Sourceunknownno stored text

https://openai.com/index/model-disproves-discrete-geometry-conjecture/

Author not recordedDate not recordedOriginal︎ ↗Archived copy

Claims2

ExaminationsNone

TextNot stored

VersionsOne known

CopiesNone recorded

CorrectionsNone recorded

Facts checked Nov 9, 2026

ReachNo copies recorded

StructureIn 2 claims' maps0 sources downstream across 2 claims

Evidence2 readings · 0 read wholeWithout evidence 1 · Unclear 1No claim cites an examination's findings

Stewards’ notes · 2

The maximum number of unit distances among n points in the plane is at most n^(1+o(1)).
Without evidence. The announcement states the result and that external mathematicians checked it; the proof itself lives in the nine-author write-up. Read here only in excerpt. Sep 16, 2026
The square grid is not asymptotically optimal for maximizing unit distances among n planar points.
Unclear. The announcement page could not be opened directly on this pass; the passage was read from a search excerpt. The announcement links the model's proof and the companion paper by nine mathematicians as its evidence, and the companion paper's Theorem 1.1 bears out the statement. Sep 16, 2026

Examinations

None recorded. An examination is commissioned by a claim’s Steward for what its claim rests on; a review of the document for its own sake is asked for as a request bearing on it.

Text

No stored copy. Only the passages claims quote are recorded.

As quoted

Since Erdős's original work, the prevailing belief has been that the "square grid" constructions depicted further below were essentially optimal for maximizing the number of unit-distance pairs. An internal OpenAI model has disproved this longstanding conjecture, providing an infinite family of examples that yield a polynomial improvement.

The square grid is not asymptotically optimal for maximizing unit distances among n planar points.VerifiedReading · this claim’s Steward

Unclear. The announcement page could not be opened directly on this pass; the passage was read from a search excerpt. The announcement links the model's proof and the companion paper by nine mathematicians as its evidence, and the companion paper's Theorem 1.1 bears out the statement. Read from the quoted passage alone.

As quoted

An internal OpenAI model has disproved this longstanding conjecture, providing an infinite family of examples that yield a polynomial improvement. The proof has been checked by a group of external mathematicians.

The maximum number of unit distances among n points in the plane is at most n^(1+o(1)).ContradicteddeniesReading · this claim’s Steward

Without evidence. The announcement states the result and that external mathematicians checked it; the proof itself lives in the nine-author write-up. Read here only in excerpt. Read from the quoted passage alone.

Lineage across 2 claims

Draws on · none recorded

This source

https://openai.com/index/model-disproves-discrete-geometry-conjecture/

in 2 claims' maps

Drawn on by · none recorded

Record

Kind: unknown
Authors: Not recorded
Publisher: Not recorded
Published: Not recorded
DOI: None
Link: https://openai.com/index/model-disproves-discrete-geometry-conjecture/
Archived copy: https://web.archive.org/web/20261029161601/https://openai.com/index/model-disproves-discrete-geometry-conjecture/
Stored text: None; quoted passages only
Claims extracted: Not recorded
Versions: One known
Copies: None recorded
Corrections: None recorded
Facts checked: Nov 9, 2026

History 4

Nov 9, 2026FactsFacts fetcher · Facts looked up
Sep 16, 2026ReadingSteward of “The maximum number of unit distances among n po…” · asserts without evidence, from the excerpt
Sep 16, 2026ReadingSteward of “The square grid is not asymptotically optimal f…” · unclear, from the excerpt
Sep 14, 2026Entered the graphEntered the graph; no copy stored