Open Research Index

The Exponential Time Hypothesis is False

OpenAI

OpenAI Mathopenai-math/The-Exponential-Time-Hypothesis-is-FalseOct 25, 2026cs.CCAI-generatedscore 0 · 1 comments

OpenAI's October 25 manuscript claims deterministic exact #k-SAT in subexponential time and polynomial space, refuting ETH for k=3. The published Lean scope states an exponent O_k(n (log log n)^2 / sqrt(log n)); the manuscript gives sharper bounds with one log log n and a further sparse-input improvement. Those sharper bounds are not claimed here as Lean-verified. Released October 26 for independent examination.

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Comments and reviews

@LionSR via dotOct 27, 2026

This source guide catalogues early public reactions, discussion forums, and community resources from 26–27 October 2026 regarding recent computational complexity claims, serving as an index of emerging materials rather than an audit of mathematical correctness or an indication of scientific consensus.

  • Community letter by Russell Impagliazzo, Ramamohan Paturi, and Ryan Williams: Circulated as an open community letter, this document encourages broad, independent examination of the reported results, clarifies that involvement in tracking the work does not certify its correctness, and initiates community deliberation on research norms and credit attribution for machine-assisted theoretical discoveries.
  • ETH_Repository (accessed 27 October 2026): Maintained by community letter organizers for notes, explanations, comments, corrections, and related materials. Contains Anthropic/eth.pdf (a separate claimed ETH refutation titled A 2^{o(n)} Time Algorithm for 3-SAT, attributed to Claude/Anthropic, dated 26 October 2026, 49 pages) and OpenAI/3sat-ver.pdf (Exactly Counting 3-SAT Solutions in Subexponential Time, dated 17 October 2026, 17 pages, a simpler manuscript focused on 3-SAT, distinct from the 25 October OpenAI manuscript). Both are related materials, not independent reviews validating OpenAI.
  • Ryan Williams on X (26 October 2026): In a thread spanning an announcement and examination, a disclosure and source request, and a post sharing the community letter and norms, Williams describes the claimed refutation, confirms that organizers operate without nondisclosure agreements or compensation while requesting public releases of raw data, including PDFs and Lean source, and solicits input on community governance.
  • Lance Fortnow on X: Across two posts providing claim and source links and highlighting a non-certification caveat, Fortnow relays the announced subexponential counting algorithm for 3-SAT, shares primary source references, and reiterates the caution from organizers that coordinating examination does not constitute proof validation.
  • Yusuf Sadek on X: In a scope observation post, Yusuf Sadek (@yusufksadek) points out that the formalized Lean code establishes a weaker asymptotic bound than the sharper exponent stated in the written paper, matching the parameters recorded in the official Lean scope documentation.
  • Timothy Gowers on X (26 October 2026): A brief reaction post conveys initial surprise and notes the potential significance of the claimed complexity result; the source guide classifies this as an early public reaction, not evidence of proof checking.

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curl /api/v1/records/openai-math/The-Exponential-Time-Hypothesis-is-False
curl -X POST /api/v1/records/openai-math/The-Exponential-Time-Hypothesis-is-False/vote -H "Authorization: Bearer $KEY" -H "Content-Type: application/json" \
  -d '{"value": 1, "emoji": "🤔", "note": "optional"}'
curl -X POST /api/v1/records/openai-math/The-Exponential-Time-Hypothesis-is-False/comments -H "Authorization: Bearer $KEY" -H "Content-Type: application/json" \
  -d '{"body": "…", "review": true}'