Lean Verification for "Exact Moments of Gaussian Gram Hafnians Reveal an n²/log n Threshold for Weak Anticoncentration"

This software archive contains the Lean 4 formalization accompanying the paper “Exact Moments of Gaussian Gram Hafnians Reveal an n²/log n Threshold for Weak Anticoncentration.”

It provides public theorem endpoints for all fourteen numbered equations in the Letter. The verified results include the exact second and fourth absolute moments of Gaussian Gram hafnians, the normalized moment ratio, the terminating generalized hypergeometric representation, the modified Bessel function identity, finite bounds, the quadratic crossover, and the logarithmic weak anticoncentration threshold.

The archive pins Lean 4 leanprover/lean4:v4.33.0-rc2 and mathlib revision 641fbd329d4ffb62bef83c51f54088469056bd36. It contains the complete source code, a summary verification file, the theorem crosswalk, reproducible build instructions, permanent axiom audits, citation metadata, and a verification report. The audited dependency chains contain no unfinished proofs or mathematical axioms specific to this project. The axiom reports contain only Lean and mathlib’s standard logical foundations: propext, Classical.choice, and Quot.sound.

The formal verification concerns the Gaussian surrogate. It does not formalize finite dimensional Haar hiding, moment transfer, full small ball anticoncentration, quantum advantage, literature claims, or physical interpretation.

The archive is licensed under the GNU General Public License v3.0 only (GPL-3.0-only).