Lemma: Computational verification of L.4–L.5

The script XVI-L-artifacts/counterterm_map.py enumerates placements from the L.1/L.2 budgets, exits with status $0$, and records:

1. (C1)

   Coherence: unordered labels quotient edge interchange; wave-operator generators lie in ${\mathcal{V}}_{\mathrm{adm}}$; $15$ diagonal $\square S=0$ constraints (one per $|\gamma |\le 2$).

2. (C2)

   Jet bounds: $(2-v)+|\gamma |\le 2+s\le 4$ on all contacts; arithmetic identity $(2-v)+N=2+s$ (not a sharpness/attainment claim); prep orders $2,1,0$ by sector; switch order $\le 4$.

3. (C3)

   $W_{\rho }$ orders $\{0,1,2,3,4\}$ with $\rho \le 2$ matching XVI-K; raw contact counts (not dimensions) $14321$ before coherence; $V_{\mathrm{K}}$ block $321$; complement $14000$.

4. (C4)

   Four interpretive counterterm categories recorded; one family of wave-operator relations exhibited (not a complete constraint list); finite defect-ledger candidate types (six typed sources with image still in ${\mathcal{V}}_{\mathrm{adm}}$).

Proof. Printed lines of counterterm_map_out.txt; Appendix app:out.