Capacity Plasticity in Hierarchical Inference: A Long-Horizon Extension of Precision Conservation

Adaptive hierarchical systems regulate prediction-error weighting through precision, yet prior work has shown that such regulation is fundamentally constrained by a finite global precision budget. The earlier trilogy established three core results: (i) finite capacity induces a conservation-like geometric structure that confines redistribution to a capacity manifold; (ii) instability of redistribution modes on this manifold generates structural phase transitions; and (iii) meta-precision provides higher-order regulation of responsiveness near criticality without altering the admissible geometry. Together, these results define a local theory of bounded hierarchical responsiveness. What they do not determine is whether the capacity ceiling itself must remain fixed across longer developmental, overload-related, or transformative time scales. This paper introduces a developmental extension in which precision capacity is finite at any moment yet plastically variable across slower horizons of growth, overload, recovery, and structural reorganization. We distinguish three structurally distinct notions of capacity: nominal capacity, the formal upper bound on allocable precision; effective capacity, the stably usable range of coordinated regulation under that bound; and meta-capacity, the higher-order plastic potential through which the capacity ceiling itself may expand, contract, or reorganize. On this basis, we formulate a minimal four-time-scale dynamical framework in which the capacity manifold becomes a slowly drifting geometric object rather than a fixed structural constraint. The resulting framework preserves the conservation principle of earlier work as a quasi-static law on a time-dependent family of manifolds, subject to an adiabatic validity condition that identifies when slow capacity drift and redistribution instability interact nontrivially. Capacity plasticity is shown to be orthogonal to meta-precision in a precise sense: meta-precision rescales redistribution speed without altering the sign structure of redistribution eigenmodes, whereas capacity drift shifts the spectral landscape itself and can drive eigenmodes through zero independently of redistribution dynamics. This yields two analytically distinct routes to structural criticality—redistribution-driven and capacity-drift-driven—whose interaction is strongest when the system already operates near the stability boundary. The framework further suggests a structural asymmetry between capacity expansion and contraction: contraction may proceed through threshold effects and admit hysteresis, such that restoration of a prior ceiling requires active reorganization rather than mere removal of burden. These consequences support a four-level taxonomy of adaptive failure in which state-inference, redistribution, meta-precision, and capacity-level dysfunction are distinguished by the level of the temporal hierarchy at which regulation breaks down. More broadly, the paper suggests that adaptive intelligence must be characterized not only by error minimization or regulated criticality, but also by the capacity to reorganize the ceiling of allocable precision itself. In doing so, it identifies a form of structural change—capacity-drift-driven spectral shifts—that has not been addressed in existing hierarchical inference models.