Abstract: The persistent H0 and growth tensions in ΛCDM cosmology motivate a re-examination of the expansion paradigm’s foundational assumptions. The Dead Universe Theory (DUT) proposes an alternative in which observable galaxy separation is not due to metric expansion but results from irreversible, entropy-driven deformation of a viscoelastic spacetime continuum undergoing global gravitational retraction. This work formalizes DUT within a relativistic continuum-mechanics framework. We derive the entropic deformation tensor Ξ_μν from a variational principle and incorporate it into the Einstein field equations as G_μν + Ξ_μν = 8πG T_μν, replacing the cosmological constant with a dynamical, entropy-sourced curvature. A key prediction follows from the asymptotic stability analysis of the resulting system: a unique, non-adjustable growth index γ = (√5 − 1)/2 ≈ 0.6180339887…, the signature of the theory’s Unique Vacuum Attractor. Consequently, a high-precision measurement of the growth index consistent with γ ≈ 0.55 at the <0.01 level would strongly falsify DUT. This formulation provides a falsifiable, thermodynamically grounded geometric description of cosmic dynamics, directly linking late-time acceleration-like phenomena to residual entropy gradients of a “dead” gravitational substrate. Numerical validation of the attractor is available in the mission-grade inference pipeline (repository and preprint DOI provided in the Data/Code Availability statement). Keywords: Modified Gravity, Thermodynamic Gravity, Cosmological Tensions, Entropic Cosmology, Viscoelastic Spacetime, Growth Index. Footnote All equations and numerical predictions presented in this work are fully reproducible using the publicly available computational pipeline. The complete implementation, datasets, and inference routines are accessible in the open-source repository: https://github.com/ExtractoDAO/DUT-CMB-Scientific-Engine-3.0-NASA-ESA-Production-Grade The mathematical derivation of the theoretical framework is detailed in the companion preprint: DOI 10.20944/preprints202511.2044.v1.