{
  "generated_utc": "2026-09-22T07:33:04.444526+00:00",
  "reproduction": "python scripts/diagnose_phenomt_initial_rates.py --case single_spin high_mass_ratio --sample-rate 2048 16384 --backend torch jax --phase 0.0 0.7 --odd-rate-sweep --output receipt.json",
  "versions": {
    "python": "3.13.7",
    "numpy": "2.5.3",
    "lalsimulation": "6.2.1",
    "torch": "2.14.0",
    "jax": "0.11.2"
  },
  "precession_version": 300,
  "final_spin_mod": 4,
  "dtype": "float64",
  "device": "cpu",
  "conventions": {
    "derivative": "Initial time derivative of the returned unit axis; 9-point one-sided polynomial stencil, with a 5-point stencil sensitivity check.",
    "spin_parity": "Even=(rate(+S1)+rate(-S1))/2; odd=(rate(+S1)-rate(-S1))/2; S2=0, fixed masses/f_ref/source triad. Each J-frame is rotated back using its own initial beta and spin azimuth; initial Lhat=(0,0,1) and the complete Rz(alpha0)Ry(beta0)Rz(gamma0) reference triad are checked.",
    "physics": "Sturani T1500554v23 Eq.21: native even rate is (3/2)*kappa1*(1/x1-1)*v^6*(Lhat.S1)*(Lhat cross S1)/(L_NS*M_seconds), where S1=x1^2*chi1, L_NS is the nonspin 3PN angular momentum and kappa1=1. The v8 term is excluded as in production PV300.",
    "scope": "Binary diagnostic only. Near-zero spin-even behavior does not uniquely identify the reference equations, internal quadrupole parameter, or denominator. Finite differences, reference-frequency anchoring, spin-dependent denominators and axis definitions can affect rates. No production equations are changed.",
    "positive_control": "SpinTaylorT4 public binary with explicit quadparam1/2=0 or 1, spinO=5, tideO=0, phaseO=7, lscorr=0, lambda1/2=0. Spin vectors are chi_i=S_i/m_i^2. This directly measures spin parity without Euler-frame reconstruction; only its initial spin-even rate is compared with native PV300, not its full dynamics.",
    "odd_rate_sweep": "Opt-in sweep uses fixed sample rate 16384 Hz, phase 0, and zero companion spin. Rates and stencil uncertainties are in 1/s. It records signed carrier-frequency anchoring metrics from binary_rate and compares the selected native frontends' odd rates with the independent full v5+v7+v9 over L3PN formula; no residual fitting is performed. The SO numerator follows Sturani Eqs. (3), (22), and (25), with nonspin L from Eq. (5) and the PhenomTP Eq. (13) constraint. Amplitude residuals compare full/(2*half)-1 for each mass/frequency pair."
  },
  "results": [
    {
      "case": "single_spin",
      "in_plane_control": false,
      "parameters": {
        "mass1": 35.0,
        "mass2": 20.0,
        "spin1": [
          0.3,
          0.0,
          0.4
        ],
        "spin2": [
          0.0,
          0.0,
          0.0
        ],
        "distance_mpc": 100.0,
        "inclination": 1.1,
        "phic": 0.0,
        "f_lower_hz": 30.0,
        "f_ref_hz": 30.0
      },
      "sample_rate_hz": 2048,
      "signed_binary_rates": [
        {
          "rate_per_second": [
            2.44027243093913e-09,
            -0.7996234744360335,
            -6.606293024502986e-10
          ],
          "stencil_difference_per_second": 3.080125078451938e-07,
          "initial_axis_error": 1.4576036185475794e-17,
          "initial_triad_error": 1.9929397135264252e-17,
          "initial_carrier_frequency_hz": 29.999999653800884,
          "carrier_frequency_relative_error": 1.1539970534713007e-08,
          "epoch_seconds": -0.371898901
        },
        {
          "rate_per_second": [
            1.1281204623609388e-08,
            0.7996229037593608,
            -1.7365340221652386e-10
          ],
          "stencil_difference_per_second": 9.567459580967598e-08,
          "initial_axis_error": 2.0388215050351914e-17,
          "initial_triad_error": 2.7364864881108245e-17,
          "initial_carrier_frequency_hz": 29.999991954825116,
          "carrier_frequency_relative_error": 2.6817249609845106e-07,
          "epoch_seconds": -0.285069125
        }
      ],
      "binary_even_rate_per_second": [
        6.8607385272742594e-09,
        -2.853383363476958e-07,
        -4.1714135233341125e-10
      ],
      "binary_odd_rate_per_second": [
