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[[672,18,30]] d ≤
n
672
k
18
d
30
kd²/n
24.107
w
8

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Distance

d_X 30 · witness weight 30 (claimed upper_bound)
witness operator (support, 30 qubits)
[4, 19, 25, 58, 65, 85, 118, 142, 151, 197, 222, 285, 339, 340, 384, 415, 421, 441, 447, 449, 454, 461, 523, 525, 549, 617, 622, 644, 656, 670]
d_Z 34 · witness weight 34 (claimed upper_bound)
witness operator (support, 34 qubits)
[0, 9, 42, 67, 106, 123, 148, 228, 229, 233, 234, 235, 249, 261, 310, 318, 325, 326, 336, 362, 453, 460, 480, 486, 503, 512, 550, 553, 557, 569, 605, 629, 632, 659]
certificate none yet · distance stands as a self-certified upper bound (d ≤)

Construction & provenance

authors @vprusso
provenance submitted through the challenge
novelty novelty not audited
construction non-abelian 2BGA (Lin-Pryadko) on PGL(2,7) (order 336), n=2|G|=672; supports a=[7, 16, 331, 275], b=[121, 293, 291, 46] (element indices in the kit's BFS/regular enumeration); H_X=[L(a)|R(b)], H_Z=[R(b)^T|L(a)^T]
model Claude Claude Opus 4.8 (claimed, not verified)
date 2026-07-24
notes Found by a continual non-abelian 2BGA sweep; distance confirmed at 80M x 3 pd20 RIS (min held) before packaging.
family generalized bicycle (a tag, not a ranking)
locality unrestricted (computed from the layout)
weight class weight ≤ 8 (computed)

How this code was found

the research note submitted with this code · raw markdown · all notes

[[672,18,30]] — non-abelian 2BGA on PGL(2,7)

Direction & hypothesis

The high-rate cyclic-GB lane on Z_195 is exhausted at its distance ceiling (30-31 at weight-8, 38-39 at weight-32, confirmed by three independent harnesses). Pivot to the least-mined space: non-abelian two-block group-algebra (2BGA) codes, which reach Pareto slots abelian constructions cannot. Hypothesis: large simple/almost-simple groups give high-distance codes at moderate rate that advance the unrestricted weight-8 cell.

What was swept, and at what depth

A continual 2BGA sweep over 10 non-abelian groups (n = 2|G| <= 700), sampling weight-3-5 support pairs (a, b), building H_X = [L(a)|R(b)], H_Z = [R(b)^T|L(a)^T], computing k, and screening distance. PGL(2,7) (order 336, n = 672) supports a = [7,16,331,275], b = [121,293,291,46], check weight 8.

Distance confirmation ladder

Screened at 2M, laddered to 8M (read 30), then confirmed at 80M x 3 fresh seeds at pair-depth 20 — the minimum held at 30 on every seed. The X witness is a genuine weight-30 Z-logical (in ker H_X, outside rowspace H_Z); the Z side's lightest witnessed logical is 34, so d = min(30, 34) = 30. Both witnesses are machine-verified in the packaged file.

Dead ends

Random weight-3-5 pairs overwhelmingly give low-distance or k-collapsed codes; only a small fraction clear the eff >= 20 confirm bar. Sampling volume does not substitute for it — this is one survivor of ~730 screened pairs.

Model / harness

Search and confirmation by Claude Opus 4.8 driving a bit-packed GF(2) RIS engine (gf2_fast). Novelty vs the literature is unverified (board-only dedup).

Reproduction

Build PGL(2,7) via the projective action on P^1(F_7) (generators x->x+1, x->-1/x, x->3x on 8 points), then build_2bga(mul, a, b) from research/kit/group_algebra.py with the supports above.

