An L1 Fuzzy-Fibonacci Spacetime Framework: Lorentz-Invariant Discretization, Spherical Counter-Winding Networks, and Emergent Gauge-Higgs Dynamics

Abstract

Standard Quantum Field Theory (QFT) and theasymptotic S-matrix formalism are formulatedon a continuous L2 Cartesian spacetime manifold—a mathematical convenience that introducesunmeasurable irrational coordinates andleads to non-convergent, divergent Feynman perturbationseries. This paper proposes an alternativenon-perturbative, unitarized ”equivalentcircuit” framework where the spacetime continuumemerges as a scale-dependent statisticalproperty of a discrete, fuzzy quantum lattice.By replacing the continuous L2 norm with anL1 fuzzy logic topology governed by piecewiselinear, Fibonacci-spaced membership functions,we achieve optimal spatial and energetic packing(quasi-crystalline structure) without sharpboundaries. We argue that a Poisson-like distributionof these fuzzy energy-pixels preservesmacro-scale Lorentz invariance, so that relativityand quantum mechanics describe the same proposedtopology at different operational scales.We also map this micro-scale topology ontoa macro-scale equivalent circuit consisting of aspherical, dual-feed counter-winding spiral antenna.In the model, the left-handed (matter)and right-handed (antimatter) windings ona curved spherical manifold undergo an intrinsictopological phase lag, providing a geometric,non-perturbative interpretation of CP violationand cosmic baryon asymmetry. Bytuning the network to the characteristic waveimpedance of the vacuum (Z0 ≈ 377 Ω), Babinet’sself-complementary principle leads to ahalf-conducting, half-insulating spiral geometry.This constraint transforms lattice vertices intostable three-way junctions, suggesting a structuralinterpretation for the three generationsof quarks. The model further associates theweak interaction and the Higgs mechanism withevanescent modes and localized capacitive reactancesnear the network’s non-propagation bandgapfrequencies, without introducing independentSU(2) gauge fields or fundamental scalarfields. Finally, the fractal self-similarity of theFibonacci structure is associated with a sphericalCasimir force scaling as 1/R2 and a 1/f (flicker)noise spectrum under thermal dissipation. Thisenergy-density dependence of the emergent gravitationalcoupling G provides a geometric interpretationfor flat galactic rotation curves withoutinvoking dark matter. It also suggests a lowenergy,macroscopic test of the proposed Planckscaletopology.