Continuum Corridor from Refinement: Generator Transport, Discrete Connection Data, and Curvature-Form Pressure

Indefinite refinement forces transport to compress into local generator data. This paper shows that if refinement can proceed arbitrarily far without memory blow-up, then transport between gauge-dependent second-tier corrections cannot remain an ever-longer composition word. A “continuum corridor” requirement forces a bounded local representation: a discrete connection datum A(t;h) that summarizes near-identity transport at each location and increment. Comparing two refinement orders around a square forces a curvature-class invariant: a stable obstruction that decomposes into a “difference around a square” term plus an interaction (bracket) residue. Gauge dependence of the connection datum and gauge-meaningful status of curvature follow from transport comparability, without assuming manifolds, derivatives, differential forms, or physical field postulates.