On H's two stored sets, with the mean, ln S and g₁ fitted jointly under PG-03's three one-term forms, tying the correction exponent ω to 1/ν costs Δχ² = 11.28 (each file's covariance; 8.54 with diagonal errors) on all five sizes and 1.47 (0.59) with L = 81 left out. Is that a property of H or a fluctuation at the smallest size? Drawn afresh with the errors at 81 and 243 cut to about a seventh of the pooled stored errors and at 729 to four tenths, does the tied one-term form fail on the new files alone?

Sealed 2026-10-04, before any new sample exists (codifier). A reseal of run 099, which was withdrawn before any draw. The question, the draws, the seeds, the fit, the clause, the falsifier and controls (i), (iii), (iv) and (v) are run 099's word for word; control (ii) differs in its redraw check and in the seed scan (when it is made and where it is recorded, its exception by exact path for run 099's files, and its rule for digit strings that are not seeds), and the samples go to samples100/. Run 099's text was itself a third version: two drafts were struck before sealing and a second reader's edits were folded in; all of that is named at the end.

Why a reseal. Run 099 had each machine redraw stored files "to the stored file's md5". On BernoullisBook the redraw of H4 gave all 48,000 values of k equal to the stored file's and one line different in column 1, 4409 0.674018866165 against the stored 4409 0.674018866166: a float computed after k is fixed (perc.c, lines 59–60) and printed to twelve places (line 80), on x86_64 against arm64. The control could not be met as worded and the statistic never reads that column, so run 099 was withdrawn and this run compares column 0. On disk before this commit (the lab's record is redraws099.md, commit dccd242), read by the codifier and again by the sighted pass: BernoullisBook's redraws of H5 and H6 are identical to the stored files in whole (md5s 6c12d77b…, c6ed5e2c…) and its H4 differs in that one line only; the M5's redraw of H7 is identical in whole (65522712…) and its first 1,000 lines of H8 are identical (pre099_m5.log ends REDRAWS_PASS); the column-0 md5s are those in the frontmatter, equal for redraw and stored file on the machine that made the redraw. No sample of run 099 was drawn, so the seeds are unused.

Known at sealing, cited as known. READING-PG03.md, READING-PG03-L1.md, READING-PG03-L2S.md and READING-PG03-MOMENTS.md in full. From the last, with the file covariance on the two stored sets: all five sizes, ω free, χ² = 17.22 on 21 with 1/ν = 0.5211 (0.5150 to 0.5260), ω = 0.329 (0.28 to 0.38), B = +0.58; tied, 28.50 on 22; without 81, 14.55 on 15 free and 16.02 on 16 tied. Each stored set alone gives a tie of 3.91 and 5.03 (the blind readers' refit, diagonal, from the reading's rounded table). Timings at 2,000 samples: about 4.8 hours on BernoullisBook and 9.6 on the M5 for the counts sealed, peak 2.4 GB on H8. The simulations in R27_tree_groups/carpet_perc/sim099/ (the blind readers' scripts and logs; the sighted pass reran the three figures used here and added the refitted blind spot from its own scratch scripts).

How the question got here. Draft 1 scored "the smallest size from which one term fits". Simulation showed a second-order term of natural size is absorbed by the nine parameters (one-term misfit 0.51 in χ² at these errors, 8.71 at four times natural size, 35.27 at eight times), and the scored size came out as 81 in 200 of 200 runs under every self-consistent truth. That question cannot be answered on these sizes. Draft 2 scored the tie on all 51 points with a band on ω and the sentence "H has a correction exponent of its own". The sighted pass showed the confirm was foretold by the stored 11.28, which entered the scored quantity, and that the sentence does not follow: ω = 1/ν with a next analytic term of negative sign and 1.5 to 4 times natural size, refitted to the stored sets, fits them at χ² 15 to 23 on 22 and gives the same outcome in 85% to 97% of simulated runs, passing every control. This seal scores the tie on the new files alone and claims only what a tie can show.

