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

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