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

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{
 "what": "Exhaustive maximal-stratum classification of certified regular triangulations of T_8 that are NOT in the arXiv:2602.06888 v3 census.",
 "method": "Two samplers.  'walk': scale a census certificate's integer MIN_WEIGHTS by 10^6, add integer noise, take the lower hull -- regular by construction, then re-certified exactly (validate_triangulation + Fraction check_convexity) and skipped if it coincides with a census triangulation.  'rand': gen_fast.random_certified_triangulation (random positive-definite quadratic form plus noise), same exact certification.  Each accepted triangulation then had its ENTIRE affine subspace eta + span{delta_S} swept by compute/zonec.c, which by Haas' criterion is every maximal sign distribution it carries.",
 "walk": {
  "triangulations": 859,
  "sign_distributions": 529684800,
  "twist_rank_range": [
   6,
   26
  ],
  "distinct_M_schemes": [
   "<10 u 1<11>>",
   "<10 u 1<2 u 1<8>>>",
   "<10 u 1<6 u 1<4>>>",
   "<11 u 1<6 u 1<3>>>",
   "<12 u 1<1> u 2<3>>",
   "<12 u 2<1> u 1<5>>",
   "<13 u 1<1> u 1<6>>",
   "<13 u 1<2> u 1<5>>",
   "<13 u 1<3> u 1<4>>",
   "<13 u 1<6 u 1<1>>>",
   "<14 u 1<7>>",
   "<16 u 3<1>>",
   "<17 u 1<1> u 1<2>>",
   "<17 u 1<2 u 1<1>>>",
   "<18 u 1<3>>",
   "<5 u 1<10 u 1<5>>>",
   "<5 u 1<14 u 1<1>>>",
   "<5 u 1<1> u 1<14>>",
   "<5 u 1<2> u 1<13>>",
   "<5 u 1<3> u 1<12>>",
   "<5 u 1<4> u 1<11>>",
   "<5 u 1<5> u 1<10>>",
   "<5 u 1<7> u 1<8>>",
   "<6 u 1<10 u 1<4>>>",
   "<6 u 1<15>>",
   "<6 u 1<6 u 1<8>>>",
   "<7 u 1<10 u 1<3>>>",
   "<8 u 1<1> u 1<3> u 1<7>>",
   "<8 u 1<1> u 2<5>>",
   "<8 u 2<1> u 1<9>>",
   "<8 u 2<3> u 1<5>>",
   "<9 u 1<10 u 1<1>>>",
   "<9 u 1<1> u 1<10>>",
   "<9 u 1<2> u 1<9>>",
   "<9 u 1<3> u 1<8>>",
   "<9 u 1<4> u 1<7>>",
   "<9 u 1<5> u 1<6>>",
   "<9 u 1<6 u 1<5>>>"
  ],
  "M_schemes_outside_the_papers_38": [],
  "schemes_outside_the_published_2367": []
 },
 "rand": {
  "triangulations": 3750,
  "sign_distributions": 7728448,
  "twist_rank_range": [
   6,
   16
  ],
  "distinct_M_schemes": [
   "<17 u 1<1> u 1<2>>",
   "<18 u 1<3>>"
  ],
  "M_schemes_outside_the_papers_38": [],
  "schemes_outside_the_published_2367": []
 },
 "conclusion": "4609 certified regular triangulations outside the census, each swept exhaustively over its whole maximal stratum, realize exactly the paper's 38 M-schemes and nothing outside them.  Sample, not enumeration."
}