The Vacuum Rigidity Constant ϵ: Internal Consistency of the QRD Lattice and Resolution of the Proton Radius Puzzle

This paper presents the theoretical derivation and validation of the vacuum rigidity constant ε ≈ 5.761 × 10⁻⁴ within the framework of the PR-TAU 5.2.1 protocol. We demonstrate that ε is not an empirical fit but a unique consistency solution linking the Quantum Relational Dynamic (QRD) lattice topology to fundamental constants α, mₑ, and mₚ. By introducing the Mass-Energy-Rigidity equivalence and the Shannon-Tau information limit, we provide a unified solution to the proton radius anomaly and a new framework for cosmological expansion through torsion relaxation.