nx_abstat_aa_gate.nx

nx_abstat_aa_gate.nx -- A/A CALIBRATION, A-PRIORI SAMPLE SIZE, ALWAYS-VALID MONITORING and CUPED for the contrast core (gameengine GE51): the four published requirements for an honest improvement claim, each read from a mirrored primary source and each proven here by a seeded fixture with a KNOWN effect. (1) the A/A bar -- "the null hypothesis should be rejected about 5 percent of the time when a 95 percent confidence level is used" (Kohavi et al., KDD 2007, ref ge-expguide). nx_abstat_gate carries ONE same-distribution trial; one trial cannot measure a RATE. This gate runs thousands of synthetic experiments from a SEEDED generator and asserts the rejection rate sits inside a binomial envelope DERIVED from the trial count -- a rate that is too HIGH is a lying instrument, a rate that is too LOW is a blunt one, and both fail here. (2) a-priori sample size -- n = (4 r sigma / Delta)^2 at 95 percent confidence and 90 percent power, gated against the paper's own worked examples (over 1.6 million; 25,600; under 500,000) so the number the acceptance page prints before reading the arms is the number the field would compute. (3) ALWAYS-VALID INFERENCE (Johari, Pekelis, Walsh, ref ge-alwaysvalid) -- the same A/A experiments are now MONITORED CONTINUOUSLY, one look per pushed pair from the sample floor to the end, and two rules are consulted at every look: the fixed-horizon verdict (the practice the paper measures at "fivefold" Type I inflation) and ab_always_valid (the mSPRT statistic, rejecting when its running maximum reaches ln(1/alpha)). The bar: the always-valid rate stays inside the honest envelope while the peeked fixed-horizon rate leaves it -- a positive and a negative control on the SAME sample stream, so the discrimination is measured, never assumed. The mixing variance is derived from the planted effect the way the estate derives it from the pre-declared MDE; the closed form is KAT-checked against values derived by hand from the formula before any rate is trusted. (4) CUPED (Deng, Xu, Kohavi, Walker, ref ge-cuped) -- paired fixtures (a pre-period covariate X and a metric Y = X + independent noise, so the correlation is KNOWN: rho^2 = 1/2 and theta = 1) prove the estimator's identities from the paper (theta, rho^2, var(Ycv) = var(Y)(1 - rho^2)) on 400,000 pairs, then the A/A rate of the adjusted contrast stays in the envelope, and the POWER of the adjusted contrast at a planted effect exceeds the plain contrast's power on the SAME samples -- the paper's claim ("the same power from half the users") measured as a rate, not asserted. plus a POWER control for the plain test: the same generator with a planted effect must reject almost always, or the A/A rate is cheap for the wrong reason (a test that never rejects has a perfect false-positive rate). DETERMINISTIC BY CONSTRUCTION: the estate's nofloat gates' LCG (seeded), so every rate is reproducible and a RED is an arithmetic change, never a dice roll. Samples are Irwin-Hall-4 (the sum of four uniforms), whose variance is derived from the uniform's width rather than typed. license_tier: ORIGINAL No hw writes.