{
  "schema": "bounded-two-reflections-computational-check/v1",
  "passed": true,
  "checks": [
    {
      "name": "ordered products, reflection lines and radial independence",
      "passed": true,
      "bounded_evidence": "Exact involution matrices, both product signs, and determinant rho/2 for the independent radial frame."
    },
    {
      "name": "exact logarithmic first normalization",
      "passed": true,
      "bounded_evidence": "Full coordinate conjugacy and nonzero Jacobian; involution normal component checked exactly, tangential log identity verified on s>-1 in the proof."
    },
    {
      "name": "nonlinear spectator conjugacy",
      "passed": true,
      "bounded_evidence": "Exact rational involution with changing spectator; full conjugacy and parity, not only its derivative at the fixed hypersurface."
    },
    {
      "name": "weighted normal coefficient corrections",
      "passed": true,
      "bounded_evidence": "Even k=2 forced coefficients and odd k=3 full conjugation jets, including the normal coefficient one order later and both homological-equation signs."
    },
    {
      "name": "flat difference series and step-size derivatives",
      "passed": true,
      "bounded_evidence": {
        "telescoping_samples": [
          {
            "t": "-0.35",
            "s": "0.08",
            "relative_residual": "1.19563e-101"
          },
          {
            "t": "0.1",
            "s": "0.08",
            "relative_residual": "5.739e-101"
          },
          {
            "t": "-0.35",
            "s": "0.125",
            "relative_residual": "4.49758e-102"
          },
          {
            "t": "0.1",
            "s": "0.125",
            "relative_residual": "4.49758e-102"
          },
          {
            "t": "-0.35",
            "s": "0.2",
            "relative_residual": "1.49704e-101"
          },
          {
            "t": "0.1",
            "s": "0.2",
            "relative_residual": "1.12278e-101"
          },
          {
            "t": "-0.35",
            "s": "-0.125",
            "relative_residual": "4.49758e-102"
          },
          {
            "t": "0.1",
            "s": "-0.125",
            "relative_residual": "1.34927e-101"
          }
        ],
        "normal_derivative_orders": [
          0,
          1,
          2,
          3
        ],
        "guard": "Finite smooth-bump sums at specified nonzero steps; infinite smoothness and flatness are proved analytically."
      }
    },
    {
      "name": "flat perturbations of both shear components",
      "passed": true,
      "bounded_evidence": {
        "orbits": [
          {
            "s": "0.16",
            "iterates": 25,
            "t_error": "5.7052443e-18",
            "s_error": "2.6053328e-19"
          },
          {
            "s": "0.2",
            "iterates": 20,
            "t_error": "4.7616763e-12",
            "s_error": "2.7130826e-13"
          },
          {
            "s": "0.24",
            "iterates": 17,
            "t_error": "7.1421859e-9",
            "s_error": "4.7641844e-10"
          },
          {
            "s": "-0.2",
            "iterates": 20,
            "t_error": "4.7616763e-12",
            "s_error": "2.7130826e-13"
          }
        ],
        "guard": "Full nonlinear sampled iterates verify the normal-first recurrence and quadratic tangential accumulation; they do not certify an arbitrary smooth germ."
      }
    }
  ],
  "lesson_sha256": "f2f8251c913b455633a6f88882b5964257f66b1fc97e55ae42c14a1fbfc35aaa",
  "script_sha256": "de857d3b2825b0b3c9d39680e25bab8ceb8d5cae271856b29505ea22abc3f3ca",
  "finite_examples_only": true,
  "full_mathematical_review": false,
  "infinite_argument": "Parameter Borel convergence and all flat-iterate derivatives are proved in the lesson, not inferred from these finite checks."
}