Reduced Boundary Rank Is Two While Boundary Transport Multiplicity Is Three

T106 established that the baryonic interface admits three irreducible transport outcomes: admission, complement return, and residual source formation. Let \(Π_Y\) denote the admissibility projector, \(K_⊥ = I-Π_Y\) the leakage-complement projector, \(L\) the leakage injection map, and \(B=i A_L\) the leakage circulation generator. Define the reduced return family \[R(t)=L^ etBL.\] Using the explicit computation of T104, \[L^ BL = 0,\] so the first-order return contribution vanishes. The first nontrivial return appears at second order: \[C_2=L^ B^2L=-1/80(I-iσ_y),\] which lies entirely within \[span\{I,Π_Y\}=span\{Π_Y,K_⊥\}.\] Consequently, the reduced return family contributes no independent third operator direction within the reduced observable algebra. The reduced boundary operator space therefore, satisfies \[ B_Yʳᵉᵈ=span\{Π_Y,K_⊥,R(t)\}=span\{Π_Y,K_⊥\},\] giving \[{( B_Yʳᵉᵈ)=2.}\] This result does not contradict T106. The apparent discrepancy arises because transport multiplicity and operator rank count different structures. The boundary possesses three architecturally distinct transport classes, \[Tadmit,ᵣₑₜᵤᵣₙ,residual,\] But these project onto only two reduced observable operator directions. The theorem, therefore closes the earlier rank-three boundary argument and replaces it with a stronger interpretation: the factor \[Gboundary=3\] is a transport multiplicity, not an operator-rank count. The third boundary contribution survives not as a new basis direction in the reduced algebra, but as transport history, phase lag, and residual source formation, which become the subject of the later leakage and residual arcs. Dependencies:T96 (Gate Projector and Leakage Complement),T102 (Mixing Operator from Leakage Return),T103 (Surface Circulation Generator),T104 (Explicit Interference Correction),T106 (Boundary Transport Multiplicity). Epistemic Classification Solid:\[L^ BL = 0,\] \[C_2=L^ B^2L\{I,Π_Y\},\] \[( B_Yʳᵉᵈ)=2.\] Conditional: \[Gboundary=3\] as transport multiplicity, relying on the architectural distinction between admission, complement return, and residual source formation developed through T106 and the later residual program. One-Line Summary \[{The boundary has three transport classes but only two reduced operator directions; Gboundary=3 is transport multiplicity, not reduced operator rank.}\]