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vvsandClaude Opus 5 0e05c92a1b Title (Valeri): 'Root Finding by Similarity and Analogy: A Bracketing Method with One Declared Constant' - the method rests on both, and 'parameter-free' overstated it (one declared constant, two declared choices). .tex and PDF regenerated; verifier 467 OK / 0 BAD. 
Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
 2026-09-21 22:15:01 +01:00
vvsandClaude Opus 5 23d0c73231 The .tex is no longer stale: regenerated from the canonical .md by build_tex.py (pandoc 3.1.3 + pdflatex on the server; marked GENERATED, never edited by hand). PDF: 28 pages, 0 errors, 0 undefined references, 0 overfull boxes. For LaTeX the .md got braces on four n_\max subscripts (fix_md_for_latex.py; rendering identical) and Table 10 was split into totals (10) and per-problem counts (10b) so that it fits a page; numbers unchanged. verify_article on the server 467 OK / 0 BAD; regression x2 1226 passed, 0 failed. 
Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
 2026-09-21 22:07:48 +01:00
vvsandClaude Opus 5 d2a142c39e All-corpora wins/losses table: ModAB added (totals, violations, A' per problem and total difference against it on every corpus). 
Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
 2026-09-21 21:43:43 +01:00
vvsandClaude Opus 5 f80aeb5d13 Article: ModAB added - Table 8 row (2914 / 2436 / 5350; A' 118/11/25 and 32/9/4), Table 10 column (totals, bound violations, A' vs ModAB per corpus), how it is run (authors' package pymodab 1.0.9, same stopping rule, counts agree with the package's own), the evidence paragraph (ahead on every corpus p <= 0.0013, the one test 3656 vs 5535 183/34, ModAB's own benchmark all 91: 1507 vs 1588, 9 bound violations), 8.6: ModAB's linearity check at the midpoint named as the precursor of our exit judgment, abstract, conclusion, introduction, future work (the comparison no longer missing), reference 20. verify_article: every ModAB number checked; server 467 OK, 0 BAD; regression x2 1226 passed, 0 failed. 
Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
 2026-09-21 21:42:15 +01:00
vvsandClaude Opus 5 37c81b027a PREREG_modab outcome (server): M1 PASSED - A' ahead of ModAB (authors' package pymodab 1.0.9, same stopping rule, counts equal to the library's own counter). Corpus 4: A' 3656 vs ModAB 5535, per problem 183/23/34 p=7e-26. Paper protocol: APS 2438 vs 2914 (118/11/25), CHA 2005 vs 2436 (32/9/4). Six corpora: 13032 vs 16657, significant on every one. ModAB's own benchmark (Roots.jl f01-f91): all 91 - 1507 vs 1588 (56/13/22 p=1.5e-4); 78 - 1371 vs 1446. ModAB breaks the 2x-bisection bound on 9 problems (1 on corpus 1, 8 on corpus 4), A' on none. ModAB wired outside the published grid (EXTRA_BASELINES), which stays at 264. 
Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
 2026-09-21 21:35:36 +01:00
vvsandClaude Opus 5 bfa23b223d PREREG before install and run: comparison with ModAB via the authors' own package pymodab 1.0.9 (native wrapper of their C code); the same stopping rule as every rival (aTol 1e-12, rTol 8.9e-16, no |f| stop - read in ModAB.c), evaluations counted by our wrapper, budget 200. A' and ModAB frozen. M1 on the fourth corpus (total and sign test), M2-M4 reported (six corpora, paper protocol, guarantee, ModAB's own Roots.jl benchmark). Priority note: ModAB's linearity check at the midpoint is a precursor of our exit judgment, named in 8.6 whatever the outcome. 
Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
 2026-09-21 21:27:06 +01:00
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