### CODEHASH 6e909a06632570deb680  2026-10-20 10:00:51  cert_barrier.py 5998313329980.3135 0.15399 0.2
Barrier certificate: X=5998313329980.3135 t0=0.15399 y0=0.2 N=690891
moments: 20 blocks, 23s
step   0 t=[0.000000,0.000200] ylo=0.5896 pts= 1826 h=1.55e-03 min|f|>=4.7994 Dz<=646.1 Dt<=4261.6 E<=2.3e-05 margin=3.4477 wind=0 [2s]
step   1 t=[0.000200,0.000921] ylo=0.5883 pts=  952 h=2.97e-03 min|f|>=4.7864 Dz<=645.5 Dt<=4255.8 E<=2.3e-05 margin=0.7612 wind=0 [3s]
step   2 t=[0.000921,0.001641] ylo=0.5871 pts=  956 h=2.96e-03 min|f|>=4.7403 Dz<=630.7 Dt<=4158.3 E<=2.2e-05 margin=0.8142 wind=0 [4s]
step   3 t=[0.001641,0.002370] ylo=0.5859 pts=  942 h=3.00e-03 min|f|>=4.6950 Dz<=616.3 Dt<=4063.7 E<=2.2e-05 margin=0.8049 wind=0 [5s]
step   4 t=[0.002370,0.003110] ylo=0.5846 pts=  932 h=3.04e-03 min|f|>=4.6498 Dz<=602.0 Dt<=3970.0 E<=2.1e-05 margin=0.7994 wind=0 [6s]
step   5 t=[0.003110,0.003859] ylo=0.5833 pts=  918 h=3.09e-03 min|f|>=4.6048 Dz<=587.9 Dt<=3877.4 E<=2.1e-05 margin=0.7910 wind=0 [7s]
step   6 t=[0.003859,0.004619] ylo=0.5820 pts=  908 h=3.13e-03 min|f|>=4.5599 Dz<=574.0 Dt<=3785.9 E<=2.0e-05 margin=0.7856 wind=0 [8s]
step   7 t=[0.004619,0.005390] ylo=0.5807 pts=  894 h=3.18e-03 min|f|>=4.5152 Dz<=560.2 Dt<=3695.3 E<=2.0e-05 margin=0.7769 wind=0 [9s]
step   8 t=[0.005390,0.006172] ylo=0.5793 pts=  884 h=3.22e-03 min|f|>=4.4705 Dz<=546.6 Dt<=3605.8 E<=1.9e-05 margin=0.7721 wind=0 [10s]
step   9 t=[0.006172,0.006966] ylo=0.5780 pts=  870 h=3.27e-03 min|f|>=4.4261 Dz<=533.1 Dt<=3517.3 E<=1.9e-05 margin=0.7631 wind=0 [11s]
step  10 t=[0.006966,0.007771] ylo=0.5766 pts=  860 h=3.31e-03 min|f|>=4.3817 Dz<=519.8 Dt<=3429.9 E<=1.8e-05 margin=0.7589 wind=0 [12s]
step  11 t=[0.007771,0.008588] ylo=0.5752 pts=  846 h=3.37e-03 min|f|>=4.3375 Dz<=506.6 Dt<=3343.4 E<=1.8e-05 margin=0.7497 wind=0 [13s]
step  12 t=[0.008588,0.009419] ylo=0.5737 pts=  834 h=3.42e-03 min|f|>=4.2934 Dz<=493.6 Dt<=3258.0 E<=1.7e-05 margin=0.7431 wind=0 [14s]
step  13 t=[0.009419,0.010262] ylo=0.5722 pts=  822 h=3.48e-03 min|f|>=4.2494 Dz<=480.8 Dt<=3173.6 E<=1.7e-05 margin=0.7368 wind=0 [15s]
step  14 t=[0.010262,0.011119] ylo=0.5707 pts=  810 h=3.53e-03 min|f|>=4.2055 Dz<=468.1 Dt<=3090.2 E<=1.6e-05 margin=0.7303 wind=0 [16s]
step  15 t=[0.011119,0.011990] ylo=0.5692 pts=  798 h=3.59e-03 min|f|>=4.1617 Dz<=455.6 Dt<=3007.9 E<=1.6e-05 margin=0.7242 wind=0 [17s]
step  16 t=[0.011990,0.012876] ylo=0.5677 pts=  786 h=3.65e-03 min|f|>=4.1181 Dz<=443.2 Dt<=2926.5 E<=1.5e-05 margin=0.7179 wind=0 [18s]
