A Source-to-Endpoint Construction for Compact-Simple Yang–Mills Existence and Mass Gap

This archival research paper presents a source-to-endpoint construction for compact-simple Yang-Mills theory on four-dimensional Euclidean spacetime. The manuscript develops a finite-type Yang-Mills coherence source, proves a normalized source-level terminal mass gap, constructs a reflection-positive Euclidean source functional, recovers the ordinary compact-simple Yang-Mills Euclidean observable endpoint, applies Osterwalder-Schrader reconstruction, and transfers the source gap to physical Hamiltonian spectral exclusion by calibrated temporal bridge transfer. The central organizing principle is that endpoint-visible data are not counted as physical spectral data unless they survive source generation, closure, quotienting, primitive terminal readout, Euclidean reconstruction, ordinary endpoint recovery, and calibrated spectral transfer. This v1.0 archival release is provided as a public preprint for independent inspection, verification, criticism, and refinement. It has not been externally peer reviewed.