Parity checks

X-checks 336 · Z-checks 336
H_X (336 checks, sparse supports)
[53, 55, 184, 299, 390, 503, 531, 632] [8, 115, 188, 333, 394, 493, 596, 660] [116, 121, 284, 287, 352, 586, 639, 665] [117, 122, 285, 286, 379, 484, 621, 622] [23, 95, 214, 330, 399, 432, 558, 586] [24, 215, 253, 276, 372, 634, 651, 661] [25, 196, 216, 275, 422, 483, 539, 556] [0, 223, 227, 285, 362, 521, 607, 624] [26, 183, 208, 298, 455, 568, 585, 637] [127, 183, 191, 321, 356, 436, 528, 615] [99, 189, 224, 236, 370, 561, 634, 669] [109, 217, 225, 283, 348, 378, 591, 618] [58, 98, 265, 284, 437, 472, 507, 634] [59, 185, 306, 326, 417, 455, 557, 642] [60, 118, 186, 325, 398, 467, 538, 550] [61, 158, 272, 306, 339, 607, 664, 669] [0, 187, 223, 334, 462, 466, 553, 560] [62, 232, 287, 307, 375, 397, 510, 575] [63, 174, 272, 308, 415, 554, 621, 642] [64, 221, 270, 271, 369, 421, 572, 668] [1, 191, 211, 299, 367, 438, 531, 554] [2, 236, 315, 319, 403, 534, 573, 628] [3, 109, 307, 316, 417, 434, 476, 654] [14, 54, 275, 289, 340, 491, 557, 659] [65, 93, 110, 203, 441, 447, 573, 626] [47, 66, 256, 281, 386, 454, 537, 670] [54, 57, 194, 316, 360, 497, 561, 564] [93, 205, 240, 246, 389, 427, 517, 538] [136, 239, 245, 281, 442, 452, 456, 595] [44, 192, 315, 317, 382, 470, 645, 653] [130, 205, 220, 335, 407, 414, 500, 652] [157, 181, 206, 255, 374, 463, 515, 538] [76, 156, 204, 207, 350, 416, 504, 541] [52, 132, 189, 227, 488, 532, 600, 642] [126, 164, 184, 190, 387, 393, 462, 496] [36, 231, 295, 334, 342, 546, 554, 664] [89, 94, 111, 292, 361, 523, 527, 620] [102, 128, 208, 218, 418, 435, 603, 627] [129, 136, 219, 252, 387, 449, 483, 494] [131, 151, 257, 334, 384, 449, 487, 493] [78, 132, 196, 214, 412, 439, 551, 613] [78, 89, 132, 253, 490, 496, 509, 534] [1, 262, 299, 328, 348, 393, 459, 543] [2, 96, 278, 315, 412, 479, 516, 665] [3, 35, 277, 316, 388, 426, 448, 579] [133, 195, 259, 299, 338, 503, 605, 615] [134, 243, 298, 311, 336, 457, 463, 512] [111, 135, 151, 323, 404, 530, 549, 563] [32, 168, 170, 300, 363, 465, 524, 615] [31, 167, 169, 313, 345, 495, 589, 597] [4, 21, 194, 333, 413, 489, 573, 574] [5, 112, 246, 287, 379, 436, 483, 516] [6, 218, 245, 286, 366, 407, 425, 426] [7, 56, 193, 315, 344, 596, 599, 626] [8, 115, 226, 284, 401, 406, 431, 440] [9, 117, 205, 325, 365, 451, 508, 577] [10, 206, 259, 320, 432, 516, 544, 637] [11, 207, 311, 324, 446, 475, 543, 658] [37, 118, 232, 271, 346, 441, 478, 506] [38, 119, 174, 199, 351, 425, 551, 643] [30, 120, 198, 270, 376, 380, 513, 619] [16, 73, 137, 224, 411, 458, 523, 536] [19, 106, 283, 310, 409, 467, 535, 584] [107, 