{
  "schema": "submanifold-finite-check/v1",
  "passed": true,
  "lesson": "homogeneous-submanifold-normal-forms.md",
  "lesson_sha256": "3a182f28488d8023ad6ddf5129fd46fd43de65c58f70a37a47c140e2192ac4a6",
  "script_sha256": "a4d8f92adbd1b2347e2c86dd99364b4a31729ba4a77eb56a8361c292562e5a8e",
  "checks": [
    {
      "name": "three-block and quotient dimensions after symplectic changes",
      "models": [
        {
          "N": 5,
          "radical_k": 2,
          "restricted_half_rank": 2,
          "orthogonal_rank": 2,
          "quotient_rank": 6,
          "coisotropic": false
        },
        {
          "N": 3,
          "radical_k": 1,
          "restricted_half_rank": 1,
          "orthogonal_rank": 2,
          "quotient_rank": 4,
          "coisotropic": false
        },
        {
          "N": 3,
          "radical_k": 2,
          "restricted_half_rank": 1,
          "orthogonal_rank": 0,
          "quotient_rank": 2,
          "coisotropic": true
        },
        {
          "N": 2,
          "radical_k": 0,
          "restricted_half_rank": 1,
          "orthogonal_rank": 2,
          "quotient_rank": 4,
          "coisotropic": false
        },
        {
          "N": 2,
          "radical_k": 2,
          "restricted_half_rank": 0,
          "orthogonal_rank": 0,
          "quotient_rank": 0,
          "coisotropic": true
        },
        {
          "N": 2,
          "radical_k": 0,
          "restricted_half_rank": 2,
          "orthogonal_rank": 0,
          "quotient_rank": 4,
          "coisotropic": true
        }
      ],
      "passed": true
    },
    {
      "name": "actual canonical-pair flow map, signs and dilation",
      "flow_map": "(Q1,q,P1,p) -> (Q1-q^2/2,q,P1,p+q P1)",
      "full_symplectic_pullback": true,
      "canonical_one_form_preserved": true,
      "f_is_exactly_p": true,
      "parameter_derivatives": "d/dq=H_f, d/dp=-H_q",
      "coordinate_brackets_checked": 16,
      "passed": true
    },
    {
      "name": "both induction reductions in the mixed submanifold",
      "constraint_rank": 3,
      "defining_bracket_rank": 2,
      "restricted_rank": 2,
      "radical_dimension": 1,
      "passed": true
    },
    {
      "name": "noncommuting characteristic defining fields",
      "bracket": "2 q2 p3",
      "commutator_on_V": "2 q2 d/dq3",
      "bracket_vanishes_on_V": true,
      "passed": true
    },
    {
      "name": "one characteristic foliation with both radial behaviors",
      "restricted_rank": 2,
      "characteristic_tangent": "d/dxi2",
      "one_form": "xi1 dx1",
      "radial_tangent_if_and_only_if": "xi1=0",
      "defining_Hamilton_field_on_V": "-xi2 d/dxi2",
      "passed": true
    },
    {
      "name": "translated quotient graph gives the exact tensor norm",
      "actual_matrix_norm": 8.649421946003098,
      "predicted_norm": 8.649421946003097,
      "equality_test_norm": 8.649421946003098,
      "critical_FIO_order": "-1/2",
      "passed": true
    }
  ],
  "scope": "Six bounded exact linear/coordinate models and an independently assembled finite translation/averaging operator. They test dimensions, signs, example geometry and norms; they do not certify the general submanifold theorem or FIO sharpness proof.",
  "independent_mathematical_review": false
}