{
  "schema": "bounded-folded-form-computational-check/v1",
  "passed": true,
  "checks": [
    {
      "name": "ambient/restricted radicals and simple-zero counterexample",
      "passed": true,
      "bounded_evidence": "Exact four-dimensional ranks and top Pfaffians; a closed form with a simple top zero but zero restricted rank fails the stated theorem hypothesis."
    },
    {
      "name": "first-jet mixed-pair normalization",
      "passed": true,
      "bounded_evidence": "Full nonlinear closed example; every coefficient of the model pullback error vanishes to second normal order; collar Jacobian and exact reflection pullback checked."
    },
    {
      "name": "relative primitive and actual Moser flow",
      "passed": true,
      "bounded_evidence": {
        "exact_relative_primitive": true,
        "smooth_field_and_contraction": true,
        "implicit_flow_samples": [
          {
            "s": "-0.2",
            "time": "0.0",
            "pullback_residual": "0.0"
          },
          {
            "s": "-0.2",
            "time": "0.5",
            "pullback_residual": "3.0682e-92"
          },
          {
            "s": "-0.2",
            "time": "1.0",
            "pullback_residual": "0.0"
          },
          {
            "s": "-0.05",
            "time": "0.0",
            "pullback_residual": "0.0"
          },
          {
            "s": "-0.05",
            "time": "0.5",
            "pullback_residual": "7.6705e-93"
          },
          {
            "s": "-0.05",
            "time": "1.0",
            "pullback_residual": "7.6705e-93"
          },
          {
            "s": "0.05",
            "time": "0.0",
            "pullback_residual": "0.0"
          },
          {
            "s": "0.05",
            "time": "0.5",
            "pullback_residual": "0.0"
          },
          {
            "s": "0.05",
            "time": "1.0",
            "pullback_residual": "7.6705e-93"
          },
          {
            "s": "0.2",
            "time": "0.0",
            "pullback_residual": "0.0"
          },
          {
            "s": "0.2",
            "time": "0.5",
            "pullback_residual": "3.0682e-92"
          },
          {
            "s": "0.2",
            "time": "1.0",
            "pullback_residual": "0.0"
          }
        ],
        "guard": "Implicit nonlinear flows at specified initial values/times, independently differentiated; the arbitrary-form Moser theorem is proved analytically."
      }
    },
    {
      "name": "reflection-preserving exact remainder normalization",
      "passed": true,
      "bounded_evidence": "Full odd normal coordinate and its form pullback, plus exact equivariance of the nontrivial Moser field."
    },
    {
      "name": "full homogeneous normalizing map and radial exclusion",
      "passed": true,
      "bounded_evidence": "Exact one-form and two-form pullbacks including mixed frequency terms; all Euler degrees; a nonzero radial field with vanishing restricted canonical one-form supplies the excluded case."
    },
    {
      "name": "full target extension, coefficient-closure defect and signed areas",
      "passed": true,
      "bounded_evidence": "Exact bad negative-side coordinate pullback and actual Hamiltonian target collar; nonclosed coefficient extension; both source patch integrals and target integral with their stated orientations."
    }
  ],
  "lesson_sha256": "f516adc6b91dae6f87f35cfec39d71653b4da33c38571abcd1fe5e9ca4a3d2b8",
  "script_sha256": "089ca1bf75a0f0481854450d808e8af32dc87049d60193056804ba527420b7e7",
  "finite_examples_only": true,
  "full_mathematical_review": false
}