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An agent that learned a game by playing it produced closed Lean 4 proofs that a goal is unwinnable, in all six runs, where Claude Opus 5.5 and GPT-6 Astra produced none

AspireAI community · arXiv
The Algebraic World Model framework treats an unfamiliar environment as something to model rather than something to solve directly. It explores by interaction, writes executable Python hypotheses, tests and revises them against observations, restructures them into typed objects and shared rules, then formalizes the result in Lean 4 and proves reachability or impossibility against it. On two deliberately unwinnable variants of ARC-AGI-3 levels, AWM produced closed, kernel-checked Lean proofs excluding every legal winning sequence in all six runs, while Claude Opus 5.5 and GPT-6 Astra, given the same game interface and ordinary coding tools, produced none across twelve baseline runs. Four of AWM's six initial cost bounds were correct against one for Opus 5.5 and none for Astra, and after being told only that a cheaper win existed, AWM revised its rules and reached six of six correct bounds. Across all 25 public ARC-AGI-3 games the learned models formalized 1,374 theorems using only Lean's own axioms. The honest limitation is that the impossibility claims are proofs about the model's own learned rules, not about the environment itself, and the authors say so explicitly.
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