Structural Phase Transitions in Capacity-Constrained Precision Hierarchies

Adaptive systems governed by hierarchical precision regulation are commonly describedin terms of stability, error minimization, and resource-constrained optimization. Yet thestructural conditions under which such systems undergo qualitative reorganization remainunderexplored. This paper demonstrates that precision-regulated hierarchical systems ad-mit genuine structural phase transitions—critical reorganizations of inferential architecturearising from constrained precision redistribution.Under finite global precision capacity, redistribution eigenmodes generically determinestability, and their eigenvalue crossings constitute the precise spectral mechanism of struc-tural phase transition. We formalize a general…