Selective Memory Coupling and the Origin of Mass Hierarchy in History-Dependent Gravity (Paper XLIX)

The origin of particle mass hierarchy remains one of the fundamental open problems in physics. While the Standard Model explains mass generation through local electroweak symmetry breaking, it does not provide a dynamical explanation for the enormous separation between the neutrino mass scale (approximately 0.05 eV) and the Higgs boson mass (125 GeV) — a difference exceeding twelve orders of magnitude. In this work, we investigate mass generation within the framework of History-Dependent Gravity (HDG), a nonlocal theory where quantum fields interact with the temporal memory structure of spacetime through a spectral memory kernel. Building on the spectral representation of the memory operator and Functional Renormalization Group (FRG) analysis developed in previous works (Papers XLII, XLV, XLVII, and XLVIII), we introduce the principle of selective memory coupling. The central result is that the coupling of a quantum field to the infrared memory sector is not universal, but depends dynamically on the ratio between its local mass scale and the cosmological infrared scale. We derive a History-Dependent Decoupling relation showing that particles with large local masses are naturally insensitive to cosmological memory, while fields with vanishing or extremely small local mass remain dominated by the integrated history of spacetime. The observed mass hierarchy is consequently reinterpreted not as a hierarchy of fundamental parameters, but as a dynamical hierarchy of memory susceptibilities generated by the infrared RG structure of spacetime. The framework makes testable predictions for ultra-light particles, time-varying neutrino masses, and modified gravitational dynamics at cosmological scales.