Technical Lean evidence record
Checked Artifact: Roth’s Theorem (mathlib)
Proof Atlas collected build, no-sorry, axiom, and clean-source evidence directly from the pinned upstream declaration.
ProofAtlas record
What has been checked
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
rothNumberNat_isLittleO_id- Module
Mathlib.Combinatorics.Additive.Corner.Roth- Source file checked
Mathlib/Combinatorics/Additive/Corner/Roth.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 page indexes Mathlib’s qualitative asymptotic declaration for the natural-number Roth function. Here rothNumberNat N is the maximum cardinality of a ThreeAPFree subset of Finset.range N = {0,…,N−1}, and ThreeAPFree excludes nontrivial a,b,c in the set with a+c=b+b. The exact conclusion is an IsLittleO atTop relation after coercion to ℝ. It does not state an explicit decay rate, a finite threshold, a modern quantitative bound, or a theorem about longer progressions.
This checker record is evidence for the exact formal statement only. It does not establish novelty, transfer a historical acceptance decision, or authorize publication.