The $\mathcal{M}$-$\mathcal{A}$ Information Channel: A Quantum-Theoretic Characterization of the Information Interface in Higher-Dimensional Embedding Frameworks

We characterize, in the language of quantum channel theory, the information interface between a four-dimensional observable manifold $\mathcal M$ and a higher-dimensional substratum $\mathcal A$ proposed in the Absolute Frame Theory. We show that the routing term of the interaction Lagrangian induces a completely positive trace-preserving map $\Phi_{\mathcal{M}\to \mathcal{A}}: \mathcal{B}(H_{\mathcal M}) \to \mathcal{B}(H_{\mathcal A})$ whose effective output dimension is fixed by the action quantization axiom. By computing the four standard capacities of this channel: (i) quantum capacity $Q$; (ii) classical capacity $C$; (iii) entanglement-assisted classical capacity $C_E$; and (iv) private classical capacity $P$, we show that each carries distinct physical interpretation: $Q$ bounds the number of coherent pointers that can be sustained simultaneously, $C$ bounds the rate of classical information transmissible from $\mathcal M$ to $\mathcal A$, $C_E - C$ quantifies the structural cost imposed by the thermodynamic isolation axiom, and $P$ relates to the recoverability of information once transferred. We discuss the framework as a quantum-theoretic instantiation of a multidimensional informational substratum, a notion structurally related to the historical concept of aether but free of the empirical constraints that refuted its classical version. We show that the channel framework yields a natural resolution of the black hole information paradox: information transferred through $\Phi_{\mathcal{M}\to \mathcal{A}}$ to the substratum is not destroyed by horizon formation, only made operationally inaccessible to observers confined to $\mathcal M$. We discuss connections with holographic frameworks, implications for the macroscopic-classical transition, and the experimental signatures accessible through current quantum information platforms.