{"schema_version":"onlylabs.public_signal.v1","title":"OpenAI Writing: An OpenAI model has disproved a central conjecture in discrete geometry","description":"OpenAI writing signal with public source context, captured evidence pages, related signals, and data-business radar classification.","url":"https://onlylabs.fyi/signals/29737ac4-911a-44fb-88ed-c2f5fabcfd99","json_url":"https://onlylabs.fyi/signals/29737ac4-911a-44fb-88ed-c2f5fabcfd99/signal.json","generated_at":"2026-06-08T15:45:02.504+00:00","org":{"slug":"openai","name":"OpenAI","category":"frontier-lab","category_label":"Frontier lab","dossier_url":"https://onlylabs.fyi/labs/openai","dossier_json_url":"https://onlylabs.fyi/labs/openai/dossier.json"},"related_urls":{"signal":"https://onlylabs.fyi/signals/29737ac4-911a-44fb-88ed-c2f5fabcfd99","signal_json":"https://onlylabs.fyi/signals/29737ac4-911a-44fb-88ed-c2f5fabcfd99/signal.json","source":"https://openai.com/index/model-disproves-discrete-geometry-conjecture","lab_dossier":"https://onlylabs.fyi/labs/openai","lab_dossier_json":"https://onlylabs.fyi/labs/openai/dossier.json","analysis":"https://onlylabs.fyi/analysis/openai","analysis_json":"https://onlylabs.fyi/analysis/openai/analysis.json","analysis_evidence_json":"https://onlylabs.fyi/analysis/openai/evidence.json","category":"https://onlylabs.fyi/frontier","category_json":"https://onlylabs.fyi/frontier.json","category_feed":"https://onlylabs.fyi/frontier/feed.xml","category_signals_json":"https://onlylabs.fyi/signals.json","topic":"https://onlylabs.fyi/topics/talking","topic_signals_json":"https://onlylabs.fyi/topics/talking/signals.json","topic_feed":"https://onlylabs.fyi/topics/talking/feed.xml","data_business":null},"answer_pack":{"answer":"OpenAI published An OpenAI model has disproved a central conjecture in discrete geometry. 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This is the planar unit distance problem, first posed by Paul Erdős in 1946. It is one of the best-known questions in combinatorial geometry, easy to state and remarkably difficult to resolve. The 2005 book Research Problems in Discrete Geometry, by Brass, Moser, and Pach, calls it “possibly the best known (and simplest to explain) problem in combinatorial geometry.” Noga Alon, a leading combinatorialist at Princeton, describes it as “one of Erdős’ favorite problems.” Erdős even offered a monetary prize for resolving this problem. Today, we share a breakthrough on the unit distance problem. Since Erdős’s original work, the prevailing belief has been that the “square grid” constructions depicted further below were essentially optimal for maximizing the number of unit-distance pairs. 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