K  file rid12_certs_87_100.json md5 b4a0fea93c285bbc00759f373a46bc90; C = 87/100 = 0.87; A = 99/70; A^2 = 9801/4900 > 2: True; degree 12; cells 181; complete flag True
M  E Z^k, k <= 12: recursion == integer-partition formula: True; kappa_n = int x^(n-2) dK (n <= 12): True
M  every one-free-moment coefficient B_kj in span{1, m1, m2, m1^2, m1 m2}: True; m1^2 terms {(11, 3): 4620, (12, 4): 9240} (= 4620 c11 in B_3, 9240 c12 in B_4: True)
M  two-free-moment terms [(10, {'m3^2': 126}), (11, {'m3^1m4^1': 462}), (12, {'m3^2': 8316, 'm3^1m5^1': 792, 'm4^2': 462})]; equal to block counting: True; equal to the text's list: True; no monomial with >= 3 free moments: True
M  law vs formulas: Diracs max error 2.0e-44; Gaussian + two atoms max error 4.3e-41; monomials of E Z^k, k = 0..12: [1, 0, 1, 1, 2, 2, 4, 4, 7, 8, 12, 14, 21]  (0.5s)
C  c12>=0: 181/181
C  a2>=0: 181/181
C  coefficients al, be, ga, de as in the text: 181/181
C  Ec as in the text: 181/181
C  B~_j in span{1, m1, m2, m1 m2}: 181/181
C  (i) arb: 181/181
C  (i) sturm: 181/181
C  L<=U: 181/181
C  (iv) arb: 181/181
C  (iv) sturm: 181/181
C  (v) bernstein: 181/181
C  (v) taylor: 181/181
C  taylor == file bound: 181/181
C  worst Bernstein bound 0.869667577 (cell 148, 1 pieces); worst Taylor bound 0.869934363; worst vertex value of F 0.869655150; C = 0.87
C  sign patterns {('al+', 'be-'): 170, ('al-', 'be-'): 11}; bidegrees of F {(4, 3): 181}; max Ec 3.548e-03; Bernstein pieces in total 181  (2s)
T  181 cells, all inside [0, A] x [0, A^2]: True; cover D+ (a19 sweep): True ; cover D+ (second sweep, 18 strips): True; cells entirely below m2 = m1^2: 0; overlapping pairs: 0
T  cells needed for the cover (exact drop-one): 178/181; not needed: 3 [(48, [0.3535714285714286, 0.4714285714285714, 0.0, 0.12501275510204082], True), (93, [0.7071428571428572, 0.825, 0.37503826530612244, 0.5000510204081633], True), (119, [1.0607142857142857, 1.1785714285714286, 1.0001020408163266, 1.1251147959183674], True)]  (0s)
RESULT: ALL CHECKS PASSED (parts KMCT, 3s)

real	0m2.776s
user	0m9.062s
sys	0m0.127s
