# This file contains summary data from " Knot Tightening By Constrained Gradient Descent " by Ashton, Cantarella, Piatek, Rawdon. # Knot type Polygonal Ropelength Ropelength Bound Edges Residual 2_2_1 25.1415 25.1334 202 2.45124e-05 3_1 32.7437 32.7436 2400 0.00621792 4_1 42.0971 42.0887 400 0.000996335 4_2_1 40.0203 40.0122 400 0.000999549 5_1 47.2149 47.2016 392 0.00981995 5_2 49.4820 49.4701 400 0.00994775 5_2_1 49.7864 49.7716 400 0.00998078 6_1 56.7178 56.7058 480 0.000999592 6_2 57.0381 57.0235 464 0.00897204 6_3 57.8531 57.8392 463 0.000979541 6_2_1 54.3919 54.3768 436 0.000999952 6_2_2 56.7087 56.7000 562 0.000999833 6_2_3 58.1142 58.1013 558 0.00999004 6_3_1 57.8286 57.8141 464 0.00998537 6_3_2 58.0112 58.0070 930 0.000705159 6_3_3 50.5602 50.5539 406 0.00627026 7_1 61.4234 61.4067 512 0.00105833 7_2 63.8684 63.8556 528 0.00998149 7_3 63.9430 63.9285 528 0.00999358 7_4 64.2836 64.2687 515 0.00100877 7_5 65.2705 65.2560 523 0.000999532 7_6 65.7068 65.6924 536 0.000979869 7_7 65.6235 65.6086 526 0.00100393 7_2_1 64.2484 64.2345 515 0.000999487 7_2_2 65.0363 65.0204 521 0.00101952 7_2_3 65.3414 65.3257 524 0.000999871 7_2_4 65.0759 65.0602 521 0.00099954 7_2_5 66.2068 66.1915 531 0.000999894 7_2_6 66.3281 66.3147 532 0.00100556 7_2_7 55.5177 55.5095 445 0.00320787 7_2_8 57.7714 57.7631 619 0.0018494 7_3_1 65.8157 65.8062 528 0.000999748 8_1 70.9833 70.9669 592 0.00898769 8_2 71.4141 71.3985 572 0.000982684 8_3 71.1736 71.1575 570 0.00100028 8_4 71.4872 71.4704 600 0.00100103 8_5 72.1519 72.1344 592 0.00100033 8_6 72.4903 72.4725 581 0.000999848 8_7 72.2292 72.2137 584 0.00101551 8_8 72.7438 72.7241 584 0.000981272 8_9 72.4568 72.4399 580 0.000999932 8_10 72.9580 72.9379 585 0.000978418 8_11 72.9110 72.8966 585 0.000979921 8_12 73.9707 73.9518 608 0.00998976 8_13 72.8194 72.8000 583 0.000993117 8_14 73.7784 73.7612 600 0.000981486 8_15 73.9076 73.8977 608 0.0099948 8_16 73.5207 73.5054 590 0.000981316 8_17 74.5075 74.4912 608 0.00999085 8_18 74.9114 74.9063 1199 0.000900015 8_19 60.9970 60.9858 489 0.000998339 8_20 63.1066 63.0929 528 0.00099998 8_21 65.5387 65.5248 525 0.000999988 8_2_1 68.4208 68.4045 550 0.00100142 8_2_2 71.0493 71.0311 570 0.000979836 8_2_3 72.7292 72.7133 583 0.000999961 8_2_4 72.5995 72.5855 582 0.00216462 8_2_5 73.9503 73.9331 593 0.00999516 8_2_6 73.2133 73.1955 587 0.00100295 8_2_7 74.3917 74.3752 596 0.000999802 8_2_8 73.7714 73.7540 591 0.000999762 8_2_9 73.2196 73.2038 590 0.000979774 8_2_10 73.6729 73.6548 591 0.000999858 8_2_11 72.9786 72.9608 585 0.00997927 8_2_12 73.8018 73.7846 591 0.000999968 8_2_13 74.1522 74.1369 594 0.0010008 8_2_14 73.6878 73.6695 591 0.00101123 8_2_15 64.3105 64.2996 515 0.00099994 8_2_16 66.8148 66.8046 536 0.000997563 8_3_1 72.2765 72.2603 579 0.00100589 8_3_2 72.9357 72.9181 584 0.000999904 8_3_3 74.8824 74.8656 602 0.00100014 8_3_4 75.0026 74.9866 632 0.00999606 