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sim-numerics/results_analyze_flat2.txt
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vvsandClaude Opus 5 9884b21204 PREREG_flat_twice outcome: stage 1 passed (twice-in-a-row fires on 27.8% of model steps on the flat families, 8.7% on APS, 4.3% on fun1; flat/APS ratio 3.20 against the single flag's 2.47), stage 2 FAILED: under the projection APS 2806 -> 2803 (W2 holds, the per-problem edge over Chandrupatla kept at 83/28/42) but CHA 3220 -> 3341 and the flat families 1823 -> 1975 (W1, W4 fail); with G2 the same. Under safe/step the twice gate is inert (3390 -> 3388) where the single one gave 3037. 
Mechanism: the flat cycle is undershoot, undershoot, crossing, near-empty step. The single flag fires after the first undershoot and replaces the second - a useless step; the twice flag fires after the second and replaces the CROSSING, the one step of the cycle that collapses the bracket. The second undershoot's r is ~0.26, next to the 1/4 threshold, so the pair often does not even form. Again a detectability gain that did not carry to run cost. Next candidate (not pre-registered): the unkept promise AND a creep - the same step moving the same way as the previous one.

Removed a vacuous pin I had written (s2 <= max(s1, s2)). Regression on the branch: 935 pass twice; the only red test is the paper-number check.

Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
2026-09-21 13:45:20 +01:00

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sweep: 140 configurations x 199 problems (FULL)
wrote sweep_flat2.json (8s total)
====================================================================================
APS: 154 problems (top 20 of 140)
====================================================================================
configuration solved total fev over 2x
------------------------------------------------------------------------------------
pure+extP+flat2.ratio.derived3.project 153/154 2781 0
pure+extP+flat2.ratio.derived3.none 153/154 2781 0
pure+extP.ratio.derived3.project 153/154 2782 0
pure+extP.ratio.derived3.none 153/154 2782 0
flat2.ratio.derived3.none 153/154 2803 0
flat2.ratio.derived3.project 153/154 2803 0
pure.ratio.derived3.none 153/154 2806 0
pure.ratio.derived3.project 153/154 2806 0
pure.ratio.derived3.step 153/154 3036 0
pure.ratio.derived3.safe 153/154 3036 0
flat2.ratio.derived3.step 153/154 3042 0
flat2.ratio.derived3.safe 153/154 3042 0
pure+extP.ratio.derived3.step 153/154 3089 0
pure+extP.ratio.derived3.safe 153/154 3089 0
pure+extP+flat2.ratio.derived3.safe 153/154 3097 0
pure+extP+flat2.ratio.derived3.step 153/154 3097 0
flat2.exp_abs.derived3.none 153/154 3257 0
flat2.exp_abs.derived3.project 153/154 3257 0
pure.exp_abs.derived3.none 153/154 3264 0
pure.exp_abs.derived3.project 153/154 3264 0
====================================================================================
CHA: 45 problems (top 20 of 140)
====================================================================================
configuration solved total fev over 2x
------------------------------------------------------------------------------------
flat2.cbrt.derived3.credit 40/45 3016 0
pure.cbrt.derived3.credit 40/45 3016 0
pure.ratio.derived3.credit 40/45 3020 0
flat2.ratio.derived3.credit 40/45 3040 0
pure.exp_abs.derived3.credit 40/45 3049 0
pure.ratio_soft.derived3.credit 40/45 3054 0
flat2.ratio_soft.derived3.credit 40/45 3054 0
pure+extP.ratio.derived3.credit 40/45 3064 0
flat2.exp_abs.derived3.credit 40/45 3066 0
pure+extP+flat2.ratio.derived3.credit 40/45 3084 0
pure.cosine.derived3.credit 40/45 3129 0
flat2.cosine.derived3.credit 40/45 3129 0
pure.exp_sq.derived3.credit 40/45 3130 0
flat2.exp_sq.derived3.credit 40/45 3130 0
pure.rat_sq.derived3.credit 40/45 3130 0
flat2.rat_sq.derived3.credit 40/45 3130 0
flat2.rational.derived3.credit 40/45 3130 0
pure.rational.derived3.credit 40/45 3130 0
pure.sqrt.derived3.credit 40/45 3130 0
flat2.sqrt.derived3.credit 40/45 3130 0
====================================================================================
THE STAGE-0C LAW ACROSS THE GRID
====================================================================================
scale=derived3 slope c=1 (linear) mean total 6829 mean solved 193.0/199
scale=derived3 slope c=0 (quadratic) mean total 19620 mean solved 193.0/199
tent, 3-point, pairs (no gate -> flat gate) APS CHA both flat fun3-6
none 2806->2803 4104->3571 6910->6374 2707->2205 solved 193 over 15
none +G2 2782->2781 3863->3585 6645->6366 2474->2217 solved 193 over 15
step 3036->3042 3524->3522 6560->6564 2111->2111 solved 193 over 15
step +G2 3089->3097 3529->3528 6618->6625 2106->2106 solved 193 over 15
bracket 7260->7260 3604->3604 10864->10864 1730->1730 solved 193 over 0
bracket +G2 6837->6837 3650->3650 10487->10487 1717->1717 solved 193 over 0
both 7239->7239 3515->3515 10754->10754 1529->1529 solved 193 over 0
both +G2 7130->7130 3463->3463 10593->10593 1504->1504 solved 193 over 0
project 2806->2803 3220->3341 6026->6144 1823->1975 solved 193 over 0
project +G2 2782->2781 3169->3345 5951->6126 1780->1977 solved 193 over 0
safe 3036->3042 3390->3388 6426->6430 1977->1977 solved 193 over 0
safe +G2 3089->3097 3392->3386 6481->6483 1969->1964 solved 193 over 0
credit 3568->3603 3020->3040 6588->6643 1044->1064 solved 193 over 0
credit +G2 3799->3800 3064->3084 6863->6884 1044->1064 solved 193 over 0
VERDICTS
proposed rule APS 2806->2803 (Z2 ✓) CHA 3220->3341 (Z1 ✗) Z3 ✓ (0 viol, 0 cells <193) Z4 ✗ both 6144 vs Chandrupatla APS 83/28/42 p=0.00031 not accepted
proposed rule + G2 APS 2782->2781 (Z2 ✓) CHA 3169->3345 (Z1 ✗) Z3 ✓ (0 viol, 0 cells <193) Z4 ✗ both 6126 vs Chandrupatla APS 92/21/40 p=7e-06 not accepted
nine functions, projection, no gate -> flat gate, both sets:
cbrt 18003 -> 18006
cosine 19741 -> 18984
exp_abs 6652 -> 6858
exp_sq 19786 -> 16993
rat_sq 19793 -> 17677
ratio 6026 -> 6144
ratio_soft 9352 -> 9299
rational 6823 -> 6908
sqrt 13388 -> 13416
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