1# Handwritten proof sources23The complete step-numbered proofs live in `results/derivations.md` (single source of truth; copied here as `derivations.md` at the end of Stage 4):45- P1 order independence (least fixed point), P2 fort characterization, P3 orbit reduction, P4 round-based SAT soundness/completeness, P5 graph facts;6- 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);7- Lemmas 3.1–3.5: boundary ⇒ zero forcing, finite reduction, finite window, correctness of the boundary CNF and of the fort-cover CNF;8- the main theorem (§5) and the exact boundary of what is proved (§7).910Machine-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).11