nx_monte_carlo.nx

nx_monte_carlo.nx -- Monte Carlo verifier with statistical bounds. First substrate primitive grounded in CLASSICAL STATISTICAL THEORY per cardinal feedback-loras-and-negatives-are-patches-not- systems: User: "inputs from classifiers lead to known outputs all with statistical measurement i mean monte carlo or other multivariate systems prove this" The substrate doesn't invent predictability. It APPLIES the techniques (Monte Carlo, multivariate statistics, classification theory) the AI field abandoned for deep-learning opacity. ===== What this primitive does ================================== Given: - sample_fn : generates one measurement (i64 scalar) - n_samples : how many to draw - target_q10 : the target mean (in caller's chosen units) - tol_q10 : tolerance bound (output mean must be within target +/- tol) - seed : PRNG seed for reproducibility Returns: - empirical mean - empirical variance (Welford 1962 online algorithm) - verdict: TARGET_MET / OFF_TARGET / INSUFFICIENT_SAMPLES - the t-statistic for the test (caller can compute confidence intervals + decide their own threshold if 95% default is wrong for their use) ===== Statistical method ========================================= One-sample t-test (Student 1908, Welch 1947 variant for unequal variance not needed here since we test against fixed target): t = (mean - target) / (sd / sqrt(n)) |t| < critical_value for given confidence + (n-1) dof -> mean is