FQFT Paper I: A Scale-First Spectral Field Formalism for Hierarchical Matter Structure

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:
fqft_compute_v2.py

Primary experimental reference targets include:

• JUNO,
• HL-LHC,
• CASPEr-Electric,
• CMB-S4,
• LZ,
• XENONnT.