On the quantum separability of qubit registers

I show that the bipartite separability of a pure qubit state hinges critically on the combinatorial structure of its computational-basis support. Boolean cube geometry is used to introduce a taxonomy that distinguishes support-guaranteed separability from cases in which entanglement depends on probability amplitudes. I provide closed-form support counts, identify forbidden configurations that enforce multipartite entanglement, and show how these results can enable fast entanglement diagnostics in quantum circuits. This framework offers immediate utility in classical simulation, entanglement-aware circuit design, and quantum error-correcting code analysis. This establishes support geometry as a practical and scalable tool for understanding entanglement in quantum information processing.