Why Conclusions Diverge from the Same Observations: Formalizing World-Model Non-Identifiability via an Inference

Modern societies possess more information than ever before, yet they do not converge toward a single shared understanding. The same events, facts, laws, technologies, or risks can be interpreted as evidence of freedom, danger, exclusion, injustice, responsibility, or unrealized possibility. Existing discussions often treat such disagreement as a conflict of values, preferences, or beliefs. This paper argues that disagreement is already a late-stage phenomenon. The central premise is simple but not trivial: observation is not yet inference. Not every observation becomes inferentially relevant, and not every possible object in an observation sequence becomes an estimation target. A possible target becomes admissible only when a state representation can be constructed that is approximately sufficient for prediction, evaluation, or action with respect to that target. This paper develops a world-model theory of cognitive diversity and alignment by reconstructing recognition as the construction of such approximate sufficient statistics under finite informational, representational, observational, and action constraints. It formulates this position as the Multi-Phase Inference Assumption (MIA) and defines its core internal mechanism as the Multi-Phase Inference Mechanism (MIM). The framework introduces alignment maps and transformation loss to analyze how heterogeneous world models communicate without being collapsed into a single representation. World-model alignment is therefore processability, not agreement: the design of AI systems that help heterogeneous forms of intelligence remain mutually processable while preserving their distinct error-detection capacities.

A representation that scrambles the true degrees of freedom of the world cannot support reliable planning or compositional generalization. We prove that LeJEPA (alignment plus Gaussian regularization) linearly recovers the world's latent variables from nonlinear observations, a property known as linear identifiability, in a broad class of worlds where latents evolve under stationary, additive-noise transitions. Our main result is that among all such worlds, the Gaussian is the unique latent distribution for which this guarantee holds. The forward direction rests on a spectral decomposition in which each degree of nonlinearity is strictly penalized by alignment, making the linear map the optimum; the converse rules out every non-Gaussian alternative. We further prove an approximate identifiability result where the guarantee degrades gracefully, and show that linear, orthogonal identifiability enables optimal latent-space planning. We validate the theory with experiments ranging from 2D examples to 1024-dimensional latents, including distributional ablations and pixel-based robotic control. Our theory turns an empirically successful recipe into a mathematical guarantee, providing the foundation for building World Models that provably recover the structure of the world.

Klindt, LeCun, and Balestriero (arXiv:2605.26379) proved that Joint-Embedding Predictive Architectures (JEPAs) achieve linear identifiability, the linear recovery of the world's true latent variables, if and only if the world's latent dynamics follow a Gaussian, stationary process. This Gaussian boundary implies a fundamental limit on temporal consistency: for any non-Gaussian physical system, the representation error of a statistical World Model grows monotonically with time. We prove that this limit is an artifact of the statistical alignment mechanism, not a property of World Models in general. We introduce the Physics-Grounded Symbolic Architecture (PGSA) and prove three results: (1) a PGSA achieves exact linear identifiability for all physical regimes, regardless of the latent distribution; (2) the per-step error of a PGSA is bounded by numerical precision alone; and (3) as a direct consequence, a PGSA maintains temporal consistency for an unbounded number of transitions, a property we term near-infinite temporal consistency. We further prove that statistical World Models cannot achieve this property for any non-Gaussian system, regardless of model capacity or the volume of training data. The algebraic cores of four of the theorems are formalized in Lean 4 with Mathlib4 v4.31.0 (zero sorry placeholders); the Klindt et al. converse is taken as an external premise. The contrast establishes that symbolic grounding in the causal generator of the world's dynamics is the sufficient condition and, in non-Gaussian regimes, the only condition for near-infinite temporal consistency.