# 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