Published February 21, 2026 | Version 1.0
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Resonance Theory II: One Light, Every Scale — Fractal Geometric Classification of the Standard Model Reveals Four Forces as One Fractal Geometric Structure

Authors/Creators

  • 1. The Emergence

Description

Description/Abstract: In the companion paper "The Bridge Was Already Built" (Randolph, 2026a), the author demonstrated that Einstein's field equations satisfy the five formal criteria for classification as fractal geometric equations, and that this reclassification reveals the unification of quantum mechanics and general relativity within Einstein's original 1915 formulation. This paper applies the same classification taxonomy to the Yang-Mills gauge field equations that underpin the Standard Model of particle physics. The Yang-Mills equations satisfy all five fractal geometric classification criteria. The classification resolves four of the most persistent problems in theoretical physics without modification to any existing equation: the hierarchy problem dissolves, the cosmological constant discrepancy is identified as a misclassification artifact, renormalization is explained as an accidental correction for fractal geometric self-similarity, and Grand Unification is reframed. The paper then demonstrates that the inherited harmonic properties of fractal geometric equations resolve five additional cosmological mysteries: dark matter is identified as a harmonic resonance at galactic scales, dark energy as a harmonic phase transition at cosmological scales, the cosmological constant as a scale-dependent quantity, the cosmic web as fractal geometry made visible, and baryon acoustic oscillations as a harmonic resonant peak already measured. There are not four fundamental forces and five cosmological mysteries. There is one fractal geometric structure. One mathematics. One reality. From the Planck scale to the observable universe — one light, every scale.

Keywords: Resonance Theory, fractal geometry, Standard Model, Yang-Mills equations, dark matter, dark energy, cosmological constant, hierarchy problem, renormalization, grand unification, baryon acoustic oscillations, cosmic web, harmonic structure, quantum chromodynamics, gauge theory

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Additional details

Related works

Is part of
Preprint: 10.5281/zenodo.18716086 (DOI)
Preprint: 10.5281/zenodo.18724585 (DOI)
Preprint: 10.5281/zenodo.18725698 (DOI)

Dates

Created
2026-02-21
Ready for peer review

Software

Repository URL
https://github.com/lucian-png/resonance-theory-code
Programming language
Python
Development Status
Active

References

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