flat-ball-conformal-checks-20261013T212754.112172Z.json

{
  "generated_utc": "2026-10-13T21:27:54.111865+00:00",
  "status": "pass",
  "exact_checks": 713,
  "cases": [
    {
      "depth": 2,
      "auxiliary_sphere_dimension": 4,
      "auxiliary_embedding_dimension": 5,
      "operator_order": 2,
      "squared_stiffness": "(z + 2)**2/4",
      "nonlinear_power": 3,
      "t0": 1,
      "t1": 3,
      "t2": 6,
      "hessian_N0": -2,
      "hessian_N1": 0,
      "hessian_N2": 3,
      "clock_local": true,
      "squared_wave_local": true
    },
    {
      "depth": 3,
      "auxiliary_sphere_dimension": 5,
      "auxiliary_embedding_dimension": 6,
      "operator_order": 3,
      "squared_stiffness": "(z + 3)**2*(z + 4)/36",
      "nonlinear_power": 4,
      "t0": 1,
      "t1": 4,
      "t2": 10,
      "hessian_N0": -3,
      "hessian_N1": 0,
      "hessian_N2": 6,
      "clock_local": false,
      "squared_wave_local": true
    },
    {
      "depth": 4,
      "auxiliary_sphere_dimension": 6,
      "auxiliary_embedding_dimension": 7,
      "operator_order": 4,
      "squared_stiffness": "(z + 4)**2*(z + 6)**2/576",
      "nonlinear_power": 5,
      "t0": 1,
      "t1": 5,
      "t2": 15,
      "hessian_N0": -4,
      "hessian_N1": 0,
      "hessian_N2": 10,
      "clock_local": true,
      "squared_wave_local": true
    },
    {
      "depth": 5,
      "auxiliary_sphere_dimension": 7,
      "auxiliary_embedding_dimension": 8,
      "operator_order": 5,
      "squared_stiffness": "(z + 5)**2*(z + 8)**2*(z + 9)/14400",
      "nonlinear_power": 6,
      "t0": 1,
      "t1": 6,
      "t2": 21,
      "hessian_N0": -5,
      "hessian_N1": 0,
      "hessian_N2": 15,
      "clock_local": false,
      "squared_wave_local": true
    },
    {
      "depth": 6,
      "auxiliary_sphere_dimension": 8,
      "auxiliary_embedding_dimension": 9,
      "operator_order": 6,
      "squared_stiffness": "(z + 6)**2*(z + 10)**2*(z + 12)**2/518400",
      "nonlinear_power": 7,
      "t0": 1,
      "t1": 7,
      "t2": 28,
      "hessian_N0": -6,
      "hessian_N1": 0,
      "hessian_N2": 21,
      "clock_local": true,
      "squared_wave_local": true
    },
    {
      "depth": 10,
      "auxiliary_sphere_dimension": 12,
      "auxiliary_embedding_dimension": 13,
      "operator_order": 10,
      "squared_stiffness": "(z + 10)**2*(z + 18)**2*(z + 24)**2*(z + 28)**2*(z + 30)**2/13168189440000",
      "nonlinear_power": 11,
      "t0": 1,
      "t1": 11,
      "t2": 66,
      "hessian_N0": -10,
      "hessian_N1": 0,
      "hessian_N2": 55,
      "clock_local": true,
      "squared_wave_local": true
    }
  ],
  "coverage": [
    "all six depths; N=0..12 inverse Riesz eigenvalues",
    "N=0..6 full conformal commutator with raising and lowering",
    "N=0..6 explicit invariant harmonic lifts and actual ball differential operator",
    "two nonconstant rational conformal solutions at every even depth",
    "nonlinear conformal parameter jets through order 6 at all six depths",
    "symbolic factorization and recurrence; interior covariance counterexample"
  ],
  "sources": {
    "experiments/flat-ball-conformal-checks.py": "6c0340e1a77a7ca3e2fad32e6b1a5d36ecd6e92193ea63e3a8be4b73cfd97cc6"
  }
}