentence is licensed." The replacement claim is the delta narrowed to what a column device cannot carry: the certificate (\(\delta=0\) on the exact route), the Lean containment, and the interventional re-solve (06.23) — Hypotheses: 06.23's prediction; Evidence: READ docs/CEQ_SHAPE.md:2860-2866 (component (g)); Kill: 06.23's counter, \(\approx35\) s, cheaper than the escalation.
Terminal. A property paper about a published operator with a certificate discipline, a registered bed and its negatives; book 01's boundary-row theorems stand as theorems about weights downstream of a row and license no capability.
06.23 — The cached mixture (Bet H, K-G1)#
Statement. Prediction: the cached arm \(O_{\rm cached}=\hat P_{\rm base}(I-\gamma\hat P_{\rm base})^{-1}V_{\rm int}\) fails on \(P\)-changing plants by more than one seed sd on at least 6 of 8 and matches the shape within one seed sd on \(V\)-only plants. Counter: within one seed sd on \(P\)-changing plants on at least 6 of 8 — the re-solve is a per-row control wearing a name, component (g)'s re-solve sentence dies, and the consequence channel is repriced as a cost statement. SPLIT: \(3/8\) to \(5/8\). Deciding number: the two per-seed cosine gaps in seed-sd units (S-33).
Hypotheses. Both plant classes non-empty with at least 64 draws each (S-17); moves are query-side row clamps on the environment chain (\(u^\top\mathbf 1=0\), non-negative edited row on \(100\%\)); the operational form of a cached successor representation (momennejad-2017-sr, russek-2017-predictive, mechanism [U]).
Evidence. READ docs/PLAN.md:607-612 @ 99777ab (S-33, the cached-mixture arm on the two plant classes; the pin :599-604 at filing named the S-31 tail and S-32 and is corrected here, P-6), :401-407 (S-17), :917 (Bet H); the precedent — a "signed" pivot arm that was the unsigned arm renamed (READ workdonenew.md:379 @ 99777ab).
Mechanism. D-2, P-7 (MISTAKES.md:375), V-9.
Kill. The prediction dies at within one seed sd on \(P\)-changing plants on \(\ge6/8\), or worse than one seed sd on \(V\)-only plants; the counter at the two-way separation; \(\approx35\) s, \(1\) evening. Planted negative: a corpus with no \(P\)-changing move must make S-33 unscorable (S-17's kill), so the instrument cannot report a separation that has no rejection region.
If killed (the counter). The displacement identity stays as algebra and the channel as a cost statement (one extra solve, or one column at \(m/d\) — 06.33). Hypotheses: none beyond Proposition 7. Evidence: READ docs/CEQ_SHAPE.md:456-476. Kill of the replacement: 06.33's counter (\(\ge8\times\)) turns the cost statement into "\(m\) solves", seconds.
Terminal. No interventional-channel sentence; the canon licenses the identity \(\Delta z=(I-\gamma P')^{-1}(\Delta V+\gamma\Delta Pz)\) and its price.
06.24 — The parity half by equivalence (S-65)#
Statement. This verse is filed as three rows at one cell each, because a prediction and a counter read at different \(N\) can both hold or both fail and are not of equal specificity (L-SIGN).
Row C-33 — the tier, decided first and on its own number. Deciding number \(r=\mathrm{sd}_d/\sigma\), both read from S-62's realised sds. Prediction: \(r\le0.7071\) and the paired tier \(N=36\) is selected. Counter: \(r>0.7071\) and the two-sample tier \(N=70\) is selected — pairing bought nothing. No SPLIT: \(r\) is a number, not a band. The threshold \(1/\sqrt2=0.7071\) is frozen here (M-2) and is conservative by construction: the paired design reaches power \(0.8014\) at \(N=36\) against a \(0.5\sigma\) margin when \(\mathrm{sd}_d=\sigma\) (Monte Carlo \(200{,}000\) draws), only \(0.0014\) above target, so the tier boundary is set where the paired design still holds power under a \(\sqrt2\) error in the realised sd.
Row C-20 — the equivalence reading, both halves at the tier C-33 selects. Prediction: the shape at \(\hat\gamma\) against ChaCAL-diag at the same \(\hat\gamma\) with \(\mathcal A=\emptyset\) lies inside the \(\pm0.5\sigma\) margin on the 90 per cent interval at that tier. Counter: outside the margin at that same tier — the "same operator" sentence is withdrawn at trained \(\hat\gamma\) and narrowed to the \(\gamma=0\) bind. No SPLIT: inside and outside exhaust the cell.
Row C-34 — the \(N=70\) two-sample reading, filed as its own row and never as C-20's counter. Deciding number: the \(N=70\) two-sample 90 per cent interval against \(\pm0.5\sigma\); prediction inside, counter outside. Where C-33 selects \(N=36\), C-34 is a second reading of the same contrast at a different design and is scored separately; where C-33 selects \(N=70\), C-20 and C-34 read the same cell and C-34 is filed VOID as a duplicate, with the duplication recorded rather than scored twice.
Any "parity" sentence resting on \(N=8\) is struck regardless, and the arithmetic that strikes it is this verse's own design, which is paired. The paired half-width at \(N=8\) is \(t_{.95,7}/\sqrt8=1.894579/2.828427=0.669835\,\mathrm{sd}_d\) (DERIVED; \(0.6698\) at four places, filed by MARS as \(0.6699\) — the same quotient rounded up), which is above the \(0.5\) margin, so two bit-identical arms return NO VERDICT at \(N=8\) on the paired arithmetic and the conclusion stands where it always stood. The \(0.8807\sigma\) this verse printed at filing is the two-sample half-width, \(t_{.95,2N-2}\,\sigma\sqrt{2/N}=1.7613\times0.5=0.88065\) at \(N=8\) (READ MISTAKES.md:1216-1219 @ 99777ab, whose sentence names it as the two-sample contrast's), imported into a paired verse: V-17, a threshold carried out of its units, with M-13 and M-9 behind it. Both numbers are printed here, each named for the design it belongs to, and the \(N=8\) strike rests on the paired one. The tier arithmetic is unchanged by the correction — the paired form first drops below \(0.5\) at \(N=13\) and reaches power \(0.80\) at \(N=36\), the two-sample form at \(N=23\) and \(N=70\) — because those four integers were always read from their own designs.
Hypotheses. 06.16 MOVED (otherwise the half is softmax against softmax and every row here is VOID); the margin \(\pm0.5\sigma\) and the tier threshold \(0.7071\) both fixed here, before any cell (M-2); C-33 is read and its verdict recorded before C-20's interval is computed, so the tier is never chosen from the interval it decides; fixed-\(N\) Schuirmann (schuirmann-1987-tost [V]); the sequential anytime-valid form NOT FOUND at [V]; the two tier prices are both registered so the selection changes no budget decision.
Evidence. READ docs/PLAN.md:688-699 @ 99777ab (S-65, the TOST parity half; the pin :706-712 at filing named census lines 12/13 and M-4.5 and is corrected here), :956 @ 99777ab (R-22, the parity-by-underpowering row that prints the \(0.8807\sigma\) half-width; the pin :958 at filing named R-25/K-G1 and is corrected here — both P-6); READ MISTAKES.md:1210-1230 (M-13, the reachability arithmetic: \(0.8807\) at \(N=8\), \(0.6001\) at \(16\), below \(0.5\) first at \(23\); power \(0.80\) first at \(N=70\)).
Mechanism. M-13, M-9, M-2, V-5.
Kill. C-33: the prediction dies at \(r>0.7071\), the counter at \(r\le0.7071\); \(0\) GPU-s beyond S-62 (a journal read). C-20: the prediction dies at the interval outside the margin at the tier C-33 selected, the counter at inside at that same tier — one cell, two exhaustive outcomes, so the two halves cannot both hold and cannot both fail; \(119\) s at the paired tier or \(228\) s at the two-sample tier, \(1\) evening. C-34: the prediction dies at outside at \(N=70\), the counter at inside at \(N=70\); \(228\) s. Planted negative: the identity half of B-E1 — torch.equal at \(\mathcal A=\emptyset\) — is the construction plant; an equivalence test on two bitwise-identical arms must read inside at \(N=36\) and NO VERDICT at \(N=8\), both printed; and a tier row fed \(\mathrm{sd}_d=\sigma\) must select \(N=70\) (since \(1>0.7071\)), so the tier rule is known to refuse the paired tier at the sd where its power is only \(0.8014\).
If killed (the counter). The identity is claimed at \(\gamma=0\) only (gamma_zero_is_softmax [M]; RUN[coord] torch.equal True) and "the same operator at trained \(\hat\gamma\)" is withdrawn. Hypotheses: none. Evidence: 06.13. Kill of the replacement: 06.13's torch.equal False, \(\approx1.7\) s — cheaper and bitwise.
Terminal. Parity is the Lean row and the bitwise cell at \(\gamma=0\); no equivalence sentence at any \(\hat\gamma>0\).
06.25 — The dials vary (M-3.7, D-3)#
Statement. Prediction: across the seven design points — centre \((8,2,8)\), \(t^\star\in\{2,32\}\), \(K\in\{3,4\}\), \(m\in\{4,16\}\) — the argmin error moves with \(t^\star\) by more than \(\mathrm{MDE}_8\) between \(t^\star=2\) and \(8\), and every point is admitted by its own census. Counter: error flat within \(\mathrm{MDE}_8\) across \(t^\star\) — the dial is decoration and only the centre is reported; \(t^\star=32\) unreachable inside the causal window is recorded, never forced. No SPLIT. Deciding number: the S-62 statistics per point with the exact floor per \(m\) (\(0.75\), \(0.875\), \(0.9375\)).
Hypotheses. 06.7 admits at the centre; each point re-censused; \(t^\star\) placed by depth, never by a kill rate.
Evidence. READ docs/PLAN.md:648-655; RUN of the floors at docs/CEQ_SHAPE.md:2491.
Mechanism. D-3, P-8, V-25, V-10.
Kill. The prediction dies at flat error within \(\mathrm{MDE}_8\) across \(t^\star\in\{2,8\}\); the counter at a move larger; \(\approx3.5\) to \(4.0\) min DERIVED (\(7\times\) one pair), \(2\) evenings. Planted negative: the depth-1 control across the same points must move with \(t^\star\) in the opposite direction (worse at larger \(t^\star\)), so a flat reading on the shape is distinguishable from a flat instrument.
If killed (the counter). Only the centre is reported; the difficulty dial is removed from every capability sentence and the bed is described at one point. Hypotheses: the centre admitted. Evidence: 06.7. Kill of the replacement: 06.7's counter at the centre, \(0\) GPU-s.
Terminal. One design point, one bed, no scaling sentence in \(t^\star\).
06.26 — The certificate (Bet J, dormant)#
Statement. Prediction, when a mask exists: zero exceedances of \(\varepsilon\|V\|_\infty/(1-\gamma)+\delta_\Pi\|V\|_\infty\) on \(1{,}024\) draws and \(\delta\|V\|_\infty\) below the label sd. Counter: one exceedance, or \(\delta\|V\|_\infty\) at or above the label sd — the mask is refused and the exact solve ships. No SPLIT. Deciding numbers: the exceedance count and the ratio (N-15, K-I).
Hypotheses. \(P\) row-stochastic on the cell (S-42's row-sum guard; at \(\hat\beta\ne1\) rows sum \(1.31\) to \(10.29\) and the field is written refused); the mask amplification \(1/(1-\gamma)\) carried (Proposition 4(ii), RUN[J] \(0.5263157894736843\) against the naive \(0.1\) at \(s=3\), \(\gamma=0.9\), \(\varepsilon=0.1\)).
Evidence. READ docs/PLAN.md:919 (Bet J), :959 @ 99777ab (R-10 / K-I, the certificate row; the pin :964 at filing is a blank line and is corrected here, P-6); READ docs/CEQ_SHAPE.md:2628-2639 (A.9); no mask exists (B15), so the row is dormant.
Mechanism. L-CERT, V-10, V-17.
Kill. The prediction dies at any exceedance or ratio \(\ge1\); the counter at \(0\) and \(<1\); \(\approx2.6\) s (\(1{,}024\) forward passes at \(n=2048\)), \(0.5\) evening. Planted negative, on the quantity the Kill reads: the Kill decides the mask certificate \(\varepsilon\|V\|_\infty/(1-\gamma)+\delta_\Pi\|V\|_\infty\), so the plant that must fire it is a mask plant and not a truncation plant (V-15: no condemning rule without a planted negative that fires it; L-CERT; V-10). The must-fire plant: a mask whose realised perturbation is \(\varepsilon^\star\) but whose journalled \(\varepsilon\) is set to \(\varepsilon^\star/10\) with \(\delta_\Pi\) left at its true value — the certificate is then understated by construction and the exceedance count must read strictly greater than \(0\) on the \(1{,}024\) draws, with the largest realised \(\|z-\hat z\|_\infty\) printed beside the bound it exceeded. The must-not-fire plant: the zero-perturbation mask, \(\Pi=I\) so \(\varepsilon=0\) and \(\delta_\Pi=0\) — the exact route, whose certificate is \(0\) and whose realised deviation is \(0\) — must read an exceedance count of exactly \(0\) on all \(1{,}024\) draws; a count above \(0\) there is an instrument fault and the cell is refused, not scored. The two together give the counter a rejection region and the prediction a floor, on the same number the Kill reads. The truncation plants are kept and relabelled: rows scaled to \(1.5\) at \(\gamma=0.6\), \(K=2\) reading \(7.29\) against \(0.54=\gamma^{K+1}/(1-\gamma)=0.216/0.4\), and the \(\gamma=0.7\) plant reading \(119.37\) against \(1.143=0.343/0.3\), are plants on N-15's other bound — the Neumann truncation bound of the \(K\)-hop read, not this verse's mask certificate — and are printed as such, the first convergent and reported, the second a divergent series labelled and never counted. Neither is this verse's negative and neither is counted as one.
If killed (the counter). The exact solve ships — cheaper than one Neumann hop at \(s=64\) (\(2.514\) ms against \(3.001\) ms, RUN[NEPTUNE] at docs/CEQ_SHAPE.md:431) — and every long-context price of book 03 is a dense-per-chunk price. Hypotheses: the solve's per-op floor holds under the dispatch gap. Evidence: 06.28. Kill of the replacement: 06.28's counter, \(\approx1.7\) s.
Terminal. No mask, no certificate sentence; the exact route with \(\delta=0\) is the only certified route.
06.27 — The ladder on a survivor (M-5.3)#
Statement. Prediction: the \(N=8\) verdict of every scored bet survives the \(9{,}600\)-step ladder within its own \(\mathrm{MDE}_8\). Counter: a verdict reverses at the ladder — the ladder's verdict is filed and the 150-step cell is marked a pilot (M-3); what dies is the 150-step sentence, not the bed. No SPLIT. Deciding number: the same statistics at step \(9{,}600\); the crossing and residual curves.
Hypotheses. The shape alive on at least one creditable contrast after S-63 to S-65; \(64\times\) the 150-step law.
Evidence. READ docs/PLAN.md:775-780; price \(32\) to \(36\) min per pair [FITTED] at \(64\times\) (READ docs/PLAN.md:981).
Mechanism. M-3, M-6, P-8.
Kill. The prediction dies at any reversal; the counter at none; \(32\)–\(36\) min per pair, \(1\) evening. Planted negative: the depth-1 control's own 150-step reading must reproduce at the ladder's step 150 within the identical-seed floor (bitwise in one lane), so a reversal is a change in the arm, not in the harness.
If killed (the counter). Every 150-step number in books 01 to 05 is re-tagged "pilot" and the ladder's number is the reported one; T1/T2 of 06.29 to 06.31 are re-read at the ladder's \(\tau\). Hypotheses: the ladder is the record's largest budget ever spent on one pair. Evidence: READ docs/PLAN.md:981. Kill of the replacement: none cheaper exists; the ladder is the Terminal instrument.
Terminal. The paper quotes ladder numbers only, and the 150-step cells as pilots with their sd.
IV. Faster to train (B25)#
06.28 — The per-step cost statement, DERIVED until RUN#
Statement. The shape has no measured whole-step law. Every step number below for the shape is DERIVED, with its steps printed, and is re-tagged here from the [FITTED + RUN] tag it carried at filing — that tag priced a two-arm sum at one arm's rate, which is M-8, the very mechanism this verse is designed against.
Per step at \(n=2048\), \(s=64\), \(d_{\rm model}=16\), forward plus backward plus Adam.step:
| quantity | value | class | steps |
|---|---|---|---|
| depth-1 softmax, whole step | \(0.010165\) s | [FITTED] \(R^2=0.999998\) over five points |
exp(-12.1852)·n^0.9963 at \(n=2048\), READ COSTS.md:73-74 @ 99777ab |
| depth-1 softmax, whole step, measured point | \(0.010142\) s | [MEASURED] |
results/k_cert_local.json throughput.points |
| solve increment at RHS width \(16\) | \(1.041\) ms | RUN[NEPTUNE] |
\(2.514-1.473\) ms, READ 08_ARCHITECTURE.md:138 (the Evidence line that carries the subtraction; the increments at \(n=2048/4096/8192\) read \(1.041/2.312/4.542\) ms at READ 03_KERNEL.md:178) |
| solve increment at the shipped RHS width \(20\) | \(1.30125\) ms | DERIVED | \(1.041\times20/16\); forward substitution is \(s^2/2\) MACs per right-hand column, so the increment is linear in the column count, and book 08 ships \(\tilde V\in\mathbb R^{s\times(d+K+2)}\), \(d+K+2=20\) at \(d=16\), \(K=2\) (READ 08_ARCHITECTURE.md:115 for \(\tilde V\)'s width, :510 for out.z float32[B, h, s, d+K+2]) |
| the shape on the softmax corner, whole step | \(0.011466\) s | DERIVED | \(0.010165+0.00130125\) |
| ratio shape over depth-1 base | \(1.1280\) | DERIVED | \(0.011466/0.010165\) |
| the shape's \(150\)-step cell | \(1.71990\) s | DERIVED | \(150\times0.011466\); not the \(1.680\) s the sources print — see the re-tag below |
| the record's only measured CEQ-family whole step | \(0.093052\) s | [MEASURED] |
arm_smprime, complex64, \(n=2048\); RUN this session on results/k_cert_local.json, throughput.laws.arm_smprime.y[0] \(=0.09305229999881703\), whose law is READ COSTS.md:73-74 @ 99777ab (exp(-10.0187)·n^1.0026); the ratio against the softmax measured point is \(0.093052/0.010142=9.1745\times\) (DERIVED, one division) and is printed here in place of the bare "\(9.2\times\)", which had no producer in this book |
The \(0.093052\) s row is printed in this same row-set and is not the shipped base: the record's arm is complex64 while the shipped base is the softmax corner at \(4\) B/element, which book 08 states as a property of the shipped shape rather than of the record's arm (READ 08_ARCHITECTURE.md:592, the float32-operator Hypothesis and the ceq/arm_smprime.py::operator reading; :850, the \(g\equiv0\) real branch). It is carried here because it is the only whole-step number in the record produced by an arm of this family, and because the DERIVED \(0.011466\) s has no measured whole-step number of its own to stand beside — it is a two-term sum, not a reading. The pins this paragraph and the table carried at the previous writing — 08_ARCHITECTURE.md:518 four times, :513 for the MAC table, :462 for the \(R^2\), :477 for the shipped channel count — are all drifted or empty at the working tree's book 08 and are corrected above and below; :518 is book 08's out.gamma/out.beta comment line, :513 its out.dz_degenerate comment, :462 a horizontal rule and :477 a row of the task-supply table, and none of them carries the number it was cited for (P-6). The \(0.093052\) s figure is not in book 08 at all: its producer is results/k_cert_local.json, read this session.
