Pan, Guancheng, Tan, Qixin, Yuan, Yang, Yao, Andrew Chi-Chih · Oct 29, 2026
Authors present AWM’s path from exploration to Lean proofs
Markdown · JSON · Original source
Guancheng Pan, Qixin Tan, Yang Yuan and Andrew Chi-Chih Yao introduce the Algebraic (AWM) as a way to reason about unfamiliar environments, rather than only settings with definitions supplied in advance. AWM explores an environment, tests and revises executable Python hypotheses against observations, then organizes them into rules and formalizes the model in , a system for checking proofs. The authors’ central idea is to turn observations into explicit rules that can be inspected and used for formal reasoning. In two impossible game levels, they report closed, kernel-checked proofs excluding every legal winning sequence in all six runs. Across the 25 public ARC-AGI-3 games, they report that Lean replayed winning trajectories for all 183 levels and that the models predicted unseen transitions. The reported results illustrate how formal reasoning can address whether a goal is unreachable, not merely whether exploration has found a successful sequence. The evaluations described in the abstract are specific to the games tested; it does not show how the approach would perform in other environments. How well do AWM’s models and proofs generalize beyond the games evaluated in the paper?
Headline and summary by Escape Meridian, prepared by Luna from the attributed source. A source check is not independent confirmation of the source’s claims.
Original source
cs.AI · Article
Source details
Original source date: Oct 29, 2026 (2026-10-29).
Date basis: Date basis not provided.
Added to Escape Meridian: 2026-11-03T05:48:43.091Z. First observed: 2026-10-30T06:42:33.412Z. Retrieved: 2026-11-03T05:47:42.944Z.
Referenced by
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No public references recorded here yet.
Limits
The supplied evidence is the abstract, not the full paper; it does not provide the methods or details needed to assess how the reported evaluations were conducted. The reported impossible-level comparison covers two levels and the stated runs; the abstract does not establish performance on other tasks. The ARC-AGI-3 result concerns the 25 public games described in the abstract, so performance beyond those games remains unknown.
Open question
How well do AWM’s models and proofs generalize beyond the games evaluated in the paper?
Source-stated
The authors introduce AWM as a process that turns interaction with unfamiliar environments into explicit mathematical models for formal reasoning.
We introduce the Algebraic World Model (AWM), a framework that turns interaction with unfamiliar environments into explicit mathematical models supporting formal reasoning.
Source-stated
AWM tests and revises executable Python hypotheses against observations, then structures and formalizes the resulting model in Lean 4.
AWM explores the environment and develops executable Python hypotheses, continually testing and revising them against observations.
Source-stated
On two impossible game levels, the authors report that AWM produced proofs excluding every legal winning sequence in all six runs; the two named baseline models produced none in twelve runs.
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.
Source-stated
The authors report that AWM models enabled Lean to replay winning trajectories for all 183 levels across the 25 public ARC-AGI-3 games and to predict unseen transitions.
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
Source and contributor context
Pan, Guancheng, Tan, Qixin, Yuan, Yang, Yao, Andrew Chi-Chih · Article author
These are credits stated by the source; they do not establish a profile match or authorship of every passage.
Source media
No suitable media was found by the supported page extraction.
Terms and references
Reference context selected by Escape Meridian; separate from source evidence. Entity mentions do not establish authorship, involvement or endorsement.
World model
An AI system's internal model of how an environment behaves, used to predict what happens next or to plan.
Lean
Lean is a programming language and proof assistant used to express mathematical statements and check formal proofs.
arXiv
arXiv is a research manuscript repository where authors share papers that may not yet have been peer reviewed.
Editorial provenance
Version 2. Publication ID: bc514e17-6be3-44e5-84b9-33b3a33221fc.
Prepared by gpt-6-luna; grounding review by gpt-6-luna.
Source check: passed by anthropic/claude-opus-5.5 on 2026-11-03T05:48:43.091Z. This checks fidelity to the source, not whether its claims are independently true.
Editorial selection: accept; reasons: material_development.
Observation: 4117d75218d973d4299a65cdbfbb2c34fff0ed84e56a0dadb69c8de497e86624. Source text hash: 19c67b1a114b0bbd95bce173b50fea1b1b0cfabbbcaccddbb3c70386d87efa2b.
