K  file rid_slice_certs_22_25.json md5 63b3b002a3a9ebf333e5a719c3410c11; C = 22/25 = 0.88; A = 50/33; 4/(3C) = 50/33; A >= 4/(3C): True; cells 142; complete flag True
M  E Z^k, k <= 10: recursion == integer-partition formula: True; kappa_n = int x^(n-2) dK (n <= 10): True; coefficient of every free moment m3..m8 affine in (m1, m2): True; the only other term is 126 m3^2 in E Z^10: True; Poisson check max error 5.3e-46  (0.5s)
M  number of monomials of E Z^k, k = 0..10: [1, 0, 1, 1, 2, 2, 4, 4, 7, 8, 12]; E Z^10 constant term = 945 (= 9!! = 945)
C  c10>=0: 142/142
C  (i) arb: 142/142
C  (i) sturm: 142/142
C  (iii) arb: 142/142
C  (iii) sturm: 142/142
C  L<=U: 142/142
C  (iv) bernstein: 142/142
C  (iv) taylor: 142/142
C  taylor == file bound: 142/142
C  worst Bernstein bound 0.879194463 (cell 127, 1 pieces); worst Taylor bound 0.879974054; worst vertex value of F 0.879194463; C = 0.88
C  majorant degrees {8: 6, 10: 136}; bidegrees of F {(3, 2): 136, (2, 2): 6}; Bernstein pieces in total 142  (0s)
T  142 cells, all inside [0, A] x [0, A^2]: True; cover D+: True ; cells entirely below m2 = m1^2: 0; overlapping pairs: 0
T  dropping any one cell breaks the cover: 139/142
Q  (e^s - 1)/s is increasing (its derivative is int_0^s t e^t dt / s^2 > 0), so B < 1 iff q < q* = 0.388146394; certified sign change at q* -+ 1e-12: True; stated q < 0.38815 / 0.3881
Q  q = 0.1: B(q) <= 0.9036962366 <= stated 0.9037: True
Q  q = 0.2: B(q) <= 0.9314520572 <= stated 0.9315: True
Q  q = 0.25: B(q) <= 0.9472522498 <= stated 0.9473: True
Q  sup over (0, 1/4] of B/M = 1.03649495 at q = 0.1835034191 (1 - sqrt(2/3) = 0.1835034191); certified value there in [1.03649495, 1.03649495]; grid max 1.03649264; 'within 3.65%': True; limit c sqrt(e/2) = 1.0259234
RESULT: ALL CHECKS PASSED (parts KMCTQ, 73s)