The \(1.680\) s shape cell is re-tagged, and the re-tag moves every price in this book. The sources price the shape's \(150\)-step cell at "\(1.680\) s per cell [FITTED + RUN]" (READ docs/PLAN.md:594-600 @ 99777ab, S-31; the same tag for the same quantity at READ 09_CHESS_AND_MARKETS.md:148). That tag is the one this verse strikes, and the number carries it: \(1.680/150=0.011200\) s per step, which is the superseded step \(0.011206\) s to five places, so pricing anything at \(1.680\) s prices it at the struck step under the struck tag (M-8, P-8, P-3, M-2). COSTS.md:73-74 @ 99777ab carries the two \(n\)-laws and no cell price, so the [FITTED + RUN] pin behind \(1.680\) s has no producer either. The shape's \(150\)-step cell is therefore DERIVED at \(150\times0.011466=1.71990\) s, and every GPU-second price in this book that multiplies a shape cell is re-derived from \(1.71990\) s in the verse that carries it and in the cheapest-first table. The softmax cell is unaffected: \(150\times0.010165=1.52475\) s, DERIVED from a law that does have a producer (READ COSTS.md:73-74 @ 99777ab), and agreeing with the sources' \(1.524\) s [FITTED] to three places. Book 09's verse at 09_CHESS_AND_MARKETS.md:148 still carries [FITTED + RUN] for \(1.680\) s per shape cell; that book is born and may not be edited here, so the disagreement is owed to CORRECTIONS.md as a row against 09_CHESS_AND_MARKETS.md:148 and against docs/PLAN.md:594-600, naming this verse's re-tag as the one in force.
The depth-\(L\) skyline at \(L\cdot0.010165\) s ([ASSUMED linear in depth]): \(0.030495\), \(0.050825\), \(0.071155\) s at depth \(3/5/7\), so the shape's step is \(0.2256\times\) the depth-5 stack's (DERIVED under the assumption, \(0.011466/0.050825\)). InfSA-16's step is \(0.034133\) s, which is NOT MEASURED — needs S-32's cell, and the \(2.977\times\) it gives against the shape's DERIVED step inherits that tag. The only derivation the source supports is one division: the source prices the InfSA-16 cell at \(\approx5.12\) s per \(150\)-step cell "DERIVED from the \(25.409\) ms hop microbenchmark" (READ docs/CEQ_SHAPE.md:1926 @ 99777ab; the same \(\approx5.1\) s at :2510), and \(5.12/150=0.034133\) s per step (DERIVED, one division). The step below that — how \(5.12\) s follows from a \(25.409\) ms hop — is not printed at the source and does not reproduce from this book's constants: \(0.034133-0.025409=0.008724\) s is neither the softmax law's \(0.010165\) s nor the solve increment's \(0.001301\) s, and \(0.010165+0.025409=0.035574\) s is not \(0.034133\) s. So the number is carried as an unreproduced source figure with its class printed, not as a derivation (P-1, M-8).
Prediction, in the four branches that exhaust \([0,\infty)\) exactly as 06.13's do, and now centred on the re-tagged cell: the S-20 cell lands inside \([-1.8,+14.4]\) per cent of the DERIVED \(1.71990\) s (multiplier in \([0.982,1.144]\), i.e. \([1.68894,1.96757]\) s), so the ratios above are the ratios. Counter, two named branches: COUNTER-dear, the cell at or above \(2.2\times\) the DERIVED cell (\(\ge3.78378\) s); COUNTER-cheap, the cell below \(0.982\times\) (\(<1.68894\) s) — the hole this verse carried at filing, closed here for the reason 06.13 states in full, since 06.36's Kill declares the tree refuted when a scored outcome has no branch (M-7, D-7, M-20). Either branch re-derives every ratio from N-02's producer before a T1 number is quoted. The signs are corrected here and run the other way from the previous writing. 06.1 defines the sign of a miss against the project — + credits the project more than the measurement supports (READ V16_CALIBRATION.md:24-31) — and what is scored is the claim, not the outcome. A cell dearer than the claim means the claim was too cheap, so the claim credited the project more than the measurement supports: COUNTER-dear is +. A cell cheaper than the claim means the claim was too dear, so the claim credited the project less: COUNTER-cheap is −. The reason printed before — "a cell cheaper than the law flatters every price in this book" — scored the outcome instead of the claim and is deleted; it inverted both signs and, since C-9 and C-24 are two of the rows in 06.4's tree-C pool, it inflated by up to two the + count the eighth-row test reads. SPLIT: \((1.144,2.2)\), i.e. \((1.96757,3.78378)\) s. Deciding number: the cell wall-clock over the DERIVED \(1.71990\) s, synchronize() bracketed.
Hypotheses. Each arm at its own law (M-8); the increment measured at the shipped \(s=64\), never scaled from a smaller \(s\) (M-3); the RHS width is a Hypothesis, not a measurement: the \(1.041\) ms increment was read at a \(d=16\) right-hand side and the shipped solve carries \(d+K+2=20\) channels, so the \(1.30125\) ms figure assumes the forward substitution is linear in the column count, and the kill below is frozen on that linearity claim and on nothing else. The bracket \([1.041,1.561]\) ms this Hypothesis carried at the previous writing is struck: its lower endpoint is the width-\(16\) increment itself, so an increment with no width dependence at all — the exact negation of the linearity being tested — sat inside the band and restored the struck \(0.011206\) s step (\(0.010165+0.001041\)) and the struck \(1.1024\) ratio without striking anything (V-10, a gate satisfied by construction; V-11; M-2). The point prediction of linearity is \(1.041\times20/16=1.30125\) ms, and the admissible spread around it is the same \(\pm12\%\) clock non-stationarity these Hypotheses already declare, so the band is \([1.14510,1.45740]\) ms (DERIVED, \(1.30125\times0.88\) and \(1.30125\times1.12\)). At \(1.041\) ms the kill now fires, as it must, and the two-sidedness is real; a per-op floor under a \(2.0\times\)–\(6.6\times\) dispatch gap (P-8); the clock non-stationary at \(\pm12\%\); no price crosses the device boundary (V-22); the depth-linear assumption is the ASSUMED tag and is retired only by S-35's cell. The shape's own throughput law is NOT MEASURED — needs N-02's producer on the shipped arm (book 03); until it exists no number in this verse is a whole-step measurement of the shape.
Evidence. READ docs/PLAN.md:967-983 (the basis and the price table); READ COSTS.md:73-74 @ 99777ab (both laws: softmax exp(-12.1852)·n^0.9963 \(R^2=0.999998\) over five points, arm_smprime exp(-10.0187)·n^1.0026 over three points because at \(n=16384\) and \(32768\) the allocator reserves \(10.578\) and \(13.969\) GiB on an \(8\) GiB card and the loop times the PCIe bus); READ 08_ARCHITECTURE.md:138 (the increment \(2.514-1.473=1.041\) ms/step fwd+bwd at \(n=2048\), \(s=64\), \(d=16\) float32, RUN NEPTUNE, per-op floor) and READ 03_KERNEL.md:178 (the three increments \(1.041/2.312/4.542\) ms at \(n=2048/4096/8192\)); READ 08_ARCHITECTURE.md:592 and :850 (the shipped shape's float32 operator against the record's complex64 arm, so the corner-3 base is not the shipped base); READ 08_ARCHITECTURE.md:115 (\(\tilde V\in\mathbb R^{s\times(d+K+2)}\)) and :510 (out.z float32[B, h, s, d+K+2], the shipped \(20\) channels); READ 08_ARCHITECTURE.md:553-559 (the per-row MAC table and its total); READ results/k_cert_local.json (throughput.points: softmax medians \(0.010142\), \(0.020291\), \(0.040525\) s at \(n=2048/4096/8192\) — the third is \(0.040524899999581976\) at throughput.laws.softmax.y[2], printed \(0.040521\) at filing, a transcription error corrected here; throughput.laws.arm_smprime.y[0] \(=0.09305229999881703\), the \(0.093052\) s row above; the law's \(R^2\) is \(0.9999975361960808\) in the file and is printed \(0.999998\) at READ COSTS.md:73 @ 99777ab, which is the pin that carries it — the 08_ARCHITECTURE.md:462 pin this verse cited for the same figure is a horizontal rule at the working tree and is struck here, P-6); the dispatch gap READ scale/m3_flops.py:101-121; the shape's whole-step law NOT MEASURED — needs N-02.
Mechanism. M-8, M-3, P-8, V-22, C17 (git show 99777ab:V20_R15_JOURNAL.md:53: no torch.cuda.synchronize() in scripts/v15_r1.py; run order the strongest correlate of seconds at \(\rho=+0.7029\), \(p=0.0024\)).
Kill. The prediction dies at the cell \(\ge2.2\times\) the DERIVED \(1.71990\) s cell (\(\ge3.78378\) s, COUNTER-dear) or below \(0.982\times\) it (\(<1.68894\) s, COUNTER-cheap, frozen here); the counter at inside the band; a second, independent kill fires on the width Hypothesis, frozen on the linearity claim itself: a measured solve increment at RHS width \(20\) outside \([1.14510,1.45740]\) ms — \(1.30125\) ms \(\pm\) the declared \(12\) per cent clock spread — strikes the \(0.011466\) s step, the \(1.71990\) s cell and every ratio derived from them, whatever the S-20 cell reads. A measured \(1.041\) ms at width \(20\) (no width dependence whatever) fires this kill, which is the point of freezing it at the point prediction rather than at the width-\(16\) reading. Price \(\approx1.72\) s for the cell, seconds for the width, \(0.2\) evening. Planted negative, restated on a number with a producer: the InfSA-16 cell contains a \(25.409\) ms hop, so its measured whole step must read at or above \(0.025409\) s — \(\ge1.95\times\) the shape's DERIVED step (\(0.025409/0.011466=2.2160\), less the \(12\%\) clock spread) — and a timer reporting it faster than the hop it contains is refused. The \(\ge2.62\times\) plant this verse carried at filing rested on the \(0.034133\) s figure and is deleted with it: a plant may not rest on a number tagged NOT MEASURED. The arm_smprime cell must read \(\ge8.07\times\) the softmax cell (\(9.1745\times\) less the \(12\%\) spread, DERIVED), a known-\(9.1745\times\) arm the timer must report as such; the depth-1 control run twice in interleaved order must agree within \(12\%\).
If killed (the counter, or the width kill). Every ratio in 06.29 to 06.31 is replaced by the measured ratio from N-02, and until N-02 exists the shape's step is quoted as the DERIVED sum with both terms printed and the measured \(0.093052\) s beside it as the family's only reading. The replacement statement is the MAC law alone, with no wall-clock and no fit — and it counts the softmax head the shape itself executes, which the previous writing omitted. The shape does not replace a softmax layer; it contains one and adds a solve, so pricing the solve alone against \(L\) whole layers priced the arms at different rates (M-8) and contradicted book 08's own table, which book 08 was itself convicted of and repaired. At \((s,d,K,m)=(64,16,2,8)\), per head per sequence:
and the read layer's total, which is what an engineer pays, is \(\approx s^2(d\cdot\tfrac32+K+2+m/2)+msd=139{,}264\) MACs \(=2.125\times\) the head — against \(L\) softmax layers at \(L\,s^2d=65{,}536\,L\) (READ 08_ARCHITECTURE.md:553-559, the per-row table: head \(s^2d=65{,}536\); the solve's \(K+2\) indicator channels \(s^2(K+2)/2=8{,}192\); the committor head at \(\gamma=1\) on \(T\) at \(\le8{,}192\); the \(m\) clamp moves at \(16{,}384+8{,}192\); total read layer \(139{,}264\), \(2.125\times\) the head). Book 08's "\(+50\%\) causal MACs" is the head plus the \(d\) value columns alone, \(65{,}536+s^2d/2=98{,}304=1.5\times\) the head (READ 08_ARCHITECTURE.md:182, :460), and is not the layer total; both figures are printed here so the smaller cannot be quoted for the larger. The sentence "\(40{,}960\) against \(65{,}536\,L\)" — which at \(L=1\) reads the shape at \(0.625\times\) one softmax layer while the shape contains that layer — is struck. Hypotheses: the MAC count is arithmetic over the shipped channel counts and row costs of book 08's budget table, and no clock enters it; \(L\) is the skyline depth, and at \(L=1\) the honest reading is \(1.625\times\) on the \(z\) channel and \(2.125\times\) on the read layer, not a number below \(1\). Evidence: READ 08_ARCHITECTURE.md:553-559 (the per-row MAC table and its total), :460 (the Terminal that prints both figures), :115 and :510 (the shipped \(d+K+2=20\) channels), READ docs/CEQ_SHAPE.md:583-603 (§2.5). Kill of the replacement — a different number, a different instrument, a different object from the verse's, and now read on the total rather than only on the channel count, because a correct channel count with an omitted head passes a channel audit as the previous replacement did: the read layer's total recomputed from 08_ARCHITECTURE.md:553-559 at the shipped \((s,d,K,m)\) differing from \(139{,}264\), or the shipped channel width read off :115 and :510 differing from \(d+K+2\); either makes the MAC arithmetic wrong at its own shapes. Decided by a shape audit at \(0\) GPU-s with no timer at all, cheaper and more decisive than the wall-clock band. It does not rest on 06.32's exponent, whose own deciding statistic 06.32 records as confounded until normalised.
Terminal. Prices are quoted as measured points, never as laws; the only measured whole-step number of this family is \(0.093052\) s on an arm that is not the shipped base; "faster to train" has no per-step referent and 06.29 to 06.31 are VOID.
06.29 — T1 and T2 against depth-1 base self-attention#
Statement. Let \(\tau_1\) be the depth-1 control's \(\varphi\)-NRMSE at step 150 on a seed (median over 8 seeds), and let \(t_{\rm shape}(\tau_1)\) be the shape's wall-clock from initialisation to the first eval at or below \(\tau_1\) in the same lane, timers synchronised, arms interleaved. \(T1_{d1}=t_{\rm shape}(\tau_1)/t_{d1}(\tau_1)\) with \(t_{d1}(\tau_1)\) the control's own 150-step wall-clock; \(T2_{d1}\) the same ratio in draws (steps \(\times2048\)). Prediction: \(T1_{d1}\le0.50\) and \(T2_{d1}\le0.45\) — the shape passes the one-hop error by step \(66\). Both mappings are printed so the two halves and the frozen kill agree at one integer (M-2; V-17): \(T1_{d1}=k\times0.011466/(150\times0.010165)=k\times0.011466/1.52475=0.00751992\,k\) (DERIVED to six places), and \(T2_{d1}=k/150\) exactly, since \(n_{\rm train}\) is the same for both arms. The two halves bind at different integers and the smaller governs: \(T1_{d1}\le0.50\) requires \(k\le0.50/0.00751992=66.49\), i.e. \(k\le66\) (\(0.49631\) at \(k=66\), \(0.50383\) at \(k=67\)), while \(T2_{d1}\le0.45\) alone would allow \(k\le67\) (\(0.44667\) at \(k=67\), \(0.45333\) at \(k=68\)). \(T1\) is the binding half at \(k\le66\), and the Kill below is frozen there, so no integer satisfies the prediction while the kill fires and none fires the kill while both halves hold. The kill this verse carried at filing, "\(>68\)", is corrected here: at \(k=68\) the \(T2\) half is already false (\(0.45333>0.45\)) and the \(T1\) half more so (\(0.51135>0.50\)), so a kill at \(68\) would have let two integers, \(67\) and \(68\), score HOLDS on a prediction one or both of whose halves is false there. Counter, split in two named branches exactly as 06.13's and 06.28's are, because the counter as filed had a far end that carried no token: COUNTER-slow, \(T1_{d1}\in[0.89,1.44]\) — under 06.16's counter the shape is softmax at the increment, \(1.1280\times[0.7857,1.2727]\) for the clock, with \(T2_{d1}\in[0.90,1.10]\) printed beside it as the companion reading; and COUNTER-overrun, \(T1_{d1}>1.44\) — the increment realised above the clock spread, which is 06.28's COUNTER-dear branch read from the clock, signed +. The region \((1.44,\infty)\) was named in this verse's own list of numbers that make the counter range wrong and was absent from the frozen Kill, so a reading there scored COUNTER on a counter whose filed range excludes it (M-7; M-2; D-7; 06.36's Kill: "The tree is refuted if a scored outcome has no branch"). SPLIT: \(T1_{d1}\in(0.50,0.89)\).
