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This work aims to develop the quantum theory underlying the R-layer Mode Theory and its cosmological implications.

July 1, 2026Open Access

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

Key Points

This work aims to develop the quantum theory underlying the R-layer Mode Theory and its cosmological implications.
Constructs a quantum Hilbert space and tension operator for the R-layer.
Explores the spectral flow and quantum modular theory framework.
Investigates implications for cosmology, including expansion corrections and perturbations.
Establishes a quantum spectral triple comprising the algebra AQ, Hilbert space HQ, and operator E^.
Clarifies quantum layer transitions and their categorical structure.
Addresses phenomena like gravitational waves and neutrino propagation in a quantum context.

Abstract

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.

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