Minimal Foundations of the Affine-Fiber Theory — A Three-Document Package

This package contains three companion documents introducing the affine-fiber theory,an axiomatic arithmetic-dynamical framework for studying modular witnesses in affinearithmetic progressions. Document 1 — Minimal Foundations of the Affine-Fiber Theory (Draft 1.0, 3 pp.)Three definitions, two central theorems (Bridge Characterization and Affine WitnessTrajectory), a dependency table showing all further results as consequences, an openproblems section, and a correction log. Document 2 — The Minimal Morphism Data Determine the Coordinate Morphism (Draft 4.0, 2 pp.)Theorem A: the morphism conditions {M1, M2, M3'} force coordinate preservation onthe orbit. Theorem B: these conditions form an independent minimal generating set.Includes Appendix A recording the correction of a vacuous morphism condition. Document 3 — Relationship of the Affine-Fiber Theory to Existing Mathematics (Version 2, 2 pp.)A positioning note surveying the closest related frameworks (Schmidt 2024, Carranza et al.2025, inversive congruential generators, the Lonely Runner literature) and stating thecandidate contributions. These notes are released to invite mathematical scrutiny. The author particularlywelcomes identification of prior work, simplifications of the proofs, or alternativeformulations.