Every integer \(k\) carries exactly one token, printed at the constant \(0.00751992\). \(k\in[1,66]\) HOLDS (\(T1_{d1}\le0.49631\)); \(k\in[67,118]\) SPLIT (\(0.50383\) to \(0.88735\), both inside \((0.50,0.89)\)); \(k\in[119,191]\) COUNTER-slow (\(0.89487\) at \(k=119\), the first integer at or above \(0.89\); \(1.43630\) at \(k=191\), the last at or below \(1.44\)); \(k\ge192\) COUNTER-overrun (\(1.44382\) at \(k=192\)). All DERIVED by multiplication. The partition is on \(T1\) alone, its binding half, and \(T2\) is the companion reading: \(T2_{d1}=k/150\), so \(T2_{d1}\in[0.90,1.10]\) is \(k\in[135,165]\), a strictly narrower window than COUNTER-slow's, and the conjunction "\(T1\in[0.89,1.44]\) and \(T2\in[0.90,1.10]\)" the counter carried at the previous writing is unsatisfiable at every \(k\) in \([119,134]\cup[166,191]\) — the SPLIT clause "\(T2_{d1}\in(0.45,0.90)\)" was a second, disagreeing partition of the same axis and is deleted. A \(k\) in \([119,191]\) whose \(T2\) lies outside \([0.90,1.10]\) is COUNTER-slow with the \(T2\) reading printed beside it. Every \(T1\) number in this verse inherits 06.28's re-tag: the step \(0.011466\) s and the ratio \(1.1280\) are DERIVED with their two terms printed, not [FITTED + RUN], and the shape has no measured whole-step law (06.28). The numbers that make the prediction range wrong: a crossing step above \(66\); the numbers that make the counter range wrong: \(T1_{d1}<0.89\) (\(k\le118\), the shape faster in seconds despite the increment) or \(T1_{d1}>1.44\) (\(k\ge192\), COUNTER-overrun), and both ends are frozen in the Kill below. Deciding number: the crossing step read from the journal's per-step eval curve — the logger is specified: eval_trace (per-step eval NRMSE, for T2) with secs_sync and run_index (for T1) are mandatory journal fields and a missing declared field is a refusal (READ 04_BEDS_AND_INSTRUMENTS.md:238, the field list — the pin :233 this verse carried at the previous writing is 04's W2 arm_phase Kill line and is corrected here, P-6; :171, the crossing step read off that trace, likewise corrected from :170, which is 04.10's Spearman Kill). The sampling rate is reconciled here in favour of book 04's field: every step, not every tenth. At every step the crossing-step resolution is \(1\) step, so \(k=66\) and \(k=67\) are separable and this verse's kill is decidable; at every tenth step the resolution is \(10\) steps, which cannot separate 06.31's \(k=30\) boundary from \(k=39\) nor this verse's \(k=66\) from \(k=75\), and a journal sampling at ten would make both kills undecidable. The value itself is NOT MEASURED — needs S-62 run witheval_tracepopulated and book 03's synchronised, interleaved timer.
Hypotheses. Both arms reach \(\tau_1\) by construction (the control defines it); at matched parameters — the pre-head \(4{,}769\) of READ CEQ_V20_R15_CONTRACT.md:119 @ 99777ab, with the post-head count NOT MEASURED — needs book 04's recount (06.19); the ratio is against base self-attention at depth 1 and is the T1 form of CHARTER.md §1 only when the floor is a fixed distance-to-floor — here \(\tau_1\) is a distance the control attains, printed with the exact floor \(0.0\) beside it (L-FLOOR); a comparison at the shape's own floor is VOID against depth 1 because one softmax layer does not reach it at \(t^\star=8\) (obstruction 2, lineage) and a ratio with an infinite denominator is not a number.
Evidence. DERIVED from 06.28 (and re-tagged with it); the logger READ 04_BEDS_AND_INSTRUMENTS.md:238 (eval_trace, secs_sync, run_index, floor_exact, floor_zeroinfo, ceiling_hop_k, and the parenthesis striking floor_fano_k1; a missing declared field is a refusal) and :171 (the crossing step read off the trace, identical-seed floor \(0.0\) so the crossing step is exact per seed); the crossing curve itself NOT MEASURED; the record's only cost ratios were withdrawn at C17 (B25).
Mechanism. D-1, M-8, C17, V-17 (two units of "depth"), B12 (the corner descent decides which half), M-20 (this book claimed the logger unspecified while book 04 specified it; the two are reconciled here in book 04's favour).
Kill, with both counter ends frozen. The prediction dies at a crossing step \(>66\) on \(\ge4\) of 8 seeds. The counter dies at either end: at \(T1_{d1}<0.89\) (\(k\le118\)) on \(\ge6/8\), or at \(T1_{d1}>1.44\) (\(k\ge192\)) on \(\ge6/8\), which is the COUNTER-overrun branch and was named in the Statement's list but absent from this field at the previous writing. Inside the arena, \(0\) GPU-s beyond it once eval_trace is populated, \(1\) evening. Planted negative: the depth-1 control against itself in reversed run order must read \(T1=1.00\pm0.12\) and \(T2=1.00\) exactly; ChaCAL-diag at fixed \(\gamma=0.9\) (a fellow approximator with the same increment) must read \(T1\ge0.89\) against the control by construction of its step, so the instrument reports the increment where the increment is all there is; a journal whose eval_trace carries one entry per ten steps must be refused by the adjudicator, not read at resolution \(10\).
If killed (the counter). The sentence: "Against depth-1 base self-attention on BED-S the shape reaches the control's 150-step error at \([T1]\) of its GPU-seconds and \([T2]\) of its draws: it is the control at the price of one solve." The replacement is the per-step statement of 06.28 with no "to floor" clause — Hypotheses, Evidence and Kill as in 06.28 (the band check, \(\approx1.7\) s, cheaper than the arena).
Terminal. "Faster to train" in form T1 or T2 against depth-1 base is withdrawn on BED-S; the canon licenses "\(1.1280\times\) the step at \(n=2048\), DERIVED as \(0.010165+0.001301\) s, a per-op floor under a \(2.0\times\)–\(6.6\times\) dispatch gap, with no measured whole-step law for the shape".
06.30 — T1 against the depth skyline#
Statement. Let \(\tau_5\) be the depth-5 stack's \(\varphi\)-NRMSE at step 150 per seed and \(T1_{\rm sky}=t_{\rm shape}(\tau_5)/t_{\rm sky}(\tau_5)\), where \(t_{\rm sky}(\tau_5)=150\times0.050825=7.62\) s ([ASSUMED linear in depth]) and \(t_{\rm shape}(\tau_5)=k\times0.011466\) s at crossing step \(k\) (06.28's DERIVED step, re-tagged there), so the mapping constant is \(0.011466/7.62375=0.00150398\) (DERIVED to six places) and \(T1_{\rm sky}=0.00150398\,k\): \(0.0511\) at \(k=34\) (\(0.05113545\)) and \(0.2256\) at \(k=150\) (\(0.22559764\)). The constant \(0.0015047\) this verse printed at filing is corrected here: it reads \(0.225705\) at \(k=150\), outside the very band the verse files, so the printed constant and the printed range disagreed at the upper end (M-2, a threshold frozen inconsistently; V-17). The range and the crossing-step window now map into each other at both ends and at every integer between them. Prediction: \(T1_{\rm sky}\in[0.0511,0.2256]\) — the shape reaches the skyline's 150-step error within the cell and not before its first \(34\) steps, i.e. \(k\in[34,150]\), on at least 6 of 8 seeds. Counter: the shape does not reach \(\tau_5\) within 150 steps on at least 6 of 8 — \(T1_{\rm sky}\) undefined at the cell, filed COUNTER: at the 150-step budget the learned hops reach an error the exact solve does not, which is 06.16's counter seen from the clock.
One seed count, keyed on the in-band count, and a catch-all so no configuration falls through. Each of the eight seeds is placed in exactly one of three categories by its crossing step: in band (\(34\le k\le150\)), below band (\(k<34\)), not reached (\(k>150\)). The verse and row C-26 are frozen at one count, \(\ge6/8\) — the count the prediction itself already used — and the SPLIT band is re-keyed on the in-band count rather than on the "reached" count, because the reached count does not separate in-band from below-band and left a hole. The four branches:
| branch | reading (of the eight seeds) | verdict |
|---|---|---|
| HOLDS | in band on \(\ge6/8\) | prediction |
| COUNTER | not reached on \(\ge6/8\) | counter |
| LOW | below band (\(k<34\)) on \(\ge6/8\) | refutation of the prediction, scored SPLIT and signed + — the optimistic outcome carries a verdict |
| SPLIT | no category reaches \(6/8\) | SPLIT, with the ordered triple (in band, below band, not reached) printed |
The \(\ge4/8\) count the Kill carried at the previous writing is struck: it disagreed with row C-26's \(\ge6/8\) (M-2, a threshold frozen inconsistently; M-20), and even taken together the two left the configuration (5 in band, 3 below band, 0 not reached) in no branch at all — the prediction fails at \(5<6\), the counter fails at \(0\), the old SPLIT was keyed on "reached on \(3/8\) to \(5/8\)" while \(8/8\) are reached, and the old Kill needed \(\ge4/8\) outside while only \(3\) are. Under the table above that configuration is SPLIT with the triple \((5,3,0)\) printed. The old SPLIT clause "reached on \(3/8\) to \(5/8\)" is deleted with it.
The range is frozen at both ends and both ends kill. \(k<34\) on \(\ge6/8\) — the shape crossing before the first \(34\) steps — refutes the prediction exactly as \(k>150\) does, and is scored COUNTER-side, never HOLDS. The clause this verse carried at filing ("filed HOLDS with the range corrected in a superseding row") is deleted: it made every \(k\in[1,150]\) score HOLDS, so the whole region \(T1_{\rm sky}<0.0511\) was unfalsifiable and the row predicted both outcomes (M-20), and it refitted the threshold to the data that judges it (M-2). Under L-G2 a superseding row records a corrected reading, never a corrected range; a range corrected after the cell is a new prediction that may not be scored against this cell at all. The optimistic outcome \(k<34\) is the one the canon most wants and is therefore the one whose kill is frozen hardest: it is filed here, before the cell, as a refutation of this verse.
Deciding number: the crossing step \(k\) per seed, read from eval_trace at one entry per step (06.29) — NOT MEASURED — needs S-62 witheval_tracepopulated (READ 04_BEDS_AND_INSTRUMENTS.md:233) and the S-35 cell.
Hypotheses. The unmatched depth-5 stack at \(d_{\rm model}=16\) (R-SKY control) is the denominator; the matched-parameter stack of 06.20(i) is read beside it when it exists; the depth-linear step is ASSUMED and retired by S-35's own wall-clock; the exact floor \(0.0\) printed beside \(\tau_5\).
Evidence. DERIVED from 06.28; READ docs/PLAN.md:619-625 @ 99777ab (S-35's price \(\approx7.6\) s per cell, \(\approx64.8\) s at eight seeds, [ASSUMED]).
Mechanism. R-SKY, D-1, M-8, P-8, V-17.
Kill, at one seed count. The prediction dies at in band on \(\le5/8\) — that is, whenever the in-band count fails to reach \(6/8\), which covers the LOW branch (\(k<34\) on \(\ge6/8\)), the COUNTER branch (\(k>150\) on \(\ge6/8\)) and the SPLIT catch-all alike; the counter dies at not-reached on \(\le5/8\). Both are frozen at \(\ge6/8\), the same count row C-26 carries, and the \(\ge4/8\) of the previous writing is struck. Price \(\approx65.0\) s for the skyline cell (DERIVED, \(8\times5\times1.52475+4.0\) fixed; S-35's printed \(\approx64.8\) s uses \(7.6\) s per cell, READ docs/PLAN.md:619-625 @ 99777ab) plus the arena, \(1\) evening. Planted negative: an arm initialised at the exact solve (the copy plant of 06.15) must cross at \(k=1\) and fire the lower kill, so the lower end is known to be reachable on the bed as registered and is not decoration; the depth-3 stack (at \(t^\star=2\), M-3.7's point) must reach the depth-5 stack's \(\tau_5\) later than the depth-5 stack itself on a \(t^\star=8\) bed, so the instrument orders a known-shallower arm behind a deeper one.
If killed (the counter). The sentence: "At 150 steps the depth-5 stack reads \([\tau_5]\) and the shape reads \([e]>\tau_5\) on \([k]\) of 8 seeds; the shape's step is \(0.2256\times\) the stack's (DERIVED over an [ASSUMED] depth-linear denominator) and no GPU-seconds-to-floor ratio is defined at this budget." The replacement is the ladder reading of 06.27 with \(\tau_5^L\) the stack's error at step \(9{,}600\) — Hypotheses: the stack's ladder at \(\approx65\) min [ASSUMED] (\(9{,}600\times0.050825\times8\) s) plus the pair's \(32\)–\(36\) min; Evidence: READ docs/PLAN.md:981; Kill: not reached at step \(9{,}600\) on \(\ge6/8\) — more decisive because the budget is exhausted, and the only link whose price exceeds the verse's, which the depth rule permits because it is strictly more decisive.
Terminal. No T1 sentence against the depth skyline; the canon licenses the MAC law with the head the shape executes inside the count ("one head plus one solve at \(s^2d+s^2(d+K+2)/2=65{,}536+40{,}960=106{,}496\) MACs, \(1.625\times\) the head, and \(139{,}264\) MACs, \(2.125\times\) the head, for the read layer's total at \((s,d,K,m)=(64,16,2,8)\), against \(L\) layers at \(Ls^2d=65{,}536\,L\)", READ 08_ARCHITECTURE.md:553-559) and prints both wall-clocks as points, the shape's as a DERIVED sum with no measured whole-step law behind it (06.28).
06.31 — T2, draws-to-floor, both controls (B25)#
Statement. \(T2\) is the ratio of training draws (steps \(\times n_{\rm train}\)) to a fixed target: \(T2_{d1}\) at \(\tau_1\) (06.29) and \(T2_{\rm sky}\) at \(\tau_5\) (06.30). Prediction: \(T2_{\rm sky}\le0.20\) — the shape needs at most a fifth of the stack's draws to reach the stack's 150-step error, because one parameter set (\(\hat P\), one \(\gamma\)) is identified from next-state labels while five layers must each learn a hop (book 02's identifiability verse); equivalently \(k\le30\) at \(n_{\rm train}=2048\). Counter: \(T2_{\rm sky}\ge1.0\) or undefined — the shape needs at least as many draws, because under the corner descent the first draws are spent leaving \(\gamma=0\) (06.16's counter) and the sample-efficiency half is the same as depth-1's. SPLIT: \(T2_{\rm sky}\in(0.20,1.0)\). The number that makes the prediction wrong: \(k>30\) on \(\ge4\) of 8 seeds. What this row inherits from 06.28's re-tag, and what it does not: \(T2\) is a ratio of draw counts, \(T2_{\rm sky}=k/150\) at fixed \(n_{\rm train}\), so no re-tagged second enters it and its numbers stand unchanged; what it does inherit is the source of \(k\), which is the same eval_trace curve, and the fact that its companion \(T1\) rows are DERIVED and not fitted. Deciding number: the crossing step \(k\) — the logger is specified as a mandatory journal field, eval_trace per step (READ 04_BEDS_AND_INSTRUMENTS.md:233; the crossing step read off it at :170), and the value is NOT MEASURED — needs S-62 witheval_tracepopulated; the ratio is the T2 form of CHARTER.md §1 and is the only "faster" number that survives an unsynchronised clock, which is why it is filed separately from T1.
Hypotheses. Draws are counted, never timed, so C17's confound does not reach this row; the same \(\tau\) definitions; \(n_{\rm train}=2048\) for every arm; the identifiability statement is book 02's and its kill (identification at \(\ge10^{-2}\), 06.15's counter) is upstream of this row.
Evidence. DERIVED; the record holds no draws-to-floor number for any arm (B25); READ CHARTER.md:75-86.
Mechanism. M-3, M-9, D-1, B12.
Kill. The prediction dies at \(k>30\) on \(\ge4/8\); the counter at \(k\le150\) on \(\ge6/8\) with \(T2_{\rm sky}<1.0\); inside the arena and the S-35 cell, \(0\) GPU-s beyond them once the logger exists, \(0.5\) evening. Planted negative: the depth-1 control against itself must read \(T2=1.00\) exactly (draws are integers), and an arm whose learning rate is set to \(0\) must never reach any \(\tau\) and be reported "undefined", not "\(\infty\) rounded".
If killed (the counter). The sentence: "The shape reaches the depth-5 stack's 150-step error at \([T2]\) of its draws, or not within 150 steps on \([k]\) of 8 seeds; no sample-efficiency sentence is licensed." The replacement is book 02's fixed-\(\gamma\) regime re-read on the same curves (06.16's replacement), whose T2 is defined from step \(0\) without the descent — Hypotheses: \(\gamma_{\rm env}\) registered; Evidence: 06.16; Kill: \(k>150\) on \(\ge6/8\) at fixed \(\gamma\) as well, inside one pair, \(\approx34\) s, cheaper than the skyline cell.
Terminal. "Faster to train" in form T2 is withdrawn; the canon licenses "one parameter set" as a count of parameters, not of draws, and B25 is closed by the two undefined ratios printed with their crossing steps.
06.32 — The cost exponent in \(s\) (Bet L, S-66)#
Statement. The fitted quantity is seconds per step divided by \(n\) — seconds per step per unit \(n\) — and not seconds per step. Prediction: the fitted exponent of \(\mathrm{sec}/(\mathrm{step}\cdot n)\) in \(s\) over \((s,n)\in\{(64,2048),(256,2048),(1024,128),(4096,8)\}\) has an interval containing \(2\) and excluding \(3\), and the Spearman correlation of seconds against run index is insignificant at \(\alpha=0.05\). Counter: the interval excludes \(2\) toward \(3\) — depth \(s\) is visible past \(s=64\) and every long-context price is a band; or \(\rho\) comparable to the record's \(+0.7029\). SPLIT: the interval contains both \(2\) and \(3\). Deciding number: the exponent interval of the normalised statistic, and \(\rho\) (S-66; book 03's harness with a seq_len flag, two synchronize() calls and randomised order — the fifth edit no office priced).
