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   ],
   "facts": [
    "baseline-heads.json lists the 1016 heads in order",
    "its owners are 1016 distinct Leech minimal vectors",
    "its owners equal Kravatskiy's heads_U.npy",
    "its 972 integer leans equal the leans decoded here from Kravatskiy's float heads",
    "its 44 rational heads equal Kravatskiy's pickle, fraction for fraction",
    "its extra-equator lean equals the one decoded from Kravatskiy's extra_P.npy",
    "the repair vectors have squared norms 1007176 and 10209 as stated",
    "the block U = {u : <u, v> = -24} has 552 members, all owners",
    "each w = u + v is a kept minimal vector",
    "the two replaced cap points are (x_984, +1) and (x_1008, -1) (construction.tex)"
   ],
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   "choices": [],
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    "kravatsky:verifications/improved/dim25-lens-heads/data/heads_U.npy": "3c62c8c01585fbe04bd6e687475345b566522815022d72a05e7038f8bfab8043",
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    "qiushi:constructions/d25/baseline-heads.json": "b6b1dff1172ca723595c19bc4daf49448f0e8d04d506033786a8e96afbf515d6",
    "qiushi:constructions/d25/repair-points.json": "daeabf4a2614779749bf9a5c30f55d502c830e45a88ef2b52fdbbc7f87703677"
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   "seconds": 36.8,
   "jsCheck": {
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    "jsVerdict": "CERTIFIED",
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    "excludedFamilies": [
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   "dim": 43,
   "claimed": 2553792,
   "previous": 2545056,
   "verdict": "NEEDS DATA",
   "detail": "the count comes from spherical-design moment identities over a lattice section; no vector list is published. What would decide it: the vectors, or the section generators and the selected sets in exact form."
  },
  {
   "id": "qiushi-45",
   "claimant": "qiushi",
   "claimantName": "Qiushi Engine (Oxelra-AI) \u2014 arXiv:2609.35051",
   "dim": 45,
   "claimed": 7380090,
   "previous": 7379838,
   "verdict": "NEEDS DATA",
   "detail": "the count comes from spherical-design moment identities over a lattice section; no vector list is published. What would decide it: the vectors, or the section generators and the selected sets in exact form."
  },
  {
   "id": "kravatsky-49",
   "claimant": "kravatsky",
   "claimantName": "A. Kravatskiy \u2014 github.com/alexlegeartis/KissingNumbers (no arXiv paper; the write-up, paper/kissing46.pdf, is in the repository and calls dimensions 25\u201331 joint work in progress with H. Cohn and B. Lindow)",
   "dim": 49,
   "claimed": 52430140,
   "previous": 52416002,
   "verdict": "NEEDS DATA",
   "status": "classes",
   "package": "verifications/improved/dim49-63-p48-caps/",
   "detail": "no vector list is published: the count is computed from a lattice, class-size tables or a moment LP (RESULTS.md status `classes`). What would decide it: the configuration's vectors in any exact form, or a generator file this lab can run without the claimant's code."
  },
  {
   "id": "kravatsky-50",
   "claimant": "kravatsky",
   "claimantName": "A. Kravatskiy \u2014 github.com/alexlegeartis/KissingNumbers (no arXiv paper; the write-up, paper/kissing46.pdf, is in the repository and calls dimensions 25\u201331 joint work in progress with H. Cohn and B. Lindow)",
   "dim": 50,
   "claimed": 52458418,
   "previous": 52416006,
   "verdict": "NEEDS DATA",
   "status": "classes",
   "package": "verifications/improved/dim49-63-p48-caps/",
   "detail": "no vector list is published: the count is computed from a lattice, class-size tables or a moment LP (RESULTS.md status `classes`). What would decide it: the configuration's vectors in any exact form, or a generator file this lab can run without the claimant's code."
  },
  {
   "id": "kravatsky-51",
   "claimant": "kravatsky",
   "claimantName": "A. Kravatskiy \u2014 github.com/alexlegeartis/KissingNumbers (no arXiv paper; the write-up, paper/kissing46.pdf, is in the repository and calls dimensions 25\u201331 joint work in progress with H. Cohn and B. Lindow)",
   "dim": 51,
   "claimed": 52500816,
   "previous": 52416012,
   "verdict": "NEEDS DATA",
   "status": "classes",
   "package": "verifications/improved/dim49-63-p48-caps/",
   "detail": "no vector list is published: the count is computed from a lattice, class-size tables or a moment LP (RESULTS.md status `classes`). What would decide it: the configuration's vectors in any exact form, or a generator file this lab can run without the claimant's code."
  },
  {
   "id": "kravatsky-52",
   "claimant": "kravatsky",
   "claimantName": "A. Kravatskiy \u2014 github.com/alexlegeartis/KissingNumbers (no arXiv paper; the write-up, paper/kissing46.pdf, is in the repository and calls dimensions 25\u201331 joint work in progress with H. Cohn and B. Lindow)",
   "dim": 52,
   "claimed": 52585516,
   "previous": 52416024,
   "verdict": "NEEDS DATA",
   "status": "classes",
   "package": "verifications/improved/dim49-63-p48-caps/",
   "detail": "no vector list is published: the count is computed from a lattice, class-size tables or a moment LP (RESULTS.md status `classes`). What would decide it: the configuration's vectors in any exact form, or a generator file this lab can run without the claimant's code."
  },
  {
   "id": "kravatsky-53",
   "claimant": "kravatsky",
   "claimantName": "A. Kravatskiy \u2014 github.com/alexlegeartis/KissingNumbers (no arXiv paper; the write-up, paper/kissing46.pdf, is in the repository and calls dimensions 25\u201331 joint work in progress with H. Cohn and B. Lindow)",
   "dim": 53,
   "claimed": 52698222,
   "previous": 52416040,
   "verdict": "NEEDS DATA",
   "status": "classes",
   "package": "verifications/improved/dim49-63-p48-caps/",
   "detail": "no vector list is published: the count is computed from a lattice, class-size tables or a moment LP (RESULTS.md status `classes`). What would decide it: the configuration's vectors in any exact form, or a generator file this lab can run without the claimant's code."
