# command: python3 row_sweep.py 22-40:64 41-60:32 61-105:16 # started: 2026-10-27 04:26:07 UTC # Python 3.13.17, python-flint 0.9.0, numpy 2.5.3, sympy 1.14.0 # machine: 2 cores, 7 GB RAM, Linux x86_64 # sha256 of the scripts in the directory: # 62ba14c054023c20a139428938aa4561365d93366172e919afde228d09b40d4e band_check.py # e3b29b32dee33a3771e46eee7fd3c7feb9d5281a0f880fb0ea2a9dc9bde9ea99 bergeron_certificate.py # a86969c6ce89c5a3aba23d4d30aa55d8fb9924613d794ab271728fe3f2035110 circle_check.py # 0ad5f6f485561df541b4e83a0e780275e5077b2e3a6baa864ca0419d01ef15af corner_check.py # 85f217ba1cc63c5421bb2df726223642e8289baab3f46dc55e026417f27cbb21 cww_certificate.py # 1b487046af3818f1b6e61f9903bb4dd3cbdb45e7d451c23cdce74faad8cf4eb0 pn_certificate.py # ea6a0e64e29ea4599808a3cb8023f9a18bfb4469f6b282d051f24034a5903108 pn_families.py # 33684b0c7134b1b7da3e1e5fd944fe28c067fcc4255b832d327d3aea4043f665 row_check.py # 0dd9195b2ba9a6ca36055c39fd90cd069ab530072d01786042400059e129e650 row_sweep.py # b077df5d9e0b9b7bf8be56cf2ab6763e5d8167a7408763c6ba54667837f077b3 rq_certificate.py # R(x, A) for 2x(x-1) <= A <= LAM x^2: N_A < 0.999 P_A in degrees D < k <= A+/2 at every breakpoint; 22-40:64 41-60:32 61-105:16 x= 22: 2733 breakpoints up to A=30976; max N/P = 0.6301 at (A, k, lam) = (924, 472, 1.909); rel. error <= 1.8e-13; max 1.9e+47; ok 4s x= 23: 2857 breakpoints up to A=33856; max N/P = 0.6303 at (A, k, lam) = (1012, 517, 1.913); rel. error <= 1.8e-13; max 3.3e+49; ok 5s x= 24: 2981 breakpoints up to A=36864; max N/P = 0.6297 at (A, k, lam) = (1104, 563, 1.917); rel. error <= 1.9e-13; max 5.7e+51; ok 6s x= 25: 3105 breakpoints up to A=40000; max N/P = 0.6299 at (A, k, lam) = (1200, 612, 1.92); rel. error <= 2.0e-13; max 1.0e+54; ok 6s x= 26: 3229 breakpoints up to A=43264; max N/P = 0.6294 at (A, k, lam) = (1300, 662, 1.923); rel. error <= 2.1e-13; max 1.8e+56; ok 7s x= 27: 3353 breakpoints up to A=46656; max N/P = 0.6295 at (A, k, lam) = (1404, 715, 1.926); rel. error <= 2.1e-13; max 3.1e+58; ok 8s x= 28: 3477 breakpoints up to A=50176; max N/P = 0.6291 at (A, k, lam) = (1512, 769, 1.929); rel. error <= 2.2e-13; max 5.5e+60; ok 9s x= 29: 3601 breakpoints up to A=53824; max N/P = 0.6292 at (A, k, lam) = (1624, 826, 1.931); rel. error <= 2.3e-13; max 9.6e+62; ok 9s x= 30: 3725 breakpoints up to A=57600; max N/P = 0.6289 at (A, k, lam) = (1740, 884, 1.933); rel. error <= 2.4e-13; max 1.7e+65; ok 11s x= 31: 3849 breakpoints up to A=61504; max N/P = 0.6289 at (A, k, lam) = (1860, 945, 1.935); rel. error <= 2.4e-13; max 3.0e+67; ok 12s x= 32: 3973 