step  17 t=[0.012876,0.013776] ylo=0.5661 pts=  774 h=3.71e-03 min|f|>=4.0745 Dz<=431.0 Dt<=2846.2 E<=1.5e-05 margin=0.7121 wind=0 [19s]
step  18 t=[0.013776,0.014692] ylo=0.5644 pts=  762 h=3.77e-03 min|f|>=4.0311 Dz<=418.9 Dt<=2766.9 E<=1.5e-05 margin=0.7057 wind=0 [20s]
step  19 t=[0.014692,0.015625] ylo=0.5628 pts=  748 h=3.85e-03 min|f|>=3.9878 Dz<=407.0 Dt<=2688.6 E<=1.4e-05 margin=0.6982 wind=0 [21s]
step  20 t=[0.015625,0.016574] ylo=0.5611 pts=  736 h=3.92e-03 min|f|>=3.9445 Dz<=395.2 Dt<=2611.3 E<=1.4e-05 margin=0.6913 wind=0 [21s]
step  21 t=[0.016574,0.017541] ylo=0.5594 pts=  724 h=3.98e-03 min|f|>=3.9013 Dz<=383.6 Dt<=2535.0 E<=1.3e-05 margin=0.6864 wind=0 [22s]
step  22 t=[0.017541,0.018526] ylo=0.5576 pts=  710 h=4.07e-03 min|f|>=3.8583 Dz<=372.2 Dt<=2459.7 E<=1.3e-05 margin=0.6790 wind=0 [23s]
step  23 t=[0.018526,0.019530] ylo=0.5558 pts=  700 h=4.13e-03 min|f|>=3.8153 Dz<=360.9 Dt<=2385.4 E<=1.2e-05 margin=0.6748 wind=0 [24s]
step  24 t=[0.019530,0.020553] ylo=0.5540 pts=  686 h=4.22e-03 min|f|>=3.7723 Dz<=349.8 Dt<=2312.2 E<=1.2e-05 margin=0.6676 wind=0 [25s]
step  25 t=[0.020553,0.021597] ylo=0.5521 pts=  672 h=4.31e-03 min|f|>=3.7295 Dz<=338.8 Dt<=2239.9 E<=1.2e-05 margin=0.6605 wind=0 [26s]
step  26 t=[0.021597,0.022663] ylo=0.5501 pts=  662 h=4.39e-03 min|f|>=3.6867 Dz<=328.0 Dt<=2168.7 E<=1.1e-05 margin=0.6565 wind=0 [27s]
step  27 t=[0.022663,0.023751] ylo=0.5482 pts=  648 h=4.48e-03 min|f|>=3.6440 Dz<=317.3 Dt<=2098.5 E<=1.1e-05 margin=0.6494 wind=0 [28s]
step  28 t=[0.023751,0.024862] ylo=0.5461 pts=  634 h=4.59e-03 min|f|>=3.6013 Dz<=306.8 Dt<=2029.2 E<=1.0e-05 margin=0.6424 wind=0 [29s]
step  29 t=[0.024862,0.025998] ylo=0.5440 pts=  622 h=4.69e-03 min|f|>=3.5587 Dz<=296.4 Dt<=1961.0 E<=1.0e-05 margin=0.6355 wind=0 [29s]
step  30 t=[0.025998,0.027160] ylo=0.5419 pts=  610 h=4.78e-03 min|f|>=3.5161 Dz<=286.2 Dt<=1893.9 E<=9.7e-06 margin=0.6318 wind=0 [30s]
step  31 t=[0.027160,0.028348] ylo=0.5397 pts=  596 h=4.90e-03 min|f|>=3.4736 Dz<=276.2 Dt<=1827.7 E<=9.4e-06 margin=0.6250 wind=0 [31s]
step  32 t=[0.028348,0.029564] ylo=0.5374 pts=  582 h=5.03e-03 min|f|>=3.4311 Dz<=266.3 Dt<=1762.5 E<=9.0e-06 margin=0.6178 wind=0 [32s]
step  33 t=[0.029564,0.030810] ylo=0.5351 pts=  572 h=5.13e-03 min|f|>=3.3886 Dz<=256.6 Dt<=1698.4 E<=8.7e-06 margin=0.6148 wind=0 [32s]
step  34 t=[0.030810,0.032087] ylo=0.5327 pts=  558 h=5.26e-03 min|f|>=3.3461 Dz<=247.0 Dt<=1635.3 E<=8.3e-06 margin=0.6081 wind=0 [33s]
step  35 t=[0.032087,0.033396] ylo=0.5303 pts=  544 h=5.41e-03 min|f|>=3.3037 Dz<=237.6 Dt<=1573.2 E<=8.0e-06 margin=0.6014 wind=0 [34s]
