ONE AXIOM : The Lab

Title: ONE AXIOM: Complete Prediction Register with Dual-Track Verification Status (Version 4.0 / April 2026) Description: This document serves as the central registry and audit trail for the ONE AXIOM framework, an initiative to derive physical constants and structural principles of reality from a single fundamental axiom (Axiom M). Version 4.0 (April 2026) represents a significant expansion, providing a comprehensive synthesis of 390 entries derived across source documents published between November 2025 and April 2026. This edition marks the transition to a "Complete Register" status, with zero remaining entries awaiting internal proof. Key Features: Dual-Track Verification: Every entry is subjected to a rigorous dual-track methodology, converging an ontological derivation (based on group structure G = S4 × Z2^3) with an epistemological derivation (based on Relational Entropy Sq^rel). Comprehensive Scope: The register spans 8 scientific disciplines: Information Geometry, Particle Physics, Cosmology & Dark Sector, Ontology & Emergence, Fundamental Constants, Number Theory & Analysis, Foundations of Mathematics, and Algebra. Falsifiability & Transparency: Adhering to the core epistemic principle "Either we prove it, or we do not claim it," the document includes a dedicated "Shooting Range" section outlining 7 specific conditions (kill shots) under which the framework can be refuted. Classification: Entries are categorized into: P (Testable Predictions – 194 entries), SD (Structural Discoveries – 145 entries), B (Theoretical Bridges – 37 entries), and M (Meta/Audit checks – 14 entries). Status Overview (as of April 2026): Total Entries: 390 Validated (V): 318 (81.5%) – includes genuine predictions where the DOI timestamp precedes experimental results (e.g., ABC-17, ABC-42) and entries cross-referenced with 2026 experimental data. Awaiting Experiment (E): 72 (18.5%) Awaiting Proof (AP): 0 (0.0%) – All internal theoretical derivations for the current set are complete. Refuted (NOK): 0 (0.0%) Scientific Impact: The register catalogues the derivation of fundamental physical constants (e.g., $G_N$, $\alpha$, $m_H$), cosmological parameters ($\Omega_\Lambda$, $n_s$, $H_0$), and provides a unified resolution to long-standing mathematical paradoxes (Gödel, Russell, Banach-Tarski) through the lens of Groupoid-Relational Algebra (GRA) and the coherence operator (♡). The April edition incorporates latest refinements in information geometry and adjustments to dark sector interaction models.