Required closure items, recorded

(a) Coherent versus placementwise changes. XVI-K, Remark rem:coherent, distinguishes two levels, and XVI-L keeps them apart: placementwise families (a separate same-degree extension for each labelled kernel ${q^{\circ }}_{\mathsf{k}}$; XVI-K, eq:deltaCK holds at that level), and coherent changes ${\mathfrak{R}}_{\mathrm{K}}^{\prime }-{\mathfrak{R}}_{\mathrm{K}}$, linear on the actual span ${\mathcal{V}}_{\mathrm{K}}$, for which every constant-coefficient relation ${\sum }_{\mathsf{k}}{c}_{\mathsf{k}}{q^{\circ }}_{\mathsf{k}}=0$ forces ${\sum }_{\mathsf{k}}{c}_{\mathsf{k}}{C}_{\mathsf{k}\gamma }=0$ for every $\gamma$. Only coherent changes will be called renormalization-prescription changes in XVI-L (target L.4–L.5). Within coherent changes, XVI-K distinguishes those altering the XVI-J component ($C_{\{0,0\},0}\ne 0$) from those preserving it ($C_{\{0,0\},0}=0$).

(b) Declared subtraction orders. XVI-K, Remark rem:N: $N_{\mathsf{k}}:=|p|+|q|$ is a declared order, not defined through the scaling degree; $\mathrm{sd}({q^{\circ }}_{\mathsf{k}})\le 4+N_{\mathsf{k}}$, with equality for nonzero ${q^{\circ }}_{\mathsf{k}}$, and a vanishing kernel costs nothing. XVI-L adopts the same convention for the new kernels: the declared order of a numerical kernel is its total numerical derivative count, fixed before any question of vanishing is decided (target L.3).

(c) Computational artifact. The XVI-K artifact is the folder XVI-K-artifacts/ (hessian_full.py, xvi_common.py, recompute_K_dual.py, hessian_full_out.txt); the shared routines (negP, polar_s, Q_of, C2_component, ell3_of) are named functions of xvi_common.py (XVI-K, Appendix app:script). XVI-L does not modify that folder. The XVI-L artifact is the folder XVI-L-artifacts/, which contains a copy of xvi_common.py (byte-identical; scripts check this when the original is present), source_full.py with source_full_out.txt/source_full_table.txt (L.1), two_edge_full.py with two_edge_full_out.txt (L.2), kernel_inventory.py with kernel_inventory_out.txt (L.3), counterterm_map.py with counterterm_map_out.txt (L.4–L.5), and regression_L.py with regression_L_out.txt (L.6–L.7) (Appendix app:script).

(d) Verification boundary. Three kinds of evidence are distinguished throughout, as in XVI-K, Appendix app:script: symbolic constructions (exact polynomial identities in independent jet coordinates, valid for all smooth fields); coefficientwise structural checks (properties verified monomial by monomial on such a symbolic polynomial); finite exact tests (exact rational evaluation on specified test data; agreement there is not a coefficientwise equivalence proof). A statement is called “Proved locally” only if it has a written argument in this note; a statement supported only by the script is called “Computationally verified” and its kind of evidence is named.