  },
  {
   "id": "kravatsky-54",
   "claimant": "kravatsky",
   "claimantName": "A. Kravatskiy \u2014 github.com/alexlegeartis/KissingNumbers (no arXiv paper; the write-up, paper/kissing46.pdf, is in the repository and calls dimensions 25\u201331 joint work in progress with H. Cohn and B. Lindow)",
   "dim": 54,
   "claimed": 52922906,
   "previous": 52416072,
   "verdict": "NEEDS DATA",
   "status": "classes",
   "package": "verifications/improved/dim49-63-p48-caps/",
   "detail": "no vector list is published: the count is computed from a lattice, class-size tables or a moment LP (RESULTS.md status `classes`). What would decide it: the configuration's vectors in any exact form, or a generator file this lab can run without the claimant's code."
  },
  {
   "id": "kravatsky-55",
   "claimant": "kravatsky",
   "claimantName": "A. Kravatskiy \u2014 github.com/alexlegeartis/KissingNumbers (no arXiv paper; the write-up, paper/kissing46.pdf, is in the repository and calls dimensions 25\u201331 joint work in progress with H. Cohn and B. Lindow)",
   "dim": 55,
   "claimed": 53299730,
   "previous": 52416126,
   "verdict": "NEEDS DATA",
   "status": "classes",
   "package": "verifications/improved/dim49-63-p48-caps/",
   "detail": "no vector list is published: the count is computed from a lattice, class-size tables or a moment LP (RESULTS.md status `classes`). What would decide it: the configuration's vectors in any exact form, or a generator file this lab can run without the claimant's code."
  },
  {
   "id": "kravatsky-56",
   "claimant": "kravatsky",
   "claimantName": "A. Kravatskiy \u2014 github.com/alexlegeartis/KissingNumbers (no arXiv paper; the write-up, paper/kissing46.pdf, is in the repository and calls dimensions 25\u201331 joint work in progress with H. Cohn and B. Lindow)",
   "dim": 56,
   "claimed": 54085392,
   "previous": 52416240,
   "verdict": "NEEDS DATA",
   "status": "classes",
   "package": "verifications/improved/dim49-63-p48-caps/",
   "detail": "no vector list is published: the count is computed from a lattice, class-size tables or a moment LP (RESULTS.md status `classes`). What would decide it: the configuration's vectors in any exact form, or a generator file this lab can run without the claimant's code."
  },
  {
   "id": "kravatsky-57",
   "claimant": "kravatsky",
   "claimantName": "A. Kravatskiy \u2014 github.com/alexlegeartis/KissingNumbers (no arXiv paper; the write-up, paper/kissing46.pdf, is in the repository and calls dimensions 25\u201331 joint work in progress with H. Cohn and B. Lindow)",
   "dim": 57,
   "claimed": 54534176,
   "previous": 52416306,
   "verdict": "NEEDS DATA",
   "status": "classes",
   "package": "verifications/improved/dim49-63-p48-caps/",
   "detail": "no vector list is published: the count is computed from a lattice, class-size tables or a moment LP (RESULTS.md status `classes`). What would decide it: the configuration's vectors in any exact form, or a generator file this lab can run without the claimant's code."
  },
  {
   "id": "kravatsky-58",
   "claimant": "kravatsky",
   "claimantName": "A. Kravatskiy \u2014 github.com/alexlegeartis/KissingNumbers (no arXiv paper; the write-up, paper/kissing46.pdf, is in the repository and calls dimensions 25\u201331 joint work in progress with H. Cohn and B. Lindow)",
   "dim": 58,
   "claimed": 55893422,
   "previous": 52416510,
   "verdict": "NEEDS DATA",
   "status": "classes",
   "package": "verifications/improved/dim49-63-p48-caps/",
   "detail": "no vector list is published: the count is computed from a lattice, class-size tables or a moment LP (RESULTS.md status `classes`). What would decide it: the configuration's vectors in any exact form, or a generator file this lab can run without the claimant's code."
  },
  {
   "id": "kravatsky-59",
   "claimant": "kravatsky",
   "claimantName": "A. Kravatskiy \u2014 github.com/alexlegeartis/KissingNumbers (no arXiv paper; the write-up, paper/kissing46.pdf, is in the repository and calls dimensions 25\u201331 joint work in progress with H. Cohn and B. Lindow)",
   "dim": 59,
   "claimed": 56505668,
   "previous": 52416604,
   "verdict": "NEEDS DATA",
   "status": "classes",
   "package": "verifications/improved/dim49-63-p48-caps/",
   "detail": "no vector list is published: the count is computed from a lattice, class-size tables or a moment LP (RESULTS.md status `classes`). What would decide it: the configuration's vectors in any exact form, or a generator file this lab can run without the claimant's code."
  },
  {
   "id": "kravatsky-60",
   "claimant": "kravatsky",
   "claimantName": "A. Kravatskiy \u2014 github.com/alexlegeartis/KissingNumbers (no arXiv paper; the write-up, paper/kissing46.pdf, is in the repository and calls dimensions 25\u201331 joint work in progress with H. Cohn and B. Lindow)",
   "dim": 60,
   "claimed": 57477123,
   "previous": 52416841,
   "verdict": "NEEDS DATA",
   "status": "classes",
   "package": "verifications/improved/dim49-63-p48-caps/",
   "detail": "no vector list is published: the count is computed from a lattice, class-size tables or a moment LP (RESULTS.md status `classes`). What would decide it: the configuration's vectors in any exact form, or a generator file this lab can run without the claimant's code."
  },
  {
   "id": "kravatsky-61",
   "claimant": "kravatsky",
   "claimantName": "A. Kravatskiy \u2014 github.com/alexlegeartis/KissingNumbers (no arXiv paper; the write-up, paper/kissing46.pdf, is in the repository and calls dimensions 25\u201331 joint work in progress with H. Cohn and B. Lindow)",
   "dim": 61,
   "claimed": 59898694,
   "previous": 52417154,
   "verdict": "NEEDS DATA",
   "status": "classes",
   "package": "verifications/improved/dim49-63-p48-caps/",
   "detail": "no vector list is published: the count is computed from a lattice, class-size tables or a moment LP (RESULTS.md status `classes`). What would decide it: the configuration's vectors in any exact form, or a generator file this lab can run without the claimant's code."
