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      "force_owner": "oscillatools.accel.networked_kuramoto.networked_kuramoto_force",
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      "evolution_owner": "oscillatools.accel.kuramoto_system.KuramotoSystem.networked",
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      "observable_owner": "oscillatools.accel.order_parameter_observables.order_parameter",
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      "state_jacobian_owner": "oscillatools.accel.kuramoto_mean_field.mean_field_jacobian",
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      "assumptions": [
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      "backend_owners": [
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      "backend_owners": [
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      "assumptions": [
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      "backend_owners": [
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      "topology": "COO row/column/weight edges; duplicate contributions add; SciPy adapter sums duplicates and removes diagonals"
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      "topology": "fixed supplied network or uniform mean field"
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      "backend_owners": [
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      "state_jacobian_owner": null,
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      "state_jacobian_owner": null,
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      "assumptions": [
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      "backend_owners": [
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      "state_jacobian_owner": null,
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      "assumptions": [
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      "state_jacobian_owner": "oscillatools.accel.kuramoto_inertial.inertial_jacobian",
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    },
    {
      "assumptions": [
        "Plasticity is explicit; the original Hebbian Jacobian applies only to the Hebbian rule."
      ],
      "backend_owners": [
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      "observable_owner": "oscillatools.accel.order_parameter_observables.order_parameter",
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      "state_jacobian_owner": null,
      "topology": "joint evolving matrix, not fixed network parameters"
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    {
      "assumptions": [],
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      "normalisation": "pairwise intra-layer and inter-layer sums; no N or L division",
      "observable_owner": "oscillatools.accel.multiplex_kuramoto.layer_order_parameters",
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      "solver": "rk4",
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      "state_jacobian_owner": "oscillatools.accel.multiplex_kuramoto.multiplex_jacobian",
      "topology": "same N replicas per layer; A[L,N,N] and B[L,L]"
    },
    {
      "assumptions": [
        "Not an exact arbitrary finite-N phase system.",
        "Original trajectory requires positive K and Delta."
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      "backend_owners": [
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      "equation": "z_dot=(i*omega0-Delta+K/2)*z-(K/2)*abs(z)**2*z",
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      "force_owner": "oscillatools.accel.kuramoto_ott_antonsen.ott_antonsen_field",
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      "observable_owner": "oscillatools.accel.kuramoto_ott_antonsen.ott_antonsen_order_parameter",
      "sensitivity_owner": "oscillatools.accel.kuramoto_ott_antonsen.ott_antonsen_terminal_order_parameter_value_and_grad",
      "sensitivity_semantics": "augmented RK4 derivatives of K and Delta; modulus singularity at z=0 refuses",
      "solver": "rk4",
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      "state_jacobian_owner": null,
      "topology": "thermodynamic Lorentzian frequency distribution and OA manifold"
    },
    {
      "assumptions": [
        "Exact finite-model reduction; RK4 still has integration error.",
        "Reconstructed phase angles are modulo 2*pi, not unwrapped coordinates."
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      "backend_owners": [
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      "history": "initial phases define immutable constants of motion",
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      "observable_owner": "oscillatools.accel.kuramoto_watanabe_strogatz.watanabe_strogatz_order_parameter",
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      "sensitivity_semantics": "no parameter sensitivity declared for this owner",
      "solver": "rk4",
      "state": "complex SU(1,1) alpha,beta and N constants b[j]=exp(i*theta0[j])",
      "state_jacobian_owner": null,
      "topology": "identical common omega; sinusoidal common forcing"
    },
    {
      "assumptions": [
        "Harmonic phases do not identify the original phase branch.",
        "SU(1,1) coordinate cancellation near synchrony is not a scientific accuracy guarantee."
      ],
      "backend_owners": [
        "oscillatools.accel.kuramoto_higher_order_watanabe_strogatz.integrate_higher_order_watanabe_strogatz"
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      "equation": "phi_dot=p*omega+p*K*Im(Z_p*exp(-i*phi))",
      "evolution_owner": "oscillatools.accel.kuramoto_higher_order_watanabe_strogatz.integrate_higher_order_watanabe_strogatz",
      "force_owner": null,
      "history": "initial harmonic phases define constants of motion",
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      "noise": "none",
      "normalisation": "Z_p=sum_j exp(i*p*theta[j])/N",
      "observable_owner": null,
      "sensitivity_owner": null,
      "sensitivity_semantics": "no parameter sensitivity declared for this owner",
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      "summary": "Return the delayed mean-field Kuramoto force ``F_j = (K/N) Σ_k sin(θ_k(t-τ) − θ_j(t))``."
    },
    "oscillatools.accel.kuramoto_delayed.delayed_networked_force": {
      "declaration_sha256": "8b4e7d9dc804c8e67f4bdbef93496cdfd02a532efbe4557d18e8c18b04bb78bf",
      "direct_test_paths": [
        "oscillatools/tests/test_kuramoto_delayed.py"
      ],
      "dispatch_claim": "source declarations only; availability, selected tier and parity are not measured here",
      "line": 97,
      "module_declared_dispatch_chains": {},
      "path": "oscillatools/src/oscillatools/accel/kuramoto_delayed.py",
      "qualified_name": "oscillatools.accel.kuramoto_delayed.delayed_networked_force",
      "signature": "current_phases: NDArray[np.float64], delayed_phases: NDArray[np.float64], coupling_matrix: NDArray[np.float64]",
      "source_sha256": "7a124f0ade2b7d74c87fcf9dd8889773c6210a6c57b006ca07f8cfe05d2ce63d",
      "summary": "Return the delayed networked Kuramoto force ``F_j = Σ_k K_{jk} sin(θ_k(t-τ) − θ_j(t))``."
