What question did this study set out to answer?

The aim is to explore the dual role of the rigidity constant epsilon in unifying vacuum geometry and matter dynamics.

January 23, 2026Open Access

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

Key Points

The aim is to explore the dual role of the rigidity constant epsilon in unifying vacuum geometry and matter dynamics.
Developed the PR-TAU 5.2.1 protocol to analyze epsilon's role.
Used a dual approach to link structural torsion and mass coupling.
Investigated thermodynamic implications of rigidity constant.
Epsilon is determined to be approximately 5.761 × 10^{-4}.
Identified a rigidity entropy that reflects a crystalline-like order in the universe.
Introduced a thermal tension tensor formalizing vacuum regulation.

Abstract

This paper details the theoretical framework of the PR-TAU 5. 2. 1 protocol, demonstrating that the rigidity constant 5. 761 10^-4 is the key to unifying vacuum geometry and matter dynamics. Through a dual approach, we establish that 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 ₈₉, formalizing the thermal regulation of the vacuum via the superluminal phase velocity.

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