files / problems / hilbert16-degree-8 / compute / certs / deep_ball_r7.json

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{
 "what": "Exhaustive Hamming balls of radius 7 around the two census certificates that produced every known scheme outside the 2,367.",
 "method": "compute/ballc.c walks all sign vectors within Hamming distance 7 of the seed on that certificate's own (integer-certified) triangulation and emits one witness per distinct scheme fingerprint; each witness is decoded to its scheme string on the exact Python complex and diffed against the census.",
 "ball_size_per_seed": 54910660,
 "seeds": [
  {
   "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>>"
   ],
   "seconds": 1469.7
  },
  {
   "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>>>"
   ],
   "seconds": 1313.1
  }
 ],
 "conclusion": "Within Hamming distance 7 of these two certificates the eight schemes certified in the previous session are exactly the schemes outside the published 2,367 -- there is no ninth."
}