run 096Settled
../lab/runs/096-h-width-curvature-reseed.mdPredictionThe curvature replicates: the fresh c₂ is positive by at least 2 of its own errors. One clause.
FalsifierThe fresh c₂ at or below zero: run 079's curvature does not replicate and S2 keeps its scaffold on H. Between 0 and +2 errors, unanticipated. A fresh c₂ at or below −2 errors is falsified as written and reported as a reversed curvature, not as noise. Readings fixed now: confirmed, and the difference between the fresh and 079's c₂ beyond 2 combined errors (reported) — the two sets disagree beyond their errors and the between-file calibration (runs 081, 087, 092) is reopened on H. Confirmed with the leave-one-size-out c₂ (reported) dropping below +1 error when 81 or 6561 is left out — the curvature rests on the end sizes alone, read as a finite-size effect at 81 and not a correction at large L until a sixth size exists.
Sealed 2026-10-03, after run 079 was scored and after its record was read for this curvature, before any fresh sample exists (codifier). Known at sealing: samples051 and samples079 in full and every number above, which is the pre-seal glimpse and is cited as known, and run 051's set, whose c₂ is +0.00354 ± 0.00272 (+1.30 errors; the sighted pass). The five-point correction fit on run 079's values alone, w = A·L^(−1/ν)(1 + B·L^(−ω)), is ill-determined — its χ² depends on the bounds placed on B, and with B unbounded it runs away — so no clause is written on ω and no value is cited.
What this run is for. Every 1/ν in the census assumes one exponent. S2's removal test on the risers (run 087) was ill-posed with three sizes; H has five at a factor of 3 and is the one pattern where the question is well posed today. A curvature in ln w against ln L is a correction to scaling, and its sign here (pair slopes falling toward larger L) says the effective exponent at 6561 is below the asymptotic one by an amount still moving. Confirmed, every endpoint 1/ν becomes a two-parameter object on at least one pattern and the methods-programme candidate held in PG-01 since 2026-10-02 has its first datum. Falsified, the 2.85-error reading was a 1-in-230 draw (two-sided) and S2 stands.
The codifier's lead, held with conviction. The curvature replicates at about +2.5 errors on the fresh set and +3.8 pooled; the fresh pair slopes fall monotonically as 079's did; the leave-one-size-out c₂ on the fresh set stays above +1 error whichever size is dropped (on 079 it is +1.88 with 81 out and +1.33 with 6561 out, so the end sizes carry it; the lead is that fresh draws keep them); the pooled ten points still do not fix ω (reported with stated bounds on B), so the correction's exponent is the Mac Studio's (L = 19,683) and not this run's. Reported beyond the clauses: run 079's falsified period-two contrast Δ⁴ln w recomputed on the fresh set (expected within 1 error of 0); the skewness g₁ per size with the step pattern 079 reported; the square's c₂ (expected within 1 error of 0); the drift in the census's unit on each set.
Power. At 48,000 samples each ln w error is about 0.005, so c₂'s error is 0.0011 as in 079; a true c₂ of +0.0032 is 2.85 errors on the fresh set. The bar at 2 errors is passed with probability about 0.80 if the 079 value is the truth, and the 079 value was found after the fact, so the truth is probably smaller and that power is optimistic. Under no curvature the clause confirms with probability 0.023, falsifies with 0.50, and is unanticipated otherwise.
Controls, all before any scored quantity is read. (i) Reproduction. curv096.py on samples079/H4 … H8 reproduces parity079.json's per-file w to 1e−12 and ln w errors to 1e−6 with its bootstrap scheme (179001 + 9·b + j), and gives c₂ = +0.003186 ± 0.001118, χ² = 8.280 on 3, and the square's c₂ −0.00249 ± 0.00285 on that set. A failure withdraws the run. Each machine's perc reproduces samples079/H6.txt's first 1,000 k with seed 7903 before drawing. (ii) Integrity. Each H file has 48,000 lines and each square file 24,000, every k in [1, M]; no two files share their first 100 k. md5s of perc.c and of the nine graph files equal the seal's before sampling and at analysis. (iii) The square is straight. The fresh square's c₂ over its four sizes (one degree of freedom) within 3 errors of 0 (079's: −0.87 errors); a failure makes the run reported, not scored. (iv) Fresh against stored, as one test. z at each H size = (fresh ln w − 079's) / combined error; the sum of the five z² at most 16.7 (χ²₅ at p = 0.005); above it the run is withdrawn (a sampler or build difference, run 092's territory). For reference run 051 against 079 gives z = +0.52, +1.71, −0.82, +0.17, −0.33.