8_3_5 73.4072 73.3932 590 0.000995844 8_3_6 74.7320 74.7159 600 0.00099824 8_3_7 60.5897 60.5754 486 0.00119532 8_3_8 65.0195 65.0042 522 0.00100655 8_3_9 66.7076 66.6936 559 0.000980533 8_3_10 68.4580 68.4503 551 0.0208108 8_4_1 75.2748 75.2592 603 0.00100006 8_4_2 67.4087 67.3937 541 0.000999682 8_4_3 66.2969 66.2865 532 0.780186 9_1 75.5663 75.5461 624 0.00802077 9_2 78.1231 78.1066 640 0.00997484 9_3 78.2040 78.1892 640 0.00998254 9_4 78.2793 78.2665 648 8.64059e-05 9_5 78.6615 78.6447 648 0.00999417 9_6 79.5802 79.5597 639 0.000980197 9_7 79.6924 79.6731 656 0.000979897 9_8 80.0276 80.0080 656 0.00101007 9_9 79.8965 79.8778 640 0.000999938 9_10 79.8009 79.7855 656 0.00113523 9_11 80.1355 80.1180 643 0.000981742 9_12 80.0997 80.0834 664 0.000979842 9_13 80.2657 80.2498 656 0.00999582 9_14 80.0193 80.0001 672 0.000984327 9_15 80.8941 80.8725 649 0.000979831 9_16 80.1334 80.1143 642 0.000999818 9_17 80.4718 80.4530 645 0.00100032 9_18 81.5816 81.5673 672 0.00992217 9_19 80.9196 80.9004 650 0.000981217 9_20 80.2421 80.2219 643 0.00100005 9_21 81.1083 81.0920 650 0.0010001 9_22 81.0587 81.0390 649 0.000998846 9_23 81.2922 81.2733 651 0.000979562 9_24 80.9626 80.9451 648 0.000999907 9_25 81.1348 81.1198 696 0.000977105 9_26 80.9241 80.9053 648 0.00100048 9_27 81.1838 81.1813 664 0.00999324 9_28 81.0878 81.1352 664 0.00996501 9_29 81.2019 81.1821 652 0.000979844 9_30 81.4811 81.4883 672 0.000979942 9_31 81.6751 81.6581 655 0.000979062 9_32 81.5343 81.5175 653 0.000997746 9_33 82.7691 82.7541 663 0.00100114 9_34 82.1884 82.1706 658 0.000999697 9_35 79.2390 79.2165 648 0.000981383 9_36 80.2275 80.2064 644 0.000978472 9_37 81.1744 81.1674 664 0.00999228 9_38 81.7858 81.7697 655 0.000978978 9_39 81.8439 81.8264 656 0.000999482 9_40 81.6652 81.6474 654 0.000999343 9_41 81.3687 81.3540 736 0.00899161 9_42 69.4867 69.4756 557 0.000999996 9_43 71.5050 71.4901 574 0.00898749 9_44 71.5587 71.5427 608 0.000999789 9_45 74.0861 74.0761 608 0.0099754 9_46 68.6330 68.6169 552 0.00099973 9_47 74.8935 74.8785 616 0.000998991 9_48 74.0317 74.0228 608 0.00998933 9_49 73.9403 73.9286 593 0.00099957 9_2_1 78.6049 78.5862 630 0.00107787 9_2_2 79.5287 79.5152 637 0.00100115 9_2_3 79.9495 79.9312 640 0.00100055 9_2_4 78.6961 78.6764 631 0.00099991 9_2_5 79.6569 79.6384 639 0.00100118 9_2_6 80.1200 80.1017 646 0.00126944 9_2_7 81.1437 81.1261 650 0.00104121 9_2_8 80.9964 80.9766 649 0.00100133 9_2_9 80.3174 80.2999 644 0.000999724 9_2_10 80.3218 80.3036 643 0.00140283 9_2_11 82.0329 82.0140 657 0.000999221 9_2_12 81.9602 81.9414 657 0.00100137 9_2_13 79.3468 79.3280 636 0.00100112 9_2_14 80.7276 80.7104 647 0.000999788 9_2_15 80.5659 80.5458 646 0.000999236 9_2_16 81.3758 81.3565 652 0.00605 9_2_17 80.3223 80.3022 648 0.00899775 9_2_18 81.7563 81.7461 659 0.000999648 9_2_19 79.4706 79.4491 637 0.00100405 9_2_20 80.1357 80.1147 642 0.000999853 9_2_21 