{
  "artifact_id": "quad.multidim.truth",
  "claim_boundary": "The artifact certifies only the frozen dimensions, controls, integrands, and tolerances; it is not a universal accuracy claim.",
  "environment": {
    "jax": "0.10.1",
    "jax_backend": "cpu",
    "jax_enable_x64": true,
    "jaxlib": "0.10.1",
    "machine": "arm64",
    "numpy": "2.4.6",
    "platform": "macOS-26.1-arm64-arm-64bit-Mach-O",
    "python": "3.13.7"
  },
  "generator": "scripts/generate_quad_multidim_evidence.py",
  "generator_sha256": "4b66a9e996fa903250efdd345c1f8a4db75e0af5c695140f2c0cd66c7c57fec2",
  "records": [
    {
      "absolute_error": 4.440892098500626e-16,
      "controls": {
        "epsabs": 1e-09,
        "epsrel": 1e-09,
        "gradient": "replay",
        "max_evaluations": 65536
      },
      "dimension": 2,
      "dtype": "float64",
      "error_kind": 5,
      "expected_claim": "exact tensor polynomial moment",
      "family": "tensor_polynomial",
      "method": "TensorProduct",
      "method_id": "tensor_gauss_3",
      "relative_error": 1.3212571532729136e-16,
      "replay_gradient": 3.3611111111111116,
      "status": 7,
      "tolerance": 2e-13,
      "truth": 3.3611111111111107,
      "truth_source": {
        "formula": "(11/6)^2",
        "kind": "analytic"
      },
      "value": 3.361111111111111,
      "work": {
        "active_regions": 0,
        "evaluations": 9,
        "levels": 0,
        "refinements": 0,
        "replicates": 0
      }
    },
    {
      "absolute_error": 4.336808689942018e-19,
      "controls": {
        "epsabs": 1e-09,
        "epsrel": 1e-09,
        "gradient": "replay",
        "max_evaluations": 65536,
        "max_frontier": 2049,
        "max_indices": 128,
        "max_nodes": 65536
      },
      "dimension": 3,
      "dtype": "float64",
      "error_kind": 2,
      "expected_claim": "sparse polynomial moment",
      "family": "beta_product",
      "method": "Smolyak",
      "method_id": "smolyak_5",
      "relative_error": 7.494005416219809e-16,
      "replay_gradient": 0.0005787037037037041,
      "status": 0,
      "tolerance": 2e-13,
      "truth": 0.0005787037037037036,
      "truth_source": {
        "formula": "(1/12)^3",
        "kind": "analytic"
      },
      "value": 0.000578703703703704,
      "work": {
        "active_regions": 0,
        "evaluations": 177,
        "levels": 5,
        "refinements": 34,
        "replicates": 0
      }
    },
    {
      "absolute_error": 5.46611303442468e-09,
      "controls": {
        "epsabs": 1e-09,
        "epsrel": 1e-09,
        "gradient": "replay",
        "max_evaluations": 65536,
        "max_frontier": 2049,
        "max_indices": 128,
        "max_nodes": 65536
      },
      "dimension": 4,
      "dtype": "float64",
      "error_kind": 2,
      "expected_claim": "fixed sparse accuracy threshold; estimator does not claim convergence",
      "family": "separable_exponential",
      "method": "Smolyak",
      "method_id": "smolyak_5",
      "relative_error": 3.42356790859698e-08,
      "replay_gradient": 0.15966130561729847,
      "status": 8,
      "tolerance": 2e-07,
      "truth": 0.15966130015118526,
      "truth_source": {
        "formula": "(1-exp(-1))^4",
        "kind": "analytic"
      },
      "value": 0.1596613056172983,
      "work": {
        "active_regions": 0,
        "evaluations": 401,
        "levels": 5,
        "refinements": 69,
        "replicates": 0
      }
    },
    {
      "absolute_error": 2.220446049250313e-16,
      "controls": {
        "epsabs": 1e-09,
        "epsrel": 1e-09,
        "gradient": "replay",
        "max_evaluations": 65536,
        "max_regions": 1024
      },
      "dimension": 4,
      "dtype": "float64",
      "error_kind": 0,
      "expected_claim": "rotated smooth cubature convergence",
      "family": "rotated_smooth",
      "method": "AdaptiveCubature",
      "method_id": "cubature",
      "relative_error": 2.1488187573390125e-16,
