{
  "status": "PASS",
  "checks": [
    "rotation covariance",
    "direct mean-shift discrepancy",
    "zero-strength control",
    "Gram characteristic polynomial",
    "collinear and orthogonal endpoints",
    "nonlinear intervention counterexample"
  ],
  "figures": [
    {
      "id": "rotation-intervention",
      "title": "Intervention labels distinguish observationally equivalent rotations",
      "kind": "analytical_curve",
      "x_label": "Rotation angle (degrees)",
      "y_label": "Squared mismatch (dimensionless)",
      "x": {
        "name": "Rotation angle (degrees)",
        "values": [
          0,
          15,
          30,
          45,
          60,
          75,
          90,
          105,
          120,
          135,
          150,
          165,
          180
        ]
      },
      "series": [
        {
          "name": "Observational covariance discrepancy",
          "values": [
            0.0,
            0.0,
            0.0,
            2.220446049250313e-16,
            0.0,
            0.0,
            0.0,
            2.220446049250313e-16,
            1.1102230246251565e-16,
            0.0,
            0.0,
            0.0,
            0.0
          ]
        },
        {
          "name": "Fixed labeled unit mean-shift discrepancy",
          "values": [
            0.0,
            0.0681483474218634,
            0.26794919243112264,
            0.5857864376269051,
            0.9999999999999998,
            1.4823619097949585,
            1.9999999999999998,
            2.5176380902050415,
            2.9999999999999996,
            3.414213562373095,
            3.732050807568878,
            3.9318516525781364,
            4.0
          ]
        }
      ],
      "caption": "Constructed isotropic two-dimensional Gaussian; all rotations preserve observational covariance. A labeled shift delta=1 along the fixed first coordinate yields2(1-cos theta). No learned causal model."
    },
    {
      "id": "intervention-diversity",
      "title": "Nearly collinear interventions leave a weak direction",
      "kind": "analytical_curve",
      "x_label": "Angle between unit intervention directions (degrees)",
      "y_label": "Smallest Gram eigenvalue",
      "x": {
        "name": "Angle between unit intervention directions (degrees)",
        "values": [
          0,
          5,
          10,
          20,
          30,
          45,
          60,
          75,
          90
        ]
      },
      "series": [
        {
          "name": "Directional information proxy",
          "values": [
            0.0,
            0.003805301908254455,
            0.01519224698779198,
            0.06030737921409157,
            0.1339745962155614,
            0.29289321881345254,
            0.4999999999999999,
            0.7411809548974795,
            1.0
          ]
        }
      ],
      "caption": "Constructed sum uu^T+vv^T of two unit-direction outer products. Smallest eigenvalue1-|cos phi| is a linear conditioning diagnostic, not a universal identifiability or sample-complexity result."
    }
  ],
  "script_sha256": "ab90b38de2793c1bca51053769b951592ff0f4fc9b44a159fd34eaeea245b93d"
}