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Research-Stack/6-Documentation/wiki/obsidian-vault/OpenAI Unit Distance 2026 Import.md
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OpenAI Unit Distance 2026 Import

Status: external reference

Canonical repo note: 6-Documentation/docs/research/OPENAI_UNIT_DISTANCE_2026_IMPORT.md

Summary:

  • OpenAI reports an internal general-purpose reasoning model found a proof disproving Erdős's planar unit-distance conjectured upper bound.
  • The proof constructs infinitely many planar point sets with nu(n) >= n^(1 + delta).
  • The method uses algebraic number theory: class field towers, splitting primes, norm-one elements, Minkowski embeddings, lattice cuts, and injective projection to one complex coordinate.
  • Stack lesson: do not let FAMM route scars over-prune lawful long-shot cross-domain bridges.

Layer hooks:

  • L0: norm-one arithmetic witness
  • L1: projected unit-distance geometry
  • L2: latent-code/contact-graph analogy guard
  • L3: search-cost amortization
  • L4: AngrySphinx/FAMM route-prior update
  • L5: algebraic-number-theory to discrete-geometry bridge
  • L6: meta-search policy update