The Geometric Identity of Gravity: Unification and Solution to the Lepton Anomalous Magnetic Moments

This paper presents an advanced Enhanced Energy Wave Theory (EWT) that derives the Gravitational Constant (G), the Fine-Structure Constant (), and the lepton anomalous magnetic moments (aₗ) from a single, unified Geometric Identity. By modeling the vacuum as a discrete Body-Centered Cubic (BCC) lattice, the framework replaces the 26+ empirical parameters of the Standard Model with a single structural modulator (|M|) derived from the internal wave geometry of the lepton soliton. Key Achievements and Physical Mechanisms: Geometric Compression and Energy Scaling: The model establishes a causal mechanism where the soliton’s internal energy follows an E r⁵ identity, while the volumetric displacement of the surrounding Elastic Medium (EMC) follows V r³. The factor |M| acts as the universal modulator that reconciles these scaling laws, deriving G as a precise, -independent property rooted in the electron's fundamental properties. Recursive Nodal Integration (The "Onion Model"): A central breakthrough is the derivation of a recursive formula for the Anomalous Magnetic Moments (AMM) of all charged leptons (e, , ). Instead of mass-dependent perturbative loops, the model utilizes a hierarchical integration of nested nodal shells. This deterministic approach recovers experimental benchmarks for the entire lepton family, including a high-stability prediction for the Tau lepton anomaly. Unification of Constants: For the first time, a single geometric stiffness parameter provides 10-digit precise solutions for G, , and aₗ. This establishes a definitive link between gravitational strength and subatomic spin anomalies, demonstrating that both are emergent manifestations of the vacuum's elastic geometry. Predictive Superiority: The framework demonstrates an unprecedented parameter economy. By aggregating the predictive gains across gravitational and electromagnetic domains, the model provides a quantitative improvement in predictive power that significantly exceeds current Standard Model benchmarks. Testable Predictions and Falsifiability: Breakdown of Invariance (Low-Field Artefact): The model posits that the observed invariance of G is a low-field artefact of a dynamic geometric equilibrium. It predicts measurable deviations (G₄₅₅ G) in environments of extreme magnetic flux or macroscopic quantum coherence (e. g. , Bose-Einstein Condensates), where the r⁵ vs r³ equilibrium is bypassed. Recursive Lepton Scaling: The model issues a definitive test for the universality of its recursive scaling. Future high-precision measurements of the Tau lepton anomaly will serve as a critical discriminant between EWT’s structural determinism and the Standard Model's perturbative calibrations. Experimental Alignment: Predicted detection limits for gravitational shifts (G) align with state-of-the-art quantum sensors and atom interferometry (e. g. , MAGIS-100), ensuring full scientific falsifiability.