Coherent Affine Substrate Theory I–III: Premetric Foundations, Residual Affine Structure, and Emergent Time–Metric Geometry

This deposit contains the first three updated manuscripts of the Coherent Affine Substrate Theory series. The project develops a premetric, connection-first framework in which physical description begins from non-null admissibility and residual relational structure rather than from metric spacetime, external time, fields, particles, or compact objects.

CAST I introduces the foundational ordering from non-null residual structure to relation, transport, affine dynamics, coherent branches, emergent time, and emergent metricity. CAST II provides the mathematical companion: affine connection, curvature, torsion, premetric variational functionals, Hessian kernels, mode classification, coherence projectors, Schur reduction, and metric-affine reconstruction. CAST III develops the geometric reconstruction layer, giving conditional criteria for effective frame emergence, Lorentzian metric readout, coherent clocks, causal cones, proper time, and the general-relativistic limit.

The release is intentionally non-numerical. It does not claim to derive observed constants, particle spectra, gauge couplings, or empirical cosmological parameters. Its purpose is to establish the conceptual and mathematical foundation required before such downstream reductions can be responsibly attempted.