Rotkotoe: Geometric Foundations and Empirical Validation of Universal Mass Quantization

1. File: Anisotropic Shells Analysis - Complete Summary.pdf Description:This paper examines the geometric and spectral significance of anisotropic lattice shells within the golden-ratio torus geometry that defines the Rotkotoe framework. It demonstrates that the first fully anisotropic shell corresponds to the lattice vector (1, 2, 3), producing the √14 factor in the universal constant Npart=φ4014N_{\text{part}} = \varphi^{40}\sqrt{14}Npart=φ4014. The analysis confirms that this shell establishes the foundation for all higher harmonic modes and introduces a new geometric method for quantization across scales. 2. File: Mathematical Proof of √14 Factor - Rotkotoe Theory.pdf Description:This document provides the formal derivation of the √14 factor in the Rotkotoe universal constant, tracing it to the (1² + 2² + 3² = 14) lattice configuration on a golden-ratio torus. It outlines the connection between anisotropic mode selection, harmonic resonance, and the emergence of √14 as the first non-degenerate geometric shell. This work completes the geometric proof of the lower-order structure of the universal resonance constant. 3. File: Mathematical Derivation Framework - Rotkotoe.pdf Description:A rigorous mathematical framework outlining the derivation of Npart=φ4014N_{\text{part}} = \varphi^{40}\sqrt{14}Npart=φ4014 from first principles. It formalizes the geometry of the golden-ratio 3-torus, spectral shell enumeration, and hierarchical filtering mechanisms that generate the φ⁴⁰ scaling factor. The paper introduces a roadmap toward a complete proof using spectral zeta regularization and establishes the golden-ratio torus as a physically meaningful foundation for mass quantization. 4. File: Rotkotoe_ Empirical Evidence for Universal Mass Quantization.pdf Description:This empirical study validates the Rotkotoe mass quantization framework through blind tests on all Standard Model particles, using fixed constants and no fitting parameters. The results show sub-10 ppm accuracy across six of seven tested particles and confirm scale-free boson ratios to 10⁻⁸ precision. The findings demonstrate that particle masses follow integer harmonics on a golden-ratio torus, revealing the geometric origin of the mass hierarchy. 5. File: Rotkotoe RG Stability Test - Complete Results.pdf Description:This paper presents the full renormalization-group stability analysis of the Rotkotoe framework. It verifies that the integer harmonic ladder (ν) remains coherent when particle masses are evolved from pole to MS̄ scales using multi-loop QED/QCD running. The results confirm rung integrity and show that boson mass ratios remain stable at 10⁻⁸ precision, establishing renormalization-group coherence as a physical property of the Rotkotoe model.