138, 155, 179, 402, 425, 450, 620] [77, 108, 154, 301, 388, 474, 545, 640] [119, 124, 288, 320, 349, 586, 624, 627] [120, 125, 289, 324, 340, 359, 533, 545] [16, 190, 212, 298, 347, 515, 645, 648] [48, 229, 256, 310, 337, 475, 519, 524] [139, 144, 179, 186, 424, 610, 618, 627] [106, 185, 242, 301, 373, 451, 629, 635] [56, 86, 100, 278, 379, 400, 501, 610] [101, 160, 223, 266, 443, 486, 632, 638] [33, 102, 115, 265, 349, 499, 567, 671] [127, 230, 273, 296, 381, 526, 545, 575] [126, 231, 312, 322, 353, 580, 587, 593] [41, 138, 146, 329, 396, 479, 505, 509] [153, 198, 222, 300, 342, 371, 428, 489] [44, 113, 121, 211, 387, 482, 590, 667] [61, 114, 286, 319, 427, 431, 468, 523] [141, 169, 188, 264, 350, 449, 546, 588] [15, 97, 266, 285, 380, 386, 574, 584] [31, 72, 85, 328, 399, 410, 481, 517] [86, 150, 248, 278, 357, 445, 511, 548] [71, 87, 274, 277, 468, 542, 602, 613] [79, 155, 176, 209, 369, 431, 491, 566] [41, 50, 177, 257, 413, 445, 604, 651] [40, 147, 178, 331, 428, 485, 492, 502] [49, 110, 228, 309, 341, 569, 575, 596] [147, 178, 229, 318, 402, 446, 612, 619] [43, 203, 254, 328, 368, 412, 541, 626] [75, 81, 278, 292, 422, 510, 538, 604] [12, 74, 277, 330, 364, 403, 442, 502] [116, 121, 176, 306, 343, 383, 601, 628] [61, 158, 177, 188, 466, 507, 604, 617] [37, 178, 187, 232, 515, 533, 566, 656] [4, 230, 294, 333, 354, 474, 479, 599] [5, 163, 263, 287, 357, 371, 391, 403] [6, 162, 262, 286, 419, 423, 476, 648] [7, 56, 92, 215, 406, 520, 574, 578] [9, 38, 82, 325, 444, 528, 614, 633] [10, 83, 175, 320, 347, 386, 403, 518] [11, 82, 84, 324, 367, 428, 618, 662] [152, 165, 331, 333, 355, 465, 470, 549] [143, 203, 233, 249, 401, 561, 653, 668] [47, 142, 234, 291, 343, 362, 454, 658] [101, 107, 209, 254, 422, 438, 571, 653] [50, 75, 235, 297, 480, 513, 654, 660] [74, 147, 192, 317, 370, 581, 594, 649] [77, 154, 173, 269, 413, 434, 598, 602] [12, 53, 186, 330, 516, 570, 612, 650] [7, 13, 276, 288, 349, 355, 401, 592] [15, 210, 212, 285, 358, 418, 432, 599] [17, 48, 216, 321, 430, 546, 589, 623] [18, 144, 189, 309, 349, 373, 417, 485] [20, 56, 123, 235, 373, 460, 521, 569] [21, 22, 100, 223, 427, 471, 559, 583] [21, 22, 115, 182, 571, 576, 592, 651] [23, 213, 214, 227, 355, 383, 386, 572] [24, 123, 184, 215, 471, 565, 632, 642] [25, 183, 216, 318, 350, 371, 550, 587] [27, 99, 127, 252, 336, 582, 639, 659] [28, 126, 217, 335, 338, 381, 402, 633] [29, 138, 260, 331, 424, 444, 464, 649] [31, 249, 301, 313, 395, 405, 646, 659] [32, 179, 291, 300, 359, 603, 608, 611] [88, 170, 195, 219, 387, 531, 623, 660] [68, 169, 220, 243, 345, 356, 416, 635] [18, 