lean artifact · pending
Artifact ↗Source authenticated
Quasipolynomial-time solution of mean-payoff games with binary weights
Claims a deterministic algorithm computing the exact set of vertices from which Max can force nonnegative liminf mean payoff, for arbitrary signed binary weights, self-loops and parallel edges, in bit operations; a reduction gives exact rational values and optimal positional strategies for both players, energy-game minimum credits, and tropical feasibility tests within the same bound. A randomized companion of the same date gives a Las Vegas algorithm with a polynomial-time certificate check. It does NOT give a polynomial-time algorithm, which the paper names as a further improvement. Conflicting claim: Truffet (arXiv:2603.26423, and a 2025 HAL note) claims a strongly polynomial algorithm via tropical optimization; the randomized companion gives a small example on which the printed rule of version 4 loses the optimum, and makes no claim about the 2025 note.
Exact FrontierDelta
Prior state unknown→proved
Scope and record
Occurred: Sep 25, 2026
Delta type: SOURCE CLAIM
Assumptions: VibeMathed verification: unreviewed. Publication: announcement. AI contribution: ai-discovered. VibeMathed editorial classifications, scores, notes, relations, and dataset structure are CC BY 4.0. Source statements and linked content retain their own rights.
Canonical aliases: Quasipolynomial-time solution of mean-payoff games with binary weights · Mean-payoff games in quasipolynomial time
Confidence: Not scored
Registry verification: unreviewed · announcement · partial
Attribution
VibeMathed
registry · event recorded by
Unreleased internal OpenAI model
model · ai model contributor · OpenAI
Artifacts and verifiers
lean artifact · pending
Artifact ↗Compute record
No linked compute attempts recorded.
Lineage and corrections
Lean: randomized quasipolynomial mean-payoff algorithm (companion result) evidence for this event
Quasipolynomial-time solution of mean-payoff games with binary weights parent of this event
This event attributed to Unreleased internal OpenAI model
Quasipolynomial-time solution of simple stochastic and turn-based stochastic mean-payoff games evidence for this event
Claims a deterministic algorithm computing the exact set of vertices from which Max can force nonnegative liminf mean payoff, for arbitrary signed binary weights, self-loops and parallel edges, in bit operations; a reduction gives exact rational values and optimal positional strategies for both players, energy-game minimum credits, and tropical feasibility tests within the same bound. A randomized companion of the same date gives a Las Vegas algorithm with a polynomial-time certificate check. It does NOT give a polynomial-time algorithm, which the paper names as a further improvement. Conflicting claim: Truffet (arXiv:2603.26423, and a 2025 HAL note) claims a strongly polynomial algorithm via tropical optimization; the randomized companion gives a small example on which the printed rule of version 4 loses the optimum, and makes no claim about the 2025 note. parent of this event
Lean comparator statement: RandomizedMeanPayoff evidence for this event
Truffet, Max-Atom problem in strongly polynomial time (HAL note, 2025; not addressed by the release) evidence for this event
Companion: Mean-payoff parity games in quasipolynomial time evidence for this event
Companion: Randomized quasipolynomial-time mean-payoff games evidence for this event
VibeMathed record: Quasipolynomial-time solution of mean-payoff games with binary weights evidence for this event
Companion: Deterministic quasipolynomial-time mean-payoff games evidence for this event
Truffet, claimed strongly polynomial tropical LP method (arXiv:2603.26423 v4), rebutted by the randomized companion evidence for this event
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