Why the statistic is normalised, with the arithmetic that forces it. The four points do not hold \(n\) fixed: \(n\) falls from \(2048\) to \(8\), a factor of \(256\), because the residency rule refuses the dense operator at \(n=2048\), \(s=4096\) (\(137\) GB against \(7.996\) GiB). On the un-normalised statistic that variation swamps the exponent it is supposed to read. Take a solve whose cost is exactly quadratic in \(s\), \(\mathrm{cost}=c\,n\,s^2\) — the prediction's own hypothesis. Then \(\log_2\mathrm{cost}\) at the four points is \(23,27,27,27\) against \(\log_2 s=6,8,10,12\), and the OLS slope is \(S_{xy}/S_{xx}=12/20=0.60\) (DERIVED). A perfectly quadratic arm reads \(0.60\): the prediction ("contains \(2\), excludes \(3\)"), the counter ("excludes \(2\) toward \(3\)") and the SPLIT ("contains both") all fail at \(0.60\), and no half of the bet nor its band has a branch — which is D-3 and M-8 in one statistic, and is exactly what this verse's own planted negative asserts about an instrument that reads the allocator instead of the arm. Normalised, the same four points read \(\log_2(\mathrm{cost}/n)=12,16,20,24\) against \(\log_2 s=6,8,10,12\) and the slope is exactly \(2\) (DERIVED), so the prediction band is well posed on the normalised statistic and on no other. The alternative — timing at fixed \(n\) — is unavailable: the residency refusal at \((2048,4096)\) removes the point, and where that route is taken the refused point is recorded as missing, never imputed.
Hypotheses. The deciding statistic is \(\mathrm{sec}/(\mathrm{step}\cdot n)\), declared here before the sweep (M-2); the per-step cost is linear in \(n\) at fixed \(s\), which the record's own two laws assert at \(n^{0.9963}\) and \(n^{1.0026}\) (READ COSTS.md:73-74 @ 99777ab) and which the normalisation therefore assumes to within those exponents — a departure from linearity in \(n\) larger than \(\pm0.01\) in the exponent strikes the normalisation and the row with it; \(n\) declared per \(s\) from the residency model (the dense operator at \(n=2048\), \(s=4096\) is \(137\) GB against \(7.996\) GiB and is refused, and the refusal is journalled as a missing point); \(N=8\); every price quoted before the sweep is struck (K-9).
Evidence. READ docs/PLAN.md:725-731, :1074 ("S-66 K-9 (band)"); the band \(206\)–\(537\) GPU-s git show 99777ab:V20_R15_THEORY_TABLE.md:104-109; the record's \(\rho=+0.7029\), \(p=0.0024\) (C17).
Mechanism. D-3, P-8, C17, M-3, K-9.
Kill. The prediction dies at an interval on the normalised statistic excluding \(2\), or at a significant \(\rho\); the counter at containing \(2\), excluding \(3\), \(\rho\) n.s.; a third kill fires on the normalisation itself — a fitted exponent in \(n\) at fixed \(s\) outside \([0.99,1.01]\) strikes the statistic and every reading taken on it. Price \(206\)–\(537\) GPU-s, band only, \(3\) evenings. Planted negative: the depth-1 control's own normalised exponent must read an interval containing \(2\) (the causal product is quadratic in \(s\) by construction), so an instrument that reads \(3\) on softmax is reading the allocator, not the arm; and the same control's un-normalised exponent over these four points must read \(\approx0.60\), the value derived in the Statement, so the confound is demonstrated by the instrument on a known-quadratic arm before any shape number is read.
If killed (the counter). Every \(s\)-scaled price and the "plus 50 per cent" wall-clock sentence die; the MAC law stays a MAC law and measured points are quoted as points; 06.30's \(t_{\rm sky}\) and \(t_{\rm shape}\) are re-read at each \(s\) separately. Hypotheses: none. Evidence: READ docs/PLAN.md:1074. Kill of the replacement: none — a point is its own evidence; the replacement is Terminal.
Terminal. Prices at \(s=64\) only, as measured points with the dispatch gap printed; no long-context cost sentence.
06.33 — The move price (Bet G, V-17)#
Statement. Prediction: after one solve at \(n=2048\), \(s=64\), \(d=16\), \(m=8\) query-side row clamps by the Sherman–Morrison column route (one forward-substitution column at \(s^2/2\) MACs plus an \(s\,d\) inner product each) cost at or below \(0.5\times\) one solve, since \(m/d=0.5\) at \((8,16)\). Counter: at or above \(8\times\) — a re-solve per candidate is what ships and the consequence channel is repriced as \(m\) solves in every table. SPLIT: \((0.5\times,8\times)\), printed as a band with no point. Deciding number: the measured ratio, median of 14 after 2 warm-ups, synchronize() bracketed.
Hypotheses. Row clamps on the environment chain only (sherman_morrison_row [S], docstring: a token rewrite is rank \(s-i\) and is priced as a suffix re-solve at \((s-i)^2d/2\)); the denominator \((1-\gamma p'_{ii})/(1-\gamma P_{ii})>0\) for every \(\gamma<1\).
Evidence. READ docs/PLAN.md:660-667, :918; READ docs/CEQ_SHAPE.md:461-468 (Proposition 7(iii)); the record's FLOP model understated a bill by \(2\times\)–\(3\times\) (READ MISTAKES.md:469-476).
Mechanism. M-8, P-8, M-3.
Kill. The prediction dies at ratio \(>0.5\times\); the counter at \(<8\times\); seconds, \(1\) evening. Planted negative: a token rewrite at position \(i=12\), \(s=32\) has \(\mathrm{rank}(\Delta P)=20=s-i\) (RUN[J]) and its column route must disagree with the re-solve by \(O(1)\), so the instrument refuses the rank-one price where the rank is not one.
If killed (the counter). The channel is priced as \(m\) solves (\(m\cdot s^2d/2\) MACs) in every table; the T1 rows of 06.29 and 06.30 are unaffected (they price training, not inference). Hypotheses: none. Evidence: the measured ratio. Kill of the replacement: none; a measured price is Terminal.
Terminal. The interventional read costs \(m\) solves; no "one column per move" sentence.
06.34 — Determinism of the solve on the re-certified stack (N-01)#
Statement. Prediction: on the stack book 05 pins (B1: the box runs torch 2.14.0, numpy 2.4.6; the certified device is torch 2.5.1+cu121), solve_triangular repeats bitwise forward and backward over 8 repeats under use_deterministic_algorithms(True) at \(n=512\), reduction length \(64\), as the fourth determinism quantity of the device certificate. Counter: the backward raises or differs across repeats — the training step runs warn_only=True (Ruling 1) and the "first gated wing under strict mode" sentence is deleted. SPLIT: forward bitwise, backward differing below \(2.345\times10^{-3}\). Deciding number: max_abs over 8 repeats, forward and backward.
Hypotheses. The certificate's determinism block schema (results/k_cert_local.json: flag_off.forward.bitwise, .gradient.bitwise over 8 repeats); torch documents no guarantee for solve_triangular; cumsum raises under strict mode (B13).
Evidence. READ results/k_cert_local.json (arm_smprime forward, hop and gradient bitwise: true, max_abs: 0.0, 8 repeats, at git ab5b485, 2026-08-31); READ docs/PLAN.md:529-535 (N-01); READ docs/CEQ_SHAPE.md:2970-2975; the re-certified value NOT MEASURED — needs book 05's environment pin andscripts/k_cert.pyre-run (B2).
Mechanism. Ruling 1, V-16, V-23 (the control softmax was never tested under strict mode), B13.
Kill. The prediction dies at a strict-mode raise or max_abs > 0 on the backward; the counter at bitwise both ways; seconds, \(0.5\) evening after the pin. Planted negative: cumsum under the same setting must raise (the known non-deterministic kernel), so the certificate distinguishes "bitwise" from "the flag was not set".
If killed (the counter). Every deciding forward cell stays bitwise by replay (forward observed true), training is compared against the measured noise floor, and 06.13's strict-mode clause is deleted. Hypotheses: the forward is bitwise. Evidence: the certificate. Kill of the replacement: forward max_abs > 0 over 8 repeats — the same cell, bitwise-decisive.
Terminal. No determinism sentence about training; deciding cells are forward-only and bitwise, or the lane is warn_only and every price carries the noise floor.
06.35 — The language-model dial (Bet M, behind the yes)#
Statement. Prediction: \(\hat\gamma\) MOVED on at least 6 of 8 enwik8 seeds on the pinned slice, shape against ChaCAL at fixed \(\gamma=0.9\). Counter: PINNED on at least 6 of 8 — consistent with the published operator's own language-model result being worse than its baseline (digits [U]); the LM \(\gamma\) claim is retired and \(\gamma\) stays a bed-side dial. SPLIT: \(3/8\) to \(5/8\). VOID until the author's explicit yes (N-24; nothing launches, uploads or trains without it). Deciding number: \(\Lambda\) per seed under the boundary null; the perplexity delta against \(\mathrm{MDE}_8\) printed beside it and never pooled with a local number (V-22).
Hypotheses. 06.16 MOVED locally (otherwise the row is retired before it is made); the Kaggle certificate slot filled by the author's run; three sources UNPINNED with the hash cell that prints and then raises.
Evidence. READ docs/PLAN.md:868-874 (S-73), :862-867 (N-24), :920; READ COSTS.md:27-45 (the pins).
Mechanism. V-22, Ruling 10′, V-9, the Kaggle-yes rule.
Kill. The prediction dies at PINNED on \(\ge6/8\); the counter at MOVED on \(\ge6/8\); NOT MEASURED — no LM cell of the shape has ever run; \(2\) evenings after the yes. Planted negative: 06.12's plants re-run on the Kaggle device before the LM cell, both \(8/8\), with no threshold carried across the device boundary.
If killed (the counter). The sentence: "On enwik8 the trained \(\hat\gamma\) is not distinguishable from \(0\) under the boundary null on \([k]\) of 8 seeds; \(\gamma\) is a bed-side dial and the shape is ChaCAL at \(\gamma=0\) on natural text." The replacement claim is none on natural text; the canon's LM sentence is the containment (softmax at \(\gamma=0\) bitwise). Hypotheses: none. Evidence: 06.13. Kill of the replacement: 06.13's, \(\approx1.7\) s.
Terminal. No language-model sentence; the row stays VOID or COUNTER in the column and the canon says which.
V. The tree#
06.36 — The three sentences and the verses that die on each#
Statement. The master tree of book 00 reads this row. Tree A (every prediction holds; the half the column says is less likely): 06.11 \(7/7\) on the seven admissible bare-[M] targets with the four [U]-blocked rows (:2606, :2608, :2609, :2619) still uncited; 06.7 admits; 06.10 does not strike; 06.15 identified; 06.16 MOVED \(\ge6/8\); 06.21 \(\ge10\); 06.17 above by more than \(\mathrm{MDE}_8\); 06.18 below the floor; 06.22 separated; 06.20(ii) inside \(\mathrm{MDE}_8\); 06.33 \(\le0.5\times\); 06.24 C-33 selecting a tier and C-20 inside at that tier; 06.29 to 06.31 in their prediction ranges. Sentence: docs/PLAN.md:1052 with every bracket a journal number, and A1 (06.19) and T2 (06.31) as the two licensed words; A2 is not merely unearned but unreachable at BED-S scale (06.20(i)), so no leaf of any tree carries an A2 sentence, and T1 against the skyline is \(0.2256\,k/150\) (DERIVED over an [ASSUMED] depth-linear denominator). Tree B (every counter holds; the point estimate): 06.11 at most \(6/7\) on the seven admissible bare-[M] targets, i.e. \(7/9\) on the nine bare-[M] rows and \(7/11\) on the eleven [M]-graded rows, with all four [U]-blocked names listed; 06.7 admits after one sink-share repair; 06.15 identified; 06.16 PINNED; 06.21 SPLIT; 06.17 within; 06.18 straddles; 06.22 and 06.24 VOID; 06.20(ii) inside; 06.33 SPLIT; 06.29 \(T1_{d1}\in[0.89,1.44]\); 06.30 and 06.31 undefined. Sentence: READ docs/PLAN.md:1054 @ 99777ab (tree B, "the median outcome"; the pin :1058-1060 this verse carried at filing names the smaller-deaths heading and its table header and is corrected here, P-6), and neither word of CHARTER.md §1 is earned. Tree C (the bed does not admit): 06.7 counter; 06.8, 06.9's arena half alone (C-32), 06.10 and 06.15 to 06.27 VOID; 06.6, 06.7, 06.9's \(0\) GPU-s half, 06.11, 06.12, 06.13, 06.14, 06.28, 06.32, 06.33 and 06.34 still run and are scored under tree C — eleven verses for eleven rows — they need neither BED-S admission nor the arena, 06.7 being the verse whose counter defines tree C and therefore scored rather than voided by it, 06.9's C-5 being read on the S-12 census draws at \(0\) GPU-s before any arm, and 06.13 and 06.14 being hosted on BED-M's e3_t2 and the R1 retake; their rows are the tree-C pool 06.4 reads (C-2, C-3, C-5, C-7, C-8, C-9, C-10, C-24, C-28, C-29, C-30 — eleven, the ten of the previous writing plus C-5, which 06.4 had voided as "C-5's arena half", a half C-5 does not have); sentence READ docs/PLAN.md:1056 @ 99777ab (tree C, "the shape dies at its weakest component, before a GPU-second"; the pin :1064-1066 this verse carried at filing names rows of the smaller-deaths table and is corrected here, P-6). Tree A's pin :1052 was re-verified at 99777ab and is correct as cited.
Hypotheses. The three trees are exhaustive on 06.7's binary and 06.16's three-way outcome; mixed outcomes are read verse by verse and the sentence is assembled from each verse's If-killed or Statement, never from a fourth template.
Evidence. READ docs/PLAN.md:1048-1077; D-CALIB-1 makes tree B the planning estimate and, after 06.4's counter, the reported one.
Mechanism. D-7, P-3, M-20 (one tree per outcome, in one place, so no two sections predict opposite outcomes), D-CALIB-4 (the cheapest discriminating measurement of the optimistic half runs first: 06.7, then 06.5, then 06.16).
Kill. The tree is refuted if a scored outcome has no branch — decided by the coordinator's read of the verdict file against this verse, \(0\) GPU-s, \(0.2\) evening. Planted negative: the mixed outcome "06.16 MOVED with 06.22's counter at \(N=16\)" must resolve to tree B's sentence with the boundary clause replaced by 06.22's If-killed sentence, and the coordinator's read must print which verse supplied each clause.
If killed. The replacement is the verse-by-verse assembly rule stated in Hypotheses, applied without the three templates — Hypotheses: every verse has an If-killed sentence (L-VERSE); Evidence: this book; Kill: a verse whose If-killed sentence is missing, which CORRECTIONS.md records as NO REPLACEMENT PRE-WRITTEN, \(0\) GPU-s.
Terminal. The canon licenses, on every leaf, the identities RUN, the census printed, the floors, the controls and the negatives; nothing else.
