Equation 677 Database

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Magma eb4277a6f765…

magma eb4277a6f765
Size
961
Isomorphism class hash
eb4277a6f76520456b7c51df4a5eac0427e786a4489481d7fc60e9ba60c6aa9d
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Submitted by
omegaestable
Submitted at
2026-07-29 16:26:05
Display reorder
957,926,818,387,725,756,297,880,632,477,663,271,210,87,787,244,539,29,849,508,570,343,158,314,98,601,441,411,694,41,135,140,939,908,823,392,730,761,302,885,637,482,668,276,215,92,792,249,544,3,854,513,575,348,163,319,103,606,446,416,699,46,51,145,944,913,828,397,735,766,307,890,642,487,673,250,189,66,797,223,549,8,859,518,580,353,168,324,108,611,451,421,704,709,56,150,949,918,833,402,740,771,281,895,647,492,678,255,194,71,802,228,554,13,864,523,585,358,173,329,113,616,456,426,431,714,61,155,954,923,838,376,745,776,286,900,652,497,683,260,199,76,807,233,559,18,869,528,590,363,178,334,118,621,461,466,405,688,35,129,936,905,812,381,719,750,291,874,626,471,657,265,204,81,781,238,533,23,843,502,564,368,183,339,123,595,600,440,410,693,40,134,956,925,817,386,724,755,296,879,631,476,662,270,209,86,786,243,538,28,848,507,569,373,157,313,97,102,605,445,415,698,45,139,938,907,822,391,729,760,301,884,636,481,667,275,214,91,791,248,543,2,853,512,574,347,162,318,323,107,610,450,420,703,50,144,943,912,827,396,734,765,306,889,641,486,672,280,188,65,796,222,548,7,858,517,579,352,167,172,328,112,615,455,425,708,55,149,948,917,832,401,739,770,311,894,646,491,677,254,193,70,801,227,553,12,863,522,584,357,362,177,333,117,620,460,430,713,60,154,953,922,837,375,744,775,285,899,651,496,682,259,198,75,806,232,558,17,868,527,589,563,367,182,338,122,594,465,435,687,34,128,935,904,811,380,718,749,290,873,625,470,656,264,203,80,780,237,532,22,842,501,506,568,372,187,312,96,599,439,409,692,39,133,955,924,816,385,723,754,295,878,630,475,661,269,208,85,785,242,537,27,847,852,511,573,346,161,317,101,604,444,414,697,44,138,937,906,821,390,728,759,300,883,635,480,666,274,213,90,790,247,542,32,6,857,516,578,351,166,322,106,609,449,419,702,49,143,942,911,826,395,733,764,305,888,640,485,671,279,218,64,795,221,547,552,11,862,521,583,356,171,327,111,614,454,424,707,54,148,947,916,831,400,738,769,310,893,645,490,676,253,192,69,800,226,231,557,16,867,526,588,361,176,332,116,619,459,429,712,59,153,952,921,836,374,743,774,284,898,650,495,681,258,197,74,805,779,236,531,21,841,500,562,366,181,337,121,593,464,434,686,33,127,934,903,810,379,717,748,289,872,624,469,655,263,202,79,84,784,241,536,26,846,505,567,371,186,342,95,598,438,408,691,38,132,960,929,815,384,722,753,294,877,629,474,660,268,207,212,89,789,246,541,31,851,510,572,345,160,316,100,603,443,413,696,43,137,959,928,820,389,727,758,299,882,634,479,665,273,278,217,94,794,220,546,5,856,515,577,350,165,321,105,608,448,418,701,48,142,941,910,825,394,732,763,304,887,639,484,670,675,252,191,68,799,225,551,10,861,520,582,355,170,326,110,613,453,423,706,53,147,946,915,830,399,737,768,309,892,644,489,494,680,257,196,73,804,230,556,15,866,525,587,360,175,331,115,618,458,428,711,58,152,951,920,835,404,742,773,283,897,649,623,468,654,262,201,78,778,235,530,20,840,499,561,365,180,336,120,592,463,433,685,63,126,933,902,809,378,716,747,288,871,876,628,473,659,267,206,83,783,240,535,25,845,504,566,370,185,341,125,597,437,407,690,37,131,930,1,814,383,721,752,293,298,881,633,478,664,272,211,88,788,245,540,30,850,509,571,344,159,315,99,602,442,412,695,42,136,958,927,819,388,726,757,762,303,886,638,483,669,277,216,93,793,219,545,4,855,514,576,349,164,320,104,607,447,417,700,47,141,940,909,824,393,731,736,767,308,891,643,488,674,251,190,67,798,224,550,9,860,519,581,354,169,325,109,612,452,422,705,52,146,945,914,829,398,403,741,772,282,896,648,493,679,256,195,72,803,229,555,14,865,524,586,359,174,330,114,617,457,427,710,57,151,950,919,834,808,377,715,746,287,870,622,467,653,261,200,77,777,234,529,19,839,498,560,364,179,335,119,591,462,432,684,62,156,932,901,0,813,382,720,751,292,875,627,472,658,266,205,82,782,239,534,24,844,503,565,369,184,340,124,596,436,406,689,36,130,931 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

961-element magma on Z_31 x Z_31: difference-indexed cocycle tower over magma#60f580e4 (B31), by the same recipe as magma#b9f3f9a0 (M155). Carrier: Z_31 x Z_31. Element encoding: i = 31*x + r, x in Z_31 (base), r in Z_31 (fibre). Base operation: x * y = 5*x - 4*y + 1 (mod 31). Fibre law and cocycle: (x,r) <> (y,t) = (x*y, (5*r + 27*t + h[(y-x) mod 31]) mod 31) with h = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]. E677 for the tower is equivalent to the Z_31-linear cocycle system a*b^2*h(d) + b^2*h(4d-1) + b*h(10d+6) + h(23d-23) = 0 (mod q) for all d in Z_31 [indices mod 31]; at (a,b)=(5,27) its solution space is 1-dimensional. Every solution mod 31 at (5,27) is a constant vector; with h == 1 the fibre law is 5r - 4t + 1 = the base law itself, so this table IS literally B31 x B31, the direct square of magma#60f580e4. a+b-1 = 0 here, so constant fibre shears cannot remove h, but the base-linear shear (x,r) -> (x, r + c*x) does (delta = c); every constant-h tower collapses to the c=0 product, and NO genuinely twisted tower exists at order 961 for ANY E677 affine fibre pair mod 31 (the session-27 decision computation: each nullspace lies inside the exact coboundary space). Invariants (verified exhaustively on the raw table): Equation 677 at all 961^2 pairs; Equation 255 at every point; 0 idempotents; rows and columns bijective (left/right cancellative quasigroup); translation group transitive; diagonal-orbit lengths (ell-profile) {10: 961}. Provenance: melvyn lab session 27, cocycle tower over magma#60f580e4 (B31); recipe as in magma#b9f3f9a0 (M155).

last edited by omegaestable at 2026-07-29 16:26:05 · history