# command: python3 corner_check.py 1000 60
# started: 2026-10-27 02:08:40 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) c_k >= c_{k-2} and c_k >= c_{k-3} for k <= (n^2-2n)/2: true for all 2 <= n <= 1000
    => FStep holds at the corner (a+1, a+1) for every 2 <= a <= 999
(B) Stanley's theorem: (1+q)C_n/(1+q^n) palindromic and unimodal for all 2 <= n <= 1000
(C) C_n not nondecreasing on [2, n(n-1)/2] exactly for n in [4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 15]
    on the corner range [2, (n^2-2n)/2]: (a, first failing degree) = [(4, 7), (5, 7), (6, 13), (8, 31)]
(F) (1+q)C_n unimodal: true for all 2 <= n <= 1000
(D) Proposition 8.12 identity and corner inequality: verified for 2 <= a <= 60
(E) Lemma 8.11 (FStep at the corner <=> q-Catalan form): verified for 2 <= a <= 60
time 415.6s

real	6m55.634s
user	6m35.570s
sys	0m0.563s
# finished: 2026-10-27 02:15:36 UTC