Persistence-Weighted Path Amplitudes — Entropy-Weighted Calculus on a Single Configuration Space

Persistence, Redundancy, and the Origin of Connection

Requiring distinctions to persist under repeated variation imposes structural constraints prior to the introduction of physical primitives. Irreversible loss, path dependence, and curvature follow as necessary features of comparison once persistence is enforced. When curvature obstructs global equivalence, redundancy of local description becomes unavoidable. Consistency of composed comparison then forces the introduction of a representative-independent transport rule. A connection is derived as the minimal structure required to relate locally equivalent descriptions across variation, without assuming geometry, dynamics, symmetry, or physical fields.