What this run is for. It says whether the stored preference against the tied one-term form is H's or a fluctuation at 81, on draws that share nothing with the stored ones. It cuts the spread of the fitted pair for PG-03 L4's band. It does not test whether one term is enough, and it does not say what replaces the tied form.

The codifier's lead, held with conviction. T(new) near 50. The tied form fails on H. The codifier's further belief, which this run cannot test, is that the reason is an exponent of H's own near 0.33.

Power. The sighted pass's 200 simulated runs per truth, on the new files alone: with ω free at the stored fit, T(new) of 36 to 78, all 200 at or above 25 and 87% at or above 40; with ω = 1/ν, at most 4.7. The new errors are about a seventh of the pooled stored errors at 81 and 243 and four tenths at 729; the new files carry nearly all the weight there, five sixths at 729, 60% at 2187 and half at 6561.

What a fit that holds does and does not bound. "One term fits" bounds a second term only below about eight times natural size. A hidden term of natural size moves the one-term prediction of ln S at 19,683 by about ±0.0023 (the blind readers' simulation). Reported with the results, for L4's band.

Reported, not scored. Per file the three moments with errors and covariance. The free and tied fits on the new files alone, on all seventeen files, and without 81: χ², its form part (the fit to the per-size pooled values) and consistency part (the files' scatter about them), the pair with intervals from the continuous profile, every amplitude. T on all seventeen files, and ω from that free fit beside the stored 0.329 (0.28 to 0.38). The same with diagonal errors. Residuals of the free fit size by size. Predictions at 19,683 for ln S, the mean and g₁ from the free and tied fits, beside the pure power law's, and the shift of each when a term of ±B²·L^−2ω is added to the truth and one term refitted. z at 81, new against stored. W80 and the median on the three largest sizes. Wall time and peak footprint per file.

What the controls can and cannot see (the sighted pass and the second reader). (iii)'s new-against- stored test is limited by the stored errors, so it is taken on the four larger sizes: a difference at 81 is the thing the run is asking about and must not void it. The twins test has a floor as well as a ceiling, since two halves that agree too well are as wrong as two that disagree. (iv) detects errors under-estimated by 15% almost always and by 10% about two times in three; a 10% mis-estimate moves T by about 20%, which reaches no bar from the expected values; the errors of H6, H7 and H8 are not block-checked. (v) catches a whole stream drawn twice; two single samples sharing a state are excluded exactly by (ii)'s arithmetic. Machine is confounded with size, so each machine redraws stored files in full before it draws.

The reductio this seal passed. By construction: T is non-negative; the tied fit is nested in the free one; the two halves of H4 and of H5 enter both fits alike. Negation: ω = 1/ν, and then T(new) is a few units. Twins: the two halves (control iii). Neighbours: the square, where 1/ν is known and the stored one-term fit gives ω = 0.62 (0.22 to 1.24; READING-PG03.md), compatible with ω = 1/ν = 0.75; the same question there is a null case with real power and is not part of this run. Invariance: writing the correction outside the logarithm differs from this form by a second-order term of half natural size, which the fit cannot see (misfit 0.12). A pass without the mechanism: named in the falsifier line. Cost: 4.8 hours on BernoullisBook, 9.6 on the M5; the redraws are already made.

Readers. Blind readers on draft 1 (sharpness, second reading, reductio, by simulation): the scored quantity could not come out as predicted; redesign on the tie. A sighted pass on draft 2 (a Code chat on the M5): seeds and perc.c hold; the three simulation figures reproduce; the confirm was foretold and over-read; score on the new files alone; minimisation text; control (ii)'s seed arithmetic; the twins' floor; control (v)'s wording. A second reader on this frontmatter alone: the new-against-stored control moved off 81, where it would have voided falsifying runs; the twins as one quadratic form per graph; pooled and combined errors defined; (iv)'s bounds widened to 0.90 to 1.10; the free fit's own χ² mapped; full redraws against the machine confound; the bound on B kept off the singular point; the command line, bond counts, file names and what happens to a run not scored.

