This paper establishes that ordered three-fibre propagator loops built from the mediated fibre Hamiltonians on Q₅ are route-dependent and entanglement-generating. The central result is that two distinct loop orderings W₁₂₃ and W₁₃₂ differ by 4Γβτ²M at leading order, where M is a non-separable operator on the canonical fibre bipartition ℂ²⊗ℂ². The entanglement generator M is shown to coincide with the oriented type-(1,2) defect-plane operator D₍₁,₂₎, and is further identified as the fibre restriction of a global operator on the full Q₅ Hilbert space, establishing its geometric origin. All results vanish in the shell-linear limit β=0, require no free parameters beyond those fixed in Theorems 7 and 8, and are classified epistemically as proven, conditional, or not yet established.
Craig Edwin Holdway (Mon,) studied this question.