{
  "module": "qutip_validation",
  "status": "pass",
  "generated_at": "2026-07-21T21:19:19Z",
  "python_version": "3.8+",
  "dependencies": {
    "numpy": ">=1.19.0",
    "scipy": ">=1.5.0",
    "qutip": ">=4.5.0"
  },
  "inputs": {
    "base_spin": 2,
    "base_dimension": 5,
    "tensor_product_rank": 3,
    "total_hilbert_dimension": 125
  },
  "results": {
    "carrier_dimension": 125,
    "kernel_dimension": 47,
    "coherence_fraction": 0.376,
    "coherence_fraction_exact": "47/125",
    "spectral_gap": 11664,
    "casimir_eigenvalue_spectrum": {
      "lambda_0": 0,
      "lambda_2": 2,
      "lambda_6": 6,
      "lambda_12": 12,
      "lambda_20": 20,
      "lambda_30": 30,
      "lambda_42": 42
    },
    "kernel_operator": "K = (C - 6I)(C - 30I)",
    "target_casimir_roots": [6, 30],
    "target_j_values": [2, 5],
    "kernel_multiplicity_j2": 5,
    "kernel_dimension_j2": 25,
    "kernel_multiplicity_j5": 11,
    "kernel_dimension_j5": 22,
    "total_kernel_dimension": 47
  },
  "tolerances": {
    "eigenvalue_rounding_decimals": 5,
    "floating_point_epsilon": 1e-10,
    "dimension_check_exact": true,
    "coherence_fraction_tolerance": 1e-3
  },
  "checks": [
    {
      "name": "Hilbert space dimension",
      "expected": 125,
      "computed": 125,
      "pass": true,
      "tolerance": "exact"
    },
    {
      "name": "Kernel dimension (E_47)",
      "expected": 47,
      "computed": 47,
      "pass": true,
      "tolerance": "exact"
    },
    {
      "name": "Coherence fraction (Ω_c)",
      "expected": 0.376,
      "computed": 0.376,
      "pass": true,
      "tolerance": 0.001,
      "relative_error": 0.0
    },
    {
      "name": "Spectral gap (γ)",
      "expected": 11664,
      "computed": 11664,
      "pass": true,
      "tolerance": "exact"
    },
    {
      "name": "Tensor product decomposition",
      "description": "5 ⊗ 5 ⊗ 5 decomposes into irreps with total dimension 125",
      "pass": true
    },
    {
      "name": "Kernel filter idempotence",
      "description": "K² eigenvalues at kernel are zero (projector property)",
      "pass": true
    },
    {
      "name": "Casimir eigenvalue clustering",
      "description": "All states segregate by j quantum number via Casimir operator",
      "pass": true
    }
  ],
  "source_commit": "1d0457cc6b91316bd8184cb8bbc1b11accb697a3",
  "source_file": "tests/qutip_validation.py",
  "mathematical_framework": {
    "hilbert_space": "V = V_2 ⊗ V_2 ⊗ V_2 where V_2 is Spin-2 irrep",
    "casimir_operator": "C = J_x² + J_y² + J_z² with eigenvalues λ = j(j+1)",
    "kernel_filter": "K = (C - 6I)(C - 30I) targets j=2 (λ=6) and j=5 (λ=30) sectors",
    "invariant_kernel": "E_47 = ker(K) is the 47-dimensional invariant subspace",
    "coherence_constant": "Ω_c = dim(E_47) / dim(V) = 47/125 = 0.376"
  },
  "reproducibility": {
    "instructions": "Run: python tests/qutip_validation.py",
    "expected_output": "All VALID checks in console output",
    "random_seed": "None (deterministic spectral decomposition)",
    "floating_point_notes": "Eigenvalue rounding to 5 decimals removes numerical artifacts from diagonalization"
  },
  "notes": [
    "QuTiP's eigenenergies() method performs full diagonalization of Hermitian operators.",
    "Kernel dimension extracted by counting eigenvalues == 0.0 after rounding.",
    "Spectral gap is smallest positive eigenvalue of K², indicating decay rate of transient noise.",
    "All computations are deterministic (no Monte Carlo sampling).",
    "This validation forms the quantum foundation of the E47 paradigm."
  ]
}