The bipartite hinge of the minimal subfactor

The index-two subfactor carries a bipartite boundary: one side is the discrete, timeless skeleton (companion paper I); the other is the temporal, contingent sector where the modular flow acts non-trivially. This paper identifies that boundary precisely as the fusion/braiding divide of the modular tensor category completion. The boundary is sharp: the Ising fusion category admits exactly eight unitary braided completions (the Ising modular tensor categories), and their classification shows the residual freedom is a single irreducible binary — the central charge c = 1/2 versus c = 7/2 — which the discrete skeleton cannot fix. This binary is the one-bit that lives at the hinge. All scaffolding (the realization of the conformal net, modular = geometric via Bisognano–Wichmann, the sixteenfold way) is imported and verified at source. This is companion paper II of a quartet.