{
  "schema": "bounded-maslov-topology-check/v1",
  "passed": true,
  "lesson_sha256": "7b11a19102cd0bb2eb8d5ca24dd4f50a48fb02bf1eff214c0a88199b2b0ca772",
  "script_sha256": "a5f3ad8efda75ed4fa4dfa2d2f8b8523f9a760e2ed91e45b6c95fbc636176a34",
  "checks": [
    {
      "name": "both fully oriented one-dimensional generators",
      "passed": true,
      "positive_crossing_form": "pi",
      "positive_determinant_square_winding": 1,
      "scope": "Exact vectors, full symplectic derivative and determinant square; not arbitrary-loop classification."
    },
    {
      "name": "actual ordered Gaussian coordinate and reciprocal switches",
      "passed": true,
      "B_values": [
        2,
        -2
      ],
      "half_signatures": [
        -1,
        0
      ],
      "positive_coefficient_product": "-i",
      "positive_reciprocal_frame_and_dual_product": "i",
      "scope": "Both switch directions, including zero-signature remaining blocks in five dimensions."
    },
    {
      "name": "full nonconstant Schur and section-derivative calculation",
      "passed": true,
      "three_dimensional_marked_kernel": [
        "1",
        "-1/2",
        "2/3"
      ],
      "crossing_form": 1,
      "normal_block_determinant": -6,
      "full_determinant_derivative": -6,
      "scope": "Nonzero marked off-diagonal block, varying indefinite normal block, all inverse derivatives and extension-vector cancellations; also both public 2x2 examples."
    },
    {
      "name": "regular indefinite crossing and exact simple split",
      "passed": true,
      "original_crossing_form": [
        2,
        -3
      ],
      "ordered_signs": [
        -1,
        1
      ],
      "total": 0,
      "scope": "Exact local matrices and both determinant derivatives; supported arbitrary-path homotopy remains a written argument."
    },
    {
      "name": "five actual unitary/real plane frames and SU2 column formula",
      "passed": true,
      "dimensions": [
        1,
        2,
        3,
        4,
        5
      ],
      "scope": "Unitary matrices, isotropic real spans, identical projection matrices after reflection, determinant sign/square and explicit SU2 formula; no simple-connectedness inference from samples."
    },
    {
      "name": "exact noncommuting determinant ratio and phase derivative",
      "passed": true,
      "commutator_entry": "2*t*(t-1)",
      "scope": "Entire rational two-variable matrix path, not just diagonal or marked-point substitution."
    },
    {
      "name": "positive-square-root Sylvester derivatives in six dimensions",
      "passed": true,
      "scope": "Explicit inverse on all entries of six positive diagonal models. General smooth square-root dependence is the implicit-theorem proof in the lesson."
    },
    {
      "name": "five exact crossing inventories and independent branch/winding samples",
      "passed": true,
      "loops": [
        {
          "coordinate_windings": [
            1
          ],
          "exact_times": [
            "9/22"
          ],
          "index": 1,
          "independent_numerical_winding": 1.0,
          "coefficient_product": "-I"
        },
        {
          "coordinate_windings": [
            -1
          ],
          "exact_times": [
            "13/22"
          ],
          "index": -1,
          "independent_numerical_winding": -0.9999999999999999,
          "coefficient_product": "I"
        },
        {
          "coordinate_windings": [
            4
          ],
          "exact_times": [
            "9/88",
            "31/88",
            "53/88",
            "75/88"
          ],
          "index": 4,
          "independent_numerical_winding": 4.0,
          "coefficient_product": "1"
        },
        {
          "coordinate_windings": [
            2,
            -1,
            3
          ],
          "exact_times": [
            "11/102",
            "9/44",
            "15/34",
            "17/26",
            "31/44",
            "79/102"
          ],
          "index": 4,
          "independent_numerical_winding": 4.0,
          "coefficient_product": "1"
        },
        {
          "coordinate_windings": [
            -2,
            1,
            -3
          ],
          "exact_times": [
            "23/102",
            "13/44",
            "9/26",
            "19/34",
            "35/44",
            "91/102"
          ],
          "index": -4,
          "independent_numerical_winding": -4.0,
          "coefficient_product": "1"
        }
      ],
      "branch_samples_per_side": 1601,
      "scope": "Exact rational simple-crossing times; independent 4001-point determinant unwrapping and both transverse branch formulas. These finite samples do not prove the winding/crossing theorem."
    },
    {
      "name": "complete ordinary tangent Gauss-map example",
      "passed": true,
      "unit_tangent_crossing_form": "2*pi",
      "determinant_square_winding": 2,
      "coefficient_product": -1,
      "scope": "Exact embedded-circle derivative, full tangent vector and determinant derivative; the circle is ordinary and not conic."
    },
    {
      "name": "eight bounded stratum dimension inventories and solution completeness",
      "passed": true,
      "dimensions": [
        {
          "n": 1,
          "target_dimension": 1
        },
        {
          "n": 2,
          "target_dimension": 3
        },
        {
          "n": 3,
          "target_dimension": 6
        },
        {
          "n": 4,
          "target_dimension": 10
        },
        {
          "n": 5,
          "target_dimension": 15
        },
        {
          "n": 6,
          "target_dimension": 21
        },
        {
          "n": 7,
          "target_dimension": 28
        },
        {
          "n": 8,
          "target_dimension": 36
        }
      ],
      "exercise_solutions": 14,
      "scope": "Arithmetic of the imported stratum codimension and exercise-marker/control-byte checks; the actual strata and critical-value proofs are written mathematics."
    },
    {
      "name": "nonunitary common-complement shear with a horizontal spectator",
      "passed": true,
      "original_frequency_projection_singular_for_entire_loop": true,
      "transformed_frequency_determinant_at_crossing": 2,
      "sampled_windings": [
        {
          "shear_parameter": 0,
          "winding": 1.0
        },
        {
          "shear_parameter": 0.25,
          "winding": 1.0
        },
        {
          "shear_parameter": 0.5,
          "winding": 1.0000000000000002
        },
        {
          "shear_parameter": 0.75,
          "winding": 1.0
        },
        {
          "shear_parameter": 1,
          "winding": 1.0
        }
      ],
      "scope": "Exact shear symplecticity and complete crossing-form identity; five finite winding controls. The fixed-frame determinant changes pointwise, so it cannot be treated as symplectically invariant. Its winding is invariant by the written homotopy proof."
    }
  ],
  "whole_course_complete": false,
  "generality_guard": "Exact bounded examples and finite numerical samples do not establish arbitrary-loop topology, smoothing, lifting or generic perturbation. Those require the written proofs and independent review."
}