Census rows closed#
| row | what is broken | closing verses | what closes it |
|---|---|---|---|
| B5, on admission | no CEQ arm trained; BED-S has no cell, no realised sd, no measured \(t^\star\) | 06.5, 06.6, 06.15 | the realised sd is C-1's deciding number with the reprice pre-written; \(t^\star\)'s placement is C-2's with the reroute chain; the first FOUND record with the shape's kind is C-11's, and RUN this session reads arm_phase absent and no shape kind in results/ |
| B5, on tree C (06.7's counter — the book's own point estimate under D-CALIB, 7 of 8 optimistic, \(p=0.0352\)) | the same row, with no batch admitted | 06.5's Terminal, 06.7 | S-62 never fires, so no realised sd is printed: B5 closes on this branch by the census's printed failure line plus the row "realised paired sd NOT MEASURED — needs an admitted batch", and by nothing else; the trained-arm and measured-\(t^\star\) halves close by the same failure line and no number |
| B6 | the calibration column: 9 checked, 9 adverse, 7 of 8 optimistic, \(p=0.0352\) | 06.2, 06.3, 06.4 | the nine rows reproduced with producing files; forty rows filed (C-1 to C-40) with the denominator — the thirty-nine of C-1 to C-39 — fixed before scoring and C-40 excluded from the count it reads; the eighth-row test with the \(0.75\) rule's engagement pre-written |
| B25 | "faster to train" never defined or measured; only per-op floors and the withdrawn it.3 ratios | 06.28, 06.29, 06.30, 06.31 | T1 and T2 defined at \(\tau_1\) and \(\tau_5\) with synchronised, interleaved timers and draws counted; ranges \(T1_{d1}\le0.50\) / \([0.89,1.44]\), \(T1_{\rm sky}\in[0.0511,0.2256]\) / undefined, \(T2_{\rm sky}\le0.20\) / \(\ge1.0\), each frozen at both ends with the crossing step that makes it wrong; the per-step step \(0.011466\) s and the ratios \(1.1280\) and \(0.2256\) re-tagged DERIVED with their terms printed (06.28) — the shape has no measured whole-step law, and the family's only measured whole step, \(0.093052\) s on arm_smprime, is printed beside them as a number belonging to an arm that is not the shipped base |
Kills, cheapest first#
| verse | kill number (frozen) | price | replacement verse or route |
|---|---|---|---|
| 06.2 | any cell differing from V16_CALIBRATION.md:40-48 @ 99777ab |
\(0\) GPU-s | the union census \(10\) of \(\ge17\) |
| 06.1 | a token outside the four; a hash mismatch not halting | \(0\) GPU-s | the record's three-token adjudicator |
| 06.3 | the file hashed after the first cell's timestamp | \(0\) GPU-s | the thirteen-bet file of S-60 (Bets A to M, 13/13 signed; PLAN's 24/24 owed to CORRECTIONS.md) |
| 06.36 | a scored outcome with no branch | \(0\) GPU-s | verse-by-verse assembly |
| 06.4 | \(\ge6\) of the first 8 scored rows + |
\(0\) GPU-s | D-CALIB-1 on the canon's rows; next-eight sub-column |
| 06.6 | \(t^\star\) unplaceable or admitted-region sd \(\le0.05\) | \(0\) GPU-s | \(t^\star\to2\) / deeper graph; then the substrate cross-check; then reprice \(N\) |
| 06.7 | any of the five admission lines failing | \(0\) GPU-s | tree C; 06.6's chain |
| 06.9 | sink-move fraction \(\ge0.5\); flag rule at \(\mathrm{acc}_{\rm shape}-\mathrm{MDE}_8\) | \(0\) GPU-s | conditioned column; committor-vector head only |
| 06.11 | any of the seven admissible bare-[M] targets red |
\(0\) GPU-s | [S] with the float instance; parity plus the [U] confirmation for the unit; arena waits |
| 06.8 | honest probe \(R^2\ge0.5\) | \(\le1.524\) s | re-registered label; then 06.10's Terminal |
| 06.12 | either plant \(<8/8\) | seconds | the ablation instrument |
| 06.33 | column route \(>0.5\times\) one solve | seconds | \(m\) solves in every table |
| 06.34 | strict-mode backward raises or differs | seconds | warn_only; forward-only bitwise cells |
| 06.28 | the S-20 cell \(\ge2.2\times\) the law (COUNTER-dear) or \(<0.982\times\) the law, \(<1.65024\) s (COUNTER-cheap); or a measured solve increment at RHS width \(20\) outside \([1.041,1.561]\) ms | \(\approx1.7\) s | measured ratios from N-02; then the MAC law alone, killed by a shape audit at \(0\) GPU-s |
| 06.13 | torch.equal False; a plant passing; cell out of band on either side (\(\ge2.2\times\) COUNTER-dear, \(<0.982\times\) COUNTER-cheap); strict-mode forward max_abs > 0 |
\(\approx1.7\)–\(17.4\) s | re-tagged prices; warn_only lane |
| 06.26 | one exceedance on \(1{,}024\) draws; \(\delta\|V\|_\infty\ge\) label sd | \(\approx2.6\) s | the exact solve, dense per chunk |
| 06.14 | \(\le2\) of 3 capped seeds crossing | \(\approx9.65\) s | "mechanism unresolved" kept |
| 06.16 | PINNED on \(\ge6/8\) | \(0\) GPU-s \(+\le17.4\) s | fixed-\(\gamma_{\rm env}\) regime (book 02); 06.22, 06.24, 06.35 VOID |
| 06.5 | realised sd \(\ge0.109199\) | \(\approx34\) s | \(N=16\), \(\mathrm{MDE}_{16}\) |
| 06.15 | modal band \(\ge10^{-2}\) on \(\ge6/8\); modal band \(<10^{-3}\) on \(\ge6/8\) is VOID; no band at \(6/8\) is SPLIT with the triple printed | inside \(\approx98\) s | learnability reading; the ladder on the sup-norm |
| 06.17 | cosine gap \(\le\mathrm{MDE}_8(\cos)\) | inside the pair | the displacement identity as algebra and price |
| 06.18 | \(\mathrm{CP}_{\rm upper}\ge0.875\) (the exact zero-information floor; the Fano row is decoration at \(I=0\)) | inside the pair | \(N=16\) at \(\approx68\) s; then vector head only |
| 06.19 | \(\Delta_{A1}\) outside \([0.40,0.85]\) — \(<0.40\) or \(>0.85\) | inside the pair | reproduction reading with 06.15 beside it |
| 06.21 | ratio \(\le2\) | inside the pair | residual as diagnostic; one solve as cost |
| 06.29 | crossing step \(>66\) on \(\ge4/8\); the counter at either end — \(k\le118\) (\(T1_{d1}<0.89\)) or \(k\ge192\) (\(T1_{d1}>1.44\), COUNTER-overrun) on \(\ge6/8\) | inside the arena + eval_trace |
06.28's per-step statement |
| 06.31 | \(k>30\) on \(\ge4/8\) | inside the arena + S-35 | fixed-\(\gamma\) curves; then Terminal |
| 06.23 | within one seed sd on \(P\)-changing plants on \(\ge6/8\) | \(\approx35\) s | identity plus price; 06.33 |
| 06.10 | 0-hop MLP's paired gap \(\le\mathrm{MDE}_{\rm McN}=0.04378\sqrt d\) on \(4{,}096\) paired eval draws, or McNemar \(p>0.05\) with that \(\mathrm{MDE}_{\rm McN}\) printed — never a seed-level non-rejection at \(N=8\) (M-13) | \(\approx0.5\) GPU-min | book 04's joint-consistency bed; 06.21's kill |
| 06.20 | (i) A2 UNREACHABLE at \(4{,}769\) — refuted only by a recount with a gap \(\le1\) parameter; (ii) unmatched stack short by \(>\mathrm{MDE}_8\), or the shape ahead by \(>\mathrm{MDE}_8\) | \(0\) GPU-s; \(\approx64.8\) s per stack | A2 on the joint bed at \(p\ge4{,}687{,}500\); 06.21's kill |
| 06.30 | in band (\(34\le k\le150\)) on \(\le5/8\) — one seed count, \(\ge6/8\), covering LOW (\(k<34\)), COUNTER (\(k>150\)) and the SPLIT catch-all | \(\approx65.0\) s + arena | the ladder at \(\tau_5^L\) |
| 06.22 | either half failing: within \(\mathrm{MDE}_8\) on \(\ge6/8\), or residual within \(2\times\); the two mixed outcomes are the named branches SPLIT-sep and SPLIT-res | \(\approx52\) s \(+44\) s | tree B; delta narrowed to certificate, Lean, re-solve |
| 06.24 | C-33: \(r=\mathrm{sd}_d/\sigma>0.7071\); C-20: interval outside \(\pm0.5\sigma\) at the tier C-33 selects; C-34: outside at \(N=70\) | \(0\) GPU-s; \(119\) s or \(228\) s | parity at \(\gamma=0\) only |
| 06.25 | error flat within \(\mathrm{MDE}_8\) across \(t^\star\) | \(\approx3.5\)–\(4.0\) min | the centre alone |
| 06.32 | the normalised exponent interval (sec/step per unit \(n\)) excluding \(2\); \(\rho\) significant; or the exponent in \(n\) outside \([0.99,1.01]\) | \(206\)–\(537\) GPU-s | points, not laws |
| 06.27 | any \(N=8\) verdict reversing at step \(9{,}600\) | \(32\)–\(36\) min per pair | the ladder's number; 150-step cells as pilots |
| 06.35 | PINNED on \(\ge6/8\) enwik8 seeds | NOT MEASURED; behind the yes |
containment only on natural text |
Limits, collected once. No number in this book is a result: no CEQ arm has been trained, BED-S has no cell, and every \(\mathrm{MDE}_8\) is the record's row-2 placeholder until 06.5 fills it. The depth-linear skyline step and every ratio derived from it are [ASSUMED] and retired only by S-35's wall-clock. The shape has no measured whole-step law at all: \(0.011466\) s is a DERIVED two-term sum whose second term, \(1.301\) ms, is itself a width-scaled reading of a \(1.041\) ms increment measured at a \(16\)-column right-hand side against the shipped \(20\), and the ratios \(1.1280\) and \(0.2256\) are DERIVED from it — a per-op floor under a \(2.0\times\)–\(6.6\times\) dispatch gap on a device whose certificate is stale (B2); the only measured whole step in this family, \(0.093052\) s, belongs to arm_smprime and not to the shipped base. The crossing steps that decide T1 and T2 are read from eval_trace, secs_sync and run_index, which book 04 makes mandatory journal fields whose absence is a refusal (READ 04_BEDS_AND_INSTRUMENTS.md:233; the crossing step read off the trace at :170); the sampling rate is reconciled at one entry per step, and the four rows are unscorable not because the logger is unspecified but because no cell has run to populate it. A2 at matched parameters is unreachable at BED-S's \(4{,}769\) parameters and not merely unmeasured: Ruling 3's per-cent form demands a \(1.53\)-parameter match there, and its absolute form and per-cent form are simultaneously satisfiable only at \(p\ge4{,}687{,}500\), so A2 waits on a joint-consistency bed that does not yet exist. The tight restricted-view Fano is decoration on this bed at \(I=0\) and is printed as such; the exact zero-information floor \(0.875\) is the only floor that decides. The boundary-null citation is owed: the theorem is now named in 06.12 — the half–half mixture \(\tfrac12\chi^2_0+\tfrac12\chi^2_1\) for a likelihood ratio at a parameter-space boundary, \(95\) per cent point \(2.705543\) — with the exact grep -c commands and the two key strings searched printed beside it, and the reference itself NOT FOUND at [V-eq]; the absence blocks every PINNED verdict (\(\Lambda\le2.705543\)) in 06.12, 06.16 and 06.35 and blocks nothing else, the MOVED threshold \(\ln4096=8.317766\) resting on the declared held-out size alone. InfSA-16's per-step \(0.034133\) s is NOT MEASURED — needs S-32's cell: it divides the source's \(\approx5.12\) s cell by \(150\) steps and the step below that does not reproduce from this book's constants, so the \(2.977\times\) it gives is tagged with it and the plant that depended on it is replaced by one on the \(25.409\) ms hop. Forty rows are filed, C-1 to C-40; the denominator is the thirty-nine of C-1 to C-39, with C-40 excluded from the count it reads by 06.3's Hypotheses, and it now carries a row for each of book 09's deciding cells — the two \(0\)-GPU-s censuses 09.10 and 09.32 (C-35, C-37), the two first cells 09.13 and 09.34 (C-36, C-38) and 09.31's PnL row against the market-following rule (C-39) — because the two uses the author names are where the module is decided and a denominator without them scores everything except the thing that matters. Those five are VOID until book 09's generators exist. The denominator is fixed here so that the eighth-row test measures the author's calibration and not the auditor's appetite.
Attacks answered#
MARS's findings, repair round 1, batch 1 of 2. Every finding is reproduced verbatim in the four fields it was filed with — flaw, mechanism, number, severity — beside the repair applied, its verse id, and what changed. Nothing is softened; where a finding could not be repaired the verse stays and its Terminal is now in force. A finding that reads more gently here than when filed would itself be a defect.
06.28 — severity strike; replacement survives as filed: false#
Flaw (verbatim). "The shape's per-step cost 0.011206 s is tagged [FITTED + RUN] but is a DERIVED sum of the softmax arm's fitted law and an operator microbenchmark; the shape has no measured whole-step law, the increment was measured at RHS width d=16 while book 08 specifies d+K+2=20 solve channels, and the only measured CEQ-family whole-step number in the tree is never printed beside the ratio."
Mechanism (verbatim). "M-8 (pricing every arm at one arm's rate) — the exact mechanism 06.28's Hypotheses claim to be designed against; P-1; P-8"
Number (verbatim). "COSTS.md:73-74 @ 99777ab: softmax exp(-12.1852)*n^0.9963 = 0.010165 s at n=2048; arm_smprime exp(-10.0187)*n^1.0026 = 0.09290 s at n=2048, i.e. 9.14x, both at s=64, d_model=16, fwd+bwd+Adam.step. 08_ARCHITECTURE.md:462 states the same as 9.2x dearer ... 0.093052 s [MEASURED]. The increment 1.041 ms = 2.514-1.473 ms is measured on a d=16 right-hand side; 08_ARCHITECTURE.md:462 sizes z at 4s(d+K+2) B = 20 channels, a 20/16 = 1.25x widening the derivation omits (corrected increment 1.301 ms, step 0.011466 s, ratio 1.1280 not 1.1024)."
Repair applied — 06.28. The [FITTED + RUN] tag is deleted and the step is re-tagged DERIVED with its steps printed, in a table that gives every term its own class: the softmax law [FITTED], its measured point [MEASURED], the \(1.041\) ms increment RUN[NEPTUNE] at RHS width \(16\), the \(1.301\) ms increment DERIVED as \(1.041\times20/16\), the step \(0.011466\) s DERIVED as the sum, the ratio \(1.1280\) DERIVED. The RHS width is stated as a Hypothesis with its own kill — a measured increment at width \(20\) outside \([1.041,1.561]\) ms strikes the step and every ratio from it, whatever the S-20 cell reads — because the forward substitution's linearity in the column count is an assumption, not a reading. The record's only measured CEQ-family whole step, \(0.093052\) s on arm_smprime at \(9.2\times\) the softmax law, is printed in the same row-set with book 08's sentence that the corner-3 base is complex64 and is not the shipped base (READ 08_ARCHITECTURE.md:518), and with COSTS.md's note that its law is fitted over three points because the other two time the PCIe bus. A second planted negative is added: the arm_smprime cell must read \(\ge8.1\times\) the softmax cell. The re-tag is inherited explicitly by 06.29 (\(k\le66\), counter \([0.89,1.44]\)), 06.30 (\(T1_{\rm sky}=0.0015047\,k\), \(0.2256\) at \(k=150\)), 06.31 (stated there: \(T2\) is a draw ratio and inherits the source of \(k\), not a second), the B25 closure row and the Limits paragraph. The replacement is replaced: the old If-killed rested on 06.32's exponent, whose own statistic 06.32 now records as confounded, so it died with the verse. The new replacement is the MAC law alone — \(s^2(d+K+2)/2=40{,}960\) against \(Ls^2d=65{,}536\,L\) — with a kill on a different number, a different instrument and a different object: the shipped channel count audited against 08_ARCHITECTURE.md:108 and :477, decided at \(0\) GPU-s with no timer.
06.30 — severity strike; replacement survives as filed: false#
Flaw (verbatim). "The optimistic side of the prediction range is not a kill: the verse states in the open that a crossing step below the range is scored HOLDS with the range rewritten afterwards, so no outcome better than predicted can score against the project."
Mechanism (verbatim). "M-20 (a pre-registration that predicts both outcomes); M-2 (a threshold refitted to the data it judges); D-CALIB-5"
Number (verbatim). "Verse text: \"The number that makes the prediction range wrong: \(k<34\) on \(\ge6/8\) (the shape crosses before the first tenth of the cell, the lower bound was too high, filed HOLDS with the range corrected in a superseding row)\". The frozen Kill reads only \"the prediction dies at not reached on \(\ge4\) of 8 within 150 steps\", so every k in [1,150] scores HOLDS and the region T1_sky<0.05 is unfalsifiable."
Repair applied — 06.30. The superseding-row clause is deleted, with the reason printed in the verse: under L-G2 a superseding row records a corrected reading, never a corrected range, and a range corrected after the cell is a new prediction that may not be scored against that cell at all. Both ends are frozen and both ends kill: the Kill now reads "\(T1_{\rm sky}\) outside \([0.0511,0.2256]\) on \(\ge4\) of 8 — \(k<34\) or not reached within 150 steps". The verse states in the open that the outcome most favourable to the project is the one whose kill is frozen hardest. A planted negative is added so the lower end is reachable rather than decorative: the copy plant of 06.15, an arm initialised at the exact solve, must cross at \(k=1\) and fire the lower kill. The band endpoints read \([0.0511,0.2256]\) rather than the finding's \([0.05,0.22]\) because the step is \(0.011466\) s and not \(0.011206\) s after 06.28's repair above; the integer window \(k\in[34,150]\) is the one row C-26 of 06.3 already carries, and verse and column now agree. The finding's demand is met in full: no \(k\) in \([1,150]\) outside the band scores HOLDS, and the region below the band is a refutation.
06.19 — severity strike; replacement survives as filed: false#
Flaw (verbatim). "The prediction range's upper end is unfalsifiable and the sentence naming which numbers break the range is backwards: the most favourable outcome for the project lies outside the range and does not kill it, while both named failure conditions break the lower end and none breaks the upper."
Mechanism (verbatim). "M-20; M-2; D-CALIB-5"
Number (verbatim). "At m=8 the chance accuracy is 1/8=0.125. Under the prediction's own conditions acc_shape=1.0 and acc_d1=0.125 give Delta_A1 = 0.875 > 0.85, outside [0.40,0.85], yet the Kill fires only at Delta_A1 < 0.40. The verse says \"acc_shape<0.90 (the upper end fails)\": a smaller acc_shape lowers Delta_A1 and fails the LOWER end. No stated number produces Delta_A1 > 0.85."
Repair applied — 06.19. The two mislabelled directions are corrected in the verse text with the monotonicity printed (\(\Delta_{A1}\) decreases in \(\mathrm{acc}_{d1}\), increases in \(\mathrm{acc}_{\rm shape}\)), so both previously named numbers are filed where they belong, at the lower end. The upper-end killer is stated explicitly — \(\Delta_{A1}>0.85\), reached whenever \(\mathrm{acc}_{d1}<\mathrm{acc}_{\rm shape}-0.85\) — with the finding's own instance printed as the reachability witness: \(\mathrm{acc}_{\rm shape}=1.00\) against the \(m=8\) chance rate \(0.125\) gives \(\Delta_{A1}=0.875>0.85\). The Kill is frozen two-sided: the prediction dies at \(\Delta_{A1}\) outside \([0.40,0.85]\). A planted negative is added so the upper end fires on a known plant: the copy plant of 06.15 with the one-hop control at chance must read \(\Delta_{A1}\ge0.85\). The If-killed now writes three sentences, one per outcome, and the upper-break sentence says in the open that the contrast is a reproduction-versus-non-reproduction contrast, VOID as a capability number, so the outcome cannot be quoted as a success. Row C-15 of 06.3 already carried "\(\Delta_{A1}>0.85\) is the upper break, the prediction's other kill"; verse and column now agree.
06.20 — severity strike; replacement survives as filed: false#
Flaw (verbatim). "Ruling 3's 0.032 per cent is imported out of its units: applied to a 4,769-parameter arm it demands a match to within 1.53 parameters, which no integer d_model reaches, so the A2 cell is unreachable as registered; Ruling 3's own text permits a 1.5k absolute gap."
Mechanism (verbatim). "V-17 (a threshold imported out of its units); V-11 (a precondition no real draw satisfies); Ruling 3"
Number (verbatim). "0.032% x 4,769 = 1.526 parameters. V17K_RULINGS.md:56-59 @ 99777ab: \"0.032% residual is MATCHED ... Do NOT re-architect to close 1.5k params\" — the tolerance was set on the 25,736,232 vs 25,728,000 LM pair (8,232/25,728,000 = 0.032%). A depth-5 stack's count moves in steps of order d_model per layer, so no setting lands within 1.53 of 4,769."
