Field-Equation Pressure from Curvature Stability: Bianchi Constraint and the Source Slot from Refinement-of-Refinement

Field equations emerge from stable curvature bookkeeping under refinement. This paper extends the forced corridor sequence by requiring that curvature—already defined as a refinement-stable holonomy residue—remain computable without word-explosion when the refinement procedure itself is refined. That “refinement-of-refinement” constraint forces a Bianchi-type cancellation law as the unique compressible closure for curvature accounting. When cancellation is permitted to fail in a controlled, refinement-stable way, the failure is forced to occupy a dedicated source slot: a gauge-meaningful defect term that preserves representational stability. No manifolds, derivatives, exterior calculus, metrics, or empirical assumptions are used.