Explicit Interference Correction from Q5 Leakage Return

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 \(C=L^ BL\), and T103 identified the leakage generator \(B=iA_L\) 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: \[L^ B L = 0.\] This occurs because the leakage generator transports amplitude through the helical chain \[e_3 ↔ e_4 ↔ e_5,\] 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 \[C_2=L^ B^2 L=-1/80(I-iσ_y),\] which is Hermitian and generates the leading observable correction. Applying the T100 renormalization procedure yields normalized probability shifts \[Δ_+=-sinφ\,sin(4θ)/160,Δ_-=+sinφ\,sin(4θ)/160,\] with \[Δ_+ + Δ_- = 0.\] The resulting observable probabilities are \[P_+ᵒᵇˢ=cos^2θ-η^2/2sinφ\,sin(4θ)/160+O(η^3),\] \[P_-ᵒᵇˢ=sin^2θ+η^2/2sinφ\,sin(4θ)/160+O(η^3).\] The correction is therefore second order in the leakage coupling and possesses a characteristic angular envelope \(sin(4θ)\). This replaces the earlier minimal placeholder structure of T101 and introduces a richer node pattern, with nulls at \[θ = 0, π/4, π/2,\] together with maxima at \[θ = π/8, 3π/8.\] The phase dependence is proportional to \(sinφ\), arising from the \(e± iπ/4\) phases contained in the leakage generator \(A_L\). 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 \(sinφ\,sin(4θ)\) as the characteristic observable signature of leakage-return transport.