Recent activity
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31ae2815…· Comment: Size-85 idempotent right-cancellative magma satisfying Eq 677 and Eq 255. The carrier is the cyclic group Z_85 (= Z_5 ×… -
689663a9…· Reorder set to0,6,11,14,18,26,29,32,37,40,45,48,61,68,75,78,1,5,12,16,22,25,31,34,36,44,51,55,59,67,71,77,2,7,10,13,17,20,28,35,38,43,53,57,60,65,74,79,3,4,9,21,24,39,42,47,50,54,58,63,66,70,73,76,8,15,19,23,27,30,33,41,46,49,52,56,62,64,69,72,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95 -
689663a9…· Comment: Size-96 idempotent right-cancellative magma satisfying Eq 677 and Eq 255. A '6-petal disjoint partition' construction —… -
875876e7…· Reorder set to62,3,4,11,14,17,20,27,30,33,36,43,46,49,52,59,2,7,10,13,16,23,26,29,32,39,42,45,48,55,58,60,61,63,64,65,66,67,68,69,70,71,72,73,74,75,0,6,9,12,19,22,25,28,35,38,41,44,51,54,57,1,5,8,15,18,21,24,31,34,37,40,47,50,53,56 -
875876e7…· Comment: Size-76 idempotent right-cancellative magma satisfying Eq 677 and Eq 255. The structure is a **'pencil' of 5 size-16 sub… -
n=15
size 15 · Commentary: No Eq 677 magma of size 15 is currently known; the existence question is OPEN but several substantial partial results re…
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n=10
size 10 · Commentary: No magma of size 10 satisfies Equation 677. Jose Brox confirmed this with an exhaustive Mace4 search taking 39 hours (Z…
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n=10
size 10 · Commentary: No magma of size 10 satisfies Equation 677. Jose Brox confirmed this with an exhaustive Mace4 search taking 39 hours (Z…
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f304c339…· Reorder set to0,2,151,68,318,179,219,294,108,16,267,86,24,138,145,134,291,282,218,1,32,9,348,119,279,203,252,136,168,164,276,93,30,71,53,175,204,312,50,342,28,62,137,228,59,340,305,106,356,319,207,105,241,269,181,278,235,122,360,215,127,97,180,205,195,200,92,210,117,185,107,102,112,132,190,220,343,27,307,170,66,133,159,176,198,114,4,41,199,48,25,271,163,247,274,324,347,316,55,111,240,310,283,345,186,64,229,233,246,142,110,67,212,33,261,317,315,125,70,79,182,255,248,339,298,157,331,201,82,126,244,3,280,281,37,169,6,173,272,141,209,257,135,208,58,284,76,124,35,353,98,14,153,17,123,104,83,237,297,149,39,15,309,160,166,31,306,333,56,188,189,46,7,227,5,21,223,113,287,299,296,224,94,139,150,323,143,73,29,156,99,12,184,51,301,161,304,34,292,78,118,148,183,328,26,155,10,144,232,120,357,275,239,77,326,293,243,222,65,355,256,43,121,196,152,334,250,74,165,22,314,158,20,194,44,193,154,61,302,338,242,311,88,36,109,171,128,57,337,230,221,236,202,351,300,54,177,23,45,273,264,100,359,101,335,268,63,42,213,286,140,19,262,103,214,358,146,40,277,129,178,81,11,289,174,91,327,192,167,254,325,265,341,13,90,258,211,290,80,349,47,226,89,308,162,322,303,266,344,285,253,8,260,249,187,131,84,87,75,206,130,336,320,216,332,263,96,95,313,18,49,346,231,225,52,330,354,259,85,172,295,197,234,352,69,329,191,38,350,217,288,72,270,115,245,147,116,251,60,238,321 -
f304c339…· Comment: Size-361 = 19² idempotent right-cancellative magma satisfying Eq 677 and Eq 255. The carrier is the additive group of F_… -
91224574…· Comment: Size-361 = 19² idempotent right-cancellative magma satisfying Eq 677 and Eq 255. The carrier is the additive group of F_… -
c5c647a9…· Comment: Size-361 = 19² idempotent right-cancellative magma satisfying Eq 677 and Eq 255. The carrier is the additive group of F_… -
n=361
size 361 · Commentary: Size 361 = 19² admits Eq 677 magmas via near-field-style constructions. Currently 3 magmas in the DB, all idempotent rig…
