nx_var_lib.nx

nx_var_lib.nx -- F991 (risk core): VALUE-AT-RISK + EXPECTED SHORTFALL, integer-exact, fail-closed. A risk number computed from too few observations is worse than no number -- it looks authoritative and is meaningless, and that is how blow-ups happen. So the sovereign property here is that the tail is only reported when the data can support it: a 99% VaR needs at least ~100 observations to have a single point in the tail, and asking for one from 10 data points REFUSES (fail-closed) rather than inventing a quantile. Everything is integer minor units, no float -- a reproducible risk number an auditor can redo. Two measures: Historical VaR -- the loss at the confidence quantile (the threshold a loss exceeds only (1-c) of the time) Expected Shortfall (CVaR) -- the MEAN of the losses AT OR BEYOND the VaR quantile. This is the coherent, sub-additive tail measure Basel III adopted over VaR; ES >= VaR always, and it sees the shape of the tail VaR ignores. Reporting ES is the state of the art. Convention: losses[] are POSITIVE numbers (a loss of 500 = 500); larger = worse. SCALE ENVELOPE (declared): var_sort is selection sort O(n^2) on a COPY (never mutates the caller's array); a merge/quick sort is the rung for very long series. DRY: composes nx_matter_lib helpers. license_tier: ORIGINAL LIB.