46, 221, 239, 343, 421, 429, 646] [74, 103, 153, 168, 549, 623, 657, 670] [39, 75, 167, 222, 375, 449, 533, 614] [40, 42, 236, 317, 368, 455, 486, 657] [43, 122, 149, 212, 501, 502, 562, 665] [48, 181, 202, 267, 416, 457, 508, 609] [49, 90, 204, 314, 391, 498, 579, 588] [88, 108, 140, 237, 364, 473, 565, 576] [83, 142, 143, 312, 358, 437, 448, 552] [94, 206, 258, 260, 364, 610, 612, 648] [153, 199, 222, 313, 354, 446, 456, 483] [27, 42, 141, 289, 446, 481, 528, 553] [43, 98, 137, 203, 472, 534, 542, 578] [44, 47, 97, 161, 494, 522, 552, 638] [19, 155, 251, 267, 346, 563, 621, 652] [18, 154, 250, 314, 339, 351, 388, 656] [102, 108, 238, 244, 385, 544, 602, 662] [95, 202, 207, 302, 392, 410, 597, 652] [90, 94, 206, 323, 366, 502, 511, 650] [22, 36, 193, 334, 348, 456, 500, 507] [43, 235, 297, 316, 440, 488, 569, 579] [49, 79, 164, 215, 377, 497, 507, 639] [57, 87, 182, 277, 368, 509, 640, 655] [58, 150, 269, 332, 384, 504, 644, 668] [15, 71, 280, 329, 355, 426, 439, 606] [63, 93, 237, 308, 348, 361, 372, 644] [66, 94, 165, 331, 558, 581, 608, 622] [65, 95, 131, 257, 401, 461, 514, 525] [103, 120, 125, 221, 454, 478, 524, 598] [39, 119, 124, 308, 383, 404, 555, 560] [55, 101, 112, 213, 453, 503, 506, 574] [131, 193, 202, 321, 345, 517, 588, 636] [51, 78, 226, 283, 423, 426, 626, 633] [95, 207, 241, 261, 405, 437, 537, 605] [84, 234, 253, 290, 376, 408, 473, 486] [83, 196, 233, 282, 453, 548, 567, 655] [39, 81, 133, 191, 414, 506, 543, 582] [41, 109, 180, 297, 400, 504, 540, 576] [45, 76, 171, 294, 385, 445, 589, 665] [11, 29, 172, 263, 467, 603, 615, 657] [10, 148, 173, 262, 382, 439, 512, 576] [147, 152, 173, 175, 396, 527, 600, 657] [50, 82, 151, 172, 465, 489, 582, 591] [140, 159, 170, 187, 367, 374, 413, 639] [33, 244, 256, 279, 376, 416, 429, 439] [110, 160, 166, 254, 470, 498, 501, 534] [2, 162, 248, 251, 397, 514, 547, 562] [32, 73, 268, 327, 366, 526, 530, 619] [104, 162, 225, 248, 467, 487, 563, 568] [71, 237, 251, 280, 476, 490, 536, 558] [150, 197, 250, 269, 415, 461, 630, 666] [99, 219, 224, 294, 565, 604, 625, 645] [16, 263, 298, 327, 346, 366, 370, 637] [33, 38, 150, 265, 505, 555, 580, 588] [30, 34, 175, 326, 362, 370, 496, 540] [53, 55, 214, 279, 337, 459, 631, 661] [26, 89, 166, 208, 341, 347, 424, 562] [88, 96, 195, 280, 433, 440, 459, 464] [35, 68, 243, 269, 378, 564, 646, 663] [13, 130, 200, 276, 427, 493, 555, 558] [14, 129, 176, 275, 353, 375, 454, 495] [13, 17, 230, 321, 351, 395, 464, 500] [18, 80, 163, 189, 448, 555, 619, 647] [19, 162, 171, 283, 418, 517, 547, 591] [20, 123, 158, 181, 385, 462, 480, 647] [14, 27, 167, 