Math Mapgenerated 2026-10-25 · a354234
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run 072Settled

Run 069 found the width-standardized crossing curve indistinguishable across carpets by a Kolmogorov–Smirnov distance, but reported a moment that is not flat: the skewness of the standardized threshold distribution at L = 6561 is positive on every carpet (+0.11 to +0.55) and near zero on the square (+0.011), and in the three twin pairs whose exponents separate, the lower-exponent member has the lower skewness. On the carpets where it can be tested, is skewness reproducible across reseeds (X, Y, Z) and stable across sizes (fourteen carpets)? Only if it is does the twin separation mean anything.

slug
skewness-fingerprint
state
run
created
2026-09-30
sealed
2026-09-30
builds_on
[069, 063]
concepts
[fractal-dimension]
statistic
R27_tree_groups/carpet_perc/ (Lab_Tree_Model). No new sampling. For each stored threshold sample, compute the sample skewness g₁ of the raw thresholds (skewness is unchanged by shifting and scaling, so run 069's standardization is not needed), with its error by a 2,000-resample bootstrap of that sample (seeds 72001 upward). The sample size of every file is reported; a missing or unreadable file makes that comparison unscored. Reseed test: g₁ at L = 6561 from run 061's and run 063's samples of X, Y and Z. Size test: g₁ at L = 729 against L = 6561 on the fourteen carpets of run 069 (same files). Twin comparison, reported and not scored (its g₁ values were known at sealing, and the pairs were chosen because their exponents separate): g₁ at L = 6561 for X/X1, X/X2, Y/Y1 and Z/Z1 with combined bootstrap errors. For each comparison, the combined error is the root sum of squares of the two bootstrap errors. Reported, not scored: the square's g₁ at 729 and 2187, excess kurtosis alongside, and g₁ against measured 1/ν across all carpets.
script
R27_tree_groups/carpet_perc/ (Lab_Tree_Model)
artifacts
[R27_tree_groups/carpet_perc/RESULTS072.md, R27_tree_groups/carpet_perc/skew072.json]
outcome
confirmed
source
../lab/runs/072-skewness-fingerprint.md

Prediction(A) Reproducible: for all three of X, Y, Z, the reseed difference in g₁ is within 2 combined errors. (B) Stable with size: on at least 70% of the carpets with both sizes readable (10 of 14 if all are), g₁ at 729 and at 6561 agree within 2 combined errors. Confirmed if A and B both hold.

Falsifier(A) 2 or 3 of X, Y, Z differ beyond 3 combined errors across reseeds — skewness is sampling noise; the run is falsified and B is reported only. (B) more than 40% of the readable carpets (6 or more of 14) differ beyond 3 combined errors across sizes — skewness is still moving with L. Outcomes between prediction and falsifier on either clause are unanticipated. The run is falsified if either clause is falsified. The twin comparison decides nothing; if A and B hold, a twin clause is sealed next on fresh reseeds of the twins.

Sealed 2026-09-30, after run 069 was scored and before any skewness error, reseed skewness or 729-size skewness was computed (codifier). Known at sealing: run 069's reported g₁ at L = 6561 for the fourteen carpets and the square (the numbers the lead rests on), and a normal-theory error of about 0.027. Not known: bootstrap errors (heavy tails would widen them), any g₁ at L = 729, any g₁ from run 061's samples.

The reductio this seal passed first. Object: the same stored samples and standardization as run 069, so the moment is taken on the object whose KS distance was flat. By construction: the twin separation was suggested by the very numbers it would test, so it is reported only; the scored clauses are the ones no number on hand answers (reseed and size stability). Null: if skewness were pure noise, reseed differences would be about √2 times one error, and 2 of 3 beyond 3 errors would be rare. Negation: a world where skewness drifts with L shows g₁ changing between 729 and 6561 on most carpets — the carpets' falling local slopes make that a live possibility, which is why clause B exists. Cost: minutes, stored data only. Reviewed before commit by a second reader (OPS.md); its seven edits — the twin clause moved to reported, the Y/Y1 exclusion removed with it, the shared-X dependence made moot, one outcome rule for clause A, raw skewness bootstrapped without standardization, a rule for missing files, and the claim narrowed to the carpets tested — are folded in.

Scored 2026-09-30 — confirmed

Scored by the codifier from RESULTS072.md (86143cd), as written. Every file was present and readable (8,000 samples each), so no comparison is unscored.

(A) Reproducible — holds. Reseed differences at L = 6561, run 061 against run 063: X −0.88, Y +0.72, Z −1.63 combined errors, all within 2. Bootstrap errors (0.026–0.042) came out close to the normal-theory 0.027; the tails did not widen them much.

(B) Stable with size — holds, at its floor. Ten of fourteen carpets agree between 729 and 6561 within 2 combined errors, exactly the 70% the clause asks for. Two differ beyond 3 (T +5.16, X −3.22), well short of the falsifier's six. Beyond 2 but within 3: Z −2.83, X1 +2.54.

What the pass does not say. Four of fourteen beyond 2 errors, where noise gives about 0.6, has probability about 0.3%. So skewness is reproducible at a fixed size, but on some carpets it is still moving with L: T falls from +0.36 to +0.17, X and Z rise, X1 falls. The clause was written for exactly this worry, and it passed by the smallest margin it allowed.

Consequence for the twin clause, reported. The seal's next step is a twin clause on fresh reseeds. The size drift reaches the twins. At 6561 the twin ordering is the lead's (X above X1 by +4.33, above X2 by +5.67, Z above Z1 by +3.18). At 729, from the same table, X/X1 reverses sign (−1.43), X/X2 holds (+4.41), and Z/Z1 weakens (+1.94). A twin clause must therefore name its size: fixed at 6561, with 729 reported. The X/X1 ordering is itself size-dependent on the stored samples.

Reported: skewness is not a proxy for the exponent. Spearman(g₁ at 6561, 1/ν) over the fourteen carpets is +0.156 (Pearson −0.003). If skewness separates twins, it does so as a second coordinate, not as a restatement of 1/ν. The square stays at zero within error at both sizes (+0.009, +0.011).

generated 2026-10-25the lab index