Lemma: Reported computation for M.4

contact_collapse.py, helmholtz_check.py and matching_probe.py exit with status $0$. Kernels are computed exactly over $\mathbb{Q}$ in each block of $(D,\text{reflection parity})$; there are $40$ blocks, of maximal size $292$. The procedure has three steps: rows independent mod $p$ are selected; the exact nullspace of the selected rows is computed; and every candidate kernel vector is verified exactly against all rows. Since $\ker (\text{all rows})\subseteq \ker (\text{selected})$, verified equality is exact. The adjoint implementation is unit-tested against Euler derivatives of random quadratic Lagrangians computed by the independent route. Archives: collapse_kernel_certificates.txt, helmholtz_certificates.txt, matching_certificates.txt. The full collapse matrices are regenerated deterministically by the scripts and are not stored; they have about $6.7\times 10^5$ (formal) and $1.5\times 10^6$ (adjoint-defect) nonzero entries.