nx_multivariate.nx

nx_multivariate.nx -- multi-axis Monte Carlo verifier with Bonferroni family-wise correction. User: "inputs from classifiers lead to known outputs all with statistical measurement i mean monte carlo or other multivariate systems prove this". Closes the multivariate half of the predictability cardinal. Single-axis MC verification (nx_monte_carlo.nx) handles ONE measurable property at a time. Real generation needs to verify MANY properties simultaneously: age AND gender AND ethnicity AND pose AND lighting AND style all within their target distributions. ===== Statistical method ========================================= Two ways to extend single-axis t-test to multivariate: (a) Hotelling T-squared (Hotelling 1931): joint test with full covariance matrix. Optimal power; requires N x N matrix inverse for N axes. (b) Per-axis t-tests + Bonferroni correction (Bonferroni 1936 / Dunn 1961): independent test per axis; correct family- wise alpha by dividing by N_axes. Conservative but no matrix inverse; works for arbitrary axis count. We ship (b) for v1. Hotelling T² queued (nx_matrix has det / inv for 2x2 + 3x3; arbitrary N needs LU-decomp primitive). Bonferroni: to maintain family-wise alpha = 0.05 across N axes, each per-axis test uses alpha_individual = 0.05 / N. Critical t-value increases accordingly. Conservative because it assumes worst-case correlation; actual independence makes it overpowered, but the worst case is what statistical guarantees need. Decision rule: For each axis i: verify with nx_monte_carlo using corrected critical t. If ANY axis returns OFF_TARGET: overall OFF_TARGET. If ALL axes return TARGET_MET: overall TARGET_MET.