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vvsandClaude Opus 5 b677283afc Article: the similarity in the step is earned, not scaffolding; literature in place. 
S-ablation of A' (server): A' with each of the nine similarity functions in the step - tent 4443 on the paper protocol (13032 over 855 problems), the nearest other function e^-|z| 4988 (+12%; +9% over six corpora), quadratic ones 18410-18422 (+315%); ranking as the contraction law predicts; guarantee held with every S. The audit of section 7 rerun on the regenerated sweeps (APS unchanged: triple by shape -493 with the tent, +250 with 1/sqrt(1+z^2); defect -283 vs +215).

Text: abstract and section 3 no longer call the similarity scaffolding - the tent making the step Newton's is a property of the similarity chosen; a paragraph in section 7 on the audit; Table 9a; new 8.6 'What is known, and what is new' - Lagouanelle (the order estimate of 7.1 / 10.5), Rall and Hansen-Patrick (8.1), the log-log slope / COC / ACOC (8.2, formula 6), Schroeder and Traub (the split 7 = false position on sign(f)|f|^(1/m)), Brent's acceptance condition (half), Dekker/Brent (tolerance step); what we found no counterpart for is the decision layer by similarity and analogy and the step set by a similarity whose form is decisive. References 13-19. verify_article: Table 9a, the percentages and the audit numbers added; server 446 OK, 0 BAD; regression x2 1226 passed, 0 failed.

Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
 2026-09-21 21:22:41 +01:00
vvsandClaude Opus 5 667f243f54 Article proof-reading: the introduction no longer says the four new corpora were unseen (three were used to close the last two gaps; only the fourth was run once after the code was frozen); a repeated clause in 8.2 merged. verify_article also recomputes every sign-test p printed in Section 9. Server: 411 OK, 0 BAD; regression x2 1226 passed, 0 failed. 
Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
 2026-09-21 21:03:15 +01:00
vvsandClaude Opus 5 16b9ab87f1 Article (canonical .md), step 2: abstract, introduction, a note in section 3, the close of 7.4, negative results 12-16, conclusion, future work and references 8-12 rewritten for the proposed method A'; two statements that could not be recomputed rephrased. verify_article: expected values updated to the regenerated sweeps, the gate cells renamed (progress.*; their CHA values had moved unnoticed, 2991 -> 3047, 2851 -> 2888, not quoted in the paper), and verify_flat_regime_and_oos() added - Sections 8-9, Tables 8-11, items 12-16 and the abstract, recomputed from server files and fresh diagnosis runs. Verifier on the server: 401 OK, 0 BAD, 'every number stated in the paper matches the sweep data'. Server regression x2: 1226 passed, 0 failed. 
Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
 2026-09-21 20:56:58 +01:00
vvsandClaude Opus 5 8bf595d9be Article (canonical .md), step 1: 42 stale numbers brought to the regenerated server sweeps (Tables 3-7, 5.3, 7.1-7.4, section 10), statements that no longer hold rephrased ((2)+(3) not worse than either alone on the wide-bracket set; the best constant-free configuration is no longer defect); the rule of section 3 renamed the base rule; new Section 8 (the flat regime recognised by analogy: the flag, the analogy with its own past, the translation limit, the split from the order, five more readings, the proposed method A', Tables 8-9) and Section 9 (out-of-sample evidence on four more corpora, Tables 10-11); negative results and conclusion renumbered 10-11. Abstract, introduction, conclusion and verify_article still to update. 
Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
 2026-09-21 20:44:31 +01:00
vvsandClaude Opus 5 92fb8c5c04 A' on the paper's own protocol (published roots, server): APS 2438, CHA 2005 (4443) vs Chandrupatla 2787/2441 (5228); per problem 103/20/30 and 29/4/7; earned-budget variant 3608/2807; guarantee held under every safeguard. Leave-one-out ablation of A' on all six corpora: regime +5336, point +3115, sub +959, close +473, half +376, exp +338, G2 +89 (2/6 corpora), contra +28 (3/6) - every component positive in sum, G2 and contra marginal. 
Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
 2026-09-21 20:37:09 +01:00
vvsandClaude Opus 5 2c458c51dc Fix: _local_order divided by fp*fp that underflows to 0 for a tiny nonzero slope (ZeroDivisionError, caught by the sweep harness and charged as a failure - this is what had moved Table 6's order cells after the sign fix). Pinned by a test that fails on the old code. Every sweep file regenerated on the server (run_all_sweeps.sh). verify_article: skip result files that are not grid lists (it crashed on the out-of-sample dicts). Verifier now completes: 224 OK, 57 stale numbers in the paper to update (Table 6 again 7 of 7). 
Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
 2026-09-21 20:34:19 +01:00
vvsandClaude Opus 5 80610e5c27 table_all_corpora: the problem count was hardcoded as 1055; it is 855 (154+45+206+78+132+240) - now computed. Totals unchanged. 
Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
 2026-09-21 20:20:11 +01:00
vvsandClaude Opus 5 94d81f24d8 Wins and losses of A' on all six corpora (1055 problems), server numbers only: the seen-corpora run is replaced by its Linux rerun (differences of 1-3 from Windows). Totals: A' 13032, Chandrupatla 16481, Brent 24565, TOMS748 23649. A' vs Chandrupatla per problem significant on 5 of 6 corpora; the applied+GSL corpus is parity (1382 = 1382, 48/52/32 p=0.09). 
Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
 2026-09-21 20:18:54 +01:00
vvsandClaude Opus 5 6d2531e6ea PREREG_close_sub outcome - the ONE check on the fourth corpus (server): A' TRANSFERS. 240 problems: A' 3656 vs Chandrupatla 5717 (-36%), per problem 177/35/28 p=1e-27, guarantee held (Brent 50 and TOMS748 37 violations), all solved; A' below A (4547). Without the targeted classes: 2403 vs 3569, 107/31/22 p=1e-14. Ablation: sub earned (+893, D3 1807 -> 924), close NOT earned on this corpus (-2) though it earned on the seen applied corpus. Per class vs Chandrupatla: D1 random polynomial simple root 20/8/12 (433 vs 419), D2 multiple 39/1/0, D3 fractional power 37/1/2, D4 exp+sin sums 23/14/3, D5 compositions 25/8/7 (503 vs 1017), D6 odd around the root 33/3/4. 
Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
 2026-09-21 20:08:29 +01:00
vvsandClaude Opus 5 8027d7f5ef A' code frozen BEFORE the corpus-4 run (PREREG_close_sub): close (borrowed Dekker/Brent tolerance step, only after a kept promise) and sub (overshoot branch m <= 2/3; the shallow memory is not cleared by the exit - amendment documented). Development on the five seen corpora (uniform sign-change criterion): A' below A everywhere; vs Chandrupatla APS 103/31, CHA 31/10, new-1 109/65, Roots.jl 44/20 p=0.004, applied 48/32 p=0.09 with total 1382 vs 1380. Tests: 1223 passed (full), 358 (gate files). 
Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
 2026-09-21 20:02:43 +01:00
vvsandClaude Opus 5 657df10634 PREREG before code and run: repair the two base-step gaps - close (Dekker/Brent's tolerance step, named as borrowed) and sub (the second branch of |1 - 1/m| > 1/2: enter the regime for m <= 2/3 on an overshooting unkept promise) - and test A' = A + close + sub once on a FOURTH corpus (corpus_fourth.py, seed 20260922, 240 problems in six new families, two of them targeted), committed now; development only on the seen corpora. F1-F3 transfer, F4 the repairs earned. 
Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
 2026-09-21 19:54:13 +01:00
vvsandClaude Opus 5 c2b0eea0f6 PREREG_applied outcome (server): variant A does NOT transfer - total 1580 vs Chandrupatla 1382 (+14%), per problem 40/46/46 p=0.59; guarantee held, 132/132 solved. Wins where roots are (near-)multiple: Kepler e->1 20/11/4, van der Waals near-critical 9/7/4. Losses traced to two gaps in the BASE step (the plain rule loses the same): (1) no bracket closing at the end - on sin[3,4] the root is reached in 7 evaluations (|f| 1e-16) but the far end stays 1.3e-7 away and 17 halvings follow, where Chandrupatla steps a tolerance past the root (Dekker/Brent's device); likely also the IRR losses (1/0/11); (2) roots of order < 1 (sqrt|x| sgn x): the step overshoots and oscillates (+0.15, -0.10, +0.066 ... ratio 0.8), 84 vs 4 - the unkept-promise flag only sees undershoots, the regime only m >= 2. 
Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
 2026-09-21 19:49:36 +01:00
vvsandClaude Opus 5 8ea89dd38d PREREG before any run: third corpus - the GSL root-finding test suite (10, published) and 122 physics/engineering equations on grids fixed beforehand (Kepler incl. e up to 0.999, Colebrook-White, Lambert W, Planck/Wien, van der Waals CO2 incl. near-critical, IRR, finite square well). T1-T3 as before; GSL part reported separately; per equation breakdown. 
Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
 2026-09-21 19:47:21 +01:00
vvsandClaude Opus 5 554ec0c0ae PREREG_roots_jl outcome (server): variant A does NOT transfer by the stop rule on the Roots.jl / ModAB benchmark. 78 out-of-sample problems: total 1464 vs Chandrupatla 1566 (-6.5%, R1 holds), per problem 38/10/30 p=0.4 (R2 fails), guarantee held and all solved (R3); strict f24-f91 the same picture (1340 vs 1454, 35/6/25 p=0.25). B does not transfer either (32/11/35). Same structure as the first new corpus: multiple/flat roots 331 vs 481 (10:3); the rest 1133 vs 1085, per problem 28/10/27 - parity. Largest loss f32 (4 - tan x near the pole, 41 vs 12). Against Brent and TOMS748 A wins (47/25 p=0.013, 55/20 p=6e-5); they break the 2x-bisection bound on 11 and 9 problems, A on none. 
Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
 2026-09-21 19:40:05 +01:00
vvsandClaude Opus 5 97af3ae767 PREREG before any run: second independent corpus - the Roots.jl bracketing benchmark (from the ModAB benchmark, Ganchovski & Traykov), f01-f91 transcribed; 13 problems equal to APS/Chandrupatla functions excluded objectively (7-point identity test), verdict on the other 78; strict view f24-f91; success = sign change within 1e-6 (no roots given, jumps and poles present). R1-R3 as in the first out-of-sample check. 
Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
 2026-09-21 19:38:26 +01:00
vvsandClaude Opus 5 a86a9ed263 PREREG_out_of_sample outcome (server). Variant A (G2 + contra + remembered analogy + order point + exp limit + half) TRANSFERS: new corpus 3492 vs Chandrupatla 3899, per problem 105/34/67 p=0.0046, guarantee held, solved 205 = 205. Variant B (defect + remembered + point + exp) does NOT (total 3587 below, but per problem 95/33/78 p=0.22; loses the exponential class 9/5/26). Per class the transfer is carried by the multiple/flat-root class C3 (1194 vs 1792, 37/0/3); on C0-C2 A is at par per problem and ~6% dearer in total, C4 ~ par, C5 (near-cancelling) 691 vs 574. Ablation: every component earns its place on at least one set (contra only on APS/CHA: +9/+22, NEW -8; G2 only on NEW: +82). Addendum: C0.05 is SciPy's random step function - seeded and its cache cleared before every run for reproducibility; two unseeded runs gave the same verdicts. 
Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
 2026-09-21 19:33:07 +01:00
vvsandClaude Opus 5 47361dabea PREREG before any run: out-of-sample corpus and ablation for the two strongest variants. corpus_new.py (seed 20260921): SciPy 'original' (6) + five generated classes x 40 (smooth simple, transcendental simple, multiple/flat |x-r|^p p~U(2,20), exponential flank, near-cancelling terms), built and validity-checked only (no method has seen it). O1-O3 = transfers (total below Chandrupatla, per-problem sign test p<0.05, guarantee); O4 vs the plain rule; per class. Leave-one-out ablation of every component on APS, CHA and the new corpus. 
Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
 2026-09-21 19:30:27 +01:00
vvsandClaude Opus 5 bbb16ec81c PREREG_half_contra outcome: ACCEPTED (server = smoke in every projection cell; 0 violations in the guaranteed family). 
'half': the step promises the root in the half near x (S >= 1/2) while the bracket line puts it in the far half (smaller |f| at the far end) -> halve.
  half alone                                  APS 2806 -> 2564 (!)  CHA 3220 -> 3202
  G2 + contra + rem + point + exp + half      APS 2773 -> 2559  CHA 2073 -> 2047  both 4606 (all of H1-H4; goal kept)
     per problem vs Chandrupatla: APS 98/17/38 p=2.7e-7, CHA 27/6/7 p=8e-4
  contra + rem + point + exp + half (no G2)   APS 2551  CHA 2044  both 4595 (H2 fails by 24)
  with defect it does not combine (APS 2531 -> 2651): the two refuse overlapping steps.
fun9: 77 -> 68 (Chandrupatla 55); fun9.5 24 -> 16.
Server regression x2: 1204 passed, 1 failed = the paper-number check.

Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
 2026-09-21 19:24:31 +01:00
vvsandClaude Opus 5 3d74b4531b PREREG before code and run: remove the false promise 'the root is here'. Two models of which half holds the root: the step (S >= 1/2 -> the near half) and the bracket line (smaller |f| at the far end -> the far half); if they disagree, halve. Component 'half'; pairs without/with on none and the two accepted exp cells, +/- G2; H1-H4, goal kept; the post-crossing risk written down. 
Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
 2026-09-21 19:16:24 +01:00
vvsandClaude Opus 5 cc82156cde Why the translation limit fired late on the fun9.5 flank (diagnostics only). The limit itself reads correctly: at x = 10.89 the pair has lx 1.09, lf 1.5e-3 -> m = inf, and the regime is entered at the next flag (10.39), after which the flank is halved (5.19, 2.60, 1.30). It fires late because the flank configurations do NOT recur from 20.25 to 10.89: (1) the near-zero step 20.2502 -> 20.2501 (overconfident S ~ 1 from a slope dominated by f(81) = 1.5e35) makes the next triples degenerate (xi ~ 0, then -1.7e7) and pollutes the memory; (2) our three-point step on exp is not a translation - it alternates long/short (xi -1.43, -0.46, -4.10, -0.03, -13.9) and first repeats at lag 5 (state 10 ~ state 5). 9 evaluations from 20.25 to 10.39 where one halving would do: ~8 of the +10 gap on fun9.5. 
Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
 2026-09-21 18:49:19 +01:00
vvsandClaude Opus 5 baa93963cf PREREG_flat_exp_limit outcome: ACCEPTED (server numbers equal to the smoke in every projection cell; 0 violations in the guaranteed family). 
Translation limit of the analogy (f shrank, x-scale did not -> m = inf):
  defect + remembered + point + exp        APS 2531  CHA 1972  both 4503
  G2 + defect + remembered + point + exp   APS 2588  CHA 1997  both 4585
  G2 + contra + remembered + point + exp   APS 2773  CHA 2073  both 4846
  Chandrupatla                             APS 2787  CHA 2441  both 5228
Per problem against Chandrupatla now SIGNIFICANT ON BOTH SETS: G2+contra+rem+pt+exp APS 98/18/37 p=1.5e-7, CHA 28/3/9 p=0.0026; defect+rem+pt+exp APS 86/20/47 p=9e-4, CHA 27/3/10 p=0.0076.
NOT where predicted: fun9 only -1..-3; the gain is on the flat families (x^9 177 -> 161, x^19 339 -> 167).
Server regression x2: 1179 passed, 1 failed = the paper-number check.

Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
 2026-09-21 18:44:23 +01:00
vvsandClaude Opus 5 e887691d09 PREREG before code and run: the exponential limit of the analogy. When the analogous pair's f shrank but its x-scale did not (translation self-similarity, exp(x-1) = exp(x)/e), read m = inf - the boundary of the same definition, no new constant; the order point then is the midpoint. Composite component 'exp'. Pairs without/with exp on the four order-point variants +/- G2; E1-E4, goal retention; false-entry risk written down. 
Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
 2026-09-21 18:36:36 +01:00
vvsandClaude Opus 5 485f25f165 Why the fun9 well is closed only partly (diagnostics only, method unchanged). The well itself IS closed: reaching the root's side takes 4 evaluations with contra/defect against Chandrupatla's 3 (13 and 33 before). The remaining +20 (75 vs 55) is after it: (1) the exponential flank on the widest brackets - our step moves ~1 per evaluation down exp(x) (f/f' = 1), 10 evaluations where Chandrupatla halves 3 times; the analogy entry comes late because exp is self-similar by TRANSLATION, not scaling - the pair's x-scale does not shrink, so m = ln(f ratio)/ln(x ratio) is undefined or negative; (2) overconfident near-zero steps - on a steep flank the three-point slope is huge, z ~ 0, S ~ 1, the model promises the root at a point that is not it: 8 wasted evaluations on fun9 (27 without the decisions). 
Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
 2026-09-21 18:35:07 +01:00
vvsandClaude Opus 5 08863c170c PREREG_flat_order_point outcome: ACCEPTED, and the GOAL is reached - below Chandrupatla on BOTH sets (server numbers, all projection cells equal to the smoke). 
Splitting in the flat regime at the point from the analogous pair's order (t = |FA|^(1/m) / (|FA|^(1/m) + |FB|^(1/m))) instead of the midpoint:
  G2 + analogy + order point         APS 2780  CHA 2221  both 5001   (P1-P4 all hold; vs Chandrupatla 2787 / 2441 / 5228)
  G2 + contra + remembered + point   APS 2775  CHA 2119  both 4894   (P3 fails by 2 against its midpoint twin)
  defect + remembered + point        APS 2532  CHA 2164  both 4696   (P3 fails by 2)
Flat fun3-6: 1234 -> 847 (analogy), 1151 -> 743 (remembered) - below pure bisection 1044 and Chandrupatla 1068.
Per problem on the wide set vs Chandrupatla now 20-24 wins / 13-17 losses (p 0.1-0.7, not significant); on the canonical set the edge is kept (95/20/38 p=8e-7).
Guarantee: 0 violations and >= 193 solved in every project/safe/credit cell.
Server regression x2: 1150 passed, 1 failed = the paper-number check.

Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
 2026-09-21 18:13:10 +01:00
vvsandClaude Opus 5 d1be3bbd05 PREREG before code and run: split at the point from the analogous pair's order m (t = |FA|^(1/m) / (|FA|^(1/m) + |FB|^(1/m))) instead of the midpoint, in the flat regime entered by analogy (flatanalogpt, flatanalogmempt). Exit generalised to any regime point: f(x) nearer to FA(1-t) + FB t than to 0. Paired against the midpoint twins with the same entry; P1-P4, goal reported; the one-sided stall risk written down beforehand. 
Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
 2026-09-21 18:00:24 +01:00
vvsandClaude Opus 5 63cf9fb768 Comparative table of wins and losses (server numbers): five variants of the proposed rule against library Chandrupatla, Brent, TOMS748 - totals, per-problem sign tests, wide-bracket families. Server defcontra grid matches the smoke in every projection cell but one (defect+G2 CHA 3183 vs 3182). 
Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
 2026-09-21 16:00:05 +01:00
vvsandClaude Opus 5 3d9287ec2c PREREG_defect_contra_flat outcome (smoke, all 199 problems). Goal (below Chandrupatla on both) NOT reached by any cell: best CHA 2537 vs 2441. Best total: defect+flatanalogmem APS 2530 / CHA 2561 = 5091 < Chandrupatla 5228 (first time), C1-C3 hold; ablation: defect earns APS +284 (costs CHA 9), remembered analogy earns CHA +649 (costs APS 7). contra earned without defect (APS 2806 -> 2785, CHA 3220 -> 3198; with the remembered analogy 2792 / 2537, the best CHA), redundant with defect (defect+contra = defect). fun9: 105 -> 81 (Chandrupatla 55). Remaining CHA gap 120: flat +88, fun1 +20, fun9 +26. Server regression x2: 1116 passed, 1 failed = the paper-number check. 
Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
 2026-09-21 15:57:15 +01:00
vvsandClaude Opus 5 3c92d610d6 PREREG before code and run: both directions. (1) defect decision combined with the flat regime (analogy / remembered analogy) for canonical headroom; (2) contra: halve when the local secant's sign contradicts the bracket's - the fun9 cause (a near-cancelling left end, |f| doubling 17 steps in a row); traces: 3/5 fun9, 7/154 canonical, 0 flat. Composite prestep 'a+b+c', one per category; factorial grid on the proposed rule +/- G2; decided on the smoke; goal = below Chandrupatla on both; ablation of every component of the best cell. 
Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
 2026-09-21 15:45:03 +01:00
vvsandClaude Opus 5 441373800b PREREG_flat_analogy_mem outcome (decided on the smoke, all 199 problems): NOT accepted. Remembering the analogy until the next flag: CHA 2635 -> 2552 (G2: 2625 -> 2548; flat fun3-6 1234 -> 1151, M4 holds) but APS 2806 -> 2814 (G2: 2782 -> 2787 = Chandrupatla, M2 fails) - the extra false entries. Server regression x2: 1069 passed, 1 failed = the expected paper-number check. 
Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
 2026-09-21 15:06:37 +01:00
vvsandClaude Opus 5 4bf8634757 PREREG before code and run: entry with the analogy remembered. The judgment (nearer to own past than to the line, m >= 2) is made at every gate state; once it holds, the run is flagged analogous and the regime is entered at the next unkept promise; an exit (midpoint judged linear) clears it. Stop rule M1-M4 (M4: CHA below flatanalog, 2635 / 2625 with G2); goal vs Chandrupatla reported. 
Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
 2026-09-21 15:00:19 +01:00
vvsandClaude Opus 5 b7271a1ce4 Why the analogy entry is late on the flat families (diagnostics only, method unchanged). At flag moments before entry: unlike-past 118, no-memory 7, m<2 2 - the order is not the bottleneck. The period-4 cycle: the flag rises in the phases whose configuration does NOT recur (the undershoot whose relative step shrinks every cycle, and the crossing); the recurring phases have the flag down and read the true order (fun4 = 6(x-2)^5: m ~ 4.9). The entry demands both at the same state. Remembering the analogy until the next flag: flat entry state 12.9 -> 8.2; problems entered APS 3 -> 8, fun9 0 -> 1. 
Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
 2026-09-21 14:58:20 +01:00
vvsandClaude Opus 5 1842eb0765 Flat regime: exit by midpoint similarity (flatstickexit), one judgment at entry and exit (flatjudge), entry by analogy (flatanalog). 
PREREG_flat_exit: NOT accepted - APS 2806 -> 3125, CHA 3220 -> 2503 (the exit is earned: APS 6897 without it).
PREREG_flat_judge: NOT accepted (smoke) - APS 3009, CHA 2486: at the model's point f is small by construction, the judgment cannot tell flat from simple there.
PREREG_flat_analogy: ACCEPTED with G2. Entry = unkept promise AND the (xi, phi) configuration nearer to its own past than to the line AND the pair's similarity exponent m >= 2. Projection + G2: APS 2782 -> 2780 (below Chandrupatla 2787, per problem 95/20/38 p=8e-7), CHA 3169 -> 2625, guarantee holds. Without G2: APS 2806 -> 2807 (fails by one call), CHA 2635. Simple roots are spared exactly (cost unchanged); flat families 1823 -> 1238, entry comes late. Goal (below Chandrupatla on both) NOT met: CHA 2625 vs 2441, per problem 9/6/25.
Server regression x2: 1052 passed, 1 failed = the expected paper-number check.

Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
 2026-09-21 14:55:45 +01:00
vvsandClaude Opus 5 42bfab4330 PREREG before code and run: entry into the flat regime by analogy. The dimensionless configuration (xi, phi) of the last three points is nearer to a past one than to the line phi = xi, AND the pair's similarity exponent m = ln(f shrink)/ln(x shrink) >= 2, on top of the unkept promise; midpoint exit as flatstickexit. Basis (diag_flat_analogy.py, traces only): entry would fire on 3/154 canonical, 20/20 flat, 0/15 fun2/8/9. Stop rule N1-N3; goal (below Chandrupatla on both) reported; expectation written: APS ~2806, CHA ~2454. 
Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
 2026-09-21 14:48:30 +01:00
vvsandClaude Opus 5 1dbda21182 PREREG before code and run: one similarity judgment at entry and exit of the flat regime. At every new point, before the bracket moves: flat if |f| < |f - L(x)| (L = the line through the bracket ends), linear if the reverse. Entry = unkept promise AND flat; exit at a midpoint = linear. Goal: below Chandrupatla on BOTH sets (J1 CHA < 2441, J2 APS < 2787); decided on the smoke (all 199 problems), server only to confirm. Basis (where_we_lose.py, saved results): with the exit the flat families are at par with Chandrupatla; the rest of the loss is false entries on simple roots. 
Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
 2026-09-21 14:40:12 +01:00
vvsandClaude Opus 5 f8dd8d9931 PREREG before code and run: exit from the sticky flat regime by similarity at the midpoint. In the regime every step halves; at each midpoint f(M) is compared with the two predictions, linear L = (FA+FB)/2 and flat 0; the regime is left when |f(M) - L| < |f(M)|. Ordinal, no constant; re-entry by the same flag. Stop rule X1-X3; X6 = the exit must beat the sticky midpoint without exit. 
Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
 2026-09-21 14:32:57 +01:00
vvsandClaude Opus 5 f8c17c4ed1 PREREG_flat_stick outcome: NOT accepted. Sticky regime under the projection: CHA 3220 -> 3019 (W1 holds), flat fun3-6 1823 -> 1057 (W4, near pure bisection 1044), guarantee holds (W3), but APS 2806 -> 6781 (W2 fails): the unkept-promise flag enters on 134/154 APS problems and 20/25 non-flat CHA problems, and a false entry now sticks to the end of the run. W6 fails: the order read from the promise is m = inf in 163/174 entries (r >= 1/e; our step is not a pure tangent), so the derived split equals the midpoint on CHA (3019 both). Audit bug fixed and pinned: an infinite |f| at an end made the split nan. Server regression x2: 999 passed, 1 failed = the expected paper-number check. 
Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
 2026-09-21 14:14:35 +01:00
vvsandClaude Opus 5 1192c68501 PREREG before code and run: sticky flat regime. Entry = the unkept promise (r >= 1/4); from then on every step splits the bracket. Order m from the promise itself, r = (1-1/m)^m (r >= 1/e -> m = inf); split point t = |FA|^(1/m) / (|FA|^(1/m) + |FB|^(1/m)), which tends to the midpoint at m = inf. Ablation flatstickmid (sticky midpoint). Stop rule W1-W3; W6 for the derived ratio. Ceiling from sweep_full: flat problems bisected -> CHA 2441; split 1:k near side k=2.5 -> 2146, non-monotone in k, so k is derived, not chosen. 
Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
 2026-09-21 14:06:46 +01:00
vvsandClaude Opus 5 5a1edffcfc PREREG_flat_creep outcome: NOT accepted. Unkept promise AND creep under the projection: APS 2806 -> 2878 (V2 fails), CHA 3220 -> 3354 (V1 fails), flat fun3-6 1823 -> 1991 (V4 fails), guarantee holds (V3). With G2: 2782 -> 2842, 3169 -> 3318. Under safe CHA 3390 -> 3149, weaker than the single flag (3037). None of the three flat-regime gates pays under the projection: its budget already does their work. Server regression x2: 952 passed, 1 failed = the expected paper-number check (46 numbers after the signfix, pending the paper decision). 
Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
 2026-09-21 13:55:37 +01:00
vvsandClaude Opus 5 35eb9416d3 PREREG before code and run: flat gate = unkept promise (r >= 1/4, no crossing) AND creep (last two moves the same way). Decided by the full grid directly (V1-V5, stop rule); firing rates reported for information only. 
Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
 2026-09-21 13:46:58 +01:00
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
vvsandClaude Opus 5 6a8bb2315f PREREG before code and run: flat regime by the promise failing TWICE in a row (same r* = 1/4, a counter of consecutive unkept model steps, any other step resets it). Stage 1 detectability (T1, T2 against the single flag's 2.48 ratio), stage 2 in the method only if stage 1 passes (W1-W5, stop rule). 
Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
 2026-09-21 13:35:37 +01:00
vvsandClaude Opus 5 e7e74d71e5 Flat regime (PREREG_flat_regime): the unkept-promise flag - after a model step that did not cross the root, r = f_new/f_old >= 1/4, the tangent-versus-halving break-even at m = 2 - RECOGNISES the regime (stage 1: 53.6% of model steps flagged on the flat families against 21.6% on APS and 17.0% on fun1; recall ten times the m>=2 estimator's 5.8%) and cuts the wide-bracket set by 350-490 wherever the budget does not already bind: safe 3390 -> 3037, step 3524 -> 3037, unguarded 4104 -> 3198. 
NOT accepted into the proposed rule by the stop rule: under the projection the flat families are already budget-bound (CHA 3220 -> 3198 only) while the false flags on APS cost 2806 -> 3029 (Z2 fails); with G2 both sets fail. The per-problem edge over Chandrupatla on APS turns into 26/72/55. Guarantee intact in every cell. Next candidate, not pre-registered: require the promise to fail twice in a row.

Regression on the branch: 918 pass (twice); the one red test is the paper-number check awaiting the paper update.

Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
 2026-09-21 13:25:56 +01:00
vvsandClaude Opus 5 9df1aa5f13 PREREG before code and run: flat regime recognised by the model's unkept promise - after a model step that did not cross the root, r = f_new/f_old >= 1/4, the break-even of a tangent step against a halving at m = 2 ((1-1/2)^2). Stage 1 detectability (F1), stage 2 in the method only if stage 1 passes (Z1-Z5, stop rule). 
Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
 2026-09-21 13:02:40 +01:00
vvsandClaude Opus 5 68df1d25db Sign tests by product underflowed: FIXED everywhere (branch, not master - the paper is not yet updated). FA * fnew < 0.0 with FA ~ -1e-200, fnew ~ 1e-150 is -0.0 and '-0.0 < 0.0' is False, so on flat functions (x^19) the bracket update moved the wrong end, the root left the bracket and the run still reported convergence - the proposed rule returned 4.9e-9, bisection 3.5e-9, ITP 1.6e-8 with a claimed 1e-12 bracket; the 1e-6 harness scored them solved. Same defect in our bisection, false-position family, Ridders, Brent, ITP and twelve copies in stage scripts, simroot/sim.py and one test; all replaced by _opposite / _same_sign, pinned by test_sign_underflow. 
Impact, every sweep regenerated: the paper's key configurations are unchanged to the evaluation (proposed 2806/3220, credit 3568/3020, Chandrupatla, TOMS 748, Brent, bisection); 46 stated numbers move (ITP CHA 2857 -> 2896, ITP oracle 2611 -> 2647, record CHA figures by 14-18, the grid means by ~1%) and one finding weakens: the measured-order exponent of section 7.1 was cheaper in 29 of 60 far cells and 7 of 7 safeguards; with the fix 12 of 61 and 6 of 7, and on the wide-bracket set it now loses in every safeguard and drops 5 problems.

PREREG G1-G3 outcome on the fixed code: G2 (repeating step pattern, period from the data) PASSES Y1-Y4 and is ACCEPTED by the stop rule - proposed rule APS 2806 -> 2782 (below Chandrupatla's 2787), CHA 3220 -> 3169, both 6026 -> 5951, per problem vs Chandrupatla on APS 95/20/38 p = 8e-7. G1 fails Y1/Y2 (its Y3 miss was the sign bug), G3 fails Y2, A fails Y2. Regression 887 pass; the two red tests are the paper-number check (awaiting the paper update) and test_blend (fixed since, copy in stage16).

Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
 2026-09-21 12:49:01 +01:00
vvsandClaude Opus 5 29ab49599c PREREG before code and run: when is lengthening appropriate - G1 confirmed geometric series of three steps, G2 repeating step pattern with the period from the data (gate S_R > 1/2), G3 steps AND results (1/(1-min(S_step, S_res)), S_res = 0 after a sign change). Five-way paired grid, criteria Y1-Y6, stop rule: accept only if Y1, Y2 and Y3 all hold. 
Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
 2026-09-21 12:16:25 +01:00
vvsandClaude Opus 5 99be33a632 A in the method (extrapolate='steps', default 'none' = published bit for bit): NOT accepted into the proposed rule by the declared stop rule - X2 fails. Proposed rule without -> with A: APS 2806 -> 2967 (X2 FAIL), CHA 3220 -> 2925 (X1 pass), flat fun3-6 1823 -> 1524 (X4 pass), guarantee intact, 0 violations in 39 family cells (X3 pass). The per-problem edge over Chandrupatla on APS is lost (87/24/42, p=9e-5 -> 42/62/49, p=0.53). 