Readers of this reseal. A second reader on the frontmatter alone: the binary check contradicted the rule for redrawing (now the binary's md5 is a record and a condition for reusing a redraw); the seed scan's exception is by exact path; a reused redraw must be the file its log names; each machine checks only its own graphs; the commands are written out; the verdict is fixed in a log before the first draw and not evaluated again; which directory is read and which written. A sighted pass with the disk on both machines (an agent launched by the codifier, read-only on both repositories): all 29 of its checks pass — every md5, line count, log line and file name the passage cites reproduces, and so does what the passage leans on (the field separator, the loader's column, the stored files equal on both machines, the run number free); the seed scan as first worded would have failed on digit strings that are not seeds (0.7934 in run 058's table, 1.522718 in reading_pg03_l1.py), the same class of fault that withdrew run 099, and is reworded; the perc.c line reference; the sentence saying what changed. The pass ran the scan itself: no script, run file or seed-named JSON key uses or names these seeds outside run 099's run file and run099.sh, and no seed block made by arithmetic reaches 511001–525000. The changed passage went back to the sighted pass twice after these edits; on its second reading the scan was moved before the draws, where run 096's was, so that a run file sealed during the draws cannot trip it. What the redraw check does not show (second reader): it bounds a per-sample difference in k between the machines at about 6 in 100,000 on H4 to H6, and on H7 and H8 it is the same machine, binary and thread count as the stored files, so there it shows determinism only.

During the draws (2026-10-04, codifier; no sealed field changed). The lab reported three readings of this seal, made before any statistic of a new file was computed. All three touch controls or reported items, none the scored clause, and the codifier takes them as the seal's meaning. (1) "Without 81" is fitted both on the new files alone and on all seventeen. (2) In control (iii)'s new-against-stored z the stored value at a size is the equal-weight mean of its two stored files (runs 079 and 096), by the same rule the seal gives for a size with two new files. (3) The ±B²·L^−2ω shift is added in ln S to the free fit's values and one term refitted without noise, as sim099 defines it. Two slips by the lab, both before any new file was read and both corrected by it: the seed scan's first version assumed 2,000 replicates for every seed formula (runs 084 and 094 use 20 and 10) and was fixed before the scan was committed; and the scan was run once more after the draws began, which overwrote the working copy of pre100.json and was undone from commit 74eb99f (the committed record never changed). One thing the report must carry: H8 on the M5 shared the machine with one single-threaded process from 17:02 on (run 101's quenches and two short level-4 searches), so its wall time is an upper bound and not a clean figure for sizing L4's draw.

Scored 2026-10-05 — confirmed

Scored on 2026-10-05, Phoenix time, from R27_tree_groups/carpet_perc/RESULTS100.md and fit100.json (commit c82c98e). A scoring reader, given those files, the sealed clause and a draft of this note without the lead, checked every number present in the results files, recomputed T(new), the twins, the three Σz² and the block mean, and found no copying error and five sentences that said more than the numbers allow; its edits are folded in, and the largest is named below. It could not check commit hashes, the stored figures quoted from earlier readings, or the events under Tools, which are from the lab's report and git.

From: PG-03's line L6. The stored sets preferred a correction exponent of its own to ω = 1/ν by 11.28 in χ², and by 1.47 with L = 81 left out. What the run did to it: on fresh draws the tied one-term form fails by 96.7 on five sizes, and by 5.4 on four.

Controls. All five pass; stage one was committed (ed346bd) before stage two made any fit on the new files. (i) The stored sets give χ² 17.2211 on 21 free and 28.5013 on 22 tied (sealed 17.22 and 28.50, each within 0.05). (ii) Line counts as sealed, every x in (0, 1), the md5s of perc.c and the five graphs as recorded, both redraw verdicts REDRAWS_PASS, the seed scan unused, the seeds x₀ pairwise distinct on every graph. (iii) Twins: 1.174 (H4) + 0.496 (H5) = 1.670, inside 0.87 to 16.81. New against stored over 243 to 6561: Σz² of 3.26 (ln S), 1.66 (mean) and 2.15 (g₁), each under 14.86. (iv) The mean of the twelve block ratios is 0.9935, inside 0.90 to 1.10; single ratios run from 0.821 to 1.178. (v) No run of 8 consecutive k occurs twice on any graph.