Reported, not scored. Per-file p_med, w, ln w, g₁, g₂ with errors on the fresh set; the pair slopes and the drift on each of the three sets; c₂ on 079's set, 051's set, 079 + fresh pooled and all three pooled; the fresh c₂ against 079's (difference over combined error); leave-one-size-out c₂ on the fresh set and pooled; a block check of the fresh H8 ln w error (8 consecutive blocks, spread over bootstrap error, as run 092); the ω profile with B bounded to |B| ≤ 10 on the pooled ten points and on all fifteen; Δ⁴ln w and Δ⁴g₁ on the fresh set beside run 079's; the square's c₂ and 1/ν; wall time and peak RSS per file and machine, with the k-for-k reproduction counts.
The reductio this seal passed first. By construction: c₂ from a quadratic fit on five points is one number with one error, not a shape; a ripple with period ln 9 in ln L (P-048's inkling) would enter c₂ only through its sampling at five points, and the reported Δ⁴ln w is the contrast that reads it. Negation: no curvature — then 079's χ² of 8.28 was a 4% draw, the reading in PG-01's S2 note is withdrawn, and S2's first data against it is gone. Invariance: c₂ does not depend on the bootstrap base (the errors do, at the 1% level; reported). Cost: BernoullisBook, seven times the M5 per thread (run 087's times), takes about 7 hours for H7, 8 for sq2187 and under an hour for the rest, about 15 hours in all; H8 on the M5 is 13,690 s at 9 threads (run 079), after 094. Two machines is the price of not waiting three days.
Reviewed before commit by a sighted pass and second reading (a Code chat, 2026-10-03), whose edits are folded in: the bootstrap block moved off runs 082–083's streams; run 079's bootstrap scheme described as it is; clause B dropped (with equal errors it was decided by A and passed on the glimpse) and replaced by reported consistency and leave-one-size-out readings; the power paragraph corrected and the post-hoc caveat added; control (iv) made one χ² test; the cost corrected from a night to three days on BernoullisBook alone, hence the split across machines; the ω number dropped; run 051's c₂ cited as known.
2026-10-03, the M5's H8 script ran on after finishing (lab; not part of the seal). run096.sh was edited on the M5 at 17:32 (the bernoulli-resume mode, added after BernoullisBook lost power during H7) while the M5's own instance (run096.sh m5, started 13:24) was still running from that file. zsh reads a script as it goes, so after its H8 draw finished (START 16:34:06, DONE 20:47:14, 48,000 lines, committed 98335ad) and it printed ALL_FINISHED, it continued from a shifted offset, printed ./run096.sh:48: command not found: f.txt, and started a second draw of H8 with the same seed (7925) into the same path. That second draw was killed at 22:08 before it wrote anything (script 29349 first, then the time and perc processes 69332, 69333; nothing else). No sealed file changed: samples096/H8.txt on disk is byte for byte the committed file (md5 6b31c838f2637eb52c33ce3f17c834a9; perc writes its output only on completion). The one loss is samples096/H8.err: the second draw truncated it in the second the first finished, so the committed copy is empty and H8's peak RSS is not recorded; its wall time, 15,188 s at 9 threads, is taken from run096_m5.log. BernoullisBook's copy of the script was written at 17:32:50 and its process started at 17:32:51; it was not edited after and is unaffected. The rule this breaks is a known one: a script that is running is not edited in place — a changed copy gets a new name.
confirmedScored on 2026-10-04. A scoring reader, given the results file, the sealed clauses and this note without the lead, checked every number and outcome and refitted the ω profile from the printed ln w values; its edits are folded in. Figures marked "the reader's refit" are not the lab's and are for the lab to confirm. One sentence, marked, was added after the reading.
From: the owner's question about base 3 (2026-10-03, PG-01's S2 entry), which singled out H as the one census pattern with a size at every power of 3; then run 079's record, read after the fact for a bend; scaffold S2 and the methods programme held since 2026-10-02. What the run did to it: the bend is there on fresh seeds, at 3.7 of its errors. On the fresh set a single power of L between 81 and 6561 is rejected (χ² = 13.548 on 3, p about 0.004). Whether the bend is H's or the estimator's is not separated.
Controls. All four pass. (i) Run 079's per-file w and ln w errors reproduce exactly, with c₂ = +0.003186 ± 0.001118, χ² = 8.280 on 3 and the square's c₂ −0.00249 ± 0.00285, as the seal states; both machines reproduce samples079/H6.txt's first 1,000 k. (ii) Line counts, k ranges, no shared openings, md5s equal. (iii) Fresh square c₂ = −0.00172 ± 0.00276 (−0.62 errors; bound 3). (iv) z = +0.53, +0.12, +0.11, +0.72, +0.90; Σz² = 1.63 (bound 16.7). All five z are positive (two-sided chance 0.06); read as one common offset between the two sets that is 1.1 errors, and a common offset does not enter c₂.
