Duality of the ϵ Constant: Consistency Between Vacuum Structure and Matter Dynamics

This paper details the theoretical framework of the PR-TAU 5.2.1 protocol, demonstrating that the rigidity constant ε ≈ 5.761 × 10⁻⁴ is the key to unifying vacuum geometry and matter dynamics. Through a dual approach, we establish that ε is both the expression of the structural torsion deficit of the Quantum Relational Dynamic (QRD) lattice and the coupling mediator between leptonic and baryonic masses. This study extends the duality to thermodynamic consequences, revealing a rigidity entropy S_ that maintains the universe in a crystalline-like quasi-order. Finally, we introduce the thermal tension tensor Θᵢⱼ, formalizing the thermal regulation of the vacuum via the superluminal phase velocity .