Technical Lean evidence record

Checked Artifact: Banach Fixed-Point Theorem (mathlib)

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

Four separate status axes

Upstream indexedPinned source bytes verified locally

Locally reproducedExact upstream declaration replayed

Reviewed page2 of 3 presentation reviews recorded

Accepted Atlas resultNot recorded for the preferred artifact

These states distinguish upstream identity, local reproduction, review, and Atlas acceptance. This page is part of the public, read-only Mathlib landmark collection.

Mechanical evidence

Declaration checked: ContractingWith.exists_fixedPoint
Module: Mathlib.Topology.MetricSpace.Contracting
Source file checked: Mathlib/Topology/MetricSpace/Contracting.lean
Package commit: 5e932f97dd25535344f80f9dd8da3aab83df0fe6
Build: passed · transcript retained
Unfinished proof steps: None found by the recorded no-sorry scan
Axiom closure: Classical.choice, Quot.sound, propext
Clean collection provenance: Recorded

Evidence boundary

This target indexes Mathlib's complete extended-metric-space contraction theorem from a starting point with finite first displacement. It gives a fixed point, convergence of iterates, and a geometric error bound. Uniqueness is a companion theorem, not part of this selected declaration.

This checker record is evidence for the exact formal statement only. It does not establish novelty, transfer a historical acceptance decision, or authorize publication.