R-layer Mode Theory (RLMT) XLI‑J: RLMT and Black Hole Quantum Information — An R-layer Resolution of the Information Paradox

This volume develops a unified description of black hole quantum information within the framework of R-layer Mode Theory (RLMT). Microscopic information is encoded in conserved Small-AUP/MUP modes, while macroscopic geometry emerges from the tension field σ(x) and its R-wave excitations. Hawking radiation is reinterpreted as a dimensional reduction of R-wave dynamics with backreaction encoded in a scale-dependent dissipation kernel TR(k). The instability of black hole interiors, emphasized by Hotta, is mapped to fluctuations in the mode imbalance and the dissipative dynamics of the tension field. The island formula and entanglement wedge reconstruction are given an R-layer interpretation, where islands arise as portions of the R-layer entanglement wedge. Observational consequences include PTA-band suppression, CMB B-mode modifications, interferometer-scale corrections, and GW–neutrino correlations.