Cosmic Elastic Theory III: Formal Derivation of Tension Decay and the Emergence of Kinematic Acceleration

The Cosmic Elastic Theory (CET) models the physical spacetime as an isotensive field: a structural regime that maintains constant tension through a continuous process of tension restoration. This field is not a fluid, not a mechanical medium, and does not introduce new fundamental parameters; rather, it provides a processual reinterpretation of quantities already present in standard physics. Dissipation arises whenever an energetic excitation interacts with the restoring dynamics of this isotensive field. We show that phenomena traditionally treated as unrelated — the microscopic decay of low-energy excitations, the geometric elongation responsible for cosmological redshift, and the curvature response associated with gravitation — all follow the same universal dissipative saturation law. Across all regimes, the dissipation rate decreases as the excitation energy approaches the isotensive baseline, producing a characteristic saturation plateau. This functional form is reconstructed both from microscopic decay data and from cosmological luminosity–distance relations (Pantheon, CEERS/JWST), indicating a scale-invariant dissipative mechanism. To formalize this universality, we derive the complex CET Lagrangian. Its real sector yields the reversible curvature dynamics, while its imaginary sector generates the first-order dissipative law. The resulting complex Euler–Lagrange equations recover the observed saturation curve without introducing additional free parameters, establishing a single variational origin for dissipation, curvature, and cosmological expansion. We further analyze the transition zone, where the dissipative channel reaches its processual limit and a change of regime in the geometric response emerges. This region explains the residual modulation of redshift along the line of sight and connects the microscopic dissipation law to the macroscopic behavior of the Hubble flow. Thus, CET provides a unified, scale-invariant dissipative framework in which microscopic relaxation, gravitational curvature, and cosmic expansion arise as different expressions of the same underlying processual mechanism.