Resolving the Granularity Crisis in Climate AI: A Causal Geometric Theory

Climate science faces a fundamental challenge: while artificial intelligence can model complex systems, it lacks a principled theory of granularity—the ability to identify at what scale climate processes operate and why they emerge. Here we resolve this by introducing a unified information‑geometric theory that mathematizes granularity, embedding it intrinsically into AI architecture alongside causality. We prove three foundational advances: (1) climate AI corresponds to smooth maps between causal‑granularity manifolds; (2) causal interpretability reduces to injectivity of the Fisher mapping; (3) optimal granularity emerges from minimizing $\mathcal{I}$‑divergence, replacing empirical scale choice. Our framework for the first time establishes granularity as a learnable geometric object, enabling AI to discover the scale of causation rather than impose it. This transforms climate AI from correlation-based fitting into scale-aware causal reasoning, providing the first mathematical foundation for interpretable, multiscale prediction in an era of escalating extremes.