Acceleration Without Dark Energy, Priced: The Instability Claim Through the Correspondence Gate

Prices Alexander, Temple & Vogler's radial-instability claim (Proc. R. Soc. A 482:20250912: pressureless k=0 Friedmann locally unstable at the Big Bang; generic underdense radial perturbations evolve into a family admitting accelerations without a cosmological constant or dark energy) through the consistency gate of Ling, Yang, Yu & Zhang's two-way correspondence (arXiv:2611.02358) between static vacuum geometries and modified Friedmann dynamics, with its universal restriction on spatial-curvature dependence. The dynamics inventory of the instability claim: GR's own k=0 Friedmann background, unmodified Einstein-Euler evolution, and no modified Friedmann dynamics proposed anywhere — so the gate passes vacuously, and the vacuity is the priced fact: the claim is classified, definitively, as an initial-data/inhomogeneity claim inside unmodified GR, not a dynamics claim. Against the house record: the bounce line's homogeneous backgrounds are neither used nor threatened (no join, printed as no join), and the vacuum file is unmoved — the claim produces no rho_Lambda and the packet spends no solve. Its genericity and magnitude burdens stand open as its authors left them. DERIVED-INDEPENDENT. Quantum gravity NOT SOLVED; vacuum catastrophe NOT SOLVED.