252, 469, 495, 519, 601] [13, 28, 168, 335, 429, 492, 577, 636] [5, 29, 255, 260, 365, 382, 585, 623] [30, 59, 166, 270, 358, 377, 485, 488] [157, 251, 267, 330, 361, 397, 515, 537] [87, 146, 276, 329, 532, 567, 573, 613] [86, 145, 275, 332, 358, 389, 608, 654] [105, 163, 224, 274, 411, 617, 644, 655] [68, 107, 141, 197, 405, 430, 456, 587] [44, 47, 244, 327, 369, 463, 595, 600] [23, 152, 201, 302, 478, 482, 492, 624] [30, 71, 160, 266, 420, 484, 600, 661] [84, 142, 143, 273, 369, 380, 392, 417] [76, 156, 274, 312, 472, 556, 630, 663] [157, 248, 255, 273, 346, 477, 522, 609] [34, 116, 136, 326, 408, 551, 553, 645] [20, 35, 258, 272, 373, 388, 418, 593] [27, 39, 191, 302, 367, 469, 566, 643] [40, 137, 236, 303, 341, 420, 542, 641] [41, 109, 161, 304, 408, 445, 583, 630] [19, 45, 240, 308, 357, 487, 508, 607] [50, 123, 177, 228, 400, 471, 474, 669] [22, 51, 135, 226, 425, 476, 577, 578] [21, 52, 201, 227, 372, 396, 513, 638] [54, 57, 91, 216, 481, 620, 625, 635] [58, 211, 284, 305, 392, 541, 565, 664] [59, 113, 306, 319, 341, 353, 372, 448] [60, 118, 149, 307, 422, 477, 527, 547] [54, 62, 104, 307, 491, 512, 563, 629] [64, 197, 221, 281, 399, 552, 666, 670] [57, 67, 192, 318, 393, 405, 411, 424] [58, 69, 157, 296, 441, 462, 536, 658] [15, 70, 156, 322, 337, 378, 394, 668] [66, 72, 161, 329, 442, 514, 539, 624] [65, 73, 137, 332, 447, 530, 606, 616] [6, 104, 139, 300, 360, 444, 535, 637] [5, 105, 242, 313, 344, 350, 389, 625] [82, 91, 125, 151, 354, 469, 535, 608] [92, 124, 152, 175, 398, 532, 638, 641] [1, 72, 161, 225, 487, 560, 570, 587] [102, 108, 180, 261, 460, 518, 640, 658] [42, 101, 107, 260, 393, 550, 559, 594] [37, 67, 204, 318, 438, 585, 597, 616] [138, 155, 172, 280, 360, 423, 492, 526] [156, 250, 292, 314, 430, 434, 441, 617] [67, 96, 241, 271, 399, 450, 472, 503] [9, 97, 199, 234, 452, 519, 545, 559] [34, 98, 198, 233, 411, 486, 580, 651] [81, 100, 106, 240, 365, 419, 443, 480] [28, 140, 180, 288, 392, 396, 406, 544] [6, 76, 148, 261, 440, 463, 505, 635] [51, 83, 196, 304, 452, 468, 501, 505] [49, 171, 204, 209, 436, 590, 654, 671] [48, 80, 181, 238, 374, 529, 614, 663] [69, 98, 198, 297, 420, 471, 499, 616] [55, 85, 235, 328, 409, 497, 572, 605] [99, 228, 309, 325, 406, 455, 480, 629] [16, 135, 320, 323, 397, 458, 622, 627] [1, 201, 302, 324, 402, 473, 533, 560] [32, 158, 159, 264, 384, 391, 529, 582] [38, 60, 174, 279, 414, 423, 430, 496] [52, 84, 253, 303, 377, 420, 482, 540] [40, 77, 145, 332, 380, 435, 465, 579] [26, 81, 185, 292, 477, 512, 550, 669] [8, 195, 210, 305, 353, 460, 605, 636] [12, 144, 182, 239, 344, 408, 544, 