{
  "acceptance": {
    "angular_points_exceed_twice_highest_mode": true,
    "exact_constraint_residual_zero": true,
    "finest_grid_residual_below_tolerance": true,
    "holomorphy_residual_strictly_decreases": true,
    "overall": true,
    "scalar_determinant_above_margin": true,
    "scalar_determinant_positive_on_all_grids": true,
    "thresholds": {
      "exact_regularization_residual": "0",
      "finest_grid_max_holomorphy_residual": "0.003",
      "minimum_scalar_determinant_sqrt": "0.9"
    }
  },
  "benchmark": "two-mode-(1,0,n)-superstratum-consistency",
  "environment": {
    "executed": {
      "mpmath": "1.3.0",
      "python": "3.11.4",
      "sympy": "1.13.3"
    },
    "pinned": {
      "mpmath": "1.3.0",
      "python": "3.11.4",
      "sympy": "1.13.3"
    },
    "symbolic_assumptions": "Q1,Q5,Ry and real mode amplitudes are exact positive rationals; a is the positive square root of a^2.",
    "version_drift_allowed": false
  },
  "exact_results": {
    "JL": "398/25",
    "JR": "398/25",
    "QP": "42/25",
    "a2": "199/25",
    "c2": "52/25",
    "regularity_residual": "0"
  },
  "failure_cases": [
    {
      "change": "c^2 is shifted by +1/20 while Q1, Q5, Ry and a^2 are fixed",
      "expected_detection": "nonzero regularity/asymptotic-periodicity residual",
      "name": "uncoiffured-secondary-coefficient",
      "passes": false,
      "regularity_residual": "-1/20"
    },
    {
      "change": "replace (b1,b3)=(6/5,4/5) by (4,3)",
      "derived_a2": "-7/2",
      "expected_detection": "negative cap-size parameter, so regularity fails",
      "name": "over-rotating-mode-amplitudes",
      "passes": false
    },
    {
      "change": "use four angular points for a highest mode n=3",
      "expected_detection": "grid does not resolve the quadratic Fourier content",
      "name": "aliased-angular-grid",
      "passes": false
    }
  ],
  "inputs": {
    "F0": "b1*xi + b3*xi^3",
    "F1": "0",
    "Q1": "9",
    "Q5": "16",
    "Ry": "4",
    "gauge_and_periodicities": "u=(t-y)/sqrt(2), v=(t+y)/sqrt(2), y~y+2*pi*Ry, theta=sqrt(2)*v/Ry~theta+2*pi",
    "modes": [
      {
        "amplitude": "6/5",
        "k": 1,
        "m": 0,
        "n": 1
      },
      {
        "amplitude": "4/5",
        "k": 1,
        "m": 0,
        "n": 3
      }
    ],
    "xi": "rho/sqrt(1+rho^2) * exp(i*theta)"
  },
  "refinements": [
    {
      "angular_points": 64,
      "max_holomorphy_residual": "0.0361109464382",
      "min_omega_squared_factor": "17.3312533356",
      "min_scalar_determinant_sqrt": "0.962847407534",
      "parseval_coiffuring_residual": "0.0",
      "radial_points": 33,
      "rho_interval": [
        "0",
        "12"
      ],
      "working_precision_digits": 80
    },
    {
      "angular_points": 128,
      "max_holomorphy_residual": "0.00905576406139",
      "min_omega_squared_factor": "17.3235164452",
      "min_scalar_determinant_sqrt": "0.962417580287",
      "parseval_coiffuring_residual": "0.0",
      "radial_points": 65,
      "rho_interval": [
        "0",
        "12"
      ],
      "working_precision_digits": 80
    },
    {
      "angular_points": 256,
      "max_holomorphy_residual": "0.00226569610758",
      "min_omega_squared_factor": "17.3228318986",
      "min_scalar_determinant_sqrt": "0.962379549921",
      "parseval_coiffuring_residual": "0.0",
      "radial_points": 129,
      "rho_interval": [
        "0",
        "12"
      ],
      "working_precision_digits": 80
    }
  ],
  "schema_version": 1,
  "scope_notice": "Algebraic and grid checks for a published exact family; not a numerical solution of the full six-dimensional PDE system.",
  "source": {
    "arxiv": "2004.13031",
    "authors": "Daniel R. Mayerson, Robert A. Walker, and Nicholas P. Warner",
    "locator": "\u00a74.1, Eqs. (4.2)\u2013(4.4); \u00a74.3, Eqs. (4.20)\u2013(4.22); Appendix D.4\u2013D.5, Eqs. (D.38)\u2013(D.49)",
    "title": "Microstate Geometries from Gauged Supergravity in Three Dimensions",
    "truncation": "six-dimensional N=(1,0) supergravity with two anti-self-dual tensor multiplets; (1,0,n) U(1)^2 subsector"
  }
}