Math Mapgenerated 2026-10-25 · a354234
PUBLIC BUILD

run 133Settled

On fresh draws of H at L = 2187, if the comb's even-tooth period P is fitted instead of fixed at 8, do the odd teeth vanish at the fitted period?

slug
the-comb-at-its-own-period
state
run
created
2026-10-24
sealed
2026-10-24 (committed before any draw with this seed)
builds_on
[130]
concepts
[fractal-dimension, symmetry, log-periodicity, invasion-percolation, fourier-duality]
programme
PG-03
line
the comb as a broken continuous symmetry (owner thread items 8, 11b, 16)
from
run 130 (confirmed). H7's odd teeth were below the clause floor but not zero, O = 0.0098 ± 0.0015 at the fixed period 8. Run 130's premise gave a residue of that kind for a burst dimension off ln 8/ln 3, because the comb's period in burst size is 3^{D_b}, not 8. The owner's ruling, 2026-10-24 11:38 ("yes" to sealing it). The codifier's premise on synthetic densities is R27_tree_groups/carpet_perc/combfree_premise.py and .log. Guesses: docs/walk/2026-10-21-pre-registration-symmetry.md, section of 2026-10-24 12:00.
statistic
R27_tree_groups/carpet_perc/. comb133.py is a copy of comb130.py (its edges, read_counts, window, jack and draw machinery unchanged) with the period free. perc_inv is built from perc_inv.c unchanged. One configuration: H7 (graphs/H7.bin), full-side source, 4,000 draws, perc seed 133101, written to samples133/H7_s133101.bin with its .json sidecar. Window, bins and weights are run 130's at L = 2187 (32 to 48000, ratio 1.12, weight = count). The model is run 130's columns with w = 2π/(2 ln P), so k = 2, 4 sit at period P and k = 1, 3 are the odd teeth. P runs over the grid 6.50, 6.52, …, 10.00. P̂ is the grid value that minimises the weighted residual sum of squares of the pooled fit. The odd coefficients at P̂ are v = (a₁, b₁, a₃, b₃). Their covariance C is the jackknife covariance over 20 blocks of consecutive samples: (19/20)·Σ(vᵢ − v̄)(vᵢ − v̄)ᵀ, where each leave-one-block-out fit is made at the pooled P̂. Scored: χ²_odd(P̂) = vᵀC⁻¹v. Reported beside: P̂ with its jackknife error (each leave-one-out fit rescans the grid); D_b = ln P̂ / ln 3; O and E at P̂ and at P = 8; χ²_odd(8), computed the same way at P = 8; the residual sum of squares over the grid; and the same quantities on run 130's samples130/H7_s130101.bin, reported and not scored.
outcome
unanticipated
scored
2026-10-24 (blind scorer, R28_reading/133/scorer133.md)
pre_seal_glimpse
run 130's RESULTS (O(H7) = 0.0098 ± 0.0015 at P = 8). No free-period fit has been computed on any burst file.
seed_scan
{date: 2026-10-24, hash: 2eac3eda708c6c2e, files: 4646}
source
../lab/runs/133-the-comb-at-its-own-period.md

Prediction(A) χ²_odd(P̂) ≤ 20: at its own period, H carries no odd teeth, and run 130's residue was the period's. Confirmed if (A) holds.

Falsifier(A) χ²_odd(P̂) ≥ 60: the odd teeth survive at H's best period, so H's bursts carry a comb tooth its kept magnifications forbid. Between 20 and 60, unanticipated. Also unanticipated, recorded and not scored: P̂ at either end of the grid. Withdrawn if a control fails.

Statement

Run 130 confirmed that H, the Sierpinski carpet, carries only the even teeth of the comb. But its odd teeth were not quite zero. The comb's period in burst size is 8 only if bursts scale like the carpet's area. If their own dimension D_b differs from ln 8/ln 3, the period is 3^{D_b}. A fit with the period pinned at 8 then leaks into the odd teeth. This run frees the period on fresh draws. It asks whether, at H's own period, the odd teeth vanish.

Sealed 2026-10-24

As written. The lab chat reads this file above "Not part of the seal" only, plus comb130.py, perc_inv.c and combfree_premise.py.

The codifier’s lead is kept for the private site.

Scored 2026-10-24 — unanticipated

A blind scorer read the seal above the line and RESULTS133.md (1a2a1e0) and nothing else (R28_reading/133/scorer133.md). Scores are as written.

Controls. - (i) At P = 8 on run 130's samples, O and E are reproduced exactly. - (ii) χ²_odd(8) = 165.48 on the fresh draws, so the residue reproduces.

(A) Unanticipated. χ²_odd(P̂) = 33.11 at P̂ = 7.32 ± 0.04, which is between the confirm line (20) and the falsifier (60). P̂ is not at a grid end.

What the numbers say beyond the clause. 1. H's comb has its own period, and it is not 8. P̂ = 7.32 on the fresh draws and 7.34 on run 130's draws, so D_b = ln P̂/ln 3 = 1.812 ± 0.005 against ln 8/ln 3 = 1.893. The residual sum of squares halves at P̂ (142.5 against 284.9 at 8). Bursts on H scale with a dimension of their own, below the carpet's. 2. Freeing the period removed most of the odd residue, but not all. χ²_odd fell from 165 to 33. What is left is mostly the k = 3 tooth: a₃ = −0.00675 ± 0.00131, at period P̂^{2/3} ≈ 3.8 in burst size. The kept magnifications forbid it. It sits at 3/2 of H's fundamental, which only a dilation by 3^{2/3} could carry, and H has no such symmetry. It is not a harmonic of H's comb. 3. Candidates, none tested: - the full-side source, whose geometry need not respect the hierarchy (the point-source run is the lead's named next question); - a scale-dependent period, if D_b drifts across the window; - the bin ratio 1.12 beating against the period. 4. Procedural. perc_inv was not rebuilt; the existing binary was built from the sealed perc_inv.c at 10:19 today, and no control checks it. The lab chat had memory on.

Theme instance (added 2026-10-25, records). themes/symmetry.md §2.1f (the second block), written from this section. The frontmatter's theme_instance field above the line predates it and is left as sealed.

generated 2026-10-25the lab index