Composite Breakdown and High-Density Curvature Transition in Finite Reversible Closure - Paper 17

Composite Breakdown and High-Density Curvature Transition in Finite Reversible Closure - Paper 17 ABSTRACT Papers 10–15 construct a stable gauge-invariant composite sector and derive an infrared effective description with 3+1D scalar closure, Z2 grading and doubled-sector mass completion. Paper 16 identifies empirically constrained low-density deviations. Paper 17 studies the high-density regime in which the dilute composite truncation fails. Composite density is defined relative to an operational correlator-matching block scale. Two structural thresholds are introduced: An overlap threshold where composite isolation fails. A curvature-loading threshold defined by gauge-invariant holonomy statistics. We derive operational criteria for both thresholds, identify the breakdown of the derivative expansion and show that curvature loading becomes a functional of recurrence density. This provides the structural bridge to Paper 18. INTRODUCTION The Finite Reversible Closure (FRC) programme derives matter and gauge structure from strictly local, finite-dimensional reversible update. Paper 10 constructed gauge-invariant composite excitations.Papers 13–15 derived their infrared effective dynamics.Paper 16 identified low-density observable deviations and operator constraints. All of those results rely on a dilute composite regime, in which: Composite excitations are approximately isolated. Holonomy curvature fluctuations are weak. A derivative expansion is controlled. Paper 17 addresses the structural boundary of that regime. It asks; At what density does the composite quasiparticle picture break down and how does curvature loading emerge beyond that point? We introduce operational density and block-scale definitions, define gauge-invariant curvature observables and identify the transition to a curvature-dominated phase.