step  36 t=[0.033396,0.034740] ylo=0.5277 pts=  530 h=5.56e-03 min|f|>=3.2612 Dz<=228.3 Dt<=1512.1 E<=7.7e-06 margin=0.5947 wind=0 [35s]
step  37 t=[0.034740,0.036121] ylo=0.5251 pts=  520 h=5.68e-03 min|f|>=3.2188 Dz<=219.2 Dt<=1452.1 E<=7.3e-06 margin=0.5917 wind=0 [35s]
step  38 t=[0.036121,0.037539] ylo=0.5224 pts=  506 h=5.85e-03 min|f|>=3.1763 Dz<=210.3 Dt<=1393.1 E<=7.0e-06 margin=0.5852 wind=0 [36s]
step  39 t=[0.037539,0.038999] ylo=0.5196 pts=  492 h=6.02e-03 min|f|>=3.1338 Dz<=201.5 Dt<=1335.2 E<=6.7e-06 margin=0.5787 wind=0 [37s]
step  40 t=[0.038999,0.040501] ylo=0.5167 pts=  478 h=6.21e-03 min|f|>=3.0913 Dz<=192.8 Dt<=1278.3 E<=6.4e-06 margin=0.5722 wind=0 [38s]
step  41 t=[0.040501,0.042048] ylo=0.5137 pts=  464 h=6.41e-03 min|f|>=3.0487 Dz<=184.4 Dt<=1222.4 E<=6.1e-06 margin=0.5658 wind=0 [38s]
step  42 t=[0.042048,0.043645] ylo=0.5106 pts=  452 h=6.61e-03 min|f|>=3.0061 Dz<=176.1 Dt<=1167.6 E<=5.8e-06 margin=0.5601 wind=0 [39s]
step  43 t=[0.043645,0.045292] ylo=0.5073 pts=  440 h=6.80e-03 min|f|>=2.9634 Dz<=167.9 Dt<=1113.9 E<=5.5e-06 margin=0.5568 wind=0 [40s]
step  44 t=[0.045292,0.046995] ylo=0.5040 pts=  426 h=7.04e-03 min|f|>=2.9207 Dz<=160.0 Dt<=1061.3 E<=5.2e-06 margin=0.5504 wind=0 [40s]
step  45 t=[0.046995,0.048756] ylo=0.5005 pts=  412 h=7.30e-03 min|f|>=2.8778 Dz<=152.2 Dt<=1009.7 E<=5.0e-06 margin=0.5441 wind=0 [41s]
step  46 t=[0.048756,0.050580] ylo=0.4968 pts=  400 h=7.52e-03 min|f|>=2.8349 Dz<=144.5 Dt<=959.2 E<=4.7e-06 margin=0.5418 wind=0 [42s]
step  47 t=[0.050580,0.052472] ylo=0.4930 pts=  386 h=7.81e-03 min|f|>=2.7918 Dz<=137.1 Dt<=909.8 E<=4.4e-06 margin=0.5355 wind=0 [42s]
step  48 t=[0.052472,0.054436] ylo=0.4890 pts=  372 h=8.13e-03 min|f|>=2.7486 Dz<=129.8 Dt<=861.5 E<=4.2e-06 margin=0.5291 wind=0 [43s]
step  49 t=[0.054436,0.056477] ylo=0.4848 pts=  360 h=8.45e-03 min|f|>=2.7052 Dz<=122.6 Dt<=814.4 E<=3.9e-06 margin=0.5245 wind=0 [44s]
step  50 t=[0.056477,0.058603] ylo=0.4804 pts=  346 h=8.81e-03 min|f|>=2.6617 Dz<=115.7 Dt<=768.4 E<=3.7e-06 margin=0.5187 wind=0 [44s]
step  51 t=[0.058603,0.060820] ylo=0.4758 pts=  332 h=9.20e-03 min|f|>=2.6180 Dz<=108.9 Dt<=723.5 E<=3.5e-06 margin=0.5131 wind=0 [45s]
step  52 t=[0.060820,0.063136] ylo=0.4709 pts=  322 h=9.52e-03 min|f|>=2.5741 Dz<=102.3 Dt<=679.8 E<=3.2e-06 margin=0.5125 wind=0 [46s]
step  53 t=[0.063136,0.065560] ylo=0.4657 pts=  308 h=1.00e-02 min|f|>=2.5300 Dz<=95.9 Dt<=637.3 E<=3.0e-06 margin=0.5060 wind=0 [46s]
step  54 t=[0.065560,0.068100] ylo=0.4602 pts=  294 h=1.05e-02 min|f|>=2.4857 Dz<=89.7 Dt<=596.0 E<=2.8e-06 margin=0.4993 wind=0 [47s]
