### CODEHASH 6e909a06632570deb680  2026-10-13 19:31:15  cert_region_ii.py <workdir>\lam_L0174.npy 0.15399 0.2 5998313329980.3135
Certificate (ii): t0=0.15399 y0=0.2 X=5998313329980.3135  D=240
   [b_m table up to 690891: 2s]
eA+eB+eC0 <= 2.977e-07 for all x>=X+sqrt(1-y0^2), y in [y0,0.831877]
YTOP_HI 0.8318773948124809   (float upper bound of sqrt(1-2 t0); the y-intervals must reach it)
   [b_m table up to 863613: 2s]
   [b_m table up to 1079516: 2s]
   [b_m table up to 1349395: 2s]
   [b_m table up to 2059906: 6s]
OK y in [0.2,0.20500000000000002]: 11 chunks, certified |f_t0| >= 0.00594   [984s]
      x_a~5.998313e+12 N_a=690891 LB>=0.02188 extra/tail<=0.01021 |M|<=1.9646
      x_a~6.149203e+12 N_a=699527 LB>=0.02864 extra/tail<=0.01012 |M|<=1.9630
      x_a~6.303874e+12 N_a=708270 LB>=0.03535 extra/tail<=0.01889 |M|<=1.9614
      x_a~6.606820e+12 N_a=725089 LB>=0.04792 extra/tail<=0.01858 |M|<=1.9585
      x_a~6.924317e+12 N_a=742307 LB>=0.06035 extra/tail<=0.03083 |M|<=1.9555
      x_a~7.498225e+12 N_a=772457 LB>=0.08113 extra/tail<=0.04766 |M|<=1.9505
      x_a~8.519512e+12 N_a=823384 LB>=0.11361 extra/tail<=0.06963 |M|<=1.9425
      x_a~1.038146e+13 N_a=908917 LB>=0.16192 extra/tail<=0.09614 |M|<=1.9304
      x_a~1.398952e+13 N_a=1055107 LB>=0.23048 extra/tail<=0.12408 |M|<=1.9125
      x_a~2.172757e+13 N_a=1314924 LB>=0.32263 extra/tail<=0.19768 |M|<=1.8870
      x_a~5.332178e+13 N_a=2059906 LB>=0.48053 extra/tail<=0.43661 |M|<=1.8382
OK y in [0.20500000000000002,0.21500000000000002]: 9 chunks, certified |f_t0| >= 0.00966   [1827s]
      x_a~5.998313e+12 N_a=690891 LB>=0.03783 extra/tail<=0.01889 |M|<=1.9605
      x_a~6.286584e+12 N_a=707298 LB>=0.05043 extra/tail<=0.03135 |M|<=1.9575
      x_a~6.807689e+12 N_a=736029 LB>=0.07149 extra/tail<=0.03048 |M|<=1.9525
      x_a~7.372046e+12 N_a=765930 LB>=0.09215 extra/tail<=0.04711 |M|<=1.9475
      x_a~8.375988e+12 N_a=816419 LB>=0.12444 extra/tail<=0.06885 |M|<=1.9395
      x_a~1.020694e+13 N_a=901245 LB>=0.17247 extra/tail<=0.09504 |M|<=1.9275
      x_a~1.375440e+13 N_a=1046203 LB>=0.24059 extra/tail<=0.12265 |M|<=1.9097
      x_a~2.136288e+13 N_a=1303842 LB>=0.33212 extra/tail<=0.19537 |M|<=1.8843
      x_a~5.242893e+13 N_a=2042587 LB>=0.48881 extra/tail<=0.43122 |M|<=1.8357
OK y in [0.21500000000000002,0.23500000000000001]: 7 chunks, certified |f_t0| >= 0.01931   [2481s]
      x_a~5.998313e+12 N_a=690891 LB>=0.06851 extra/tail<=0.03081 |M|<=1.9522
      x_a~6.495492e+12 N_a=718954 LB>=0.08940 extra/tail<=0.04763 |M|<=1.9473
      x_a~7.380094e+12 N_a=766348 LB>=0.12206 extra/tail<=0.06961 |M|<=1.9393
      x_a~8.992953e+12 N_a=845953 LB>=0.17062 extra/tail<=0.09612 |M|<=1.9273
      x_a~1.211778e+13 N_a=981989 LB>=0.23948 extra/tail<=0.12411 |M|<=1.9095
      x_a~1.881944e+13 N_a=1223766 LB>=0.33196 extra/tail<=0.19787 |M|<=1.8841
      x_a~4.618310e+13 N_a=1917064 LB>=0.49017 extra/tail<=0.43820 |M|<=1.8356
OK y in [0.23500000000000001,0.275]: 5 chunks, certified |f_t0| >= 0.02836   [2900s]
      x_a~5.998313e+12 N_a=690891 LB>=0.12521 extra/tail<=0.07031 |M|<=1.9361
      x_a~7.309309e+12 N_a=762664 LB>=0.17438 extra/tail<=0.09713 |M|<=1.9241
      x_a~9.849348e+12 N_a=885317 LB>=0.24405 extra/tail<=0.17509 |M|<=1.9064
      x_a~1.860387e+13 N_a=1216737 LB>=0.37571 extra/tail<=0.18602 |M|<=1.8703
      x_a~4.565463e+13 N_a=1906064 LB>=0.52698 extra/tail<=0.41028 |M|<=1.8228
OK y in [0.275,0.35500000000000004]: 3 chunks, certified |f_t0| >= 0.01803   [3177s]
      x_a~5.998313e+12 N_a=690891 LB>=0.22162 extra/tail<=0.18727 |M|<=1.9050
      x_a~1.132976e+13 N_a=949523 LB>=0.35998 extra/tail<=0.19986 |M|<=1.8690
      x_a~2.780349e+13 N_a=1487458 LB>=0.51860 extra/tail<=0.44814 |M|<=1.8216
OK y in [0.35500000000000004,0.515]: 2 chunks, certified |f_t0| >= 0.01855   [3332s]
      x_a~5.998313e+12 N_a=690891 LB>=0.36045 extra/tail<=0.21325 |M|<=1.8472
      x_a~1.471967e+13 N_a=1082291 LB>=0.52364 extra/tail<=0.49022 |M|<=1.8016
OK y in [0.515,0.8318773948124809]: 2 chunks, certified |f_t0| >= 0.14245   [3489s]
      x_a~5.998313e+12 N_a=690891 LB>=0.51948 extra/tail<=0.17544 |M|<=1.7469
      x_a~1.471967e+13 N_a=1082291 LB>=0.64854 extra/tail<=0.40512 |M|<=1.7089
CERTIFIED (ii) [Arb]: t0=0.15399 y0=0.2 X=5998313329980.3135 : |f_t0| >= 0.00594 > eA+eB+eC0 (<= 2.98e-07) for all x>=X+sqrt(1-y0^2), y in [0.200000, 0.831877]; 7 y-intervals; 3489s