Recurrence-Driven Curvature Response in Finite Reversible Closure: Holonomy Loading and the Infrared Geometry Limit - Paper 18

Recurrence-Driven Curvature Response in Finite Reversible Closure: Holonomy Loading and the Infrared Geometry Limit - Paper 18 ABSTRACT Paper 17 established that gauge-invariant curvature-loading observables, defined through plaquette holonomy statistics, become functionals of recurrence content in the high-density regime. Paper 18 derives the corresponding curvature response law without assuming a background manifold or metric. Starting from holonomy variance and recurrence and occupation density proxies in the doubled composite sector, we construct a local graph-based response functional. In the weak-loading and slowly varying regime this admits an infrared geometric rewrite. General Relativity is interpreted as a macroscopic compression of a prior holonomy–recurrence response relation, rather than as a fundamental axiom. INTRODUCTION The Finite Reversible Closure (FRC) programme derives matter and gauge structure from strictly local, finite-dimensional reversible update. Papers 10–15 constructed the composite matter sector and its infrared effective description.Paper 16 identified observable deviations in the low-density regime.Paper 17 defined the breakdown of the dilute quasiparticle description and introduced curvature-loading observables based on holonomy statistics. Paper 18 now performs the gravitational step. It asks; Given that curvature-loading observables become functionals of recurrence content at high density, what is the resulting curvature response law? No background manifold or metric tensor is assumed. All structures are derived from;- Gauge-invariant holonomy operators. Composite occupation density. Z2 grading and recurrence content. Coarse-grained adjacency graph structure.