ProofAtlas

Lean evidence record

Kirchhoff’s Matrix-Tree Theorem: Lean evidence

This technical record binds the exact theorem statement to its commit-pinned Lean source, checker results, assumptions, and publication-review status.

Read theorem page
Lean buildpassed
Unfinished proof stepsNone
Publication reviewsAccepted

Exact recorded Lean statement

The declaration this evidence supports

theorem matrixTreeTheorem : MatrixTreeTheoremStatement

Line counts exclude blank lines; comments and documentation count. The total is the commit-pinned first-party Lean import closure; Mathlib and other third-party dependencies are excluded.

Technical evidence record

Source identity, checker results, and assumptions

Main Lean declaration
matrixTreeTheorem
Source commit
e5057d269d42

Mechanical evidence

Lean verification

These fields support the exact Lean declaration, not a broader informal claim.

Artifact ID
artifact.known-matrix-tree-theorem.endpoint.v001
Accepted-result title
Accepted Result: Kirchhoff’s Matrix-Tree Theorem
Accepted-result status
Accepted formalization of a known theorem
Accepted-result boundary
For every finite simple graph and every chosen root vertex, the determinant of the integer reduced Laplacian equals the number of spanning trees. Non-claim: The checked statement is for finite simple graphs, not weighted graphs, multigraphs, or directed arborescences.
Declarations covered by recorded evidence
AtlasKnownTheorems.MatrixTreeTheorem.matrixTreeTheorem
AtlasKnownTheorems.MatrixTreeTheorem.MatrixTreeTheoremStatement
Lean build
passed
Recorded build time
4.3 s one machine-dependent evidence run, not a benchmark
Evidence collected
· clean-source provenance recorded
Unfinished proof check
passed
Lean toolchain
leanprover/lean4:v4.29.1
Recorded source commit
e5057d269d42d50b1140c43f9d61e3670b6641ef
Source SHA-256
sha256:216763480d3d26cd0879954a51895d88596b6183499bb2bcda9766844247df4a
Statement alignment
accepted

Lean foundations

Standard foundations used by the proof

Lean reports the logical foundations below through Mathlib. They are standard proof-system foundations, not conjectural mathematical assumptions about this theorem. The recorded closure stays within the approved classical_mathlib_standard profile, with no unexpected axiom or unfinished-proof placeholder.

  • Classical.choice
  • Quot.sound
  • propext

Files and machine-readable evidence

Reproduce or inspect the recorded check

Use the complete first-party source bundle for reconstruction, or inspect the exact main file and checker evidence separately. Mathlib and other third-party dependencies are identified but not rebundled.

Complete checked Lean source · 1 Lean file · 1 evidence record · Download ZIPBrowse counted source onlineDownload main Lean fileDownload checker evidence (JSON)Download Apache-2.0 license

Review results

Publication reviews accepted

All four required publication-review gates are accepted for the reviewed presentation of this exact theorem. The review results are separate from the Lean build and do not broaden the formal statement.

Read the publication-review details