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Anthropic: Lean formalizations of 3SUM and shortest-path bounds

Anthropic’s formal-math repository publishes a Lean project for the 3SUM, (min,+)-product, and APSP bounds associated with the Alman–Vassilevska Williams paper.

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Sources for this record

What was already known

The paper states algorithmic improvements for polynomial-size integer inputs. The repository is a formalization source, not evidence that AI discovered the algorithms.

What changed and why it matters

Makes specific algorithmic statements and their verification configuration available for scrutiny.

The AI contribution

This is an AI-lab formalization artifact. The exact human/model contribution to this project was not established by our source review.

Limitations

The repository’s APSP bound and the paper abstract use different numerical precision. This entry does not merge those numbers or attribute algorithm discovery to AI. No local recompilation has been performed.

Verification evidence

Evidence labels show what supports the claim. Importance rates its impact if correct.

Author claim

Repository description of the represented bounds.

Accessible artifact / proof

Project configuration is available. Successful checking of these precise bounds is not inferred from the root repository’s general CI policy.

Correction and publication history

2026-10-11 · correction

The original paper now establishes the AI discovery attribution left unassessed by the earlier artifact-only record. Correct original report date and distinguish the paper’s numerical bound from the formal project. Full update; no subscriber alerts.

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