  },
  {
   "id": "kravatsky-62",
   "claimant": "kravatsky",
   "claimantName": "A. Kravatskiy \u2014 github.com/alexlegeartis/KissingNumbers (no arXiv paper; the write-up, paper/kissing46.pdf, is in the repository and calls dimensions 25\u201331 joint work in progress with H. Cohn and B. Lindow)",
   "dim": 62,
   "claimed": 71310732,
   "previous": 52417932,
   "verdict": "NEEDS DATA",
   "status": "external",
   "package": "verifications/improved/dim62-63-ers-chain/",
   "detail": "no vector list is published: the count is computed from a lattice, class-size tables or a moment LP (RESULTS.md status `external`). What would decide it: the configuration's vectors in any exact form, or a generator file this lab can run without the claimant's code."
  },
  {
   "id": "kravatsky-63",
   "claimant": "kravatsky",
   "claimantName": "A. Kravatskiy \u2014 github.com/alexlegeartis/KissingNumbers (no arXiv paper; the write-up, paper/kissing46.pdf, is in the repository and calls dimensions 25\u201331 joint work in progress with H. Cohn and B. Lindow)",
   "dim": 63,
   "claimed": 138419844,
   "previous": 52418564,
   "verdict": "NEEDS DATA",
   "status": "external",
   "package": "verifications/improved/dim62-63-ers-chain/",
   "detail": "no vector list is published: the count is computed from a lattice, class-size tables or a moment LP (RESULTS.md status `external`). What would decide it: the configuration's vectors in any exact form, or a generator file this lab can run without the claimant's code."
  },
  {
   "id": "kravatsky-68",
   "claimant": "kravatsky",
   "claimantName": "A. Kravatskiy \u2014 github.com/alexlegeartis/KissingNumbers (no arXiv paper; the write-up, paper/kissing46.pdf, is in the repository and calls dimensions 25\u201331 joint work in progress with H. Cohn and B. Lindow)",
   "dim": 68,
   "claimed": 361275480,
   "previous": 331737984,
   "verdict": "NEEDS DATA",
   "status": "lp-exact",
   "package": "verifications/improved/dim68-69-gamma72-cross-sections/",
   "detail": "no vector list is published: the count is computed from a lattice, class-size tables or a moment LP (RESULTS.md status `lp-exact`). What would decide it: the configuration's vectors in any exact form, or a generator file this lab can run without the claimant's code."
  },
  {
   "id": "kravatsky-69",
   "claimant": "kravatsky",
   "claimantName": "A. Kravatskiy \u2014 github.com/alexlegeartis/KissingNumbers (no arXiv paper; the write-up, paper/kissing46.pdf, is in the repository and calls dimensions 25\u201331 joint work in progress with H. Cohn and B. Lindow)",
   "dim": 69,
   "claimed": 627822180,
   "previous": 331737984,
   "verdict": "NEEDS DATA",
   "status": "lp-exact",
   "package": "verifications/improved/dim68-69-gamma72-cross-sections/",
   "detail": "no vector list is published: the count is computed from a lattice, class-size tables or a moment LP (RESULTS.md status `lp-exact`). What would decide it: the configuration's vectors in any exact form, or a generator file this lab can run without the claimant's code."
  },
  {
   "id": "kravatsky-70",
   "claimant": "kravatsky",
   "claimantName": "A. Kravatskiy \u2014 github.com/alexlegeartis/KissingNumbers (no arXiv paper; the write-up, paper/kissing46.pdf, is in the repository and calls dimensions 25\u201331 joint work in progress with H. Cohn and B. Lindow)",
   "dim": 70,
   "claimed": 1249778250,
   "previous": 331737984,
   "verdict": "NEEDS DATA",
   "status": "lp-exact",
   "package": "verifications/improved/dim70-71-gamma72-cross-sections/",
   "detail": "no vector list is published: the count is computed from a lattice, class-size tables or a moment LP (RESULTS.md status `lp-exact`). What would decide it: the configuration's vectors in any exact form, or a generator file this lab can run without the claimant's code."
  },
  {
   "id": "kravatsky-71",
   "claimant": "kravatsky",
   "claimantName": "A. Kravatskiy \u2014 github.com/alexlegeartis/KissingNumbers (no arXiv paper; the write-up, paper/kissing46.pdf, is in the repository and calls dimensions 25\u201331 joint work in progress with H. Cohn and B. Lindow)",
   "dim": 71,
   "claimed": 2603658750,
   "previous": 331737984,
   "verdict": "NEEDS DATA",
   "status": "lp-exact",
   "package": "verifications/improved/dim70-71-gamma72-cross-sections/",
   "detail": "no vector list is published: the count is computed from a lattice, class-size tables or a moment LP (RESULTS.md status `lp-exact`). What would decide it: the configuration's vectors in any exact form, or a generator file this lab can run without the claimant's code."
  },
  {
   "id": "kravatsky-73",
   "claimant": "kravatsky",
   "claimantName": "A. Kravatskiy \u2014 github.com/alexlegeartis/KissingNumbers (no arXiv paper; the write-up, paper/kissing46.pdf, is in the repository and calls dimensions 25\u201331 joint work in progress with H. Cohn and B. Lindow)",
   "dim": 73,
   "claimed": 6218179814,
   "previous": 6218175602,
   "verdict": "NEEDS DATA",
   "status": "classes",
   "package": "verifications/improved/dim73-95-gamma72-caps/",
   "detail": "no vector list is published: the count is computed from a lattice, class-size tables or a moment LP (RESULTS.md status `classes`). What would decide it: the configuration's vectors in any exact form, or a generator file this lab can run without the claimant's code."
  },
  {
   "id": "kravatsky-74",
   "claimant": "kravatsky",
   "claimantName": "A. Kravatskiy \u2014 github.com/alexlegeartis/KissingNumbers (no arXiv paper; the write-up, paper/kissing46.pdf, is in the repository and calls dimensions 25\u201331 joint work in progress with H. Cohn and B. Lindow)",
   "dim": 74,
   "claimed": 6218192454,
   "previous": 6218175606,
   "verdict": "NEEDS DATA",
   "status": "classes",
   "package": "verifications/improved/dim73-95-gamma72-caps/",
   "detail": "no vector list is published: the count is computed from a lattice, class-size tables or a moment LP (RESULTS.md status `classes`). What would decide it: the configuration's vectors in any exact form, or a generator file this lab can run without the claimant's code."
