Needham's Recursive Model of Particle Masses: A First-Principles Approach to the Standard Model and Beyond

Needham’s Table of Particles: A Recursive First-Principles Model from Prime Waves and Vacuum Structure Description This paper presents a zero-fit, first-principles framework for deriving the entire particle mass spectrum from recursive shell geometry. Combining the Carol Equation with the Prime Wave Theory, this model maps the emergence of all particles—Standard Model, dark matter, and beyond—through vacuum compression and transcendental recursion. The accompanying ZIP archive contains the complete Python codebase, validating that all predictions are mathematically reproducible and based entirely on first principles. Every mass is derived without empirical fitting, using only π, φ, and the Planck mass. Leptons follow a relativistic-logarithmic emergence law (RLEM), while all sectors obey recursive scaling defined by a single constant: alpha = log(π · φ) / log(π) 🔭 Key Prediction A major result is the prediction of scalar wormhole pairs at 227.78 GeV (Yro) and 250.00 GeV (Y), separated by √φ. These are not “found in data”—they are mapped from theory, just like every other resonance, through the deeper recursive geometry of the vacuum. We do not fit spikes.We explain why the spikes must be there. 🧩 Framework Features Recursive shell equations for all particle sectors Prime Wave–informed harmonic predictions A unified Needham Particle Table mapping all mass-bearing states Scalar resonance and wormhole topology criteria Predictive vacuum zones from Standard Model to curvature-bound states Fully computational and visually mapped This is not a proposal. It is a reproducible, predictive unifying structure, in which all particles emerge as resonant manifestations of vacuum recursion.