The Recursive Spectrum: Predicting the Full Subatomic Structure Through Emergent Scaling

This paper presents a unified, first-principles framework that predicts the full subatomic spectrum using recursive scaling laws derived solely from the fundamental constants π (pi), ϕ (phi), and the Needham Scaling Constant (NSC). It demonstrates that all known Standard Model particle masses—including the electron, muon, tau, proton, neutron, and Higgs boson—emerge as resonant nodes within a harmonic lattice structure governed by these constants. The model reproduces these masses with <0.1% deviation and predicts previously undetected particles consistent with dark sector phenomena. This work proposes a generative, non-fitted explanation of particle identity, reframing mass as an emergent consequence of recursive geometry at the interface of time and gravitational fields. This release is supported by four complementary studies that extend the Pi-Phi-NSC framework across particle physics and cosmology: Recursive Light Resonance Framework: A Unified Model of Emergent Particle Properties with Prediction of a Third Scalar Resonance at 285.3 GeV📄 DOI: 10.5281/zenodo.15364009 Three Exact Particle Masses from only π and ϕ: A First Principles Proof of the Pi-Phi Light Framework📄 DOI: 10.5281/zenodo.15363532 Emergent Constants, Recursive Dimensional Unfolding, and the Tetrahedral Interface of Light and Vacuum: The Unified Field Theory of Creation📄 DOI: 10.5281/zenodo.15332482 Cosmic Resonance: Extending the Light-Pi Framework from Particles to Celestial Bodies📄 DOI: 10.5281/zenodo.15337626 This paper forms the foundation of the ENSO Framework and offers a bridge between mathematics, quantum field theory, and observable particle physics—laying the groundwork for deeper experimental validation. If you would like any further information about the ENSO Framework, please contact Eric Needham: [email protected]