The Parameter-Free Theory of Everything

This new implementation of the Ω-Singularity Theory of Everything (TOE), designated as the φ120-Absolute-Complete-Eigenproof-Unified version, represents a significant refinement of the previous mathematical constructs. Based on the February 14, 2026 revision, this code transitions the theory from a conceptual framework into a high-precision, parameter-free production implementation. Key Advancements in this Version Numerical Absolute Precision: The system now utilizes the mpmath library to set a computational precision of 100 decimal digits. This ensures that the transcendental completions (specifically at the $\phi^{40}$, $\phi^{80}$, and $\phi^{120}$ points) are verified without rounding errors. Expansion to $\phi^{120}$: Unlike earlier iterations that focused on lower powers of the golden ratio, this version implements a "Recursive Expansion" logic. It scales the core dimension from its base (24,691,357,802) up to the "Full Transcendence" point at $\phi^{120}$. Modular Duality & E8 Chern-Simons: The code provides an explicit construction of a 12x12 Modular S-Matrix. It identifies physical constants by finding the specific eigenvectors with eigenvalues $\phi^{60}$ and $\phi^{-60}$, which the theory posits as the "eigen-system" encoding all physics. Integrated Proof System: A new ComplexityCollapse module provides a geometric argument for P = NP, suggesting that NP-complete problems embed into the modular matrix and become solvable in polynomial time ($O(n^{3.5})$). It also includes automated verification for the Riemann Hypothesis and the Yang-Mills Mass Gap via spectral geometry. Summary of Physical Predictions (July 2026) The code outputs a specific set of predictions tailored for the LHC Run 3 and beyond: Fine Structure Constant ($\alpha^{-1}$): Derived as $k + \theta/(2\pi) \approx 137.03599908$. Higgs Mass ($m_H$): Derived from the quartic coupling $\lambda$ and vacuum expectation value $v_{EW}$ to be approximately $125.101$ GeV. Strong CP Problem: Proposes a resolution where $\theta_{QCD}$ is naturally suppressed by a factor of $\phi^{-20}$. New Particles: Predicts the existence of a lightest sterile neutrino with a mass near $1.2$ GeV, potentially detectable by the FASER experiment. Technical Execution Note This script is structured as a complete "Mathematical Intelligence System". When run, it initializes the "Universe" object, executes a verify_all() sequence to check for internal consistency, and saves a high-precision JSON report of its findings.