R-layer Mode Theory LXXXIV: Black Hole Internal Hierarchy, Information Ascension, and the R-layer Mukhanov–Sasaki Equation

R-layer Mode Theory LXXXIV** Volume LXXXIV develops a unified, information‑theoretic description of black hole interiors within the R-layer Mode Theory (RLMT), extending the canonical mode hierarchy of Appendix X and the geometric interpretation of Appendix Y to strongly curved spacetime. The event horizon is treated as an R-layer tension boundary where AUP/MUP modes undergo hierarchical transitions into small‑AUP/MUP and CUP states. The CUP‑dominated core provides a stable internal region whose background profile R0(r) defines the black‑hole analogue of the R-layer Mukhanov–Sasaki equation. We derive the effective potential VR,ℓ(r) for a Gaussian CUP background and analyze the resulting information‑wave dynamics. The framework yields a unitary picture of black hole evaporation, in which Hawking radiation is reinterpreted as a projection from CUP/CUD information to the 4D matter layer. The internal hierarchy—CUP, CUD, Meta‑CUD, and the 22‑layer—governs information ascension during evaporation and resolves the monogamy conflict underlying the firewall paradox. The R-layer Mukhanov–Sasaki equation in a Schwarzschild background is constructed explicitly, leading to quasi‑normal mode spectra, echo‑like structures, and effective refractive‑index corrections that influence the black hole shadow. We compute representative QNM frequencies using the WKB approximation and evaluate the parameter dependence of shadow‑radius deviations, finding sub‑percent corrections consistent with current Event Horizon Telescope constraints. Volume LXXXIV thus provides the first mode‑consistent, information‑theoretic model of black hole interiors in RLMT, linking microscopic mode transitions, emergent geometry, and observable signatures. It establishes the foundation for the detailed analyses developed in Volumes LXXXIV‑A, LXXXIV‑B, and LXXXIV‑C.