Math Mapgenerated 2026-10-25 · a354234
PUBLIC BUILD

run 081Settled

Run 073 found the skewness g₁ of the crossing threshold falling between L = 729 and 6561 on two carpets, T (−0.191 ± 0.038) and X1 (−0.116 ± 0.045), while the exact one-block recursion rises at every depth on all 63 patterns. Each fall rests on one set of 8,000 samples per size, read alongside twelve other carpets, and run 079 has just shown a two-error pattern on H failing to replicate. Panel PN-005's House made replication the first question. Drawn again with fresh seeds and twice the samples, do the two falls come back?

slug
turn-reseed
state
run
created
2026-10-01
sealed
2026-10-01
builds_on
[073, 072, 079]
programme
PG-01
concepts
[fractal-dimension]
statistic
Cloud session (the container used for run 070), with the repository cloned there; perc.c unchanged. Graphs, built with gen.py exactly as the stored samples' graphs were: T at generations 3 and 4 (T3, T4; L = 729, 6561), as run 053 built them; X1 at generations 3 and 4 (graph files F3, F4), as runs 061 and 063 built them. 16,000 samples per graph, perc seeds 8101 (T3), 8102 (T4), 8103 (F3), 8104 (F4); thread count as the machine allows (perc seeds each sample from (seed, sample index), so the thread count does not change the numbers). Output samples081/<graph>.txt; the container is disposable, so each samples081 file is force-added and committed as it completes, as run070.sh did. Graph files are built with gen.py write before the control (the control reads M from the graph headers). No statistic of any samples081 file is computed until all four files are complete. Per file, threshold x = column 0 divided by M from the graph header; unbiased k-statistics k₂, k₃, k₄ (scipy.stats.kstat for point values; in bootstrap replicates, the kst() of flow074.py), g₁ = k₃/k₂^(3/2). The fall of a carpet is d = g₁(6561) − g₁(729) on the fresh samples alone. Errors: 2,000 joint bootstrap replicates; in replicate b, file j (in the order T3, T4, F3, F4; j = 0 … 3) is resampled once with numpy.random.default_rng(199001 + 4·b + j).choice(n, n, replace=True), b = 0 … 1999; bootstrap seeds 199001 … 207000. The error of any quantity is the standard deviation (ddof = 1) of its 2,000 replicate values, and "n errors" is the point value over that error. Seeds checked against every perc seed (49–7145, 7901–7909, 8001–8018, plus 490, 510, 530) and bootstrap range (up to 198006) in the carpet_perc scripts and runs 051–080: none reused. Control, checked first: the analysis code applied to the stored samples (samples053/T3.txt, T4.txt; the X1 files cumulant073.py reads for F3 and F4) reproduces cumulant073.json's g₁ for T and X1 at 729 and 6561 to an absolute 1e-6, or the run is withdrawn (kstat sums raw powers, and the platform differs from the one that wrote the json); the absolute differences are recorded. The joint bootstrap here (choice, one replicate across all four files) differs in form from run 073's; only the error scale depends on it. Script reseed081.py, output reseed081.json and RESULTS081.md.
script
R27_tree_groups/carpet_perc/reseed081.py (cloud session)
artifacts
[R27_tree_groups/carpet_perc/RESULTS081.md, R27_tree_groups/carpet_perc/reseed081.json, R27_tree_groups/carpet_perc/samples081/]
outcome
unanticipated
source
../lab/runs/081-turn-reseed.md

Prediction(A) T's fall replicates: d_T is below −3 errors. (B) X1's fall replicates: d_X1 is below −2 errors. Confirmed if both hold.

Falsifier(A) d_T above −1 error: T's fall was a sampling excursion in one set of samples. (B) d_X1 at or above 0: X1's fall does not come back. Between the confirming and falsifying thresholds, a clause is neither. The run is falsified if A is falsified, whatever B shows. With A confirmed and B falsified the run is unanticipated: T turns and X1 does not, and the case's "two carpets turn" becomes one. Confirmed if both are confirmed; otherwise unanticipated.

Sealed 2026-10-01, after panel PN-005 was filed and before any samples081 file existed (codifier). Known at sealing: runs 051–080 as scored or running, including the stored g₁ of T and X1 at 81, 729 and 6561 (run 073) and run 079's calibration. The bootstrap error on H was not too small: the six-block spread over √6 was 0.090 against a bootstrap error of 0.130 on Δ⁴g₁.

Why this run, and why in the cloud. PN-005's House declined to explain the turn before it is replicated, and it is right to. The rerun needs only the unchanged sampler and graphs the record already knows how to build, so it runs in the cloud while the M5 finishes run 080. The House's diagnostic (a coarse block-graph crossing time, recorded per sample) needs a second union–find and goes to a separate seal on the M5.