  },
  {
   "id": "kravatsky-75",
   "claimant": "kravatsky",
   "claimantName": "A. Kravatskiy \u2014 github.com/alexlegeartis/KissingNumbers (no arXiv paper; the write-up, paper/kissing46.pdf, is in the repository and calls dimensions 25\u201331 joint work in progress with H. Cohn and B. Lindow)",
   "dim": 75,
   "claimed": 6218209308,
   "previous": 6218175612,
   "verdict": "NEEDS DATA",
   "status": "classes",
   "package": "verifications/improved/dim73-95-gamma72-caps/",
   "detail": "no vector list is published: the count is computed from a lattice, class-size tables or a moment LP (RESULTS.md status `classes`). What would decide it: the configuration's vectors in any exact form, or a generator file this lab can run without the claimant's code."
  },
  {
   "id": "kravatsky-76",
   "claimant": "kravatsky",
   "claimantName": "A. Kravatskiy \u2014 github.com/alexlegeartis/KissingNumbers (no arXiv paper; the write-up, paper/kissing46.pdf, is in the repository and calls dimensions 25\u201331 joint work in progress with H. Cohn and B. Lindow)",
   "dim": 76,
   "claimed": 6218243016,
   "previous": 6218175624,
   "verdict": "NEEDS DATA",
   "status": "classes",
   "package": "verifications/improved/dim73-95-gamma72-caps/",
   "detail": "no vector list is published: the count is computed from a lattice, class-size tables or a moment LP (RESULTS.md status `classes`). What would decide it: the configuration's vectors in any exact form, or a generator file this lab can run without the claimant's code."
  },
  {
   "id": "kravatsky-77",
   "claimant": "kravatsky",
   "claimantName": "A. Kravatskiy \u2014 github.com/alexlegeartis/KissingNumbers (no arXiv paper; the write-up, paper/kissing46.pdf, is in the repository and calls dimensions 25\u201331 joint work in progress with H. Cohn and B. Lindow)",
   "dim": 77,
   "claimed": 6218285152,
   "previous": 6218175640,
   "verdict": "NEEDS DATA",
   "status": "classes",
   "package": "verifications/improved/dim73-95-gamma72-caps/",
   "detail": "no vector list is published: the count is computed from a lattice, class-size tables or a moment LP (RESULTS.md status `classes`). What would decide it: the configuration's vectors in any exact form, or a generator file this lab can run without the claimant's code."
  },
  {
   "id": "kravatsky-78",
   "claimant": "kravatsky",
   "claimantName": "A. Kravatskiy \u2014 github.com/alexlegeartis/KissingNumbers (no arXiv paper; the write-up, paper/kissing46.pdf, is in the repository and calls dimensions 25\u201331 joint work in progress with H. Cohn and B. Lindow)",
   "dim": 78,
   "claimed": 6218377840,
   "previous": 6218175672,
   "verdict": "NEEDS DATA",
   "status": "classes",
   "package": "verifications/improved/dim73-95-gamma72-caps/",
   "detail": "no vector list is published: the count is computed from a lattice, class-size tables or a moment LP (RESULTS.md status `classes`). What would decide it: the configuration's vectors in any exact form, or a generator file this lab can run without the claimant's code."
  },
  {
   "id": "kravatsky-79",
   "claimant": "kravatsky",
   "claimantName": "A. Kravatskiy \u2014 github.com/alexlegeartis/KissingNumbers (no arXiv paper; the write-up, paper/kissing46.pdf, is in the repository and calls dimensions 25\u201331 joint work in progress with H. Cohn and B. Lindow)",
   "dim": 79,
   "claimed": 6218529454,
   "previous": 6218175726,
   "verdict": "NEEDS DATA",
   "status": "classes",
   "package": "verifications/improved/dim73-95-gamma72-caps/",
   "detail": "no vector list is published: the count is computed from a lattice, class-size tables or a moment LP (RESULTS.md status `classes`). What would decide it: the configuration's vectors in any exact form, or a generator file this lab can run without the claimant's code."
  },
  {
   "id": "kravatsky-80",
   "claimant": "kravatsky",
   "claimantName": "A. Kravatskiy \u2014 github.com/alexlegeartis/KissingNumbers (no arXiv paper; the write-up, paper/kissing46.pdf, is in the repository and calls dimensions 25\u201331 joint work in progress with H. Cohn and B. Lindow)",
   "dim": 80,
   "claimed": 6218849228,
   "previous": 6218175840,
   "verdict": "NEEDS DATA",
   "status": "classes",
   "package": "verifications/improved/dim73-95-gamma72-caps/",
   "detail": "no vector list is published: the count is computed from a lattice, class-size tables or a moment LP (RESULTS.md status `classes`). What would decide it: the configuration's vectors in any exact form, or a generator file this lab can run without the claimant's code."
  },
  {
   "id": "kravatsky-81",
   "claimant": "kravatsky",
   "claimantName": "A. Kravatskiy \u2014 github.com/alexlegeartis/KissingNumbers (no arXiv paper; the write-up, paper/kissing46.pdf, is in the repository and calls dimensions 25\u201331 joint work in progress with H. Cohn and B. Lindow)",
   "dim": 81,
   "claimed": 6219034270,
   "previous": 6218175906,
   "verdict": "NEEDS DATA",
   "status": "classes",
   "package": "verifications/improved/dim73-95-gamma72-caps/",
   "detail": "no vector list is published: the count is computed from a lattice, class-size tables or a moment LP (RESULTS.md status `classes`). What would decide it: the configuration's vectors in any exact form, or a generator file this lab can run without the claimant's code."
  },
  {
   "id": "kravatsky-82",
   "claimant": "kravatsky",
   "claimantName": "A. Kravatskiy \u2014 github.com/alexlegeartis/KissingNumbers (no arXiv paper; the write-up, paper/kissing46.pdf, is in the repository and calls dimensions 25\u201331 joint work in progress with H. Cohn and B. Lindow)",
   "dim": 82,
   "claimed": 6219605578,
   "previous": 6218176110,
   "verdict": "NEEDS DATA",
   "status": "classes",
   "package": "verifications/improved/dim73-95-gamma72-caps/",
   "detail": "no vector list is published: the count is computed from a lattice, class-size tables or a moment LP (RESULTS.md status `classes`). What would decide it: the configuration's vectors in any exact form, or a generator file this lab can run without the claimant's code."
