R-layer Mode Theory (RLMT) LV: Quantum R-layer Theory

Volume LV constructs the quantum theory of the R-layer Mode Theory (RLMT). Classical information field R(x) is promoted to a quantum object described by a noncommutative algebra AQ, a Hilbert space HQ, and a quantum tension operator E^. The volume develops: quantum Hilbert space of the R-layer, quantum tension operator and spectral flow, quantum modular theory (Tomita–Takesaki), quantum spectral triple (AQ,HQ,E^), categorical structure of quantum layer transitions, quantum cosmology including corrections to expansion, perturbations, gravitational waves, and neutrino propagation. These results complete the quantum foundation of RLMT.