breakpoints up to A=65536; max N/P = 0.6286 at (A, k, lam) = (1984, 1007, 1.938); rel. error <= 2.5e-13; max 5.2e+69; ok 13s x= 33: 4097 breakpoints up to A=69696; max N/P = 0.6287 at (A, k, lam) = (2112, 1072, 1.939); rel. error <= 2.6e-13; max 9.1e+71; ok 15s x= 34: 4221 breakpoints up to A=73984; max N/P = 0.6284 at (A, k, lam) = (2244, 1138, 1.941); rel. error <= 2.6e-13; max 1.6e+74; ok 18s x= 35: 4345 breakpoints up to A=78400; max N/P = 0.6285 at (A, k, lam) = (2380, 1207, 1.943); rel. error <= 2.7e-13; max 2.8e+76; ok 19s x= 36: 4469 breakpoints up to A=82944; max N/P = 0.6283 at (A, k, lam) = (2520, 1277, 1.944); rel. error <= 2.8e-13; max 4.9e+78; ok 20s x= 37: 4593 breakpoints up to A=87616; max N/P = 0.6283 at (A, k, lam) = (2664, 1350, 1.946); rel. error <= 2.9e-13; max 8.6e+80; ok 22s x= 38: 4717 breakpoints up to A=92416; max N/P = 0.6281 at (A, k, lam) = (2812, 1424, 1.947); rel. error <= 2.9e-13; max 1.5e+83; ok 24s x= 39: 4841 breakpoints up to A=97344; max N/P = 0.6282 at (A, k, lam) = (2964, 1501, 1.949); rel. error <= 3.0e-13; max 2.7e+85; ok 26s x= 40: 4965 breakpoints up to A=102400; max N/P = 0.6280 at (A, k, lam) = (3120, 1579, 1.95); rel. error <= 3.1e-13; max 4.7e+87; ok 29s x= 41: 2465 breakpoints up to A=53792; max N/P = 0.6280 at (A, k, lam) = (3280, 1660, 1.951); rel. error <= 1.6e-13; max 1.0e+78; ok 4s x= 42: 2525 breakpoints up to A=56448; max N/P = 0.6278 at (A, k, lam) = (3444, 1742, 1.952); rel. error <= 1.6e-13; max 8.9e+79; ok 4s x= 43: 2585 breakpoints up to A=59168; max N/P = 0.6279 at (A, k, lam) = (3612, 1827, 1.953); rel. error <= 1.7e-13; max 7.9e+81; ok 4s x= 44: 2645 breakpoints up to A=61952; max N/P = 0.6277 at (A, k, lam) = (3784, 1913, 1.955); rel. error <= 1.7e-13; max 6.9e+83; ok 5s x= 45: 2705 breakpoints up to A=64800; max N/P = 0.6277 at (A, k, lam) = (3960, 2002, 1.956); rel. error <= 1.8e-13; max 6.1e+85; ok 5s x= 46: 2765 breakpoints up to A=67712; max N/P = 0.6276 at (A, k, lam) = (4140, 2092, 1.957); rel. error <= 1.8e-13; max 5.4e+87; ok 6s x= 47: 2825 breakpoints up to A=70688; max N/P = 0.6276 at (A, k, lam) = (4324, 2185, 1.957); rel. error <= 1.8e-13; max 4.8e+89; ok 7s x= 48: 2885 breakpoints up to A=73728; max N/P = 0.6275 at (A, k, lam) = (4512, 2279, 1.958); rel. error <= 1.9e-13; max 4.2e+91; ok 6s x= 49: 2945 breakpoints up to A=76832; max N/P = 0.6275 at (A, k, lam) = (4704, 2376, 1.959); rel. error <= 1.9e-13; max 3.7e+93; ok 7s x= 50: 3005 breakpoints up to A=80000; max N/P = 0.6274 at (A, k, lam) = (4900, 2474, 1.96); rel. error <= 1.9e-13; max 3.3e+95; ok 