nx_abstat_lib.nx

nx_abstat_lib.nx -- THE A/B CONTRAST CORE: two arms, replicated, per-axis, family-wise corrected. WHY THIS EXISTS (operator 2026-09-03: "validating if we are improving in ab and multivariate methodology"). The three-party acceptance ledger (nx_accept) answers "has everyone signed?". It CANNOT answer "are we improving?", because a referee row is a SINGLE-ARM, SINGLE-REPLICATE point grade: one capture, one number, no control, no variance. percept=214 floor=151 says the frame cleared the bar. It says NOTHING about whether the frame is better than the one before it, and a bar-clearing frame can be a REGRESSION from a much better predecessor. MEASURED, NOT ASSERTED -- the near-miss that motivated this lib, 2026-09-03: four point measurements of the SAME live world (/world/beach, unchanged build) returned q=5,1,5,5 and worst_ever=13,250,13,12. The spread was the measuring harness own concurrent load, not the subject. A single-arm grade would have published whichever sample the seat happened to take. Only replication plus a control arm separates the two. TWO QUESTIONS, NEVER CONFLATED. This lib answers exactly one of them and refuses to answer the other: "is it above the bar?" -> referee percept vs floor. nx_accept owns it. NOT computed here. "is it better than before?" -> this lib. A subject can be improving and below floor, or above floor and regressing. Neither verdict is derivable from the other, so a consumer must print both or say which one it is showing. WHY BONFERRONI. Acceptance is judged on MANY axes at once (face, skin, hair, garments, locomotion; frame p50/p95/p99; draws; memory). Five axes each tested at alpha=0.05 carry a ~23% chance that at least one reads "improved" by chance alone. ab_crit_t_q10 composes nx_multivariate _mv_bonferroni_critical_t_q10 so a multi-axis "we improved" is a claim rather than a lottery ticket. The table is NOT copied here -- one Bonferroni ruler in the estate, and this lib is a caller of it. NO SQUARE ROOT, AND THAT IS EXACT, NOT A SHORTCUT. The two-sample test is t = delta / sqrt(se2). Comparing t against a critical value is algebraically identical to comparing delta^2 against crit^2 * se2 whenever delta carries the sign we are testing, so this lib squares instead of rooting: no isqrt primitive, no truncation of an irrational, and the comparison is exact integer arithmetic. Q10 IS APPLIED BY THIS LIB, AND HERE IS WHY. It composes the Welford recurrence, whose running mean uses INTEGER division (mean + delta/n). On raw small integers that is lossy: pushing 4 then 5 yields mean 4, not 4.5. Pushing the SAME samples scaled by Q10 (4096, 5120) yields 4608 = 4.5 exactly. So ab_push takes RAW samples and scales them itself -- the caller cannot forget. The residual imprecision is one part in 1024 of a sample unit, named here rather than left for a reader to discover. WASM-COMPATIBLE BY CONSTRUCTION: no allocation, no syscalls, no floating point in the arithmetic path. The caller hands in a region of AB_WORDS i64 (an engine arena offset, or a native mmap), as nx_perf_lib does. license_tier: ORIGINAL No hw writes (Rule 26).