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Benefit Ledger · verified · Mathematics

GPT-5 supplies key steps on Erdős 848, a tree-count inequality, and network identifiability

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.

20 Nov 2025Tier 2 NotableMethodology 0.1

Current score

+0.28

3 base · Notable (tier 2 of 5, 3 pts)
× 0.5000 attribution · Material acceleration
× 0.4500 evidence · External expert evaluation
× 0.6000 realization · Experimentally validated
× 0.7000 durability
Event-level product before credit split: 0.28

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).

What happened

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.

Model attribution

+0.28

GPT

Supplied the density estimate for Erdős 848, generated the tree-count proofs, and proposed the leaf-fraction observable for the network model.

OpenAI’s science-acceleration paper names GPT-5 in each of these three math case studies; humans authored and checked the final proofs.

Attribution 0.5000 · Credit share 100% · OpenAI

Claims

  • GPT-5 contributed a key density estimate that Sawhney and Sellke refined into a proof of Erdős problem 848.

    outcome · supported

  • GPT-5 generated a short proof of a conjectured small-subgraph inequality in trees that the authors checked and adopted.

    outcome · supported

  • The clique-avoiding-code lower bound in the same paper is a new mathematical discovery.

    significance · disputed

Sources

primary sources

Secondary domains: Computer Science

Revision history

  • 13 Sep 2026 · 0.00 0.28

    Imported events under methodology 0.1.

GPT-5 supplies key steps on Erdős 848, a tree-count inequality, and network identifiability · NetGoodIndex