8s x= 51: 3065 breakpoints up to A=83232; max N/P = 0.6274 at (A, k, lam) = (5100, 2575, 1.961); rel. error <= 2.0e-13; max 2.9e+97; ok 8s x= 52: 3125 breakpoints up to A=86528; max N/P = 0.6273 at (A, k, lam) = (5304, 2677, 1.962); rel. error <= 2.0e-13; max 2.6e+99; ok 9s x= 53: 3185 breakpoints up to A=89888; max N/P = 0.6273 at (A, k, lam) = (5512, 2782, 1.962); rel. error <= 2.0e-13; max 2.3e+101; ok 9s x= 54: 3245 breakpoints up to A=93312; max N/P = 0.6272 at (A, k, lam) = (5724, 2888, 1.963); rel. error <= 2.1e-13; max 2.0e+103; ok 10s x= 55: 3305 breakpoints up to A=96800; max N/P = 0.6272 at (A, k, lam) = (5940, 2997, 1.964); rel. error <= 2.1e-13; max 1.8e+105; ok 11s x= 56: 3365 breakpoints up to A=100352; max N/P = 0.6271 at (A, k, lam) = (6160, 3107, 1.964); rel. error <= 2.2e-13; max 1.6e+107; ok 12s x= 57: 3425 breakpoints up to A=103968; max N/P = 0.6272 at (A, k, lam) = (6384, 3220, 1.965); rel. error <= 2.2e-13; max 1.4e+109; ok 12s x= 58: 3485 breakpoints up to A=107648; max N/P = 0.6271 at (A, k, lam) = (6612, 3334, 1.966); rel. error <= 2.2e-13; max 1.2e+111; ok 13s x= 59: 3545 breakpoints up to A=111392; max N/P = 0.6271 at (A, k, lam) = (6844, 3451, 1.966); rel. error <= 2.3e-13; max 1.1e+113; ok 14s x= 60: 3605 breakpoints up to A=115200; max N/P = 0.6270 at (A, k, lam) = (7080, 3569, 1.967); rel. error <= 2.3e-13; max 9.6e+114; ok 14s x= 61: 1713 breakpoints up to A=59536; max N/P = 0.6270 at (A, k, lam) = (7320, 3690, 1.967); rel. error <= 1.2e-13; max 1.8e+99; ok 2s x= 62: 1741 breakpoints up to A=61504; max N/P = 0.6269 at (A, k, lam) = (7564, 3812, 1.968); rel. error <= 1.2e-13; max 8.1e+100; ok 2s x= 63: 1769 breakpoints up to A=63504; max N/P = 0.6270 at (A, k, lam) = (7812, 3937, 1.968); rel. error <= 1.3e-13; max 3.6e+102; ok 3s x= 64: 1797 breakpoints up to A=65536; max N/P = 0.6269 at (A, k, lam) = (8064, 4063, 1.969); rel. error <= 1.3e-13; max 1.6e+104; ok 3s x= 65: 1825 breakpoints up to A=67600; max N/P = 0.6269 at (A, k, lam) = (8320, 4192, 1.969); rel. error <= 1.3e-13; max 7.3e+105; ok 3s x= 66: 1853 breakpoints up to A=69696; max N/P = 0.6268 at (A, k, lam) = (8580, 4322, 1.97); rel. error <= 1.3e-13; max 3.3e+107; ok 3s x= 67: 1881 breakpoints up to A=71824; max N/P = 0.6268 at (A, k, lam) = (8844, 4455, 1.97); rel. error <= 1.3e-13; max 1.5e+109; ok 3s x= 68: 1909 breakpoints up to A=73984; max N/P = 0.6268 at (A, k, lam) = (9112, 4589, 1.971); rel. error <= 1.3e-13; max 6.6e+110; ok 3s x= 69: 1937 breakpoints up to A=76176; max N/P = 0.6268 at (A, k, lam) = (9384, 4726, 1.971); rel. error <= 1.4e-13; max 3.0e+112; ok 3s x= 70: 1965 breakpoints up to A=78400; max N/P = 0.6267 at (A, k, lam) = (9660, 4864, 1.971); rel. error <= 1.4e-13; max 1.3e+114; ok 4s x= 71: 1993 breakpoints up to A=80656; max N/P = 0.6267 at (A, k, lam) = (9940, 5005, 1.972); rel. error <= 1.4e-13; max 6.0e+115; ok 4s x= 72: 2021 breakpoints up to A=82944; max N/P = 0.6267 at (A, k, lam) = (10224, 5147, 1.972); rel. error <= 1.4e-13; max 2.7e+117; ok 4s x= 73: 2049 breakpoints up to A=85264; max N/P = 0.6267 at (A, k, lam) = (10512, 5292, 1.973); rel. error <= 1.4e-13; max 1.2e+119; ok 4s x= 74: 2077 breakpoints up to A=87616; max N/P = 0.6266 at (A, k, lam) = (10804, 5438, 1.973); rel. error <= 1.5e-13; max 5.4e+120; ok 5s x= 75: 2105 breakpoints up to A=90000; max N/P = 0.6267 at (A, k, lam) = (11100, 5587, 1.973); rel. error <= 1.5e-13; max 2.4e+122; ok 5s x= 76: 2133 breakpoints up to A=92416; max N/P = 0.6266 at (A, k, lam) = (11400, 5737, 1.974); rel. error <= 1.5e-13; max 1.1e+124; ok 5s x= 77: 2161 breakpoints up to A=94864; max N/P = 0.6266 at (A, k, lam) = (11704, 5890, 1.974); rel. error <= 1.5e-13; max 4.9e+125; ok 5s x= 78: 2189 breakpoints up to A=97344; max N/P = 0.6266 at (A, k, lam) = (12012, 6044, 1.974); rel. error <= 1.5e-13; max 2.2e+127; ok 5s x= 79: 2217 breakpoints up to A=99856; max N/P = 0.6266 at (A, k, lam) = (12324, 6201, 1.975); rel. error <= 1.6e-13; max 9.8e+128; ok 6s x= 80: 2245 breakpoints up to A=102400; max N/P = 0.6265 at (A, k, lam) = (12640, 6359, 1.975); rel. error <= 1.6e-13; max 4.4e+130; ok 6s x= 81: 2273 breakpoints up to A=104976; max N/P = 0.6265 at (A, k, lam) = (12960, 6520, 1.975); rel. error <= 1.6e-13; max 2.0e+132; ok 6s x= 82: 2301 breakpoints up to A=107584; max N/P = 0.6265 at (A, k, lam) = (13284, 6682, 1.976); rel. error <= 1.6e-13; max 8.8e+133; ok 7s x= 83: 2329 breakpoints up to A=110224; max N/P = 0.6265 at (A, k, lam) = (13612, 6847, 1.976); rel. error <= 1.6e-13; max 4.0e+135; ok 7s x= 84: 2357 breakpoints up to A=112896; max N/P = 0.6265 at (A, k, lam) = (13944, 7013, 1.976); rel. error <= 1.7e-13; max 1.8e+137; ok 7s x= 85: 2385 breakpoints up to A=115600; max N/P = 0.6265 at (A, k, lam) = (14280, 7182, 1.976); rel. error <= 1.7e-13; max 7.9e+138; ok 7s x= 86: 2413 breakpoints up to A=118336; max N/P = 0.6264 at (A, k, lam) = (14620, 7352, 1.977); rel. error <= 1.7e-13; max 3.6e+140; ok 8s x= 87: 2441 breakpoints up to A=121104; max N/P = 0.6264 at (A, k, lam) = (14964, 7525, 1.977); rel. error <= 1.7e-13; max 1.6e+142; ok 8s x= 88: 2469 breakpoints up to A=123904; max