files / problems / hilbert16-degree-8 / compute / certs / productive_certs_r7.json

2.6 KB · on GitHub

{
 "what": "Exhaustive Hamming balls of radius 7 around every census M-certificate that has a scheme missing beside it (all seven).",
 "method": "compute/ballc.c on the certificate's own integer-certified triangulation; one witness per distinct scheme fingerprint, decoded to its scheme string on the exact Python complex.",
 "ball_size_per_seed": 54910660,
 "seeds": 7,
 "all_complete": true,
 "sign_vectors": 384374620,
 "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",
   "radius": 7,
   "evals": 54910660,
   "complete": true,
   "distinct_schemes": 885,
   "novel": [
    "<4 u 1<5> u 1<10>>"
   ]
  },
  {
   "seed_cert": "deg8/o22-p15-n07/(6v1(6v1(8))).pcom",
   "radius": 7,
   "evals": 54910660,
   "complete": true,
   "distinct_schemes": 1365,
   "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-p11-n11/(6v1(10v1(4))).pcom",
   "radius": 7,
   "evals": 54910660,
   "complete": true,
   "distinct_schemes": 1302,
   "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-p07-n15/(5v1(2)v1(13)).pcom",
   "radius": 7,
   "evals": 54910660,
   "complete": true,
   "distinct_schemes": 898,
   "novel": [
    "<13 u 1<3 u 1<2>>>",
    "<4 u 1<2> u 1<13>>"
   ]
  },
  {
   "seed_cert": "deg8/o22-p07-n15/(5v1(3)v1(12)).pcom",
   "radius": 7,
   "evals": 54910660,
   "complete": true,
   "distinct_schemes": 833,
   "novel": [
    "<4 u 1<3> u 1<12>>"
   ]
  },
  {
   "seed_cert": "deg8/o22-p11-n11/(8v1(1)v1(3)v1(7)).pcom",
   "radius": 7,
   "evals": 54910660,
   "complete": true,
   "distinct_schemes": 1217,
   "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(4)v1(11)).pcom",
   "radius": 7,
   "evals": 54910660,
   "complete": true,
   "distinct_schemes": 637,
   "novel": [
    "<3 u 1<4> u 1<11>>",
    "<4 u 1<2> u 1<13>>",
    "<4 u 1<4> u 1<11>>"
   ]
  }
 ]
}