Proposition

The only active reference for the weighted kernel is the jet pullback

prescription W_w_jet_pullback_via_Pi_tr_o68. The old cutoff construction is archived. Equivalence of that cutoff with this pullback is not claimed. The false pointwise bound $|T|\le C|z{|}_E^{-8}$ is removed. Annular seminorms replace it. The covariance spanning set remains a candidate list, so Gate 3 stays Partial even though Deliverables 1–3 are Constructed under this reference.