      "replay_gradient": 1.0333333333333332,
      "status": 0,
      "tolerance": 2e-12,
      "truth": 1.0333333333333334,
      "truth_source": {
        "formula": "1 + 0.1 Var(sum(X_i))",
        "kind": "analytic"
      },
      "value": 1.0333333333333332,
      "work": {
        "active_regions": 1,
        "evaluations": 57,
        "levels": 0,
        "refinements": 0,
        "replicates": 0
      }
    },
    {
      "absolute_error": 0.0,
      "controls": {
        "epsabs": 1e-09,
        "epsrel": 1e-09,
        "gradient": "replay",
        "max_evaluations": 65536
      },
      "dimension": 2,
      "dtype": "float64",
      "error_kind": 5,
      "expected_claim": "Genz reference accuracy threshold",
      "family": "genz_oscillatory",
      "method": "TensorProduct",
      "method_id": "tensor_gauss_12",
      "relative_error": 0.0,
      "replay_gradient": -0.8003996581568846,
      "status": 7,
      "tolerance": 5e-05,
      "truth": -0.8003996581568846,
      "truth_source": {
        "absolute_uncertainty": 1e-79,
        "external_owner": "Genz test-integral family; closed form evaluated by mpmath",
        "formula_id": "genz-unit-hypercube-six-family-v1:oscillatory",
        "generator": "scripts/generate_quad_b1_reference.py",
        "generator_source_sha256": "ce950bb6fff540bf5e989bd08f49960fce23dac1dd294439cb054fc169f4d8e0",
        "kind": "reference",
        "parameters": {
          "a": [
            "2/5",
            "9/20"
          ],
          "u": [
            "1/3",
            "2/3"
          ]
        },
        "precision_decimal_digits": 80,
        "reference_artifact_sha256": "227f7d9477de44f46a3448000f251e7ebfe885954f1c9e8e6ab87d293c644c30"
      },
      "value": -0.8003996581568846,
      "work": {
        "active_regions": 0,
        "evaluations": 144,
        "levels": 0,
        "refinements": 0,
        "replicates": 0
      }
    },
    {
      "absolute_error": 6.938893903907228e-18,
      "controls": {
        "epsabs": 1e-09,
        "epsrel": 1e-09,
        "gradient": "replay",
        "max_evaluations": 65536
      },
      "dimension": 2,
      "dtype": "float64",
      "error_kind": 5,
      "expected_claim": "Genz reference accuracy threshold",
      "family": "genz_product_peak",
      "method": "TensorProduct",
      "method_id": "tensor_gauss_12",
      "relative_error": 2.226692979293777e-16,
      "replay_gradient": 0.031162328926496126,
      "status": 7,
      "tolerance": 5e-05,
      "truth": 0.03116232892649612,
      "truth_source": {
        "absolute_uncertainty": 1e-79,
        "external_owner": "Genz test-integral family; closed form evaluated by mpmath",
        "formula_id": "genz-unit-hypercube-six-family-v1:product-peak",
        "generator": "scripts/generate_quad_b1_reference.py",
        "generator_source_sha256": "ce950bb6fff540bf5e989bd08f49960fce23dac1dd294439cb054fc169f4d8e0",
        "kind": "reference",
        "parameters": {
          "a": [
            "2/5",
            "9/20"
          ],
          "u": [
            "1/3",
            "2/3"
          ]
        },
        "precision_decimal_digits": 80,
        "reference_artifact_sha256": "227f7d9477de44f46a3448000f251e7ebfe885954f1c9e8e6ab87d293c644c30"
      },
      "value": 0.031162328926496126,
      "work": {
        "active_regions": 0,
        "evaluations": 144,
        "levels": 0,
        "refinements": 0,
        "replicates": 0
      }
    },
    {
      "absolute_error": 2.220446049250313e-16,
      "controls": {
        "epsabs": 1e-09,
        "epsrel": 1e-09,
        "gradient": "replay",
        "max_evaluations": 65536
      },
      "dimension": 2,
      "dtype": "float64",
      "error_kind": 5,
      "expected_claim": "Genz reference accuracy threshold",
      "family": "genz_corner_peak",
      "method": "TensorProduct",
      "method_id": "tensor_gauss_12",
      "relative_error": 5.851849219620737e-16,