581] [112, 116, 213, 335, 452, 566, 599, 631] [159, 185, 301, 314, 528, 564, 575, 647] [179, 186, 264, 267, 404, 475, 511, 585] [35, 134, 272, 293, 434, 584, 647, 667] [96, 133, 247, 271, 526, 541, 572, 631] [90, 164, 165, 194, 363, 368, 384, 661] [62, 91, 131, 246, 395, 419, 495, 511] [92, 114, 165, 245, 530, 571, 577, 613] [93, 205, 282, 309, 409, 435, 477, 592] [17, 154, 200, 238, 354, 364, 415, 466] [29, 230, 249, 273, 450, 598, 629, 636] [3, 163, 250, 274, 339, 415, 468, 616] [75, 85, 111, 167, 478, 491, 508, 525] [23, 74, 168, 268, 421, 464, 622, 641] [73, 129, 219, 259, 371, 433, 525, 595] [192, 208, 268, 327, 450, 458, 485, 648] [0, 80, 229, 295, 359, 529, 593, 643] [8, 171, 228, 294, 395, 400, 460, 628] [64, 149, 166, 254, 412, 548, 581, 590] [63, 113, 244, 279, 338, 377, 490, 663] [46, 80, 255, 295, 414, 457, 524, 667] [148, 231, 291, 312, 499, 539, 557, 667] [117, 118, 122, 200, 357, 361, 443, 549] [42, 145, 266, 289, 362, 428, 451, 497] [14, 79, 164, 231, 376, 481, 601, 664] [65, 110, 177, 268, 479, 523, 578, 656] [66, 85, 178, 256, 340, 421, 432, 652] [4, 45, 130, 240, 379, 466, 514, 614] [36, 46, 129, 239, 338, 345, 352, 670] [4, 69, 270, 296, 521, 606, 656, 662] [36, 70, 174, 322, 356, 390, 431, 666] [146, 180, 265, 288, 437, 518, 532, 596] [217, 229, 310, 326, 336, 359, 390, 618] [24, 232, 247, 303, 383, 498, 513, 536] [70, 97, 199, 317, 336, 453, 571, 598] [122, 173, 201, 262, 490, 510, 583, 649] [121, 135, 172, 263, 363, 547, 611, 641] [11, 88, 241, 290, 499, 531, 570, 594] [51, 100, 106, 145, 407, 444, 484, 569] [59, 87, 105, 242, 435, 520, 556, 561] [60, 86, 104, 139, 347, 365, 591, 620] [46, 119, 133, 259, 410, 429, 611, 631] [217, 220, 225, 295, 356, 475, 535, 554] [67, 69, 90, 194, 461, 542, 603, 632] [9, 91, 242, 246, 407, 589, 610, 659] [34, 92, 139, 245, 458, 509, 559, 633] [28, 103, 190, 323, 398, 595, 609, 649] [89, 111, 128, 226, 360, 398, 447, 621] [53, 113, 211, 296, 433, 473, 498, 593] [7, 105, 114, 319, 394, 447, 592, 655] [112, 126, 184, 247, 433, 438, 521, 551] [127, 183, 218, 293, 378, 391, 451, 611] [117, 128, 218, 252, 363, 389, 404, 584] [72, 130, 220, 311, 419, 537, 546, 643] [45, 120, 134, 311, 510, 519, 522, 529] [136, 281, 290, 310, 342, 453, 494, 570] [124, 140, 160, 237, 482, 583, 634, 650] [33, 125, 141, 197, 342, 351, 539, 597] [52, 144, 146, 182, 470, 518, 520, 540] [77, 148, 257, 261, 522, 564, 567, 660] [26, 149, 212, 322, 548, 568, 612, 628] [79, 222, 234, 291, 340, 352, 553, 662] [12, 103, 134, 190, 374, 382, 494, 527] [10, 68, 258, 282, 337, 344, 568, 640] [20, 70, 193, 202, 381, 409, 