Finite-nucleus-protected high-density extension of covariant density functionals constrained by multimessenger data

We construct a finite-nucleus-protected high-density extension of covariant density functionals by modifying only the isoscalar-vector channel outside the finite-nucleus calibration domain. The extension introduces three parameters controlling the strength, onset, and width of the high-density deformation, while the scalar and isovector channels are kept unchanged. A Bayesian analysis using heavy-ion flow constraints, massive-pulsar information, NICER mass-radius measurements, and the GW170817 tidal constraint shows that the original \ddme interaction is strongly disfavored relative to its protected high-density extension, with $\ln K=\ln(Z_{\rm ext}/Z_{\rm base})=26.67$, where $Z$ denotes the Bayesian evidence, after imposing a causal/stability filter on the reshaped EOS. In contrast, \ddpc serves as a reference functional for which the same extension is not required by the present data, giving $\ln K=-0.44$. The result supports the interpretation that the proposed extension is not an unconstrained phenomenological patch: Bayesian evidence selects it only when demanded by the combined high-density data, while finite-nucleus observables remain unchanged within numerical precision.