The result holds even when the algorithm faces an adversary with full access to all samples, all values, and the entire random seed. Shea first published a bound above 2⁻³⁶ on Oct. 10 before issuing the 2⁻³² update later that day. He has since released reproducible checks for the 2⁻³¹ calculation and called for independent review of the findings.
Wednesday, October 21, 2026
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Ryan Shea Raises OpenAI Problem 111 Bound Above 2⁻³¹
AI10 days ago
The lower bound for a one-sample matroid prophet guarantee has increased through three mathematical proofs published between Oct. 10 and Oct. 11. Ryan Shea’s latest derivation for OpenAI Problem #111 establishes a limit above 2⁻³¹, an increase of 15% over his previous 2⁻³² figure and a 31.45-fold improvement over his original proof. This sequence of updates surpasses the initial 2⁻²⁹³ bound derived by OpenAI, representing a total improvement of more than 2²⁵⁷-fold.
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