{
  "status": "PASS",
  "checks": [
    "Same predictor",
    "Hessian determinant and trace",
    "Pointwise transformed losses",
    "Untransformed circle negative control"
  ],
  "max_transformed_discrepancy": 6.591949208711867e-17,
  "continuous_maximum_certified": false,
  "empirical_benchmark": false,
  "source_proofs_verified": false,
  "figures": [
    {
      "id": "curvature-orbit",
      "kind": "analytical_curve",
      "caption": "Exact author-constructed nonzero Hessian eigenvalue c²+c⁻² at identical predictors f(x)=x. No measured generalization or deep-network benchmark.",
      "x": {
        "name": "Positive rescaling c",
        "values": [
          0.1,
          0.2,
          0.5,
          1.0,
          2.0,
          5.0,
          10.0
        ]
      },
      "series": [
        {
          "name": "Nonzero Hessian eigenvalue",
          "values": [
            100.00999999999999,
            25.039999999999996,
            4.25,
            2.0,
            4.25,
            25.04,
            100.01
          ]
        }
      ]
    },
    {
      "id": "perturbation-comparison",
      "kind": "analytical_grid",
      "caption": "Author-constructed exact nonlinear losses on 20,000 equally spaced angles, radius .1. Sampled maxima are lower bounds on continuous maxima. Transformed ellipses preserve every sampled loss; no trained-network measurement.",
      "x": {
        "name": "Positive rescaling c",
        "values": [
          0.1,
          0.2,
          0.5,
          1.0,
          2.0,
          5.0,
          10.0
        ]
      },
      "series": [
        {
          "name": "Ordinary circle sampled maximum",
          "values": [
            0.5001999534279226,
            0.12544946073884947,
            0.021775430288239094,
            0.010719606781186589,
            0.021775430288239094,
            0.12544946073884947,
            0.5001999534279226
          ]
        },
        {
          "name": "Corresponding ellipse sampled maximum",
          "values": [
            0.010719606781186589,
            0.010719606781186589,
            0.010719606781186589,
            0.010719606781186589,
            0.010719606781186589,
            0.010719606781186589,
            0.010719606781186589
          ]
        }
      ]
    }
  ],
  "verification_code_sha256": "447bd25133a1e93be8673411e1a50cc024c308363f9f688bbdf3639afba0e83d",
  "execution_date": "2026-10-28",
  "standalone_no_filesystem_mutation_verified": true
}