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Valeri's objection measured: the principle is right (a similarity step should be large far away and small near), and our sigma = |f'|D defeats it — at x=1e4 on a 2e4 bracket the normalised residual is 0.167, so S=0.833 'similar' and the step is small five thousand step-lengths from the root. Selecting sigma = min(|f'|D, max|f| at the ends) — no new constant — improves 403 to 390 on eight hand-picked wide problems but is WORSE over the grid: APS 3288 vs 2726, CHA 3111 vs 2683, so the mode is rejected by its pre-registered rule. Its extra solves are two fun7 problems landing inside the flat zero region, i.e. the scoring artefact and not a capability. Written into Negative results as the answer to the natural objection

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Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
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2026-09-21 00:19:03 +01:00
co-authored by Claude Opus 5
parent 08ffa42e98
commit cc2c499f63
8 changed files with 167 additions and 6 deletions
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results_sweep_cap.txt
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sweep: 63 configurations x 199 problems (FULL)
10/63 done, 1s elapsed
20/63 done, 1s elapsed
30/63 done, 1s elapsed
40/63 done, 1s elapsed
50/63 done, 1s elapsed
60/63 done, 1s elapsed
63/63 done, 2s elapsed
wrote sweep_cap.json (2s total)
====================================================================================
APS: 154 problems (top 20 of 63)
====================================================================================
configuration solved total fev over 2x
------------------------------------------------------------------------------------
pure+dissim+slope.exp_abs.derived3_cap.none 153/154 3288 0
pure+dissim+slope.exp_abs.derived3_cap.project 153/154 3288 0
pure+dissim+slope.exp_abs.derived3_cap.step 153/154 3385 0
pure+dissim+slope.exp_abs.derived3_cap.safe 153/154 3385 0
pure+dissim+slope.rational.derived3_cap.step 153/154 3460 0
pure+dissim+slope.rational.derived3_cap.safe 153/154 3460 0
pure+dissim+slope.rational.derived3_cap.none 153/154 3497 0
pure+dissim+slope.rational.derived3_cap.project 153/154 3497 0
pure+dissim+slope.exp_abs.derived3_cap.bracket 153/154 3537 0
pure+dissim+slope.exp_abs.derived3_cap.both 153/154 3619 0
pure+dissim+slope.exp_abs.derived3_cap.credit 153/154 4125 0
pure+dissim+slope.ratio.derived3_cap.bracket 153/154 4333 0
pure+dissim+slope.ratio.derived3_cap.both 153/154 4903 0
pure+dissim+slope.rational.derived3_cap.credit 153/154 5001 0
pure+dissim+slope.ratio.derived3_cap.step 153/154 5044 0
pure+dissim+slope.ratio.derived3_cap.safe 153/154 5044 0
pure+dissim+slope.sqrt.derived3_cap.step 153/154 6184 0
pure+dissim+slope.sqrt.derived3_cap.safe 153/154 6184 0
pure+dissim+slope.sqrt.derived3_cap.both 153/154 6216 0
pure+dissim+slope.sqrt.derived3_cap.bracket 153/154 6580 0
====================================================================================
CHA: 45 problems (top 20 of 63)
====================================================================================
configuration solved total fev over 2x
------------------------------------------------------------------------------------
pure+dissim+slope.sqrt.derived3_cap.none 42/45 2969 0
pure+dissim+slope.sqrt.derived3_cap.project 41/45 3111 0
pure+dissim+slope.exp_abs.derived3_cap.step 40/45 2658 0
pure+dissim+slope.exp_abs.derived3_cap.safe 40/45 2658 0
pure+dissim+slope.exp_abs.derived3_cap.both 40/45 2689 0
pure+dissim+slope.rational.derived3_cap.step 40/45 2790 0
pure+dissim+slope.rational.derived3_cap.safe 40/45 2790 0
pure+dissim+slope.exp_abs.derived3_cap.bracket 40/45 2796 0
pure+dissim+slope.exp_abs.derived3_cap.none 40/45 2808 0
pure+dissim+slope.exp_abs.derived3_cap.project 40/45 2808 0
pure+dissim+slope.ratio.derived3_cap.both 40/45 2906 0
pure+dissim+slope.ratio.derived3_cap.step 40/45 2959 0
pure+dissim+slope.ratio.derived3_cap.safe 40/45 2959 0
pure+dissim+slope.rational.derived3_cap.none 40/45 2970 0
pure+dissim+slope.rational.derived3_cap.project 40/45 2970 0
pure+dissim+slope.ratio.derived3_cap.bracket 40/45 2978 0
pure+dissim+slope.rational.derived3_cap.credit 40/45 2982 0
pure+dissim+slope.exp_abs.derived3_cap.credit 40/45 2991 0
pure+dissim+slope.cbrt.derived3_cap.both 40/45 3041 0
pure+dissim+slope.sqrt.derived3_cap.step 40/45 3066 0
====================================================================================
THE STAGE-0C LAW ACROSS THE GRID
====================================================================================