X5: dissimilar+slope with A reaches 2859+2545 = 5404 over both sets, the best total this line has measured (was 5511; Chandrupatla 5228) - but again by trading the canonical set (2726 -> 2859) for the wide brackets (2785 -> 2545). The one-step replay (APS no harm) did not carry over: its bracket-halving metric rewards overshooting the root, which on a simple root costs superlinear convergence in the full run - the declared one-step limitation, now measured. Among the nine functions A helps only the tent (6026 -> 5892) and slightly ratio_soft.

Also: pin 'strictly fewer evaluations on every flat problem' was wrong for 6(x-2)^5 on [0,10] - both runs are budget-bound (90 of the guaranteed 91); corrected to the measured claim. verify_article 286/286, 836 tests pass twice.

Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
 2026-09-21 12:11:06 +01:00
vvsandClaude Opus 5 a25cffad1d PREREG before code and run: step extrapolation (A) inside the method - step/(1-S) with S the ratio similarity of the proposed step and the previous displacement, capped at the far end; paired grid; criteria X1-X5 and stop rule declared against the library baselines. 
Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
 2026-09-21 11:56:36 +01:00
vvsandClaude Opus 5 2498c66358 Metric defect found by B's first run (mean = inf): an exact hit made the new width 0 and the floor (ulp of the root, 5e-324 when the root is 0) overflowed. Fixed to XTOL - an exact hit ends the run, so it is worth the halvings still needed to reach xtol - identical for every candidate; A re-run with it. 
A with the fixed metric: still PASSES A1 and A2 in both configurations - flat 0.26 -> 2.82 (proposed) and 0.35 -> 0.77 (reading 3), canonical 6.32 -> 8.49 and 9.00 -> 10.44 - but a correction to the first report: for reading 3 on the flat families step A (0.77) beats our step and NOT bisection (0.99); the first run said 1.16. B (outcome memory) FAILS its falsifier: flat 0.31 -> 0.97 and 0.58 -> 0.82 (B1 holds) but canonical 4.74 -> 2.49 and 5.52 -> 2.12 (B2 fails), bisecting on 66% and 53% of canonical states. Mechanism: the known trap - a good step can collapse the error without moving the bracket, so an outcome measured in bracket shrink condemns it; the same trap that sank the bracket-progress gate (4449) and the bracket guard (7260).

Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
 2026-09-21 11:49:39 +01:00
vvsandClaude Opus 5 2b0ee228b4 PREREG B before the run: outcome memory - bisect when the most similar past state (ratio similarity of the contraction rho, select not weight, ties -> most recent) bought less than one halving. Replay check, criteria B1-B4 and falsifier declared. 
Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
 2026-09-21 11:48:13 +01:00
vvsandClaude Opus 5 3cce10bfdf Outcome of PREREG A: PASSED on every declared criterion, both configurations. Paired, per one evaluation from the same state, bracket halvings: flat families 0.26 -> 2.87 (proposed) and 0.36 -> 1.16 (reading 3), i.e. above bisection's 1.00 (A1, A3); canonical set 8.21 -> 10.05 and 12.15 -> 12.96, no harm (A2); fun1 7.36 -> 9.01 and 7.28 -> 11.46. S > 0 on about half the canonical states (A4). Step A leaves the bracket on 6-28% of the states where it acts; excluded here, projected in a real method. One-step replay only - the whole-run effect needs the rule in the method, a separate pre-registration. 
Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
 2026-09-21 11:47:42 +01:00
vvsandClaude Opus 5 781bd15253 PREREG A before the run: similarity of successive steps as the multiplier, step d_n/(1-S), S = ratio similarity of the two displacements (0 if opposite). Replay check, one extra evaluation per state for our step, step A and the midpoint; criteria A1-A4 and falsifier declared; the one-step limitation declared. 
Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
 2026-09-21 11:46:59 +01:00
vvsandClaude Opus 5 d754689480 Outcome of PREREG_empty_step: both features FAIL by the declared criteria. Empty step (similarity of |f_n| to |f_n-1|): AUC 0.45/0.53/0.34 (proposed) and 0.46/0.51/0.31 (reading 3) against APS/fun1/other CHA; on the proposed rule it fires MORE on APS (36.0%) than on the flat families (18.9%). Repeating pattern with the period chosen from the data: separates the flat families from APS and fun1 (AUC 0.69/0.77 and 0.66/0.67; fires 77.1% vs 37.7%/38.2%, and 18.0% vs 6.2%/9.5%) but not from the other CHA families (AUC 0.41 and 0.22; fires 72.4% and 68.6%), so R1 fails and no rule is built. 
Seen after the result and therefore NOT claimed: the 'other' group contains fun7 = x exp(-1/x^2), itself a flat function whose derivatives all vanish at the root. A fair re-test needs a new pre-registration with flatness defined in advance by a property of f (f'(r) = 0), not by the grouping that just failed.

Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
 2026-09-21 11:23:47 +01:00
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