{
  "metadata": {
    "title": "Idealized radical-pair reaction: exact discrete numerical grid",
    "schema_version": 1,
    "status": "computational_benchmark_not_biological",
    "generated_utc": "2026-09-19T03:16:55.971167+00:00",
    "generation_file": "generate_spin_data.py",
    "generation_source_sha256": "14114e352a56a88b0ce8f9abadffdd633c382ff9ef158bd097f3cf87db71a75e",
    "dependencies": {
      "python": "3.9.6",
      "numpy": "2.0.2",
      "scipy": "1.13.1"
    },
    "hilbert_space_dimension": 8,
    "spin_order": [
      "electron_1",
      "electron_2",
      "spin_half_nucleus"
    ],
    "basis_per_spin": [
      "up",
      "down"
    ],
    "spin_operator_convention": "dimensionless S=Pauli/2",
    "initial_state": "electron singlet tensor unpolarized nuclear I/2",
    "hamiltonian": "Omega=H/hbar=+gamma_e*B dot (S1+S2)+S1 dot A dot I",
    "electron_gyromagnetic_magnitude_rad_per_s_per_tesla": 176085963000.0,
    "hyperfine_A_over_2pi_MHz": [
      2.0,
      2.0,
      4.0
    ],
    "hyperfine_tensor_frame": "diagonal in molecular x,y,z; z is unique axial direction",
    "field_direction": "(sin(theta)*cos(phi),sin(theta)*sin(phi),cos(theta)); grid phi=0",
    "angle_meaning": "polar angle theta between magnetic field and molecular z axis",
    "reaction": "equal singlet and triplet rates k=1/lifetime; irreversible two-product branching",
    "master_equation": "rho_dot=-i[Omega,rho]-k*rho+(Gamma/4)sum_{j=1,2;a=x,y,z}(sigma_ja*rho*sigma_ja-rho)",
    "relaxation_rate_meaning": "Gamma is the isolated electron Bloch-vector relaxation rate for stipulated isotropic local spin relaxation",
    "yield_definition": "Phi_channel=k*integral_0^infinity Tr(P_channel*rho(t))dt; channels computed independently",
    "axis_units": {
      "fields": "microtesla",
      "angles": "degrees",
      "lifetimes": "microseconds",
      "relaxations": "per_second",
      "yields": "dimensionless_probability"
    },
    "computation": "64-dimensional integrated Liouvillian linear solve using complex128",
    "grid_semantics": "Only explicitly listed discrete parameter points. No interpolation, clipping, renormalization, or empirical fit.",
    "orientation_semantics": "Fixed molecular orientation; freely rotating ensembles require separate averaging/dynamics.",
    "limitations": [
      "One model spin-1/2 nucleus; no fitted protein or cellular parameters.",
      "No nuclear Zeeman, exchange, dipolar, diffusion, back-reaction, or unequal-rate terms.",
      "Fixed hyperfine tensor and stipulated Markovian isotropic relaxation.",
      "No neuronal response, physiological relevance, entanglement witness, or consciousness score is inferred.",
      "Relaxation changes compare regimes of one quantum model, not proof against all conventional biochemical alternatives.",
      "Large displayed yield differences are model outcomes, not predicted human effect sizes."
    ]
  },
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  "lifetimes": [
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