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vvsandClaude Opus 5 8279fb6341 PREREG before the run: the empty-step feature (similarity of |f_n| to |f_n-1|, rule S > 1/2, the bisection constant) and the repeating-pattern feature with the period chosen from the data (lag maximising the mean ratio similarity of rho_j and rho_j-p over the history, lags up to half the history). Detectability only; criteria E1/E2/R1/R2 and the falsifier declared; no rule in the method. 
Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
 2026-09-21 11:23:02 +01:00
vvsandClaude Opus 5 0ec7142baf Two audits, both on existing data or traces, method untouched. (1) Where S is evaluated: only in the step length (and simpair, and two refuted modes); the slope gate, the triple by shape, the far end and 'defect' decide by comparing - which is a similarity judgment of the ordinal kind ('which is more similar'), where every decreasing S gives the same decision. Their gains depend strongly on the S in the STEP: triple by shape -493 with the tent, up to +250 with others; defect -283 with the tent, up to +215. The records are the pairing of the tent step with those judgments. 
(2) Valeri: 'similarity should solve the flat-family problem'. The similarity of two successive contraction ratios, min/max(rho_n, rho_n-1), was pre-declared as the detector; it FAILS and is inverted - AUC 0.28-0.42 flat against the rest, and 'the contraction did not speed up' fires more on APS (37.6%) than on the flat families (28.2%). The rho sequence shows why: on x^m the method runs a period-4 cycle - two Newton undershoots at exactly (1-1/m)^m (0.328 for m=5, 0.346 for m=9), one crossing, one nearly empty step (rho ~ 1) - so successive ratios are dissimilar, not constant. The safeguard is not the cause: the steps are as proposed. Candidate detectors suggested by the cycle are new hypotheses, not built.

Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
 2026-09-21 11:16:08 +01:00
vvsandClaude Opus 5 1b6c626f67 Valeri's decisions (1) competitors from the library, (2) variant a. (1) Chandrupatla is scipy.optimize.elementwise.find_root, Brent is brentq, no more per-problem best_of. Our Chandrupatla stopped on a bracket twice as wide as every other method (the factor the protocol corrects for ITP); fixed (+0.5*xtol) in baselines.py and in the two copies found by grep (stage16_blend, stage19_modern) and the traced mirror, and pinned: ours == library on every problem. Regenerating sweep_full.json changed exactly three rows - chandrupatla APS 2785->2787, CHA 2423->2441, brent CHA 4099->4115 - and nothing else (diff_sweeps.py: 0 unexpected). 
(2) The proposed method is again the scheduled projection (2806/3220/6026), its budget multiplier DECLARED as the one free constant: the canonical total is the same for every multiplier 1.25-4, the wide-bracket one is not. The earned projection is the constant-free variant (3568/3020/6588). What the old tables hid: problem by problem the proposed rule beats Chandrupatla on the canonical set 87/24/42, exact sign test p = 9e-5, while trailing him by 0.7% in total; on the wide-bracket set he is genuinely stronger (26 to 9, p = 0.006). Gap decomposition recomputed with the library: 244 (was 262), 160 of it on the flat families (two thirds), fun1 58 (a quarter, not a third as the abstract said).

Also corrected on the way: the 'subsumed by Chandrupatla' pin claimed he is better on the worst single problem - true only with the looser tolerance (84 against the credit rule's 83 once fixed); §8.3 still called zero slack degenerate, which Table 1a refutes; §5.2's Brent figure is our pure-Python implementation and now says so. verify_article.py 286/286, 802 tests pass twice.

Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
 2026-09-21 10:53:00 +01:00
vvsandClaude Opus 5 de90c7a089 Audit on Valeri's challenge: our Chandrupatla implementation stops below 2*xtol (tl = tol/span > 1/2) while every other method, SciPy's included, stops at xtol; the protocol corrected that factor for ITP and not here, and best_of let the looser run win. Corrected it costs Chandrupatla 2 evaluations on APS (2785 -> 2787) and 18 on CHA (2423 -> 2441): real, in the competitor's favour, and not what changes the picture. The public scipy.optimize.elementwise.find_root, the private _chandrupatla and ours corrected agree on all 199 problems exactly. 
What the tables' totals hid: problem by problem the scheduled projection beats Chandrupatla on APS 87/24/42, exact sign test p = 9e-5, while trailing by 0.7% in total; on CHA Chandrupatla is genuinely better (26 to 9, p = 0.006). The earned projection ties him on APS problems (79/3/71, p = 0.57). Benchmark not yet switched to the library baseline - awaiting Valeri's decision together with the framing of the proposed method.

Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
 2026-09-21 10:14:42 +01:00
vvsandClaude Opus 5 8830765454 §3.1 and Tables 2-3 of the canonical .md brought to current data (Valeri's request). §3.1 said the projection's doubling 'is not a tuning constant' and that zero slack 'behaves as bisection'; both are refuted by measurement (stage12 part 3, rerun as measure_budget_factor.py): the canonical total is 2806 for every multiplier >= 1.25, but the wide-bracket total moves monotonically, 2752 at 1.25 to 4006 at 4, and multiplier 1 costs 4817/2997, nowhere near bisection's 7530/3090. So the proposed safeguard is the EARNED projection (credit, C0 = 1 bit: bisection + 1 step, the cheapest endowment within that promise, 8395 -> 7658 -> 6588), as code and verifier had already fixed but no text said; the scheduled projection stays as the one-constant end of the trade. The text says openly that this choice was made after a question, and that it was not made for the numbers - on the canonical set it costs 762 more. 
Tables 2-3 regenerated from sweep_full.json by tables_for_md.py with the verifier's own ranking: Chandrupatla's method, missing from both, is FIRST on the canonical set (2785) and second on the wide-bracket set (2423); the proposed rule is 29th (3568) and 10th (3020); Brent 2889/4099 (was 2890/4101). The abstract, §5 text, §5.1, §5.2 (timed configuration named), §7 (records 2527/2523 are under the scheduled projection: 2523 flat for every multiplier 1.25-4, 2527 becomes 2541 at 1.25; under credit the readings give far less, best constant-free total 6494 by 'defect'), §8.4, §8.11 and the conclusion now say so: parity with the tuned methods at the price of one constant, or a constant-free rule with a tighter guarantee that trails on the canonical set. verify_article.py: 279 checks, measured tables recomputed from fresh runs; 762 tests pass twice.

Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
 2026-09-21 08:03:21 +01:00
vvsandClaude Opus 5 de1f8f726d The new sections move into the canonical text, article/sim_numerics.md (Valeri's decision): section 7 'Where the similarity is read' with 7.1 per-place similarity, 7.2 the decision place, 7.3 the fun7 scoring artefact, 7.4 the gap decomposition; negative results 8-11 appended so items 1-7 keep their numbers; abstract paragraph; Future work rewritten (the refuted log transform removed); item 6 now says aps.13.00 is a scoring artefact, not a method failure. Translated into the .md's revised names: code 'ratio' = the tent max(0,1-|z|), code 'rational' = the ratio similarity 1/(1+|z|); the proposed method stays the .md's (tent, 3-point, projection). 
Found on the way: negative item 'log change of variable' compared 3474 with 4516, the total of a DIFFERENT configuration; the honest pair is the same configuration in x, CHA 3643 -> 3474, APS 5822 -> 6940. Fixed in both texts. The gap-decomposition numbers were only traced to saved logs; they are now RECOMPUTED by verify_article.py from fresh runs of the diagnosis scripts (which return their values): 216 checks OK on Linux, 762 tests pass twice.

Open, for Valeri: the .md still says the projection's doubling is 'not a tuning constant', which simroot/pure.py (project_credit) refutes and which is why the .tex proposes credit; the .md's Tables 2-3 predate Chandrupatla's own method as a baseline (2785 APS, first place), so its 'parity' abstract is out of date; Brent 2890/4101 in the .md against 2889/4099 in the current sweep.

Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
 2026-09-21 07:48:55 +01:00
vvsandClaude Opus 5 f5d036c9d8 Why the wide-bracket gap remains, taken apart on the SAME evaluations: 'order of the model' explains only a third. Of the 262 evaluations lost on 33 problems, 178 sit on fun3-fun6 - pure powers of order 3, 5, 9, 19 - where no interpolating model works (our step 0.41-0.81 bracket halvings per evaluation, IQI from our own points 0.01-0.17) and Chandrupatla wins by BISECTING 93-100% of his steps; our step is slower than bisection there and our 2x-bisection guarantee licenses it. His band inside our step confirms it per family: fun4/5/6 573/456/456 -> 296/239/235 against his 293/228/228, while +164/+111/+170/+144 on fun1/2/8/9 where it refuses good steps - slot 2's total was two opposite effects summed. Only fun1 (58) is model order: IQI from our three points 10.37 halvings against our 0.62; a convex two-point step cannot carry IQI's negative weight (428/428 non-degenerate states; five underflowed to -0.0). 
The flat regime is not detectable by the three-point order estimate: m >= 2 (the exact condition for a tangent step to lose to a halving) fires on 0.2% of APS states and on only 5.8% of states of pure powers of order 3-19. Paper corrected where it said the whole gap is model order (widelimit, decision, abstract, future work - the refuted log transform removed). WARNING recorded in FINDINGS_model_order.md: article/sim_numerics.tex has carried a STALE header since the first commit (current text = sim_numerics.md, unchanged since 08-24); every paper edit of 09-20/21 went into the .tex, the .md has none of them. Which file is canonical is Valeri's call. The new text numbers trace to results_diag_*.txt but are not yet machine-checked by verify_article.py. Trace hook in pure_root is behaviour-neutral and pinned; 762 pass on the server twice.

Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
 2026-09-21 07:38:16 +01:00
vvsandClaude Opus 5 46c713cdd3 Regression runner on the server with pytest-xdist -n 14 (installed into ~/torchenv with Valeri's consent) and BLAS threads pinned to 1: 755 passed in 2:00 and 2:04, against 5:49 single-process on the server and 3:42 on the laptop. Single-process pytest on the server is slower than the laptop; the server only pays with parallelism. 
Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
 2026-09-21 07:10:31 +01:00
vvsandClaude Opus 5 2357379c2d Slot 2, the decision place: Chandrupatla's own acceptance band, put inside our step rule as an instrument, does NOT close the gap - CHA 3066 (project) / 2899 (credit) against his 2423, while APS doubles 2806 -> 5432, and the band is not idle (63.6% refusals). The fifth independent test of one conclusion: the remaining gap is the ORDER of the model the step is built on, not the place the similarity is read in. By the declared stop rule (M1 and M2 both false) the 'where is the similarity read' line is closed: all four places measured. 
Not empty-handed: our own parameter-free reading 'defect' - refuse when |phi - xi| > min(xi, 1 - xi) - sets a new canonical best, APS 2523 at 153/154 (previous 2527, Chandrupatla 2785), guarantee intact (0 of 135 family cells), refusing on 7.0% of steps. It is a second point on the same trade, not a replacement: 5733 over both sets against 5511, because CHA gives back 3210. Also: _shape_ratios crashed on a missing third point, which evaluate would have turned into a silent sweep of zeros; the slope-gate pin was anchored on line spelling; and the server copy had drifted (stale relax/sor.py, test_relaxation.py absent - 746 tests instead of 755). All synced, 92/92 files identical by content, 755 pass on the server.

Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
 2026-09-21 06:58:59 +01:00
vvsandClaude 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 
Also fixes a real regression from cc2c499: the derived3_cap branch was inserted in front of the derived3_m note and swallowed its division, so derived3_m silently became derived3 (2806 against 2806) and a refutation recorded in the paper stopped being reproducible. The full pin caught it; a cheap pin now guards it too. And \label{sec:method} never existed while the table on page 7 referenced it.

Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
 2026-09-21 01:17:25 +01:00
vvsandClaude 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 
Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
 2026-09-21 00:19:03 +01:00
vvsandClaude 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 
Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
 2026-09-21 00:12:58 +01:00
vvsandClaude 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) 
Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
 2026-09-21 00:09:18 +01:00
vvsandClaude 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 
Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
 2026-09-21 00:01:35 +01:00
vvsandClaude 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 
Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
 2026-09-20 23:57:49 +01:00
vvsandClaude 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 
Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
 2026-09-20 23:52:13 +01:00
vvsandClaude Opus 5 22f19c57f0 similarity in two more places MEASURED: triple by shape gives APS 2527 — below the published 2806 and below EVERY baseline including chandrupatla 2785 — and far-end by dissimilarity gives CHA 2683 (the ITP target met) with 5511 over both sets (project target 6026 beaten, ITP-oracle 5871 passed). Guarantee intact everywhere, 193/199. Neither mode is inert (38.6% / 26.9% of steps changed). A+B do NOT compose: 2884/2859 is worse than either alone — select, never weight, and never assume composability 
Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
 2026-09-20 23:45:55 +01:00
vvsandClaude Opus 5 04ee5c89b9 two more places for similarity: points='shape' (WHICH triple the model uses, argmin |phi-xi| over declared candidates — select, never weight) and direction='dissimilar' (the far end read by |f| rather than by distance); defaults bit-identical, P1-P5 pinned (7 green), inertness counters make an inert mode a failed EXPERIMENT rather than a pass; each grid writes to its own file 
Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
 2026-09-20 23:39:41 +01:00
vvsandClaude Opus 5 e4769be9a3 slope-stability gate: the PROJECT'S OWN target is met for the first time — 5922 < 6026 over both sets at 193/199 with the guarantee intact (slope.ratio.derived3.project: APS 2848 + CHA 3074), CHA improves 4516 -> 2903 (x1.56), repairs 77.5% -> 55.3%. Honest cost: APS 2806 -> 2848, which moves us from 1st to 3rd on the canonical set (chandrupatla 2785, toms748 2820), so my stricter S1 fails while the project target passes — a positioning decision, recorded not resolved. Refusal CURRENCY is what decides: bracket progress 4449 vs model shape 2848, a 1601-evaluation difference for the same 'refuse before the step' idea 
Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
 2026-09-20 23:27:43 +01:00
vvsandClaude Opus 5 a6116cd027 pre-step gate MEASURED: repairs 77.5% -> 15.9%, CHA hits the ITP target for the first time (2851 <= 2857), two sets 7440 (best of the line) — but APS grows 2806 -> 4449, so by the pre-registered stop rule the mode is NOT accepted. Cause named: my gate refuses on BRACKET PROGRESS, and this project had already measured that currency to be wrong (a secant step collapses the error while barely moving the bracket: 150 vs 86). Chandrupatla refuses on the SHAPE of the configuration. Next candidate derived, not borrowed: slope-stability gate 
Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
 2026-09-20 23:15:48 +01:00
vvsandClaude Opus 5 0617243ed4 pre-step gate: prestep='none'|'progress' (default bit-identical), refuse the similarity step BEFORE spending an evaluation when it promises less progress than bisection — two lengths already in hand, no new constant; R1-R4 pinned by tests/test_prestep_gate.py (6 green); the gate grid writes to its OWN sweep_gate.json 
Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
 2026-09-20 23:12:34 +01:00
vvsandClaude Opus 5 be10fc0b22 explained, with numbers: Chandrupatla wins the probe by REFUSING its model cheaply, not by trusting it — it accepts the interpolation on only 28% of steps, its gate costs zero evaluations (read from data already in hand) and its refusal branch still halves the bracket; ours repairs 77.5% of evaluations after the fact and drops to 0.92 halvings/eval on fun8/fun9, worse than bisection. In similarity terms: their similarity is a PRE-step GATE on dimensionless ratios (a neighbourhood of the linear configuration), ours is an IN-step SCALE on the residual magnitude — the PLACEMENT of the reading matters more than its form 
Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
 2026-09-20 23:05:22 +01:00
vvsandClaude Opus 5 84ff1c796f logarithmic march MEASURED and REFUTED: APS 6940 vs the published 2806 (2.5x worse), CHA 3115 vs the 2857 target, two sets 10414 vs <6026; the mechanism did work in the predicted direction (CHA 4516 -> 3115 = 1.45x) but the canonical set pays for it — the same trade that ended the four previous attempts, now measured for the transform too. Guarantee intact everywhere (over2x = 0) 
Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
 2026-09-20 22:59:42 +01:00
vvsandClaude Opus 5 a9060b3dcc logarithmic space mode: pure_root gains space='x'|'log' (default reproduces the published grid bit-for-bit), u = sign(x-c)*log1p(|x-c|/xtol) with c = the end of smaller |f| and s = xtol fixed by derivation; gates G1/G2' pinned by tests/test_log_space.py (7 green); sweep writes the log grid to its OWN sweep_log.json so the verified sweep_full.json is untouched 
Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
 2026-09-20 22:52:58 +01:00
vvsandClaude Opus 5 bf221531ac findings: baseline reproduces on Linux (665 passed, all 72 paper numbers match) and the two admission gates are INCOMPATIBLE in their strict form — derived, no run needed: a march needs a RATIO of distances while identity needs an ABSOLUTE unit, and no parameter-free s gives both (this also explains why cbrt worked by accident). Fork A/B recorded for Valeri 
Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
 2026-09-20 22:45:31 +01:00
vvsandClaude Opus 5 f9b062ed34 prereg: logarithmic change of variable for wide brackets — targets (6026 both sets / 2857 Chandrupatla / 193-of-199 / guarantee intact), two admission gates (parameter-free c,s; identity on narrow brackets) tested BEFORE the ranking is consulted, and the four measured dead ends restated as prohibitions 
Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
 2026-09-20 22:40:09 +01:00
vvsandClaude 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) 
Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
 2026-09-20 22:38:17 +01:00