        -4.420466096335129e-09,
        -0.7996231890976973,
        -2.4348795011688736e-10
      ],
      "native": {
        "torch": {
          "even_rate_per_second": [
            -0.0,
            0.04469737941530805,
            -0.0
          ],
          "odd_rate_per_second": [
            0.0,
            -0.7989968832777151,
            0.0
          ],
          "chi1_even_rate_per_second": [
            0.0,
            -0.10023043972794742,
            0.0
          ]
        },
        "jax": {
          "even_rate_per_second": [
            -0.0,
            0.0446973794153081,
            -0.0
          ],
          "odd_rate_per_second": [
            0.0,
            -0.7989968832777152,
            0.0
          ],
          "chi1_even_rate_per_second": [
            0.0,
            -0.10023043972794742,
            0.0
          ]
        }
      },
      "binary_even_to_odd_norm": 3.569445130024755e-07
    },
    {
      "case": "single_spin",
      "in_plane_control": false,
      "parameters": {
        "mass1": 35.0,
        "mass2": 20.0,
        "spin1": [
          0.3,
          0.0,
          0.4
        ],
        "spin2": [
          0.0,
          0.0,
          0.0
        ],
        "distance_mpc": 100.0,
        "inclination": 1.1,
        "phic": 0.7,
        "f_lower_hz": 30.0,
        "f_ref_hz": 30.0
      },
      "sample_rate_hz": 2048,
      "signed_binary_rates": [
        {
          "rate_per_second": [
            2.44027243093913e-09,
            -0.7996234744369937,
            -6.606293024502986e-10
          ],
          "stencil_difference_per_second": 3.0801314542386375e-07,
          "initial_axis_error": 1.4576036185475794e-17,
          "initial_triad_error": 1.9929397135264252e-17,
          "initial_carrier_frequency_hz": 29.999999653800884,
          "carrier_frequency_relative_error": 1.1539970534713007e-08,
          "epoch_seconds": -0.371898901
        },
        {
          "rate_per_second": [
            1.1281204623609388e-08,
            0.7996229037594367,
            -1.7365340221652386e-10
          ],
          "stencil_difference_per_second": 9.567474510245585e-08,
          "initial_axis_error": 2.0388215050351914e-17,
          "initial_triad_error": 2.7364864881108245e-17,
          "initial_carrier_frequency_hz": 29.999991954825116,
          "carrier_frequency_relative_error": 2.6817249609845106e-07,
          "epoch_seconds": -0.285069125
        }
      ],
      "binary_even_rate_per_second": [
        6.8607385272742594e-09,
        -2.8533877849401534e-07,
        -4.1714135233341125e-10
      ],
      "binary_odd_rate_per_second": [
        -4.420466096335129e-09,
        -0.7996231890982152,
        -2.4348795011688736e-10
      ],
      "native": {
        "torch": {
          "even_rate_per_second": [
            -0.0,
            0.04469737941530805,
            -0.0
          ],
          "odd_rate_per_second": [
            0.0,
            -0.7989968832777151,
            0.0
          ],
          "chi1_even_rate_per_second": [
            0.0,
            -0.10023043972794742,
            0.0
          ]
        },
        "jax": {
          "even_rate_per_second": [
            -0.0,
            0.0446973794153081,
            -0.0
          ],
          "odd_rate_per_second": [
            0.0,
            -0.7989968832777152,
            0.0
          ],
          "chi1_even_rate_per_second": [
            0.0,
            -0.10023043972794742,
            0.0
          ]
        }
      },
      "binary_even_to_odd_norm": 3.5694506578523165e-07
    },
    {
      "case": "single_spin",
      "in_plane_control": false,
      "parameters": {
        "mass1": 35.0,
        "mass2": 20.0,
        "spin1": [
          0.3,
          0.0,
          0.4
        ],
        "spin2": [
          0.0,
          0.0,
          0.0
        ],
        "distance_mpc": 100.0,
        "inclination": 1.1,
        "phic": 0.0,
        "f_lower_hz": 30.0,
        "f_ref_hz": 30.0
      },
      "sample_rate_hz": 16384,
      "signed_binary_rates": [
        {
          "rate_per_second": [
