{
  "schema": "invariant-fold-finite-check/v1",
  "passed": true,
  "lesson": "invariant-fold-continuity-and-sobolev-transfer.md",
  "lesson_sha256": "60349497c9ad814eeea0b2446fba915d15f5c119a28b277c35d17695fcdc2822",
  "script_sha256": "834fb9c2efe97833ed516068ad7abe359d3474af9ab6264cbb9f42470e17928c",
  "checks": [
    {
      "name": "full nonlinear cotangent lift and actual folds",
      "passed": true,
      "common_one_form": "Matrix([[rho*(r**2 + 2*u1), rho, 0, 0]])",
      "both_projection_determinants": "2*r*rho",
      "fold_kernels": [
        "d/dr",
        "d/du1-2*u1*d/du2-d/dr"
      ],
      "ranks_at_fold": [
        3,
        3,
        2
      ],
      "scope": "Symbolic full two-dimensional relation, three exact fold samples, and off-fold rank."
    },
    {
      "name": "joint normalization and excluded-axis limit",
      "passed": true,
      "limit_covectors": [
        0,
        1
      ],
      "ratio": "2*x",
      "scope": "Exact example, not an operator counterexample."
    },
    {
      "name": "all reducer orders and exact fractional examples",
      "passed": true,
      "examples": [
        {
          "s": "-3/4",
          "m": "1/3",
          "t": "-5/4",
          "conjugated": "-1/6"
        },
        {
          "s": "0",
          "m": "-1/6",
          "t": "0",
          "conjugated": "-1/6"
        },
        {
          "s": "7/5",
          "m": "8/3",
          "t": "-43/30",
          "conjugated": "-1/6"
        },
        {
          "s": "-5/2",
          "m": "-7/4",
          "t": "-11/12",
          "conjugated": "-1/6"
        }
      ]
    },
    {
      "name": "independent all-real weighted Fourier norm calculation",
      "passed": true,
      "models": [
        {
          "order": -0.75,
          "quadrature_norm_squared": 5.659712452012684,
          "Fourier_weight_norm_squared": 5.659712452012684,
          "relative_error": 0.0
        },
        {
          "order": -1.25,
          "quadrature_norm_squared": 2.4538069436683934,
          "Fourier_weight_norm_squared": 2.453806943668394,
          "relative_error": 1.8097968586972774e-16
        },
        {
          "order": 1.4,
          "quadrature_norm_squared": 11062.530692657288,
          "Fourier_weight_norm_squared": 11062.530692657288,
          "relative_error": 0.0
        },
        {
          "order": 0.0,
          "quadrature_norm_squared": 45.865205043440525,
          "Fourier_weight_norm_squared": 45.865205043440525,
          "relative_error": 0.0
        }
      ],
      "scope": "Finite periodic reducer identity only; no FIO norm certification."
    },
    {
      "name": "both exact recoveries with noncommuting factors",
      "passed": true,
      "scope": "Arbitrary matrices expose the required composition sides and retain every residual."
    },
    {
      "name": "common radial contraction and individual radial exclusions",
      "passed": true,
      "signs": [
        "plus common primitive",
        "minus common primitive"
      ],
      "sharpness": "corank=2 implies m<=-1/6 under universal boundedness",
      "scope": "Exact transformed relation; general Lagrangian orthogonal argument remains in the proof."
    }
  ],
  "independent_mathematical_review": false,
  "scope": "Six bounded symbolic, matrix and independent quadrature checks. General support, microlocal inversion, composition, all-real continuity and universal sharpness are proved in the lesson, not certified by samples."
}