vvs and Claude Opus 5
15b94242e0
Valeri's second point measured: the similarity function belongs to the PLACE it is read in, not to the method. False position's three-century stall is a similarity read at order one on an approach of order m: with sigma = |f(far)| the residual ratio is (e/E)^m, so raising it to the measured 1/m recovers the distance ratio exactly. Paired inside each cell, the correction is cheaper in 7 of 7 safeguards for S = 1/(1+z) - the one function that makes that place exact inverse interpolation - and in only 29 of 60 cells over all nine functions, i.e. a coin. It does NOT beat Chandrupatla (2884 against 2683 and 2423), it HARMS the slope reading (2806 -> 2854), and it does not cure false position: 127/154 and 10676 become 128/154 and 10043, where Illinois buys 153/154 and 7045 with one constant. Estimator bias measured and stated: a pure cube reads 2.830, not 3
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Also fixes a real regression from cc2c499noreply@anthropic.com >
2026-09-21 01:17:25 +01:00
vvs and Claude Opus 5
cc2c499f63
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 >
2026-09-21 00:19:03 +01:00
vvs and Claude Opus 5
08ffa42e98
CORRECTION, prompted by Valeri: the step IS a fraction of the bracket — with the ratio similarity 1-S = min(1,|f|/(|f'|D)) so step = min(D,|f|/|f'|) — and my 'absolute length cannot march' was wrong, as was the follow-up guess that we creep along one side: measured, 91.5% of our probes DO shrink the bracket, more often than Chandrupatla's 87.5%. What differs is how much each probe removes: 0.93 halvings per evaluation against 2.26. A linear model of the value axis undershoots on a wide bracket of a convex function, so the new bracket is about half; inverse quadratic interpolation lands near the root and removes four fifths. The limit is the ORDER OF THE MODEL the similarity is read against, and all three parameter-free ways round it are now measured failures (cbrt, log change of variable, derived3_m). Paper corrected
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Co-Authored-By: Claude Opus 5 <noreply@anthropic.com >
2026-09-21 00:12:58 +01:00
vvs and Claude Opus 5
0fb75be3cf
the wide-bracket gap is NOT closed, and now it has an address: the STEP RULE, not the guarantee and not the reading places. fun1 is one function at growing widths — 7/8, 12/12, 19/15, 59/24, 63/44 — so we tie when narrow and lose as it widens, while our observed order is the HIGHER one (3.63 vs 2.02); 59 on a 2e4 bracket is what bisection needs, i.e. one halving per evaluation against their 2.3. With the safeguard removed entirely we still spend 46/57/61/68 against bisection 57/77/45/45 and Chandrupatla 24/44 — worse than bisection on two of them. |f|/|f'| is an absolute length and cannot march across decades; written into the paper as the stated limit. Also fixed a tracer bug that had best_of double-counting evaluations (2993 vs 1487)
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Co-Authored-By: Claude Opus 5 <noreply@anthropic.com >
2026-09-21 00:09:18 +01:00
vvs and Claude Opus 5
8d20816163
the scoring artefact is in BOTH sets: aps.13.00 joins the five fun7 problems — 6 of 199 problems where f underflows to exactly zero on a ~3.2e-2 neighbourhood of the declared root, so every method returns a genuine root (|f(x)| below the smallest normal) and every method is scored a failure. About 1150 evaluations of EVERY two-set total are this artefact; re-scored, all methods solve 199/199 except Brent 197. Ranking unchanged: ours-by-shape 2337 on APS against chandrupatla 2593, chandrupatla 1487 on CHA against our 1740. Written into the paper as a table with both criteria; pdflatex clean, verifier green
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Co-Authored-By: Claude Opus 5 <noreply@anthropic.com >
2026-09-21 00:01:35 +01:00
vvs and Claude Opus 5
6b5870f815
chasing Chandrupatla found a property of the BENCHMARK: on all five fun7 problems f vanishes identically near the declared root (f(0+t)=0 up to 3.2e-2), every method stops at a point where f(x)=0 exactly and is scored a failure by the |x-root|<=1e-6 rule — so 1000 evaluations of EVERY wide-bracket total are an artefact and the universal '40 of 45' is a scoring statement. Re-scored: 45/45 for everyone but Brent, ranking unchanged, gap to Chandrupatla 253 (17%) and diffuse across 8 families. Written into the paper with its reproducing scripts; pdflatex clean, verifier green
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Co-Authored-By: Claude Opus 5 <noreply@anthropic.com >
2026-09-20 23:57:49 +01:00
vvs and Claude Opus 5
ee816933eb
paper updated with the placement results and machine-checked: new section 'Where the similarity is read' (2527 on APS below every method measured, 5511 over both sets, the non-composition of the two readings, and the two negatives with their numbers), abstract extended, verify_article.py now also checks every new number against its own sweep file — all green, pdflatex clean
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Co-Authored-By: Claude Opus 5 <noreply@anthropic.com >
2026-09-20 23:52:13 +01:00
vvs and Claude Opus 5
4a23aacf96
baseline: the published sim-numerics artifact as it stands (490 tests, verify_article.py checks all 72 paper numbers against sweep_full.json)
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Co-Authored-By: Claude Opus 5 <noreply@anthropic.com >
2026-09-20 22:38:17 +01:00
vvsandClaude Opus 5