{
  "generated_utc": "2026-09-22T07:34:27.692947+00:00",
  "reproduction": "python scripts/diagnose_phenomt_rotation.py --backend torch --case baseline high_mass_ratio --only22 0 --sample-rate 2048 --samples 257 --output receipt.json --reference-check --reference-backend torch --reference-case baseline high_mass_ratio --reference-rate 512 2048 8192 --reference-distance 50.0 100.0 200.0",
  "versions": {
    "python": "3.13.7",
    "numpy": "2.5.3",
    "lalsimulation": "6.2.1",
    "mpmath": "1.3.0",
    "torch": "2.14.0"
  },
  "dtype": "float64",
  "device": "cpu",
  "precession_version": 300,
  "final_spin_mod": 4,
  "parameters": {
    "baseline": {
      "mass1": 40.0,
      "mass2": 15.0,
      "spin1": [
        0.2,
        0.1,
        0.3
      ],
      "spin2": [
        0.0,
        0.1,
        -0.2
      ],
      "distance_mpc": 100.0,
      "inclination": 0.8,
      "phic": 0.3,
      "f_lower_hz": 20.0,
      "f_ref_hz": 20.0
    },
    "high_mass_ratio": {
      "mass1": 60.0,
      "mass2": 6.0,
      "spin1": [
        0.2,
        0.1,
        0.8
      ],
      "spin2": [
        0.1,
        0.0,
        0.1
      ],
      "distance_mpc": 100.0,
      "inclination": 1.2,
      "phic": 0.1,
      "f_lower_hz": 20.0,
      "f_ref_hz": 20.0
    }
  },
  "scope": "Isolated project_modes rotation/convention checks against public binary J-frame and L0 modes; does not validate native spin evolution, carrier, or physical waveform accuracy.",
  "conventions": {
    "angles": "Public alpha, acos(cosbeta), epsilon series are passed as alpha,beta,gamma.",
    "projection": "J-frame modes are projected at phi=0 with exp(2 i zeta), matching project_modes.",
    "modes": "only22=1 checks the complete l=2 set; only22=0 checks all available l=2..5 signed modes.",
    "relative_l2": "norm(project_modes output - direct J-frame projection)/norm(direct projection).",
    "inverse_l0": "For f_ref=f_min=20 Hz, Eq. 8 uses constants (-gamma_ref,-beta_ref,-alpha_ref) on all signed J modes and compares with public L0Modes.",
    "inverse_l0_status": "Full-mode inverse values are measured diagnostics; only22 inverse values are suitable for the strict convention check.",
    "reference_check": "At the initial f_ref=f_min sample, Eq. 8 implies coprec=L0. Per-ell relative metrics divide by the corresponding mode-vector norm; absolute metrics use strain units. Reference rows override the listed sample rate and distance. The factorial Wigner oracle uses 80 decimal digits, then rounds to complex128 before matrix-vector multiplication."
  },
  "results": [
    {
      "case": "baseline",
      "backend": "torch",
      "only22": 0,
      "sample_rate_hz": 2048,
      "modes": [
        [
          2,
          -2
        ],
        [
          2,
          -1
        ],
        [
          2,
          0
        ],
        [
          2,
          1
        ],
        [
          2,
          2
        ],
        [
          3,
          -3
        ],
        [
          3,
          -2
        ],
        [
          3,
          -1
        ],
        [
          3,
          0
        ],
        [
          3,
          1
        ],
        [
          3,
          2
        ],
        [
          3,
          3
        ],
        [
          4,
          -4
        ],
        [
          4,
          -3
        ],
        [
          4,
          -2
        ],
        [
          4,
          -1
        ],
        [
          4,
          0
        ],
        [
          4,
          1
        ],
        [
          4,
          2
        ],
        [
          4,
          3
        ],
        [
          4,
          4
        ],
        [
          5,
          -5
        ],
        [
          5,
          -4
        ],
        [
          5,
          -3
        ],
        [
          5,
          -2
        ],
        [
          5,
          -1
        ],
        [
          5,
          0
        ],
        [
          5,
          1
        ],
        [
          5,
          2
        ],
        [
          5,
          3
        ],
        [
          5,
          4
        ],
        [
          5,
          5
        ]
      ],
      "views": [
        {
          "theta_jn": 0.3,
          "zeta": 0.2,
          "relative_l2": 6.387219514179623e-16,
          "max_absolute": 3.803664322502939e-36,
          "reference_norm": 2.5298474394309068e-20,
          "input_mode_norm": 6.014317582269544e-20,
          "samples": 257
        },
        {
          "theta_jn": 1.1,
          "zeta": -0.4,
          "relative_l2": 6.818108503237445e-16,
          "max_absolute": 4.817175275977972e-36,
          "reference_norm": 1.4615773189370824e-20,
          "input_mode_norm": 6.014317582269544e-20,
          "samples": 257
        },
        {
          "theta_jn": 2.0,
          "zeta": 1.0,
          "relative_l2": 6.266690321561551e-16,
          "max_absolute": 3.4680071765448715e-36,
          "reference_norm": 1.3811664119568575e-20,
          "input_mode_norm": 6.014317582269544e-20,
          "samples": 257
        }
      ],
      "inverse_l0": {
        "status": "measured",
        "reason": "Full signed-mode inverse residual is reported for diagnosis; no full-mode accuracy gate is claimed.",
        "views": [
          {
            "theta_l0": 0.3,
            "zeta": 0.2,
            "relative_l2": 7.040561884408283e-11,
            "max_absolute": 8.296041157874905e-31,
            "reference_norm": 2.5934415597416512e-20,
            "input_j_mode_norm": 6.014317582269536e-20,
            "per_ell": [
              {
                "ell": 2,
                "projected_relative_l2": 1.8026790185095202e-16,
                "max_absolute": 8.411152881937987e-37,
                "reference_norm": 2.5914219146053566e-20,
                "input_j_mode_norm": 5.972937117995809e-20