            -1.0240947747641867e-09,
            -0.7996231224942111,
            -1.4916369489720792e-12
          ],
          "stencil_difference_per_second": 2.5219832205802613e-09,
          "initial_axis_error": 1.4576036185475794e-17,
          "initial_triad_error": 1.9929397135264252e-17,
          "initial_carrier_frequency_hz": 29.999999648605495,
          "carrier_frequency_relative_error": 1.1713150116499094e-08,
          "epoch_seconds": -0.371898901
        },
        {
          "rate_per_second": [
            1.0993113940237372e-10,
            0.7996227182601605,
            -1.0304156966714304e-12
          ],
          "stencil_difference_per_second": 1.3277383448160782e-09,
          "initial_axis_error": 2.0388215050351914e-17,
          "initial_triad_error": 2.7364864881108245e-17,
          "initial_carrier_frequency_hz": 29.999991962997154,
          "carrier_frequency_relative_error": 2.679000948857535e-07,
          "epoch_seconds": -0.285069125
        }
      ],
      "binary_even_rate_per_second": [
        -4.570818176809065e-10,
        -2.0211702528305509e-07,
        -1.2610263228217548e-12
      ],
      "binary_odd_rate_per_second": [
        -5.670129570832802e-10,
        -0.7996229203771859,
        -2.306106261503244e-13
      ],
      "native": {
        "torch": {
          "even_rate_per_second": [
            -0.0,
            0.04469737941530805,
            -0.0
          ],
          "odd_rate_per_second": [
            0.0,
            -0.7989968832777151,
            0.0
          ],
          "chi1_even_rate_per_second": [
            0.0,
            -0.10023043972794742,
            0.0
          ]
        },
        "jax": {
          "even_rate_per_second": [
            -0.0,
            0.0446973794153081,
            -0.0
          ],
          "odd_rate_per_second": [
            0.0,
            -0.7989968832777152,
            0.0
          ],
          "chi1_even_rate_per_second": [
            0.0,
            -0.10023043972794742,
            0.0
          ]
        }
      },
      "binary_even_to_odd_norm": 2.5276606882360977e-07
    },
    {
      "case": "single_spin",
      "in_plane_control": false,
      "parameters": {
        "mass1": 35.0,
        "mass2": 20.0,
        "spin1": [
          0.3,
          0.0,
          0.4
        ],
        "spin2": [
          0.0,
          0.0,
          0.0
        ],
        "distance_mpc": 100.0,
        "inclination": 1.1,
        "phic": 0.7,
        "f_lower_hz": 30.0,
        "f_ref_hz": 30.0
      },
      "sample_rate_hz": 16384,
      "signed_binary_rates": [
        {
          "rate_per_second": [
            -1.0240947747641867e-09,
            -0.7996231224785357,
            -1.4916369489720792e-12
          ],
          "stencil_difference_per_second": 2.5091421097728343e-09,
          "initial_axis_error": 1.4576036185475794e-17,
          "initial_triad_error": 1.9929397135264252e-17,
          "initial_carrier_frequency_hz": 29.999999648605495,
          "carrier_frequency_relative_error": 1.1713150116499094e-08,
          "epoch_seconds": -0.371898901
        },
        {
          "rate_per_second": [
            1.0993113940237372e-10,
            0.7996227182654052,
            -1.0304156966714304e-12
          ],
          "stencil_difference_per_second": 1.333476353892297e-09,
          "initial_axis_error": 2.0388215050351914e-17,
          "initial_triad_error": 2.7364864881108245e-17,
          "initial_carrier_frequency_hz": 29.999991962997154,
          "carrier_frequency_relative_error": 2.679000948857535e-07,
          "epoch_seconds": -0.285069125
        }
      ],
      "binary_even_rate_per_second": [
        -4.570818176809065e-10,
        -2.0210656526131743e-07,
        -1.2610263228217548e-12
      ],
      "binary_odd_rate_per_second": [
        -5.670129570832802e-10,
        -0.7996229203719705,
        -2.306106261503244e-13
      ],
      "native": {
        "torch": {
          "even_rate_per_second": [
            -0.0,
            0.04469737941530805,
            -0.0
          ],
          "odd_rate_per_second": [
