Complement-Paired Bulk-Mediated Phase Holonomy and Forced Middle-Projector Structure in the Fibre Transport Architecture on Q5

We study the complement-paired bulk-mediated extension of the fibre transport architecture arising from the closure-parity and fibrewise effective dynamics framework on the five-dimensional hypercube Q5Q₅Q5. Starting from the single-fibre defect generator, we pass to a parity-adapted basis in which the dynamics separates into independent transport and asymmetry phase planes. We prove that in a complement-paired reduction with shared bulk mediation, crossing compatibility forces a strict separation between the transport and asymmetry sectors. On the crossing-even transport plane, we show that nontrivial bulk-mediated coupling together with preservation of an exact inherited transport rotor forces the effective correction to be nonzero, singular, symmetric, and rank one. A direct matrix argument then establishes that the inherited rotor condition is equivalent to annihilation of the endpoint line, uniquely forcing the correction to take the form A=ρ ∣M+⟩⟨M+∣A = \, |M_+ M_+|A=ρ∣M+⟩⟨M+∣. We further show that this structure is perturbatively rigid: the middle-projector branch is the unique infinitesimal deformation preserving the inherited transport channel. The paired transport holonomy then decomposes into a protected channel with exact inherited phase e±iηpe^ i pe±iηp and a bulk-dressed complementary channel. The resulting spectral mismatch defines an exact relative phase defect Δφ (τ) =4βτ2 (p−p2−4a2), () = 4² (p - p² - 4a²), Δφ (τ) =4βτ2 (p−p2−4a2), which is invariant under fibre exchange but irreducible to independent single-fibre contributions. We identify this structure as nonfactorizable complementary holonomy: a shared phase constraint that arises only at the paired level. The bulk mediator does not act as a transport channel, but as a constraint-enforcing mechanism. All results are established within a minimal complement-paired bulk-mediated model and are explicitly classified by epistemic status and are structural and algebraic within a minimal complement-paired bulk-mediated model. This work develops Theorem 15 in the Q5 framework. See associated Zenodo records for Theorems 7, 8, 12, and 14.