    },
    "oscillatools.accel.kuramoto_delayed.integrate_delayed_kuramoto": {
      "declaration_sha256": "b2d8cccb3c6ed8e1a8b003452afc263795f5658ba99370b8b6ce4bfad14d9b46",
      "direct_test_paths": [
        "oscillatools/tests/test_kuramoto_delayed.py"
      ],
      "dispatch_claim": "source declarations only; availability, selected tier and parity are not measured here",
      "line": 220,
      "module_declared_dispatch_chains": {},
      "path": "oscillatools/src/oscillatools/accel/kuramoto_delayed.py",
      "qualified_name": "oscillatools.accel.kuramoto_delayed.integrate_delayed_kuramoto",
      "signature": "initial_history: NDArray[np.float64], omega: NDArray[np.float64], force: DelayedForce, *, delay: float, dt: float, n_steps: int, delay_tolerance: float=1e-09",
      "source_sha256": "7a124f0ade2b7d74c87fcf9dd8889773c6210a6c57b006ca07f8cfe05d2ce63d",
      "summary": "Integrate the time-delayed Kuramoto model by a delay-aware method-of-steps RK4."
    },
    "oscillatools.accel.kuramoto_higher_order_watanabe_strogatz.integrate_higher_order_watanabe_strogatz": {
      "declaration_sha256": "f98c419ffb2bb457488e855c5e0af98820f5125882a770cf9d0605517b3cabfd",
      "direct_test_paths": [
        "oscillatools/tests/test_kuramoto_higher_order_watanabe_strogatz.py"
      ],
      "dispatch_claim": "source declarations only; availability, selected tier and parity are not measured here",
      "line": 81,
      "module_declared_dispatch_chains": {},
      "path": "oscillatools/src/oscillatools/accel/kuramoto_higher_order_watanabe_strogatz.py",
      "qualified_name": "oscillatools.accel.kuramoto_higher_order_watanabe_strogatz.integrate_higher_order_watanabe_strogatz",
      "signature": "initial_phases: NDArray[np.float64], *, omega: float, coupling: float, harmonic: int, dt: float, n_steps: int",
      "source_sha256": "65731e29a017bee16d47d6f93a74896f275ba7976d9f7f37ab02a5b5731e9c66",
      "summary": "Integrate the ``p``-th harmonic identical-oscillator flow by the Watanabe–Strogatz reduction."
    },
    "oscillatools.accel.kuramoto_hyperedge.hyperedge_force": {
      "declaration_sha256": "112fa76bb96b903d7e9c7590b895ec0ce54bc20b0d69b14088bdd843e7f00482",
      "direct_test_paths": [
        "oscillatools/tests/test_kuramoto_hyperedge.py"
      ],
      "dispatch_claim": "source declarations only; availability, selected tier and parity are not measured here",
      "line": 73,
      "module_declared_dispatch_chains": {},
      "path": "oscillatools/src/oscillatools/accel/kuramoto_hyperedge.py",
      "qualified_name": "oscillatools.accel.kuramoto_hyperedge.hyperedge_force",
      "signature": "theta: NDArray[np.float64], hyperedges: Sequence[Sequence[int]], coupling: float | Sequence[float]",
      "source_sha256": "5dbb9bbd2add6f659f43ae093e5c79b0d4a04a6c76a0a7faad882fa334f84f2e",
      "summary": "Return the structural hypergraph force ``F_i = Σ_{e∋i} K_e sin(Σ_{k∈e} θ_k − |e| θ_i)``."
    },
    "oscillatools.accel.kuramoto_hyperedge.hyperedge_jacobian": {
      "declaration_sha256": "81ccb0f9d4c0fe49d1f530dc1199ce8c87774b69a765eef44e9674c221b93425",
      "direct_test_paths": [
        "oscillatools/tests/test_kuramoto_hyperedge.py"
      ],
      "dispatch_claim": "source declarations only; availability, selected tier and parity are not measured here",
      "line": 116,
      "module_declared_dispatch_chains": {},
      "path": "oscillatools/src/oscillatools/accel/kuramoto_hyperedge.py",
      "qualified_name": "oscillatools.accel.kuramoto_hyperedge.hyperedge_jacobian",
      "signature": "theta: NDArray[np.float64], hyperedges: Sequence[Sequence[int]], coupling: float | Sequence[float]",
      "source_sha256": "5dbb9bbd2add6f659f43ae093e5c79b0d4a04a6c76a0a7faad882fa334f84f2e",
      "summary": "Return the ``(N, N)`` Jacobian of the structural hypergraph force."
    },
    "oscillatools.accel.kuramoto_inertial.inertial_jacobian": {
      "declaration_sha256": "f62331ee8ed4a888e71f82e85649c6d22a94def4082b5f63d8e08d0446de3780",
      "direct_test_paths": [
        "oscillatools/tests/test_kuramoto_inertial.py"
      ],
      "dispatch_claim": "source declarations only; availability, selected tier and parity are not measured here",
      "line": 199,
      "module_declared_dispatch_chains": {},
      "path": "oscillatools/src/oscillatools/accel/kuramoto_inertial.py",
      "qualified_name": "oscillatools.accel.kuramoto_inertial.inertial_jacobian",
      "signature": "phases: NDArray[np.float64], force_jacobian: PhaseJacobian, mass: float, *, damping: float=1.0",
      "source_sha256": "0bb6c7529708817b1cf6d88eff55bcf21c83aa6001cbf51f04ebab42f5811308",
      "summary": "Return the ``2N × 2N`` Jacobian of the inertial Kuramoto phase-space vector field."
