Lemma: Reported computation for M.1

graph_general.py loads $P_A$ from the frozen XVI-L source table and ${L^{pq}}_{ij}$ from the frozen XVI-K Hessian list. It assembles the switch-free $\hat{a}$ of Definition def:aGeneral in exact $\mathbb{Q}$ arithmetic and exits with status $0$, recording the following.

1. (G1)

   Proposition prop:M1(1)–(6). The edge-interchange check is exhaustive: it runs over every enumerated ordered placement whose swap is distinct, which gives $1000$ unordered pairs.

2. (G2)

   The supports of Proposition prop:M1. Twenty labels lie in ${{\Lambda }^{\mathrm{formal}}}_{\mathrm{graph}}\setminus {{\Lambda }^{\mathrm{background}}}_{\mathrm{graph}}$.

3. (G3)

   Theorem thm:M1spec ($1065/1065$ entries).

4. (G4)

   An independent $C_2$ route via xvi_common.polar_s ($250$ comparisons).

5. (G5)

   $3282$ nonzero $(A,\lambda ,(\mu ,\nu ))$ lines. The sector-summed table has $2322$ entries with $18646$ bilinear terms.