80.6010 80.5824 649 0.00898977 9_2_22 81.0964 81.0794 650 0.00943088 9_2_23 80.2592 80.2379 644 0.000998181 9_2_24 81.7913 81.7691 656 0.000999946 9_2_25 81.7810 81.7630 656 0.0009999 9_2_26 82.1031 82.0859 658 0.00100243 9_2_27 81.0288 81.0141 649 0.00099997 9_2_28 81.3352 81.3222 652 0.000998883 9_2_29 82.1606 82.1445 659 0.00100157 9_2_30 82.2155 82.1987 659 0.00099989 9_2_31 80.5732 80.5561 646 0.000999523 9_2_32 81.4151 81.3990 652 0.00100012 9_2_33 82.1790 82.1612 658 0.000999711 9_2_34 81.8490 81.8320 655 0.00100169 9_2_35 81.2508 81.2318 651 0.000999778 9_2_36 80.7066 80.6866 647 0.00100172 9_2_37 81.9102 81.8927 656 0.000999058 9_2_38 82.6750 82.6561 663 0.000999748 9_2_39 81.8972 81.8758 656 0.000999888 9_2_40 81.9680 81.9460 657 0.000999835 9_2_41 83.6038 83.5878 670 0.00100037 9_2_42 83.6304 83.6092 670 0.000998679 9_2_43 66.2549 66.2398 531 0.00100109 9_2_44 72.2072 72.1896 579 0.00100838 9_2_45 71.0815 71.0726 886 0.00997492 9_2_46 73.8347 73.8215 592 0.00100042 9_2_47 69.9130 69.8983 657 0.00999831 9_2_48 73.6563 73.6426 590 0.000999984 9_2_49 66.0444 66.0311 530 0.000999984 9_2_50 69.3353 69.3284 556 0.000999226 9_2_51 70.5455 70.5299 565 0.000999443 9_2_52 72.8271 72.8106 585 0.000999958 9_2_53 68.0154 68.0082 755 0.00996962 9_2_54 71.0240 71.0089 569 0.000999703 9_2_55 73.8129 73.7998 592 0.00100064 9_2_56 72.9013 72.8833 594 0.000979788 9_2_57 72.2115 72.1922 584 0.00255237 9_2_58 74.1685 74.1499 595 0.000999155 9_2_59 72.3285 72.3130 582 0.00108631 9_2_60 73.5589 73.5442 589 0.000999312 9_2_61 69.3751 69.3636 557 0.00100091 9_3_1 81.1522 81.1333 652 0.000999763 9_3_2 81.7304 81.7190 656 0.000999746 9_3_3 82.2498 82.2346 660 0.00100525 9_3_4 82.5202 82.5029 662 0.000999641 9_3_5 80.2664 80.2456 643 0.00100042 9_3_6 80.9434 80.9258 649 0.000999746 9_3_7 82.0540 82.0378 658 0.000999935 9_3_8 81.1278 81.1107 650 0.000999751 9_3_9 81.5469 81.5295 655 0.000996684 9_3_10 82.3146 82.2964 660 0.00099985 9_3_11 82.0023 81.9867 658 0.0010755 9_3_12 82.4811 82.4608 661 0.00100439 9_3_13 72.2098 72.2009 875 0.00980919 9_3_14 74.4319 74.4205 598 0.00900147 9_3_15 74.2998 74.2810 596 0.00112426 9_3_16 75.0113 75.0003 601 0.000999575 9_3_17 74.1280 74.1159 595 0.247874 9_3_18 72.4529 72.4382 581 0.000999841 9_3_19 72.6412 72.6275 582 0.00101035 9_3_20 75.9995 75.9845 611 0.00100002 9_3_21 74.8967 74.8908 601 0.00100039 9_4_1 81.6096 81.5927 668 0.000979958 10_1 85.1146 85.0947 688 0.00101691 10_2 85.6050 85.5850 712 0.00100023 10_3 85.4483 85.4278 686 0.000991435 10_4 85.8181 85.7974 696 0.00100846 10_5 86.4952 86.4741 696 0.00100194 10_6 86.8353 86.8125 697 0.000979506 10_7 87.2979 87.2775 702 0.0097283 10_8 85.8620 85.8428 720 0.000980356 10_9 86.8410 86.8222 720 0.000979784 10_10 87.2060 87.1870 712 0.00999688 10_11 86.9848 86.9630 698 0.00760935 10_12 87.1055 87.0824 699 0.000991292 10_13 88.9148 88.8989 724 0.000999947 