{
  "status": "analytic sign/endpoint gates and numerical scaling checks passed",
  "scope": "probe and isolated spectral-atom diagnostics; not a numerical proof of the arithmetic theorem",
  "delta": "1/100",
  "unsmeared_sinc_integral": -0.17717525300250492,
  "smoothed_K0": -0.35434715073059375,
  "proved_upper_bound_on_K0": "-1/(3*pi)",
  "proved_total_variation_of_w": 2,
  "proved_mass_of_w": "2*pi",
  "exact_rational_gate": "6*(22/7)^2 < 100",
  "endpoint_residual_abs": 2.449274235012921e-16,
  "atom_scaling": [
    {
      "T": 2,
      "pairing": -0.35435050600500984
    },
    {
      "T": 7,
      "pairing": -0.3543505060050097
    },
    {
      "T": 19,
      "pairing": -0.35435050600500984
    },
    {
      "T": 100,
      "pairing": -0.35435050600500984
    }
  ],
  "quadrature": "binary64 adaptive Simpson diagnostic; not interval-certified"
}