R-layer Mode Theory XLII-C: AUP/MUP Field Equations, 228, and the r-Neutrino Sector

This is Version 2 of Volume XLII‑C in the R‑layer Mode Theory (RLMT) series. The update introduces a formal declaration regarding the use of Microsoft Copilot for proofreading, text refinement, and LaTeX‑related structural assistance. Minor corrections were applied to the reference list, while the theoretical content, mathematical derivations, and field‑theoretic constructions remain unchanged. Volume XLII‑C develops the field‑theoretic foundation of the AUP/MUP mode hierarchy, including scalar and spinor AUP/MUP fields, SU(2) mode symmetry, conserved currents, and the construction of the r‑neutrino sector. It also provides a rigorous functional‑analytic and category‑theoretic definition of the transcendent layer 28 as a nonlocal categorical attractor, completing the 220–227 R‑layer hierarchy. The volume forms a central part of the RLMT program, linking microscopic AUP/MUP dynamics, spectral‑triple geometry, and the gravitational/tension‑field sector. This version preserves all scientific results and improves documentation clarity and transparency regarding AI‑assisted writing.