10_14 88.3232 88.3023 736 0.0010261 10_15 87.4787 87.4606 712 0.000979185 10_16 87.4946 87.4684 702 0.000985699 10_17 87.0473 87.0277 712 0.00998848 10_18 88.4257 88.4092 728 0.000979621 10_19 87.5311 87.5099 703 0.00098045 10_20 86.8731 86.8514 698 0.000979959 10_21 87.0497 87.0343 711 0.000999057 10_22 87.2417 87.2182 701 0.000991413 10_23 88.7048 88.6901 728 0.00999682 10_24 88.4160 88.3963 720 0.00166886 10_25 88.7767 88.7587 728 0.000994731 10_26 88.4564 88.4328 711 0.00098015 10_27 89.8944 89.8795 727 0.000999869 10_28 87.5276 87.5061 712 0.00996703 10_29 89.2410 89.2238 726 0.00116525 10_30 88.3731 88.3558 717 0.000999376 10_31 88.2624 88.2401 709 0.000979897 10_32 88.6809 88.6597 712 0.000979993 10_33 88.2952 88.2744 709 0.000979857 10_34 87.0322 87.0101 699 0.00098555 10_35 88.0891 88.0697 708 0.000982115 10_36 88.0424 88.0233 707 0.000979692 10_37 88.1319 88.1153 714 0.000999835 10_38 88.3478 88.3257 710 0.000979821 10_39 88.3562 88.3323 709 0.000986038 10_40 89.2659 89.2464 727 0.00100863 10_41 89.0725 89.0553 728 0.00999693 10_42 89.9013 89.8857 727 0.000999751 10_43 89.3512 89.3366 726 0.000980157 10_44 88.8714 88.8515 714 0.00322255 10_45 89.4836 89.4621 718 0.000982692 10_46 86.4718 86.4487 712 0.00997656 10_47 87.3043 87.2821 701 0.000980999 10_48 87.3814 87.3643 720 0.00999602 10_49 88.2914 88.2705 717 0.000998073 10_50 87.3876 87.3716 800 0.000981787 10_51 88.3209 88.3002 709 0.00098231 10_52 88.0719 88.0565 715 0.000999419 10_53 88.8361 88.8180 752 0.00101025 10_54 87.5336 87.5127 720 0.00999263 10_55 88.3760 88.3699 728 0.00998728 10_56 89.0160 88.9973 728 0.00999185 10_57 89.6126 89.5946 730 0.000999798 10_58 88.9623 88.9445 723 0.000999966 10_59 89.2228 89.2090 728 0.00995441 10_60 89.3397 89.3190 718 0.000980266 10_61 86.4755 86.4561 695 0.0241498 10_62 87.5318 87.5071 703 0.00105699 10_63 88.4046 88.3861 728 0.00998227 10_64 87.4878 87.4742 720 0.00997603 10_65 88.3918 88.3725 710 0.00135295 10_66 89.0275 89.0047 728 0.000999872 10_67 88.4741 88.4534 711 0.000979823 10_68 88.1199 88.1013 720 0.00100695 10_69 89.0983 89.0778 720 0.000999786 10_70 89.2068 89.1846 716 0.000980057 10_71 89.0853 89.0699 728 0.00999226 10_72 89.1974 89.1779 768 0.000999942 10_73 89.5332 89.5130 735 0.00998888 10_74 88.1285 88.1077 708 0.000978382 10_75 88.9725 88.9524 720 0.000981812 10_76 88.3673 88.3479 712 0.000980892 10_77 88.5689 88.5471 728 0.00999768 10_78 88.5548 88.5322 712 0.000981017 10_79 88.9647 88.9488 721 0.0010001 10_80 89.1669 89.1556 725 0.000979926 10_81 90.0181 90.0007 736 0.000981576 10_82 88.7011 88.6801 713 0.000978946 10_83 89.5544 89.5314 736 0.00999433 10_84 89.6518 89.6788 736 0.0099812 10_85 87.8403 87.8164 705 0.000981325 10_86 88.7050 88.6851 714 0.000978499 10_87 89.1363 89.1173 716 0.000979621 10_88 89.5638 89.5461 776 0.000979845 10_89 89.4343 89.4178 724 0.0010019 10_90 88.9330 88.9115 714 