Summary

Math review of ui/src/lib/stats.ts found several issues. This PR fixes the real bugs and tightens edge guards, keeping the stats worker dependency-free and lean.

Fixes

Bugs

• computeProfiles dropped zAxis for descriptive stats — 3D charts silently collapsed across the z dimension while the correlation in the same bundle used z. Now passes zAxis through to computeDescriptive. (Regression test added.)
• 95% CI was a z-interval (z=1.96) on the population SD — systematically too narrow for small n. Replaced with a Student-t interval: SEM uses the sample SD (n-1) and the critical value is t*_{n-1} from a compact lookup table with 1/df linear interpolation (<0.15% max error across df=1…1000, folding to z=1.95996 in the limit). CI is now NaN for n<2.

Edge guards

• correlationMatrix diagonal is now NaN for constant (zero-spread) columns instead of a misleading 1, consistent with the NaN those columns produce off-diagonal.
• cqv guard changed from p25+p75 !== 0 to > 0 so negative-spanning distributions return NaN instead of an unstable/negative ratio.

Docs

• selectCorrelationAxis comment corrected (picks the smallest usable axis, not "prefer x").
• mad doc notes it is unscaled (no 1.4826 factor) — not a σ-equivalent.

Approach note on the t-quantile

An initial implementation used Lanczos log-gamma + Lentz continued-fraction incomplete beta + bisection inverse (~95 lines, exact to 15 digits). That was over-engineered for a UI stats panel — replaced with a 12-row lookup table + 1/df linear interpolation (~40 lines, <0.15% max error). The error is invisible at UI render precision.

Infra fix

• .lefthook.yml ui-gen-check hook used set -euo pipefail (bash-only); failed under sh (dash). Changed to set -eu.

Test plan

• vitest run — 354/354 pass (78 in stats file, 4 new)
• vue-tsc -b --noEmit — clean
• prettier --check — clean
• UI embed rebuilt; verify-gen-sync.ts confirms vizb-ui.gen.go in sync
• All pre-commit hooks pass (format, go-test, ui-gen-check)