# command: python3 rq_certificate.py --parts PF
# started: 2026-10-27 02:59:47 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
#
Certificate for Theorem 9.16 (ii) (rational q-Catalan monotonicity, x >= 201, x <= y <= 2x); arb prec = 96
k > KL = 5000 forces s < pi/sqrt(6(KL+1)) = 0.018136 < S_TOP = [0.01820 +/- 1e-10]
[A] A_r bounds verified  1s
[P] sigma >= 6, 0 < s <= [0.01820 +/- 1e-10]: verified {'G0': 1.1340891188170825, 'U': 6.424, 'kmin': 0.3016708301392576, 'far0': 0.00014731708462026715, 'far1': 0.01280361543935428, 'margin': 1.121138186293108}  0s
[F] 0 <= sigma <= 6, 1 <= nu <= 2: 1790 cells verified, 0 failed; min(G0 - sqrt(K) I0) = 0.6878 (criterion a), min margin 0.7514 (criterion b only); max A = -0.0489; min rate*xc = 23.2  1427s
ALL VERIFIED (1428s)

real	23m48.143s
user	23m13.761s
sys	0m0.193s
# finished: 2026-10-27 03:23:36 UTC