Math Mapgenerated 2026-10-25 · a354234
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run 061Falsified

Run 059's corrected exponent failed because it read the 81×81 lattice's slope at the one-block fixed point p*, where that lattice is already on the shoulder of its crossing curve. Two questions follow. (A) Read at the 81×81 lattice's own fixed point, does its slope give an exponent closer to the measured 1/ν than the one-block y — does the renormalization improve with block size? (B) After the fact, the first-order commutator D₂′(p*) ranked with the one-block exponent's error y − measured (ρ = 0.88 over eight lattices). Does that ranking hold on rooms it has never seen?

slug
own-fixed-point-and-new-rooms
state
run
created
2026-09-29
sealed
2026-09-29
builds_on
[059, 058, 055]
concepts
[fractal-dimension]
statistic
R27_tree_groups/carpet_perc/ (Lab_Tree_Model). Part A, for the square and carpets H, U, U′, T, V, A, B: the two-generation crossing probability P₂(p) of the 81×81 lattice (run 059's lattices, bonds and terminals), by Monte Carlo with 2×10⁶ samples per point. p₂* = the root of P₂(p) = p in (0, 1), located by bisection to ±0.001; λ₂ = P₂′(p₂*) by central difference at p₂* ± 0.005; y₂ = ln λ₂ / ln 81. Part B: three new carpets from run 055's 19-generator pool (mincount055.json), excluding A and B, chosen by rule before anything is computed on them: the generators whose s(4) is closest to the 25th, 50th and 75th percentiles of the remaining seventeen, ties to the lexicographically smallest hole list. For each: run 058's exact crossing polynomial (R, p*, λ, y), run 059's D₂′(p*) (P₂′(p*) − λ² with P₂′ by central difference at p* ± 0.005, 2×10⁶ samples per point), and then — only after y and D₂′ are committed as a pre-sample record — the measured 1/ν by run 051's estimator (8,000 samples, L = 81, 729, 6561, 1,000-resample bootstrap). Seeds 6101 upward, checked unused and listed. Reference values: measured 1/ν square 0.7411, H 0.547, U 0.524, B 0.5170, V 0.477, A 0.4294, T 0.374, U′ 0.276; one-block y from run 058; D₂′(p*) from run 059. Reported, not sealed: p₂* beside p* and the measured p∞ for all eleven lattices; the three new rooms' hole lists, s(4), p∞.
script
R27_tree_groups/carpet_perc/ (Lab_Tree_Model)
artifacts
[R27_tree_groups/carpet_perc/RESULTS061.md, R27_tree_groups/carpet_perc/rg061.json, R27_tree_groups/carpet_perc/perc061.json]
outcome
falsified
source
../lab/runs/061-own-fixed-point-and-new-rooms.md

Prediction(A) |y₂ − measured| < |y − measured| on at least six of the eight lattices, and y₂ orders the eight as the measured 1/ν does on at least 26 of the 28 pairs. (B) Among the three new rooms, the offset y − measured 1/ν orders exactly as D₂′(p*) does (larger D₂′, larger offset), and over all eleven lattices the Spearman correlation of D₂′(p*) with y − measured is at least 0.7.

Falsifierany of — y₂ closer than y on three or fewer of eight (a bigger block does not improve the renormalization at this size); over all eleven lattices, Spearman ρ(D₂′(p*), y − measured) ≤ 0.3 (the post-hoc ranking of run 059 does not survive new rooms). A failed Monte Carlo sanity check (P₂(0.5) on the square within 0.01 of run 059's 0.5064) withdraws the run. Between prediction and falsifier on any clause is unanticipated.

Sealed 2026-09-29 after run 059 was scored and before any two-generation fixed point or any new room was computed (codifier). Known at sealing: every number in runs 051–060, including the post-hoc ρ = 0.88 that clause B tests. Not known: any p₂*, λ₂ or y₂; which three rooms the rule selects; any number about them.

Why A should hold, and why it might not. Small-cell renormalizations are expected to approach the true exponent as the cell grows, so the 81×81 block, read at its own fixed point, should land closer than the 9×9 one. Against it: the square's own estimator bias (runs 056, 059) is about 0.01– 0.02 and does not shrink with size, so the "measured" values are not the truth either; and carpets correlate across blocks in ways a single larger block still does not capture.

