Cohomological and Thermodynamic Guardrails for Causal World Models: A Neuro-Symbolic Architecture for Verifiable Scientific Intelligence

Contemporary foundation models operate predominantly as stateless, dissipative autoregressive token predictors lacking intrinsic representations of physical conservation laws, global causal consistency, or formal mathematical truth. In our recent perspective on the two-hundred-year trajectory of artificial intelligence to 2226, we argued that stateless token prediction will yield to continuously learning, causal world models tightly coupled with formal theorem provers, rendering mathematical and physical hallucination structurally unrepresentable within the verified subspace.

$$\dot{z} = L(z) \nabla_z E(z) + M(z) \nabla_z S(z), \quad L(z) = -L(z)^T, \quad M(z) \succeq 0, \quad L(z)\nabla S = 0, \quad M(z)\nabla E = 0$$

Here, we construct the explicit mathematical and algorithmic architecture required to realize this synthesis. First, we constrain continuous neural latent trajectories on a state manifold $\mathcal{M}$ using the non-equilibrium thermodynamic GENERIC formalism, pairing skew-symmetric Poisson operators $L(z)$ (encoding Casimir and topological gauge invariants such as $d(*F - \theta F - J_s) = 0$) with symmetric positive-semidefinite friction operators $M(z) \succeq 0$ parameterized via Weil–Li quadratic positivity functionals. Second, generalizing the de Rham exactness condition $[J_s]_{\text{dR}} = 0$ and cohomology obstruction classes $\omega(\eta)$ from our extended electrodynamics framework, we organize distributed local causal models as sections of a cellular sheaf $\mathcal{F}$ over a simplicial context complex $\mathcal{K}$, showing that global causal consistency without contradiction is equivalent to the vanishing of the first cohomology group $H^1(\mathcal{K}; \mathcal{F})$.