The clause — confirmed. Fresh c₂ = +0.003938 ± 0.001076, +3.66 of its own errors; the bar was +2. A straight line through the five fresh points has χ² = 13.548 on 3; with the quadratic term, 0.164 on 2.
The two readings fixed at sealing — neither applies. The fresh c₂ against run 079's: +0.000752 ± 0.001552, +0.48 combined errors (the bar for reopening the between-file calibration was 2). Leave one size out, fresh set: +2.06 errors with 81 out and +2.09 with 6561 out (the bar for "the end sizes alone" was below +1); +3.55, +2.70 and +3.53 with 243, 729 and 2187 out. Pooled with run 079: +2.79 and +2.42 with the end sizes out; all three sets: +3.18 and +2.45. On no set does it fall below +1. Dropping either end size raises c₂'s error by a factor of 1.9 and leaves its value within 7% (+0.0041, +0.0042). The rejection of a straight line needs all five sizes: with 81 or 6561 out its χ² is 4.4 or 4.5 on 2 (the reader's refit).
What the lab reported beside the clause. - Three sets. Run 079: +0.003186 ± 0.001118 (+2.85). Run 051's 8,000-sample set: +0.003536 ± 0.002720 (+1.30). Run 079 and the fresh set pooled: +0.003577 ± 0.000776 (+4.61). All three: +0.003550 ± 0.000746 (+4.76). The three values agree with each other. The pooled figures include run 079, where the bend was first seen, so the fresh +3.66 is the only figure sealed before its data existed. - Pair slopes, fresh. 0.5556, 0.5501, 0.5371, 0.5317, each ± about 0.006: falling at every step, as run 079's did (0.5530, 0.5501, 0.5408, 0.5330). In the census's unit the drift is −0.0184 ± 0.0054 (079: −0.0147 ± 0.0058; 051: −0.0261 ± 0.0137). - Which 1/ν. The five-size fit gives 0.5436 ± 0.0013; the last pair gives 0.5317 ± 0.0061, lower by 1.95 of the last pair's errors. A reading: the fit's error belongs to a straight line the data reject, so it is not the error of H's exponent. - The correction's exponent. On the ten points with |B| ≤ 10 the pure power law has χ² = 23.135 on 8; one correction term brings it to 1.978 on 6 at ω = 0.2, B = +1.144, with 1/ν = 0.4966. On the printed rows ω from 0.2 to 0.5 is within 1 of the minimum (best-B 1/ν from 0.4966 to 0.5290) and ω up to 1.2 within 4 (1/ν up to 0.5374); from ω = 1.4 on, B sits at the bound. ω = 0.1 is disfavoured against the minimum (χ² = 10.885, 8.9 above it; on 7 degrees of freedom it is not by itself a rejected fit). The reader's refit: at ω = 0.2 the χ² is nearly flat in B up to the bound (2.04 at B = 10, where 1/ν = 0.40), and on a finer grid the bounded minimum is 1.81 at ω = 0.19 with B = 9.3 and 1/ν = 0.41. So the quoted 1/ν values are best-B values on a coarse grid, not a determined range. A reading by derivation: ln(1 + B·L^(−ω)) with positive B curves by at most ω²/4 per (ln L)², and the pooled bend needs 2c₂ = 0.0072 ± 0.0016, so ω below about 0.17 cannot reach its central value and ω below about 0.13 cannot reach it at −2 errors; the lower end is the form's, and from ω = 1.4 the fit is held by the bound on B. On all fifteen points the minimum is at ω = 0.2 with B at the bound and 1/ν = 0.3992, the runaway the seal named. A reading: ω is undetermined between about 0.15 and 1.3. In every row with B off the bound the fitted 1/ν (0.40 to 0.538) lies below the same points' pure-power-law 0.5440; with positive B the form forces that, so it is not a separate finding. - The median. p_med on H goes 0.685087, 0.685396, 0.684797, 0.684123, 0.683649: up by 0.00031 ± 0.00016, then down by 0.00060, 0.00067 and 0.00047 per tripling (7 to 17 errors each). A reading: it is not monotone and its last three steps do not shrink at one rate, a second sign, independent of the fit to w, that one power does not describe these sizes. The square's median stays within one error of 1/2. - The square. c₂ is −0.62 errors fresh and −0.87 on 079: no resolved bend. Its four-size 1/ν is 0.7429 ± 0.0028 fresh and 0.7416 ± 0.0028 on run 079, and its last pair slope 0.7485 ± 0.0085. A reading: the square lattice's exact value is 3/4, so the four-size fit sits below the known value by 2.5 errors on the fresh set and 3.0 on 079, with no resolved trend. On H the effective 1/ν falls with L, so if the fall continues the asymptotic 1/ν lies below the fitted