X72-55: Adjoint Minimal Floquet Modes and Symmetry-Pairing Reduction

Building on the two localized adjoint-compatible modes and nonzero target defect stably exhibited by Round 54's physical finite truncation, this round finds the exact reflection symmetry and antilinear symmetry of the source–adjoint problem, builds a regularized localized adjoint basis, and compresses the full target pairing into a single question of the sign of a central coefficient. Proves that on both source fibers, the two coefficients in the target pairing always share the same sign, so proving that this central coefficient is positive alone suffices to close the second-order source cancellation; the finite-truncation numerics already stabilize, from a very shallow truncation depth onward, at very high precision showing it to be positive. Route halts at STOP-C59 (adjoint central positivity / rigorous tail-bound gap): the finite-truncation positivity has still not been upgraded to a rigorous infinite-dimensional theorem, handed to the next round to rigorously construct the bound on the adjoint tail; this round also includes a numerical-verification script.