  },
  {
   "id": "kravatsky-83",
   "claimant": "kravatsky",
   "claimantName": "A. Kravatskiy \u2014 github.com/alexlegeartis/KissingNumbers (no arXiv paper; the write-up, paper/kissing46.pdf, is in the repository and calls dimensions 25\u201331 joint work in progress with H. Cohn and B. Lindow)",
   "dim": 83,
   "claimed": 6219621690,
   "previous": 6218176204,
   "verdict": "NEEDS DATA",
   "status": "classes",
   "package": "verifications/improved/dim73-95-gamma72-caps/",
   "detail": "no vector list is published: the count is computed from a lattice, class-size tables or a moment LP (RESULTS.md status `classes`). What would decide it: the configuration's vectors in any exact form, or a generator file this lab can run without the claimant's code."
  },
  {
   "id": "kravatsky-84",
   "claimant": "kravatsky",
   "claimantName": "A. Kravatskiy \u2014 github.com/alexlegeartis/KissingNumbers (no arXiv paper; the write-up, paper/kissing46.pdf, is in the repository and calls dimensions 25\u201331 joint work in progress with H. Cohn and B. Lindow)",
   "dim": 84,
   "claimed": 6220293304,
   "previous": 6218176441,
   "verdict": "NEEDS DATA",
   "status": "classes",
   "package": "verifications/improved/dim73-95-gamma72-caps/",
   "detail": "no vector list is published: the count is computed from a lattice, class-size tables or a moment LP (RESULTS.md status `classes`). What would decide it: the configuration's vectors in any exact form, or a generator file this lab can run without the claimant's code."
  },
  {
   "id": "kravatsky-85",
   "claimant": "kravatsky",
   "claimantName": "A. Kravatskiy \u2014 github.com/alexlegeartis/KissingNumbers (no arXiv paper; the write-up, paper/kissing46.pdf, is in the repository and calls dimensions 25\u201331 joint work in progress with H. Cohn and B. Lindow)",
   "dim": 85,
   "claimed": 6220745414,
   "previous": 6218176754,
   "verdict": "NEEDS DATA",
   "status": "classes",
   "package": "verifications/improved/dim73-95-gamma72-caps/",
   "detail": "no vector list is published: the count is computed from a lattice, class-size tables or a moment LP (RESULTS.md status `classes`). What would decide it: the configuration's vectors in any exact form, or a generator file this lab can run without the claimant's code."
  },
  {
   "id": "kravatsky-86",
   "claimant": "kravatsky",
   "claimantName": "A. Kravatskiy \u2014 github.com/alexlegeartis/KissingNumbers (no arXiv paper; the write-up, paper/kissing46.pdf, is in the repository and calls dimensions 25\u201331 joint work in progress with H. Cohn and B. Lindow)",
   "dim": 86,
   "claimed": 6223567844,
   "previous": 6218177532,
   "verdict": "NEEDS DATA",
   "status": "classes",
   "package": "verifications/improved/dim73-95-gamma72-caps/",
   "detail": "no vector list is published: the count is computed from a lattice, class-size tables or a moment LP (RESULTS.md status `classes`). What would decide it: the configuration's vectors in any exact form, or a generator file this lab can run without the claimant's code."
  },
  {
   "id": "kravatsky-87",
   "claimant": "kravatsky",
   "claimantName": "A. Kravatskiy \u2014 github.com/alexlegeartis/KissingNumbers (no arXiv paper; the write-up, paper/kissing46.pdf, is in the repository and calls dimensions 25\u201331 joint work in progress with H. Cohn and B. Lindow)",
   "dim": 87,
   "claimed": 6224703598,
   "previous": 6218178164,
   "verdict": "NEEDS DATA",
   "status": "classes",
   "package": "verifications/improved/dim73-95-gamma72-caps/",
   "detail": "no vector list is published: the count is computed from a lattice, class-size tables or a moment LP (RESULTS.md status `classes`). What would decide it: the configuration's vectors in any exact form, or a generator file this lab can run without the claimant's code."
  },
  {
   "id": "kravatsky-88",
   "claimant": "kravatsky",
   "claimantName": "A. Kravatskiy \u2014 github.com/alexlegeartis/KissingNumbers (no arXiv paper; the write-up, paper/kissing46.pdf, is in the repository and calls dimensions 25\u201331 joint work in progress with H. Cohn and B. Lindow)",
   "dim": 88,
   "claimed": 6230206492,
   "previous": 6218179920,
   "verdict": "NEEDS DATA",
   "status": "classes",
   "package": "verifications/improved/dim73-95-gamma72-caps/",
   "detail": "no vector list is published: the count is computed from a lattice, class-size tables or a moment LP (RESULTS.md status `classes`). What would decide it: the configuration's vectors in any exact form, or a generator file this lab can run without the claimant's code."
  },
  {
   "id": "kravatsky-89",
   "claimant": "kravatsky",
   "claimantName": "A. Kravatskiy \u2014 github.com/alexlegeartis/KissingNumbers (no arXiv paper; the write-up, paper/kissing46.pdf, is in the repository and calls dimensions 25\u201331 joint work in progress with H. Cohn and B. Lindow)",
   "dim": 89,
   "claimed": 6233054848,
   "previous": 6218181330,
   "verdict": "NEEDS DATA",
   "status": "classes",
   "package": "verifications/improved/dim73-95-gamma72-caps/",
   "detail": "no vector list is published: the count is computed from a lattice, class-size tables or a moment LP (RESULTS.md status `classes`). What would decide it: the configuration's vectors in any exact form, or a generator file this lab can run without the claimant's code."
  },
  {
   "id": "kravatsky-90",
   "claimant": "kravatsky",
   "claimantName": "A. Kravatskiy \u2014 github.com/alexlegeartis/KissingNumbers (no arXiv paper; the write-up, paper/kissing46.pdf, is in the repository and calls dimensions 25\u201331 joint work in progress with H. Cohn and B. Lindow)",
   "dim": 90,
   "claimed": 6238744788,
   "previous": 6218183254,
   "verdict": "NEEDS DATA",
   "status": "classes",
   "package": "verifications/improved/dim73-95-gamma72-caps/",
   "detail": "no vector list is published: the count is computed from a lattice, class-size tables or a moment LP (RESULTS.md status `classes`). What would decide it: the configuration's vectors in any exact form, or a generator file this lab can run without the claimant's code."
