Lean verification record

Checked Artifact: Handshaking Lemma (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: SimpleGraph.even_card_odd_degree_vertices
Module: Mathlib.Combinatorics.SimpleGraph.DegreeSum
Source file checked: Mathlib/Combinatorics/SimpleGraph/DegreeSum.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 odd-degree parity form of the handshaking lemma. For a simple graph G on a finite vertex type V, with decidable adjacency, the selected declaration concludes Even #{v | Odd (G.degree v)}. The degree-sum identity is a supporting declaration in the checked route, not the selected endpoint. The result allows zero odd-degree vertices and does not prescribe an exact positive number, pair odd vertices by edges, require connectivity, or classify finite graphs.

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