Repair applied — 06.20. Reading (i) no longer files an A2 prediction. The verse derives, at its own geometry, that Ruling 3's per-cent form demands \(0.032\%\times4{,}769=1.526\) parameters at BED-S scale (V-17), and that its two forms — the per-cent tolerance and the absolute "do not re-architect to close \(1.5\)k params" — are simultaneously satisfiable only at \(p\ge1{,}500/0.00032=4{,}687{,}500\) parameters (DERIVED). The LM pair at \(25{,}728{,}000\) clears that; \(4{,}769\) misses it by three orders of magnitude. The matched-parameter A2 instance is declared UNREACHABLE at \(4{,}769\) and routed to book 04's joint-consistency bed at a count at or above \(4{,}687{,}500\), where the match is stated as an absolute count band with both exact integers printed in the table header and the residual reported in parameters, never in per cent — the integers themselves NOT MEASURED — needs book 04's recount. The unreachability is itself decidable and carries its own kill (a recounted pair with a gap of at most \(1\) parameter restores an A2 row here) and its own plant (a stack stepped by one in \(d_{\rm model}\) must print a count differing from \(4{,}769\) by more than \(1.53\)). Reading (ii), Bet D at the unmatched depth-5 stack, is the reading that runs and is now two-sided. Row C-16 of 06.3 already carried "The matched-parameter A2 instance is UNREACHABLE at \(4{,}769\) and files no row here"; the verse, the column, 06.10's Hypotheses, 06.36's tree A and the Terminal now agree, and no leaf of any tree carries an A2 sentence.
06.13 — severity strike; replacement survives as filed: false#
Flaw (verbatim). "The Evidence cites the device certificate for a bitwise backward the certificate records only with the determinism flag OFF; with the flag ON — the regime the prediction asserts — the certificate records the gradient as not executable."
Mechanism (verbatim). "V-16 (an instrument that cannot measure, reporting a pass); V-24; P-6; B13"
Number (verbatim). "results/k_cert_local.json (arm: arm_smprime, git ab5b485): determinism.flag_off.gradient = {bitwise: true, max_abs: 0.0, repeats: 8}; determinism.flag_on.gradient = {executable: false, error: \"RuntimeError: cumsum_cuda_kernel does not have a deterministic implementation\"}. The verse's prediction is \"solve_triangular repeats bitwise forward and backward over 8 repeats under use_deterministic_algorithms(True)\"."
Repair applied — 06.13. The citation is split by flag and both readings printed with their exact fields: flag_off.forward, .hop and .gradient all bitwise: true, max_abs: 0.0, repeats: 8; flag_on.forward and .hop bitwise: true, max_abs: 0.0, repeats: 8; flag_on.gradient executable: false with the cumsum_cuda_kernel error quoted — together with the certificate's own note that arm_smprime reduces with CUMPROD and that cumsum is measured only as the contrast. The backward half is removed from this verse's prediction: the Statement predicts the strict-mode forward only, the Kill reads on the forward's max_abs over 8 repeats, and a strict-mode backward raise is stated not to decide this verse. The record's solve_triangular strict-mode forward-and-backward sentence is pinned to its own producer, READ docs/CEQ_SHAPE.md:2680 @ 99777ab (RUN[NEPTUNE], undocumented — B13), is not used as evidence here, and the re-certified value is filed NOT MEASURED — needs N-01 (06.34). The If-killed's deletion of "the first gated wing whose training step runs strict" now names what that sentence rested on. Row C-9 of 06.3 already read "strict-mode forward"; verse and column now agree.
06.11 — severity strike; replacement survives as filed: false#
Flaw (verbatim). "The prediction 10/10 is refuted at its own Evidence pin before any build runs: the cited target list already grades two rows as demoted pending unconfirmed Mathlib names, and the counter's point estimate names one row where the source names two."
Mechanism (verbatim). "P-11 (a contract citing its own [M]-tagged theorem as settled); V-10 (a gate whose outcome is fixed by construction); L-LEAN"
Number (verbatim). "docs/CEQ_SHAPE.md:2608 @ 99777ab: lower_triangular_isUnit, diag_one_sub_smul_pos — \"[M]->[S] until Matrix.det_of_lowerTriangular [U] is confirmed\"; :2609: resolvent_fromBlocks, segmentation_blockdiag — \"[M]->[S] (inv_fromBlocks_zero21_of_isUnit_iff [U])\". Eight rows carry a bare [M]; two are already [M]->[S]. The counter states \"one row demoted\"."
Repair applied — 06.11 and 06.36. The verse itself already carried the repair when this batch opened: the prediction is filed as \(8/8\) on the eight bare-[M] targets, all eight named; the two [U]-blocked rows are carried separately, both graded lines quoted at :2608 and :2609, and never cited as proved; the counter's point estimate on the ten-row denominator is \(8/10\) with both blocked names listed, with the L-SIGN reason printed. Verified line by line against the source pins this session and left standing. What was not repaired, and is repaired here, is the contradiction it left in 06.36: the master tree still read "06.11 \(10/10\)" on tree A and "06.11 \(9/10\)" on tree B — the two counts this finding refutes. Tree A now reads \(8/8\) on the bare-[M] targets with the two [U]-blocked rows still uncited, and tree B at most \(7/8\), i.e. \(8/10\) with both blocked names listed (M-20: two sections may not predict different outcomes).
06.18 — severity strike; replacement survives as filed: false#
Flaw (verbatim). "The deciding floor is the tight restricted-view Fano evaluated at zero mutual information, an instance the source that supplies the bound explicitly excludes, and the verse's own Hypotheses state the restriction and the forbidden instance in one sentence."
Mechanism (verbatim). "L-DOM (a theorem outside its domain census); V-25; P-10; L-FLOOR"
Number (verbatim). "docs/CEQ_SHAPE.md:2491 @ 99777ab: the tight Fano is \"used only where I(X_{<=k}; a*) > 0\". The verse's Hypotheses: \"the tight Fano used only where \(I>0\) is computed (\(0.7124\) at \(m=8\), \(I=0\))\". At m=8, I=0 the admissible floor is the exact zero-information floor 0.875 (same source line, RUN); 0.7124 = (ln 8 - ln 2)/ln 7 is 0.1626 looser than the floor the bed actually has."
Repair applied — 06.18. The deciding number is now \(\mathrm{CP}_{\rm upper}<0.875\), the exact zero-information floor \(1-\max_a\hat\pi(a^\star)\) read at the realised class distribution, \(0.875\) being its value at uniform \(m=8\); the counter is \(\mathrm{CP}_{\rm lower}\ge0.875\) and the SPLIT is the straddle of \(0.875\). The Fano row survives as a printed row only where the plug-in \(I\) over the one-hop view reads strictly positive with its sampling error; where \(I\) reads \(0\) — which is this bed's own registration — the row prints "\(I=0\): Fano decoration, not a floor (L-DOM)" in place of a value, and the verse states in the open that \(0.7124\) is \(0.1626\) looser than the floor the bed actually has, so deciding against it would license a capability sentence at an error rate the zero-information floor already forbids. Book 04's journal rule is cited beside it: floor_fano_k1 is struck from the mandatory field list and a cell carrying it is refused (READ 04_BEDS_AND_INSTRUMENTS.md:233). A second planted negative calibrates the Fano row in both directions on 06.9's flag plant. Mechanisms L-DOM, V-25 and P-10 are added. Row C-14 of 06.3 and 06.19's Hypotheses are reconciled to the same rule.
06.24 — severity strike; replacement survives as filed: false#
Flaw (verbatim). "The counter is not of equal specificity to the prediction: the two halves are read at different designs and different N, so both can hold or both fail, and the verse's own Kill contradicts the Statement by putting both at N=36."
Mechanism (verbatim). "L-SIGN (a counter-prediction of equal specificity beside every prediction); D-7; M-7 (a pre-registration with a hole)"
Number (verbatim). "Statement: prediction \"inside the +-0.5 sigma margin ... at the paired tier \(N=36\)\"; counter \"outside at the two-sample tier \(N=70\)\". Kill: \"The prediction dies at the interval outside the margin at \(N=36\); the counter at inside at \(N=36\).\" The two sentences disagree on the counter's cell."
Repair applied — 06.24. The verse is refiled as three rows at one cell each. Row C-33 is the tier selection, made a filed row with its own deciding number \(r=\mathrm{sd}_d/\sigma\) from S-62's realised sds: prediction \(r\le0.7071\) selecting the paired tier \(N=36\), counter \(r>0.7071\) selecting the two-sample tier \(N=70\), no SPLIT because \(r\) is a number and not a band; the threshold \(1/\sqrt2\) is frozen here and its conservatism derived — the paired design reaches power \(0.8014\) at \(N=36\) against a \(0.5\sigma\) margin when \(\mathrm{sd}_d=\sigma\), only \(0.0014\) above target, so the boundary is set where power survives a \(\sqrt2\) error in the sd. Row C-20 files both halves at the tier C-33 selects — inside against outside at one cell, exhaustive, so they can neither both hold nor both fail. Row C-34 files the \(N=70\) two-sample reading as its own row, never as C-20's counter, and is VOID as a duplicate where C-33 selects \(N=70\). The Hypotheses add that C-33 is read and recorded before C-20's interval is computed, so the tier is never chosen from the interval it decides, and that both tier prices are pre-registered so the selection changes no budget decision. A plant is added: a tier row fed \(\mathrm{sd}_d=\sigma\) must select \(N=70\). Rows C-20, C-33 and C-34 of 06.3 already carried this shape; the verse now matches them, and the Kill reads on the selected tier in all three rows.
06.22 — severity strike; replacement survives as filed: true#
Flaw (verbatim). "Statement and Kill disagree on the prediction's conjunction: the Statement requires both the NRMSE gap and the residual ratio, the Kill kills the prediction only when both fail, so a mixed outcome scores HOLDS on a prediction that is false as written and no branch covers it."
Mechanism (verbatim). "M-7 (a pre-registration with a hole); D-7; M-20"
Number (verbatim). "Statement: prediction = gap > MDE_8 on >=6/8 and residual smaller by more than 2x. Kill: \"The prediction dies at within \(\mathrm{MDE}_8\) on \(\ge6/8\) with residual within \(2\times\); the counter at separated by more on \(\ge6/8\) or residual ratio \(>2\).\" The outcome (gap > MDE_8, residual within 2x) kills the counter, does not kill the prediction, and is not the declared SPLIT (\"escalation\")."
Repair applied — 06.22. The Kill is made a conjunction matching the Statement: the prediction dies if either half fails — gap within \(\mathrm{MDE}_8\) on \(\ge6/8\), or residual ratio at or below \(2\times\), either one alone — and the counter, being the opposite conjunction, dies if either of its halves fails. The two mixed outcomes are given their own named branches in a four-row branch table, each with the sentence it licenses: SPLIT-sep (separated, not residual — component (e)'s residual claim dies and only the read claim escalates to \(N=16\)) and SPLIT-res (residual, not separated — the capability sentence is withdrawn and the residual is filed as 06.21's diagnostic column). Both are scored wrong with the sign of the optimistic half under 06.1, and the verse states that neither is "escalation": escalation is what the COUNTER branch triggers and is named as such. Row C-18 of 06.3 already named the two mixed outcomes; the verse now matches it, and the pre-written replacement — which MARS found survives — is untouched.
06.32 — severity strike; replacement survives as filed: false#
Flaw (verbatim). "The deciding statistic is confounded: the exponent in s is fitted over four points whose per-step size n varies by a factor of 256, so a solve whose true cost is exactly quadratic in s reads an exponent that neither contains 2 nor lies toward 3, and no half of the bet nor its SPLIT has a branch."
Mechanism (verbatim). "D-3; M-8; V-17; K-9"
Number (verbatim). "Points (s,n) = {(64,2048),(256,2048),(1024,128),(4096,8)} (docs/PLAN.md:727 @ 99777ab). Under cost = c.n.s^2, log2 cost at the four points is 23, 27, 27, 27 against log2 s = 6, 8, 10, 12. OLS slope = Sxy/Sxx = 12/20 = 0.60. The prediction (\"contains 2, excludes 3\"), the counter (\"excludes 2 toward 3\") and the SPLIT (\"contains both\") all fail at 0.60."
Repair applied — 06.32. The deciding statistic is redefined as seconds per step per unit \(n\), declared in the Statement and added as the first Hypothesis, before the sweep (M-2). The finding's arithmetic is reproduced inside the verse as the reason: under \(\mathrm{cost}=c\,n\,s^2\) the un-normalised \(\log_2\) costs are \(23,27,27,27\) against \(\log_2 s=6,8,10,12\) and the OLS slope is \(S_{xy}/S_{xx}=12/20=0.60\), at which the prediction, the counter and the SPLIT all fail and no branch exists; normalised, the same points read \(12,16,20,24\) and the slope is exactly \(2\), so the band is well posed on the normalised statistic and on no other. The normalisation's own assumption — linearity in \(n\) at fixed \(s\), asserted by the record's two laws at \(n^{0.9963}\) and \(n^{1.0026}\) — carries a third kill: a fitted exponent in \(n\) outside \([0.99,1.01]\) strikes the statistic and every reading on it. The residency refusal at \((2048,4096)\) is journalled as a missing point, never imputed. A second planted negative is added: the depth-1 control's un-normalised exponent over these four points must read \(\approx0.60\), so the confound is demonstrated on a known-quadratic arm before any shape number is read — which is what the verse's own planted negative already asserted about reading the allocator instead of the arm. Row C-28 of 06.3 already read "per unit \(n\)"; the verse now matches it.
06.5 (first finding) — severity strike; replacement survives as filed: false#
Flaw (verbatim). "The replacement's kill rests on a comparison that is false at the book's own numbers: MDE_16 = 0.081841 is not larger than the largest contrast any bet can show, so the Terminal it reaches is not licensed."
Mechanism (verbatim). "M-3; M-9; V-17"
Number (verbatim). "The verse: \"sd at \(N=16\) still above \(0.109199\) makes \(\mathrm{MDE}_{16}=0.081841\) larger than the largest contrast any bet can show ... the \(\varphi\)-NRMSE contrasts are capped by the floor at \(0.0\)\". The cap is softmax's one-hop error, not zero: 06.19 files Delta_A1 in [0.40,0.85], 06.14's one-hop threshold is 0.7071067811865476, and 06.14's uncapped eval NRMSE readings are 1.152430 / 1.113403 / 1.139404. Each exceeds 0.081841 by 4.9x to 14x."
Repair applied — 06.5. Already repaired when this batch opened; verified against the finding's numbers this session and left standing, unsoftened. The false comparison is deleted and the verse strikes it by name: "The claim that 'the \(\varphi\)-NRMSE contrasts are capped by the floor at \(0.0\) against softmax's one-hop error' is struck here as false", with every one of the finding's counter-numbers printed and divided out — \(1.152430\), \(1.113403\) and \(1.139404\) at \(14.08\times\), \(13.60\times\) and \(13.92\times\) \(\mathrm{MDE}_{16}=0.081841\), the one-hop threshold \(0.7071067811865476\) at \(8.64\times\), and the filed \(\Delta_{A1}\) band's lower end \(0.40\) at \(4.89\times\), all DERIVED by division. The replacement's kill is rebuilt as a conjunction asserting no cap — "the realised sd at \(N=16\) still at or above \(0.109199\) and the smallest filed contrast, read in its own realised sd units, below \(\mathrm{MDE}_{16}\)" — with the contrast list printed in the same block and the per-statistic units separated, and the row reads NOT MEASURED — needs S-62's realised sd per statistic (book 04) where that sd is not yet printed.
06.4 — severity strike; replacement survives as filed: false#
Flaw (verbatim). "The list of the eight rows scorable under tree C contradicts 06.7's own If-killed and 06.36's tree C: it names three rows those verses declare VOID and omits three the tree says still run."
Mechanism (verbatim). "M-20 (two sections predicting different outcomes); D-7; M-7"
Number (verbatim). "06.4 Hypotheses: \"under tree C the eight are drawn from C-1, C-2, C-3, C-4, C-5, C-7, C-8, C-9, C-10 and C-30\". 06.7 If-killed: \"Every cell from S-14 to S-65 is VOID and unscored (06.8 to 06.27 file VOID)\" — this voids C-4 (06.8, S-14/S-15) and C-5 (06.9, R-07/R-24); docs/PLAN.md:368 @ 99777ab voids the arena, so C-1 (06.5, S-62's realised sd) is VOID too. 06.36: \"Tree C ... 06.28, 06.32, 06.33, 06.34 still run\" = C-24, C-28, C-29, C-30, of which 06.4 names only C-30. The surviving eight are C-2, C-3, C-7, C-8, C-9, C-10, C-24, C-28, C-29, C-30, not the ten listed."
Repair applied — 06.4, 06.7 and 06.36. 06.4's list was already rewritten to C-2, C-3, C-7, C-8, C-9, C-10, C-24, C-28, C-29 and C-30, with the S-20 and S-52 cells named BED-M-hosted so PLAN's blanket sweep does not reach them; verified this session and left standing. The two sections it still contradicted are repaired here. 06.7's If-killed now reads that the VOID sweep is the cards on BED-S — 06.8, 06.9's arena half (C-32), 06.10 and 06.15 to 06.27 — and is not every verse in the numeric span: 06.11 (a Lean build), 06.12 (S-61's synthetic plants), 06.13 (S-20 on BED-M's e3_t2) and 06.14 (S-52, the R1 retake) are hosted outside the S-14-to-S-65 range and still run. 06.36's tree C now lists 06.6, 06.11, 06.12, 06.13, 06.14, 06.28, 06.32, 06.33 and 06.34 as still running, with their rows named as exactly the tree-C pool 06.4 reads. All three sections now state one outcome.
06.5 (second finding) — severity strike; replacement survives as filed: false#
Flaw (verbatim). "The Terminal claims B5's \"no realised sd\" is closed whichever half holds, but the print it relies on comes from the arena, which the book's own point estimate (06.7's counter, tree C) forbids; on the reported branch B5 is not closed."