0.000980234 10_91 88.9611 88.9435 768 0.000977397 10_92 89.6200 89.6011 728 0.00100005 10_93 88.3962 88.3773 792 0.000979652 10_94 88.8514 88.8306 713 0.00097991 10_95 90.0056 89.9848 723 0.000979668 10_96 89.5493 89.5284 717 0.00018365 10_97 89.4340 89.4163 724 0.000999872 10_98 89.7172 89.6969 736 0.00999481 10_99 88.8926 88.8734 728 0.0099926 10_100 88.7124 88.6927 744 0.00101003 10_101 89.7344 89.7210 736 0.00999705 10_102 88.7969 88.7734 713 0.000979674 10_103 88.7971 88.7914 728 0.00999479 10_104 91.7476 91.7280 752 0.00999683 10_105 89.8260 89.8055 721 0.000979902 10_106 89.1546 89.1319 716 0.000979055 10_107 89.7525 89.7356 721 0.000980096 10_108 88.5137 88.4932 711 0.00127554 10_109 91.1966 91.1789 808 0.000979798 10_110 89.6275 89.6114 720 0.000979638 10_111 89.6677 89.6438 721 0.000979851 10_112 89.5744 89.5529 719 0.00104599 10_113 90.2239 90.2141 736 0.00999934 10_114 89.3062 89.2856 725 0.00100087 10_115 90.4340 90.4176 736 0.000978725 10_116 90.2703 90.2583 736 0.00998661 10_117 89.5335 89.5245 736 0.00998396 10_118 89.5261 89.5094 720 0.00099987 10_119 90.1394 90.1226 730 0.000999834 10_120 90.1862 90.1674 728 0.00100037 10_121 89.9375 89.9240 872 0.00099989 10_122 89.8258 89.8094 729 0.000999203 10_123 92.3646 92.3565 1498 0.0016528 10_124 71.0894 71.0739 576 0.00100133 10_125 74.9907 74.9778 616 0.00998345 10_126 77.6202 77.6026 640 0.00999723 10_127 80.0235 80.0124 656 0.00998882 10_128 76.4187 76.4026 613 0.000988223 10_129 78.5739 78.5553 631 0.00902523 10_130 78.8499 78.8356 704 0.000999987 10_131 81.2871 81.2678 652 0.00959976 10_132 74.7441 74.7330 600 0.000980876 10_133 77.1813 77.1631 620 0.000980018 10_134 78.6521 78.6377 648 0.00999485 10_135 81.2305 81.2157 657 0.00100006 10_136 78.0398 78.0276 640 0.00999149 10_137 79.6352 79.6185 640 0.000979856 10_138 82.5504 82.5320 663 0.00899453 10_139 72.9001 72.8944 600 0.000979731 10_140 73.8610 73.8477 608 0.0099924 10_141 76.9687 76.9543 632 0.00100144 10_142 75.8951 75.8754 616 0.000980204 10_143 78.2422 78.2307 640 0.00993363 10_144 81.4378 81.4275 664 0.00995796 10_145 75.9194 75.9076 632 0.00102699 10_146 79.7416 79.7322 656 0.00998505 10_147 79.1666 79.1571 648 0.000999813 10_148 79.0893 79.0742 635 0.000981385 10_149 81.0500 81.0318 656 0.00100026 10_150 80.1392 80.1219 644 0.000979903 10_151 81.8414 81.8207 657 0.000979813 10_152 79.1715 79.1556 648 0.00999625 10_153 80.4764 80.4648 656 0.0091785 10_154 81.5405 81.5218 655 0.00115132 10_155 78.0648 78.0503 640 0.00998753 10_156 79.5639 79.5443 639 0.0009799 10_157 81.4731 81.4568 712 0.000979535 10_158 81.6398 81.6220 656 0.000980822 10_159 79.8863 79.8692 642 0.000979791 10_160 78.1529 78.1472 640 0.00998455 10_161 74.5460 74.5302 598 0.00899311 10_162 81.0033 80.9838 650 0.000985909 10_163 82.6629 82.6548 1080 0.00899697 10_164 82.1862 82.1698 660 0.000979519 10_165 82.8211 82.8040 665 0.000979783