The scored quantity. T(new) = 109.149 − 12.406 = 96.743, the tied fit's χ² on 13 degrees of freedom less the free fit's on 12, on the seven new files alone with each file's covariance. No fit is within 1e-6 of a bound. The clause asked for at least 25: confirmed. The free fit's own χ² on the new files, 12.406 on 12, is under 26.22, so the reading "both one-term forms fail" does not apply.

What a confirm says, by the readings fixed in the seal. The tied one-term form fails on H, on draws that share no seed, no x₀ and no run of 8 consecutive k with the stored ones. The falsifier's reading, that the stored preference was a fluctuation at 81, does not apply. How much of the stored 11.28 was fluctuation is not determined by this run. It does not say the correction exponent is H's own, and it does not say what replaces the tied form.

What leaving 81 out does, and what it does not show (reported, not scored). With L = 81 left out, tying costs 5.441 on the five remaining new files (6.096 on 7 against 0.655 on 6) and 7.087 on the thirteen remaining files of all seventeen (25.692 on 31 against 18.604 on 30). With 81 in: 96.743 and 134.231. With diagonal errors the four figures are 4.995, 5.426, 81.196 and 110.817. So the cost of the tie depends on 81 being in the fit. It is not at 81: in the five-size tied fit on the new files the residuals at 81 are at most 1.2 pooled errors, and those at 243 to 6561 reach 4.4 (the mean at 729) and 4.1 (g₁ at 6561). The files at 81 are the most precise by a factor of seven and the tied fit goes through them; what it cannot then do is reach the larger sizes. No other size was left out, so "the smallest size" has been compared with nothing. This corrects the draft of this note, which said the failure "sits at 81", and it corrects the same sentence in the moments reading of 4 October (the stored 11.28 against 1.47), which rested on the same single leave-one-out. On four sizes, 5.441 is under the seal's 6.63: at the seal's bar the one-term forms do not separate there (a reading; the bar was sealed for the five-size quantity; as χ² on one degree of freedom 5.441 is about 2.3 standard errors and 7.087 about 2.7, and the second contains the first).

The fitted pair with and without 81 (reported). Free fit on the new files: 1/ν = 0.5260 (0.5234 to 0.5284) and ω = 0.3009 (0.2810 to 0.3216) on five sizes; 0.5111 (0.4917 to 0.5210) and 0.2952 (0.2168 to 0.3873) on four. On all seventeen: 0.5246 (0.5225 to 0.5266) and 0.3045 (0.2877 to 0.3218); without 81, 0.5111 (0.4969 to 0.5192) and 0.3086 (0.2389 to 0.3852). Intervals are Δχ² ≤ 1 on the profile. ω is near 0.30 in all four. Readings, each with its size. 1/ν is lower by 0.015 (new files) and 0.014 (all) without 81. The two fits share four of five sizes, so the gap between their intervals is not a test; on the four-size profile the five-size value 0.5260 sits at Δχ² of at most 4.76, about two standard errors. A cleaner figure from the same table (the scoring reader's arithmetic): adding the three pooled values at 81, with no new parameter, raises the free fit's form part from 0.159 on 3 to 10.736 on 6, which is 10.58 on 3 (p about 0.014); on all files 16.24 on 3 (p about 0.001). The four-size free fit is close to interpolating (form part 0.159 on 3, every residual under 0.33). Is this a second term absorbed by the exponent? The run's own shift table says a term of ±B²·L^(−2ω), natural size, is absorbed by a free refit at a cost of 0.276 and 0.261 in χ² and moves 1/ν by 0.0035 either way, to 0.5226 and 0.5296. The move seen here is four times that. So a hidden term of natural size does not account for it; one several times natural size could, and the seal's body had already named that case (ω = 1/ν with a next analytic term 1.5 to 4 times natural size). Nothing here tells the two apart.

