simroot/pure.py: flatlagmempt / flatbandmempt / flatflagmempt - A' with only the flat detector
swapped (Lagouanelle without declining outside (0,1), with memory; Chandrupatla's band; none).
A' itself is untouched: bit-identical to the compiled simbracket on all 868 problems (x2).
sweep_controls.py: K2 through sweep_fourth's harness, K1 with the oracle order m*.
Amendment 1: m* <= 0 is undefined (aps.15.22-30, C0.04 crashed the first full attempt).
Amendment 2 (after the smokes; only corpus-level K1 sums and corpus-4 K2 sums were seen): each
side's slope rounded to 0.01, m* defined only when both sides show a zero (jumps C0.03,
aps.15.21), group 'multiple/fractional' = m* >= 2 or m* <= 2/3, the branches of section 8.1
(simple roots measured at 0.99999 fell under the registered 'm* < 1').
tests/test_article_numbers.py: the verifier test runs on Linux only (the paper's numbers are a
Linux run; libm's last digit differs elsewhere, e.g. 4461 vs 4462).
Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
K1 (point 5): library Chandrupatla and Brent on sign(f)|f|^(1/m*) with the true order m* - an upper
bound for "transform and interpolate". K2 (point 6): A' with only the flat detector swapped -
Lagouanelle with the same memory (hysteresis), Chandrupatla's band, and no detector at all.
Decisive corpus: corpus 4; criteria C1-C5 and what the paper says under every outcome, including
withdrawing the claim that the analogy carries the gain if any control matches A'.
Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
Point 1. The base step's order is Muller's 1.839, not 2: the derivative of the parabola through
the last three points errs by f'''/6 (x_n - x_{n-1})(x_n - x_{n-2}) = O(e_{n-1} e_{n-2}).
order_high_precision.py (3000 digits, to 1e-2900): 1.840 on cos x - x, e^x - 2, x^3 - x - 2,
sin x - 1/2; 2.000 only on x^2 - 2; two-point 1.618. The double-precision medians (2.000, 1.94)
are removed from the text.
Point 3. Every protocol number is re-scored under the criterion of section 9 - a sign change
within 1e-6 or f(x) == 0. rescore_uniform.py re-runs all 2779 distinct configurations of the 25
protocol sweeps on APS and CHA (the runs did not keep x) -> sweep_uniform.json, same row format;
it reproduces the APS/CHA lines of Table 10 exactly (built-in check). verify_article.py,
audit_similarity_places.py and the gap diagnostics read the re-scored data; the multiplier and
endowment measurements score by the same criterion. Table 7 (two criteria side by side) is gone;
7.3 now explains why the criterion is a sign change. Consequences stated in the text: the base
rule 2634 / 2357 against Chandrupatla 2595 / 1505 (1.5% behind on APS, no longer "level"); A'
2259 / 1074 (12.9% and 28.6% below Chandrupatla); the defect reading 2351 is second to the
shape reading 2337, not the record; the remembered analogy is level with no regime (2633 vs
2634) under this criterion; Table 9a's range is 19% to 425%.
Point 8. report_sweep.head_to_head counts every problem, failures charged (it counted only the
problems both methods solved, which is why Table 8 rows summed to 153 and 40). Family-level
comparisons added (A' vs Chandrupatla 8/1/6 of 15 and 7/0/2 of 9 families, not significant), and
an independence paragraph in section 9.
Point 11. sweep_itp.py: ITP (recommended constants and per-problem oracle) on all six corpora ->
Table 10; behind A' on every corpus, 0 bound violations.
Points 7, 9, 10 and the internals: the 2x bound is ours, not the rivals' promise; the law
predicts the group order only; "outside the proven bracket" explained (narrowest bracket of all
observed signs); 7.4's fun1 paragraph corrected (five costs under safe; the unguarded numbers
belong to fun1.4, fun1.5 and to fun3.1, fun5.1 separately); Table 1's last cell; the corpus-4
composition and odd multiplicities stated, also in the abstract.
build_tex.py: pdflatex output decoded with errors="replace" (a UTF-8 character cut by TeX's log
wrap crashed the build). Table 10 column widths rebalanced.
Checks: verify_article on the server 500 OK / 0 BAD (467 existing with the new values, 33 new);
regression x2 on the server 1232 passed, 0 failed; PDF 28 pages, 0 errors, 0 undefined, 0 overfull.
Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
lib/simbracket/_core.pyx ports exactly the A' path of simroot.pure.pure_root (tent similarity,
three-point scale, projection c=2, contra+flatanalogmempt+exp+half+close+sub, pattern) with
Python's semantics kept where they differ from C: min/max keep the first argument on ties and
NaN, float division by zero raises, math.log raises at 0, and math.hypot and the builtin sum
(compensated since 3.12) are called rather than re-coded. find_root(f, a, b, xtol, maxfev) ->
(x, nfev, converged); evaluation_bound(a, b, xtol) = 2*ceil(log2(|b-a|/xtol)) + 3.
tests/test_simbracket_equivalence.py: bit-identical x and evaluation count against pure_root on
all 868 problems of the six corpora (the 91 Roots.jl problems in full), at xtol 1e-12 and 1e-8
and with the budget cut to 12; errors match; the loaded module is the compiled one. 7/7 on
Windows and on Linux. check_simbracket.py: removing any one component from the reference
makes 36 to 455 problems differ (the test discriminates); the compiled form is 4x faster.
The wheel carries only the compiled extension; _core.c is generated (gen_c.py) and ignored.
Regression on the server x2: 1232 passed, 0 failed.
Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
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>
'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>
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>
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>
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>
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>
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>
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>
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>
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>
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>
(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>
(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>
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>
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>
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>
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>
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>
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>
vvsandClaude Opus 5