      "replay_gradient": 0.37944348289175855,
      "status": 7,
      "tolerance": 5e-05,
      "truth": 0.3794434828917588,
      "truth_source": {
        "absolute_uncertainty": 1e-79,
        "external_owner": "Genz test-integral family; closed form evaluated by mpmath",
        "formula_id": "genz-unit-hypercube-six-family-v1:corner-peak",
        "generator": "scripts/generate_quad_b1_reference.py",
        "generator_source_sha256": "ce950bb6fff540bf5e989bd08f49960fce23dac1dd294439cb054fc169f4d8e0",
        "kind": "reference",
        "parameters": {
          "a": [
            "2/5",
            "9/20"
          ],
          "u": [
            "1/3",
            "2/3"
          ]
        },
        "precision_decimal_digits": 80,
        "reference_artifact_sha256": "227f7d9477de44f46a3448000f251e7ebfe885954f1c9e8e6ab87d293c644c30"
      },
      "value": 0.37944348289175855,
      "work": {
        "active_regions": 0,
        "evaluations": 144,
        "levels": 0,
        "refinements": 0,
        "replicates": 0
      }
    },
    {
      "absolute_error": 1.1102230246251565e-16,
      "controls": {
        "epsabs": 1e-09,
        "epsrel": 1e-09,
        "gradient": "replay",
        "max_evaluations": 65536
      },
      "dimension": 2,
      "dtype": "float64",
      "error_kind": 5,
      "expected_claim": "Genz reference accuracy threshold",
      "family": "genz_gaussian",
      "method": "TensorProduct",
      "method_id": "tensor_gauss_12",
      "relative_error": 1.1552880249250037e-16,
      "replay_gradient": 0.9609924111324772,
      "status": 7,
      "tolerance": 5e-05,
      "truth": 0.9609924111324771,
      "truth_source": {
        "absolute_uncertainty": 1e-79,
        "external_owner": "Genz test-integral family; closed form evaluated by mpmath",
        "formula_id": "genz-unit-hypercube-six-family-v1:gaussian",
        "generator": "scripts/generate_quad_b1_reference.py",
        "generator_source_sha256": "ce950bb6fff540bf5e989bd08f49960fce23dac1dd294439cb054fc169f4d8e0",
        "kind": "reference",
        "parameters": {
          "a": [
            "2/5",
            "9/20"
          ],
          "u": [
            "1/3",
            "2/3"
          ]
        },
        "precision_decimal_digits": 80,
        "reference_artifact_sha256": "227f7d9477de44f46a3448000f251e7ebfe885954f1c9e8e6ab87d293c644c30"
      },
      "value": 0.9609924111324772,
      "work": {
        "active_regions": 0,
        "evaluations": 144,
        "levels": 0,
        "refinements": 0,
        "replicates": 0
      }
    },
    {
      "absolute_error": 3.294287065358503e-11,
      "controls": {
        "epsabs": 1e-09,
        "epsrel": 1e-09,
        "gradient": "replay",
        "max_evaluations": 65536,
        "max_regions": 1024
      },
      "dimension": 2,
      "dtype": "float64",
      "error_kind": 0,
      "expected_claim": "Genz reference accuracy threshold",
      "family": "genz_continuous",
      "method": "AdaptiveCubature",
      "method_id": "cubature",
      "relative_error": 4.1463190671597973e-11,
      "replay_gradient": 0.7945088190600008,
      "status": 0,
      "tolerance": 5e-05,
      "truth": 0.7945088190270579,
      "truth_source": {
        "absolute_uncertainty": 1e-79,
        "external_owner": "Genz test-integral family; closed form evaluated by mpmath",
        "formula_id": "genz-unit-hypercube-six-family-v1:continuous",
        "generator": "scripts/generate_quad_b1_reference.py",
        "generator_source_sha256": "ce950bb6fff540bf5e989bd08f49960fce23dac1dd294439cb054fc169f4d8e0",
        "kind": "reference",
        "parameters": {
          "a": [
            "2/5",
            "9/20"
          ],
          "u": [
            "1/3",
            "2/3"
          ]
        },
        "precision_decimal_digits": 80,
        "reference_artifact_sha256": "227f7d9477de44f46a3448000f251e7ebfe885954f1c9e8e6ab87d293c644c30"
      },
      "value": 0.7945088190600008,
