'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>
vvsandClaude Opus 5