{"data":{"event":{"id":"cc9fd926-5101-48e3-bbac-c16d14d423a7","slug":"gpt5-sawhney-sellke-math-collaborations","title":"GPT-5 supplies key steps on Erdős 848, a tree-count inequality, and network identifiability","short_summary":"In a 20 November 2025 OpenAI science-acceleration paper, GPT-5 helped Mehtaab Sawhney and Mark Sellke finish Erdős problem 848, produced a short proof of a conjectured small-subgraph inequality in trees that Bubeck, Sellke, and Yin checked, and pointed to leaf fraction as the statistic that identifies a hidden network parameter.","full_description":"These are three documented math outcomes from the same GPT-5 collaboration paper, bundled because they share a date, model, and source. For Erdős 848, GPT-5 proposed a density estimate / odd-number constraint that Sawhney and Sellke refined into a complete proof; humans remained the authors. For tree subgraph counts, GPT-5 produced short self-contained proofs of a known inequality and a conjectured one, which the authors adopted after checking. For a growing-network model, GPT-5 identified the limiting leaf fraction as the observable that makes a hidden attachment parameter identifiable; the authors completed the proof. A fourth case in the same paper, clique-avoiding codes, is excluded: OpenAI later found the bound already in the literature. This is human-led collaboration, not autonomous discovery, and not GPT-5.6 Sol.\n\nUpdate (2026-09-17): Auditing Language Models for Hidden Objectives Marks,* Treutlein,* et al., 2025 We deliberately train a language model with a hidden objective and use it as a testbed for studying alignment audits.. Auditing Language Models for Hidden Objectives Marks,* Treutlein,* et al., 2025 We deliberately train a language model with a hidden objective and use it as a testbed for studying alignment audits.","ledger_type":"benefit","primary_domain_id":"23d935bb-b857-4b2b-9471-d568bb848a66","event_status":"verified","event_date":"2025-11-20T00:00:00.000Z","discovery_date":"2025-11-20T00:00:00.000Z","first_published_date":"2025-11-20T00:00:00.000Z","last_reviewed_date":"2026-09-17T00:00:00.000Z","geographic_scope":"International","affected_population":"Combinatorics and probability research communities","base_impact_tier":2,"base_score":"3.00","attribution_multiplier":"0.5000","evidence_multiplier":"0.5000","realization_multiplier":"0.6000","durability_multiplier":"0.7000","current_event_score":"0.315000","confidence_level":"high","score_explanation":"Three publishable collaborative theorems are notable (tier 2). Humans completed and checked the proofs (AI attribution 0.50). Evidence is a curated lab case-study paper (0.45). Realization is completed mathematics adopted by named authors (0.60). 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