# Handwritten proof sources

The complete step-numbered proofs live in results/derivations.md (single source of truth; copied here as derivations.md at the end of Stage 4):

• P1 order independence (least fixed point), P2 fort characterization, P3 orbit reduction, P4 round-based SAT soundness/completeness, P5 graph facts;
• P6 isomorphism P(n,k) ≅ P(n,l) for kl ≡ 1 (mod n), P7 uniform 12-vertex construction, P8 first-force boundary lemma, P9 column deletion (k = 5);
• Lemmas 3.1–3.5: boundary ⇒ zero forcing, finite reduction, finite window, correctness of the boundary CNF and of the fort-cover CNF;
• the main theorem (§5) and the exact boundary of what is proved (§7).

Machine-checked inputs to the theorem are in ../certificates/ (DIMACS + DRAT + drat-trim transcripts, hashes in results/boundary_certificates.jsonl and results/lower_bound_certificates.jsonl) and in results/brute_force_runs.jsonl (exhaustive enumeration counts).