Mechanism (verbatim). "D-CALIB-1; D-4 (registration without admission); FOUND-not-NAMED"
Number (verbatim). "06.5 Terminal: \"B5's 'no realised sd' is closed by the print itself, whichever half holds\". docs/PLAN.md:368 @ 99777ab (S-12 KILL): \"The bed is not admitted, no arm runs, every card from S-14 to S-65 is VOID\". S-62 is the arena card that prints the realised sd. 06.7's counter is the point estimate under D-CALIB (7 of 8 optimistic, p=0.0352)."
Repair applied — 06.5 and the census-rows table. 06.5's Terminal was already rewritten to state the closure conditionally — "B5's 'no realised sd' half closes only on admission … on that branch, which is the book's own point estimate (06.7's counter under D-CALIB, 7 of 8 optimistic, \(p=0.0352\)), B5 is closed by the census's printed failure line plus the row 'realised paired sd NOT MEASURED — needs an admitted batch', and by nothing else" — verified this session and left standing. What the Terminal promised and the book did not deliver was its last clause, "the census-rows table carries both branches": the table carried one row. It now carries two — "B5, on admission" and "B5, on tree C (06.7's counter — the book's own point estimate under D-CALIB, 7 of 8 optimistic, \(p=0.0352\))" — the second stating that S-62 never fires, that no realised sd is printed, and that the trained-arm and measured-\(t^\star\) halves close by the same failure line and no number.
06.29 — severity strike; replacement survives as filed: true#
Flaw (verbatim). "The book claims the crossing-step logger that decides T1 and T2 is unspecified, while the neighbouring instruments book already specifies it as a mandatory journal field, and the two books disagree on its sampling rate."
Mechanism (verbatim). "M-20; P-4 (claimed scaffolding that does not exist — here, claimed absence of scaffolding that does); D-7"
Number (verbatim). "06.29: \"NOT MEASURED - needs book 04's per-step evaluation logger inside S-62 (eval every 10 steps on the held-out $4096$)\"; 06's Limits: \"a per-step evaluation logger the plan does not yet specify; until book 04 specifies it those four rows are filed and unscorable\". 04_BEDS_AND_INSTRUMENTS.md:215 already requires the fields eval_trace (per-step eval NRMSE, for T2) and secs_sync and run_index (for T1), \"a missing declared field is a refusal\", and 04:152 reads the crossing step off that trace."
Repair applied — 06.29, 06.30, 06.31 and the Limits. The "the plan does not yet specify" clause is deleted from the Limits and replaced by the citation: eval_trace (per-step eval NRMSE, for T2), secs_sync and run_index (for T1) are mandatory journal fields and a missing declared field is a refusal — READ 04_BEDS_AND_INSTRUMENTS.md:233, which is the field list the finding cites at :215 and which sits at :233 at this book's HEAD, with the crossing step read off that trace at :170 (the finding's :152), where the identical-seed floor \(0.0\) makes the crossing step exact per seed. The sampling rate is reconciled in favour of book 04's field: every step, not every tenth, and the resolution that choice implies is printed — at one entry per step the crossing-step resolution is \(1\) step, so \(k=66\) and \(k=67\) are separable and both this verse's kill and 06.31's \(k=30\) boundary are decidable; at one entry per ten steps the resolution is \(10\) steps, which separates neither, and a journal sampling at ten is added as a planted negative the adjudicator must refuse rather than read at resolution \(10\). The four rows are now stated to be unscorable because no cell has run to populate the field, not because the logger is unspecified. Mechanism M-20 is added to 06.29 naming the reconciliation.
06.3 (first finding) — severity strike; replacement survives as filed: false#
Flaw (verbatim). "The 31-row denominator carries no row for either use the CHARTER §0 says decides the module, and the book that owns those uses files no prediction at all, so 06.1's rule that every prediction row of the canon is scored is unmet exactly where the module is decided."
Mechanism (verbatim). "D-7 (a prediction filed without its counter); L-SIGN; D-CALIB-2"
Number (verbatim). "RUN this session: grep -in \"chess\\|market\" docs/canon/06_PREDICTIONS.md returns 0 hits; grep -c \"Prediction:\" docs/canon/09_CHESS_AND_MARKETS.md returns 0. 09 schedules deciding cells 09.10 (chess census, 0 GPU-s), 09.13, 09.14, 09.32 (market census, 0 GPU-s), 09.34, and 09.31 is titled \"PnL under constraints as a scored prediction, with its counter and SPLIT band\" — none appears among C-1..C-31."
Repair applied — 06.3 and the Limits. The denominator was already extended when this batch opened: rows C-35 (09.10, the chess census at \(0\) GPU-s), C-36 (09.13, the first chess cell), C-37 (09.32, the market census with the martingale-identity plant), C-38 (09.34, the first market cell with the market's Brier and log score as the printed baseline) and C-39 (09.31, the paired per-contract PnL difference against the market-following rule as the counter, with the e-process value) each carry a prediction, a counter of equal specificity, a SPLIT band and a deciding number; the Hypotheses record that C-35 to C-39 are VOID until book 09's generators exist. Verified this session and left standing. What was not repaired is the sentence the finding's required repair names last: the closing Limits still read "Thirty-one rows is the whole denominator". It now reads "Forty rows are filed, C-1 to C-40; the denominator is the thirty-nine of C-1 to C-39", with C-40 excluded from the count it reads, the five book-09 rows named, and the reason printed — the two uses the author names are where the module is decided, and a denominator without them scores everything except the thing that matters. The B6 row of the census table, which read "thirty-one rows filed", is corrected to the same counts.
06.3 (second finding) — severity strike; replacement survives as filed: false#
Flaw (verbatim). "The pre-written replacement cannot pass its own refusal check: the file it names holds seven rows while the check it cites demands twenty-four."
Mechanism (verbatim). "V-9 (a repair that changes nothing); M-7; P-4"
Number (verbatim). "06.3 If-killed: \"the five-bet file of S-60 alone (Bets A to E plus S-52's and the blank LM row)\" = 7 rows. 06.3 Kill's planted negative cites 24/24 at READ docs/PLAN.md:576; docs/PLAN.md:576 @ 99777ab: \"measure the count of rows with both halves signed against the count of rows: it must read 24/24.\" docs/PLAN.md §5.5 lists thirteen bets A to M, not five."
Repair applied — 06.3 and the kills table. The If-killed was already rewritten when this batch opened: the replacement file is named by its actual content, the thirteen bets A to M of READ docs/PLAN.md:912-924 @ 99777ab (Bet I being S-52's and Bet M the language-model row left blank until an LM cell exists); the count check that file must pass is stated as 13/13 rows with both halves signed; PLAN's 24/24 is refused as a check the replacement may not inherit and is owed to CORRECTIONS.md as a row against docs/PLAN.md:576; and S-60's own seven-row build line at :574 is quoted and set aside in favour of the table, which is the file's content. Verified this session and left standing. What was not repaired is the "Kills, cheapest first" table, which still routed 06.3 to "the five-bet file of S-60"; that row now reads "the thirteen-bet file of S-60 (Bets A to M, 13/13 signed; PLAN's 24/24 owed to CORRECTIONS.md)".
Open findings after this batch: none. Every finding of severity strike in batch 1 is repaired in the verse it names, and no verse was deleted to escape one. Six findings (06.11, 06.5 first, 06.4, 06.5 second, 06.3 first, 06.3 second) were carried in part by an earlier batch; each was verified against its source pin this session, left standing where correct, and completed here where the earlier repair had left a contradicting section, table row or closing sentence behind — those completions are recorded above and are why none of the six is closed on its verse alone. Three replacements that MARS found died with their verses were re-derived rather than renamed: 06.28's (now the MAC law killed by a \(0\)-GPU-s shape audit against 08_ARCHITECTURE.md:108/:477 — a different number, a different instrument, a different object from the wall-clock band it replaces), 06.20's (now A2 on a joint-consistency bed at \(p\ge4{,}687{,}500\), where the residual is stated in parameters and the kill is 06.21's residual ratio, not a parameter count), and 06.5's (now a conjunction on the realised sd and the smallest printed contrast, asserting no cap).
MARS's findings, repair round 1, batch 2 of 2. Same rule as batch 1: every finding reproduced verbatim in the four fields it was filed with — flaw, mechanism, number, severity — beside the repair applied, its verse id, and what changed. Every finding of this batch was filed with replacement_survives: true, so no pre-written replacement of this batch died with its verse and none had to be re-derived; where a replacement was touched at all, the change is stated. Nothing is softened.
06.13 — severity strike; replacement survives as filed: true#
Flaw (verbatim). "The outcome partition has a hole below the prediction band: a cell faster than the law falls in no branch, which is precisely the condition 06.36's own Kill declares refuting."
Mechanism (verbatim). "M-7 (a pre-registration with a hole); D-7; M-20"
Number (verbatim). "Prediction: the cell inside [-1.8, +14.4] per cent of 1.680 s, i.e. multiplier in [0.982, 1.144]. SPLIT: (1.144, 2.2). Counter: >= 2.2. The interval [0, 0.982) is unbranched. 06.36 Kill: \"The tree is refuted if a scored outcome has no branch\". Same hole in 06.28 and in rows C-9 and C-24 of 06.3."
Repair applied — 06.13, 06.28. The fourth branch is added in both verses, named, and given its own sentence. The counter is split into COUNTER-dear (cell \(\ge2.2\times\) the law) and COUNTER-cheap (cell \(<0.982\times\) the law, frozen at \(<1.65024\) s against the law's \(1.680\) s), so the prediction band \([0.982,1.144]\), the SPLIT band \((1.144,2.2)\) and the two counter branches exhaust \([0,\infty)\) with no interval left over. COUNTER-cheap is scored COUNTER and signed + — a cell cheaper than the law flatters every price in this book — and licenses "the fitted law over-predicts the cell by \([\cdot]\) per cent; every [FITTED] price in this book is re-tagged the P-8 floor it was declared to be and re-measured by N-02's producer before any GPU-minute is quoted, with the sign of the miss printed." Both Kills now name both directions, and both rows of the cheapest-first table carry them. Rows C-9 and C-24 of 06.3 already carried the fourth branch from batch 1; verse and column now agree.
06.20 — severity strike; replacement survives as filed: true#
Flaw (verbatim). "The matched parameter count is quoted as an established number in one verse and as an unperformed recount in the next, and its source says it is the number to be recounted, not the recounted number."
Mechanism (verbatim). "P-3 (a stale claim never retracted); Ruling 3; M-2"
Number (verbatim). "06.19: \"at matched parameters (\(4{,}769\) recounted per arm with the \([m,K+2]\) head, Ruling 3)\". 06.20: \"the matched-parameter instance of the depth-5 stack at \(4{,}769\) parameters NOT MEASURED - needs book 04's recount\". docs/PLAN.md:314 @ 99777ab: \"the \(4{,}769\) of READ CEQ_V20_R15_CONTRACT.md:119 recounted, never assumed, once a \([m,K+2]\) head or a vector readout is attached\"."
Repair applied — 06.19, 06.20, 06.29. \(4{,}769\) is written everywhere as the pre-head count with the class READ CEQ_V20_R15_CONTRACT.md:119 @ 99777ab (verified this session: the line reads "4,769 params matched (exact counts printed), 150 steps, N=8, one"), and the post-head count with the \([m,K+2]\) readout attached is filed NOT MEASURED — needs book 04's recount in the same breath. 06.19's deciding-number sentence "recounted per arm with the \([m,K+2]\) head" asserted the recount as performed and is struck in the verse, with the strike printed there rather than silently rewritten: the source line is the instruction to recount, not its result. 06.19's If-killed sentence now reads "at a pre-head matched count of \(4{,}769\) … the post-head counts printed as two integers or the row unscored". 06.29's Hypotheses carry the same pair. 06.20(i) prints the class at the first appearance of the number and states that no verse of this book may print the recount as performed. 06.10 already carried the pre-head/post-head split from batch 1.
06.1 — severity strike; replacement survives as filed: true#
Flaw (verbatim). "Fourteen READ pins name the wrong card or a blank line; under CHARTER §3 the pin is what makes the citation admissible, so each load-bearing number cited through them is unverified at its stated location."
Mechanism (verbatim). "P-6 (line-reference drift); P-1; P-2"
Number (verbatim). "All at 99777ab. 06.6 :1067-1069 cited for \"the DAG's depth is a registered dial\" = smaller-deaths rows for S-20/S-62/R-21. 06.7 :1057 cited for the sink share [0.362,1.000] = blank line; the number lives at :352 and :1054. 06.11 :232 cited for \"169 theorems over 12 files\" = J-L18's PASS/KILL; the 169 is at :231. 06.14 :950 cited for C15's \"13 of 40\" = R-16/K-D2; the 13 of 40 is at :644. 06.15 :640-645 cited for S-62's K-D2 line = S-51 tail and S-50; S-62 is at :626-633. 06.18 and 06.36 :1058-1060 cited for tree B's sentence = the smaller-deaths heading and table header; tree B is at :1054. 06.20 and 06.30 :611-617 cited for S-35 = S-33 tail and S-34; S-35 is at :619-625 (02_THEORY_TRAINING.md:467 cites it correctly). 06.22 :589-595 cited for S-31 = S-30; S-31 is at :594-600. 06.22 :688-693 cited for S-64 = S-65; S-64 is at :682-687. 06.23 :599-604 cited for S-33 = S-31 tail and S-32; S-33 is at :607-612. 06.24 :706-712 cited for S-65 = census lines 12/13 and M-4.5; S-65 is at :688-699. 06.24 :958 cited for R-22 = R-25/K-G1; R-22 is at :956. 06.26 :964 cited for R-10 = blank; R-10 is at :959. 06.36 :1064-1066 cited for tree C's sentence = smaller-deaths rows; tree C is at :1056."
Repair applied — 06.1, and the twelve verses that carry the pins. All fourteen are re-pinned to the lines the finding names, each correction printed in the verse that carried the wrong pin so the drift is on the record and not silently fixed. The audit is recorded in 06.1 as a paragraph listing every re-pin, because under CHARTER.md §3 the pin is what makes the citation admissible and a book that re-pins without saying so has hidden a P-6. Every number those pins carry was re-read at the corrected line at 99777ab and reproduced: 13 of 40 and the one-hop threshold \(0.7071067811865476\) at :644; S-62's K-P kill and realised-sd block at :626-633; S-35's \(\approx7.6\) s per cell [ASSUMED] and \(\approx64.8\) s at eight seeds at :619-625 — the same pin 02_THEORY_TRAINING.md:467 uses, as the finding requires; S-64's \(\approx44\) s (\(3\times8\times1.681+4\)) at :682-687; S-65's \(119\) s paired at \(N=36\) and \(228\) s two-sample at \(N=70\) at :688-699; R-22's \(0.8807\sigma\) against the \(0.5\sigma\) margin at :956; R-10's one exceedance on \(1{,}024\) draws and \(\delta\|V\|_\infty\) against the label sd at :959; S-31's \(1.680\) s per cell and \(\approx52\) s for three arms at :594-600; S-33's \(1.680\) s per cell and \(\approx35\) s for two batches at :607-612; tree B's sentence at :1054 and tree C's at :1056. The pins of 06.6, 06.7 and 06.11 were corrected in batch 1 and are listed in the audit for completeness. Tree A's :1052 and the sink-share :352 were re-verified and were already correct.
06.30 — severity repair; replacement survives as filed: true#
Flaw (verbatim). "The stated range and the stated crossing-step interval are inconsistent at both ends; neither endpoint of k in [34,150] maps into T1_sky in [0.05,0.22]."
Mechanism (verbatim). "M-2 (thresholds frozen); V-17"
Number (verbatim). "T1_sky = k*0.011206/7.62375 = 0.00146988k. At k=34: 0.049976 < 0.05. At k=150: 0.220482 > 0.22. The verse's own constant 0.0014700 and its own value 0.2205 at k=150 both fall outside the range [0.05,0.22] it files."
Repair applied — 06.30. The mapping constant is printed at six places and recomputed on the step the verse now carries: \(0.011466/7.62375=0.00150398\), so \(T1_{\rm sky}=0.00150398\,k\), reading \(0.05113545\) at \(k=34\) and \(0.22559764\) at \(k=150\) — both inside the filed band \([0.0511,0.2256]\), at both ends and at every integer between. The constant \(0.0015047\) the verse printed after batch 1 is corrected with the reason printed in the verse: it reads \(0.225705\) at \(k=150\), outside the band the same verse files, so the printed constant and the printed range disagreed at the upper end. The finding's own arithmetic used the pre-batch-1 step \(0.011206\) s and the band \([0.05,0.22]\); the defect it names — range and crossing-step window not mapping into each other at either end — is the same defect at the new constant and is repaired at the new constant, not argued away by the change of step.
06.24 — severity repair; replacement survives as filed: true#
Flaw (verbatim). "The 0.8807 sigma half-width used to strike every N=8 parity sentence is the two-sample formula, applied inside a verse whose declared design is paired."
Mechanism (verbatim). "V-17 (a threshold imported out of its units); M-13; M-9"
Number (verbatim). "MISTAKES.md:1216-1219 @ 99777ab: \"The 90% confidence interval for a two-sample contrast has half-width t(.95, 2N-2) . sigma . sqrt(2/N) ... at N = 8 the half-width is 0.8807\". Check: t(.95,14)=1.7613, sqrt(2/8)=0.5, product 0.88065. The paired half-width at N=8 is t(.95,7)/sqrt(8) = 1.8946/2.8284 = 0.6699 sd_d — still above the 0.5 margin, so the conclusion survives, but the printed number is from the other design."
Repair applied — 06.24, 06.10. The paired half-width is printed as the number that strikes the \(N=8\) parity sentence: \(t_{.95,7}/\sqrt8=1.894579/2.828427=0.669835\,\mathrm{sd}_d\), above the \(0.5\) margin, so two bit-identical arms return NO VERDICT at \(N=8\) on the verse's own paired design. \(0.8807\sigma\) is kept and named for what it is, the two-sample half-width \(t_{.95,14}\,\sigma\sqrt{2/8}=1.7613\times0.5=0.88065\) of READ MISTAKES.md:1216-1219 @ 99777ab, imported out of its units at filing. The quotient is written \(0.669835\) rather than the finding's \(0.6699\) because \(1.894579/2.828427=0.6698345\) — the same number, rounded up at the fourth place in the finding and printed to six here so the two designs cannot be confused by a rounding; 06.10's copy of it is corrected to match. The conclusion is unchanged and is not softened: no parity sentence at \(N=8\), on either design.
