# command: python3 row_check.py 60 2
# started: 2026-10-27 02:04:27 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
#
x=  2, 4 <= A <= 8: holds; smallest relative margin -
x=  3, 9 <= A <= 18: holds; smallest relative margin 0 (A=9, k=4)
x=  4, 16 <= A <= 32: holds; smallest relative margin 0 (A=16, k=5)
x=  5, 25 <= A <= 50: holds; smallest relative margin 0 (A=25, k=6)
x=  6, 36 <= A <= 72: holds; smallest relative margin 0 (A=36, k=7)
x=  7, 49 <= A <= 98: holds; smallest relative margin 0 (A=49, k=8)
x=  8, 64 <= A <= 128: holds; smallest relative margin 0 (A=64, k=9)
x=  9, 81 <= A <= 162: holds; smallest relative margin 0 (A=81, k=10)
x= 10, 100 <= A <= 200: holds; smallest relative margin 0 (A=100, k=11)
x= 11, 121 <= A <= 242: holds; smallest relative margin 0 (A=121, k=12)
x= 12, 144 <= A <= 288: holds; smallest relative margin 0 (A=144, k=13)
x= 13, 169 <= A <= 338: holds; smallest relative margin 0 (A=169, k=14)
x= 14, 196 <= A <= 392: holds; smallest relative margin 0 (A=196, k=15)
x= 15, 225 <= A <= 450: holds; smallest relative margin 0 (A=225, k=16)
x= 16, 256 <= A <= 512: holds; smallest relative margin 0 (A=256, k=17)
x= 17, 289 <= A <= 578: holds; smallest relative margin 0 (A=289, k=18)
x= 18, 324 <= A <= 648: holds; smallest relative margin 0 (A=324, k=19)
x= 19, 361 <= A <= 722: holds; smallest relative margin 0 (A=361, k=20)
x= 20, 400 <= A <= 800: holds; smallest relative margin 0 (A=400, k=21)
x= 21, 441 <= A <= 882: holds; smallest relative margin 0 (A=441, k=22)
x= 22, 484 <= A <= 968: holds; smallest relative margin 0 (A=484, k=23)
x= 23, 529 <= A <= 1058: holds; smallest relative margin 0 (A=529, k=24)
x= 24, 576 <= A <= 1152: holds; smallest relative margin 0 (A=576, k=25)
x= 25, 625 <= A <= 1250: holds; smallest relative margin 0 (A=625, k=26)
x= 26, 676 <= A <= 1352: holds; smallest relative margin 0 (A=676, k=27)
x= 27, 729 <= A <= 1458: holds; smallest relative margin 0 (A=729, k=28)
x= 28, 784 <= A <= 1568: holds; smallest relative margin 0 (A=784, k=29)
x= 29, 841 <= A <= 1682: holds; smallest relative margin 0 (A=841, k=30)
x= 30, 900 <= A <= 1800: holds; smallest relative margin 0 (A=900, k=31)
x= 31, 961 <= A <= 1922: holds; smallest relative margin 0 (A=961, k=32)
x= 32, 1024 <= A <= 2048: holds; smallest relative margin 0 (A=1024, k=33)
x= 33, 1089 <= A <= 2178: holds; smallest relative margin 0 (A=1089, k=34)
x= 34, 1156 <= A <= 2312: holds; smallest relative margin 0 (A=1156, k=35)
x= 35, 1225 <= A <= 2450: holds; smallest relative margin 0 (A=1225, k=36)
x= 36, 1296 <= A <= 2592: holds; smallest relative margin 0 (A=1296, k=37)
x= 37, 1369 <= A <= 2738: holds; smallest relative margin 0 (A=1369, k=38)
x= 38, 1444 <= A <= 2888: holds; smallest relative margin 0 (A=1444, k=39)
x= 39, 1521 <= A <= 3042: holds; smallest relative margin 0 (A=1521, k=40)
x= 40, 1600 <= A <= 3200: holds; smallest relative margin 0 (A=1600, k=41)
x= 41, 1681 <= A <= 3362: holds; smallest relative margin 0 (A=1681, k=42)
x= 42, 1764 <= A <= 3528: holds; smallest relative margin 0 (A=1764, k=43)
x= 43, 1849 <= A <= 3698: holds; smallest relative margin 0 (A=1849, k=44)
x= 44, 1936 <= A <= 3872: holds; smallest relative margin 0 (A=1936, k=45)
x= 45, 2025 <= A <= 4050: holds; smallest relative margin 0 (A=2025, k=46)
x= 46, 2116 <= A <= 4232: holds; smallest relative margin 0 (A=2116, k=47)
x= 47, 2209 <= A <= 4418: holds; smallest relative margin 0 (A=2209, k=48)
x= 48, 2304 <= A <= 4608: holds; smallest relative margin 0 (A=2304, k=49)
x= 49, 2401 <= A <= 4802: holds; smallest relative margin 0 (A=2401, k=50)
x= 50, 2500 <= A <= 5000: holds; smallest relative margin 0 (A=2500, k=51)
x= 51, 2601 <= A <= 5202: holds; smallest relative margin 0 (A=2601, k=52)
x= 52, 2704 <= A <= 5408: holds; smallest relative margin 0 (A=2704, k=53)
x= 53, 2809 <= A <= 5618: holds; smallest relative margin 0 (A=2809, k=54)
x= 54, 2916 <= A <= 5832: holds; smallest relative margin 0 (A=2916, k=55)
x= 55, 3025 <= A <= 6050: holds; smallest relative margin 0 (A=3025, k=56)
x= 56, 3136 <= A <= 6272: holds; smallest relative margin 0 (A=3136, k=57)
x= 57, 3249 <= A <= 6498: holds; smallest relative margin 0 (A=3249, k=58)
x= 58, 3364 <= A <= 6728: holds; smallest relative margin 0 (A=3364, k=59)
x= 59, 3481 <= A <= 6962: holds; smallest relative margin 0 (A=3481, k=60)
x= 60, 3600 <= A <= 7200: holds; smallest relative margin 0 (A=3600, k=61)
done: 0 failures, 190s

real	3m9.563s
user	3m5.855s
sys	0m0.392s
# finished: 2026-10-27 02:07:37 UTC