Three-machine unit-job scheduling with precedence constraints (Garey-Johnson OPEN8): is P3|prec,p_j=1|Cmax in P?

Theorem 1.1: a uniform deterministic algorithm constructs a minimum-makespan schedule for unit-length jobs with arbitrary precedence constraints on three identical machines, and decides feasibility for a deadline $1\le T\le n$ exactly, in $O((L+2)^{150020})$ Turing machine steps. The method decomposes schedules into gaps whose job sets have bounded-size global Boolean descriptions and searches them by dynamic programming. The exponent is astronomically large and no practical claim is made. It does not settle $m\ge4$ fixed machines, which remains open.

Exact FrontierDelta

Prior state unknown→proved

Scope and record

Occurred: Sep 24, 2026

Delta type: SOURCE CLAIM

Assumptions: VibeMathed verification: lean-checked. 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: Three-machine unit-job scheduling with precedence constraints (Garey-Johnson OPEN8): is P3|prec,p_j=1|Cmax in P? · P3|prec,pj=1|Cmax

Confidence: Not scored

Registry verification: lean checked · announcement · candidate

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VibeMathed
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Unreleased internal OpenAI model
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VibeMathed record: Three-machine unit-job scheduling with precedence constraints (Garey-Johnson OPEN8): is P3|prec,p_j=1|Cmax in P?

specialist registry · passed

No independent mathematician has checked this yet. Checked here: Theorem 1.1 of the manuscript was read against the problem as stated there (explicit DAG, unit jobs, three identical machines, no release dates); it claims a deterministic algorithm producing a minimum-makespan schedule and deciding feasibility for a given deadline in $O((L+2)^{150020})$ multitape Turing machine steps. The proof was not refereed. The challenge is not in the formalization catalogue (lean/formalization.yaml); it is found through lean/docs/124.md, and its solution module OAI.Computability.Scheduling.Main exists at the pinned commit. The statement ComparatorChallenges/ThreeMachine.lean was read here: it encodes instances and answers as bit strings and asserts one fixed multitape machine and constant $C$ such that, for every nonempty acyclic instance and every deadline option with $1\le T\le n$ , the machine halts within $C(L+2)^{150020}$ steps with a correct output (an optimal schedule, or a feasible schedule or a correct 'infeasible'). This states the headline claim, polynomiality included. Not rebuilt here.