'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>
