run 063Settled
../lab/runs/063-cut-twins.mdPrediction(A) Cut counts do not set the miss: at least one of the four comparisons has |Δmiss| ≥ 0.015. (B) The weak version holds: Spearman(ln c, y₂ − measured) over H, U, V, A, B is at least 0.9.
Falsifier(A) all four |Δmiss| ≤ 0.008 — twins have equal misses within noise, and cut counts may carry the miss. (B) Spearman at most 0.3. If max |y₂ − y| over H, U, V, A, B is below 0.006 (the smallest gap between adjacent one-block misses), clause B is reported as inherited and uninformative — neither confirmed nor falsified — because the one-block order already has ρ = 1. Between prediction and falsifier on either clause is unanticipated. If run 061 withdraws its Part A, clause B is withdrawn; clause A is withdrawn only if both measurements of an original are unusable; a failed estimator control in stage 2 (the square, as in run 061) withdraws clause A.
Sealed 2026-09-29, while run 061 is sampling, before any of its exponents or two-step values for H, U, V, A, B has been computed, and before any polynomial of a twin has been computed (codifier). Known at sealing: runs 051–062 including 062's Part A (every N(g) and c in the pool); run 061's pre-sample record; one line of run 061's Part A log, Z's y₂ = 0.5533 against y = 0.5435, which is what P-048's deduction rests on and which enters neither clause. Reviewed before commit by a second reader (OPS.md); its three edits — the originals re-measured, clause B on fixed reference values, and an inherited-order guard — are folded in. Not known: any twin's y or exponent; any of run 061's measured 1/ν; any y₂ for H, U, V, A, B.
Noise. Each measured 1/ν carries a run-to-run spread of about 0.004 (run 056); Δmiss combines two measurements and the twins' exact y, so its spread is about 0.006. The threshold 0.015 is 2.5 spreads; 0.008 is the noise band used in run 062. With four comparisons, one exceeding 0.015 by chance is a few-percent event under the null. Comparisons 5–X and 12–X share X's value, which is why each original is measured twice.
Why A should hold, and how it could pass without the mechanism. P-048's Deduction 2: the same c at a larger block gave a different exponent for Z, so c cannot be the whole story, and twins share c and N₁ exactly. Against: twins may have nearly identical polynomials, so that nothing differs to detect. If every twin's y lies within 0.002 of its original's, clause A still tests whether their measured exponents agree, but a pass then says little about y; that case is reported.
Why B. If c describes the one-block approximation's error rather than the physics, the ordering it gives should survive one more block, even as values shift. With five points, ρ ≥ 0.9 allows one adjacent swap; B and H differ by 0.008 in the one-block miss, the pair most likely to swap.
What the outcomes mean. A confirmed: the miss depends on the pattern's geometry beyond its cut counts, and the next object is what twins differ in. A falsified: cut counts alone set the one-block exponent's error, and P-048's Deduction 2 needs another reading of Z's shift. B confirmed with A confirmed: c orders the error of the approximation at every block size, but does not set the exponent. B falsified: c's order was a one-block accident.
confirmedScored by the codifier from RESULTS063.md (cdd879b), as written. The chained analysis failed on a sanity-file parse and was re-run by hand with no sample file changed (analyze063.log); that does not touch the statistic.
Control holds. P₂(0.5) on the 81×81 square = 0.505985, within 0.01 of 0.5064. (Reported, not a clause: the square replica on L = 81, 729, 2187 gives 0.7357 ± 0.0049, the estimator's known low side — run 061's eight repeats averaged 0.741.)
Clause A — confirmed. Three of four comparisons exceed 0.015: entry 5 – X +0.0228 ± 0.0049, entry 12 – X +0.0400 ± 0.0048, entry 11 – Z +0.0229 ± 0.0045; entry 10 – Y +0.0076 ± 0.0049. Cut counts do not set the miss. Against the reseed floor sealed in P-048 (s = 0.0045 from the X, Y, Z re-measurements, s_gap = 0.0055): the three large gaps are 4.1, 7.2 and 4.1 s_gap; entry 10 – Y is 1.4 s_gap, within reseed spread. The two X twins also differ from each other by 0.0172 ± 0.0056 (entry 5 – entry 12).
Clause B — confirmed. Spearman(ln c, y₂ − 1/ν) over H, U, V, A, B = 0.9, at the threshold. Not inherited by the letter of the seal (max |y₂ − y| = 0.0265 > 0.006), but by its spirit: y₂ − y itself correlates −0.6 with ln c, and y − 1/ν correlates 1.0. The 0.9 is the one-block order surviving one adjacent swap (H and B), not new information carried by the two-step shift.
What it settles, and what it opens. Every twin measures below its original — X1 −0.0149, X2 −0.0298, Y1 −0.0050, Z1 −0.0385 in 1/ν — while one-block y puts three of the four twins above. So the y₉ ranking that held across the ten patterns of CASE-26 fails on twins: X/X1 and X/X2 invert beyond noise (2.7 and 5.4 s_gap), Y/Y1 inverts within noise, Z/Z1 holds. With Y/P2 (CASE-26's already-measured twin pair, also inverted), four of five twin pairs run against y₉, against 5 of 45 pairs in the ten-pattern record. A lead for the next seal, not a result of this one: y₉'s ranking may ride on cut structure — it orders patterns whose cut counts differ and carries no information between patterns whose cut counts coincide. Open: why all four twins sit below their originals (the originals' selection rule in run 062 should be checked before any reading).
generated 2026-10-25the lab index