Topological Constraints in a Discrete Vacuum Lattice: A Unified Approach to Multi-Scale Observational Anomalies

This work presents the Coherent Field Model (CFM) in a symmetry-locked framework, replacing arbitrary empirical parameters with geometric identities derived from a discrete vacuum lattice. By defining the recovery constant R as the leading-order topological residue of a Hopf-linked manifold projection (R = 1 - (2π)^(-4)), the model demonstrates internal consistency across five independent observational anomalies: the Muon g-2 residual, the Proton Charge Radius puzzle, the Lithium-7 abundance, the Hubble Tension, and the Pioneer Anomaly. The paper introduces a Topological Stiffness Tensor to extend the Einstein Field Equations, providing scale-dependent phenomenology where the vacuum's non-ideal recovery efficiency manifests in both subatomic and cosmological observations. Exploratory correspondences with the Baryon Acoustic Oscillation scale are highlighted, while limitations and pathways for rigorous foundational derivations are clearly delineated.