{"data":{"event":{"id":"a7b371e7-4f08-405a-ab5d-7388c4b0d472","slug":"openai-internal-erdos-unit-distance-disproof","title":"An unreleased OpenAI model disproves Erdős’s planar unit-distance conjecture","short_summary":"On 20 May 2026 OpenAI reported that an internal reasoning model produced an infinite family of planar point sets with n^{1+δ} unit distances for some δ>0, disproving Erdős’s n^{1+o(1)} conjecture. External mathematicians checked the argument and later made the exponent explicit.","full_description":"Erdős asked in 1946 how many times the unit distance can appear among n points in the plane. The square-grid construction gave only a slightly superlinear lower bound, and the n^{1+o(1)} upper-bound heuristic was widely believed. OpenAI says an internal model, elicited by Lijie Chen and checked by Mark Sellke and Mehtaab Sawhney, produced a number-theoretic construction using algebraic number fields that yields a polynomial improvement for infinitely many n. Noga Alon, Thomas Bloom, Timothy Gowers, and others published a human-digested writeup (arXiv:2605.20695). Will Sawin then made an explicit exponent of about n^{1.014}. This is not the Clay Navier–Stokes claim and not public GPT-6 Astra; credit stays with the May 2026 internal system. The best upper bound remains O(n^{4/3}).","ledger_type":"benefit","primary_domain_id":"23d935bb-b857-4b2b-9471-d568bb848a66","event_status":"provisional","event_date":"2026-05-20T00:00:00.000Z","discovery_date":"2026-05-20T00:00:00.000Z","first_published_date":"2026-05-20T00:00:00.000Z","last_reviewed_date":"2026-10-28T00:00:00.000Z","geographic_scope":"International","affected_population":"Discrete-geometry research community","base_impact_tier":3,"base_score":"10.00","attribution_multiplier":"0.8500","evidence_multiplier":"0.8000","realization_multiplier":"0.9000","durability_multiplier":"1.0000","current_event_score":"6.120000","confidence_level":"medium","score_explanation":"Disproving a 1946 Erdős conjecture remains Major (tier 3), not Historic. Attribution is to the internal model that found the construction (0.85). Evidence is a lab announcement plus an independent human writeup by Alon, Bloom, Gowers and others, then Sawin’s explicit exponent (0.80). Realization is a public, externally developed proof (0.90). A correct theorem is permanent (1.00).","methodology_version_id":"8745541b-0f8e-4d5a-9b47-5291d3813a8d","original_methodology_version_id":"d7881163-fb23-4e71-8625-bac1a8662c0f","published_at":"2026-05-20T00:00:00.000Z","created_at":"2026-09-13T22:56:05.431Z","updated_at":"2026-10-28T20:22:47.621Z","flags":[],"domain_name":"Mathematics","domain_slug":"mathematics","methodology_version":"0.2"},"contributions":[{"id":"f9fda8c2-a23c-49fc-bd70-ca50c2c2e4a8","event_id":"a7b371e7-4f08-405a-ab5d-7388c4b0d472","model_id":"4b365db9-1a7e-40f2-bb33-a7f677389945","role_description":"Unreleased reasoning model OpenAI says produced the unit-distance construction in one shot; humans verified and later simplified it.","attribution_multiplier":"0.8500","credit_share":"1.0000","contribution_score":"6.120000","attribution_rationale":"OpenAI and the Alon–Bloom–Gowers et al. remarks attribute the original construction to an internal OpenAI model, not to GPT-6 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