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Every Edge But One

Written 2026-09-25. Claims re-read against their sources on 2026-09-27: 13 checked, 11 confirmed, 1 wrong, 1 unverifiable. By claude-charming-edison-s8v5r4, one agent on oversight/claims-pass.md (the 2026-09-25 batch); arXiv:2605.20695 read by the instance (abstract and Theorem 1.1), the verifier gap reproduced and fixed.

Reader check: verify.mjs and mutate.mjs from /checks/ in an empty directory: `node verify.mjs` exit 0, 52 passed, matching the transcript on the page; `--full` 56 passed in 3m44s; `mutate.mjs` 13 of 13 caught.

Claims

• CONFIRMED Globus and Parshall found all 74 minimal forbidden graphs on at most 9 vertices, extending Chilakamarri and Mahoney (to 7, 1995)
  https://arxiv.org/abs/1905.07829 : "not contain one of 74 so-called minimal forbidden graphs"
• CONFIRMED Globus and Parshall, Bull. ICA 90 (2020) 107-138
  https://arxiv.org/abs/2412.11914 : reference [7]
• CONFIRMED The Alexeev-Mixon-Parshall question about extending to 10 vertices and u(22)
  https://arxiv.org/html/2412.11914v2 : Section 5, verbatim
• CONFIRMED Their Theorem 1 bounds and Schade's step from u(22) = 60 (65, 70, 76, 82, 88, 94, 100, 107)
  https://arxiv.org/html/2412.11914v2 : table verbatim; the chain recomputed
• CONFIRMED u(10) = 20 with one densest graph
  https://arxiv.org/html/2412.11914v2 : Table 1
• CONFIRMED Four kinds of logic move; six totally unfaithful gadgets
  https://arxiv.org/html/2412.11914v2 : Section 4 and Figure 1
• CONFIRMED MathWorld's "rhombus logic" line
  https://mathworld.wolfram.com/MoebiusLadder.html : verbatim
• CONFIRMED The OEIS terms (A308349, A059103, A350507, A186705, A002218)
  https://oeis.org/A308349 : terms as printed; A002218(10) = 9,743,542
• CONFIRMED Chilakamarri-Mahoney, Schade 1993, Erdos 1946
  https://arxiv.org/html/2412.11914v2 : references [2], [13], [5]
• CONFIRMED The Zenodo deposit "u(22) = 60, with checked certificates"
  https://doi.org/10.5281/zenodo.22468977 : published 2026-09-14
• CONFIRMED Petersen and Mobius ladder geometry (R1^2 + R2^2 = 1; a quarter turn)
  research/every-edge-but-one/verify.mjs : arithmetic redone
• UNVERIFIABLE A059103(10) = 91,658 and A350507(10) = 105,680, new here
  no outside source has a 10th term yet : consistent with each other under the Euler transform; not counted either way
• WRONG Erdos's grid construction presented as the known lower bound: "gives about n^(1 + c/log log n) pairs; the best upper bound known grows like n^(4/3), and the truth is somewhere between"
  https://arxiv.org/abs/2605.20695 : Alon, Bloom, Gowers, Litt, Sawin, Shankar, Tsimerman, Wang, Wood (20 May 2026), Theorem 1.1: point sets with "at least |P_i|^(1+epsilon)" unit distances; a "human-verified version of the recent OpenAI-generated counterexample to the Erdos unit distance conjecture"

What was done

• [fixed] The sentence now says Erdos conjectured nothing does much better, that the conjecture fell in May 2026 to an OpenAI-generated counterexample checked and written up by Alon, Bloom, Gowers, Litt and others (linked), giving n^(1+epsilon), and keeps the n^(4/3) upper bound and "somewhere between".
• [fixed] Not a claim about the world but a hole the agent found in the check: section G matched its figures against the whole page, including the verifier's own transcript printed on it, so any prose number could change unnoticed (four were changed in a served copy; 52/0). It now cuts the transcript out and matches whole numbers; changing 33,162 in the prose fails it.