            0.0,
            -0.7989968832777151,
            0.0
          ],
          "chi1_even_rate_per_second": [
            0.0,
            -0.10023043972794742,
            0.0
          ]
        },
        "jax": {
          "even_rate_per_second": [
            -0.0,
            0.0446973794153081,
            -0.0
          ],
          "odd_rate_per_second": [
            0.0,
            -0.7989968832777152,
            0.0
          ],
          "chi1_even_rate_per_second": [
            0.0,
            -0.10023043972794742,
            0.0
          ]
        }
      },
      "binary_even_to_odd_norm": 2.527529876657242e-07
    },
    {
      "case": "single_spin",
      "in_plane_control": true,
      "parameters": {
        "mass1": 35.0,
        "mass2": 20.0,
        "spin1": [
          0.3,
          0.0,
          0.0
        ],
        "spin2": [
          0.0,
          0.0,
          0.0
        ],
        "distance_mpc": 100.0,
        "inclination": 1.1,
        "phic": 0.0,
        "f_lower_hz": 30.0,
        "f_ref_hz": 30.0
      },
      "sample_rate_hz": 2048,
      "signed_binary_rates": [
        {
          "rate_per_second": [
            -2.4670832647625178e-08,
            -0.7996235502469354,
            -7.33932236015911e-10
          ],
          "stencil_difference_per_second": 3.467693196695801e-07,
          "initial_axis_error": 1.655380591496271e-17,
          "initial_triad_error": 2.306654588333982e-17,
          "initial_carrier_frequency_hz": 30.00000000008537,
          "carrier_frequency_relative_error": 2.8457236567192012e-12,
          "epoch_seconds": -0.327520047
        },
        {
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            -7.339322230025931e-10
          ],
          "stencil_difference_per_second": 3.467716510475366e-07,
          "initial_axis_error": 1.655380591496271e-17,
          "initial_triad_error": 2.306654588333982e-17,
          "initial_carrier_frequency_hz": 30.00000000008537,
          "carrier_frequency_relative_error": 2.8457236567192012e-12,
          "epoch_seconds": -0.327520047
        }
      ],
      "binary_even_rate_per_second": [
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        1.3551937350086973e-12,
        -7.33932229509252e-10
      ],
      "binary_odd_rate_per_second": [
        -2.4670832647190918e-08,
        -0.7996235502482907,
        -6.506658946623769e-18
      ],
      "native": {
        "torch": {
          "even_rate_per_second": [
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            0.0,
            -0.0
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          "odd_rate_per_second": [
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            -0.7989968832777151,
            0.0
          ],
          "chi1_even_rate_per_second": [
            0.0,
            0.0,
            0.0
          ]
        },
        "jax": {
          "even_rate_per_second": [
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            0.0,
            -0.0
          ],
          "odd_rate_per_second": [
            0.0,
            -0.7989968832777152,
            0.0
          ],
          "chi1_even_rate_per_second": [
            0.0,
            0.0,
            0.0
          ]
        }
      },
      "binary_even_to_odd_norm": 9.178487557697767e-10
    },
    {
      "case": "single_spin",
      "in_plane_control": true,
      "parameters": {
        "mass1": 35.0,
        "mass2": 20.0,
        "spin1": [
          0.3,
          0.0,
          0.0
        ],
        "spin2": [
          0.0,
          0.0,
          0.0
        ],
        "distance_mpc": 100.0,
        "inclination": 1.1,
        "phic": 0.7,
        "f_lower_hz": 30.0,
        "f_ref_hz": 30.0
      },
      "sample_rate_hz": 2048,
      "signed_binary_rates": [
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          "rate_per_second": [
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            -7.33932236015911e-10
          ],
          "stencil_difference_per_second": 3.4677066935059124e-07,
          "initial_axis_error": 4.284782081263001e-17,
