run 121Settled
../lab/runs/121-o2-separation-out-of-sample.mdPrediction(A) on (N), both off-diagonal cells are 0. (B) on (R), both off-diagonal cells are 0. Each scored separately; confirmed if (A) holds; (B) reported as held or not.
Falsifier(A) any rule of (N) in an off-diagonal cell. Unanticipated: a rule with |O₂| < 1e−9 after the 40-digit recomputation, or a rule whose period-3 status changes between the sealed scan and a rescan on a ten-times finer grid (run only on rules with |O₂| < 1e−3) — recorded, not scored. Withdrawn if control (i) or (ii) fails, or the dual check fails at 50 digits on any pair.
Run 120 showed, on 286 rules, that a hump map's core carries a Li–Yorke-ordered point exactly when the map has a 3-cycle. Seen once, that is a pattern; this run asks whether it holds where nobody has looked — longer bands and larger k, and rules drawn at random from the whole box, which are not symmetric and can have several humps. −∞ counts as O₂ < 0; monotone maps and zero-length cores are listed and left out of the table; the dual check runs at a named precision.
As written. The lab chat reads this file above "Not part of the seal" only, and rule114.py, core120.py, o2_premise.py, RESULTS114.md and RESULTS120.md for the method.
withdrawnScored by a blind reader given the seal above the "Not part of the seal" heading and the lab's numbers (R27_tree_groups/carpet_perc/RESULTS121.md). Controls held (run 120's table reproduced, 4.9e−16; logistic −0.06406, +0.06627). The dual check failed at 50 digits on four pairs, which the seal made a withdrawal on any pair. Reported:
| (N) 394 named rules, k = 13 … 16 | (R) 4,000 random box rules, k = 7, 8 | |
|---|---|---|
| O₂ ≥ 0, period three | 253 | 0 |
| O₂ ≥ 0, none | 0 | 0 |
| O₂ < 0, period three | 0 | 0 |
| O₂ < 0, none | 141 | 3,411 |
| left out | 0 | 589 (588 monotone, 1 zero-length core) |
Faults in the seal's wording (the reader's six, kept, and the codifier's): the dual check named a precision and not a pass threshold at it, and 50 digits was not enough on single-term rules whose dual sits at 1 − 10⁻³⁰ — the same artefact as run 120, one precision step further, a fault of the codifier's that two runs now share; the statistic said "critical point at the global maximum" and pointed to core120's definition, which takes the first zero of R′ — they differ on multi-humped rules, and core120 chose a local minimum on 758 of them; (R) was meant to test multi-humped maps and none had a 3-cycle, so the table's left column is empty and (B) tested nothing; "each scored separately" and "(B) reported" contradict; the 40-digit recomputation was gated on double values, and three random rules at −1e−8 in double are 1e−31 at 50 digits.
Reading (the codifier's, after the score): two withdrawals in a row on the same control is a fault in the control, not in O₂. The dual check is a check on the code (the conjugation is exact; any difference is rounding), and it has now withdrawn two runs whose substance held: O₂'s sign separates period three exactly on all 680 named rules computed (286 in run 120, 394 here), with no exception at any k from 2 to 16. Next: the dual check becomes a control on the sign (O₂ and its dual have the same sign at the working precision), with the value comparison reported beside; core120's critical-point selection is fixed to the global maximum before any multi-humped rule is used; and the random-rule test needs rules that have 3-cycles, so it should draw from the band-rule neighbourhood (perturbations of the 124 period-3 rules), not uniformly from a box where chaos is rare.
generated 2026-10-25the lab index