# command: python3 circle_check.py
# started: 2026-10-27 02:07:37 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
#
(A) g(x) = (x/2)^2/sinh^2(x/2):  min_{0<x<=2} -g'(x)/x = 0.1133 (>= 1/10);  min_{0<=x<=1} g(x)-g(x+1) = 0.0793 (>= 0.079)
(B) Lemma 9.5, n=40, r in {n, n-1}, 4 values of s, 6 of theta: max exact/bound = 0.157 (<= 1)
(C) Lemma 9.3, n=60: max over tests of sup|L^(r)| / bound = 0.998 (<= 1);  Lemma 9.4: max ratio = 0.969 (<= 1)
(D) Lemma 9.2, n=12: max |formula - (c_k - c_{k-1})| = 1.8e-13
(E) n=1001: min over 41 saddle points of (local lower bound - |rest|)/M = 0.9642 at k = 1003 (lambda = 3); 58s

real	1m2.361s
user	0m59.612s
sys	0m0.059s
# finished: 2026-10-27 02:08:40 UTC