{
  "assessment": "verified",
  "claim": 1,
  "destructive_control": {
    "errors": [
      0.5,
      0.5,
      0.5,
      0.5
    ],
    "mutation": "negate the conjugate intercept sign"
  },
  "error_vs_spacing_exponent": 2.0,
  "exact_theorem_rate_for_instance": "||f-f_grid||_infinity=h\u00b2/8",
  "finite_grid_rows": [
    {
      "atoms": 5,
      "cells_exhausted": 4,
      "exact_uniform_error": "1/32",
      "spacing": 0.5,
      "uniform_error": 0.03125
    },
    {
      "atoms": 9,
      "cells_exhausted": 8,
      "exact_uniform_error": "1/128",
      "spacing": 0.25,
      "uniform_error": 0.0078125
    },
    {
      "atoms": 17,
      "cells_exhausted": 16,
      "exact_uniform_error": "1/512",
      "spacing": 0.125,
      "uniform_error": 0.001953125
    },
    {
      "atoms": 33,
      "cells_exhausted": 32,
      "exact_uniform_error": "1/2048",
      "spacing": 0.0625,
      "uniform_error": 0.00048828125
    },
    {
      "atoms": 65,
      "cells_exhausted": 64,
      "exact_uniform_error": "1/8192",
      "spacing": 0.03125,
      "uniform_error": 0.0001220703125
    },
    {
      "atoms": 129,
      "cells_exhausted": 128,
      "exact_uniform_error": "1/32768",
      "spacing": 0.015625,
      "uniform_error": 3.0517578125e-05
    }
  ],
  "literal_claim": "Theorem 1 (Section V.A) establishes that finitely \u1ef8-convex functions form a dense subset of all \u1ef8-convex functions, giving a universal approximation property for generalized convex functions.",
  "native_instance": "Phi(x,y)=xy on X=Y=[-1,1], f(x)=x\u00b2/2, f^X(y)=y\u00b2/2"
}