"""Certified boundary window (L3): for fixed p and each n in [NMIN, NMAX], build F(n,p) = "exists X, |X| = p, |dX| <= 11" (Lemma 3.4), solve with proof logging (CaDiCaL 1.9.5 via python-sat), write DIMACS + DRAT to code/proofs/certificates/boundary/, check the proof with drat-trim, and record everything in results/boundary_certificates.jsonl. SAT outcomes (obstructions) are recorded with the explicit X and go to results/counterexamples.jsonl. usage: python3 code/run_boundary_window.py P NMIN NMAX [workers] python3 code/run_boundary_window.py --job P N """ import json import os import subprocess import sys import time from concurrent.futures import ThreadPoolExecutor import common from graph_constructor import edge_list_sha256, edges_formula, label from sat_or_ilp_solver import boundary_clauses, boundary_of, solve_with_proof CERT_DIR = os.path.join(common.CERTS, "boundary") def job(p, n): os.makedirs(CERT_DIR, exist_ok=True) t0 = time.time() cl, x, z, nv = boundary_clauses(n, 5, p, 11) cnf_path = os.path.join(CERT_DIR, "P%d_5_p%d_b11.cnf" % (n, p)) proof_path = os.path.join(CERT_DIR, "P%d_5_p%d_b11.drat" % (n, p)) r = solve_with_proof(cl, nv, "cadical195", cnf_path, proof_path) r.update({"n": n, "k": 5, "p": p, "bound": 11, "graph_sha256": edge_list_sha256(edges_formula(n, 5)), "x_vars": "1..%d" % (2 * n), "z_vars": "%d..%d" % (2 * n + 1, 4 * n), "wall_seconds": round(time.time() - t0, 3), "utc": common.utcnow(), "peak_rss_mb": round(common.peak_rss_mb(), 1)}) r.update(common.versions()) if r["sat"]: model = r.pop("model") X = [w for w in range(2 * n) if model[x[w] - 1] > 0] r["X"] = [label(w, n) for w in X] r["boundary"] = [label(w, n) for w in boundary_of(n, 5, X)] r["boundary_size"] = len(r["boundary"]) assert len(X) == p and r["boundary_size"] <= 11 os.remove(cnf_path) return r def run_sub(args): p, n = args out = subprocess.run([sys.executable, os.path.abspath(__file__), "--job", str(p), str(n)], capture_output=True, text=True) if out.returncode != 0: return {"n": n, "p": p, "error": out.stderr[-800:]} return json.loads(out.stdout.strip().splitlines()[-1]) if __name__ == "__main__": if sys.argv[1] == "--job": print(json.dumps(job(int(sys.argv[2]), int(sys.argv[3])))) sys.exit(0) p, nmin, nmax = (int(a) for a in sys.argv[1:4]) workers = int(sys.argv[4]) if len(sys.argv) > 4 else 8 out = os.path.join(common.RESULTS, "boundary_certificates.jsonl") common.log_event("F", "boundary_window_start", p=p, nmin=nmin, nmax=nmax, workers=workers) tasks = [(p, n) for n in range(nmin, nmax + 1)] with ThreadPoolExecutor(max_workers=workers) as ex: for r in ex.map(run_sub, tasks): common.append_jsonl(out, r) if "error" in r: print("n=%d p=%d ERROR %s" % (r["n"], r["p"], r["error"]), flush=True) elif r["sat"]: common.append_jsonl(os.path.join(common.RESULTS, "counterexamples.jsonl"), {"type": "boundary_obstruction", "n": r["n"], "p": r["p"], "X": r["X"], "boundary": r["boundary"], "utc": r["utc"]}) print("n=%d p=%d SAT (obstruction) |dX|=%d" % (r["n"], r["p"], r["boundary_size"]), flush=True) else: print("n=%d p=%d UNSAT solve=%.1fs check=%.1fs verified=%s exit=%d" % ( r["n"], r["p"], r["solve_seconds"], r["checker_seconds"], r["checker_verified"], r["checker_exit"]), flush=True) common.log_event("F", "boundary_window_end", p=p, nmin=nmin, nmax=nmax)