Lean verification record

Checked Artifact: Finite-Dimensional Spectral 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: LinearMap.IsSymmetric.diagonalization_apply_self_apply
Module: Mathlib.Analysis.InnerProductSpace.Spectrum
Source file checked: Mathlib/Analysis/InnerProductSpace/Spectrum.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 coordinatewise diagonalization theorem for a self-adjoint linear endomorphism of a finite-dimensional inner-product space over an RCLike field. It uses Mathlib's isometric equivalence with the direct sum of eigenspaces. It is not the infinite-dimensional spectral theorem, a theorem for arbitrary normal operators, or a claim about a user-chosen matrix basis.

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