Lean Verification for "Local Anticoncentration for Gaussian Boson Sampling via Conditional Wishart Geometry"

Version 1.1.0 provides the updated Lean verification materials for Hongru Zhao's paper, Local Anticoncentration for Gaussian Boson Sampling via Conditional Wishart Geometry. It succeeds version 1.0.0, which was deposited under the paper's earlier title, Shifted Anticoncentration of Complex Gaussian Gram Hafnians via Conditional Wishart Geometry.

Connection with GitHub: https://github.com/HongruZhao/ComplexGramHafnians is the development repository for the focused verification of manuscript Theorems 2.1 and 2.3. Those main-theorem statements are proved for the actual complex Gaussian matrix models without additional scientific axioms. This Zenodo update includes an exact source snapshot of that repository at commit 95ab10dc594ac92207054413220ae9fd2adab08c. The source snapshot is included so that this release remains reproducible independently of subsequent changes to the GitHub repository.

Zenodo has the broader archival scope: in addition to the focused GitHub snapshot, it includes the extended production formalization, current paper-to-code alignment, historical equation crosswalk, exact-arithmetic certificates, dated build and axiom audits, and checksums. This is a Lean-only archive; manuscript PDFs and LaTeX sources are not included. The extended development includes sharp independent-factor perturbation bounds, Fourier compression, conditional Wishart identities, symmetric Gaussian limits, Wick obstruction, and related results.

The audited main-theorem and selected broader endpoints use zero project scientific axioms and only standard Lean foundations. Their stated hypotheses remain explicit. Production source identity was checked against the successful recorded builds; packaging does not claim a new Lean run. The historical crosswalk applies to the earlier manuscript. The revised polynomial-threshold corollary still has an unassembled Gaussian-law composition, the conditional density conclusion retains integrability hypotheses, and the sharp threshold remains open. The companion finite-Haar application is outside this Gaussian archive. Complete unconditional formalization of every statement in the revised manuscript is not claimed.

Copyright 2026 Hongru Zhao. Licensed under GPL-3.0-only.