{
  "origin": "coordinator_exact_symbolic_check_not_formal_certificate",
  "source_sha256": "6776902687fa24498e9bc0084edb02b1630009b90b7b06a7e2fba0e6d697397c",
  "checker_sha256": "603f5196bc577fbb29d0f8f110687281acff9944b137970992b96a02a84bf316",
  "sympy_version": "1.14.0",
  "SO5_isotropic_two_plane": {
    "dimension": 3,
    "nonzero_bracket": "[u1,u2]=-z",
    "central_dimension": 1,
    "is_abelian": false,
    "levi_minus_I_verified": true
  },
  "SO8_maximal_isotropic_four_plane": {
    "dimension": 6,
    "is_abelian": true,
    "module": "exterior square of standard SL4",
    "distinct_weights": 6,
    "root_action_connected": true
  },
  "line_parabolic_formula_checks": {
    "dimensions_checked": [
      2,
      3,
      4,
      6
    ],
    "is_abelian": true
  },
  "limitations": [
    "Does not certify algebraic-group rank and Levi theorems.",
    "Does not verify the lifting, descent, dynamics, or main arithmeticity theorem.",
    "The accompanying mathematical argument, not finite dimension sampling, supplies the general classification."
  ]
}