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OpenAI posts math and computing claims; physics proof held back

2 sources · 2 articlesFirst reported Updated ()3
What's new

First merged summary.

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

OpenAI released math and computer-science claims for public review while a physics group withholds its AI artifacts.

OpenAI said internal models produced a claimed proof of Sogge’s local smoothing conjecture in every dimension, which would also resolve the Kakeya and Stein restriction conjectures, plus a claim that the Exponential Time Hypothesis is false and a four-dimensional quantum-field-theory existence result covering QCD. Math and computer-science write-ups and Lean formalizations are public on GitHub; the physics group is withholding the AI outputs while writing its own account. External experts are shepherding release without nondisclosure agreements or pay. OpenAI News says shepherds set three release paths; The Verge says outside shepherds cover the computing and physics claims, with the math materials posted unverified. Named reviewers include Russell Impagliazzo, Ramamohan Paturi, and Ryan Williams on computing, and David Gross on physics. OpenAI says it will not seek academic credit; AGMAI advisers recommended against early selective access.

Key facts
  • Local-smoothing model output dated October 18, 2026; Lean formalization the next day.
  • The math argument relies on a novel auxiliary partial differential equation.
  • The ETH claim covers exact counting for fixed-width CNF, including 3-SAT.
  • The physics result is called mathematically rigorous but is not fully public.
  • Participants are unpaid, unbound by NDAs, and do not speak for OpenAI.
  • AGMAI cited unequal access, borrowed reputation, and biased selection.
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Timeline

dated events in the reporting · oldest first
  1. Oct 18, 2026Local-smoothing model output obtained. · OpenAI News
  2. Oct 19, 2026Local-smoothing result formalized in Lean. · OpenAI News
  3. Oct 26, 2026OpenAI announced the three scientific claims and release plans. · OpenAI News

What each outlet adds

beyond the shared facts
  • OpenAI NewsDates the smoothing output and says OpenAI seeks no academic credit.
  • The VergeNames reviewers, QCD scope, 3-SAT detail, and AGMAI objections.
Organizations
OpenAI

Coverage

oldest first · one row per article · UTC
  1. · 5d ago OpenAI NewsFirst report

    OpenAI shares AI math, complexity and physics results with academics

    Shepherds chose three release paths; Lean writeups for the math and ETH results are already public.

  2. · 4d ago The Verge · AI

    OpenAI posts claimed math, computing, and physics breakthroughs

    Outside groups will examine an ETH refutation and a QCD proof, while the math write-up is released unverified.