  },
  {
   "id": "kravatsky-91",
   "claimant": "kravatsky",
   "claimantName": "A. Kravatskiy \u2014 github.com/alexlegeartis/KissingNumbers (no arXiv paper; the write-up, paper/kissing46.pdf, is in the repository and calls dimensions 25\u201331 joint work in progress with H. Cohn and B. Lindow)",
   "dim": 91,
   "claimed": 6247801034,
   "previous": 6218187548,
   "verdict": "NEEDS DATA",
   "status": "classes",
   "package": "verifications/improved/dim73-95-gamma72-caps/",
   "detail": "no vector list is published: the count is computed from a lattice, class-size tables or a moment LP (RESULTS.md status `classes`). What would decide it: the configuration's vectors in any exact form, or a generator file this lab can run without the claimant's code."
  },
  {
   "id": "kravatsky-92",
   "claimant": "kravatsky",
   "claimantName": "A. Kravatskiy \u2014 github.com/alexlegeartis/KissingNumbers (no arXiv paper; the write-up, paper/kissing46.pdf, is in the repository and calls dimensions 25\u201331 joint work in progress with H. Cohn and B. Lindow)",
   "dim": 92,
   "claimed": 6266405667,
   "previous": 6218195048,
   "verdict": "NEEDS DATA",
   "status": "classes",
   "package": "verifications/improved/dim73-95-gamma72-caps/",
   "detail": "no vector list is published: the count is computed from a lattice, class-size tables or a moment LP (RESULTS.md status `classes`). What would decide it: the configuration's vectors in any exact form, or a generator file this lab can run without the claimant's code."
  },
  {
   "id": "kravatsky-93",
   "claimant": "kravatsky",
   "claimantName": "A. Kravatskiy \u2014 github.com/alexlegeartis/KissingNumbers (no arXiv paper; the write-up, paper/kissing46.pdf, is in the repository and calls dimensions 25\u201331 joint work in progress with H. Cohn and B. Lindow)",
   "dim": 93,
   "claimed": 6294850360,
   "previous": 6218205368,
   "verdict": "NEEDS DATA",
   "status": "classes",
   "package": "verifications/improved/dim73-95-gamma72-caps/",
   "detail": "no vector list is published: the count is computed from a lattice, class-size tables or a moment LP (RESULTS.md status `classes`). What would decide it: the configuration's vectors in any exact form, or a generator file this lab can run without the claimant's code."
  },
  {
   "id": "kravatsky-94",
   "claimant": "kravatsky",
   "claimantName": "A. Kravatskiy \u2014 github.com/alexlegeartis/KissingNumbers (no arXiv paper; the write-up, paper/kissing46.pdf, is in the repository and calls dimensions 25\u201331 joint work in progress with H. Cohn and B. Lindow)",
   "dim": 94,
   "claimed": 6355739600,
   "previous": 6218225496,
   "verdict": "NEEDS DATA",
   "status": "classes",
   "package": "verifications/improved/dim73-95-gamma72-caps/",
   "detail": "no vector list is published: the count is computed from a lattice, class-size tables or a moment LP (RESULTS.md status `classes`). What would decide it: the configuration's vectors in any exact form, or a generator file this lab can run without the claimant's code."
  },
  {
   "id": "kravatsky-95",
   "claimant": "kravatsky",
   "claimantName": "A. Kravatskiy \u2014 github.com/alexlegeartis/KissingNumbers (no arXiv paper; the write-up, paper/kissing46.pdf, is in the repository and calls dimensions 25\u201331 joint work in progress with H. Cohn and B. Lindow)",
   "dim": 95,
   "claimed": 6473065046,
   "previous": 6218268750,
   "verdict": "NEEDS DATA",
   "status": "classes",
   "package": "verifications/improved/dim73-95-gamma72-caps/",
   "detail": "no vector list is published: the count is computed from a lattice, class-size tables or a moment LP (RESULTS.md status `classes`). What would decide it: the configuration's vectors in any exact form, or a generator file this lab can run without the claimant's code."
  },
  {
   "id": "kravatsky-96",
   "claimant": "kravatsky",
   "claimantName": "A. Kravatskiy \u2014 github.com/alexlegeartis/KissingNumbers (no arXiv paper; the write-up, paper/kissing46.pdf, is in the repository and calls dimensions 25\u201331 joint work in progress with H. Cohn and B. Lindow)",
   "dim": 96,
   "claimed": 12886999232,
   "previous": 6218372160,
   "verdict": "NEEDS DATA",
   "status": "external",
   "package": "verifications/closed/dim96-ers-takeover/",
   "detail": "no vector list is published: the count is computed from a lattice, class-size tables or a moment LP (RESULTS.md status `external`). What would decide it: the configuration's vectors in any exact form, or a generator file this lab can run without the claimant's code."
