Lemma: Computational verification of L.7 regressions

The script XVI-L-artifacts/regression_L.py exits with status $0$ and records:

1. (R1)

   $C_2$-only truncation: numerical labels equal ${\mathcal{V}}_{\mathrm{K}}$ (25 unordered); ordered count $45$; max $N=2$.

2. (R2)

   Constant-slot truncation of that sector: single label $\{0,0\}$; recovers the XVI-J slot pattern $a=b=p=q=0$.

3. (R3)

   Combinatorial prerequisites for the exact-restriction identities ${\mathfrak{R}}_{\mathrm{L}}{|}_{{\mathcal{V}}_{\mathrm{K}}}={\mathfrak{R}}_{\mathrm{K}}$ and ${\mathfrak{R}}_{\mathrm{K}}(S^2)={\bar{q}}^{\mathfrak{R}}$ (written analytic proofs; the script does not claim distributional scale proofs); net sign $+1$ of the relative-variable computation recorded.

4. (R4)

   Scale-family combinatorial bookkeeping / illustrative recovery: ${\varpi }_{\mu }(z)=\varpi ((\mu /{\mu }_0)z)$ recovers $\varpi$ at $\mu ={\mu }_0$; contact-order bound $N$ for scale differences recorded.

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