one. - Skewness. g₁ on H rises 0.165, 0.246, 0.323, 0.350, 0.364; the steps are +0.081, +0.077, +0.027, +0.014 (each ± about 0.02; 079's: +0.097, +0.064, +0.062, +0.020). A reading: g₁ rises by 0.16 from 81 to 729 and by 0.04 ± 0.02 from 729 to 6561 (079: 0.08), and g₂ is flat from 729, so the pile's shape changes mostly below 729 while the pair slope is still falling above it. The square's g₁ stays within 0.03 of zero. - The period-two contrast. Δ⁴ ln w = −0.01654 ± 0.04113 (−0.40 errors; 079: −0.20). No period-two term is detected. Δ⁴ g₁ = +0.0836 ± 0.1232. - The errors. Eight blocks of 6,000 on H8 give SD/√8 = 0.00570 against the bootstrap's 0.00480, ratio 1.187. Eight blocks fix an SD to about 27%, so the ratio is consistent with 1; taken at face value on H8 it moves the clause from +3.66 to +3.48, and on all five sizes to +3.08 (the reader's arithmetic). The other way: the quadratic fit's χ² is 0.164 and 0.165 on 2 in the two independent sets, smaller than the errors predict (joint chance about 0.01), which would make the clause stronger. On the bootstrap base, run 079's samples give c₂ = +0.003186 ± 0.001118 and +0.003199 ± 0.001115 under the two bases. - Cost. H7 21,131 s and sq2187 22,165 s on BernoullisBook at 4 threads; H8 15,188 s on the M5 at 9. H7 was drawn twice: BernoullisBook lost power during the first draw and the resume mode redrew it in full with the sealed seed (commit 75c4a14; perc writes its file only on completion, so no partial draw was read). H8's peak memory is not recorded (lab note above).
What it means for the programme. S2's first scored datum is against it on H: over 81 to 6561 a straight line is rejected, and the endpoint 1/ν becomes a two-parameter object there (the seal's wording). Whether S2 is struck is the programme's decision. It is one pattern. The census patterns have three sizes each, where a bend can be measured but nothing checks it; PG-01's S2 entry cites P-050's fall on 44 of 49. Not established: the correction's exponent; the asymptotic 1/ν of H; whether the census order changes when each pattern is read with a correction; and whether the bend is H's or the estimator's, since on the one lattice whose exponent is known the same estimator's fit sits 2.5 and 3.0 errors below it. A reading: a sixth size (19,683) would narrow ω (by the reader's refit the predicted ln w there spans three 48,000-sample errors between ω = 0.2 and 1.3). The methods programme held under S2 has its first datum (the seal's wording). Added after the reading, the codifier's arithmetic from the printed c₂ values: the two square sets average to c₂ = −0.0021 ± 0.0020, and the pooled H value differs from that by +0.0057 ± 0.0021 (2.7 errors); on the fresh sets alone the difference is 1.9. So an estimator that bends alike on both lattices is disfavoured, not excluded, and that comparison was chosen after the data.
How the tools did. The seal carries one clause and control (iv) as one test, the sighted pass's two edits; both stand. The seal withheld a clause on ω because the fit depends on the bound placed on B; the fifteen-point profile ran to that bound, and by the reader's refit the ten-point one is within 0.06 of doing so. The power paragraph expected the truth to be smaller than run 079's value because that value was found after the fact; the fresh value is larger by 0.5 combined errors. Under-specified: control (iii) tests that the square is straight, not that its exponent is 3/4, and it could not have seen a bend of H's size on the square (that would be 1.4 of the square's errors, with half the samples and one size fewer). The ω grid's step of 0.1 puts the printed minimum one step from a disfavoured point and hides the flat direction in B. The printed table skips ω = 0.7, 0.9, 1.1 and 1.3. Not used: the Δ⁴ contrasts and g₂ read nothing new. Operations: one script edited while running (OPS, "A script that is running is never edited in place"), one power loss, one lost memory figure. The scoring reader changed the note in eighteen places; the largest were the ω paragraph, which the draft had stated as a determined range, and the square control's lack of power, which the draft had missed.
generated 2026-10-25the lab index