The Dimensionless Universe: An Ab Initio Derivation of G, H₀, and the Particle Spectrum from Geometric Axioms

This repository contains the complete computational framework and source code for the **Dimensionless Universe**, a phenomenological theory that derives the fundamental constants of nature from first principles. The model demonstrates that the properties of reality—from the masses of elementary particles and the gravitational constant ($G$) to the Hubble expansion rate ($H₀$)—emerge from a unified geometric lattice defined solely by the mathematical constant **π** and its associated geometries. The included Python scripts and high-precision engines (with 110-digit accuracy) provide a complete, reproducible, and falsifiable proof of the theory's claims, tested against experimental data from CODATA, the Particle Data Group (PDG), and NIST. Theoretical Framework The core hypothesis posits that mass, forces, and the structure of spacetime are not arbitrary but are deterministic consequences of a geometric code. The model operates with **zero free parameters**, deriving all physical values from a small set of geometric axioms. 1. The Geometric Origin of Mass and Stability Particle rest masses are identified as resonant integer nodes (k) on a discrete geometric lattice. The theory provides a unified scaling law that connects leptons, mesons, and hadrons, explaining their mass hierarchy and stability. M(k) = k · Base Scale · Topological Correction Key Derivations: The model reproduces the proton mass (as $6\pi^5$) and the muon mass with a relative error of less than 0.002% and explains particle lifetimes by reinterpreting decay as a function of geometric asymmetry ("intrinsic velocity"). 2. Charge Topology and the Weak Interaction This framework resolves the "isobar blindness" problem by defining electric charge and nuclear stability as properties of number theory. The model shows that beta decay is a deterministic mechanism for restoring geometric symmetry in atomic nuclei. Symmetric Z (Composite): Corresponds to stable lattice configurations. Asymmetric Z (Prime): Induces topological stress, leading to radioactive decay. 3. Grand Unification: Gravity and Cosmology from the Micro-Scale The project culminates in the analytical derivation of the gravitational constant ($G$) and the Hubble constant ($H₀$) from the geometric properties of the proton. This unifies the micro-scale (Quantum Mechanics) with the macro-scale (Cosmology). Gtheory = f(mp,geom, αgeom, dimensions)H₀theory = f(mp,geom, Gtheory) The calculated value for $G$ matches CODATA data with a deviation of 0.0037%, and the derived $H₀$ corresponds to the Planck 2018 satellite data. Repository Contents and Key Scripts Core Verification Engines The_Geometric_Universe_MASTER_TEST.pyThe primary script for a complete audit of the theory. It runs a suite of tests across all physical scales (micro to macro) and performs a Monte Carlo simulation to verify the statistical significance (>2.7σ) of the geometric framework. FairTest.pyA "Discovery Mode" module that scans the energy spectrum, demonstrating that known particles (Pion, Kaon, Proton, Tau) spontaneously align with lattice nodes without manual tuning or parameterization. Charge_Symmetry_Test.pyThis script provides proof of the topological origin of nuclear stability, correctly distinguishing between stable and unstable isobars (e.g., rubidium-87 vs. strontium-87) based on the geometry of the proton number (Z). Key Proofs and Visualizations Tau_Ladder_Visualizer.pyGenerates a graph demonstrating that hadrons and leptons lie on a single, continuous geometric scale defined by adjacent integers k=16, 17, 18, challenging their traditional classification. Alpha_Wall_Precision_Test.pyProvides the computational proof for the "Alpha Wall," a geometric principle that correctly predicts the termination of the stable periodic table at Lead-208. Generative_Atom_Spectroscope.pyA verification engine that derives the spectral lines of hydrogen-like atoms, demonstrating that relativistic effects are an inherent property of the model's geometry. Supporting Documentation FINAL_THEORY_REPORT.txtThe complete, automated output from the master test, summarizing the final statistical verdict and the model's precision. Falsification_Tests/A directory containing scripts and reports from tests designed to challenge and potentially disprove the theory, confirming its robustness. Conclusion This repository provides computational evidence for a new, parameter-free foundation for physics. The high-precision alignment of the model's predictions with experimental data across more than 40 orders of magnitude—from the muon to the Hubble constant—suggests that physical reality is an emergent property of a single, coherent geometric system. # [e-mail]