This software archive contains the Lean 4 formalization accompanying the paper “Asymptotic independence of the log determinant and coherence under the Gaussian diagonal covariance null.” It provides kernel-checked exact counterparts or explicitly proved finite assemblies for all 12 named mathematical results and all 50 labeled equations in the main paper. It also includes paper-facing endpoints for the unconditional and conditional pair-block factorization, the conditional overshoot inequality and its all-regime limit, the falling-factorial indicator identity, the alternating binomial partial-sum identity, and the factorial Bonferroni inequalities. The archive pins Lean 4 leanprover/lean4:v4.33.0-rc2 and mathlib revision 641fbd329d4ffb62bef83c51f54088469056bd36. It contains the complete source code, an endpoint catalog in the paper’s notation, the equation-coverage ledger, and build, placeholder, and axiom audits. The paper-specific interface contains no unfinished proof placeholders or paper-specific axioms. The endpoint audit reports only Lean and mathlib’s standard logical foundations propext, Classical.choice, and Quot.sound.