This paper analyzes dual axial‑torsion channels for palindromic Weyl data (A,0,B,0,A), showing that the two sky‑projected coefficients satisfy an exact reflection law and share the same six protected real‑sky zeros except on type‑D walls, where the corresponding great circle is quiet in both channels. It identifies a dyad‑invariant symplectic pairing II=AA′ with weight zero, equal to the Lorentz square of the reconstructed torsion offset. Under a conditional two‑line closure with recurrent flags, preserved lines, fixed Cartan generators, and normalized lifts, the paired offsets admit a closed anchored formula with doubled phase weight. The Mixmaster input is a Weyl‑channel winding theorem only; no recurrent flags, closure realization, or torsionful transport is proved.
Hiroyuki Shioiri (Sat,) studied this question.