  }
 ],
 "calibrations": [
  {
   "id": "cal-e8-240",
   "claim": "K(8) = 240: the E8 roots, 6720 contacts",
   "expectContacts": 6720,
   "ok": true,
   "result": {
    "n": 240,
    "dim": 8,
    "norm": [
     8,
     0,
     0,
     0
    ],
    "normShow": "8",
    "families": [
     {
      "name": "E8 roots",
      "n": 240,
      "note": "",
      "path": "gemm",
      "freeNorm": false,
      "maxAbsCoefficient": 2
     }
    ],
    "pairs": 28680,
    "pairsExpected": 28680,
    "contacts": 6720,
    "violations": 0,
    "verdict": "CERTIFIED",
    "blocks": [
     {
      "a": "E8 roots",
      "b": "E8 roots",
      "pairs": 28680,
      "contacts": 6720,
      "violations": 0,
      "maxDot": [
       4,
       0,
       0,
       0
      ],
      "maxDotShow": "4",
      "maxCos": 0.5,
      "nearestNonContactDot": [
       0,
       0,
       0,
       0
      ],
      "nearestNonContactShow": "0",
      "nearestNonContactCos": 0.0,
      "gemm": {
       "worstPartialSum": 32,
       "precision": "float32",
       "bound": "2^24",
       "path": "rational"
      },
      "seconds": 0.03
     }
    ],
    "spotCheck": {
     "pairs": 397,
     "disagreements": 0,
     "how": "sampled pairs re-decided in plain Python integers (no numpy, no BLAS)"
    },
    "bigintFallbacks": 0,
    "seconds": 0.0,
    "maxDot": [
     4,
     0,
     0,
     0
    ],
    "maxDotShow": "4",
    "maxCos": 0.5,
    "nearestNonContactCos": 0.0
   }
  },
  {
   "id": "cal-leech-196560",
   "claim": "K(24) = 196560 (Odlyzko\u2013Sloane, Levenshtein 1979): the Leech minimal vectors",
   "expectContacts": 452088000,
   "ok": true,
   "result": {
    "n": 196560,
    "dim": 24,
    "norm": [
     32,
     0,
     0,
     0
    ],
    "normShow": "32",
    "families": [
     {
      "name": "Leech shell",
      "n": 196560,
      "note": "the 196560 minimal vectors, Cohn units",
      "path": "gemm",
      "freeNorm": false,
      "maxAbsCoefficient": 4
     }
    ],
    "pairs": 19317818520,
    "pairsExpected": 19317818520,
    "contacts": 452088000,
    "violations": 0,
    "verdict": "CERTIFIED",
    "blocks": [
     {
      "a": "Leech shell",
      "b": "Leech shell",
      "pairs": 19317818520,
      "contacts": 452088000,
      "violations": 0,
      "maxDot": [
       16,
       0,
       0,
       0
      ],
      "maxDotShow": "16",
      "maxCos": 0.5,
      "nearestNonContactDot": [
       8,
       0,
       0,
       0
      ],
      "nearestNonContactShow": "8",
      "nearestNonContactCos": 0.25,
      "gemm": {
       "worstPartialSum": 384,
       "precision": "float32",
       "bound": "2^24",
       "path": "rational"
      },
      "seconds": 21.53
     }
    ],
    "spotCheck": {
     "pairs": 400,
     "disagreements": 0,
     "how": "sampled pairs re-decided in plain Python integers (no numpy, no BLAS)"
    },
    "bigintFallbacks": 0,
    "seconds": 21.6,
    "maxDot": [
     16,
     0,
     0,
     0
    ],
    "maxDotShow": "16",
    "maxCos": 0.5,
    "nearestNonContactCos": 0.25
   }
  }
 ],
 "what": "The September 2026 wave of kissing-number lower-bound claims (dimensions 18 and 25\u201331, three claimants), every published configuration rebuilt from pinned bytes and every pair decided exactly over Q(sqrt2, sqrt3).",
 "grammar": {
  "WITNESSED": "the published bytes are already an exact proof",
  "REPAIRED": "our exact witness built from their bytes, the float-to-exact distance measured",
  "UNWITNESSED": "the bytes fail exactly and no repair was built \u2014 a finding about the bytes, never a refutation of the bound",
  "NEEDS DATA": "no vector list is published; the row states what would decide it",
  "QUEUED": "bytes exist; not decided in this wave"
 },
 "tables": {
  "kravatsky": {
   "18": {
    "claimed": 8358,
    "previous": 7654,
    "status": "exhausted",
    "package": "verifications/improved/dim18-bent-hexagon/"
   },
   "25": {
    "claimed": 197579,
    "previous": 197056,
    "status": "exhausted",
    "package": "verifications/improved/dim25-lens-heads/"
   },
   "26": {
    "claimed": 199806,
    "previous": 198550,
    "status": "exhausted",
    "package": "verifications/improved/dim26-27-iota-triangles/"
   },
   "27": {
    "claimed": 201566,
    "previous": 200044,
    "status": "exhausted",
    "package": "verifications/improved/dim26-27-iota-triangles/"
   },
   "28": {
    "claimed": 204896,
    "previous": 204520,
    "status": "classes",
    "package": "verifications/improved/dim28-norm8-frame-layer/"
   },
   "29": {
    "claimed": 209968,
    "previous": 209496,
    "status": "classes",
    "package": "verifications/improved/dim29-30-frame-layer/"
   },
   "30": {
    "claimed": 221012,
    "previous": 220440,
    "status": "classes",
    "package": "verifications/improved/dim29-30-frame-layer/"
   },
   "31": {
    "claimed": 238662,
    "previous": 238350,
    "status": "classes",
    "package": "verifications/improved/dim31-frame-layer/"
   },
   "38": {
    "claimed": 591612,
    "previous": 566652,
    "status": "exhausted",
    "package": "verifications/improved/dim38-leech-large-codimension/"
   },
   "39": {
    "claimed": 756116,
    "previous": 755988,
    "status": "external",
    "package": "verifications/improved/dim39-ers-constant-weight/"
   },
   "49": {
    "claimed": 52430140,
    "previous": 52416002,
    "status": "classes",
    "package": "verifications/improved/dim49-63-p48-caps/"
   },
   "50": {
    "claimed": 52458418,
    "previous": 52416006,
    "status": "classes",
    "package": "verifications/improved/dim49-63-p48-caps/"
   },
   "51": {
    "claimed": 52500816,
    "previous": 52416012,
    "status": "classes",
    "package": "verifications/improved/dim49-63-p48-caps/"
   },
   "52": {
    "claimed": 52585516,
    "previous": 52416024,
    "status": "classes",
    "package": "verifications/improved/dim49-63-p48-caps/"
   },
   "53": {
    "claimed": 52698222,
    "previous": 52416040,
    "status": "classes",
    "package": "verifications/improved/dim49-63-p48-caps/"
   },
   "54": {
    "claimed": 52922906,
    "previous": 52416072,
    "status": "classes",
    "package": "verifications/improved/dim49-63-p48-caps/"
   },
   "55": {
    "claimed": 53299730,
    "previous": 52416126,
    "status": "classes",
    "package": "verifications/improved/dim49-63-p48-caps/"
   },
   "56": {
    "claimed": 54085392,
    "previous": 52416240,
    "status": "classes",
    "package": "verifications/improved/dim49-63-p48-caps/"
   },
   "57": {
    "claimed": 54534176,
    "previous": 52416306,
    "status": "classes",
