The General Theory of Irreversible Distinguishability III: Fields and Gauge Structure from Local Refinement

This paper derives internal symmetries, gauge redundancy, charge quantization, andquantum field structure as necessary consequences of local refinement over emergentspacetime. Building on the spacetime and causal structure established in Paper II,we show that local Hilbert spaces, tensor-product composition, gauge connections,holonomy, and curvature arise as consistency requirements for unresolved refinementunder finite propagation and irreversible loss. Charge is shown to correspond to discretepersistent internal symmetry classes, and quantum fields emerge as refinement-denselimits of locally gauge-covariant degrees of freedom. No physical fields, particles, forces,action principles, or quantization procedures are postulated. Quantum field theoryarises as a structural consequence of refinement, locality, and loss.