Duality of the Constant ϵ: Consistency between Vacuum Structure and Matter Dynamics (Extended Version)

This paper outlines the theoretical framework of the PR-TAU 5.2.1 protocol, demonstrating that the rigidity constant ϵ ≈ 5.761 × 10-4 constitutes the key to unification between vacuum geometry and matter dynamics. Through a dual approach, we establish that ϵ is simultaneously the expression of the structural torsion defect of the Dynamic Relational Quanta (DRQ) lattice and the mediator of forces coupling leptonic and baryonic masses. The study extends this duality to thermodynamic consequences, revealing a rigidity entropy S TAU that maintains the universe in a state of crystalline quasi-order. Finally, we introduce the thermal tension tensor Θ ij , formalizing the thermal regulation of the vacuum by the superluminal phase velocity v OTA. This model offers a resolution to current metrological anomalies while paving the way for topological engineering of space-time.