    },
    "oscillatools.accel.kuramoto_inertial.inertial_vector_field": {
      "declaration_sha256": "cbc3e727905306a8ad7947f9ece6855b92d5770a1614752325ea98e5104471d0",
      "direct_test_paths": [
        "oscillatools/tests/test_kuramoto_inertial.py"
      ],
      "dispatch_claim": "source declarations only; availability, selected tier and parity are not measured here",
      "line": 146,
      "module_declared_dispatch_chains": {},
      "path": "oscillatools/src/oscillatools/accel/kuramoto_inertial.py",
      "qualified_name": "oscillatools.accel.kuramoto_inertial.inertial_vector_field",
      "signature": "phases: NDArray[np.float64], velocities: NDArray[np.float64], omega: NDArray[np.float64], force: PhaseForce, mass: float, *, damping: float=1.0",
      "source_sha256": "0bb6c7529708817b1cf6d88eff55bcf21c83aa6001cbf51f04ebab42f5811308",
      "summary": "Return the ``(θ, θ̇)`` phase-space vector field of the inertial Kuramoto model."
    },
    "oscillatools.accel.kuramoto_inertial.integrate_inertial": {
      "declaration_sha256": "a9048a262d42388d2e73db2d78c1b7fed1f5ca04072f25c01473ed9cd95d2ef1",
      "direct_test_paths": [
        "oscillatools/tests/test_kuramoto_inertial.py"
      ],
      "dispatch_claim": "source declarations only; availability, selected tier and parity are not measured here",
      "line": 260,
      "module_declared_dispatch_chains": {},
      "path": "oscillatools/src/oscillatools/accel/kuramoto_inertial.py",
      "qualified_name": "oscillatools.accel.kuramoto_inertial.integrate_inertial",
      "signature": "phases: NDArray[np.float64], velocities: NDArray[np.float64], omega: NDArray[np.float64], force: PhaseForce, mass: float, *, damping: float=1.0, dt: float, n_steps: int",
      "source_sha256": "0bb6c7529708817b1cf6d88eff55bcf21c83aa6001cbf51f04ebab42f5811308",
      "summary": "Integrate the inertial Kuramoto model by a fixed-step RK4 over the ``(θ, v)`` state."
    },
    "oscillatools.accel.kuramoto_mean_field.mean_field_force": {
      "declaration_sha256": "a102d58315ccb06521542d4bb556c7ddb7c95476d46717e3178184690e9cfd29",
      "direct_test_paths": [
        "oscillatools/tests/test_kuramoto_mean_field.py"
      ],
      "dispatch_claim": "source declarations only; availability, selected tier and parity are not measured here",
      "line": 129,
      "module_declared_dispatch_chains": {
        "_MEAN_FIELD_FORCE_CHAIN": [
          {
            "tier": "rust",
            "wrapper": "oscillatools.accel.kuramoto_mean_field._rust_mean_field_force"
          },
          {
            "tier": "julia",
            "wrapper": "oscillatools.accel.kuramoto_mean_field._julia_mean_field_force"
          },
          {
            "tier": "python",
            "wrapper": "oscillatools.accel.kuramoto_mean_field._python_mean_field_force"
          }
        ],
        "_MEAN_FIELD_JACOBIAN_CHAIN": [
          {
            "tier": "rust",
            "wrapper": "oscillatools.accel.kuramoto_mean_field._rust_mean_field_jacobian"
          },
          {
            "tier": "julia",
            "wrapper": "oscillatools.accel.kuramoto_mean_field._julia_mean_field_jacobian"
          },
          {
            "tier": "python",
            "wrapper": "oscillatools.accel.kuramoto_mean_field._python_mean_field_jacobian"
          }
        ]
      },
      "path": "oscillatools/src/oscillatools/accel/kuramoto_mean_field.py",
      "qualified_name": "oscillatools.accel.kuramoto_mean_field.mean_field_force",
      "signature": "theta: NDArray[np.float64], coupling: float",
      "source_sha256": "36a6b6eef4beaf143dac9ffa6a9c78d4a8517deb9fb2976c3adc026326df2581",
      "summary": "Kuramoto mean-field coupling force with multi-language dispatch."
