
T104 computes the explicit observable interference correction generated by Q5 leakage-return transport. T101 established the admissible structure of a hidden-half correction term but left the correction function unspecified. T102 derived the leakage-return operator \(C=L^\dagger BL\), and T103 identified the leakage generator \(B=i\mathcal{A}_L\) from the explicit Q5 leakage adjacency. T104 completes the chain by directly computing the resulting interference correction. The central structural result is that first-order mixing vanishes identically: \[L^\dagger B L = 0.\] This occurs because the leakage generator transports amplitude through the helical chain \[e_3 \leftrightarrow e_4 \leftrightarrow e_5,\] while the observable return map extracts only the boundary modes \(e_3\) and \(e_5\). A single application of \(B\) moves amplitude into the middle gate-null mode \(e_4\), preventing any first-order return contribution. Observable mixing therefore begins only at second order. The first nontrivial return operator is \[C_2=L^\dagger B^2 L=-\frac{1}{80}(I-i\sigma_y),\] which is Hermitian and generates the leading observable correction. Applying the T100 renormalization procedure yields normalized probability shifts \[\Delta_+=-\frac{\sin\phi\,\sin(4\theta)}{160},\qquad\Delta_-=+\frac{\sin\phi\,\sin(4\theta)}{160},\] with \[\Delta_+ + \Delta_- = 0.\] The resulting observable probabilities are \[P_+^{\mathrm{obs}}=\cos^2\theta-\frac{\eta^2}{2}\frac{\sin\phi\,\sin(4\theta)}{160}+O(\eta^3),\] \[P_-^{\mathrm{obs}}=\sin^2\theta+\frac{\eta^2}{2}\frac{\sin\phi\,\sin(4\theta)}{160}+O(\eta^3).\] The correction is therefore second order in the leakage coupling and possesses a characteristic angular envelope \(\sin(4\theta)\). This replaces the earlier minimal placeholder structure of T101 and introduces a richer node pattern, with nulls at \[\theta = 0,\quad \frac{\pi}{4},\quad \frac{\pi}{2},\] together with maxima at \[\theta = \frac{\pi}{8},\quad \frac{3\pi}{8}.\] The phase dependence is proportional to \(\sin\phi\), arising from the \(e^{\pm i\pi/4}\) phases contained in the leakage generator \(\mathcal{A}_L\). This shifts the correction into quadrature relative to the leading Born interference fringe. T104 establishes that the Q5 leakage-return mechanism produces a fully explicit interference correction that is antisymmetric between output channels, conserves total probability, vanishes at the required endpoints, and emerges naturally from the two-step transport structure of the leakage chain. The theorem replaces the phenomenological correction function of T101 with a direct Q5-derived prediction and identifies \(\sin\phi\,\sin(4\theta)\) as the characteristic observable signature of leakage-return transport.
