{
  "schema_version": 1,
  "release": "2.2.0",
  "inventory": "docs/reference/capabilities.json",
  "inventory_release": "2.2.0",
  "families": [
    {
      "family": "bessel_elliptic_exponential_integral",
      "status": "qualified",
      "risk": "standard",
      "input_domain": "Finite real double inputs within each function's documented validated domain, including stated endpoint limits and exclusions.",
      "budget": {
        "kind": "relative_error",
        "metric": "Absolute difference from independent reference values, with the test's 5e-13 absolute floor and 5e-12 relative allowance",
        "limit": 5e-12,
        "unit": "function output units"
      },
      "reference": {
        "method": "120-digit decimal reference corpora, independent quadrature for E1 values, and documented mathematical identities",
        "source": "Repository-generated reference include files cite NIST DLMF; reference generators use decimal arithmetic and Gauss-Legendre quadrature",
        "precision": "At least 120 decimal digits during reference generation, rounded to IEEE-754 binary64 literals",
        "parameters": "Bessel small and large arguments; modified Bessel domain and scale cases; incomplete and complete elliptic integrals including Pi; Jacobi quarter periods; Ei/E1 tails; convergent 2F1 parameter and argument fixtures",
        "license": "Repository-authored generators and fixtures under MIT; mathematical reference material is cited from NIST DLMF",
        "regeneration": "Run the generate_*_data.py tools referenced by each include header, then run the cited special-function test units"
      },
      "tests": [
        {"path": "tests/TestSpecialFunctions.pas", "assertions": ["procedure TTestBessel.TestJReferenceCorpus;", "procedure TTestBessel.TestYReferenceCorpus;", "Y0 negative domain"], "kind": "independent decimal references, identities, and domain edges"},
        {"path": "tests/TestModifiedBessel.pas", "assertions": ["procedure TTestModifiedBessel.TestReferenceCorpus;", "I/K Wronskian", "K0 negative domain"], "kind": "independent decimal references, identities, and domain edges"},
        {"path": "tests/TestEllipticIntegrals.pas", "assertions": ["procedure TTestEllipticIntegrals.TestIncompleteReferenceCorpus;", "procedure TTestEllipticIntegrals.TestThirdKindReferenceValues;", "F(phi, 0)"], "kind": "decimal/quadrature references and endpoint/domain checks"},
        {"path": "tests/TestJacobiElliptic.pas", "assertions": ["procedure TTestJacobiElliptic.TestIndependentReferences;", "sn(K,m)=1", "infinite parameter"], "kind": "independent decimal references, quarter-period identities, and domain edges"},
        {"path": "tests/TestExponentialIntegrals.pas", "assertions": ["procedure TTestExponentialIntegrals.TestEiReferenceCorpus;", "procedure TTestExponentialIntegrals.TestE1ReferenceCorpus;", "Ei below validated range"], "kind": "independent decimal/quadrature references and pole/domain checks"},
        {"path": "tests/TestGaussHypergeometric.pas", "assertions": ["procedure TTestGaussHypergeometric.TestReferenceCorpus;", "F(1,1;2;0.5) identity", "X above range"], "kind": "independent decimal references, identities, and convergence-domain checks"}
      ],
      "edge_cases": [
        "Function-specific poles and finite endpoint limits are checked explicitly.",
        "NaN, infinity, and out-of-domain values follow the documented rejection behavior.",
        "Elliptic Pi principal-value poles, unsupported characteristics, and hypergeometric analytic continuation are excluded."
      ],
      "documentation": "docs/guides/domains/math-base.md"
    },
    {
      "family": "remaining_advanced_spectral_linear_algebra",
      "status": "qualified",
      "risk": "standard",
      "input_domain": "Finite real or complex double dense matrices and regular real or complex matrix pencils in documented supported dimensions.",
      "budget": {
        "kind": "residual",
        "metric": "Normalized reconstruction, orthogonality/unitarity, and generalized eigenpair residuals; maximum explicit generalized residual fixture threshold",
        "limit": 1e-7,
        "unit": "dimensionless normalized residual"
      },
      "reference": {
        "method": "Independently reconstructed Schur factorizations, known eigenvalue fixtures, orthogonality/unitarity checks, and normalized homogeneous generalized-eigenpair residuals",
        "source": "Repository-authored fixtures and independently computed residuals in TestDenseDecompositions",
        "precision": "IEEE-754 binary64 real and complex arithmetic",
        "parameters": "Real/complex Hessenberg and Schur factors, nonsymmetric real eigenpairs, finite and infinite generalized eigenvalues, and real/complex 3x3 pencils",
        "license": "Repository-authored tests under MIT; no third-party reference data",
        "regeneration": "Run TestDenseDecompositions; recompute the stated factor reconstructions and normalized homogeneous eigenpair residuals from the fixtures"
      },
      "tests": [
        {"path": "tests/TestDenseDecompositions.pas", "assertions": ["real generalized Schur reconstructs A", "finite generalized eigenpair residual is small", "3x3 generalized eigenvectors report small residuals"], "kind": "factor reconstruction and normalized eigenpair residual"},
        {"path": "tests/TestDenseDecompositions.pas", "assertions": ["complex generalized Schur reconstructs A", "complex generalized eigenpair residual is small", "3x3 complex generalized eigenpair residual is small"], "kind": "complex factor reconstruction and normalized eigenpair residual"}
      ],
      "edge_cases": [
        "Singular B produces projective infinite generalized eigenvalues where supported.",
        "Empty inputs, invalid dimensions, non-finite entries, and bounded-iteration failures have explicit tests.",
        "Repeated or clustered eigenvalues may rotate their eigenvector basis; polynomial and interior-target workflows are outside this family."
      ],
      "documentation": "docs/guides/domains/dense-linear-algebra.md"
    }
  ]
}