N/P = 0.6264 at (A, k, lam) = (15312, 7699, 1.977); rel. error <= 1.7e-13; max 7.2e+143; ok 8s x= 89: 2497 breakpoints up to A=126736; max N/P = 0.6264 at (A, k, lam) = (15664, 7876, 1.978); rel. error <= 1.7e-13; max 3.2e+145; ok 9s x= 90: 2525 breakpoints up to A=129600; max N/P = 0.6264 at (A, k, lam) = (16020, 8054, 1.978); rel. error <= 1.8e-13; max 1.4e+147; ok 9s x= 91: 2553 breakpoints up to A=132496; max N/P = 0.6264 at (A, k, lam) = (16380, 8235, 1.978); rel. error <= 1.8e-13; max 6.5e+148; ok 9s x= 92: 2581 breakpoints up to A=135424; max N/P = 0.6263 at (A, k, lam) = (16744, 8417, 1.978); rel. error <= 1.8e-13; max 2.9e+150; ok 10s x= 93: 2609 breakpoints up to A=138384; max N/P = 0.6263 at (A, k, lam) = (17112, 8602, 1.978); rel. error <= 1.8e-13; max 1.3e+152; ok 11s x= 94: 2637 breakpoints up to A=141376; max N/P = 0.6263 at (A, k, lam) = (17484, 8788, 1.979); rel. error <= 1.8e-13; max 5.8e+153; ok 11s x= 95: 2665 breakpoints up to A=144400; max N/P = 0.6263 at (A, k, lam) = (17860, 8977, 1.979); rel. error <= 1.9e-13; max 2.6e+155; ok 11s x= 96: 2693 breakpoints up to A=147456; max N/P = 0.6263 at (A, k, lam) = (18240, 9167, 1.979); rel. error <= 1.9e-13; max 1.2e+157; ok 11s x= 97: 2721 breakpoints up to A=150544; max N/P = 0.6263 at (A, k, lam) = (18624, 9360, 1.979); rel. error <= 1.9e-13; max 5.3e+158; ok 13s x= 98: 2749 breakpoints up to A=153664; max N/P = 0.6262 at (A, k, lam) = (19012, 9554, 1.98); rel. error <= 1.9e-13; max 2.4e+160; ok 12s x= 99: 2777 breakpoints up to A=156816; max N/P = 0.6263 at (A, k, lam) = (19404, 9751, 1.98); rel. error <= 1.9e-13; max 1.1e+162; ok 13s x=100: 2805 breakpoints up to A=160000; max N/P = 0.6262 at (A, k, lam) = (19800, 9949, 1.98); rel. error <= 2.0e-13; max 4.8e+163; ok 14s x=101: 2833 breakpoints up to A=163216; max N/P = 0.6262 at (A, k, lam) = (20200, 10150, 1.98); rel. error <= 2.0e-13; max 2.1e+165; ok 14s x=102: 2861 breakpoints up to A=166464; max N/P = 0.6262 at (A, k, lam) = (20604, 10352, 1.98); rel. error <= 2.0e-13; max 9.6e+166; ok 15s x=103: 2889 breakpoints up to A=169744; max N/P = 0.6262 at (A, k, lam) = (21012, 10557, 1.981); rel. error <= 2.0e-13; max 4.3e+168; ok 15s x=104: 2917 breakpoints up to A=173056; max N/P = 0.6262 at (A, k, lam) = (21424, 10763, 1.981); rel. error <= 2.0e-13; max 1.9e+170; ok 16s x=105: 2945 breakpoints up to A=176400; max N/P = 0.6262 at (A, k, lam) = (21840, 10972, 1.981); rel. error <= 2.1e-13; max 8.6e+171; ok 16s ALL VERIFIED (774s) real 12m54.104s user 12m45.786s sys 0m0.195s # finished: 2026-10-27 04:39:01 UTC