A Vacuum-Driven Spherical Boundary Cosmology: Exact Junction-Condition Dynamics, Stability, and the Domain of Observational Viability

We construct a mathematically rigorous cosmological model in which the observable Universe is modeled as a finite, spherically symmetric fluid region bounded by a timelike hypersurface Sigma, embedded in an exterior Schwarzschild de Sitter vacuum. The boundary dynamics follow from the Darmois Israel junction conditions, yielding an effective equation of motion R double dot equals alpha over R squared plus O of R to the minus three, where alpha is an effective parameter encoding the surface stress energy of the boundary layer together with the exterior cosmological constant. We derive the shell conservation law for a general linear equation of state p equals w sigma, decompose alpha into its physical constituents (alpha surface, alpha mass, alpha Lambda), and present the exact implicit solution R of t, verified numerically to machine precision (less than 10 to the minus 14) via the analytic first integral. A complete linear stability analysis proves that radial perturbations are stable if and only if alpha is greater than zero.We subject the illustrative parameter choice Omega alpha approximately 0.09 used to visualize the model's observational sector to an explicit multi parameter sensitivity analysis, a Monte Carlo uncertainty propagation, and a domain of validity audit. This audit identifies an internal consistency requirement with direct observational consequences: for Omega alpha greater than zero the SBU expansion law becomes imaginary beyond z max equals one over Omega alpha, so the model cannot, in its present single shell form, be extended to recombination (z star approximately 1100) or to the z approximately 10 to 15 regime relevant to JWST early galaxy candidates. We then go beyond illustrative comparison and perform an explicit joint fit of Omega alpha and H0 to the real, binned Pantheon Type Ia supernova compilation and the DESI Data Release 1 baryon acoustic oscillation measurements, using exactly the same number of free parameters as a flat Lambda CDM fit to the same fifty data points. The result is decisive: the best fit SBU model gives chi squared over degrees of freedom equal to 8.19, versus 1.34 for Lambda CDM, a difference of delta chi squared approximately 329 that constitutes very strong evidence against the single shell, constant equation of state SBU model as a competitor to Lambda CDM by standard model selection criteria.Motivated by this result and by the domain of validity constraint, we construct and test a two component generalization that separates the interior mass and exterior Lambda contributions from the shell's own equation of state term. This removes the redshift ceiling entirely and fits the same real data comparably to Lambda CDM (delta AIC approximately 0.2), but we show, via a stability formula that reduces exactly to the original radial stability theorem in the appropriate limit, that every viable point in this extended parameter space is linearly unstable against radial perturbations at the present epoch. We then show that this instability is not a fundamental obstruction. Adding a second, small amplitude, rapidly decaying shell component restores linear stability while remaining valid to recombination and fitting real data at only a modest statistical cost (delta AIC approximately 3.8 relative to Lambda CDM), at the price of requiring an exotic, microphysically unmotivated equation of state for the stabilizing component.A systematic energy condition analysis of this stabilizing component shows that its exoticism is structural rather than a matter of tuning. It must violate the null energy condition, since every alternative respecting the null energy condition either forces the exterior cosmological constant to be negative (contradicting the model's own assumptions) or destroys the domain of validity fix almost immediately. This sharpens the open question of the shell's microphysical origin into a specific, falsifiable requirement, namely bounded null energy condition violation of a particular magnitude and profile, of the kind subject to established quantum inequality constraints, rather than leaving it unconstrained. This complete arc, from decisive exclusion through a domain of validity fix that trades one problem for another to an explicit resolution with a precisely characterized remaining obstruction, is reported as a central, falsifiable body of findings of this work, together with the model's rigorously established mathematical core, a dedicated Scientific and Technical Risk Assessment, and a phased Roadmap, Experimental Validation, and Falsifiability program. The heuristic reinterpretation of the Cosmic Microwave Background through a boundary layer framework is retained strictly as an unproven conjecture, explicitly separated from the derived background dynamics.