Identifiability Without Gaussianity: Symbolic World Models and Near-Infinite Temporal Consistency

arXiv 2026 58.5 method, theory

TLDR

Proves symbolic world models achieve exact identifiability and near-infinite temporal consistency, overcoming Gaussian limitations of statistical world models.

Reasoning

The paper presents strong theoretical results with formal proofs in Lean 4, addressing a fundamental limitation of statistical world models. However, it lacks real-world experiments or empirical validation, and the abstract does not discuss practical applications or benchmarks.

Read-first score

Read-first score 58.5, weighted from topical fit, citation, graph, method, reproducibility, and recency signals. Original total remains 24.

Methodology quality 18%

100

Screens visible abstract and analysis fields for experiment, dataset, baseline, metric, and limitation evidence. markers=analysis,dataset,experiment,result,validation

Recency 6%

100

Uses a gentle age decay so recent papers surface without erasing older foundations. 2026

Citation impact 18%

95.1

Uses OpenAlex-shaped citation metadata as a bibliometric attention signal, separate from paper quality. citation_normalized_percentile=0.95104632

Reproducibility 18%

Screens links and visible text for paper, code, dataset, artifact, and repository signals. pdf=True; code=False; dataset=False; markers=artifact,dataset

Topical relevance 29%

34.3

Uses existing LLM keyword relevance scores normalized to 0-100. world model,world simulator,generative world model,interactive world model,video world model,world dynamics prediction,model-based reinforcement learning world model

Citation velocity 12%

Citation velocity estimates citations per publication-year to reduce old-paper bias. velocity=0.00

Field roles

FoundationFrontierBridgeMethodology anchor

Rank sensitivity

Stability: volatile; rank range: 495.

Keyword Scores

world model

world dynamics prediction

generative world model

model-based reinforcement learning world model

world simulator

interactive world model

video world model

Deep Analysis

Innovations

Proving that the Gaussian boundary on temporal consistency is an artifact of the statistical alignment mechanism, not a property of World Models in general.
Introducing the Physics-Grounded Symbolic Architecture (PGSA) that achieves exact linear identifiability for all physical regimes regardless of latent distribution.
Proving that PGSA maintains near-infinite temporal consistency (unbounded number of transitions with per-step error bounded by numerical precision).
Proving that statistical World Models cannot achieve near-infinite temporal consistency for any non-Gaussian system, regardless of capacity or data volume.
Formalizing the algebraic cores of four theorems in Lean 4 with Mathlib4 (zero sorry placeholders).

Methodology

The paper presents theoretical proofs contrasting statistical Joint-Embedding Predictive Architectures (JEPAs) with the proposed Physics-Grounded Symbolic Architecture (PGSA). It establishes conditions for linear identifiability and temporal consistency through mathematical analysis, and formalizes key theorems in the Lean 4 proof assistant. No empirical experiments or datasets are mentioned.

Key Results

PGSA achieves exact linear identifiability for all physical regimes, with per-step error bounded only by numerical precision, enabling near-infinite temporal consistency. In contrast, statistical World Models cannot achieve this property for any non-Gaussian system, regardless of model capacity or training data volume.

Limitations

The Klindt et al. converse is taken as an external premise and not proven within the paper.
The formalization in Lean 4 covers only the algebraic cores of four theorems, not the full proofs.
The approach requires symbolic grounding in the causal generator of the world's dynamics, which may not be available or feasible in all real-world settings.
The paper is purely theoretical with no empirical validation or experimental results.

Resources

Paper