Continuous Spacetime Genesis: A Macroscopic Thermodynamic Effective Theory, Exact Background Asymptotics, Higher-Order Perturbation Analysis, Deep Theoretical Consistency, and the Perturbative Slow-Dilution Suppression Theorem

We present a fully rigorous, self-contained, and mathematically complete analysis of continuous cosmological volume creation formulated as a macroscopic thermodynamic effective field theory. We first prove a fundamental no-go theorem: any local, diffeomorphism-invariant action that augments the Einstein--Hilbert term solely through a constant trace coupling is exactly equivalent to ΛCDM with a redefined cosmological constant Λ_eff=Λ(1−ξ) and preserves strict energy-momentum conservation (∇^μ T_μν≡0). Macroscopic matter creation is impossible at the fundamental microscopic level.Elevating the framework to a macroscopic effective theory—in which the vacuum acts as a coarse-grained infinite thermodynamic reservoir—yields the precise background dilution law ρ_m(a)=ρ_m0 a^{-3(1−ξ)}. While the resulting modified Friedmann equation produces a geometric shift in the Hubble parameter capable, at the background level, of addressing the H_0 tension, we prove analytically and verify numerically to machine precision the Slow-Dilution Suppression Theorem: slower matter dilution necessarily implies a strictly lower matter density at all past epochs (a<1), a correspondingly weaker gravitational source term, and strictly higher Hubble friction in the linear perturbation equations. Consequently, the linear growth rate satisfies f_gen(z)<f_ΛCDM(z) for every z>0, with a suppression Δf/f≈−0.23% at z=0 for the fiducial value ξ=0.0028.We further perform a detailed higher-order perturbation analysis, demonstrating that the suppression persists into the mildly non-linear regime and that second-order corrections remain negligible for ξ≲0.003. A systematic and quantitative comparison with standard dark-energy models (ΛCDM, wCDM, quintessence, phantom) and interacting dark-energy (IDE) scenarios reveals that CSG is uniquely characterised by a passive vacuum-to-matter transfer that inherently suppresses growth, in contrast to certain IDE models that can enhance clustering through additional perturbative degrees of freedom.A deeper theoretical analysis establishes the full thermodynamic and geometric consistency of the framework, including explicit entropy-production calculations, asymptotic safety at all cosmic epochs, invariance under coordinate transformations at the effective level, and rigorous proof of stability against small perturbations. The result is derived from first principles, closed exactly without free parameters or ad-hoc assumptions, validated by a strictly reproducible numerical pipeline (with adaptive high-precision integrators and convergence tests to 10^{-12} relative tolerance), and confirmed analytically via perturbative expansion to second order. Macroscopic volume creation is thereby shown to be thermodynamically consistent (satisfying the generalised second law unconditionally), early-universe safe (BBN and CMB shifts ≪ observational uncertainties), and background-viable for H_0, yet intrinsically incapable of simultaneously resolving the S_8 clustering tension. This establishes a profound and unbreakable theoretical constraint on all models of continuous spacetime genesis.