Foundational kernel paper of the Fractal Quantum Field Theory (FQFT) research program. This work introduces a scale-first framework in which Planck-scale spacetime is modeled using Ramanujan graph structures and spectral geometry, with low-energy quantum field behavior emerging from a higher-dimensional fractal geometric regime. The paper establishes the primary mathematical and physical foundation of the FQFT framework, including: the graph-based geometric construction, the fractal measure-space formalism, the dimensional renormalization structure, the spectral fixed-point mechanism, recovery of standard quantum field theory behavior at low energies, and the emergence of hierarchical particle structure from graph spectral organization. Key results include: identification of a non-trivial dimensional fixed point, derivation of a three-generation particle structure from spectral band organization, construction of a scale-first mass hierarchy framework, and a set of experimentally testable phenomenological predictions related to neutrino ordering, Higgs-sector behavior, dark matter searches, and precision particle physics observables. The publication serves as the formal kernel paper for the ten-paper FQFT research series and provides the foundational definitions, operators, fixed-point structures, and spectral framework required for the subsequent particle, gravitational, and cosmological developments in the series. Companion reproducibility software: fqftcomputeᵥ2. py Primary experimental reference targets include: JUNO, HL-LHC, CASPEr-Electric, CMB-S4, LZ, XENONnT.
Ivan Petrov Pasev (Mon,) studied this question.