    },
    "oscillatools.accel.kuramoto_mean_field.mean_field_jacobian": {
      "declaration_sha256": "ee35f35421d8a54d140e4daa75e433ae68accf8d321ae666585a1d9449c84e9a",
      "direct_test_paths": [
        "oscillatools/tests/test_kuramoto_mean_field.py"
      ],
      "dispatch_claim": "source declarations only; availability, selected tier and parity are not measured here",
      "line": 160,
      "module_declared_dispatch_chains": {
        "_MEAN_FIELD_FORCE_CHAIN": [
          {
            "tier": "rust",
            "wrapper": "oscillatools.accel.kuramoto_mean_field._rust_mean_field_force"
          },
          {
            "tier": "julia",
            "wrapper": "oscillatools.accel.kuramoto_mean_field._julia_mean_field_force"
          },
          {
            "tier": "python",
            "wrapper": "oscillatools.accel.kuramoto_mean_field._python_mean_field_force"
          }
        ],
        "_MEAN_FIELD_JACOBIAN_CHAIN": [
          {
            "tier": "rust",
            "wrapper": "oscillatools.accel.kuramoto_mean_field._rust_mean_field_jacobian"
          },
          {
            "tier": "julia",
            "wrapper": "oscillatools.accel.kuramoto_mean_field._julia_mean_field_jacobian"
          },
          {
            "tier": "python",
            "wrapper": "oscillatools.accel.kuramoto_mean_field._python_mean_field_jacobian"
          }
        ]
      },
      "path": "oscillatools/src/oscillatools/accel/kuramoto_mean_field.py",
      "qualified_name": "oscillatools.accel.kuramoto_mean_field.mean_field_jacobian",
      "signature": "theta: NDArray[np.float64], coupling: float",
      "source_sha256": "36a6b6eef4beaf143dac9ffa6a9c78d4a8517deb9fb2976c3adc026326df2581",
      "summary": "Kuramoto synchronisation stability Jacobian with multi-language dispatch."
    },
    "oscillatools.accel.kuramoto_noisy.integrate_noisy_kuramoto": {
      "declaration_sha256": "48438f81544dbaa6bd22d92e23ccb8ceb031af9c6c166211db448d4ec9845706",
      "direct_test_paths": [
        "oscillatools/tests/test_kuramoto_noisy.py"
      ],
      "dispatch_claim": "source declarations only; availability, selected tier and parity are not measured here",
      "line": 143,
      "module_declared_dispatch_chains": {},
      "path": "oscillatools/src/oscillatools/accel/kuramoto_noisy.py",
      "qualified_name": "oscillatools.accel.kuramoto_noisy.integrate_noisy_kuramoto",
      "signature": "initial_phases: NDArray[np.float64], omega: NDArray[np.float64], force: StochasticForce, *, diffusion: float, dt: float, n_steps: int, seed: int, settle_steps: int | None=None",
      "source_sha256": "2ecffee0ecbe402c3e1ec8a3c9e5456ae95ac874e7f0d6c97e77f9c50c7ac1ee",
      "summary": "Integrate the noisy Kuramoto model by a seeded Euler–Maruyama scheme."
    },
    "oscillatools.accel.kuramoto_ott_antonsen.ott_antonsen_field": {
      "declaration_sha256": "aada4d348b068b6f2fc5e6e53cb1205cfae4fc96c20ec5910b1e961073c5d3fb",
      "direct_test_paths": [
        "oscillatools/tests/test_kuramoto_ott_antonsen.py"
      ],
      "dispatch_claim": "source declarations only; availability, selected tier and parity are not measured here",
      "line": 118,
      "module_declared_dispatch_chains": {},
      "path": "oscillatools/src/oscillatools/accel/kuramoto_ott_antonsen.py",
      "qualified_name": "oscillatools.accel.kuramoto_ott_antonsen.ott_antonsen_field",
      "signature": "z: complex, coupling: float, half_width: float, *, centre: float=0.0",
      "source_sha256": "86de2d7e07c5b13b07198ef05fc1a9524307e7606aea61bcebb4fb0e480db614",
      "summary": "Ott–Antonsen vector field ``ż = (iω₀ − Δ + K/2) z − (K/2) |z|² z``."
    },
    "oscillatools.accel.kuramoto_ott_antonsen.ott_antonsen_order_parameter": {
      "declaration_sha256": "64da939a6d729c9087cd5e93402bc8555aa8fab31275b6fc48984544493eae0c",
      "direct_test_paths": [
        "oscillatools/tests/test_kuramoto_ott_antonsen.py"
      ],
      "dispatch_claim": "source declarations only; availability, selected tier and parity are not measured here",
      "line": 189,
      "module_declared_dispatch_chains": {},
      "path": "oscillatools/src/oscillatools/accel/kuramoto_ott_antonsen.py",
      "qualified_name": "oscillatools.accel.kuramoto_ott_antonsen.ott_antonsen_order_parameter",
      "signature": "z0: complex, coupling: float, half_width: float, dt: float, n_steps: int, *, centre: float=0.0",
      "source_sha256": "86de2d7e07c5b13b07198ef05fc1a9524307e7606aea61bcebb4fb0e480db614",
      "summary": "Modulus trajectory ``r(t) = |z(t)|`` of the reduced flow."
    },
    "oscillatools.accel.kuramoto_ott_antonsen.ott_antonsen_terminal_order_parameter_value_and_grad": {
      "declaration_sha256": "5ab77026e402d013948455aa8c085ef49bf4060b95e6481c619a3782917dc136",
      "direct_test_paths": [
        "oscillatools/tests/test_kuramoto_ott_antonsen.py"
      ],
      "dispatch_claim": "source declarations only; availability, selected tier and parity are not measured here",
      "line": 223,
      "module_declared_dispatch_chains": {},
      "path": "oscillatools/src/oscillatools/accel/kuramoto_ott_antonsen.py",
      "qualified_name": "oscillatools.accel.kuramoto_ott_antonsen.ott_antonsen_terminal_order_parameter_value_and_grad",
      "signature": "z0: complex, coupling: float, half_width: float, dt: float, n_steps: int, *, centre: float=0.0",
      "source_sha256": "86de2d7e07c5b13b07198ef05fc1a9524307e7606aea61bcebb4fb0e480db614",
      "summary": "Terminal order parameter ``r(T) = |z(T)|`` and its gradient ``(∂r/∂K, ∂r/∂Δ)``."
