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https://arxiv.org/html/2605.20695v1

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Copy ofRemarks on the disproof of the unit distance conjecture
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Text57 sections
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Text271 passages · 0 marked

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Back to Abstract0 passages
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1 Introduction0 passages
2 Proof and further overview0 passages
3 Noga Alon0 passages
4 Thomas Bloom0 passages
5 W T Gowers0 passages
6 Daniel Litt0 passages
7 Will Sawin0 passages
8 Arul Shankar0 passages
9 Jacob Tsimerman0 passages
10 Victor Wang0 passages
11 Melanie Matchett Wood0 passages
References0 passages
License: CC BY 4.01 passage
Remarks on the disproof of the unit distance conjecture0 passages
Noga Alon0 passages
Email address: nalon@math.princeton.edu1 passage
Email address: thomas.bloom@manchester.ac.uk1 passage
Email address: w.t.gowers@dpmms.cam.ac.uk1 passage
Email address: daniel.litt@utoronto.ca1 passage
Email address: wsawin@math.princeton.edu1 passage
Email address: ashankar@math.toronto.edu1 passage
Email address: jacobt@math.toronto.edu1 passage
Email address: vywang@as.edu.tw1 passage
Email address: mmwood@math.harvard.edu2 passages
Contents0 passages
1 Introduction0 passages
2 Proof and further overview0 passages
3 Noga Alon0 passages
4 Thomas Bloom0 passages
5 W T Gowers0 passages
6 Daniel Litt0 passages
7 Will Sawin0 passages
8 Arul Shankar0 passages
9 Jacob Tsimerman0 passages
10 Victor Wang0 passages
11 Melanie Matchett Wood0 passages
References0 passages
1. Introduction21 passages
Acknowledgements1 passage
2. Proof and further overview57 passages
3. Noga Alon6 passages
4. Thomas Bloom22 passages
5. W T Gowers23 passages
6. Daniel Litt6 passages
7. Will Sawin12 passages
8. Arul Shankar5 passages
9. Jacob Tsimerman3 passages
10. Victor Wang6 passages
11. Melanie Matchett Wood5 passages
References78 references
Instructions for reporting errors7 passages
Major funding support from0 passages

Not found in the text 1

As quoted

In his original work, he noted that a set of n points may have at most O(n^{3/2}) unit distances via noting that the unit distance graph cannot contain a K_{2,3} (two unit circles can only intersect in at most 2 points) while using a √n × √n grid to show that a set of n points may have n^{1+Ω(1/log log n)} unit distances.

The maximum number of unit distances among n planar points is at least n^(1+c/log log n) for some constant c > 0.VerifiedReading · this claim’s Steward

Without evidence. The introduction restates the bound and names the grid construction as its source, but proves nothing about it; the paper's own mathematics concerns the number-field construction that beats this bound.

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On sets of distances of n points (Erdős, American Mathematical Monthly 53, 1946)journal articleMay 19461 claimRestates it faithfully, on 1 claim.
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https://arxiv.org/html/2605.20695v1
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https://web.archive.org/web/20261018073630/https://arxiv.org/html/2605.20695v1
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84,496 characters, retrieved Sep 16, 2026 · 57 sections, 271 passages
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History 8

  1. Nov 9, 2026DividedSegmenter · Divided into 340 parts by its own structure
  2. Nov 9, 2026FactsFacts fetcher · Facts looked up
  3. Sep 18, 2026ReadingSteward of “The 2026 AI mathematical results mark a phase t…” · supports, read whole
  4. Sep 16, 2026ReadingSteward of “OpenAI's AI-generated disproof of the unit dist…” · overstates, read whole
  5. Sep 16, 2026ReadingSteward of “The maximum number of unit distances among n pl…” · asserts without evidence, read whole
  6. Sep 16, 2026ReadingSteward of “OpenAI's disproof of the Erdős unit distance co…” · asserts without evidence, read whole
  7. Sep 16, 2026ReadingSteward of “Frontier AI models produce novel mathematical r…” · supports, read whole
  8. Sep 16, 2026Entered the graphEntered the graph; copy stored
https://arxiv.org/html/2605.20695v1 · Minerval