The codifier's lead, held with conviction. Both falls are real. On honest errors, T's −0.191 is 5.0 errors, and correcting for fourteen carpets read at once (two-sided) moves that only to about 4.4, still far beyond chance. X1's −0.116 is weaker: 2.6 errors, with a multiplicity-corrected chance of about 0.13 (two-sided) under no effect. If they come back, the turn has two carriers and the mechanism question is live. If T's does not come back, the case closes as H's alternation did.

Power, stated. At 16,000 samples the per-value error is about 0.03/√2 ≈ 0.020, and the error of a fall about 0.028 (T) and 0.032 (X1), scaling run 073's. If the stored falls are true: - A sits near −6.8 errors. - B sits near −3.6, and is confirmed with probability about 0.95.

If each fall is half its stored size (the winner's curse): - A sits near −3.4 (confirmed with probability about 0.65). - B sits near −1.8 (confirmed with probability about 0.43).

At half size, A lands in its neither-band (between −3 and −1 errors) with probability about 0.34, so the most likely outcome then is unanticipated.

Under no fall, A is falsified with probability about 0.84, and B with probability 0.5.

The reductio this seal passed first. By construction: each clause reads only fresh samples, at sizes and on graphs fixed above, and nothing is fitted. Negation: if the stored falls were excursions, the fresh d's land where the other twelve carpets' steps from 729 to 6561 sit (−0.05 to +0.16), and A's falsifier fires. What a lone clause decides is in the falsifier line. Cost: in the cloud at 4 threads, T4 took 10,273 s for 8,000 samples and peaked at 1.2 GB (run 070), so each 6561 graph needs about 5.7 hours at 16,000. F4 has not been timed in the cloud and is assumed equal. Both together take about 12 hours; the 729 graphs take minutes. Memory grows with thread count (2.25 GB at 8 threads on the M5).

An untouched third copy of T. samples070/T3.txt and T4.txt (run 070's machine control, 8,000 samples each, seeds 7002 and 7003) are an existing independent replicate of T whose g₁ nobody has computed. They are not opened before sealing and enter no clause. The report gives d_T on them alone and pooled with samples081.

Reported, not scored. - The fresh g₁ and g₂ of every file, with errors. - The fresh falls beside run 073's, and their inverse-variance combination. - The fresh width w = q₀.₈ − q₀.₂ and the pair slope of ln w between 729 and 6561, each a 1/ν estimate, for each carpet. - PN-005's seat and House forecasts that this run decides: House F1 and F2, and Framing's. The codifier scores them, not the lab.

Reviewed before commit by a second reader (OPS.md); its edits are folded in: run 070's unread T samples named and reported; the control's tolerance set to 1e-6 across platforms; the multiplicity figures and B's power corrected; the cloud cost and memory stated as measured; files committed as they complete.

Scored 2026-10-02 — unanticipated

Scored by the codifier from RESULTS081.md and reseed081.json as committed on the cloud session's branch (793adb3, origin/claude/loving-keller-vztgzr; the branch reaches main when run 086's files are merged with it), as written. A scoring reader (OPS.md) read the note against the results before commit; its edits are folded in.

Control first — passes. reseed081.py on the stored samples reproduces cumulant073.json's g₁ for T and X1 at 729 and 6561 to 1.9e−10 or better (tolerance 1e−6). The VM restarted twice during F4; perc seeds each sample from (seed, index) and writes only at the end, so the third, completed run is the file the first would have written. Noted, not a departure.

(A) Confirmed. T's fall replicates on fresh seeds: d_T = −0.1111 ± 0.0308, −3.60 errors, below −3. (B) Falsified. X1's fall does not come back: d_X1 = +0.1171 ± 0.0352, +3.32 errors, at or above 0 — and not near it. As the falsifier line prescribes, A confirmed with B falsified is unanticipated: T turns and X1 does not, and CASE-28's "two carpets turn" becomes one. The codifier's lead ("both falls are real") was wrong on X1.

What the numbers say beyond the clauses.