    "package": "verifications/improved/dim49-63-p48-caps/"
   },
   "58": {
    "claimed": 55893422,
    "previous": 52416510,
    "status": "classes",
    "package": "verifications/improved/dim49-63-p48-caps/"
   },
   "59": {
    "claimed": 56505668,
    "previous": 52416604,
    "status": "classes",
    "package": "verifications/improved/dim49-63-p48-caps/"
   },
   "60": {
    "claimed": 57477123,
    "previous": 52416841,
    "status": "classes",
    "package": "verifications/improved/dim49-63-p48-caps/"
   },
   "61": {
    "claimed": 59898694,
    "previous": 52417154,
    "status": "classes",
    "package": "verifications/improved/dim49-63-p48-caps/"
   },
   "62": {
    "claimed": 71310732,
    "previous": 52417932,
    "status": "external",
    "package": "verifications/improved/dim62-63-ers-chain/"
   },
   "63": {
    "claimed": 138419844,
    "previous": 52418564,
    "status": "external",
    "package": "verifications/improved/dim62-63-ers-chain/"
   },
   "68": {
    "claimed": 361275480,
    "previous": 331737984,
    "status": "lp-exact",
    "package": "verifications/improved/dim68-69-gamma72-cross-sections/"
   },
   "69": {
    "claimed": 627822180,
    "previous": 331737984,
    "status": "lp-exact",
    "package": "verifications/improved/dim68-69-gamma72-cross-sections/"
   },
   "70": {
    "claimed": 1249778250,
    "previous": 331737984,
    "status": "lp-exact",
    "package": "verifications/improved/dim70-71-gamma72-cross-sections/"
   },
   "71": {
    "claimed": 2603658750,
    "previous": 331737984,
    "status": "lp-exact",
    "package": "verifications/improved/dim70-71-gamma72-cross-sections/"
   },
   "73": {
    "claimed": 6218179814,
    "previous": 6218175602,
    "status": "classes",
    "package": "verifications/improved/dim73-95-gamma72-caps/"
   },
   "74": {
    "claimed": 6218192454,
    "previous": 6218175606,
    "status": "classes",
    "package": "verifications/improved/dim73-95-gamma72-caps/"
   },
   "75": {
    "claimed": 6218209308,
    "previous": 6218175612,
    "status": "classes",
    "package": "verifications/improved/dim73-95-gamma72-caps/"
   },
   "76": {
    "claimed": 6218243016,
    "previous": 6218175624,
    "status": "classes",
    "package": "verifications/improved/dim73-95-gamma72-caps/"
   },
   "77": {
    "claimed": 6218285152,
    "previous": 6218175640,
    "status": "classes",
    "package": "verifications/improved/dim73-95-gamma72-caps/"
   },
   "78": {
    "claimed": 6218377840,
    "previous": 6218175672,
    "status": "classes",
    "package": "verifications/improved/dim73-95-gamma72-caps/"
   },
   "79": {
    "claimed": 6218529454,
    "previous": 6218175726,
    "status": "classes",
    "package": "verifications/improved/dim73-95-gamma72-caps/"
   },
   "80": {
    "claimed": 6218849228,
    "previous": 6218175840,
    "status": "classes",
    "package": "verifications/improved/dim73-95-gamma72-caps/"
   },
   "81": {
    "claimed": 6219034270,
    "previous": 6218175906,
    "status": "classes",
    "package": "verifications/improved/dim73-95-gamma72-caps/"
   },
   "82": {
    "claimed": 6219605578,
    "previous": 6218176110,
    "status": "classes",
    "package": "verifications/improved/dim73-95-gamma72-caps/"
   },
   "83": {
    "claimed": 6219621690,
    "previous": 6218176204,
    "status": "classes",
    "package": "verifications/improved/dim73-95-gamma72-caps/"
   },
   "84": {
    "claimed": 6220293304,
    "previous": 6218176441,
    "status": "classes",
    "package": "verifications/improved/dim73-95-gamma72-caps/"
   },
   "85": {
    "claimed": 6220745414,
    "previous": 6218176754,
    "status": "classes",
    "package": "verifications/improved/dim73-95-gamma72-caps/"
   },
   "86": {
    "claimed": 6223567844,
    "previous": 6218177532,
    "status": "classes",
    "package": "verifications/improved/dim73-95-gamma72-caps/"
   },
   "87": {
    "claimed": 6224703598,
    "previous": 6218178164,
    "status": "classes",
    "package": "verifications/improved/dim73-95-gamma72-caps/"
   },
   "88": {
    "claimed": 6230206492,
    "previous": 6218179920,
    "status": "classes",
    "package": "verifications/improved/dim73-95-gamma72-caps/"
   },
   "89": {
    "claimed": 6233054848,
    "previous": 6218181330,
    "status": "classes",
    "package": "verifications/improved/dim73-95-gamma72-caps/"
   },
   "90": {
    "claimed": 6238744788,
    "previous": 6218183254,
    "status": "classes",
    "package": "verifications/improved/dim73-95-gamma72-caps/"
   },
   "91": {
    "claimed": 6247801034,
    "previous": 6218187548,
    "status": "classes",
    "package": "verifications/improved/dim73-95-gamma72-caps/"
   },
   "92": {
    "claimed": 6266405667,
    "previous": 6218195048,
    "status": "classes",
    "package": "verifications/improved/dim73-95-gamma72-caps/"
   },
   "93": {
    "claimed": 6294850360,
    "previous": 6218205368,
    "status": "classes",
    "package": "verifications/improved/dim73-95-gamma72-caps/"
   },
   "94": {
    "claimed": 6355739600,
    "previous": 6218225496,
    "status": "classes",
    "package": "verifications/improved/dim73-95-gamma72-caps/"
   },
   "95": {
    "claimed": 6473065046,
    "previous": 6218268750,
    "status": "classes",
    "package": "verifications/improved/dim73-95-gamma72-caps/"
   },
   "96": {
    "claimed": 12886999232,
    "previous": 6218372160,
    "status": "external",
    "package": "verifications/closed/dim96-ers-takeover/"
   }
  },
  "takhanov-yun": {
   "25": {
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 "pins": {
  "manifest": "corpus/kissing/wave.meta.json",
  "manifestSha256": "46944fd54423669b8240c2e3fafe7c1b1fd45a4b9eeba285e7e3a1fed80fd4c7"
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  "python": "3.9.6",
  "numpy": "2.0.2",
  "cpus": 8,
  "blas": "Accelerate (numpy build config)"
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 "generated": "2026-10-05T06:46:59Z",
 "git": "f7c6c9a",
 "reds": [
  {
   "red": "d18: one sign of one tier-B word flipped",
   "caught": true,
   "violations": 34
  },
  {
   "red": "d18: a tier-B point rotated by 30 degrees, from 30 to 0",
   "caught": true,
   "violations": 8
  },
  {
   "red": "d18: one equator vector listed twice",
   "caught": true,
   "violations": 1
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  {
   "red": "d18: one coordinate moved by 1/6, off the sphere",
   "caught": true
  },
  {
   "red": "a forced tie 2 - 1*sqrt4 raises instead of returning a sign",
   "caught": true
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 ],
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