files / problems / hilbert16-degree-8 / compute / certs / mcert_balls_r6.json
{
"what": "Exhaustive Hamming balls of radius 6 around every one of the 38 22-oval (M-curve) certificates of arXiv:2602.06888 v3.",
"method": "compute/ballc.c on each certificate's own integer-certified triangulation; one witness per distinct scheme fingerprint, each decoded to its scheme string on the exact Python complex and diffed against the replayed 2,367.",
"ball_size_per_seed": 9531040,
"seeds": 38,
"all_complete": true,
"sign_vectors": 362179520,
"distinct_schemes_total": 1922,
"schemes_outside_the_published_2367": [
"<13 u 1<3 u 1<2>>>",
"<3 u 1<4> u 1<11>>",
"<4 u 1<2> u 1<13>>",
"<4 u 1<3> u 1<12>>",
"<4 u 1<4> u 1<11>>",
"<4 u 1<5> u 1<10>>",
"<5 u 1<1> u 1<3> u 1<7>>",
"<5 u 1<6 u 1<7>>>",
"<5 u 1<6 u 1<8>>>",
"<6 u 1<1> u 1<3> u 1<7>>",
"<6 u 1<4 u 1<8>>>",
"<6 u 1<5 u 1<8>>>",
"<6 u 1<6 u 1<6>>>",
"<6 u 1<6 u 1<7>>>",
"<6 u 1<8 u 1<4>>>",
"<6 u 1<9 u 1<4>>>",
"<7 u 1<1> u 1<3> u 1<7>>"
],
"per_seed": [
{
"seed_cert": "deg8/o22-p07-n15/(5v1(5)v1(10)).pcom",
"evals": 9531040,
"complete": true,
"distinct_schemes": 840,
"novel": [
"<4 u 1<5> u 1<10>>"
]
},
{
"seed_cert": "deg8/o22-p11-n11/(6v1(10v1(4))).pcom",
"evals": 9531040,
"complete": true,
"distinct_schemes": 1194,
"novel": [
"<6 u 1<4 u 1<8>>>",
"<6 u 1<5 u 1<8>>>",
"<6 u 1<8 u 1<4>>>",
"<6 u 1<9 u 1<4>>>"
]
},
{
"seed_cert": "deg8/o22-p15-n07/(13v1(3)v1(4)).pcom",
"evals": 9531040,
"complete": true,
"distinct_schemes": 615,
"novel": []
},
{
"seed_cert": "deg8/o22-p19-n03/(17v1(2v1(1))).pcom",
"evals": 9531040,
"complete": true,
"distinct_schemes": 407,
"novel": []
},
{
"seed_cert": "deg8/o22-p15-n07/(12v1(1)v2(3)).pcom",
"evals": 9531040,
"complete": true,
"distinct_schemes": 930,
"novel": []
},
{
"seed_cert": "deg8/o22-p11-n11/(8v2(1)v1(9)).pcom",
"evals": 9531040,
"complete": true,
"distinct_schemes": 652,
"novel": []
},
{
"seed_cert": "deg8/o22-p11-n11/(8v2(3)v1(5)).pcom",
"evals": 9531040,
"complete": true,
"distinct_schemes": 1085,
"novel": []
},
{
"seed_cert": "deg8/o22-p19-n03/(17v1(1)v1(2)).pcom",
"evals": 9531040,
"complete": true,
"distinct_schemes": 439,
"novel": []
},
{
"seed_cert": "deg8/o22-p19-n03/(16v3(1)).pcom",
"evals": 9531040,
"complete": true,
"distinct_schemes": 488,
"novel": []
},
{
"seed_cert": "deg8/o22-p11-n11/(9v1(4)v1(7)).pcom",
"evals": 9531040,
"complete": true,
"distinct_schemes": 548,
"novel": []
},
{
"seed_cert": "deg8/o22-p11-n11/(9v1(5)v1(6)).pcom",
"evals": 9531040,
"complete": true,
"distinct_schemes": 591,
"novel": []
},
{
"seed_cert": "deg8/o22-p15-n07/(6v1(6v1(8))).pcom",
"evals": 9531040,
"complete": true,
"distinct_schemes": 1292,
"novel": [
"<5 u 1<6 u 1<7>>>",
"<5 u 1<6 u 1<8>>>",
"<6 u 1<5 u 1<8>>>",
"<6 u 1<6 u 1<6>>>",
"<6 u 1<6 u 1<7>>>",
"<6 u 1<8 u 1<4>>>",
"<6 u 1<9 u 1<4>>>"
]
},
{
"seed_cert": "deg8/o22-p15-n07/(13v1(6v1(1))).pcom",
"evals": 9531040,
"complete": true,
"distinct_schemes": 693,
"novel": []
},
{
"seed_cert": "deg8/o22-p19-n03/(18v1(3)).pcom",
"evals": 9531040,
"complete": true,
"distinct_schemes": 396,
"novel": []
},
{
"seed_cert": "deg8/o22-p11-n11/(9v1(1)v1(10)).pcom",
"evals": 9531040,
"complete": true,
"distinct_schemes": 630,
"novel": []
},
{