  1. X1's two measurements disagree by more than either's error allows. Run 073's −0.116 ± 0.045 and this run's +0.117 ± 0.035 are 4.1 combined errors apart (p ≈ 4e−5 under equal means) on independent samples of the same graphs. The two sets' widths agree (1/ν pair slope 0.5317 ± 0.0053 against 0.5323), so the graphs are the same object; the disagreement is in g₁ itself. Either the bootstrap error of g₁ at 8,000–16,000 samples understates the between-set spread on this carpet, or one set is a 4-error excursion; this run cannot tell which.
  1. T's three independent sets are all negative, and together say it more weakly than either of the two that found a fall. Run 073: −0.191 ± 0.038; this run: −0.111 ± 0.031; run 070's unread T samples (opened here for the first time, 8,000 per size): −0.022 ± 0.040. All three are negative. Recomputed from the reported values: the inverse-variance mean is −0.110 ± 0.021, but χ² about it is 9.3 on 2 degrees of freedom (p ≈ 0.009), so the three are not consistent at their stated errors; scaling the error by √(χ²/2) gives −0.110 ± 0.045, 2.5 errors. The reading: T's turn is negative in all three sets, 2.5 errors on the scaled combination (three negatives alone is a one-in-eight chance under no turn), and its size is known to about ±0.045, not ±0.02. Item 1 on X1 and this on T point the same way: on both carpets the between-set spread of the 729→6561 g₁ difference exceeds the bootstrap error (T p ≈ 0.009 on three sets; X1 4.1 errors on one pair). The size of the excess is poorly determined — the point factor is 2.2 on T, with a 68% range of about 1.6–5 on two degrees of freedom; on X1 the single pair gives about 4 with a range of 3–20 — and neither carpet distinguishes a uniform under-coverage from one anomalous set (on T, 070 sits 3.1 pair-errors from 073 while 081 sits 1.6 and 1.8 from each). Run 079's six-block calibration found the bootstrap not too small on H's Δ⁴g₁ (0.130 against 0.090); PN-005's House inferred under-coverage from H and was contradicted by 079; on the turn's own quantity, on two carpets, the between-set spread reads as supporting the House's premise, though not its route to it through H. A calibration is the next zero-compute step: the between-quarter spread of g₁ within each 16,000-sample file (and within runs 073's and 070's files) against the bootstrap error, on T and X1 — the 079 check on this quantity.
  1. The fresh T sample flattens at 6561. g₁ +0.360 → +0.249 and g₂ +0.311 ± 0.069 → +0.006 ± 0.052 (3.5 errors): the excess kurtosis is consistent with zero at 6561. X1's fresh g₂ is unchanged within error (+0.393 ± 0.073 → +0.441 ± 0.073). Reported. Pooling run 070's T samples with these (24,000 per size) gives d_T = −0.0808 ± 0.0242 (−3.3 errors); run 073's and this run's X1 falls combine to +0.028 ± 0.028 — the cleanest statement that X1's two sets cancel.
  1. 1/ν from fresh widths. T 0.3492 ± 0.0050 against the recorded 0.3743 (run 073's own 729→6561 local slope 0.3646); X1 0.5317 ± 0.0053 against 0.5359 (0.5323). T's pair slope is below its recorded exponent by 0.025 — five of the pair slope's errors, the recorded exponent's own error not included — and below run 073's local slope by 0.015 (3 errors); the two are different estimators, so this is a comparison, not a discrepancy. X1's is within one error. Reported, and read beside run 087's two-term fit when it lands.

PN-005's forecasts, scored (panels/SEAT-RECORD.md). Framing's "no reproducible sign change … −0.08 to +0.08": falsified on the claim — the fall reproduces at −3.6 errors; the point estimate −0.111 ± 0.031 lies outside the interval by one error. House F1 "remains negative but smaller than −0.191 … −0.16 to −0.02": confirmed on sign and interval (the forecast assumed 48,000 samples; this run drew 16,000). House F2 "|reseeded X1 difference| < 0.05 … −0.07 to +0.03": falsified — +0.117 ± 0.035, outside the interval by 2.5 errors. The House's adopted premise that the ±0.03 bootstrap error reads too tight, contradicted by run 079's calibration on H, gains support on the turn's own quantity (items 1 and 2); it is scored supported-by-recomputation, not confirmed, until the calibration in item 2 runs.

What it does to PG-01. L1 keeps T and loses X1: the turn has one replicated carrier. Run 089's reading (T's step-map difference lives in the early-crossing tail; X's step maps are one shape with a drifting fixed point) stands beside a T whose fall is three-for-three in sign. The error of the turn's size is the open instrument question, and it is cheap.

Lab notes. Cloud container, 4 threads: T4 15,769 s, F4 17,440 s on the third attempt; files force-added as they completed, no statistic computed before all four existed; bootstrap seeds as sealed, run 070's reported bootstrap at 207001–211000 (outside the seal's range, chosen by the lab, used nowhere else). reseed081.json predates the row-form rule and carries no rows; the database chat's adapter list.

Calibration note, 2026-10-02 (post-score; the numbers are from the sighted pass SIGHTED-D2D3-2.md, dd1c6cf, computed for a seal draft that was thereby glimpsed in full and is filed here as a note instead)

Ten files — T at 729 and 6561 from runs 073, 070, 081; X1 from 073, 081 — each split into 8 consecutive blocks (independent draws, since perc seeds each sample from (seed, index)); g₁ per block; s_B = sd/√8 against the whole-file bootstrap error (2,000 replicates, seeds 391001–391010).

generated 2026-10-25the lab index