      "work": {
        "active_regions": 149,
        "evaluations": 5049,
        "levels": 19,
        "refinements": 148,
        "replicates": 0
      }
    },
    {
      "absolute_error": 4.724265423305951e-11,
      "controls": {
        "epsabs": 1e-09,
        "epsrel": 1e-09,
        "gradient": "replay",
        "max_evaluations": 65536,
        "max_regions": 1024
      },
      "dimension": 2,
      "dtype": "float64",
      "error_kind": 0,
      "expected_claim": "Genz reference accuracy threshold",
      "family": "genz_discontinuous",
      "method": "AdaptiveCubature",
      "method_id": "cubature",
      "relative_error": 1.7041217876261993e-10,
      "replay_gradient": 0.2772258096108065,
      "status": 0,
      "tolerance": 5e-05,
      "truth": 0.2772258096580491,
      "truth_source": {
        "absolute_uncertainty": 1e-79,
        "external_owner": "Genz test-integral family; closed form evaluated by mpmath",
        "formula_id": "genz-unit-hypercube-six-family-v1:discontinuous-first-two-axes",
        "generator": "scripts/generate_quad_b1_reference.py",
        "generator_source_sha256": "ce950bb6fff540bf5e989bd08f49960fce23dac1dd294439cb054fc169f4d8e0",
        "kind": "reference",
        "parameters": {
          "a": [
            "2/5",
            "9/20"
          ],
          "u": [
            "1/3",
            "2/3"
          ]
        },
        "precision_decimal_digits": 80,
        "reference_artifact_sha256": "227f7d9477de44f46a3448000f251e7ebfe885954f1c9e8e6ab87d293c644c30"
      },
      "value": 0.27722580961080645,
      "work": {
        "active_regions": 284,
        "evaluations": 9639,
        "levels": 34,
        "refinements": 283,
        "replicates": 0
      }
    },
    {
      "absolute_error": 8.326672684688674e-17,
      "controls": {
        "epsabs": 1e-09,
        "epsrel": 1e-09,
        "gradient": "replay",
        "max_evaluations": 65536
      },
      "dimension": 2,
      "dtype": "float64",
      "error_kind": 1,
      "expected_claim": "localized adaptive-tensor convergence",
      "family": "localized_peak",
      "method": "AdaptiveTensorClenshawCurtis",
      "method_id": "adaptive_tensor",
      "relative_error": 6.657407476857332e-16,
      "replay_gradient": 0.12507380258207249,
      "status": 0,
      "tolerance": 2e-07,
      "truth": 0.1250738025820725,
      "truth_source": {
        "formula": "product of finite Gaussian error-function factors",
        "kind": "analytic"
      },
      "value": 0.12507380258207243,
      "work": {
        "active_regions": 0,
        "evaluations": 3201,
        "levels": 5,
        "refinements": 6,
        "replicates": 0
      }
    },
    {
      "absolute_error": 1.3010426069826053e-18,
      "controls": {
        "epsabs": 1e-09,
        "epsrel": 1e-09,
        "gradient": "replay",
        "max_evaluations": 65536
      },
      "dimension": 2,
      "dtype": "float64",
      "error_kind": 5,
      "expected_claim": "fixed boundary-layer accuracy threshold",
      "family": "boundary_layer",
      "method": "TensorProduct",
      "method_id": "tensor_gauss_20",
      "relative_error": 5.20417044938361e-16,
      "replay_gradient": 0.002499999989694231,
      "status": 7,
      "tolerance": 2e-07,
      "truth": 0.002499999989694232,
      "truth_source": {
        "formula": "((1-exp(-20))/20)^2",
        "kind": "analytic"
      },
      "value": 0.002499999989694231,
      "work": {
        "active_regions": 0,
        "evaluations": 400,
        "levels": 0,
        "refinements": 0,
        "replicates": 0
      }
    }
  ],
  "schema_version": 1,
  "validation_families": [
    "tensor_polynomial",
    "beta_product",
    "separable_exponential",
    "rotated_smooth",
    "genz_oscillatory",
    "genz_product_peak",
    "genz_corner_peak",
    "genz_gaussian",
    "genz_continuous",
    "genz_discontinuous",
    "localized_peak",
    "boundary_layer"
  ]
}
