Math Mapgenerated 2026-10-25 · a354234
PUBLIC BUILD

run 127Falsified

On the census generators other than generator 1, 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-resealed
state
run
created
2026-10-23
sealed
2026-10-23 (committed before any census operator's support is examined, apart from generator 1's, seen in run 126's RFI)
builds_on
[119, 122, 126]
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. Run 126, withdrawn before compute because its control (i) was mis-specified (OPS instance 17); this seal is 126 with the control computed on the operators it builds.
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 except index 1, the observed count against the predicted count in oneway_rule_pred.log. Generator 1 is built and reported (its count, 64,350, was seen in run 126's RFI) and is not scored. 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
2026-10-24
outcome
falsified
outcome_note
by the falsifier as written — 10 of 62 scored generators differ from the rule's count (7, 8, 12, 19, 21, 32, 42, 43, 46, 47). All 23 with a connected interior match, and all 10 mismatches have a disconnected interior (30 other disconnected ones match). The unanticipated clause fired: 314,856 one-way pairs with neither subset in U, all on the ten. Not anticipated: every mismatched count is still k(511 − k), with another k (generators 42, 43, 46, 47: 256 against the predicted 112). The product form, a cut between a set U′ and its complement, survives; the identification of U from the right-column holes fails where the interior is disconnected. Controls pass. M5, 28,071 s.
pre_seal_glimpse
the rule's predicted counts (from geometry); generator 1's observed count (64,350, equal to its prediction), seen in run 126's RFI; transfer_op.json's row-sum and memory fields. No other census operator's support.
source
../lab/runs/127-one-way-pairs-from-geometry-resealed.md

Prediction(A) the observed count equals the predicted count on all 62 scored generators: 0 on the 7 the rule clears, and the stated count on each of the other 55. 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

Run 126 as sealed, resealed with its control computed on the operators it builds. E1 asks whether the block is reversible in any metric that weights states. A single one-way pair rules that out. The owner's blind chat derived a rule: the count is |U|·(511 − |U|), set by the right-column holes alone. Applied to the census from geometry, it gives an exact integer per generator. This run counts them on the 62 not yet seen.

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. The lab chat for run 126 may continue as this run's chat; its script needs only the control (i) check changed, re-pinned before launch.

Ruling on the lab chat's stop, 2026-10-24 08:50 (operational, not the seal). The run stopped at 62 of 63 builds on the prompt's 7.5 GB memory guard, which was set for two workers sharing 16 GB. It is not part of the seal. Build generator 63 alone on one worker, with the same pinned script and a guard of 12 GB, then collect all 63 and write up as sealed. The ten mismatches already observed are scored as sealed. Generator 63's build completes the record but cannot reverse the verdict.

Scored 2026-10-24 — falsified

Scored by a blind reader given the seal above the "Not part of the seal" heading, with the operational ruling, and RESULTS127.md (R28_reading/127/scorer127.md). The reader's faults 1 and 2 are the codifier's, carried over when run 126 was resealed: the builds entry still named oneway126.py, and control (ii)'s noise still came from run 119 (OPS instance 18).

Reading (the codifier's, after the score). The blind chat's rule is right in form and wrong in one ingredient. The one-way pairs are always a cut, U′ × complement, with count |U′|(511 − |U′|). Its U, read off the right-column holes, is the right U′ exactly when the interior is connected (23 of 23). On disconnected interiors it is right 30 times in 40 and wrong 10 times. That localises the failure to how islands change which outputs are unreachable. The next question is not a seal: what is U′ on the ten, and what separates them from the thirty? It goes to the formation step with the pair lists in oneway127.json, which name U′ directly. One more point for E1: whatever U′ is, 56 of the 63 generators have one-way pairs, so on those Q is irreversible in every state-weighting metric. That is E1's step 1 answered for the census, whatever the rule.

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

generated 2026-10-25the lab index