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Experts review AI labs’ unendorsed claims to refute ETH

2 sources · 2 articlesFirst reported Updated ()1
What's new

First merged summary.

Merged summary · x-ai/grok-4.7 · rewritten as coverage arrivesSummaries by Vani AI

Outside computer scientists are reviewing OpenAI’s and Anthropic’s unendorsed claims that models refuted the Exponential Time Hypothesis.

OpenAI says its system refuted the Exponential Time Hypothesis and proved Christopher Sogge’s 1991 local-smoothing conjecture in every dimension, implying the Kakeya and Stein restriction conjectures. It translated math and computer-science proofs into Lean and asked outside experts to review them. Ryan Williams, Russell Impagliazzo, and Ramamohan Paturi are checking the ETH claim without pay or NDAs and say their role is not an endorsement. TechCrunch reports Anthropic later issued its own claimed refutation, while Williams says unusual proof parts need review, ETH-based papers would be revisited if it holds, and OpenAI is reasonably confident cryptography is safe. OpenAI is publishing the proofs and will fund a conference.

Key facts
  • Lean checks that a proof matches its formal statement, not the intended problem.
  • Local smoothing had previously been proved only in two dimensions, in 2019.
  • ETH was first published in 1999 by Impagliazzo and Paturi.
  • Williams said SAT-solving gains within 12 months are possible, or there may be none.
  • OpenAI published the math on GitHub and committed to fund a conference.
  • The ETH reviewers plan interim findings and say review is not an endorsement.
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Timeline

dated events in the reporting · oldest first
  1. Oct 27, 2026OpenAI releases claimed ETH and math proofs for review · The Decoder
  2. Oct 27, 2026Anthropic releases its own claimed ETH refutation · TechCrunch

What each outlet adds

beyond the shared facts
  • The DecoderLocal-smoothing claim, Lean limits, unpaid reviewers, and a Nobel laureate shepherd.
  • TechCrunchAnthropic’s separate claim, crypto confidence, and ETH’s 1999 origin.
Vendors
OpenAI
Organizations
MITUC San DiegoOpenAIAnthropic

Coverage

oldest first · one row per article · UTC
  1. · 4d ago The DecoderFirst report

    OpenAI asks experts to check AI proofs in math, CS, and physics

    OpenAI says models disproved the Exponential Time Hypothesis and proved local smoothing in every dimension; reviewers have not endorsed the claims.

  2. · 3d ago TechCrunch · AI

    OpenAI and Anthropic claim models refuted the Exponential Time Hypothesis

    Computer scientists are reviewing claimed sub-exponential algorithms, including whether they weaken assumptions behind some cryptography.