646, 671] [17, 153, 233, 249, 493, 594, 625, 666] [64, 78, 241, 290, 442, 459, 580, 653] [63, 132, 258, 282, 390, 520, 562, 602] [114, 169, 188, 210, 500, 525, 556, 671] [62, 170, 187, 305, 474, 543, 601, 609] [2, 143, 247, 303, 488, 586, 590, 606] [25, 61, 293, 304, 352, 443, 617, 630] [0, 210, 243, 305, 381, 385, 410, 557] [3, 142, 293, 304, 339, 343, 484, 504] [24, 128, 200, 238, 489, 607, 644, 650] [25, 176, 209, 213, 375, 394, 506, 552] [31, 37, 159, 264, 436, 457, 461, 469]
H_Z (336 checks, sparse supports)
[46, 121, 291, 293, 343, 352, 611, 667] [68, 183, 225, 322, 356, 378, 568, 587] [45, 122, 278, 287, 357, 379, 510, 665] [15, 143, 270, 332, 358, 380, 606, 668] [23, 66, 285, 320, 386, 432, 622, 624] [88, 184, 211, 219, 387, 433, 531, 565] [35, 77, 314, 316, 388, 434, 564, 579] [93, 105, 128, 332, 389, 435, 447, 644] [53, 229, 258, 322, 337, 390, 593, 612] [49, 127, 159, 287, 391, 436, 575, 639] [58, 142, 180, 207, 392, 437, 504, 658] [67, 101, 184, 299, 393, 438, 503, 632] [11, 42, 147, 153, 428, 446, 594, 657] [65, 73, 111, 114, 447, 523, 525, 530] [32, 80, 120, 229, 359, 524, 529, 619] [59, 143, 189, 316, 417, 448, 488, 561] [2, 287, 320, 330, 397, 403, 516, 586] [75, 188, 219, 257, 449, 525, 604, 660] [96, 138, 230, 268, 450, 464, 479, 526] [103, 111, 118, 152, 398, 478, 527, 549] [9, 127, 289, 301, 451, 528, 545, 659] [83, 97, 213, 281, 386, 452, 453, 552] [112, 136, 196, 199, 452, 453, 483, 551] [66, 125, 275, 291, 340, 454, 539, 608] [26, 228, 236, 306, 341, 455, 628, 669] [36, 153, 197, 281, 342, 456, 666, 670] [7, 105, 182, 282, 344, 520, 592, 655] [48, 264, 295, 311, 457, 475, 529, 546] [92, 135, 137, 268, 458, 530, 578, 641] [55, 195, 241, 299, 459, 503, 531, 605] [52, 146, 175, 180, 396, 518, 532, 540] [20, 102, 171, 210, 385, 418, 460, 671] [90, 131, 150, 264, 384, 461, 511, 588] [19, 85, 202, 205, 409, 508, 517, 652] [10, 108, 180, 182, 518, 544, 576, 640] [77, 97, 120, 273, 380, 522, 545, 598] [5, 153, 216, 219, 371, 483, 623, 625] [70, 114, 115, 209, 394, 431, 571, 671] [31, 171, 246, 321, 395, 436, 517, 589] [17, 130, 188, 334, 466, 493, 500, 546] [60, 162, 172, 283, 423, 467, 547, 591] [149, 196, 254, 278, 412, 422, 501, 548] [11, 186, 225, 310, 467, 475, 570, 618] [3, 51, 71, 286, 426, 468, 476, 484] [60, 81, 205, 255, 365, 414, 477, 538] [74, 122, 323, 331, 502, 549, 622, 649] [29, 168, 195, 321, 464, 615, 623, 636] [93, 118, 157, 292, 361, 441, 477, 538] [39, 151, 252, 264, 404, 449, 469, 582] [144, 166, 192, 331, 424, 470, 485, 581] [25, 81, 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raw submission JSON