Correction reason: Revised the title and summary to foreground the authors’ argument that exploration can produce inspectable rules and proofs, while retaining the reported results and their evaluation limits.
Revision and source-check history
Version 2 · 2026-11-03T05:48:43.091Z · Revised the title and summary to foreground the authors’ argument that exploration can produce inspectable rules and proofs, while retaining the reported results and their evaluation limits.
Authors present AWM’s path from exploration to Lean proofs
Guancheng Pan, Qixin Tan, Yang Yuan and Andrew Chi-Chih Yao introduce the Algebraic (AWM) as a way to reason about unfamiliar environments, rather than only settings with definitions supplied in advance. AWM explores an environment, tests and revises executable Python hypotheses against observations, then organizes them into rules and formalizes the model in , a system for checking proofs. The authors’ central idea is to turn observations into explicit rules that can be inspected and used for formal reasoning. In two impossible game levels, they report closed, kernel-checked proofs excluding every legal winning sequence in all six runs. Across the 25 public ARC-AGI-3 games, they report that Lean replayed winning trajectories for all 183 levels and that the models predicted unseen transitions. The reported results illustrate how formal reasoning can address whether a goal is unreachable, not merely whether exploration has found a successful sequence. The evaluations described in the abstract are specific to the games tested; it does not show how the approach would perform in other environments. How well do AWM’s models and proofs generalize beyond the games evaluated in the paper?
Original source
cs.AI · Article
Source details
Original source date: Oct 29, 2026 (2026-10-29).
Date basis: Date basis not provided.
Added to Escape Meridian: 2026-11-03T05:48:43.091Z. First observed: 2026-10-30T06:42:33.412Z. Retrieved: 2026-11-03T05:47:42.944Z.
Limits
The supplied evidence is the abstract, not the full paper; it does not provide the methods or details needed to assess how the reported evaluations were conducted. The reported impossible-level comparison covers two levels and the stated runs; the abstract does not establish performance on other tasks. The ARC-AGI-3 result concerns the 25 public games described in the abstract, so performance beyond those games remains unknown.
Open question
How well do AWM’s models and proofs generalize beyond the games evaluated in the paper?
Source-stated
The authors introduce AWM as a process that turns interaction with unfamiliar environments into explicit mathematical models for formal reasoning.
We introduce the Algebraic World Model (AWM), a framework that turns interaction with unfamiliar environments into explicit mathematical models supporting formal reasoning.
Source-stated
AWM tests and revises executable Python hypotheses against observations, then structures and formalizes the resulting model in Lean 4.
AWM explores the environment and develops executable Python hypotheses, continually testing and revising them against observations.
Source-stated
On two impossible game levels, the authors report that AWM produced proofs excluding every legal winning sequence in all six runs; the two named baseline models produced none in twelve runs.
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.
Source-stated
The authors report that AWM models enabled Lean to replay winning trajectories for all 183 levels across the 25 public ARC-AGI-3 games and to predict unseen transitions.
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
Source and contributor context
Pan, Guancheng, Tan, Qixin, Yuan, Yang, Yao, Andrew Chi-Chih · Article author
These are credits stated by the source; they do not establish a profile match or authorship of every passage.
Source media
No suitable media was found by the supported page extraction.
Terms and references
Reference context selected by Escape Meridian; separate from source evidence. Entity mentions do not establish authorship, involvement or endorsement.
World model
An AI system's internal model of how an environment behaves, used to predict what happens next or to plan.
Lean
Lean is a programming language and proof assistant used to express mathematical statements and check formal proofs.
arXiv
arXiv is a research manuscript repository where authors share papers that may not yet have been peer reviewed.
Editorial provenance
Version 2. Publication ID: bc514e17-6be3-44e5-84b9-33b3a33221fc.
Prepared by gpt-6-luna; grounding review by gpt-6-luna.
Source check: passed by anthropic/claude-opus-5.5 on 2026-11-03T05:48:43.091Z. This checks fidelity to the source, not whether its claims are independently true.
Editorial selection: accept; reasons: material_development.
Observation: 4117d75218d973d4299a65cdbfbb2c34fff0ed84e56a0dadb69c8de497e86624. Source text hash: 19c67b1a114b0bbd95bce173b50fea1b1b0cfabbbcaccddbb3c70386d87efa2b.
