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.

翻译：Klindt、LeCun和Balestriero（arXiv:2605.26379）证明，联合嵌入预测架构（JEPA）实现线性可辨识性（即线性恢复世界的真实隐变量）当且仅当世界的隐动态服从高斯平稳过程。这一高斯边界意味着时间一致性的根本限制：对于任何非高斯物理系统，统计世界模型的表示误差随时间单调增长。我们证明该限制源于统计对齐机制，而非世界模型的普遍性质。我们引入基于物理基础的符号架构（PGSA），并证明三个结论：（1）PGSA对所有物理场景实现精确线性可辨识性，无论隐分布如何；（2）PGSA的每步误差仅受数值精度约束；（3）直接推论是PGSA对无限次状态转移保持时间一致性，我们将此性质称为近乎无限的时间一致性。我们进一步证明，统计世界模型无法对任何非高斯系统实现该性质，无论模型容量或训练数据量如何。其中四个定理的代数核心已在Lean 4（Mathlib4 v4.31.0）中形式化验证（零个未填充占位符）；Klindt等人的逆命题作为外部前提引用。这一对比表明，符号化根植于世界动态的因果生成器是充分条件，且在非高斯场景中，是实现近乎无限时间一致性的唯一条件。