"seed_cert": "deg8/o22-p11-n11/(5v1(10v1(5))).pcom",
"evals": 9531040,
"complete": true,
"distinct_schemes": 920,
"novel": []
},
{
"seed_cert": "deg8/o22-p07-n15/(5v1(7)v1(8)).pcom",
"evals": 9531040,
"complete": true,
"distinct_schemes": 596,
"novel": []
},
{
"seed_cert": "deg8/o22-p07-n15/(6v1(15)).pcom",
"evals": 9531040,
"complete": true,
"distinct_schemes": 599,
"novel": []
},
{
"seed_cert": "deg8/o22-p07-n15/(5v1(3)v1(12)).pcom",
"evals": 9531040,
"complete": true,
"distinct_schemes": 790,
"novel": [
"<4 u 1<3> u 1<12>>"
]
},
{
"seed_cert": "deg8/o22-p15-n07/(9v1(6v1(5))).pcom",
"evals": 9531040,
"complete": true,
"distinct_schemes": 817,
"novel": []
},
{
"seed_cert": "deg8/o22-p11-n11/(8v1(1)v1(3)v1(7)).pcom",
"evals": 9531040,
"complete": true,
"distinct_schemes": 1085,
"novel": [
"<5 u 1<1> u 1<3> u 1<7>>",
"<6 u 1<1> u 1<3> u 1<7>>",
"<7 u 1<1> u 1<3> u 1<7>>"
]
},
{
"seed_cert": "deg8/o22-p07-n15/(5v1(14v1(1))).pcom",
"evals": 9531040,
"complete": true,
"distinct_schemes": 641,
"novel": []
},
{
"seed_cert": "deg8/o22-p07-n15/(5v1(1)v1(14)).pcom",
"evals": 9531040,
"complete": true,
"distinct_schemes": 837,
"novel": []
},
{
"seed_cert": "deg8/o22-p07-n15/(5v1(2)v1(13)).pcom",
"evals": 9531040,
"complete": true,
"distinct_schemes": 818,
"novel": [
"<13 u 1<3 u 1<2>>>",
"<4 u 1<2> u 1<13>>"
]
},
{
"seed_cert": "deg8/o22-p07-n15/(5v1(4)v1(11)).pcom",
"evals": 9531040,
"complete": true,
"distinct_schemes": 616,
"novel": [
"<3 u 1<4> u 1<11>>",
"<4 u 1<2> u 1<13>>",
"<4 u 1<4> u 1<11>>"
]
},
{
"seed_cert": "deg8/o22-p15-n07/(10v1(6v1(4))).pcom",
"evals": 9531040,
"complete": true,
"distinct_schemes": 1028,
"novel": []
},
{
"seed_cert": "deg8/o22-p19-n03/(10v1(2v1(8))).pcom",
"evals": 9531040,
"complete": true,
"distinct_schemes": 1223,
"novel": []
},
{
"seed_cert": "deg8/o22-p15-n07/(13v1(2)v1(5)).pcom",
"evals": 9531040,
"complete": true,
"distinct_schemes": 453,
"novel": []
},
{
"seed_cert": "deg8/o22-p11-n11/(9v1(3)v1(8)).pcom",
"evals": 9531040,
"complete": true,
"distinct_schemes": 435,
"novel": []
},
{
"seed_cert": "deg8/o22-p15-n07/(13v1(1)v1(6)).pcom",
"evals": 9531040,
"complete": true,
"distinct_schemes": 643,
"novel": []
},
{
"seed_cert": "deg8/o22-p11-n11/(10v1(11)).pcom",
"evals": 9531040,
"complete": true,
"distinct_schemes": 541,
"novel": []
},
{
"seed_cert": "deg8/o22-p15-n07/(14v1(7)).pcom",
"evals": 9531040,
"complete": true,
"distinct_schemes": 375,
"novel": []
},
{
"seed_cert": "deg8/o22-p15-n07/(11v1(6v1(3))).pcom",
"evals": 9531040,
"complete": true,
"distinct_schemes": 601,
"novel": []
},
{
"seed_cert": "deg8/o22-p11-n11/(9v1(2)v1(9)).pcom",
"evals": 9531040,
"complete": true,
"distinct_schemes": 970,
"novel": []
},
{
"seed_cert": "deg8/o22-p11-n11/(8v1(1)v2(5)).pcom",
"evals": 9531040,
"complete": true,
"distinct_schemes": 806,
"novel": []
},
{
"seed_cert": "deg8/o22-p15-n07/(12v2(1)v1(5)).pcom",
"evals": 9531040,
"complete": true,
"distinct_schemes": 674,
"novel": []
},
{
"seed_cert": "deg8/o22-p11-n11/(9v1(10v1(1))).pcom",
"evals": 9531040,
"complete": true,
"distinct_schemes": 477,
"novel": []
},
{
"seed_cert": "deg8/o22-p11-n11/(7v1(10v1(3))).pcom",
"evals": 9531040,
"complete": true,
"distinct_schemes": 772,
"novel": []
}
]
}