Paired Symmetric Cancellation Across the Barrier

T89 establishes algebraic cancellation of the symmetric transport sector across the orientation-reversing Q5 barrier. Native and dual kernel operators \(M_n,D_n\) and \(M_d,D_d\) are related by the boundary inversion map \(Θ\), which reverses ordered products:\[Θ(M_nD_n)Θ⁻¹=D_dM_d,Θ(D_nM_n)Θ⁻¹=M_dD_d.\]This induces the symmetric-sector transport relation\[S_d=Θ S_nΘ⁻¹,\]where\[S_n=12(M_nD_n+D_nM_n),_d=12(D_dM_d+M_dD_d).\] Using the T28-T29 extraction framework, only the order-sensitive commutator component contributes to observable transport:\[A_n=12[M_n,D_n].\]The symmetric anticommutator sector lies in the null class of the transport functional:\[ L(S_n)=0.\]Thus, the admissible crossing channel selects the commutator sector and excludes persistent symmetric transport contributions. The paired consistency condition across the orientation-reversing boundary then forces cancellation within the admissible crossing sector:\[S_n+S_d=0,\]equivalently\[S_n+Θ S_nΘ⁻¹=0.\] Substituting this into the paired first-order transport expansion gives\[T=(I+ε(A+S_n))(I+ε(A+S_d)) =I+2ε A+O(ε^2).\]With\[ε=1{320},\]The effective transport becomes\[T=I+1{160}A+O(ε^2),=iσ_y.\] T89 complements T88. T88 established cancellation geometrically through admissible \(Y\)-gate crossing and paired inversion. T89 establishes the same cancellation algebraically through ordering reversal, commutator/anticommutator decomposition, and admissible-sector consistency. Together, they provide geometric and algebraic foundations for first-order rotational purity of paired Q5 transport. Solid results:\[Θ(M_nD_n)Θ⁻¹=D_dM_d,\]\[S_d=Θ S_nΘ⁻¹,\]\[ L(S_n)=0,\]and commutator-sector selection as the admissible transport channel. Conditional boundary:\[S_n+S_d=0\]is established within the admissible crossing sector of the T17/T48 paired architecture and is not claimed as a global raw-sector vanishing theorem.