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91224574…· Reorder set to0,2,296,277,169,103,97,358,359,269,231,51,247,90,48,243,126,34,210,1,42,181,40,219,250,309,74,308,166,137,193,143,88,119,130,317,197,336,158,57,91,212,324,134,55,208,16,323,332,265,13,196,152,351,89,145,234,120,32,299,183,307,261,64,133,187,30,298,78,326,209,156,109,81,240,127,344,77,165,172,195,36,154,111,254,281,33,343,75,232,178,19,216,352,228,136,12,113,189,100,44,306,107,241,58,220,287,278,61,253,10,179,279,257,226,87,46,291,242,272,175,164,43,98,238,92,121,353,29,354,205,264,85,341,47,45,255,79,171,198,3,135,202,6,186,224,314,313,142,148,124,322,132,37,188,266,138,35,83,214,114,245,125,304,312,69,192,303,331,161,86,262,17,194,49,112,63,292,66,15,284,141,118,105,311,246,225,283,258,94,327,52,260,176,8,207,191,319,147,129,346,50,84,203,140,11,229,318,153,99,22,54,68,71,289,123,316,230,263,267,199,117,297,20,146,110,251,288,293,27,73,294,321,268,204,302,151,256,104,59,76,128,235,182,122,25,115,295,360,340,335,275,330,350,270,310,325,300,345,280,355,315,305,285,320,290,28,72,338,160,70,167,227,190,173,31,14,149,211,106,347,249,223,276,339,9,67,144,333,206,155,101,65,342,162,244,222,218,185,271,168,334,26,23,215,7,282,108,273,184,56,95,248,39,5,301,174,102,274,236,252,53,131,239,62,217,139,213,328,180,201,356,150,163,96,329,60,21,337,18,157,4,233,82,177,41,116,286,348,237,24,357,349,170,200,159,259,38,80,93,221 -
c5c647a9…· Reorder set to0,2,165,128,219,85,25,310,350,67,44,64,351,318,36,89,205,123,172,1,81,307,298,119,130,321,31,226,259,252,222,30,338,121,114,280,301,93,249,236,21,331,120,109,288,317,91,11,83,311,290,104,131,328,20,232,242,77,340,300,35,95,209,138,175,12,10,162,133,215,99,26,308,341,74,54,39,69,173,189,98,266,158,258,314,253,154,267,96,181,164,62,22,282,296,213,334,244,47,132,7,66,274,279,65,15,139,41,247,325,211,297,156,281,355,246,270,312,115,28,153,234,159,33,118,316,263,245,346,55,218,206,53,182,326,223,358,204,140,134,137,152,200,343,225,333,188,241,169,87,168,250,220,63,125,344,278,184,289,186,275,357,126,68,228,94,102,52,56,111,80,293,342,193,315,4,320,339,18,313,197,359,285,171,110,272,212,261,103,166,117,231,13,40,24,185,37,48,9,237,116,145,167,322,61,70,337,170,147,284,92,49,180,141,151,190,59,82,294,6,207,239,309,360,319,229,217,16,227,19,58,27,195,34,50,3,221,107,157,160,327,60,71,332,177,155,106,187,303,8,329,330,14,305,183,352,283,176,113,271,202,262,100,161,295,349,347,265,196,299,194,268,354,135,73,230,90,101,46,42,112,84,238,78,136,210,142,127,124,150,214,348,233,336,192,240,178,97,179,251,198,323,235,353,23,149,224,143,38,105,302,260,256,345,43,216,208,45,356,255,273,306,108,75,269,264,76,17,122,57,254,324,203,291,146,287,201,335,257,51,129,5,243,304,248,148,276,88,199,163,79,29,286,292,32,72,174,191,86,277,144 -
n=343
size 343 · Commentary: Size 343 = 7³ currently has 5 magmas in the DB, falling into two distinct families. Family A: Dickson-near-field-style…
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ff552011…· Comment: Size-343 = 7³ idempotent right-cancellative magma satisfying Eq 677 and Eq 255. The carrier is the additive group (Z/7)³… -
ff552011…· Reorder set to0,3,342,18,24,6,21,2,168,325,134,257,90,154,165,96,331,160,131,8,254,339,233,139,20,36,73,55,93,5,328,260,157,162,128,76,333,142,39,58,227,23,230,79,136,61,26,336,42,1,218,261,232,104,174,145,222,252,223,57,269,313,243,66,120,338,71,298,163,278,251,80,40,92,340,198,141,284,277,11,187,75,320,106,300,211,140,149,205,82,291,280,191,193,203,268,28,314,224,171,267,151,229,7,101,274,317,17,103,184,281,72,258,310,220,249,54,219,266,208,88,137,288,146,297,202,117,169,335,275,68,63,304,197,34,190,311,200,286,265,77,204,37,138,98,248,337,29,10,112,19,270,253,49,302,235,332,295,247,33,279,324,161,91,83,237,38,129,84,111,45,53,318,167,228,319,110,118,209,150,242,125,12,133,102,213,312,64,178,179,293,159,186,59,182,192,177,4,264,107,148,221,226,166,69,341,301,272,123,65,323,287,14,78,100,271,181,31,283,196,262,308,194,206,307,216,217,263,246,255,60,201,245,43,334,135,74,95,85,303,143,199,294,214,152,256,32,115,273,52,13,22,41,327,94,240,132,155,86,236,322,121,144,119,113,212,185,173,153,62,195,296,180,27,305,326,250,282,238,289,170,87,48,321,231,114,47,67,15,105,306,172,127,207,16,259,109,46,25,35,276,116,239,124,122,215,316,147,241,30,329,285,292,299,244,130,70,99,175,210,9,309,158,44,97,126,89,330,234,290,188,156,189,183,176,56,108,164,51,225,50,81,315 -
