Canonical Bloch Hamiltonian and Berry Connection of Q5 Transport

This Theorem shows that the geometric structure of T40 arises canonically from the reduced transport operator itself, not from an external construction. Four results are established. The cyclic reduced physical operator Q⊥ (λ) = α (λ) I + β (λ) σₓ + γ (λ) σᵦ + μ (λ) R with R = −σᵧ defines a canonical two-state Bloch Hamiltonian Hgeom (λ) = β (λ) σₓ − μ (λ) σᵧ + γ (λ) σᵦ with Bloch vector h (λ) = (β (λ), −μ (λ), γ (λ) ). The rotational trace functional μ (Q) = ½Tr (QR) selects the coefficient of R = −σᵧ and isolates the component generating infinitesimal azimuthal rotations of the Bloch vector, μ (Q) dλ is a one-form proportional to the infinitesimal azimuthal displacement. Under adiabatic transport on a closed cycle with h (λ) ≠ 0, the Berry phase is γBerry = −½Ωĥ. The rotational trace one-form satisfies: μ (Q) dλ = ½ (1 − cosΘ (λ) ) ∂_λΦ (λ) dλ + df (λ) differing from the Berry connection only by an exact differential, so for any closed cycle ∮μ (Q) dλ = γBerry. Under the normalization equating the rotational trace functional with the Berry connection: μₒbs = γBerry. The observable phase is not merely realizable as a geometric phase; it is intrinsically the Berry phase of the canonical two-state system determined by the same reduced operator family. Status: Canonical Bloch Hamiltonian construction exact. Rotational trace as azimuthal generator exact via Pauli trace identities. Berry phase formula for two-level systems is a standard result. Connection-level identification is solid, rotational trace one-form differs from Berry connection by exact differential, which vanishes on closed cycles. Identification μₒbs = γBerry holds under normalization condition equating rotational trace functional with Berry connection — natural but not yet derived from Q5 first principles. Holonomy-level independence from normalization is addressed in T42. Dependencies: T39, T40.