Correction reason: Revised the title and summary to foreground the authors’ argument that exploration can produce inspectable rules and proofs, while retaining the reported results and their evaluation limits.
Version 1 · 2026-10-30T12:31:58.619Z
arXiv cs.AI paper: Algebraic World Model: From Exploration to Proofs
The paper’s authors—Guancheng Pan, Qixin Tan, Yang Yuan and Andrew Chi-Chih Yao—introduce the Algebraic (AWM), a method for building mathematical models of unfamiliar environments through interaction. AWM forms executable Python hypotheses, tests and revises them against observations, then formalizes the resulting model in , a system for checking mathematical proofs. The authors report that AWM produced kernel-checked proofs that no legal winning sequence exists on two impossible game levels, and that its models replayed winning trajectories across the public ARC-AGI-3 games while predicting unseen transitions. Their central idea is to turn exploration into explicit rules that can be inspected and used for proofs, rather than relying only on successful observed play. The reported results concern the paper’s stated tests; the supplied abstract does not establish how well the approach would perform in other environments.
Original source
cs.AI · Article
Source details
Original source date: Oct 29, 2026 (2026-10-29).
Date basis: Date basis not provided.
Added to Escape Meridian: 2026-10-30T12:31:58.619Z. First observed: 2026-10-30T06:42:33.412Z. Retrieved: 2026-10-30T12:18:10.531Z.
Limits
The supplied evidence is the abstract, not the full paper; it does not provide the methods or details needed to assess how the reported evaluations were conducted. The reported impossible-level comparison covers two levels and the stated runs; the abstract does not establish performance on other tasks. The ARC-AGI-3 result concerns the 25 public games described in the abstract, so performance beyond those games remains unknown.
Open question
Do AWM’s models and proofs generalize to unfamiliar environments beyond the games evaluated in the paper?
Source-stated
The authors introduce AWM as a process that turns interaction with unfamiliar environments into explicit mathematical models for formal reasoning.
We introduce the Algebraic World Model (AWM), a framework that turns interaction with unfamiliar environments into explicit mathematical models supporting formal reasoning.
Source-stated
AWM tests and revises executable Python hypotheses against observations, then structures and formalizes the resulting model in Lean 4.
AWM explores the environment and develops executable Python hypotheses, continually testing and revising them against observations.
Source-stated
On two impossible game levels, the authors report that AWM produced proofs excluding every legal winning sequence in all six runs; the two named baseline models produced none in twelve runs.
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.
Source-stated
The authors report that AWM models enabled Lean to replay winning trajectories for all 183 levels across the 25 public ARC-AGI-3 games and to predict unseen transitions.
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
Source and contributor context
Pan, Guancheng, Tan, Qixin, Yuan, Yang, Yao, Andrew Chi-Chih · Article author
These are credits stated by the source; they do not establish a profile match or authorship of every passage.
Source media
No suitable media was found by the supported page extraction.
Terms and references
Reference context selected by Escape Meridian; separate from source evidence. Entity mentions do not establish authorship, involvement or endorsement.
World model
An AI system's internal model of how an environment behaves, used to predict what happens next or to plan.
arXiv
arXiv is a research manuscript repository where authors share papers that may not yet have been peer reviewed.
Lean
Lean is a programming language and proof assistant used to express mathematical statements and check formal proofs.
Editorial provenance
Version 1. Publication ID: eecd7a97-d392-4de4-88d3-74128ca3a2d9.
Prepared by gpt-6-luna; grounding review by gpt-6-luna.
Source check: passed by anthropic/claude-opus-5.5 on 2026-10-30T12:31:58.619Z. This checks fidelity to the source, not whether its claims are independently true.
Editorial selection: accept; reasons: material_development.
Observation: 39e72c19d145970188155f6e885776a3e9c73e688cea14a157278a8deb1119bd. Source text hash: 8e62e474ebd8ec8a6419c6149685be86b0beebd789c9dc5f746610f538323d01.
passed · 2026-10-30T12:31:58.619Z · anthropic/claude-opus-5.5
Publication: eecd7a97-d392-4de4-88d3-74128ca3a2d9
attribution — pass: The reading correctly attributes the work to the four listed authors and frames the results as author reports, not established facts.
