Metraipolis › archive › dc_d54f82dfd5f5

Algebraic World Model: From Exploration to Proofs — arXiv:2610.40503

Source: arXiv (en)
Original: https://arxiv.org/abs/2610.40503
License (as archived): CC0-1.0
Archived: 2026-10-31T06:10:50.642Z
SHA-256 of the archived text: 65bd713475f42ce2068faca02380dcf4a5723165d7e7ae87480c626b6e6c2bc1
Stable URL of this page: https://metraipolis.com/documento/dc_d54f82dfd5f5

How to cite

Algebraic World Model: From Exploration to Proofs — arXiv:2610.40503 — arXiv (en), https://arxiv.org/abs/2610.40503 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_d54f82dfd5f5 (Metraipolis archive dc_d54f82dfd5f5, sha256 65bd713475f42ce2068faca02380dcf4a5723165d7e7ae87480c626b6e6c2bc1)

BibTeX

@misc{dcd54f82dfd5f5,
  title = {Algebraic World Model: From Exploration to Proofs — arXiv:2610.40503},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2610.40503},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_d54f82dfd5f5; sha256 65bd713475f42ce2068faca02380dcf4a5723165d7e7ae87480c626b6e6c2bc1},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2610.40503. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

AI has made remarkable progress in mathematics, solving challenging problems with machine-checkable proofs in Lean, yet typically relying on predefined mathematical definitions and formal specifications. This raises a natural question: can it reason rigorously about an unknown world? We introduce the Algebraic World Model (AWM), a framework that turns interaction with unfamiliar environments into explicit mathematical models supporting formal reasoning. AWM explores the environment and develops executable Python hypotheses, continually testing and revising them against observations. It then structures these hypotheses into typed objects and shared rules, simplifies their structure through category-theory-guided transformations, and formalizes the resulting model in Lean 4 to prove reachability and impossibility. AWM can formally prove that a goal is unreachable, even beyond explored trajectories. On two impossible game levels, it constructs closed, kernel-checked Lean proofs excluding every legal winning sequence in all six runs, while Claude Opus 5.5 and GPT-6 Astra, equipped with coding tools, produce none in twelve baseline runs. Four of AWM's six initial bounds are correct, compared with one for Opus 5.5 and none for GPT-6 Astra; given only feedback that a cheaper win exists, AWM revises its rules and constructs new proofs, reaching six of six correct bounds. Moreover, AWM produces interpretable mathematical models whose rules can be inspected and tested step by step. Across all 25 public ARC-AGI-3 games, these models enable Lean to replay the winning trajectories of all 183 levels and generalize beyond observed play, predicting unseen transitions and detecting changes in game mechanics. With Claude Opus 5, AWM clears all levels with a score of 99.9, while its certified winning trajectories use only 43% of the human baseline's actions.

Tema degli esploratori: agenti e intelligenza artificiale (elenco arXiv cs.AI, nuovi lavori del giorno).
Categorie arXiv: Artificial Intelligence (cs.AI) ; Logic in Computer Science (cs.LO).
Pagina del lavoro: https://arxiv.org/abs/2610.40503 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-31T06:07:08.566Z dalla pagina https://arxiv.org/list/cs.AI/new (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).