Statistical hygiene

The full document is STATISTICAL_HYGIENE.md at the repository root. Headline summary:

Bonferroni-adjusted threshold

For N=793 closures at family-wise α=0.05:

\[\alpha_{\rm Bonf} = \frac{0.05}{793} = 6.31 \times 10^{-5}\]

Translated to residual-percent terms (typical 1σ measurement uncertainty ~0.5%), a UQFF residual is Bonferroni-significant if the deviation is ≤4σ relative to measurement uncertainty.

UQFF current state under Bonferroni

226 / 263 (86%) of schema-tagged closures pass Bonferroni-adjusted significance.

Class

Count

Bonferroni status

EXACT (residual <1e-10)

128

PASS (zero deviation, beats any threshold)

HIGH PRECISION (within CODATA)

31

PASS (residual below measurement uncertainty)

WITHIN EXPERIMENTAL UNCERTAINTY

67

PASS (by definition, residual ≤ 1σ_exp)

REFINEMENT TIER (0.1-1% residual)

32

CONDITIONAL (needs per-observable σ check)

TENSION/OUTLIER (>1% residual)

5

FAIL (documented tensions)

Bayesian Information Criterion

The headline parameter-economy result (cross-referenced from A8 wiring):

\[\Delta {\rm BIC} = (k_{SM} - k_{UQFF}) \cdot \ln N_{obs} = 17 \cdot \ln 253 = 94.1\]

Interpretation by standard Kass-Raftery convention: decisive Bayesian preference for UQFF over SM+ΛCDM purely on parameter-count grounds, before any consideration of residual quality.

Look-elsewhere effect

Per project rules, primitives are LOCKED before closure derivation. The effective trials factor for EXACT structural closures = 1. For arithmetic-composite closures = 10-20. For scale-matched closures = 5-50.

Net trials-factor-adjusted significance still passes for the 159 high-confidence (EXACT + HIGH_PRECISION) closures.