Cosmic Microwave Background Isotropy in a Two-Boundary Finite Universe: Exact Lapse Shell Solution, Coupled Light-Cone ISW Multipoles, and the PA-05 Subcritical Frontier Gate in Relativity of Matter

This work confronts the two-boundary finite-domain cosmography of Relativity of Matter (RM) with cosmic microwave background isotropy and spectral constraints. The manifested domain is bounded by an inner Ignition Core at r_c = 87.5 fm and an outer Silentium frontier at RΣ,0 = 55 Gly. Including the stresses of the global elastic sector and the zero-mode kinetic completion, the linear lapse equation yields the dynamical screening mass m²(T) = [3ρ_m(T) + 4u_γ(T) − 2P ³R(T)] / (4P), with a comoving screening range of approximately 12.18 Gly today and 95.06 Mpc at recombination. The observed CMB past light cone does not intersect the Silentium frontier for observers within 9.78 Gly of the centre, while the ordinary boundary Sachs-Wolfe imprint at last scattering is exponentially suppressed to approximately 2 × 10⁻¹⁴. The coupled lapse-matter perturbation system is derived from the quadratic RM action. On the clock-synchronized branch, δΣ ≡ νΣ − 1 = 0, the boundary-induced perturbation problem is homogeneous and the Silentium contribution to all ISW multipoles vanishes. For a deliberately forced non-zero boundary-clock departure, the integrated lapse equation separates two physical closures. In Branch A, the frontier flux is absorbed by the inner core, effectively requiring |δΣ| ≲ 10⁻⁴. In Branch B, the flux acts on the cosmological zero-mode equation. The exact zero-mean shell profile is then propagated through the complete dust perturbation system and projected on the past light cone. For Branch B, Planck quadrupole constraints give |δΣ,0| ≲ 0.27–1.4 for an observer at 100 Mpc and ≲ 0.028–0.15 at 1 Gly, depending on the assumed boundary history δΣ ∝ 1, a¹ᐟ², or a. Matter back-reaction reduces the lapse-only ISW signal by approximately 13–19%. The induced dipole is weaker and partly degenerate with the kinematic CMB dipole. Post-recombination photon perturbations are conservatively bounded using |δγ| ≤ 4|n|. Within this bracket, they modify the computed ISW kernels by at most 1.7%, establishing percent-level numerical robustness without claiming a complete collisionless Boltzmann hierarchy. The resulting bounds provide the CMB isotropy conditions that any viable RM frontier dynamics and cosmological expansion closure must satisfy.