          "initial_triad_error": 6.057882960316446e-17,
          "initial_carrier_frequency_hz": 30.00000000008537,
          "carrier_frequency_relative_error": 2.8457236567192012e-12,
          "epoch_seconds": -0.327520047
        },
        {
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          ],
          "stencil_difference_per_second": 3.4677037689017293e-07,
          "initial_axis_error": 1.655380591496271e-17,
          "initial_triad_error": 2.306654588333982e-17,
          "initial_carrier_frequency_hz": 30.00000000008537,
          "carrier_frequency_relative_error": 2.8457236567192012e-12,
          "epoch_seconds": -0.327520047
        }
      ],
      "binary_even_rate_per_second": [
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        -1.1657341758564144e-13,
        -7.33932229509252e-10
      ],
      "binary_odd_rate_per_second": [
        -2.4670832647190918e-08,
        -0.7996235502484044,
        -6.506658946623769e-18
      ],
      "native": {
        "torch": {
          "even_rate_per_second": [
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            0.0,
            -0.0
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          "odd_rate_per_second": [
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            0.0
          ],
          "chi1_even_rate_per_second": [
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            0.0,
            0.0
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        },
        "jax": {
          "even_rate_per_second": [
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            0.0,
            -0.0
          ],
          "odd_rate_per_second": [
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            -0.7989968832777152,
            0.0
          ],
          "chi1_even_rate_per_second": [
            0.0,
            0.0,
            0.0
          ]
        }
      },
      "binary_even_to_odd_norm": 9.178472026482557e-10
    },
    {
      "case": "single_spin",
      "in_plane_control": true,
      "parameters": {
        "mass1": 35.0,
        "mass2": 20.0,
        "spin1": [
          0.3,
          0.0,
          0.0
        ],
        "spin2": [
          0.0,
          0.0,
          0.0
        ],
        "distance_mpc": 100.0,
        "inclination": 1.1,
        "phic": 0.0,
        "f_lower_hz": 30.0,
        "f_ref_hz": 30.0
      },
      "sample_rate_hz": 16384,
      "signed_binary_rates": [
        {
          "rate_per_second": [
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            -0.7996231402853592,
            -6.550147659401569e-13
          ],
          "stencil_difference_per_second": 1.8368882943273314e-09,
          "initial_axis_error": 1.655380591496271e-17,
          "initial_triad_error": 2.306654588333982e-17,
          "initial_carrier_frequency_hz": 30.000000004094964,
          "carrier_frequency_relative_error": 1.3649881225319405e-10,
          "epoch_seconds": -0.327520047
        },
        {
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          ],
          "stencil_difference_per_second": 1.8600951205481364e-09,
          "initial_axis_error": 1.655380591496271e-17,
          "initial_triad_error": 2.306654588333982e-17,
          "initial_carrier_frequency_hz": 30.000000004094964,
          "carrier_frequency_relative_error": 1.3649881225319405e-10,
          "epoch_seconds": -0.327520047
        }
      ],
      "binary_even_rate_per_second": [
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        1.3352874361771683e-11,
        -6.550082592844738e-13
      ],
      "binary_odd_rate_per_second": [
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        -0.7996231402987121,
        -6.506655683137759e-18
      ],
      "native": {
        "torch": {
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          "odd_rate_per_second": [
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          "chi1_even_rate_per_second": [
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        },
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