Conformal Stability of the Spectral Hierarchy: Ghost-Freedom, Anomaly Matching, and the Vanishing of R² at ξ=1/6

We consider the weighted operator hierarchy Ô = a D̂_F ⊕ b₁ B̂_scalar ⊕ b₂ B̂_gauge ⊕ c P₄ studied in the companion paper (DOI: 10.5281/zenodo.22757934), subject to the ghost-freedom condition on the massive spin-2 mode and to Euler-charge (anomaly) matching. That paper works at minimal scalar coupling, ξ=0, where the sum of heat-kernel coefficients a₄(Ô) reduces to a pure R² term proportional to b₁. Here we study the companion question at the fully conformal point ξ=1/6, where all four sectors are conformally covariant. We show, in closed form rather than by numerical hypothesis, that a₄(Ô)≡0 on the anomaly-matching line at ξ=1/6. We then show that the ghost-freedom hyperplane is completely insensitive to any deformation of a sector's endomorphism proportional to the scalar curvature (such as ξ or a Dirac curvature coupling φ), and that it responds evenly — to quadratic order and with no linear term — to any deformation built from the traceless Ricci tensor (such deformations occur in the gauge and Paneitz sectors). In every sector this symmetry singles out an isolated point or pair of points in that sector's internal parameter space, but never fixes the relative weights a:b₁:b₂:c themselves. The absence of the R² term at ξ=1/6 is therefore a collective property of all four sectors sitting simultaneously at their true conformal points, not an accident of any one of them. Conformality of Ô is a stability condition rather than an aesthetic choice.