Lean verification record

Checked Artifact: Classification of Pythagorean Triples (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: PythagoreanTriple.classification
Module: Mathlib.NumberTheory.PythagoreanTriples
Source file checked: Mathlib/NumberTheory/PythagoreanTriples.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 integer if-and-only-if classification of Pythagorean triples. Here PythagoreanTriple x y z is exactly x * x + y * y = z * z. The parameters k, m, and n are integers; the two leg formulas may be swapped, and z may be either k * (m ^ 2 + n ^ 2) or -k * (m ^ 2 + n ^ 2). The endpoint does not require a primitive or positive triple, does not require the parameters to be coprime or of opposite parity, and does not claim unique or canonical parameters. It is not the rational-unit-circle formulation.

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