Math Mapgenerated 2026-10-25 · a354234
PUBLIC BUILD

run 126Settled

On the 63 census generators, does the number of one-way pairs of the block transfer operator equal |U|·(511 − |U|), with U fixed by the right-column holes alone?

slug
one-way-pairs-from-geometry
state
run
created
2026-10-23
sealed
2026-10-23 (committed before any census operator's support is examined)
builds_on
[119, 122]
concepts
[transfer-operator, symmetry, reversibility, percolation]
programme
PG-01
line
the block as an operator (the symmetry theme's E1, step 1)
from
docs/design/2026-10-22-symmetry-ladder.md §3d (E1 begins with whether Q is reversible in any diagonal metric; a single one-way pair rules it out). The rule tested is the owner's blind chat's (thread item 36). It was formed and checked on 5 × 5 grids that chat built itself, and it never saw a census generator. Its per-generator predictions on the census were computed from geometry alone before this seal (R27_tree_groups/carpet_perc/oneway_rule_pred.py and .log). The forecasts and the codifier's guesses are in docs/walk/2026-10-21-pre-registration-symmetry.md (sections of 19:30, 19:45 and 20:20). The owner's ruling, 2026-10-23 20:16.
statistic
R27_tree_groups/carpet_perc/. transfer_op.build_T and generator are imported, not edited, and oneway_rule_pred.py is imported for U, not edited. For each of the 63 census generators, build T = build_T(generator(index), 0.5). The support does not depend on p in (0, 1), since every bond configuration has positive probability. Q is T restricted to the 511 non-empty subsets. A one-way pair is an unordered pair {S, S′} of distinct non-empty subsets with exactly one of Q[S, S′], Q[S′, S] positive. Positive means > 0; the smallest possible entry is 2^−144 ≈ 4.5e−44, far above zero in float64, and entries are sums of positive terms, so nothing cancels. Scored: for each generator, the observed count against the predicted count in oneway_rule_pred.log. Reported beside, per generator: the observed count; |U|; whether census068.json records the interior as connected (interior_connected_without_ring, interior_components); and for every mismatch, the observed one-way pairs that do and do not involve a member of U. Also reported: wall time and peak memory per build.
scored
2026-10-23
outcome
withdrawn
outcome_note
before compute, on the lab chat's RFI (Phase 0 and the controls on generator 1). Control (i) was mis-specified. Its noise was taken from run 119's p* flip builds (1.33e−12), but the p = 0.5 operators the run builds have row-sum deviations up to 2.26e−11 in transfer_op.json, so the line 1e−11 fails on generators 57–63 by construction. And "T[∅, ∅] = 1" is exact in no stored build (1 + 1.3e−13). The seal's memory figure was also wrong (7,093 MiB is the p* peak; at p = 0.5 it is 5,637). Only generator 1 was built; its count was seen and is excluded from the reseal's score. Resealed as run 127 with the control computed on the p = 0.5 builds (OPS instance 17).
pre_seal_glimpse
the rule's predicted counts (from geometry); census068.json's interior-connectivity fields, not opened against the predictions. No support of any census operator.
source
../lab/runs/126-one-way-pairs-from-geometry.md

Prediction(A) the observed count equals the predicted count on all 63 generators: 0 on the 7 the rule clears, and the stated count on each of the other 56. Confirmed if (A) holds.

Falsifier(A) any generator whose count differs from the prediction. Unanticipated, recorded and not scored: a one-way pair in which neither subset is in U. Withdrawn if a control fails.

Statement

E1 asks whether the block is reversible in any metric that weights states. A single transition possible one way but not back rules that out absolutely. The owner's blind chat derived a rule for how many such pairs a holed grid has. Only holes beside the right column matter; interior holes add none. It checked the rule exactly on small grids of its own. Applied to our 63 census generators from their geometry alone, the rule gives 63 exact integers. This run counts them.

Sealed 2026-10-23

As written. The lab chat reads this file above "Not part of the seal" only, and transfer_op.py and oneway_rule_pred.py (and its .log) for the method.

Withdrawn 2026-10-23, before compute

The lab chat stopped at its controls and asked (RFI). The ruling is that the run in hand cannot proceed as sealed: its control (i) fails on 7 generators by construction, which no reading of the wording repairs. That is a premise not computed on the operators the run builds, so the run is withdrawn before compute and resealed as run 127. Generator 1's count (64,350) was seen in the RFI, by the lab chat and by the codifier. It is reported in run 127 and not scored there.

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

generated 2026-10-25the lab index