              },
              {
                "ell": 3,
                "projected_relative_l2": 3.5224451820698834e-16,
                "max_absolute": 8.737489915704332e-38,
                "reference_norm": 9.3783610476186e-22,
                "input_j_mode_norm": 6.737429534490838e-21
              },
              {
                "ell": 4,
                "projected_relative_l2": 8.058491087077777e-16,
                "max_absolute": 3.009178902981709e-38,
                "reference_norm": 8.971275045232096e-23,
                "input_j_mode_norm": 1.962870793000515e-21
              },
              {
                "ell": 5,
                "projected_relative_l2": 2.231410512484712e-07,
                "max_absolute": 8.296080178840757e-31,
                "reference_norm": 8.18285088978799e-24,
                "input_j_mode_norm": 5.983293442608767e-22
              }
            ],
            "samples": 257
          },
          {
            "theta_l0": 1.1,
            "zeta": -0.4,
            "relative_l2": 9.094768180217095e-11,
            "max_absolute": 6.723126531672993e-31,
            "reference_norm": 1.6270091951505218e-20,
            "input_j_mode_norm": 6.014317582269536e-20,
            "per_ell": [
              {
                "ell": 2,
                "projected_relative_l2": 1.5531932660099047e-16,
                "max_absolute": 5.3196801709626755e-37,
                "reference_norm": 1.6193235330635287e-20,
                "input_j_mode_norm": 5.972937117995809e-20
              },
              {
                "ell": 3,
                "projected_relative_l2": 2.7300205248722605e-16,
                "max_absolute": 1.8844608008273444e-37,
                "reference_norm": 2.1484016306601667e-21,
                "input_j_mode_norm": 6.737429534490838e-21
              },
              {
                "ell": 4,
                "projected_relative_l2": 2.2573864445215513e-16,
                "max_absolute": 9.991701981989444e-38,
                "reference_norm": 6.334435582052851e-22,
                "input_j_mode_norm": 1.962870793000515e-21
              },
              {
                "ell": 5,
                "projected_relative_l2": 8.500887989876648e-09,
                "max_absolute": 6.723107268031765e-31,
                "reference_norm": 1.740671881780847e-22,
                "input_j_mode_norm": 5.983293442608767e-22
              }
            ],
            "samples": 257
          },
          {
            "theta_l0": 2.0,
            "zeta": 1.0,
            "relative_l2": 1.0359135208804736e-10,
            "max_absolute": 5.811231777170905e-31,
            "reference_norm": 1.2346870608476853e-20,
            "input_j_mode_norm": 6.014317582269536e-20,
            "per_ell": [
              {
                "ell": 2,
                "projected_relative_l2": 3.1611447822303643e-16,
                "max_absolute": 7.754699793211446e-37,
                "reference_norm": 1.2340685507607298e-20,
                "input_j_mode_norm": 5.972937117995809e-20
              },
              {
                "ell": 3,
                "projected_relative_l2": 5.320151224998886e-16,
                "max_absolute": 2.741700404922865e-37,
                "reference_norm": 1.7899313917300267e-21,
                "input_j_mode_norm": 6.737429534490838e-21
              },
              {
                "ell": 4,
                "projected_relative_l2": 6.317080394443852e-16,
                "max_absolute": 2.1289108148801267e-37,
                "reference_norm": 6.251106196344789e-22,
                "input_j_mode_norm": 1.962870793000515e-21
              },
              {
                "ell": 5,
                "projected_relative_l2": 6.772584042288993e-09,
                "max_absolute": 5.811244227587714e-31,
                "reference_norm": 1.8885387231613556e-22,
                "input_j_mode_norm": 5.983293442608767e-22
              }
            ],
            "samples": 257
          }
        ]
      }
    },
    {
      "case": "high_mass_ratio",
      "backend": "torch",
      "only22": 0,
      "sample_rate_hz": 2048,
      "modes": [
        [
          2,
          -2
        ],
        [
          2,
          -1
        ],
        [
          2,
          0
        ],
        [
          2,
          1
        ],
        [
          2,
          2
        ],
        [
          3,
          -3
        ],
        [
          3,
          -2
        ],
        [
          3,
          -1
        ],
        [
          3,
          0
        ],
        [
          3,
          1
        ],
        [
          3,
          2
        ],
        [
          3,
          3
        ],
        [
          4,
          -4
        ],
        [
          4,
          -3
        ],
        [
          4,
          -2
        ],
        [
          4,
          -1
        ],
        [
          4,
          0
        ],
        [
          4,
          1
        ],
        [
          4,
          2
        ],
        [
          4,
          3
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        [
          4,
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        ],
        [
          5,
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        ],
        [
          5,
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        ],
        [
          5,
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        ],
        [
          5,
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        ],
        [
          5,
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        [
          5,
          4
        ],
        [
          5,
          5
        ]
      ],
      "views": [
        {
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          "relative_l2": 5.874562281376403e-16,
