Spectral-Propagator Interpretation of the Transported Phase Mismatch

This Theorem shows that the propagated rotational mismatch between the protected and dressed transport channels is governed by the same spectral split (p − ω) that drives the T15 phase defect, read through a distinct propagator-level extraction. The protected channel has generator G₋ = pJ (pure antisymmetric rotor); the dressed channel has G₊ = pJ + 2aσ_z (antisymmetric core plus traceless symmetric deformation). The dressed propagator satisfies G₊² = −ω²I where ω = √(p² − 4a²), shifting the effective transport frequency from p to ω. The normalized propagated mismatch is: Δ̂μ(η) = −i[(p/ω)sin(ηω) − sin(ηp)] = −i(p − ω)Ξ(η,p,a) Five corollaries are established: shared common antisymmetric rotational carrier; generator-level invisibility of the symmetric deformation (Tr(SR) = 0 for symmetric S, antisymmetric R); exact factorization through (p − ω); generic visibility with isolated blind times characterized by p·sin(ηω) = ω·sin(ηp); small-deformation asymptotics of blind times governed by tan(ηp) = ηp; and discrete angular accumulation T_rot^k = cos(kθ)I + sin(kθ)A. T30 does not replace T15. T15 gives the exact phase defect. T30 gives the spectral-propagator interpretation of its rotational manifestation through a different readout of the same core. Status: Corollaries 30.1–30.5 solid by direct algebraic computation. All results are conditional on T15 architecture (identification of p and a) and T16/T17/T20 framework (Δφ(τ) = μ chain). Six-segment kernel expansion of Ξ in terms of [M_n, D_n] remains open. Dependencies: T15, T16, T17, T18, T19, T20, T23, T24, T25, T26, T27, T28, T29.