Cosmic Expansion in Relativity of Matter: Universal Constitutive Volume Creation, PA–05 Cadence Trigger, and Smooth Volume Turnaround

We present the consolidated formulation (Version 8.7) of the cosmic-expansion programme in Relativity of Matter (RM), fully aligned with the companion non-singular Black-Core theory (Version 12.5, DOI: 10.5281/zenodo.23614337), the homogeneous bulk closure (Version 5, DOI: 10.5281/zenodo.22791787), and the finite-domain CMB isotropy analysis (Version 5.0, DOI: 10.5281/zenodo.23887664). Key results established in this work:1. Silentium Boundary Theorem & Postulate B Coherence: We establish the spatial Dirichlet variational completion of the three-curvature action against Silentium, prove its exact Young–Laplace coherence with Global Elasticity Postulate B on a finite domain (λ_z >= R_Σ/2, x < 1.92), and derive the differentiated homogeneous expansion identity (DYN–EXACT) together with the DeWitt zero-mode supermetric target κ_kin = 9(λ_0 − 1/3) and G_cosmo/G = 6/κ_kin = 2/(3λ_0 − 1).2. Orthogonal Zero-Mode Projector & Global Closure (G0–CAN): Using the finite-k CLG–1 scalar reduction, we prove an exact Dirac rank loss at k = 0 (det Ω_SC ∝ k^20) and establish via the finite-domain projector theorem (SU–PROJ, H = H_0 ⊕ H_⊥) that the local kinetic-conformal sector (λ_local = 1/3 for k ≠ 0) and the homogeneous expansion mode e = ln(V_g/V_ref) (δe_k = 0 for k ≠ 0) act on orthogonal subspaces. We formulate the minimal global-volume kinetic completion S_G0[η] = −η (2P / 3c_Æ^2) ∫ (V_g / N̄) ė^2 dT, yielding κ_kin = 6η and G_cosmo = G/η. The modern BBN bound G_BBN/G_0 = 0.99 (+0.06 / −0.05) constrains 5.71 <= κ_kin <= 6.38 (0.952 <= η <= 1.063), while the GR-normalized closure postulate η = 1 yields κ_kin = 6, λ_0 = 1, and G_cosmo = G without introducing any local scalar ghost (G0–STAB) and ensuring canonically regular passage through H = 0 (G0–TURN).3. Action-Derived Finite-k Growth & Background Reconstruction: Eliminating the elastic stock between F2 and DYN–EXACT yields the background-screening relation κ_kin (P/c_Æ^2) Ḣ = P (3)R − (3/2)ρ_m − 2u_γ + 2P/λ_z^2 (BG–H). Incorporating the quadratic-action CMB audit, the expanding-background lapse mass m_bg^2 = λ_z^-2 − κ_kin Ḣ/(2c_Æ^2) and the exact constrained scalar system (GRW–EX) supersede the former quasi-Newtonian screened-G law, recovering the local Newton constant G on survey scales with O[(a m_bg/k)^2] corrections.4. Universal Constitutive Volume Creation (UC–1) & PA–05 Cadence Trigger: We separate the mechanical frontier surface work μ_∂^(z) from the universal State-Æ volume-creation density U_∂ = P / ℓ_*^2 (k_Æ = ℓ_*^2 / P), yielding the strictly subluminal radiative frontier speed root β_∂ (PA05–V / RAD–V). We construct the gauge-reduced EM–phase Hessian from the minimal cadence-phase action N_γ = N χ_γ(q) (CAD–A), proving rank(C) <= 1 and deriving the basis-invariant Schur-complement Exclusion discriminant X_EM = 2u_γ s_A (K_ϕ^-1)^AB s_B = 1 at marginal rank loss, together with the cubic soft-mode closure g_3 = u_γ,c (CAD–G3).5. Two-Boundary Misner–Sharp Shell Identity & Black-Core Return Ledger: We formulate the exact shell identity (GH–PG–2) between the inner Ignition Core and the outer Silentium frontier, refuting Painlevé–Gullstrand shift rescues of the Gauss-compactness bound. For the astrophysical Black-Core population, we separate the geometric State-Æ volume V_Æ from the constitutive State-E stock V_E, derive the accretion-weighted M^3 continuum drain law Γ_drain (with Γ_drain / 3H V_Æ <= 10^-29 today), and establish the smooth physical-volume turnaround criteria (BAL–1 to BAL–6) and the quasi-static Sturm–Liouville reduction for the interface cadence ratio N_b/N̄.