Meta-Precision under Finite Capacity: Spectral Governance in Hierarchical Inference

Adaptive systems operating under finite inferential capacity must redistribute precisionacross hierarchical levels, and such redistribution can generate structural instabilities as domi-nant modes approach criticality. Previous work established that bounded global precision givesrise to redistribution eigenmodes and local structural phase transitions in hierarchical inference.This paper advances that framework by introducing meta-precision, a higher-order control vari-able that regulates the rate of precision redistribution in response to the local spectral state ofthe constrained dynamics.We formalize this idea on a finite-capacity manifold as a coupled slow–fast system: precisionredistribution evolves on a…