Lean verification record

Checked Artifact: Birkhoff–von Neumann Theorem (mathlib)

Proof Atlas collected build, no-sorry, axiom, and clean-source evidence directly from the pinned upstream declaration.

Verification result

The recorded Lean checks passed

Build replaypassed with retained transcript
Unfinished stepsNone found
Source identityPinned commit and file recorded
Dependency profileAxiom closure recorded

Reproducibility details

What the checker recorded

Declaration checked: doublyStochastic_eq_convexHull_permMatrix
Module: Mathlib.Analysis.Convex.Birkhoff
Source file checked: Mathlib/Analysis/Convex/Birkhoff.lean
Package commit: 5e932f97dd25535344f80f9dd8da3aab83df0fe6
Build transcript: passed · retained with this record
Unfinished proof steps: None found by the recorded no-sorry scan
Axiom closure: Classical.choice, Quot.sound, propext
Collection provenance: Clean source state recorded

ProofAtlas record

What has been checked

Upstream indexedPinned source bytes verified locally

Locally reproducedExact upstream declaration replayed

Reviewed pageCurrent public presentation reviewed

Accepted Atlas resultNot recorded for the preferred artifact

Mathlib is the source of the theorem; the local Lean replay and page review are separate.

Evidence boundary

Exact formal statement only

This page indexes Mathlib’s finite square-matrix convex-hull identity over a linearly ordered field. It proves existence of convex decompositions into permutation matrices, not uniqueness, a canonical or minimal decomposition, an algorithmic complexity bound, an assignment-optimization theorem, or the separate majorization characterization. The extreme-point identity is a companion declaration, not the selected endpoint.

This checker record does not establish novelty, transfer a historical acceptance decision, or authorize publication.