06.10 — severity repair; replacement survives as filed: true#
Flaw (verbatim). "The counter — which sends the whole canon down tree C, the most destructive branch — fires on a failure to reject at the widest interval in the book, and the book refuses exactly this reading two verses later."
Mechanism (verbatim). "M-13 (an equivalence margin registered without a reachability check); M-9; V-5"
Number (verbatim). "06.10 counter: \"the 0-hop MLP inside the half-width, or \(p>0.05\)\" where the half-width is the shape's Clopper-Pearson at N=8. MISTAKES.md:1216-1222 @ 99777ab records that at N=8 the half-width (0.8807 sigma two-sample; 0.6699 sd_d paired) exceeds the 0.5 sigma margin, and \"TOST power at a true difference of zero ... reads 0.000 at N = 8\". 06.22 files the opposing rule: \"never 'within TOST' at \(N=8\) (M-13)\"."
Repair applied — 06.10, and the cheapest-first table. The seed-level equivalence reading at \(N=8\) is deleted from the deciding number and the kill is moved onto McNemar at the eval draw count, with the minimum detectable difference fixed in the verse before any cell: on \(n_{\rm eval}=4096\) paired draws, rejection at \(\lvert b-c\rvert/\sqrt{b+c}>1.96\) and power \(0.80\) at \(\ge2.8016\), so \(\mathrm{MDE}_{\rm McN}=2.8016\sqrt{d/4096}=0.04378\sqrt d\) — \(0.01384\) at a discordant fraction \(d=0.10\), \(0.03095\) at \(d=0.50\). A non-rejection now carries a detectable-effect size and may fire tree C; a non-rejection with no printed \(\mathrm{MDE}_{\rm McN}\) may not; and no non-rejection at \(N=8\) seeds may fire tree C at all, which is the rule 06.22 files and which this verse now files in the same words. The verse body carried this from batch 1; what this finding closes is the stale row in the cheapest-first table, which still read "0-hop MLP inside the half-width or \(p>0.05\)" and would have sent a reader down tree C on the very reading the verse refuses. The row now prints the McNemar form and the M-13 prohibition.
06.29 — severity repair; replacement survives as filed: true#
Flaw (verbatim). "The two halves of one prediction disagree with each other and with the frozen kill at the crossing step the verse itself names."
Mechanism (verbatim). "M-2 (a threshold frozen inconsistently); V-17"
Number (verbatim). "T1_d1 = k0.011206/(1500.010165) = 0.0073494k; T2_d1 = k/150. At k=68: T1 = 0.49976 <= 0.50 (prediction holds) but T2 = 0.453333 > 0.45 (prediction fails). The Kill reads \"The prediction dies at a crossing step \(>68\)\", so k=68 does not kill a prediction one of whose halves is false there. T2 <= 0.45 requires k <= 67."
Repair applied — 06.29. Both mappings are printed in the verse: \(T1_{d1}=k\times0.011466/1.52475=0.00751992\,k\) and \(T2_{d1}=k/150\) exactly. The two halves bind at different integers and the verse now says which governs: \(T1\) binds at \(k\le66\) (\(0.49631\) at \(66\), \(0.50383\) at \(67\)) while \(T2\) alone would allow \(k\le67\) (\(0.44667\) at \(67\), \(0.45333\) at \(68\)), so the frozen kill is \(k>66\) and no integer satisfies the prediction while the kill fires, nor fires the kill while both halves hold. The finding's arithmetic used the pre-batch-1 step \(0.011206\) s, where the binding half was \(T2\) at \(k\le67\) and the filed kill at \(>68\) let two integers score HOLDS on a false prediction; at the current step the binding half is \(T1\) and the integer is \(66\). The defect the finding names — the two halves and the kill agreeing at no single integer — is closed by printing both mappings and naming the binding half, which is exactly its required repair, and the verse records the filed kill "\(>68\)" and why it was wrong rather than deleting it.
06.26 — severity repair; replacement survives as filed: true#
Flaw (verbatim). "The planted negative exercises a different bound from the one the Kill decides, so the plant cannot make the verse's own kill fire (V-15)."
Mechanism (verbatim). "V-15 (no condemning rule without a planted negative that fires it); L-CERT; V-10"
Number (verbatim). "Statement's certificate: epsilon||V||_inf/(1-gamma) + delta_Pi||V||_inf. Planted negative: \"rows scaled to \(1.5\) at \(\gamma=0.6\), \(K=2\) must read \(7.29\) against the bound \(0.54\)\" — 0.54 = gamma^{K+1}/(1-gamma) = 0.216/0.4, the Neumann truncation bound, not the mask certificate; and 7.29 = 0.9^3/(1-0.9), the tail of the row-sum-1.5 series. The gamma=0.7 plant's 1.143 = 0.343/0.3 is the same truncation bound."
Repair applied — 06.26. Two plants on the quantity the Kill actually reads are added. Must fire: a mask whose realised perturbation is \(\varepsilon^\star\) but whose journalled \(\varepsilon\) is \(\varepsilon^\star/10\) with \(\delta_\Pi\) at its true value — the certificate is understated by construction, the exceedance count must read strictly above \(0\) on the \(1{,}024\) draws, and the largest realised \(\|z-\hat z\|_\infty\) is printed beside the bound it exceeded. Must not fire: the zero-perturbation mask, \(\Pi=I\), \(\varepsilon=0\), \(\delta_\Pi=0\) — the exact route, certificate \(0\), realised deviation \(0\) — must read an exceedance count of exactly \(0\); a count above \(0\) there is an instrument fault and the cell is refused, not scored. The truncation plants are kept and relabelled in place as N-15's other bound: \(0.54=\gamma^{K+1}/(1-\gamma)=0.216/0.4\) and \(1.143=0.343/0.3\) are the Neumann truncation bound of the \(K\)-hop read, not this verse's mask certificate, the first convergent and reported, the second divergent and never counted — and the verse says in the open that neither is its negative.
06.12 — severity repair; replacement survives as filed: true#
Flaw (verbatim). "A RUN-class negative result is asserted with neither the command nor the keys it searched, so it cannot be reproduced, and the boundary null it disqualifies still gates Bet C with no admissible citation."
Mechanism (verbatim). "P-1 (a number with no live producer); P-2; L-EQ"
Number (verbatim). "06.12 Evidence: \"the citation for the boundary null is owed (not in docs/references.bib, RUN grep -c this session reads \(0\) for the two candidate keys) and the canon does not name it\". Neither key is named and no command string is given; CHARTER §3 requires \"cited as RUN with the exact command\". The quantile 2.705543 and the threshold ln 4096 = 8.317766 rest on the unnamed null."
Repair applied — 06.12, and the Limits paragraph. The exact commands and their outputs are printed, RUN this session: grep -c 'chernoff' docs/references.bib \(=0\); grep -c 'self-liang' docs/references.bib \(=0\); grep -niEc 'chernoff|self.?liang|chibar|chi-bar' docs/references.bib \(=0\). The two candidate key strings are named — chernoff-1954-boundary and self-liang-1987-boundary — so the negative is reproducible. The theorem is named so a reader can supply the reference: the asymptotic null of a likelihood ratio at a parameter-space boundary is the half–half mixture \(\tfrac12\chi^2_0+\tfrac12\chi^2_1\), \(95\) per cent point \(2.705543\), classically Chernoff (1954) and Self and Liang (1987, boundary case 5), both NOT FOUND at [V-eq] in this tree. What the absence blocks is stated exactly: every PINNED verdict, \(\Lambda\le2.705543\), in 06.12, 06.16 and 06.35, including this verse's own \(8/8\) PINNED plant count. It does not block the MOVED threshold: \(\ln4096=8.317766\) is read off the declared held-out size \(n_{\rm eval}=4096\) and stands without the null — the finding's sentence that both rest on it is narrowed here to the one that does, with the arithmetic for the other printed.
06.4 — severity repair; replacement survives as filed: true#
Flaw (verbatim). "The verse files a prediction and a counter but has no row in the denominator it predicts about, so the canon's own meta-prediction escapes the calibration column it institutes."
Mechanism (verbatim). "D-CALIB-5 (the row is appended whether or not it flatters); D-7; L-SIGN"
Number (verbatim). "06.3's table runs C-1 (06.5) to C-31 (06.35), 31 rows, one per verse 06.5-06.35; 06.4 has no row. 06.3 closes: \"Thirty-one rows is the whole denominator\". 06.1: \"Every prediction row of the canon is scored with exactly one token\"."
Repair applied — 06.3, 06.4, the B6 census row and the Limits paragraph. 06.4 is row C-40 of 06.3's table, with its deciding number printed there — the count of + among the first eight scored non-VOID rows of C-1 to C-39 — prediction \(\le4\), counter \(\ge6\), SPLIT exactly \(5\). It is scored after that eighth row and excluded from the count it reads by an explicit clause in 06.3's Hypotheses, so the meta-row sits in the column without entering its own denominator, which is the thirty-nine of C-1 to C-39. D-CALIB-5 is stated as applying to it in full: the row is appended whether or not it flatters. The repair was applied in batch 1 when the column was extended to forty rows; this finding is answered by the same construction and is recorded here so the batch-2 sheet is complete rather than silently short.
06.28 (second finding, repair) — severity repair; replacement survives as filed: true#
Flaw (verbatim). "InfSA-16's per-step figure is tagged DERIVED from a stated hop time, but no arithmetic on the book's own constants reproduces it."
Mechanism (verbatim). "P-1; M-8"
Number (verbatim). "\"InfSA-16's step is \(0.034133\) s (DERIVED from the \(25.409\) ms hop), \(3.046\times\) the shape's.\" Softmax law 0.010165 + 0.025409 = 0.035574 s, not 0.034133; 0.034133 - 0.025409 = 0.008724 s, which is neither the softmax law nor the PV op. The 3.046x ratio reproduces from 0.034133/0.011206 = 3.0460, so only the derivation is missing."
Repair applied — 06.28, and the Limits paragraph. The figure is re-tagged NOT MEASURED — needs S-32's cell, and the ratio against the shape's step — \(2.977\times\) after batch 1's step correction, \(3.046\times\) as the finding read it at the old step — inherits the tag. The one derivation the source supports is printed: READ docs/CEQ_SHAPE.md:1926 @ 99777ab prices the InfSA-16 cell at \(\approx5.12\) s per \(150\)-step cell (the same \(\approx5.1\) s at :2510), and \(5.12/150=0.034133\) s per step, one division. The step below that — how \(5.12\) s follows from a \(25.409\) ms hop — is not printed at the source, and the verse now says so with the finding's own arithmetic printed as the demonstration: \(0.010165+0.025409=0.035574\neq0.034133\), and \(0.034133-0.025409=0.008724\) s is neither the softmax law nor the solve increment. The dependent plant is deleted, not weakened: a plant may not rest on a NOT MEASURED number, so "the InfSA-16 cell must read \(\ge2.62\times\) the shape's cell" is replaced by a plant on a number with a producer — the cell contains a \(25.409\) ms hop, so its measured whole step must read at or above \(0.025409\) s, \(\ge1.95\times\) the shape's DERIVED step (\(0.025409/0.011466=2.2160\) less the \(12\%\) clock spread), and a timer reporting the arm faster than the hop it contains is refused.
06.7 — severity repair; replacement survives as filed: true#
Flaw (verbatim). "The Hypotheses misidentify two of the census lines they invoke, so the admission decision names a line the census does not have."
Mechanism (verbatim). "P-6; V-8; D-4"
Number (verbatim). "06.7 Hypotheses: \"the corpus-alone probe and the zero-hop read included as lines 8 and 9\". docs/PLAN.md:366 @ 99777ab (S-12): line (8) is \"the corpus-alone probe of S-15\"; line (9) is \"\(I(s_0;a^\star)=0\) by plug-in\". The zero-hop read is card S-14 (docs/PLAN.md:380-386), not a census line."
Repair applied — 06.7. The Hypotheses name lines 8 and 9 as the corpus-alone probe of S-15 and \(I(s_0;a^\star)=0\) by plug-in, pinned to READ docs/PLAN.md:365 @ 99777ab, and cite the zero-hop read separately as card S-14 (READ docs/PLAN.md:380-386 @ 99777ab), which 06.8 owns and which the census does not carry as a line. The verse prints the correction rather than absorbing it, with the rule it violated stated: an admission decision (D-4) may not name a line the census does not have. Applied in batch 1; recorded here so the batch-2 sheet carries every finding it was filed with.
06.9 — severity repair; replacement survives as filed: true#
Flaw (verbatim). "The verse and 06.19 are each a precondition of the other: R-24's deciding number needs the arena accuracy that 06.19 measures, and 06.19's Hypotheses require 06.9 to have held first."
Mechanism (verbatim). "D-4 (registration without admission); M-7; D-3"
Number (verbatim). "06.9 deciding number: \"the flag rule's accuracy against the shape's (R-24), at \(0\) GPU-s before any arm and at the arena for the paired half\", with the firing number \"\(\mathrm{acc}_{\rm shape}-\mathrm{MDE}_8\)\". 06.19 Hypotheses: \"06.7, 06.8, 06.9 and 06.10 hold (the argmin is not a static task, not a leak, not a flag lookup)\". acc_shape and MDE_8 are both S-62 outputs."
Repair applied — 06.9, 06.3. R-24 is filed as two rows with the circularity named in the verse. C-5, the \(0\) GPU-s half, is decidable against the printed exact zero-information floor \(0.875\) alone, computed at construction on the census draws before any arm exists: a closed-form rule on the membership flags whose argmin error reads below \(0.875\) strikes BED-S's argmin head at \(0\) GPU-s. C-32, the arena half, is the paired accuracy difference against \(\mathrm{acc}_{\rm shape}-\mathrm{MDE}_8\) and is read after 06.19's cell. 06.19's Hypotheses now depend on the \(0\) GPU-s half alone, so neither verse is the other's precondition. Both rows are in 06.3's column with their own deciding numbers, and the planted negative for C-5 — a bed whose move token carries the target's membership flag, which must read the flag rule's error at \(0.0\) and fire C-5's kill before any arm — is filed with it. Applied in batch 1; recorded here in full.
06.28 (third finding, note) — severity note; replacement survives as filed: true#
Flaw (verbatim). "Two READ-class numbers are transcribed from their sources with the wrong digits."
Mechanism (verbatim). "P-6; P-2"
Number (verbatim). "results/k_cert_local.json throughput.laws.softmax.y[2] = 0.040524899999581976; the verse prints 0.040521. COSTS.md:73 @ 99777ab prints the softmax law's R-squared as 0.999998; the verse prints 0.9999975 (08_ARCHITECTURE.md:462 prints 0.999998, matching the source)."
Repair applied — 06.28. The median at \(n=8192\) is printed \(0.040525\), with the file's full value \(0.040524899999581976\) at throughput.laws.softmax.y[2] beside it and the mis-transcription named as such (RUN this session on results/k_cert_local.json). The \(R^2\) was corrected to \(0.999998\) in batch 1 and now carries the file's own \(0.9999975361960808\) beside it, with the note that COSTS.md:73 @ 99777ab and 08_ARCHITECTURE.md:462 both print \(0.999998\), so this book, the cost table and the architecture book agree on the digits.
06.15 — severity note; replacement survives as filed: true#
Flaw (verbatim). "The three-way band with an at-least-six-of-eight rule leaves reachable seed splits with no branch, and the SPLIT clause can name two bands at once."
Mechanism (verbatim). "M-7; D-7; M-9"
Number (verbatim). "Bands: identified [1e-3, 1e-2), counter >= 1e-2, VOID < 1e-3, each on >= 6/8; SPLIT \"3/8 to 5/8\". The split (3 identified, 3 counter, 2 VOID) has no band at >= 6/8 and two bands in [3,5]; the split (5,3,0) likewise names two."
Repair applied — 06.15. The scoring rule is the modal band with its count, frozen in the verse: the eight per-seed sup-norms are binned into the three bands, the modal band and its count are printed, and the token is HOLDS if the modal band is \([10^{-3},10^{-2})\) at \(\ge6/8\), COUNTER if it is \(\ge10^{-2}\) at \(\ge6/8\), VOID if it is \(<10^{-3}\) at \(\ge6/8\). Every other configuration is SPLIT, ties for the mode included, and a SPLIT row prints the ordered triple \((\,\text{identified},\text{counter},\text{VOID}\,)\) so the reading is recoverable. Exactly one token is reachable per outcome and every outcome reaches one: the finding's \((3,3,2)\) is SPLIT with its triple printed, \((5,3,0)\) is SPLIT, \((6,2,0)\) is HOLDS. The Kill and the cheapest-first row carry the same rule, and row C-11 of 06.3 — which already read "the modal band … with its count" after batch 1 — now matches the verse word for word.
Batch 2, closed. Fifteen findings: three strike, ten repair, two note; fifteen repaired, none left OPEN, no verse deleted and no Terminal newly in force from this batch. Every finding of this batch was filed replacement_survives: true, so no pre-written replacement died with its verse; two replacements were nonetheless changed because the finding reached them — 06.26's planted negatives, which now exercise the mask certificate the Kill reads rather than N-15's truncation bound, and 06.28's InfSA plant, which now rests on the \(25.409\) ms hop rather than on a NOT MEASURED step. Three repairs are made by subtraction: a plant deleted (06.28's \(\ge2.62\times\)), a claim struck in place (06.19's "recounted per arm"), and a printed constant withdrawn (06.30's \(0.0015047\)). Where a finding's own arithmetic used a constant batch 1 had already changed — 06.29's \(0.011206\) s step, 06.30's \([0.05,0.22]\) band — the defect is repaired at the current constant and the finding's numbers are reproduced verbatim above, so no repair is credited to a change of denominator. Four findings (06.4, 06.7, 06.9, and 06.10's counter) were closed in the verse body by batch 1 and are recorded here in full rather than dropped; two of them left a stale table row or closing sentence behind, which this batch completed — 06.10's cheapest-first row and 06.15's Kill and table row.