Why B is the real test. Run 059's ρ = 0.88 was found by looking at the eight lattices after the fact, which is the pattern this project exists to test rather than believe. Three rooms chosen by a fixed rule, with D₂′ recorded before their exponents are sampled, are the out-of-sample check. With three rooms, an exact ordering happens by chance one time in six, so the eleven-lattice correlation carries the weight.

What the outcomes mean. Confirmed on A: the renormalization converges with block size and the one-block polynomial's error is the finite-cell error it looks like. Confirmed on B: the first-order commutator predicts how far the one-block exponent is off — a correction term with the Taylor structure the thread has been circling. Falsified on B: the 0.88 was a pattern in eight points, not a law.

Second-reader review, 2026-09-29 — after launch, so it cannot change the scoring. Run 061 was sealed before OPS.md adopted the second reader (N-037); this is the first review, done by an agent given only the sealed text, after Part B's pre-sample record (fcc77fd) was committed. Its points, recorded before any result is read: - Part A can fail without the hypothesis failing. The measured references read low (the square by ~0.009, 056), so a y₂ that moves toward the true value can land further from the measured one; four lattices have one-block offsets of the bias's size. 6/8 is fragile for that reason. Reading the square against its exact 0.75, and reporting the signed shift y₂ − y, is the fairer check. - The bisection tolerance (±0.001) is the weak spot, not the Monte Carlo noise. Reading the slope up to 0.001 off the root moves y₂ by ~0.002–0.006, comparable to the run-to-run spread; SE(y₂) from sampling is only ~0.0004–0.0013. - ln λ₂ / ln 81 blends scales 1→81, so it still contains the one-block error; ln(λ₂/λ) / ln 9 is the direct test of improvement with block size. - Part A's ordering clause is nearly automatic: y already orders all eight exactly. - Part B's eleven-lattice ρ is mostly in-sample (eight of eleven points are where 0.88 was found); ≥ 0.7 is roughly a coin flip without a mechanism and ≤ 0.3 is almost unreachable. The genuinely new evidence is the three rooms' order (1 in 6 by chance), and those rooms may sit closer together than the estimator resolves. - A shared confound is possible: D₂′ is read at p*, the same shoulder point that sank 059, so it may track the estimator's finite-size bias rather than the renormalization's error. The scoring will report, beside the sealed verdict: the square against 0.75, the signed shift y₂ − y, ln(λ₂/λ)/ln 9, the three new rooms' order on its own, and the eight-lattice ρ separately.

Scored 2026-09-29 — falsified

Scored by the codifier from RESULTS061.md (73e0136, times corrected 465cb8a), as written. Sanity check passed (P₂(0.5) = 0.5070).

Clause A: falsified. y₂ is closer to the measured 1/ν than y on 1 of 8 lattices — the square (0.0026 against 0.0198) — and farther on all seven carpets; the falsifier (three or fewer) fires. The ordering half holds perfectly: y₂ orders the eight as the measured 1/ν on 28 of 28 pairs. y₂ > y on all eleven lattices: the bigger block moves every exponent up, toward the square's exact 0.75 and away from every carpet's measured value. This is what probe P-048 deduced before the result (Deduction 3, filed from one logged value): on these carpets the block renormalization does not converge monotonically to the measured exponent. And it is N-037's first pattern once more: the order is exact, the magnitude gets worse.

Clause B: unanticipated. The sealed order by D₂′ (X > Y > Z in the miss) fails: the misses are X +0.0011, Z +0.0154, Y +0.0361, so only Y > Z of the three pairs holds. The eleven-lattice Spearman ρ(D₂′, miss) = 0.50, between the prediction (≥ 0.7) and the falsifier (≤ 0.3). The post-hoc 0.88 of run 059 did not survive new rooms; D₂′ ranks, at best, loosely.

Reported readings. The three new rooms break run 058's exact ordering by y: y(Y) = 0.5495 > y(Z) = 0.5435 but measured 1/ν(Y) = 0.5134 < 1/ν(Z) = 0.5281, a gap of 0.015 (about three spreads). y₂ also has Y above Z. Y's pair slopes drift (0.526 → 0.501), as do U's (0.539 → 0.509); X's and Z's are flat. X's miss is zero within noise — the null case the transforms pass asked for (P-048), found by accident. The reviewer's extra readings: the square's y₂ (0.7385) is within 0.012 of 0.75; the signed shift y₂ − y is positive everywhere, largest on B (+0.0265) and V (+0.0247).

generated 2026-10-25the lab index