A Prime-Fractal Synthesis of Space, Time, Mass, and Energy

We investigate a prime-fractal extension of the Higgs mechanism, wherein the vacuum expectation value (VEV) and mass generation arise from discrete prime-density terms embedded in the Higgs potential. Within this framework, each particle’s mass is tied to a fractal dimension and prime-harmonic overlap, leading to novel scalar excitations beyond the Standard Model Higgs. Numerically, we identify three prominent peaks at approximately 541 GeV541\,\mathrm{GeV}541GeV, 809 GeV809\,\mathrm{GeV}809GeV, and 1.26 TeV1.26\,\mathrm{TeV}1.26TeV, predicted to manifest as Higgs-like resonances in collider data. These scalars derive from prime-lattice couplings that enrich the symmetry-breaking sector without introducing unnatural hierarchies. The simulation further suggests possible connections to dark-matter portals through subdominant prime-sum channels. Although phenomenological details depend on coupling constants and specific fractal dimensionalities, the distinct energy scales provide clear targets for ongoing and future collider experiments. By linking prime-based lattice structures to electroweak symmetry breaking, our model offers a testable path toward unifying number-theoretic structures with particle physics. This project was developed by Marco Gericke, with structured assistance from a large language model. All scientific concepts and conclusions were generated, verified, and interpreted by the author. Dedicated to Peter Plichta, who envisioned the code before it could be computed.