**Authors:** Supplementary analysis for Roland (2026), MSCF v2.1.7
**Abstract.** We close the three structural gaps identified in the Matter-Space Coupling Framework: (A) a covariant derivation of the interior resistance factor directly from the MSCF effective action $S_{\text{MSCF}}$, eliminating the need for Axiom 6 specialization as an independent closure; (B) a quantum field theory analysis of the ghost window establishing finite, bounded particle production through a transient-ghost Bogoliubov calculation; (C) a complete stability analysis across all equation-of-state transitions in cosmological history. These results upgrade the interior barrier from "axiom-motivated" to "action-derived," establish quantum consistency of the bounce, and prove that no epoch in the physical evolution of the universe passes through a genuinely unstable regime.
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The MSCF effective action (Eq. 20 of the main text) is:
$$S_{\text{MSCF}} = \int d^4x \sqrt{-g} \left[ \frac{R}{16\pi G} - V(\chi) + \lambda(g^{\mu\nu}\partial_\mu\phi\partial_\nu\phi + 1) \right] + S_m$$
with $V(\chi) = \alpha\chi^4$ and $\alpha = 1/(1728\pi^2 G^2 \rho_{\text{crit}})$.
In the cosmological sector (FLRW), this action produces the modified Friedmann equation $H^2 = (8\pi G/3)\rho(1 - \rho/\rho_{\text{crit}})$. The interior of a Schwarzschild black hole is *also* a cosmological spacetime — specifically, a Kantowski-Sachs (KS) anisotropic cosmology. The same action, reduced to KS symmetry, must therefore produce modified interior dynamics. We show that these modified dynamics contain the resistance factor $\Omega(x_g)$ as a derived consequence.
The Schwarzschild interior admits the Kantowski-Sachs form:
$$ds^2 = -d\tau^2 + A^2(\tau)\,dx^2 + B^2(\tau)\,d\Omega^2$$
where $\tau$ is proper time along the infalling causal flow, $B(\tau) = r(\tau)$ is the areal radius (decreasing from $r_s$ at the horizon to 0 at the classical singularity), and $A(\tau)$ encodes the stretching along the formerly timelike direction. For standard Schwarzschild:
$$B(\tau) = r_s\left(\frac{3}{2}\frac{c\,\tau_{\text{sing}} - c\,\tau}{r_s}\right)^{2/3}, \quad A^2(\tau) = \frac{r_s}{B(\tau)} - 1$$
The mimetic field $\phi = \tau$ satisfies $g^{\mu\nu}\partial_\mu\phi\partial_\nu\phi = g^{\tau\tau} = -1$ identically. The causal flow vector is $n^\mu = \delta^\mu_\tau$.
The expansion scalar of the causal flow congruence is:
$$\chi = \nabla_\mu n^\mu = \frac{\dot{A}}{A} + \frac{2\dot{B}}{B} \equiv H_A + 2H_B$$