Surface Circulation Generator from Q5 Leakage Geometry

T103 derives the explicit surface-circulation generator governing the evolution of leakage-sector amplitude within the extended Q5 transport architecture. Earlier theorems established the existence of a leakage sector (T93), derived the residual return mechanism (T94), identified the gate projector and leakage complement (T96), and showed that observable mixing corrections arise from the operator \[C = K^ B K\] (T102). The remaining missing ingredient is the explicit form of the surface generator \(B\). The theorem constructs \(B\) from the underlying Q5 leakage geometry. Leakage amplitude that fails gate admission is not destroyed but is redistributed along structured circulation paths within the leakage sector. These circulation paths define an internal transport algebra whose generator is represented by \[B.\] The generator is shown to be anti-Hermitian, \[B^ = -B,\] ensuring norm-preserving evolution of leakage-sector amplitude through \[etB.\] This establishes leakage circulation as a conservative redistribution process rather than a dissipative loss mechanism. The theorem further identifies the geometric origin of the leakage dynamics. The circulation generator arises from the adjacency and transport structure of the Q5 leakage surface, providing the first explicit bridge between abstract leakage evolution and the underlying architectural geometry. Leakage return is therefore governed by a concrete transport operator rather than an unspecified dynamical process. Substituting the resulting generator into \[C = K^ B K\] completes the derivational chain initiated in T102. Observable mixing corrections, interference deviations, and conjugate-half probability redistribution are no longer controlled by an abstract operator but by a generator determined directly from Q5 structure. T103, therefore, occupies a foundational position in the sequence. T102 derives the form of the mixing operator. T103 derives the generator that defines it. Together, they transform the conjugate-half mixing program from a phenomenological correction theory into a transport-derived consequence of leakage-sector geometry. The theorem establishes the leakage-surface generator as the dynamical core of the extended Q5 return architecture and provides the structural input required for the explicit interference-correction calculations developed in T104.