PASS  kappa_+ = 49/20 satisfies kappa_+^2 = 2401/400 > 6

== Theorem 1.2(d), first line: m_0..m_44 from the definition of the operators (direct moments of this run), J = 20 ==
   exact enclosure of this run: 2.585794744033 < c < 2.586036943331   0.250011133605 < w < 0.253121331264
PASS  stated: 2.58579 < c < 2.58604
PASS  stated: 0.25001 < w < 0.25313
PASS  Table 2 row 1: (2.585794744, 2.586036944) and (0.250011133, 0.253121332) contain it, and agree to the digits shown
PASS  2w > 1/2 from the direct moments alone   w - 1/4 > 1.113e-05
PASS  first verification run's intervals 2.58579474 < c < 2.58603695, 0.25001113 < w < 0.25312134 contain the enclosure
PASS  directly at the stated end points: F_up(2.58579) < 0 < F_lo(2.58604)

== the remarks after Table 2 ==
PASS  2582/1000 > 2 sqrt(5/3)
   with kappa_+ = 2.582 (Certificate A), m_0..m_44: 2.585794 < c < 2.589857,  0.0717 < w < 0.6144
PASS  note: 'only 0.0717 < w < 0.6145' with the constant of Certificate A   (the value depends slightly on the rational chosen above 2 sqrt(5/3))
   m_0..m_42, kappa_+ = 49/20: 2.585778291 < c < 2.586144965,  0.249394 < w < 0.253963
PASS  note: with m_0..m_42 the lower bound for w is 0.2493 (below 1/4)
   k_2..k_48 (model cumulants of this run; this run has direct moments only up to m_44): 0.250720 < w < 0.252158
PASS  note: from m_0..m_48, w > 0.25072

== Table 2, rows 2-5, and Theorem 1.2(d), second line (cumulants of the model) ==
   J =  78 (k_2..k_160): width of the c-interval 8.765e-15, of the w-interval 3.152e-13   [note: 8.8e-15, 3.2e-13]   (0s)
PASS  J = 78: widths agree with Table 2 (two digits are printed there; tolerance 5 per cent)
   J =  98 (k_2..k_200): width of the c-interval 2.208e-18, of the w-interval 9.704e-17   [note: 2.2e-18, 9.7e-17]   (0s)
PASS  J = 98: widths agree with Table 2 (two digits are printed there; tolerance 5 per cent)
   J = 151 (k_2..k_306): width of the c-interval 6.415e-28, of the w-interval 4.179e-26   [note: 6.4e-28, 4.2e-26]   (0s)
PASS  J = 151: widths agree with Table 2 (two digits are printed there; tolerance 5 per cent)
   J = 278 (k_2..k_560): width of the c-interval 9.019e-51, of the w-interval 1.045e-48   [note: 9.0e-51, 1.0e-48]   (1s)
PASS  J = 278: widths agree with Table 2 (two digits are printed there; tolerance 5 per cent)
   J = 151: 2.58582660604820444863151523603252 < c < 2.58582660604820444863151523667405
            0.251331654638419314530505656642 < w < 0.251331654638419314530505698430
PASS  Theorem 1.2(d): 2.58582660604820444863151523603 < c < 2.58582660604820444863151523668
PASS  Theorem 1.2(d): 0.251331654638419314530505656 < w < 0.251331654638419314530505699
PASS  the same enclosure from the cumulants k_2..k_306 of the package's file
PASS  directly at the stated end points: F_up(z_-) < 0 < F_lo(z_+)
PASS  caption of Table 2: 2.585826606048203 < c < 2.585826606048213 and 0.25133165463828 < w < 0.25133165463861 contain the J = 78 enclosure
PASS  the intervals of rows 2-5 are nested
   J = 278: c = 2.585826606048204448631515236116841507809242807997919952...  /  2.585826606048204448631515236116841507809242807997928971
            w = 0.25133165463841931453050567432858126056719804177373...  /  0.25133165463841931453050567432858126056719804177478
PASS  displayed digits of c (49 decimals) lie in the J = 278 enclosure
PASS  displayed digits of w (44 decimals) lie in the J = 278 enclosure
PASS  abstract: c = 2.585826606048204448..., w = 0.251331654638419314...
PASS  Figure 1: 1 - 2w = 0.4973...
PASS  Step 6: w <= 2/c^2 < 1/3
TOTAL failures: 0   (1s)
