R-layer Mode Theory (RLMT) XLV: Observables, Hierarchy, Geometry, and Quantum-Gravity Closure

This volume completes the R-layer Mode Theory (RMT) program by integrating observational anomalies, numerical mode analysis, and the geometric hierarchy of tensorial layers.It develops a unified tensorial formalism, defines CP-even and CP-odd projection operators, and establishes explicit links between mode amplitudes and measurable quantities such as the muon g−2 and EDMs.The T-layer tension field and its geometric potential are formulated using the AUP/MUP/CUP mode structure.The result is a closed, testable framework connecting modes, geometry, and experiment.