code/check_orbits.py

#!/usr/bin/env python3
"""Exhaust the five-coordinate covering antichains and check the supplied orbits."""
import itertools,json,time
from pathlib import Path
ROOT=Path(__file__).resolve().parents[1]
def run():
    start=time.perf_counter();families=set()
    def extend(next_mask,chosen,used):
        if used==31:families.add(tuple(chosen))
        for m in range(next_mask,32):
            if all((m&h)!=m and (m&h)!=h for h in chosen):
                extend(m+1,chosen+[m],used|m)
    extend(1,[],0)
    data=json.loads((ROOT/'data/legacy_catalogue.json').read_text());seen=set()
    for rec in data['representatives']:
        fam=tuple(rec['facets']);orb=set()
        for p in itertools.permutations(range(5)):
            orb.add(tuple(sorted(sum(1<<p[i] for i in range(5) if m&(1<<i)) for m in fam)))
        assert min(orb)==fam and len(orb)==rec['orbit_size']
        assert not seen.intersection(orb);seen.update(orb)
    assert seen==families and len(families)==6894
    keys={(c['index'],c['body']) for c in data['certificates']}
    assert keys==set(itertools.product(range(180),['P','Q']))
    report={'status':'PASS','covering_antichains':len(families),'coordinate_permutation_orbits':len(data['representatives']),
            'primal_polar_records':len(keys),'model_presentations':2*len(families),
            'elapsed_seconds':round(time.perf_counter()-start,3),'unrestricted_5d_theorem_proved':False}
    (ROOT/'verification/orbit_report.json').write_text(json.dumps(report,indent=2)+'\n');print(json.dumps(report,indent=2))
if __name__=='__main__':run()