run 070Settled
../lab/runs/070-cross-class-stacks.mdPrediction(M, machine control) the cloud's T lands within 2√2·s = 0.0127 of its recorded 0.3743. (C, control) each pair's two orders agree within 2√2·s = 0.0127. (A) v(X,T) < m(X,T) − 2σ_XT, with m(X,T) = 0.4626. (B) v(U′,T) < m(U′,T) − 2σ_UT, with m(U′,T) = 0.3249. Confirmed if A and B both hold. A and B test the averaging hypothesis only: holding means the stack falls below the arithmetic mean; it says nothing for or against a geometric-mean rule, which this run cannot separate (see below).
FalsifierBoth pairs at or above m − 2σ — cross-class stacks average after all and run 067's X∘U′ deficit was particular to that pair. Exactly one of A, B holding is unanticipated. A pair whose orders are apart by more than 3√2·s is withdrawn alone (the other pair is scored, and the run is then unanticipated at best); apart by between 2√2·s and 3√2·s, it is scored and flagged. The machine control failing (cloud T more than 0.0127 from 0.3743) withdraws the whole run as a machine artefact, and it moves to the M5. Withdrawn as underpowered if the median bootstrap error on the four stacks' endpoint exponents exceeds 1.5·s = 0.0068. Reported, not scored: v against the geometric mean of the parents (X,T 0.4540; U′,T 0.3211) — at these parent gaps the geometric and arithmetic means differ by 0.009 and 0.004, so this run cannot separate them and says so; each stack's stage-1 y against the parents' one-block mean.
Sealed 2026-09-29, after run 067 was scored and before any stacked lattice involving T was built (codifier). Known at sealing: runs 051–069; run 068's stage-1 census (committed, not read by the codifier for this seal; it contains no stacked quantity). Not known: any quantity of these four stacks.
Why below. Run 067's reading: a bottleneck level (fewer minimum cuts) governs more than its share, so a stack of unequal cut classes falls below the parents' mean, and equal classes average. Here both pairs mix classes (4 with 3; 2 with 3), so both should fall below. Conviction moderate: the rule is one pair old.
The reductio this seal passed first (OPS.md). Object: the same stacked builder, estimator and noise unit as run 067, so the comparison with 067 is like for like; the new element is the machine. Invariance: the two orders of a pair differ by one top level of an infinite object, so their exponents are equal as a theorem — the control also checks the cloud build against the theorem. By construction: parents are fixed recorded values, so no parent is re-measured on a different machine. Negation: a world where only X∘U′ fell below shows both pairs within 2σ of their means. Null: a 2σ one-sided excursion happens about 2.3% of the time per pair. Transform: the contrapositive — if a cross-class pair averages, "class mismatch pulls down" is false as stated — is exactly the falsifier.
Reviewed before commit by a second reader (OPS.md); its seven edits — the arithmetic-only scope of A and B stated, per-pair withdrawal, the shared-parent correlation named, a cloud machine control on T, the bootstrap gate tied to s, stage 1 marked report-only, and the 2-cycle defined — are folded in.
A note on the machine. This is the lab's first run on cloud compute. The cloud container may be slower than the M5 and may be reclaimed if idle, so the run checkpoints: each lattice's thresholds are committed to the run's branch as soon as they finish. A run that cannot finish in the container is withdrawn, not extrapolated, and moves to the M5 unchanged.
unanticipatedScored by the codifier from RESULTS070.md (merged in 4ed12fa, PR #3), as written.
(M) Machine control — holds. The cloud's T: 0.3745 ± 0.0037 against the recorded 0.3743 (+0.0002; limit 0.0127). The run stands on the cloud.
(C) Order agreement. X,T: X∘T 0.4706, T∘X 0.4775, gap 0.0069, inside 0.0127. U′,T: U′∘T 0.3211, T∘U′ 0.3438, gap 0.0227, beyond the 0.0191 withdrawal line: U′,T is withdrawn alone, as the falsifier provides. Bootstrap gate met (median error 0.0040 against 0.0068).
(A) X,T below its mean — fails, in the opposite direction. v = 0.4740 against m = 0.4626: v − m = +0.0115, +2.73σ above the mean, not below it.
(B) U′,T — withdrawn. Reported: v − m = +0.0075 (+1.67σ), also above.
Outcome. With one pair withdrawn the run is "unanticipated at best", and the falsifier as written ("both pairs at or above m − 2σ") cannot be met by one scored pair, so the outcome is unanticipated. In substance the sealed rule is refuted: the only scored pair lies 2.7σ on the wrong side, and the withdrawn one lies on the same side. The seal did not say what a single surviving pair decides; that gap is the codifier's, and OPS.md now requires every falsifier to state it.
Reported, read post hoc. - Last local slopes (OPS rule). Stacks: X∘T 0.4474, T∘X 0.4832, U′∘T 0.2874, T∘U′ 0.3255. Parents: X 0.5520, T 0.351 (run 053), U′ 0.249. On last local slopes the pairs read +0.014 (X,T) and +0.007 (U′,T) above the parents' mean: the same sign as the endpoints. - Geometric mean. v lies above it too (+0.020, +0.011). - One-block values (stage 1). y exceeds the parents' one-block mean by +0.0022 (X,T) and +0.0052 (U′,T): the same sign as the lattice, a third to a half the size. In run 067 the one-block value and the lattice moved in opposite directions (X∘U′); the one-block map does not predict the direction. - Three cross-class pairs, three answers. X∘U′ below its mean (−3.5σ, run 067), X∘T above (+2.7σ), U′∘T above (+1.7σ, withdrawn); the same-class X∘Y averages. No ordering of the parents by exponent, cut class, N₁ or one-block p* (X 0.740, T 0.832, U′ 0.943) gives the three signs. The stacked exponent is not a function of the two parents' exponents. - The order gap. The two orders are one infinite object, so their exponents agree in the limit; at L = 6561 they differ by 0.0069 (X,T, 1.2 errors) and 0.0227 (U′,T, 4.1 errors), with the local slopes of the two orders moving in opposite directions for X,T. The top generation still carries a correction of that size. A stack alternates two generators each generation, so the order gap measures a generation-parity term directly (P-048, hump programme). - Machine. 4 cores, 15 GB; 2.8–3.0 h per L = 6561 lattice, about 4× the M5; 1.2 GB peak; 14.5 h in all, surviving one worker restart. The lab's first cloud run is a working option for L ≤ 6561.
generated 2026-10-25the lab index