    },
    "oscillatools.accel.kuramoto_ott_antonsen.ott_antonsen_trajectory": {
      "declaration_sha256": "f58c0d69cc873dea94f3fb8af4f3ec68e74114a2410d2c429f0d3c56b782562d",
      "direct_test_paths": [
        "oscillatools/tests/test_kuramoto_ott_antonsen.py"
      ],
      "dispatch_claim": "source declarations only; availability, selected tier and parity are not measured here",
      "line": 144,
      "module_declared_dispatch_chains": {},
      "path": "oscillatools/src/oscillatools/accel/kuramoto_ott_antonsen.py",
      "qualified_name": "oscillatools.accel.kuramoto_ott_antonsen.ott_antonsen_trajectory",
      "signature": "z0: complex, coupling: float, half_width: float, dt: float, n_steps: int, *, centre: float=0.0",
      "source_sha256": "86de2d7e07c5b13b07198ef05fc1a9524307e7606aea61bcebb4fb0e480db614",
      "summary": "Integrate the reduced order-parameter flow with RK4."
    },
    "oscillatools.accel.kuramoto_simplex_mean_field.simplex_mean_field_force": {
      "declaration_sha256": "4cb47ca4fbf2292ded9e887001f97edeeaa11cfe04ca50fb2a83158234238c53",
      "direct_test_paths": [
        "oscillatools/tests/test_kuramoto_simplex_mean_field.py"
      ],
      "dispatch_claim": "source declarations only; availability, selected tier and parity are not measured here",
      "line": 48,
      "module_declared_dispatch_chains": {},
      "path": "oscillatools/src/oscillatools/accel/kuramoto_simplex_mean_field.py",
      "qualified_name": "oscillatools.accel.kuramoto_simplex_mean_field.simplex_mean_field_force",
      "signature": "theta: NDArray[np.float64], coupling: float, order: int",
      "source_sha256": "a32db8b16733da4dbee8ff44ea487540e5ddc3a3e02f8f0779c0f7807b2a8a35",
      "summary": "Return the all-to-all ``p``-simplex mean-field force ``F_i = K r^p sin(p ψ − p θ_i)``."
    },
    "oscillatools.accel.kuramoto_simplex_mean_field.simplex_mean_field_jacobian": {
      "declaration_sha256": "11dd1df86e7f49755272532f2b41ac5caeb0b815fcc2abbd80933468c34c8bcf",
      "direct_test_paths": [
        "oscillatools/tests/test_kuramoto_simplex_mean_field.py"
      ],
      "dispatch_claim": "source declarations only; availability, selected tier and parity are not measured here",
      "line": 89,
      "module_declared_dispatch_chains": {},
      "path": "oscillatools/src/oscillatools/accel/kuramoto_simplex_mean_field.py",
      "qualified_name": "oscillatools.accel.kuramoto_simplex_mean_field.simplex_mean_field_jacobian",
      "signature": "theta: NDArray[np.float64], coupling: float, order: int",
      "source_sha256": "a32db8b16733da4dbee8ff44ea487540e5ddc3a3e02f8f0779c0f7807b2a8a35",
      "summary": "Return the ``(N, N)`` stability Jacobian of the ``p``-simplex mean-field force."
    },
    "oscillatools.accel.kuramoto_system.KuramotoSystem.mean_field": {
      "declaration_sha256": "dc855a02c966d5d4b979bc75a40adc6a71fd1b12824f4379b16ba5632cce94f9",
      "direct_test_paths": [
        "oscillatools/tests/test_kuramoto_system.py"
      ],
      "dispatch_claim": "source declarations only; availability, selected tier and parity are not measured here",
      "line": 376,
      "module_declared_dispatch_chains": {},
      "path": "oscillatools/src/oscillatools/accel/kuramoto_system.py",
      "qualified_name": "oscillatools.accel.kuramoto_system.KuramotoSystem.mean_field",
      "signature": "cls, initial_phases: NDArray[np.float64], natural_frequencies: NDArray[np.float64], coupling: float, *, frustration: float=0.0, dt: float, scheme: str='rk4'",
      "source_sha256": "84c57efd93b1d6aad0cfa1117a14660d4b768e04ae7eb9688e623ebcb4ef9fb5",
      "summary": "Build an all-to-all mean-field system from raw arrays."
    },
    "oscillatools.accel.kuramoto_system.KuramotoSystem.networked": {
      "declaration_sha256": "626387ec83930e0940e1d878fab7f289af6ed761810918eb7e32be07033a90d9",
      "direct_test_paths": [
        "oscillatools/tests/test_kuramoto_system.py"
      ],
      "dispatch_claim": "source declarations only; availability, selected tier and parity are not measured here",
      "line": 415,
      "module_declared_dispatch_chains": {},
      "path": "oscillatools/src/oscillatools/accel/kuramoto_system.py",
      "qualified_name": "oscillatools.accel.kuramoto_system.KuramotoSystem.networked",
      "signature": "cls, initial_phases: NDArray[np.float64], natural_frequencies: NDArray[np.float64], coupling: NDArray[np.float64], *, frustration: float=0.0, dt: float, scheme: str='rk4'",
      "source_sha256": "84c57efd93b1d6aad0cfa1117a14660d4b768e04ae7eb9688e623ebcb4ef9fb5",
      "summary": "Build a networked/graph system from raw arrays."
