Continuous Spacetime Genesis: A Geometrically Motivated Covariant Framework for Volume Creation, Thermodynamic Consistency, and Specific Perturbative Signatures

We present a fully covariant, action-derived framework for cosmological volume creation. By introducing a minimal trace modification to the Einstein--Hilbert action (ℒ_𝒢 = 2ξ ρ_Λ), we derive a well-defined Spacetime Genesis source tensor 𝒢_μν. While mathematically isomorphic at the unperturbed background level to specific Running Vacuum Models (RVM), the fundamental physical distinction of our approach emerges decisively in the perturbation sector. The action derivation ensures intrinsic Diffeomorphism Invariance, inherently mandating a non-clustering vacuum (δρ_Λ ≡ 0) without resorting to the phenomenological sound-speed ansätze (c_{s,Λ}²) typically required to close the Euler-continuity hierarchy. We analytically establish the asymptotic safety of this framework; the genesis contribution scales as 𝒪(a^{3(1-ξ)}), ensuring negligible shifts (≲ 0.3%) in the CMB acoustic sound horizon (r_s) and pristine preservation of BBN bounds. Utilizing a compressed Gaussian likelihood over Planck 2018 and DESI 2024 BAO data as a preliminary proof-of-concept, Bayesian inference recovers a genesis coupling of ξ = 0.0028 ± 0.0004 (95% C.I.). This organically resolves the background H_0 tension while satisfying the Second Law of Thermodynamics. By solving the modified Newtonian-gauge perturbation ODEs, we predict a specific ∼ 3-4% enhancement in the linear growth rate f(z) at z ∼ 1. We provide the explicit analytical roadmap required to implement this uniquely parameter-free cosmic friction reduction into full Einstein-Boltzmann solvers (e.g., CLASS/CAMB) for advanced cross-validation against Stage-IV full-shape BAO and σ_8 structure formation datasets.