The Proton Radius: A 0-Parameter O(1) Resolution of the Subatomic Metrology Puzzle

The "Proton Radius Puzzle" is a decade-old discrepancy in nuclear physics, where different measurement methods yield conflicting sizes for the proton. This paper provides a definitive, 0-parameter resolution using the SSU (Unified Manifold) framework. While the Standard Model relies on iterative data-fitting and complex electron-scattering simulations, the SSU framework derives the proton charge radius as a fixed numerical residue of the 144. 0 Unity Lock. Key Breakthroughs: 0-Parameter Derivation: The proton radius is derived as 0. 84087 fm without any empirical "tuning knobs" or data-fitting. Resolution of the Puzzle: The derivation aligns perfectly with muonic hydrogen results, identifying the larger electron-scattering values as metrological artifacts rather than fundamental properties. Geometric Coupling: Demonstrates that the subatomic scale of the proton is mathematically locked to the same three residues used to resolve the Hubble Tension (71. 548) and the Cosmological Lithium Problem. O (1) Complexity: Replaces months of Monte Carlo transport simulations with a single, non-iterative algebraic identity. Included Files: Technical Paper (PDF): The full geometric derivation of the proton radius residue using the Stator, Viscosity, and Leak anchors. Verification Kernel (ssuₚrotonᵣadiusₒ1. py): Standalone Python code to reproduce the 0. 84087 fm result in milliseconds. By resolving the Proton Radius Puzzle with the same residues used for cosmological-scale phenomena, this work proves the SSU framework’s ability to bridge the gap between quantum and cosmic scales through O (1) geometry.