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Importance: major
VerificationAuthor claimAccessible artifact / proofIndependent checking
full solutionai assisted

AI-assisted disproof of the Erdős unit-distance conjecture

The human-verified writeup gives a fixed ε>0 and growing planar point sets with at least n^(1+ε) unit distances.

Sources for this record

What was already known

Erdős conjectured at most n^(1+o(1)) unit distances.

What changed and why it matters

Advances the stated target relative to the recorded baseline.

The AI contribution

An internal OpenAI model generated the construction; nine named mathematicians wrote and checked the digested argument.

Limitations

The original model’s exponent is not made explicit in this entry. Sawin’s explicit refinement is human work; no optimal upper bound is determined.

Verification evidence

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

Author claim

Theorem 1.1 and the accompanying attribution.

Accessible artifact / proof

Human-readable mathematical reconstruction.

Independent checking

The nine named mathematicians describe a human-verified reconstruction. AIProofWatch did not independently reproduce it.

Checker: Alon, Bloom, Gowers, Litt, Sawin, Shankar, Tsimerman, Wang and Wood
Scope: The fixed-positive-exponent disproof of the Erdős unit-distance conjecture.
Basis: Reported by the linked checker

Correction and publication history