# command: python3 pn_certificate.py --xc 201 --jobs 2
# started: 2026-10-27 02:18:27 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
#
sources: pn_certificate.py 1b487046af3818f1, rq_certificate.py b077df5d9e0b9b7b, cww_certificate.py 85f217ba1cc63c54
Theorem 9.24 (i): R(x, A) for x >= 201, 2x(x-1) < A <= 16.0 x^2; arb prec = 96
    table depth 0: 2986 leaves, 200 to split, 0 failed
    table depth 1: 3186 leaves, 0 to split, 0 failed
[T] table: 69 sigma x 44 nu base cells -> 3186 leaves, 0 failed; min score 0.676  5090s
    criterion depth 0: 29609 ok, 244 to refine, 0 failed
    criterion depth 1: 29853 ok, 0 to refine, 0 failed
[C] criterion, sigma <= 6: 29853 boxes verified, 0 failed; min margin 0.0007  32s
[P] sigma >= 6: 13 s-cells, min pl/Lu = 0.743; sup N/P = 0.0201 < 0.728: verified  1s
ALL VERIFIED (5122s)

real	85m22.553s
user	100m54.943s
sys	0m0.825s
# finished: 2026-10-27 03:43:50 UTC