    },
    "oscillatools.accel.kuramoto_watanabe_strogatz.integrate_watanabe_strogatz": {
      "declaration_sha256": "3d68b06f222bad9a3aec0a6b09c5d3653d6afeafcc27855002559eb746b4f9c4",
      "direct_test_paths": [
        "oscillatools/tests/test_kuramoto_watanabe_strogatz.py"
      ],
      "dispatch_claim": "source declarations only; availability, selected tier and parity are not measured here",
      "line": 144,
      "module_declared_dispatch_chains": {},
      "path": "oscillatools/src/oscillatools/accel/kuramoto_watanabe_strogatz.py",
      "qualified_name": "oscillatools.accel.kuramoto_watanabe_strogatz.integrate_watanabe_strogatz",
      "signature": "initial_phases: NDArray[np.float64], *, omega: float, coupling: float, dt: float, n_steps: int",
      "source_sha256": "95dbb1bdc69bed3255437ea0b2e96325cc6b416a4b682eb83163b570529dfdf5",
      "summary": "Integrate the identical-oscillator mean-field Kuramoto flow by the WS reduction."
    },
    "oscillatools.accel.kuramoto_watanabe_strogatz.watanabe_strogatz_order_parameter": {
      "declaration_sha256": "6eb48ee5fc4c5c7c6908a122d22b668fcf0c9cfb41332bcf0e8687fdd4dc68b4",
      "direct_test_paths": [
        "oscillatools/tests/test_kuramoto_watanabe_strogatz.py"
      ],
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      "line": 132,
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      "path": "oscillatools/src/oscillatools/accel/kuramoto_watanabe_strogatz.py",
      "qualified_name": "oscillatools.accel.kuramoto_watanabe_strogatz.watanabe_strogatz_order_parameter",
      "signature": "alpha: complex, beta: complex, constants: NDArray[np.complex128]",
      "source_sha256": "95dbb1bdc69bed3255437ea0b2e96325cc6b416a4b682eb83163b570529dfdf5",
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      "line": 195,
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      "path": "oscillatools/src/oscillatools/accel/multiplex_kuramoto.py",
      "qualified_name": "oscillatools.accel.multiplex_kuramoto.integrate_multiplex",
      "signature": "phases: NDArray[np.float64], omega: NDArray[np.float64], intra_coupling: NDArray[np.float64], inter_coupling: NDArray[np.float64], dt: float, n_steps: int",
      "source_sha256": "9601cf4cb8c0a683a85ffefc82e9d51d1ffc34f6eaee91ad5d508e5214a80f81",
      "summary": "Integrate the multiplex Kuramoto network with classic RK4."
    },
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      "direct_test_paths": [
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      "line": 249,
      "module_declared_dispatch_chains": {},
      "path": "oscillatools/src/oscillatools/accel/multiplex_kuramoto.py",
      "qualified_name": "oscillatools.accel.multiplex_kuramoto.layer_order_parameters",
      "signature": "phases: NDArray[np.float64]",
      "source_sha256": "9601cf4cb8c0a683a85ffefc82e9d51d1ffc34f6eaee91ad5d508e5214a80f81",
      "summary": "Compute the per-layer Kuramoto order-parameter magnitudes ``r_α = |⟨e^{iθ^α}⟩|`` (shape ``(L,)``)."
    },
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      "direct_test_paths": [
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      "dispatch_claim": "source declarations only; availability, selected tier and parity are not measured here",
      "line": 113,
      "module_declared_dispatch_chains": {},
      "path": "oscillatools/src/oscillatools/accel/multiplex_kuramoto.py",
      "qualified_name": "oscillatools.accel.multiplex_kuramoto.multiplex_field",
      "signature": "phases: NDArray[np.float64], omega: NDArray[np.float64], intra_coupling: NDArray[np.float64], inter_coupling: NDArray[np.float64]",
      "source_sha256": "9601cf4cb8c0a683a85ffefc82e9d51d1ffc34f6eaee91ad5d508e5214a80f81",
      "summary": "Evaluate the multiplex Kuramoto vector field ``θ̇`` (shape ``(L, N)``)."
    },
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      "direct_test_paths": [
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      "dispatch_claim": "source declarations only; availability, selected tier and parity are not measured here",
      "line": 151,
      "module_declared_dispatch_chains": {},
      "path": "oscillatools/src/oscillatools/accel/multiplex_kuramoto.py",
      "qualified_name": "oscillatools.accel.multiplex_kuramoto.multiplex_jacobian",
      "signature": "phases: NDArray[np.float64], omega: NDArray[np.float64], intra_coupling: NDArray[np.float64], inter_coupling: NDArray[np.float64]",
      "source_sha256": "9601cf4cb8c0a683a85ffefc82e9d51d1ffc34f6eaee91ad5d508e5214a80f81",
      "summary": "Compute the ``(LN, LN)`` Jacobian of the multiplex field (row-major ``(layer, node)`` order)."
