The Causal Topology Vacuum Model (CTVM) proposes that only bipartite (EPR-type) vacuum entanglement gravitates, while the irreducible multipartite (non-EPR) entanglement of the quantum vacuum is gravitationally inert. Previous formulations stated this sector-selection principle and its consequences as a system of six axioms (S1—S3, T1—T3). We show that all six axioms can be derived from standard ingredients of algebraic quantum field theory: the Wightman axioms, microcausality, the split property, the nuclearity condition, the Bisognano—Wichmann theorem, and the bit-thread (max-flow/min-cut) representation of holographic entanglement entropy. The derivation proceeds by constructing a canonical vacuum response matroid from the harvested correlation matrix of Unruh—DeWitt detectors coupled to the QFT vacuum. Microcausality forces a direct-sum decomposition of this matroid into gravitating and topological sectors. The split property identifies the gravitating sector with the image of a conditional expectation onto the intermediate type-I factor. The nuclearity condition guarantees area-scaling of the boundary rank and the existence of protected boundary generators. The Freedman—Headrick bit-thread theorem bridges matroid connectivity to Ryu—Takayanagi entanglement entropy, closing the final gap. No new physics beyond standard QFT is invoked. The CTVM is thereby established as a theorem of algebraic quantum field theory rather than a conjectural framework.