Math Mapgenerated 2026-10-25 · a354234
PUBLIC BUILD

run 132Settled

On five census blocks no operator run has built (20, 35, 36, 39, 44), does the graph-only core rule say exactly which single-cell toggles give the same block operator? Two things are asked. Which off-diagonal wedge toggles c give T_c = T_{cᵀ} under the main-diagonal mirror? Which pairs of visible wedge toggles give T_c = T_d?

slug
the-operator-sees-the-core
state
run
created
2026-10-24
sealed
2026-10-24 (committed before any operator is built on blocks 20, 35, 36, 39 or 44)
builds_on
[119, 122]
concepts
[transfer-operator, symmetry, percolation, network-reliability]
programme
PG-01
line
the block as an operator (what T can see)
from
run 122 (confirmed). T sees a cell exactly when the cell lies on a route between two boundary cells. Its reading left two observations unexplained. The main-diagonal mirror sometimes leaves T unchanged (cell (2,3) on two blocks), and different cells sometimes give the same T. A formation reader was fenced to blocks already built, with graph computation allowed everywhere (R28_reading/formation/tblind/REPORT.md). It explained both by a network reduction of the kept-cell graph: prune, merge series and parallel edges, and replace two-ended terminal-free pockets by one edge. It predicted every reserved block's mirror equalities and equal-T classes from the graph alone (R28_reading/formation/tblind/predictions_all63.json). Guesses: docs/walk/2026-10-21-pre-registration-symmetry.md, section of 2026-10-24 12:40.
statistic
R27_tree_groups/carpet_perc/. tblind132.py is a copy of vis122.py restricted to indices 20, 35, 36, 39 and 44. Its p* is vis122.py's: float(Decimal(p_star_40_digits)), asserted equal to transfer_op.json's stored p at p_label star. Its flips, transposed flips and key names are vis122.py's. transfer_op.build_T and generator, and e3_119.flipped, are imported and not edited. For each block, build T(K) unflipped, T_c = build_T(flipped(idx, c), p*) for the 15 wedge cells c = (i, j) with 0 ≤ i ≤ j ≤ 4, and T_{cᵀ} for the 10 off-diagonal ones. That is 130 builds. Visible means Δ_c = max over entries |T_c − T(K)| > 1e−11. Scored: (A) for every off-diagonal wedge cell that is visible, whether D_c = max|T_c − T_{cᵀ}| ≤ 1e−11, against predictions_all63.json's T_c_equals_T_cT. (B) for every unordered pair {c, d} of distinct visible wedge cells on the same block, whether max|T_c − T_d| ≤ 1e−11, against "c and d lie in one list of the block's equal_T_classes". Reported beside: every Δ_c, D_c and pairwise difference; σ₁…σ₄ of every T; build time and peak RSS; and whether visible in the json matches Δ_c on all 75 flips.
outcome
confirmed
scored
2026-10-24 (blind scorer, R28_reading/132/scorer132.md)
pre_seal_glimpse
runs 119 and 122 and the formation reader's builds on blocks 12, 8, 19, 42, 7 and 38. No operator has been built on blocks 20, 35, 36, 39 or 44.
source
../lab/runs/132-the-operator-sees-the-core.md

Prediction(A) D_c ≤ 1e−11 on exactly the five predicted cells, (2,3) on each of the five blocks, and D_c > 1e−11 on the other 43 visible off-diagonal cells. (B) max|T_c − T_d| ≤ 1e−11 on exactly the five predicted pairs, one per block, and above it on every other pair of visible wedge cells. Each is scored separately. Confirmed if both hold.

Falsifier(A) any visible off-diagonal cell whose D_c falls on the other side of 1e−11 from its prediction. (B) any pair whose equality differs from its prediction. A falsified clause says the core does not decide T. Unanticipated, recorded and not scored: a flip whose visibility differs from the json's visible, since run 122's rule is not this run's clause. Withdrawn if a control fails.

Statement

T is the block's crossing operator: given which left cells are wet, the chance of each set of wet right cells. Run 122 showed that T sees a cell exactly when the cell lies on a route between two boundary cells. But T sees less than that. Sometimes toggling a cell and toggling its mirror image give the same T, and sometimes two different cells do. A formation reader explained both with network reliability. Strip the kept-cell graph to the edges that lie on routes, merge series and parallel edges, and replace each pocket that touches the rest at only two cells by a single edge. Two toggles give the same T exactly when the resulting cores match with every boundary cell fixed. The block-cut tree is too coarse: what decides is the two-cell separations inside a component.

The rule was formed on blocks already built. This run builds five blocks no run has built and checks every prediction the graph makes on them. Each block has exactly one mirror-equal cell, (2,3), and one equal pair. The other 43 visible mirror comparisons and every other pair must differ.

Sealed 2026-10-24

As written. The lab chat reads this file above "Not part of the seal" only, plus vis122.py, e3_119.py, transfer_op.py and predictions_all63.json.

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

Scored 2026-10-24 — confirmed

A blind scorer read the seal above the line and RESULTS132.md (386ebc8) and nothing else (R28_reading/132/scorer132.md). It checked every per-cell and pairwise table itself. Scores are as written.

Controls. (i) σ₁…σ₄ of the five unflipped operators match to 6.4e−16 relative. (ii) Block 8 at (2,3) gives 4.441e−16.

(A) Confirmed. Of 48 visible off-diagonal cells, D_c ≤ 1e−11 on exactly the five predicted, (2,3) on each block (1.1e−16 to 2.2e−16). The other 43 are all 4.065e−3 or more. (B) Confirmed. Of 442 pairs of visible cells, exactly the five predicted are at or below 1e−11 (5.6e−17 to 2.2e−16). The other 437 are all 3.03e−3 or more.

What the numbers say beyond the clauses. 1. Which single-cell toggles give the same block operator is read from the graph alone, before any operator is built. Strip the kept-cell graph to its network-reliability core: prune dead ends, merge series and parallel links, and replace two-ended pockets by single links. Two toggles give the same T exactly when the cores match with every boundary cell fixed. The predictions were made on five blocks no operator run had built, and all 490 comparisons fell on the predicted side, by at least 13 orders of magnitude. 2. The json's visible matches Δ_c on all 75 flips, which reconfirms run 122's route criterion. 3. This was the sufficient direction of the reader's rule. Necessity (unequal cores give unequal T) is unrefuted on 437 + 43 more comparisons.

Procedural. The memory stop and restart (tblind132b.py, memory guard only) are filed as OPS instance 20. Builds from the two scripts agree wherever they should. The lab chat had memory on.

Theme instance (added 2026-10-25, records). themes/symmetry.md §2.1h, 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