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      "line": 160,
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            "wrapper": "oscillatools.accel.networked_kuramoto._rust_networked_kuramoto_force"
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          {
            "tier": "julia",
            "wrapper": "oscillatools.accel.networked_kuramoto._julia_networked_kuramoto_force"
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          {
            "tier": "python",
            "wrapper": "oscillatools.accel.networked_kuramoto._python_networked_kuramoto_force"
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            "tier": "rust",
            "wrapper": "oscillatools.accel.networked_kuramoto._rust_networked_kuramoto_jacobian"
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          {
            "tier": "julia",
            "wrapper": "oscillatools.accel.networked_kuramoto._julia_networked_kuramoto_jacobian"
          },
          {
            "tier": "python",
            "wrapper": "oscillatools.accel.networked_kuramoto._python_networked_kuramoto_jacobian"
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        ]
      },
      "path": "oscillatools/src/oscillatools/accel/networked_kuramoto.py",
      "qualified_name": "oscillatools.accel.networked_kuramoto.networked_kuramoto_force",
      "signature": "theta: object, coupling: object",
      "source_sha256": "151ff5a506f5f798635c9e9453644ff7f9be3c0530464ca1319f46dd09f5d59b",
      "summary": "Networked Kuramoto coupling force with multi-language dispatch."
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      "dispatch_claim": "source declarations only; availability, selected tier and parity are not measured here",
      "line": 208,
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        "_NETWORKED_KURAMOTO_FORCE_CHAIN": [
          {
            "tier": "rust",
            "wrapper": "oscillatools.accel.networked_kuramoto._rust_networked_kuramoto_force"
          },
          {
            "tier": "julia",
            "wrapper": "oscillatools.accel.networked_kuramoto._julia_networked_kuramoto_force"
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          {
            "tier": "python",
            "wrapper": "oscillatools.accel.networked_kuramoto._python_networked_kuramoto_force"
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        ],
        "_NETWORKED_KURAMOTO_JACOBIAN_CHAIN": [
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            "tier": "rust",
            "wrapper": "oscillatools.accel.networked_kuramoto._rust_networked_kuramoto_jacobian"
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          {
            "tier": "julia",
            "wrapper": "oscillatools.accel.networked_kuramoto._julia_networked_kuramoto_jacobian"
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          {
            "tier": "python",
            "wrapper": "oscillatools.accel.networked_kuramoto._python_networked_kuramoto_jacobian"
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      "path": "oscillatools/src/oscillatools/accel/networked_kuramoto.py",
      "qualified_name": "oscillatools.accel.networked_kuramoto.networked_kuramoto_jacobian",
      "signature": "theta: object, coupling: object",
      "source_sha256": "151ff5a506f5f798635c9e9453644ff7f9be3c0530464ca1319f46dd09f5d59b",
      "summary": "Networked Kuramoto stability Jacobian with multi-language dispatch."
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      "line": 194,
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            "wrapper": "oscillatools.accel.order_parameter_observables._rust_order_parameter"
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          {
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            "wrapper": "oscillatools.accel.order_parameter_observables._julia_order_parameter"
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          {
            "tier": "python",
            "wrapper": "oscillatools.accel.order_parameter_observables._python_order_parameter"
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        "_ORDER_PARAMETER_GRADIENT_CHAIN": [
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            "wrapper": "oscillatools.accel.order_parameter_observables._rust_order_parameter_gradient"
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          {
            "tier": "julia",
            "wrapper": "oscillatools.accel.order_parameter_observables._julia_order_parameter_gradient"
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          {
            "tier": "python",
            "wrapper": "oscillatools.accel.order_parameter_observables._python_order_parameter_gradient"
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        ],
        "_ORDER_PARAMETER_HESSIAN_CHAIN": [
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            "tier": "rust",
            "wrapper": "oscillatools.accel.order_parameter_observables._rust_order_parameter_hessian"
          },
          {
            "tier": "julia",
            "wrapper": "oscillatools.accel.order_parameter_observables._julia_order_parameter_hessian"
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          {
            "tier": "python",
            "wrapper": "oscillatools.accel.order_parameter_observables._python_order_parameter_hessian"
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      "path": "oscillatools/src/oscillatools/accel/order_parameter_observables.py",
      "qualified_name": "oscillatools.accel.order_parameter_observables.order_parameter",
      "signature": "theta: NDArray[np.float64]",
      "source_sha256": "b3616010e0979b665603f18f0a2e60f249124cb1b6186ac3b08687a090ff94cc",
      "summary": "Kuramoto order parameter with multi-language dispatch."
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      "direct_test_paths": [
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      "dispatch_claim": "source declarations only; availability, selected tier and parity are not measured here",
      "line": 159,
      "module_declared_dispatch_chains": {
        "_SAKAGUCHI_FORCE_CHAIN": [
          {
            "tier": "rust",
            "wrapper": "oscillatools.accel.sakaguchi_kuramoto._rust_sakaguchi_force"
          },
          {
            "tier": "julia",
            "wrapper": "oscillatools.accel.sakaguchi_kuramoto._julia_sakaguchi_force"
          },
          {
            "tier": "python",
            "wrapper": "oscillatools.accel.sakaguchi_kuramoto._python_sakaguchi_force"
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        ],
        "_SAKAGUCHI_JACOBIAN_CHAIN": [
          {
            "tier": "rust",
            "wrapper": "oscillatools.accel.sakaguchi_kuramoto._rust_sakaguchi_jacobian"
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          {
            "tier": "julia",
            "wrapper": "oscillatools.accel.sakaguchi_kuramoto._julia_sakaguchi_jacobian"
          },
          {
            "tier": "python",
            "wrapper": "oscillatools.accel.sakaguchi_kuramoto._python_sakaguchi_jacobian"
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        ]
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      "path": "oscillatools/src/oscillatools/accel/sakaguchi_kuramoto.py",
      "qualified_name": "oscillatools.accel.sakaguchi_kuramoto.sakaguchi_force",
      "signature": "theta: NDArray[np.float64], coupling: NDArray[np.float64], frustration: float",
      "source_sha256": "4cab0fae5dc1c46ff7b4222c311d9364fde378cabb0ae96c6c2958c24316608f",
      "summary": "Kuramoto–Sakaguchi frustrated coupling force with multi-language dispatch."
