Differential Corridor from Refinement: Germ Connection Fields, Directed Comparison, and Yield-Corridor Pressure

Refinement without word-explosion forces a germ-level connection field. Building on the continuum corridor result, this paper formalizes a refinement preorder with a directedness principle so any two increments admit a common comparison tier without assuming metrics or real-analysis limits. Edge-class connection data stabilizes into a germ object that acts like a connection field, with gauge variation becoming a local transformation rule. Curvature is treated as conserved order-sensitivity pushed into the transport tier as a stable holonomy residue. The paper then states the next pressure: if transport preserves an already-forced yield/norm invariant, admissible germ transport is constrained to the infinitesimal symmetry class of that invariant (the yield/norm corridor), setting up the Hamiltonian/generator step.