step  55 t=[0.068100,0.070770] ylo=0.4544 pts=  282 h=1.10e-02 min|f|>=2.4410 Dz<=83.7 Dt<=555.9 E<=2.6e-06 margin=0.4975 wind=0 [47s]
step  56 t=[0.070770,0.073580] ylo=0.4481 pts=  268 h=1.16e-02 min|f|>=2.3961 Dz<=77.8 Dt<=517.1 E<=2.4e-06 margin=0.4906 wind=0 [48s]
step  57 t=[0.073580,0.076546] ylo=0.4415 pts=  256 h=1.22e-02 min|f|>=2.3509 Dz<=72.2 Dt<=479.5 E<=2.2e-06 margin=0.4887 wind=0 [48s]
step  58 t=[0.076546,0.079684] ylo=0.4343 pts=  242 h=1.30e-02 min|f|>=2.3053 Dz<=66.7 Dt<=443.2 E<=2.0e-06 margin=0.4811 wind=0 [49s]
step  59 t=[0.079684,0.083012] ylo=0.4266 pts=  230 h=1.37e-02 min|f|>=2.2594 Dz<=61.5 Dt<=408.3 E<=1.9e-06 margin=0.4789 wind=0 [49s]
step  60 t=[0.083012,0.086554] ylo=0.4182 pts=  218 h=1.45e-02 min|f|>=2.2130 Dz<=56.5 Dt<=374.8 E<=1.7e-06 margin=0.4749 wind=0 [50s]
step  61 t=[0.086554,0.090333] ylo=0.4090 pts=  204 h=1.56e-02 min|f|>=2.1663 Dz<=51.7 Dt<=342.7 E<=1.5e-06 margin=0.4674 wind=0 [50s]
step  62 t=[0.090333,0.094379] ylo=0.3990 pts=  192 h=1.67e-02 min|f|>=2.1191 Dz<=47.1 Dt<=312.0 E<=1.4e-06 margin=0.4632 wind=0 [51s]
step  63 t=[0.094379,0.098726] ylo=0.3880 pts=  182 h=1.79e-02 min|f|>=2.0714 Dz<=42.8 Dt<=282.9 E<=1.2e-06 margin=0.4594 wind=0 [51s]
step  64 t=[0.098726,0.103412] ylo=0.3757 pts=  170 h=1.92e-02 min|f|>=2.0232 Dz<=38.8 Dt<=255.3 E<=1.1e-06 margin=0.4538 wind=0 [51s]
step  65 t=[0.103412,0.108537] ylo=0.3618 pts=  164 h=2.00e-02 min|f|>=1.9745 Dz<=35.0 Dt<=229.6 E<=9.9e-07 margin=0.4475 wind=0 [52s]
step  66 t=[0.108537,0.114195] ylo=0.3458 pts=  166 h=2.00e-02 min|f|>=1.9248 Dz<=31.5 Dt<=205.6 E<=8.7e-07 margin=0.4459 wind=0 [52s]
step  67 t=[0.114195,0.120457] ylo=0.3272 pts=  168 h=2.00e-02 min|f|>=1.8738 Dz<=28.4 Dt<=183.2 E<=7.6e-07 margin=0.4432 wind=0 [53s]
step  68 t=[0.120457,0.127402] ylo=0.3052 pts=  170 h=2.00e-02 min|f|>=1.8218 Dz<=25.6 Dt<=162.7 E<=6.7e-07 margin=0.4363 wind=0 [53s]
step  69 t=[0.127402,0.135104] ylo=0.2789 pts=  174 h=2.00e-02 min|f|>=1.7688 Dz<=23.3 Dt<=144.6 E<=5.8e-07 margin=0.4227 wind=0 [53s]
step  70 t=[0.135104,0.143603] ylo=0.2465 pts=  176 h=2.00e-02 min|f|>=1.7154 Dz<=21.7 Dt<=129.6 E<=5.1e-07 margin=0.3968 wind=0 [54s]
step  71 t=[0.143603,0.152852] ylo=0.2056 pts=  180 h=2.00e-02 min|f|>=1.6620 Dz<=21.3 Dt<=119.2 E<=4.6e-07 margin=0.3459 wind=0 [54s]
step  72 t=[0.152852,0.153990] ylo=0.2000 pts=  180 h=2.00e-02 min|f|>=1.6098 Dz<=16.2 Dt<=88.4 E<=3.1e-07 margin=1.3473 wind=0 [55s]
CERTIFIED (iii) [Arb]: barrier X=5998313329980.3135, t in [0,0.15399] (last step ends at 0.15399000000000002 >= t0), y0=0.2: no zeros of H_t; 73 steps, 39840 evaluations, min margin 0.3459, 55s