nx_analyst_infer.nx

nx_analyst_infer.nx -- STATISTICAL INFERENCE for the general Nishi analyst: the "is it actually real?" layer that every SOTA analyst tool (pandas/scipy, R, DuckDB+stats) reports and ours did not. THE GAP THIS CLOSES (measured 2026-07-23, ws=analyst-sota): nx_analyst_multi computes Pearson r and nx_analyst_report NAMES A KEY DRIVER from it -- with NO significance guard whatsoever. The driver was a bare argmax over |r|, so the report named one at ANY sample size. Its capstone gate happens to run at n=300 where its r=-172 IS real, so no live finding was false -- but nothing in the code said so, and the same call at n=8 returns the same confident sentence about pure noise (this organ's T2/T4 teeth show the flip). Naming a driver that cannot be distinguished from noise is the liar-kill law applied to statistics. The ecosystem ALREADY had sovereign inference (nx_survey_stats: chi-square vs a data-driven critical table, fail-closed past the table, 95% proportion margin) but it was locked inside the SURVEY vertical and consumed se_ballots. This organ is the general, dataset-agnostic extraction (rule 15 DRY): it takes a bare r and n, so ANY caller -- dataframe, store, timeseries, survey -- can ask "is it real?". METHOD: Student-t test on a correlation coefficient. t = r*sqrt(n-2)/sqrt(1-r^2), df = n-2, compared to a two-tailed alpha=.05 critical value. Both sides are SQUARED so the whole test is INTEGER-EXACT -- no sqrt, no float, bit-reproducible (the ecosystem's integer-exact-analytics EXCEED holds through inference): t^2 > tc^2 <=> rp^2 * (n-2) > ceil( tcp^2 * (SCALE_SQ - rp^2) / SCALE_SQ ) with rp = r*1000 and tcp = t_crit*1000. The RHS division rounds UP so truncation can only make the test STRICTER -- an integer-rounding artifact can never manufacture a false "significant". FAIL-CLOSED BY CONSTRUCTION (mirrors nx_survey_stats' own adversary guard): - n < 3 -> df < 1 -> CANNOT TEST (-1), never silently "not significant" - df not tabulated -> use the largest tabulated df <= query. t_crit DECREASES in df, so a lower-df row is a LARGER threshold = conservative. No usable row at all -> tcrit 0 -> NOT significant. license_tier: ORIGINAL No hardware writes (Rule 26).