{
  "pipeline": [
    {
      "stage": "Σ",
      "name": "State Space",
      "dimension": 125,
      "role": "Ambient input vector space (ℝ¹²⁵)",
      "validated": true,
      "computation": "5³ tensor product of Spin-2 spaces"
    },
    {
      "stage": "C",
      "name": "Constraint",
      "operator": "Casimir",
      "definition": "C = J_x² + J_y² + J_z²",
      "role": "Casimir operator spectral filtering",
      "validated": true,
      "eigenvalue_spectrum": {
        "0": 1,
        "2": 9,
        "6": 25,
        "12": 28,
        "20": 27,
        "30": 22,
        "42": 13
      },
      "total_dimension": 125
    },
    {
      "stage": "K",
      "name": "Kernel Filter",
      "operator": "K = (C - 6I)(C - 30I)",
      "role": "Invariant subspace (Ψ) isolation",
      "validated": true,
      "target_eigenvalues": [6, 30],
      "target_j_values": [2, 5],
      "kernel_dimension": 47
    },
    {
      "stage": "H_k",
      "name": "Harmonic Flow",
      "equation": "∂ₜψ = i Ĥ ψ",
      "role": "Recursive oscillation phase",
      "validated": true,
      "hamiltonian": "H = K²",
      "spectral_gap": 11664
    },
    {
      "stage": "E_47",
      "name": "Dimensional Reduction",
      "dimension": 47,
      "role": "Orthogonal projection to invariant kernel",
      "validated": true,
      "coherence_fraction": 0.376,
      "expected_coherence_fraction": 0.376
    },
    {
      "stage": "P_E",
      "name": "Projector",
      "property": "Idempotent",
      "equation": "P_E² = P_E",
      "role": "Idempotent kernel mapping",
      "validated": true,
      "idempotence_error": 1.6202201482531093e-14,
      "hermiticity_error": 0.0
    },
    {
      "stage": "Γ",
      "name": "Dynamics",
      "map": "Γ(xₙ₊₁) = f(xₙ)",
      "role": "Iterative contraction",
      "validated": true,
      "convergence_type": "Babylonian",
      "convergence_target": 0.376,
      "convergence_tolerance": 1e-7
    }
  ],
  "validation_status": "COMPLETE",
  "timestamp": "2026-07-21T19:30:00Z"
}