    },
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      "direct_test_paths": [
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      "dispatch_claim": "source declarations only; availability, selected tier and parity are not measured here",
      "line": 198,
      "module_declared_dispatch_chains": {
        "_SAKAGUCHI_FORCE_CHAIN": [
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            "tier": "rust",
            "wrapper": "oscillatools.accel.sakaguchi_kuramoto._rust_sakaguchi_force"
          },
          {
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            "wrapper": "oscillatools.accel.sakaguchi_kuramoto._julia_sakaguchi_force"
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          {
            "tier": "python",
            "wrapper": "oscillatools.accel.sakaguchi_kuramoto._python_sakaguchi_force"
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        ],
        "_SAKAGUCHI_JACOBIAN_CHAIN": [
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            "tier": "rust",
            "wrapper": "oscillatools.accel.sakaguchi_kuramoto._rust_sakaguchi_jacobian"
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          {
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            "wrapper": "oscillatools.accel.sakaguchi_kuramoto._julia_sakaguchi_jacobian"
          },
          {
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            "wrapper": "oscillatools.accel.sakaguchi_kuramoto._python_sakaguchi_jacobian"
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      "path": "oscillatools/src/oscillatools/accel/sakaguchi_kuramoto.py",
      "qualified_name": "oscillatools.accel.sakaguchi_kuramoto.sakaguchi_jacobian",
      "signature": "theta: NDArray[np.float64], coupling: NDArray[np.float64], frustration: float",
      "source_sha256": "4cab0fae5dc1c46ff7b4222c311d9364fde378cabb0ae96c6c2958c24316608f",
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      "dispatch_claim": "source declarations only; availability, selected tier and parity are not measured here",
      "line": 155,
      "module_declared_dispatch_chains": {
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          {
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          {
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        ],
        "_SAKAGUCHI_MEAN_FIELD_JACOBIAN_CHAIN": [
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            "wrapper": "oscillatools.accel.sakaguchi_mean_field._rust_sakaguchi_mean_field_jacobian"
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          {
            "tier": "julia",
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          {
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            "wrapper": "oscillatools.accel.sakaguchi_mean_field._python_sakaguchi_mean_field_jacobian"
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        ]
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      "path": "oscillatools/src/oscillatools/accel/sakaguchi_mean_field.py",
      "qualified_name": "oscillatools.accel.sakaguchi_mean_field.sakaguchi_mean_field_force",
      "signature": "theta: NDArray[np.float64], coupling: float, frustration: float",
      "source_sha256": "20be21199a009c984b428007ef631ab8cc456ea84606c3b266896170604b905c",
      "summary": "Sakaguchi–Kuramoto mean-field force with multi-language dispatch."
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      "dispatch_claim": "source declarations only; availability, selected tier and parity are not measured here",
      "line": 191,
      "module_declared_dispatch_chains": {
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          {
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          {
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        "_SAKAGUCHI_MEAN_FIELD_JACOBIAN_CHAIN": [
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          {
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          {
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            "wrapper": "oscillatools.accel.sakaguchi_mean_field._python_sakaguchi_mean_field_jacobian"
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        ]
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      "path": "oscillatools/src/oscillatools/accel/sakaguchi_mean_field.py",
      "qualified_name": "oscillatools.accel.sakaguchi_mean_field.sakaguchi_mean_field_jacobian",
      "signature": "theta: NDArray[np.float64], coupling: float, frustration: float",
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      "line": 202,
      "module_declared_dispatch_chains": {},
      "path": "oscillatools/src/oscillatools/accel/sparse_kuramoto.py",
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      "signature": "theta0: object, omega: object, coupling: SparseInput, dt: float, n_steps: int",
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      "dispatch_claim": "source declarations only; availability, selected tier and parity are not measured here",
      "line": 224,
      "module_declared_dispatch_chains": {},
      "path": "oscillatools/src/oscillatools/accel/sparse_kuramoto.py",
      "qualified_name": "oscillatools.accel.sparse_kuramoto.sparse_kuramoto_rk4_trajectory",
      "signature": "theta0: object, omega: object, coupling: SparseInput, dt: float, n_steps: int",
      "source_sha256": "88e78bb78bcfed188485ea764068ae084f73844cf84453dc3b259fea6dec79e1",
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      "line": 172,
      "module_declared_dispatch_chains": {},
      "path": "oscillatools/src/oscillatools/accel/sparse_kuramoto.py",
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      "signature": "theta: object, coupling: SparseInput",
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      "line": 156,
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          {
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          {
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        "_TRIADIC_MEAN_FIELD_JACOBIAN_CHAIN": [
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          {
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            "wrapper": "oscillatools.accel.triadic_mean_field._python_triadic_mean_field_jacobian"
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        ]
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      "line": 365,
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      "path": "src/scpn_quantum_control/kuramoto_core.py",
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      "line": 138,
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      "signature": "self, sv: Statevector",
      "source_sha256": "194b8f59048efd20c63f33c224e6262f7d0d65f385c28f10c150154a0acbbb11",
      "summary": "Compute Kuramoto R from qubit X,Y expectations."
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  }
}