          "max_absolute": 2.071006217084368e-36,
          "reference_norm": 1.405833357326126e-20,
          "input_mode_norm": 3.4069248673063466e-20,
          "samples": 257
        },
        {
          "theta_jn": 1.1,
          "zeta": -0.4,
          "relative_l2": 7.128128529753002e-16,
          "max_absolute": 1.698579168271515e-36,
          "reference_norm": 8.591821625350258e-21,
          "input_mode_norm": 3.4069248673063466e-20,
          "samples": 257
        },
        {
          "theta_jn": 2.0,
          "zeta": 1.0,
          "relative_l2": 7.4678003158313e-16,
          "max_absolute": 1.8064407284917394e-36,
          "reference_norm": 8.217822084479762e-21,
          "input_mode_norm": 3.4069248673063466e-20,
          "samples": 257
        }
      ],
      "inverse_l0": {
        "status": "measured",
        "reason": "Full signed-mode inverse residual is reported for diagnosis; no full-mode accuracy gate is claimed.",
        "views": [
          {
            "theta_l0": 0.3,
            "zeta": 0.2,
            "relative_l2": 8.069744912424537e-10,
            "max_absolute": 3.686579563094992e-30,
            "reference_norm": 1.4447049869538976e-20,
            "input_j_mode_norm": 3.4069248673063466e-20,
            "per_ell": [
              {
                "ell": 2,
                "projected_relative_l2": 1.9272431195724264e-16,
                "max_absolute": 7.754699793211446e-37,
                "reference_norm": 1.4408613245797977e-20,
                "input_j_mode_norm": 3.326654917008428e-20
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                "max_absolute": 1.2758988097162341e-37,
                "reference_norm": 1.0144436847080924e-21,
                "input_j_mode_norm": 6.968807105666899e-21
              },
              {
                "ell": 4,
                "projected_relative_l2": 6.437558182100099e-16,
                "max_absolute": 2.387228350066198e-38,
                "reference_norm": 1.1766100978661892e-22,
                "input_j_mode_norm": 2.197605869671317e-21
              },
              {
                "ell": 5,
                "projected_relative_l2": 7.372911849913149e-07,
                "max_absolute": 3.6865814997014564e-30,
                "reference_norm": 1.5812479068511443e-23,
                "input_j_mode_norm": 8.103501878782097e-22
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            ],
            "samples": 257
          },
          {
            "theta_l0": 1.1,
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            "max_absolute": 3.0162265799057096e-30,
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              {
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                "input_j_mode_norm": 8.103501878782097e-22
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            "samples": 257
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          {
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                "input_j_mode_norm": 6.968807105666899e-21
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              {
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                "reference_norm": 6.746338011502005e-22,
                "input_j_mode_norm": 2.197605869671317e-21
              },
              {
                "ell": 5,
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                "reference_norm": 2.699917979098083e-22,
                "input_j_mode_norm": 8.103501878782097e-22
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            ],
            "samples": 257
          }
        ]
      }
    }
  ],
  "reference_results": [
    {
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      "case": "baseline",
      "sample_rate_hz": 512,
      "distance_mpc": 50.0,
      "reference_angles": {
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        "beta": 0.1217976388304497,
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      "rows": [
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          "coprec_l0": {
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            "max_over_m_absolute": 1.5679092305554883e-37,
            "max_over_m_m": 1,
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          "pm2_amplitudes": {
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            "inverse_predicted": {
              "-2": 4.095188366235871e-21,
              "2": 4.09518836623587e-21
            },
            "l0_public": {
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              "2": 4.09518836623587e-21
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          },
          "native_matrix_unitarity_error": 7.050858231721621e-16,
          "native_forward_relative_l2": 2.6221510344424096e-16,
          "native_roundtrip_relative_l2": 2.95745192485576e-16,
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            "native_matrix_relative_l2": 1.7099884775664954e-16,
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          "coprec_norm": 5.7946757296741294e-21,
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        {
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          "pm2_amplitudes": {
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              "2": 2.938735877055719e-39
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          },
          "native_matrix_unitarity_error": 6.803879321178177e-16,
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        {
          "ell": 4,
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          "coprec_l0": {
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            "pm2_max_absolute": 7.572949016808052e-40
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          "inverse_l0": {
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