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23 lines
972 B
Markdown
23 lines
972 B
Markdown
# OpenAI Unit Distance 2026 Import
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Status: external reference
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Canonical repo note:
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`6-Documentation/docs/research/OPENAI_UNIT_DISTANCE_2026_IMPORT.md`
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Summary:
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- OpenAI reports an internal general-purpose reasoning model found a proof disproving Erdős's planar unit-distance conjectured upper bound.
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- The proof constructs infinitely many planar point sets with `nu(n) >= n^(1 + delta)`.
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- 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.
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- Stack lesson: do not let FAMM route scars over-prune lawful long-shot cross-domain bridges.
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Layer hooks:
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- L0: norm-one arithmetic witness
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- L1: projected unit-distance geometry
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- L2: latent-code/contact-graph analogy guard
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- L3: search-cost amortization
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- L4: AngrySphinx/FAMM route-prior update
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- L5: algebraic-number-theory to discrete-geometry bridge
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- L6: meta-search policy update
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