The free one-term form is acceptable on the new files and poor on all seventeen (reported). New files: 12.406 on 12, form part 10.736 on 6 (p about 0.10), ln S at 729 off by −2.43 pooled errors. All seventeen: 48.526 on 42 in total, but the form part is 18.261 on 6 (p about 0.006), with ln S off by −2.22 and −2.14 at 729 and 2187; the total hides it behind a consistency part of 30.265 on 36. The seal ties the reading "both one-term forms fail" to the new files, where it does not apply; it is recorded here that on all seventeen the free one-term form is under strain in ln S.

Other reported items. ω from the free fit on all seventeen files is 0.3045 (0.2877 to 0.3218), beside the stored 0.329 (0.28 to 0.38). z at 81, new against stored: +0.57 (ln S), +3.00 (mean), −1.26 (g₁); not a control. The stored mean at 81 is 0.6857705 ± 0.0000845 and the new one 0.6860264 ± 0.0000120; the chance of one |z| of 3 among the three at 81 is under 1%, among all fifteen about 4%. Residuals of the free fit on the new files in ln S, in pooled errors: −0.39, +1.11, −2.43, −0.85, +1.41 from 81 to 6561; those of the mean and g₁ are within 0.6. Predictions at 19,683 from the new files: ln S −6.621829 (free) and −6.631197 (tied); mean 0.6833995 and 0.6834833; g₁ +0.42309 and +0.36369. A single power gives ln S −6.662381 ± 0.001488, from a fit that fails outright (χ² 196.8 on 5), and a mean of 0.6833590 ± 0.0000306 from one power through the last three sizes with no degree of freedom left. A term of ±B²·L^(−2ω) added to the free fit's values and the free form refitted moves the ln S prediction by ±0.00233, the mean by about 1e-6 and g₁ by −0.0025 and +0.0022. The fits' own errors on these predictions were not asked for by the seal and are not in the results. The new errors are about a seventh of the stored ones at 81 and at 243 and about 0.45 of them at 729. Wall times: H4 and H5 on BernoullisBook 68 to 971 s a file, H6 13,721 s; H7 on the M5 4,734 s (two short level-4 searches ran beside it); H8 29,942 s with a peak of 2.56 GB, an upper bound, the M5 being shared with run 101's quenches from 17:02.

What it does not say. Not that one term is enough: the seal's body set that question aside as unanswerable on these sizes. Not that ω ≈ 0.30 is an exponent of H. Not which pair L4's band should be drawn from: the five-size and four-size free fits give 1/ν of 0.526 and 0.511 on the new files (0.525 and 0.511 on all).

The codifier's lead, scored (the scoring reader did not see it). "T(new) near 50. The tied form fails on H." The direction held. The size did not: 96.7 is twice the lead, and above every one of the sighted pass's 200 simulated runs with the stored free fit as the truth (36 to 78). A reading: the stored free fit is not the truth either. The further belief the seal called untestable here, an exponent of H's own near 0.33, stays untested; the free ω on the new files is 0.301 (0.281 to 0.322). And the codifier's first draft of this note read the leave-one-out as locating the failure at 81, which the tied fit's residuals contradict; the scoring reader caught it.

Tools. The lab's assessment stands: perc.c unchanged and each machine's binary redrew stored files with column 0 equal before drawing; fit100.py reproduces the stored sets and the reading's without-81 and diagonal values. Two things happened to the run from outside. A data policy committed during the draws (78bb217) stopped tracking new samples files, so H8's .txt is untracked and attested by a sidecar that still says tracked: true from draw time; the lab neither edited the sidecar nor force-added the file, and changed only the text of fit100.py's times table (506069d) so that it reports what git holds, re-running stage two to identical numbers. And a read by another session rebuilt the lab database at 23:07 on 4 October while H8 was drawing (docs/DATABASE-AUDIT.md §5); H8's wall time was already an upper bound. The seed scan was run once more by mistake after the draws began and the committed record restored unchanged.