# command: python3 cww_certificate.py
# started: 2026-10-27 02:15:36 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 C' (q-Catalan unimodality for n >= 1001); python-flint arb, prec = 96 bits
k > K0 = 10000 forces s < pi/sqrt(6(K0+1)) = 0.012825 <= S_TOP = [0.012830 +/- 1e-11]
[A] A_r upper bounds {3: 1.00993, 4: 1.03778, 5: 1.07918, 6: 1.12766} (values used: {3: '[1.011 +/- 1e-8]', 4: '[1.039 +/- 1e-8]', 5: '[1.080 +/- 3e-8]', 6: '[1.130 +/- 1e-8]'})  1s
[L] exact, K0 = 10000, 16 <= n <= K0: failures of c_{k-1} <= c_k: none; equalities with k >= n+2: none  20s
[P] 0 < s <= [0.012830 +/- 1e-11], sigma >= 6: verified  G0 >= 1.1550, far terms <= 1.33e-07 + 1.64e-05, margin 1.1550, kappa_min = 0.3093, U = 7.664  0s
[F] 0 <= sigma <= 6, n >= 1001: 179/179 cells verified; min(G0 - sqrt(K) I0) = 1.0970, min G2/(K^1.5 I1) = 1.232, 15 cells via (1-rho)-form (min margin 1.0788); max A = -0.0338 (< -5/N0), min rate = 0.0316 (> 6/N0)  762s
ALL VERIFIED (783s)

real	13m2.917s
user	9m53.206s
sys	0m0.267s
# finished: 2026-10-27 02:28:40 UTC