K  file rid12_certs_867_1000.json md5 9e0e29f9e31e005f3d44b79a3052feeb; C = 867/1000 = 0.867; A = 99/70; A^2 = 9801/4900 > 2: True; degree 12; cells 1122; 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: 1122/1122
C  a2>=0: 1122/1122
C  coefficients al, be, ga, de as in the text: 1122/1122
C  Ec as in the text: 1122/1122
C  B~_j in span{1, m1, m2, m1 m2}: 1122/1122
C  (i) arb: 1122/1122
C  (i) sturm: 1122/1122
C  L<=U: 1122/1122
C  (iv) arb: 1122/1122
C  (iv) sturm: 1122/1122
C  (v) bernstein: 1122/1122
C  (v) taylor: 1122/1122
C  taylor == file bound: 1122/1122
C  worst Bernstein bound 0.866992662 (cell 600, 1 pieces); worst Taylor bound 0.866997687; worst vertex value of F 0.866992662; C = 0.867
C  sign patterns {('al+', 'be-'): 922, ('al-', 'be-'): 200}; bidegrees of F {(4, 3): 1122}; max Ec 3.548e-03; Bernstein pieces in total 1122  (12s)
T  1122 cells, all inside [0, A] x [0, A^2]: True; cover D+ (a19 sweep): True ; cover D+ (second sweep, 106 strips): True; cells entirely below m2 = m1^2: 0; overlapping pairs: 0
T  cells needed for the cover (exact drop-one): 1119/1122; not needed: 3 [(48, [0.3535714285714286, 0.4714285714285714, 0.0, 0.12501275510204082], True), (91, [0.7071428571428572, 0.825, 0.37503826530612244, 0.5000510204081633], True), (109, [1.0607142857142857, 1.1785714285714286, 1.0001020408163266, 1.1251147959183674], True)]  (1s)
Q  B(q)^2 = c^2 (e^s - 1)/s with s = ln(1/(1-q)) is increasing, so B < 1 iff q < q* = 0.4207821911; certified sign change at q* -+ 1e-12: True; B < 1 at the stated thresholds ['0.4207', '0.42078']: [True, True]
Q  q = 0.1: B(q) <= 0.8903461786 <= stated 0.8904: True
Q  q = 0.2: B(q) <= 0.91769197 <= stated 0.9177: True
Q  q = 0.25: B(q) <= 0.9332587507 <= stated 0.9333: True
Q  sup over (0, 1/4] of B/M = 1.0211831 at q = 0.1835034191 (1 - sqrt(2/3) = 0.1835034191); certified value there in [1.0211831, 1.0211831]; grid max 1.02118081; stated sup 1.02118, 'within 2.12%': True; limit c sqrt(e/2) = 1.0107677 (stated 1.0108)
RESULT: ALL CHECKS PASSED (parts KMCTQ, 87s)

real	1m26.661s
user	2m7.638s
sys	0m0.132s