ba90950a…· Reorder set to0,3,414,30,701,51,485,732,502,423,790,858,159,212,359,799,537,899,108,765,898,442,757,275,521,381,235,389,818,131,932,1,422,107,388,50,358,274,17,789,764,817,484,798,520,413,857,897,130,731,536,380,29,158,441,931,501,913,234,700,211,756,924,827,464,254,747,249,333,320,138,307,347,715,591,606,170,664,678,576,955,621,198,549,65,651,636,185,457,847,43,565,83,553,110,53,277,792,820,801,416,885,719,383,161,934,901,703,759,425,391,361,5,767,487,508,860,118,524,32,444,504,237,214,96,56,780,804,888,386,937,691,428,364,770,511,121,20,507,217,113,280,823,404,722,149,904,762,394,8,490,863,527,447,225,960,881,878,284,875,876,296,880,872,882,873,295,293,289,877,294,869,287,879,883,870,283,292,297,290,871,286,285,874,288,291,916,35,192,72,628,685,613,354,327,739,834,557,449,658,205,583,177,707,145,241,471,90,839,643,541,947,671,598,299,340,261,928,174,47,704,189,142,69,238,625,468,682,87,610,851,351,640,324,538,736,959,831,668,554,595,461,311,655,337,202,258,580,2,778,730,233,372,412,440,421,816,535,699,273,856,930,106,483,379,210,16,896,500,402,797,28,755,788,129,912,49,519,157,925,321,171,550,44,748,716,956,186,828,139,665,66,566,250,592,622,458,465,308,679,652,84,334,607,199,848,255,348,577,637,926,957,251,653,349,45,666,466,200,322,187,593,85,578,734,67,309,849,172,829,623,335,638,717,567,680,256,551,140,459,608,101,376,775,222,727,13,230,893,369,497,409,399,437,794,418,25,813,752,532,785,696,126,270,909,868,61,942,516,103,154,480,915,738,144,597,684,204,642,34,833,240,298,612,582,540,191,556,470,339,353,176,946,71,448,89,260,326,706,670,627,657,853,922,619,318,455,168,477,547,305,41,676,745,649,713,81,953,331,183,604,825,196,136,845,662,267,78,345,563,574,247,634,589,917,355,206,91,300,614,558,146,948,36,313,569,840,341,686,450,242,672,178,740,163,629,262,599,644,472,584,73,835,708,542,923,306,954,846,248,169,650,826,346,620,42,332,663,635,463,714,197,564,319,677,184,253,590,548,82,137,575,456,746,605,64,100,496,531,515,12,432,908,375,408,784,117,229,24,867,774,398,695,153,892,812,60,221,436,125,479,368,751,941,726,808,269,98,810,373,749,772,529,219,782,724,693,10,123,227,282,890,906,366,865,494,58,406,939,396,513,434,115,806,151,430,492,22,94,417,689,488,505,793,162,362,525,111,886,760,509,223,821,935,6,18,54,720,426,861,215,802,902,768,445,278,384,392,119,927,467,735,336,141,350,594,173,681,958,201,68,639,460,46,86,830,257,252,323,310,718,609,667,579,624,552,654,188,850,568,99,783,891,940,431,773,124,495,116,811,725,907,397,478,530,228,59,807,374,694,367,514,23,220,268,407,152,750,11,866,435,919,180,616,601,315,837,452,193,165,133,474,842,544,659,302,264,38,75,688,357,742,560,646,571,710,244,93,631,950,586,328,929,733,360,443,819,702,859,109,382,4,503,800,758,132,52,160,766,236,415,424,523,276,933,486,213,884,390,31,791,900,522,914,239,352,669,203,190,88,737,312,175,626,641,555,259,143,611,945,656,48,469,325,596,581,70,852,832,338,705,683,539,462,918,147,687,630,836,301,570,179,473,356,949,451,263,709,615,841,741,585,207,37,243,600,543,559,342,164,74,92,314,673,645,920,194,303,561,951,316,843,674,245,181,166,265,647,587,838,545,343,79,617,134,39,572,329,453,660,743,632,602,475,76,711,33,534,15,911,411,105,27,777,698,895,63,439,482,754,729,272,499,518,420,378,787,232,855,401,156,815,209,128,371,944,796,97,692,493,150,528,889,512,809,9,57,429,218,905,433,387,122,405,491,781,365,114,763,226,938,21,723,864,805,771,281,395,102,894,419,127,104,728,400,533,62,377,370,26,271,155,14,438,786,943,776,498,814,910,481,231,795,697,517,208,410,753,854,95,363,822,862,385,506,761,55,769,403,526,936,216,393,779,510,721,446,690,112,7,803,120,148,224,427,279,489,887,19,903,921,675,824,573,476,952,266,618,744,195,246,546,330,77,317,648,135,633,304,182,344,454,712,844,588,40,603,562,167,80,661 -
ba90950a…· Comment: Size-961 = 31² idempotent right-cancellative magma satisfying Eq 677 and Eq 255, in the AG(2, 31) line family. The 992 =…