'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>
vvsandClaude Opus 5