T89 establishes algebraic cancellation of the symmetric transport sector across the orientation-reversing Q5 barrier. Native and dual kernel operators \ (Mₙ, Dₙ\) and \ (Md, Dd\) are related by the boundary inversion map \ (\), which reverses ordered products: \ (MₙDₙ) ^-1=DdMd, (DₙMₙ) ^-1=MdDd. induces the symmetric-sector transport relationd= Sₙ^-1, ₙ=12 (MₙDₙ+DₙMₙ), d=12 (DdMd+MdDd). \ Using the T28-T29 extraction framework, only the order-sensitive commutator component contributes to observable transport: ₙ=12[Mₙ, Dₙ. \]The symmetric anticommutator sector lies in the null class of the transport functional: \ L (Sₙ) =0. , 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: ₙ+Sd=0, ₙ+ Sₙ^-1=0. \ Substituting this into the paired first-order transport expansion gives= (I+ (A+Sₙ) ) (I+ (A+Sd) ) =I+2 A+O (²). \=1320, effective transport becomes=I+1160A+O (²), =iᵧ. \ 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: \ (MₙDₙ) ^-1=DdMd, \d= Sₙ^-1, \\ L (Sₙ) =0, commutator-sector selection as the admissible transport channel. Conditional boundary: ₙ+Sd=0 established within the admissible crossing sector of the T17/T48 paired architecture and is not claimed as a global raw-sector vanishing theorem.
Craig Edwin Holdway (Sat,) studied this question.