ν ≈ 0.28 with a threshold still rising (0.866, 0.877, 0.881). Reseal with the estimator that passes the control, all three carpets at three common sizes: does the arrangement of holes change the class at fixed dimension, or only the threshold?

slug: carpet-class-reseal
state: run
created: 2026-09-28
sealed: 2026-09-28
statistic: Bond percolation on the nearest-neighbour graph of kept cells, left–right spanning, open boundary, union–find in C (R27_tree_groups/carpet_perc/, extended). Per sample, the exact spanning threshold p_c^(i) (bonds added in a uniformly random order; the fraction present when the first spanning cluster appears). p*(L) = median of p_c^(i); w(L) = q₀.₈ − q₀.₂ of p_c^(i); 1/ν = −slope of log w against log L. Samples: 8,000 per graph. Graphs: carpet H (3×3 centre removed) at L = 81, 243, 729, 2187, 6561 (generations 4–8); carpet U (run 049's sealed list) at L = 81, 729, 6561 (generations 2–4); carpet U′ = 9×9 generator removing {1,4,7}² ∪ {(2,2),(2,6),(6,2),(6,6),(3,3),(3,5),(5,3),(5,5)} (all holes single cells, connected, 64 of 81 kept) at L = 81, 729, 6561. The common sizes L = 81, 729, 6561 are the scored comparison for all three; H's full range is reported. Controls: square lattice at L = 81, 243, 729, 2187 with the same estimator; gasket at generations 6–10. Bootstrap (1,000 resamples) error on every 1/ν. Reported, not sealed: spanning-cluster D_f at p*, extrapolated p∞ from p*(L) = p∞ − A·L^(−1/ν).
script: R27_tree_groups/carpet_perc/ (Lab_Tree_Model)
artifacts: [R27_tree_groups/carpet_perc/perc051.json, R27_tree_groups/carpet_perc/RESULTS051.md]
builds_on: [049]
concepts: [fractal-dimension]
measured: 2026-09-28
outcome: confirmed
next: Is U′ a new class or a finitely-ramified crossover? Its 1/ν (0.276) sits beside the gasket's (0.263) and the p∞ clause could not tell them apart (the gasket, p_c = 1, extrapolates to 0.870). Measure U′'s minimal block-to-block cut set against generation — bounded means effectively finitely ramified | builds_on: 051
source: ../lab/runs/051-carpet-class-reseal.md

Prediction(1) Controls: square 1/ν = 0.75 ± 0.04 and p* → 0.500 ± 0.002; gasket p*(L) rising at every generation. (2) H and U are one class: |1/ν(H) − 1/ν(U)| ≤ 0.03 on the common sizes. (3) U′ is a different class, not a missing transition: its p*(L) increments shrink (p*(6561) − p*(729) < p*(729) − p*(81)) and extrapolate to p∞ < 0.92, and |1/ν(U′) − 1/ν(H)| ≥ 0.10 on the common sizes. At fixed dimension the room changes the class — through hole connectivity (U′'s singletons meet at corners), not hole size.

Falsifierany of — |1/ν(U′) − 1/ν(H)| ≤ 0.05 on the common sizes (U′'s 0.28 in run 049 was a small-size crossover, and at equal dimension all three carpets are one class: dimension decides class, the room only the threshold); U′'s p*(L) increments do not shrink or extrapolate to p∞ ≥ 0.97 (U′ has no transition at p < 1 at these sizes — it behaves as finitely ramified, and the room decides existence, not class). Either control failing withdraws the run. Between prediction and falsifier is unanticipated.

VerdictCONFIRMED on every clause; controls pass (square 1/ν = 0.7508 ± 0.0049, p* → 0.5000; gasket p* rising 0.751 → 0.812 over generations 6–10). H and U one class: 1/ν = 0.5468 ± 0.0039 and 0.5239 ± 0.0040 on L = 81, 729, 6561, Δ = 0.023 ≤ 0.03. U′ its own class: 1/ν = 0.2755 ± 0.0039, Δ from H = 0.271 ≥ 0.10; p*(L) = 0.8654, 0.8771, 0.8810, increments shrinking (0.0117, 0.0039), extrapolated p∞ = 0.888 < 0.92. At fixed dimension the arrangement of holes changed the class; hole size did not.

Sealed 2026-09-28 after run 049 was scored and before any of these samples was drawn (codifier). This is a reseal with a glimpse, recorded: run 049's full numbers were known (H, U, U′, square, gasket, D_f, p∞ extrapolations). The predictions for H vs U and for U′ are written knowing them; clause (2) is the unsealed 049 result restated at a size (6561) not yet measured for H, and clause (3) takes a position run 049 did not — that U′'s drift is convergence to its own threshold and class, not an absent transition. The estimator is the grid-free one that passed run 049's square control (0.753); the p-grid is gone, which removes 049's failure mode.

What the outcomes mean. Confirmed: at fixed dimension the class depends on the room, and on corner-contact of holes rather than hole size — §43's reading survives on fractals, and the H/U contrast was simply the wrong contrast. Falsified on the class clause: dimension decides class on connected carpets and §43's "room" reading gets nothing from fractals. Falsified on existence: U′ is effectively finitely ramified at these sizes, and ramification — the literature's variable — is what the room controls.

Scored 2026-09-28 (codifier; R27_tree_groups/carpet_perc/RESULTS051.md, Lab_Tree_Model). Confirmed on every clause, with one weakness in the seal that the controls exposed.

The class moved with the room at fixed dimension, and not by hole size: H (one 9-cell hole per block) and U (dominoes and singletons) are one class (0.547, 0.524); U′ (singletons meeting at corners) is at 0.276, far from both. Spanning-cluster D_f barely moves (1.839, 1.838, 1.857).
The p∞ clause had no discriminating power. The gasket, whose threshold is exactly 1, also extrapolates below 0.92 (0.870) at these sizes, so "p∞ < 0.92" could not have separated a transition below 1 from a drift to 1. What does separate them is the increment ratio: U′'s shrinks by 0.33 per factor 9 in L, the gasket's by ~0.57 per factor 8 — U′ converges faster. The seal's existence reading therefore rests on that ratio, not on the clause that confirmed it.
U′'s exponent is the gasket's. 0.276 against 0.263. The confirmed reading — "U′ is its own class" — has a competitor the seal did not name: U′ is effectively finitely ramified at these sizes (corner-touching holes pinch its blocks) and sits in the gasket's crossover. That is the next: on this run. Dictionary §43 gains its first sealed support, conditional on it.

generated 2026-10-25the lab index