Collapse and Freeze as Failures of Information Geometry: A Substrate-Independent Account of Hierarchical Failure Modes

The companion papers establish that collapse and freeze are the necessary failure modes of hierarchically organized adaptive systems, and that this necessity follows from physical first principles for most of the derivation. A gap remains: while the failure modes are physically grounded at the level of individual systems, their appearance across wildly different physical substrates — neurons, organizations, stars, ecosystems — has not been formally justified. Why should the same failure modes appear in systems with completely different physical implementations? This paper answers that question using information geometry. We show that collapse and freeze are failures of Fisher information geometry — a mathematical structure defined for any system that maintains a probability distribution over states. Because Fisher information geometry is substrate-independent by construction, any system maintaining such a distribution is subject to the same geometric failure modes regardless of physical implementation. We formalize collapse as the flattening of the Fisher information metric (approach to maximum entropy, minimum curvature, undirected revision) and freeze as metric misalignment (concentrated distribution with high curvature pointing away from the true environmental distribution). We show that the Critic's function is geodesic tracking in Fisher information space, that the freeze threshold is a natural distance condition in the metric, and that the synchronic/diachronic incompleteness distinction corresponds to two geometrically distinct types of distance — support gap and KL divergence respectively. We connect the framework to Bennett and Suzuki's weakness maximization, showing that it is equivalent to free energy minimization in the Fisher metric, and identify the information-geometric completion of their Autopoietic Theorem. The paper generates five new falsifiable predictions beyond those of the axiomatic and physics papers.