Math Mapgenerated 2026-10-25 · a354234
PUBLIC BUILD

run 107Settled

Does the orbit through which the cut-2 wall enters the second ring order the lattice exponent? Thirteen of the nineteen cut-2 patterns have a lattice 1/ν (runs 068, 071, 080); every midline-entry pattern is above every corner- or off-axis-entry pattern (0.303 at the lowest midline, 0.276 at the highest other). Six are unmeasured: midline entry #49, #54, #55; off-axis entry #42, #43, #46. Do the six fall on the sides the orbit assigns them?

slug
cut2-wall-entry-orbit
state
run
created
2026-10-19
sealed
2026-10-19 (committed before any graph is built or sample drawn)
builds_on
[068, 071, 080, 098]
concepts
[fractal-dimension, correction-to-scaling]
programme
PG-01
line
L4, bands and the census
from
the owner's reading of the Carpet Census Atlas on 2026-10-19 (docs/walk/2026-10-19-owner-thread-atlas-hyperbolic.md §2): within cut 2, sorted by y₉, the patterns whose second-ring midpoint cells are holes come first, and #19 breaks the run. Checked the same evening against gen.py and census068.json: C₁ = 2 is exactly a wall of holes (8-connected) across the interior from the top ring row to the bottom, so the ring rows are the whole cut, and the wall's entry cell on the second ring's top side falls in one of three D4 orbits — the midpoint (column 4), a corner (columns 1, 7) or the off-axis cells (columns 2, 3, 5, 6).
statistic
R27_tree_groups/carpet_perc/ (Lab_Tree_Model). perc.c unchanged (md5 e341b2c86677a0ce71cc9a6e3de5982d, recorded before sampling). Graphs cen<i>_<g>.bin for i ∈ {49, 54, 55, 42, 43, 46}, g = 2, 3, 4 (L = 81, 729, 6561), built by python3 gen.py write cen<i>_<g> from census068.json where not already on disk, md5s recorded before sampling. 8,000 samples per file, 8 threads. Run 071's estimator exactly (analyze071.py's method): per-sample threshold k/M with M from the graph header, p* = median, w = q₀.₈ − q₀.₂ at each size, 1/ν = −slope of log w against log L over the three sizes, both local slopes reported, error = standard deviation over 1,000 bootstrap resamples (numpy default_rng, seed 107101 + rank, patterns in the order 49, 54, 55, 42, 43, 46), error gate 0.008 as in run 071 (a pattern over the gate is reported and not scored). Perc seeds 107001–107018, one per file in that order (49_2, 49_3, 49_4, 54_2, …), scanned clean on 2026-10-19 against every .py, .md, .json, .sh in the repository. Scored quantity: for each of the six, its 1/ν against the line 0.290.
controls
(i) the estimator reproduces run 071: analyze071.py's method applied to samples071/cen1_{2,3,4}.txt gives 1/ν = 0.5260 ± 0.0040 to the stated digits; (ii) each graph's bond count M and vertex count equal gen.py's for that pattern and generation, and the crossing fraction at g = 2 is neither 0 nor 1 (several of the six are disconnected at generation 2 — #49 and #42 have 66 components, #54 and #46 261, #55 521 — and run 068 measured #50, #53 and #38 of the same kind, so disconnection does not by itself empty the pile; a pattern whose 81-file has no crossing in 8,000 samples is withdrawn and named); (iii) the sampler is one sampler: the first 200 lines of each file equal the output of a 200-sample run with the same seed (run 092's keyed-by-index check); (iv) run 098's p_med at 729 for the six (0.75959 #49; the 098 values for 54, 55, 42, 43, 46 as RESULTS098 records them) are reproduced by this run's 729 files within 3 combined errors.
reported
the thirteen measured values beside the six, by orbit; the local slopes; within the off-axis group, whether y₉ orders the lattice; p* at 6561 for each. On BernoullisBook, a replicate of #49 at 6561 with seed 107021 (8,000 samples), reported as the between-machine spread of p_med and w against the bootstrap errors (run 092 found r₈ ≤ 1.42 for seed spread); not scored.
outcome
unanticipated
pre_seal_glimpse
the thirteen lattice values (RESULTS068, RESULTS071, RESULTS080) and run 098's p_med at 729 for all six were read by the codifier before sealing; they are the record, not this run's data. No sample of this run exists.
source
../lab/runs/107-cut2-wall-entry-orbit.md

