Why quantum closure is still a separate gate

Even for the admitted prepared free polynomials, the classical rule $s_{\mathrm{rel}}$ has not been proved a derivation of ${\star }_H$. Its compatibility would require contraction identities for the fixed covariance and the nonlinear rule, followed by the appropriate renormalized Ward identities for mixed products.

For a constructed quantum differential

recursive insertion closure would require, at order $n$,

The right-hand side is not an anomaly calculation until all its maps and products are defined. Bulk and initial-surface pieces require an actual support analysis before a decomposition into anomaly sectors is asserted.

Renormalized BV and multiple-insertion Ward identities supply the general setting for these questions FRBV,BFR,FrobWard. They do not supply the missing maps for the sharp Cauchy insertion.