Conceptual Companion and Structural Guide for the SU(2) Yang–Mills Osterwalder–Schrader Construction

This record contains a conceptual companion and structural guide to the primary manuscript archived at DOI: 10.5281/zenodo.20158540. The companion reconstructs the proof architecture of the primary manuscript section by section. It is designed to clarify the conceptual role, strategic objective, technical interpretation, and dependency structure of each major component of the construction. The primary manuscript presents a proposed reflection-positive construction framework for a subsequential SU(2) Yang–Mills Osterwalder–Schrader continuum theory with positive Hamiltonian mass gap and renormalized distributional Schwinger–Dyson Yang–Mills identity. This companion is not a substitute for the formal proof. It is an interpretive and structural guide intended to make the theorem architecture, proof dependencies, terminology ladder, and scope restrictions easier to navigate. The companion preserves the same scope discipline as the primary manuscript: the construction discussed is subsequential, SU(2)-specific, reflection-positive, Osterwalder–Schrader reconstructed, nontrivial through the reflected-tube sector, positively gapped in the reconstructed OS Hamiltonian sense, and Yang–Mills identified through the renormalized distributional Schwinger–Dyson identity. No uniqueness of the continuum limit is claimed, no extension to all compact simple gauge groups is claimed, and no pointwise classical Yang–Mills field equation is asserted. This record includes the compiled companion PDF, the LaTeX source archive exported from Overleaf, and a README file describing the deposit contents.