{
  "schema": "bounded-simultaneous-folded-form-check/v1",
  "checks": [
    {
      "name": "full homogeneous involution models in three dimensions",
      "passed": true,
      "bounded_evidence": "n=2,3,4: exact one-/two-form pullbacks, squared maps, ambient/restricted ranks, simple determinant factor and three independent reflection/radial directions."
    },
    {
      "name": "smooth fields versus singular Hamiltonians and exact half-to-full degree change",
      "passed": true,
      "bounded_evidence": "A nontrivial admissible Hamiltonian and singular position Hamiltonian are explicitly compared; Y,Z commutation/weights and full primitive change are exact."
    },
    {
      "name": "full nonlinear and negative-sign ordinary scalar normalization",
      "passed": true,
      "bounded_evidence": "Full rational pullback for B=t(1+bt^2), parity/Jacobian, and independent exact conjugacy for G=-8t, B=-t/2, A=4."
    },
    {
      "name": "full nonlinear homogeneous normalization",
      "passed": true,
      "bounded_evidence": "Polynomial odd R with simple zero gives rational smooth S,T. All mixed terms of the full one-/two-form pullbacks, coordinate weights, parity and marked Jacobian are checked."
    },
    {
      "name": "actual nonlinear integral inverse and both conjugacy equations",
      "passed": true,
      "bounded_evidence": {
        "example": "V=2b+4b^3, W=-2b^3/3-12b^5/5",
        "exact_constraint_elimination": true,
        "independently_differentiated_inverse_samples": [
          {
            "t": "-0.3",
            "first_shift_residual": "8.04306e-87",
            "last_shift_residual": "5.02691e-88"
          },
          {
            "t": "-0.1",
            "first_shift_residual": "2.01076e-87",
            "last_shift_residual": "1.57091e-89"
          },
          {
            "t": "0.1",
            "first_shift_residual": "2.01076e-87",
            "last_shift_residual": "1.57091e-89"
          },
          {
            "t": "0.3",
            "first_shift_residual": "8.04306e-87",
            "last_shift_residual": "5.02691e-88"
          }
        ],
        "guard": "Finite full-map examples; arbitrary smooth inverse is proved by the inverse function theorem in the lesson."
      }
    },
    {
      "name": "two genuine hypothesis/correction failures",
      "passed": true,
      "bounded_evidence": "A degree-one folded form with distinct homogeneous preserving reflections has radial vector in their span and zero restricted primitive. Omitting the cubic last-position shift has a nonzero full two-form defect."
    }
  ],
  "passed": true,
  "lesson": "two-reflections-in-folded-symplectic-coordinates.md",
  "lesson_sha256": "1c619a26fe49895aabc17e3d14ce9ed74748364bd4111159adf71eab572c0e9d",
  "script_sha256": "0dfe29c62e5e5c3702e2b46bd0031894e8ea79a10554fb62c2dd9ee8b51202ae",
  "guard": "Exact bounded examples and numerical residuals do not independently verify the arbitrary-form spectator-flow and normal-form proofs."
}