PredictionEach of #49, #54, #55 (midline entry) has 1/ν above 0.290 by more than 2 of its error, and each of #42, #43, #46 (off-axis entry) has 1/ν below 0.290 by more than 2 of its error. Six clauses; confirmed only if all six hold.

Falsifierany one of the six on the other side of 0.290 by more than 2 of its error. Unanticipated: any value within 2 errors of 0.290 (the line is crossed by neither side cleanly), or a pattern over the error gate. Withdrawn if a control fails.

Sealed 2026-10-19

The question, statistic, prediction, falsifier and controls above are sealed as written; the scored line is 0.290 for all six. The lab chat does not read this file's lead. The replicate on BernoullisBook is a control reading, not a scored clause.

Scored 2026-10-20 — unanticipated

Scored by a blind reader given the seal without its lead and RESULTS107.md (reader output: six clauses, five hold as written; #49 at 0.2922 ± 0.0035 is +0.62 errors above the line, which meets "any value within 2 errors of 0.290"; the falsifier "any one of the six on the other side of 0.290 by more than 2 of its error" is met by none). Controls: (i) pass (0.5260 ± 0.0040); (ii) counts pass for all 18 graphs; crossing fraction 1.0000 at g = 2 for all six — ruled passed on the control's own named trigger ("a pattern whose 81-file has no crossing in 8,000 samples is withdrawn"), none empty; the literal "neither 0 nor 1" is a check perc cannot fail in mode 1, since every sample is run to its crossing, and is recorded as the seal's fault (OPS); (iii) 18 of 18 bit-identical; (iv) run 098's p_med at 729 reproduced, largest difference 2.35 combined errors (#43).

#orbit1/νerroroffset from 0.290, in errors
#49midline0.29220.0035+0.62
#54midline0.30240.0039+3.17
#55midline0.29840.0038+2.18
#42off-axis0.25920.0036−8.50
#43off-axis0.25550.0039−8.89
#46off-axis0.25580.0041−8.44

Reading (the codifier's, after the score): the orbit separation held — every midline value above every off-axis value, the nearest pair (#49, #42) eight errors apart — and the seal missed its own clause because the line 0.290 was placed 0.013 under the lowest measured midline value (#53, 0.303) when run 098 had already shown #49 below #50 at 729; a line at 0.280 would have confirmed. The prediction's substance was the owner's and held; the margin was the codifier's and did not. Within the off-axis three, y₉ does not order the lattice (y₉ ties #42 and #43). The BernoullisBook replicate of #49 at 6561 (seed 107021, 4 threads; md5 40ab6299f722036b18e0affc0499937c; landed 2026-10-20, lab commits fd0a100 and 243c2c8): p_med 0.75623 ± 0.00020 against the M5 file's 0.75627 ± 0.00018 (−0.15 combined errors); w 0.02172 ± 0.00024 against 0.02195 ± 0.00026 (−0.65). The between-machine spread at 6561 is inside the within-file error on both statistics — a reported control, not scored. The replicate's sidecar carries no wall time (BB's .err holds only the done line) and the lab's bootstrap seed for it, 107121, was its own choice, unscanned; perc.c on BB was the sealed md5 (checked at bundling, 2026-10-19).

Faults in the seal's wording (reader's list, kept): control (ii)'s literal test cannot be satisfied by the instrument and the seal gives no precedence between it and the named trigger; "equal gen.py's" vs an independent recount; "combined error" undefined; rounded vs unrounded comparison at the 2-error line (#55 at 2.18); orbit labels assumed available to the lab; p_med/p* name one quantity; no precedence between unanticipated and falsified.

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

generated 2026-10-25the lab index