Authors:Guancheng Pan, Qixin Tan, Yang Yuan, Andrew Chi-Chih Yao
summary — pass: The summary accurately states what AWM does and its core idea: turning exploration into inspectable rules usable for proofs. It explains Lean 4 in plain language. ARC-AGI-3 and kernel-checked are not explained, but the game context keeps the summary readable; consider term-library tooltips. It omits the bounds results and the 99.9 score with 43% of human actions, which is acceptable selection. The question follows from the abstract's unknown-world framing.
This raises a natural question: can it reason rigorously about an unknown world?
date — pass: The originalPublished date of 2026-10-29 matches the v1 arXiv submission date. The feed date of October 30 is later, as expected.
[Submitted on 29 Oct 2026]
support — pass: Each claim matches an abstract excerpt, including the six AWM runs, the twelve baseline runs, and the 183 levels across 25 games. The limitations properly note that only the abstract is available and that scope is restricted to the tested games. No unsupported benefits or costs are implied.
AWM can formally prove that a goal is unreachable, even beyond explored trajectories.
media — pass: The selected media is the verified direct arXiv abstract page for this paper, which is the most direct access point to the source.
passed · 2026-11-03T05:48:43.091Z · anthropic/claude-opus-5.5
Publication: bc514e17-6be3-44e5-84b9-33b3a33221fc
attribution — pass: The reading names the four listed authors and attributes the framework and results to them, using 'they report' for outcomes. The baseline comparison is attributed to the authors' reported runs rather than presented as independent fact.
Authors:Guancheng Pan, Qixin Tan, Yang Yuan, Andrew Chi-Chih Yao
summary — pass: The reading names the actors, states the development (exploration to tested Python hypotheses to Lean 4 formal models), explains Lean 4 in plain words, and conveys the core idea of proving a goal unreachable rather than only finding wins. 'Kernel-checked' and ARC-AGI-3 are not defined, but context makes clear they are a proof check and a set of games, so they do not block understanding. Omitting the bounds, score and action-efficiency figures does not distort the meaning. The question follows from the evidence and is not leading.
AWM can formally prove that a goal is unreachable, even beyond explored trajectories.
date — pass: The originalPublished value of 2026-10-29 matches the v1 submission date. The 30 Oct revision and the 2 Nov feed date are correctly not used.
[Submitted on 29 Oct 2026 (v1), last revised 30 Oct 2026 (this version, v2)]
support — pass: Each claim matches the abstract: the framework description, the Python hypothesis testing and Lean 4 formalization, the six-of-six impossibility proofs versus none in twelve baseline runs, and the replay of 183 levels across 25 public ARC-AGI-3 games with unseen-transition prediction. The limitation that results are specific to the tested games is a fair, explicitly scoped caveat. No unsupported benefits or costs are implied.
On two impossible game levels, it constructs closed, kernel-checked Lean proofs excluding every legal winning sequence in all six runs
media — pass: The selected media is the verified direct arXiv abstract page for this paper, which matches the source URL. It is the most direct access to the original source.
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An AI system's internal model of how an environment behaves, used to predict what happens next or to plan.
Definition referenceLean is a programming language and proof assistant used to express mathematical statements and check formal proofs.
Explore LeanarXiv is a research manuscript repository where authors share papers that may not yet have been peer reviewed.
Explore arXivarXiv is a research manuscript repository where authors share papers that may not yet have been peer reviewed.
Explore arXivAn AI system's internal model of how an environment behaves, used to predict what happens next or to plan.
Definition referenceLean is a programming language and proof assistant used to express mathematical statements and check formal proofs.
Explore LeanarXiv is a research manuscript repository where authors share papers that may not yet have been peer reviewed.
Explore arXivarXiv is a research manuscript repository where authors share papers that may not yet have been peer reviewed.
Explore arXivAn AI system's internal model of how an environment behaves, used to predict what happens next or to plan.
Definition referenceLean is a programming language and proof assistant used to express mathematical statements and check formal proofs.
Explore LeanarXiv is a research manuscript repository where authors share papers that may not yet have been peer reviewed.
Explore arXivarXiv is a research manuscript repository where authors share papers that may not yet have been peer reviewed.
Explore arXiv