Emergent de Sitter Expansion and Closed Topology from the Cosmic Fabric Model as an Open Thermodynamic System: Resolving the Negative Bulk Modulus Paradox

The Cosmic Fabric Model establishes a continuum-mechanics isomorphism to General Relativity by representing physical space as an elastic three-dimensional hyperplate embedded in a four-dimensional spatial bulk. Reproducing vacuum kinematics requires a vanishing P-wave modulus, which in turn implies a negative bulk modulus—an apparent thermodynamic instability in a closed system. This paradox is resolved by recasting the framework as an open system: the instability is not pathological but instead drives cosmic expansion. In this interpretation, the observable universe is a lower-energy solid formed through continuous solidification from a higher-dimensional precursor fluid. Using multiplicative kinematics from finite-growth mechanics, the model shows that solidification kinetics naturally introduce a rate-dependent bulk viscosity that regularizes the instability into steady expansion. The resulting state maintains a small residual elastic strain while the volume grows at a constant rate, yielding an exact de Sitter expansion for the vacuum sector, the counterpart of the cosmological constant of the standard fit. Because this growth law is local to each material element, large-scale homogeneity and isotropy are not assumed a priori; they emerge from a uniform initial solidification front and the marginal stability of the homogeneous expansion mode. Imposing local frame covariance at the open phase boundary prohibits observable lateral slip, which uniquely constrains the global geometry to a hyperspherical configuration. Observational constraints further exclude a bounded shell, implying a closed, centrosymmetric hypersphere. The open-system formulation also restores a well-posed description of global energy conservation. The framework makes five falsifiable predictions, including two decisive observational tests: a strictly closed spatial geometry and a dark-energy equation of state approaching w = −1 in the ideal-reservoir limit, with any deviations directly quantifying non-ideal behavior of the precursor fluid. These results are not adjustable; they follow directly from the governing assumptions and interfacial conditions, and thus render the model definitively testable. This preprint continues a line of work on the Cosmic Fabric Model published in Int. J. Mod. Phys. D 27, 1850083 (2018); 28, 1950096 (2019); and 28, 1950082 (2019), and in Rep. Adv. Phys. Sci. 2, 1850011 (2018).