Extraction of the Rotational Phase Coefficient

This Theorem derives the canonical extraction formula for the rotational phase coefficient μ from the terminal retained residue Ω_term. Given the transported collapsed object Q⊥ = P⊥ · Ψ · Π_col(Π_A · Ω_term · Π_A) · Ψ⁻¹ · P⊥ on the transverse phase plane P⊥ = span{u₂, u₄}, three equivalent extraction formulas are established: Primary: μ = ½ Tr(Q⊥ · R), verified by direct matrix computation showing Tr(I·R) = Tr(σ_z·R) = Tr(σ_x·R) = 0 and Tr(R·R) = 2. Antisymmetric off-diagonal: μ = (1/2i)(⟨u₂|Q⊥|u₄⟩ − ⟨u₄|Q⊥|u₂⟩), which holds for all γ since the symmetric contribution cancels. Pinned entry: The antisymmetric part of the (u₂, u₄) entry of the transported collapsed object equals iμ. The identity μ = Δφ(τ) is confirmed within the frozen T20/T26 normalization bridge. The explicit six-segment kernel expansion of μ in terms of minimal kernel generators is identified as the next open frontier. Status: Extraction formula solid by direct matrix computation. Identity μ = Δφ(τ) solid within T20/T26 normalization bridge. Six-segment kernel expansion not yet derived. Dependencies: T15, T20, T23, T26.