Holonomy Equivalence of Reduced Q5 Transport and Canonical Berry Transport

This Theorem establishes that the Q5 transport holonomy and the Berry holonomy of the canonical Bloch system are the same closed-loop invariant, not merely comparable representatives. Under the conditions that the reduced transport family is cyclic and nondegenerate, the induced Bloch loop is well-defined and closed, and adiabatic transport is defined on the eigenbundle: HolQ5 := ∮μ(Q)dλ = Hol_Berry = γ_Berry (mod 2π) The proof follows directly from T41: the rotational trace one-form μ(Q)dλ differs from the Berry connection only by an exact differential, which integrates to zero on a closed loop. The gauge-invariant holonomy lemma confirms that the loop integral is independent of admissible gauge transformations preserving the cyclic transport class. The distinction between the Q5 transport phase and geometric Berry phase is therefore one of representation, not of underlying invariant. Status: Gauge-invariant holonomy lemma exact, follows from exact-differential argument of T41. Holonomy equivalence exact at the closed-loop level, independent of gauge. Inherits the normalization condition required for the T41 connection-level identification. No additional assumptions introduced beyond T41. Dependencies: T39, T40, T41.