{
  "schema": "ferrofinder.endpoint_parent_recovery.v4_variable_cell",
  "status": "complete",
  "input_atom_count": 24,
  "input_formula": "F20V4",
  "input_spacegroup": "Cc",
  "input_pointgroup": "m",
  "input_is_polar_point_group": true,
  "input_energy_eV": -121.1230623072979,
  "input_cartesian_polarization_e_A2": [
    0.00017099709345205674,
    1.0498028025128461e-17,
    -0.0005549840288170199
  ],
  "input_reduced_polarization": [
    0.006522297247876223,
    7.394187310515106e-16,
    -0.02428302766870887
  ],
  "input_formal_targets": [
    {
      "orbit_id": 0,
      "representative_formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ]
    },
    {
      "orbit_id": 1,
      "representative_formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        -0.5
      ]
    },
    {
      "orbit_id": 2,
      "representative_formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.0
      ]
    },
    {
      "orbit_id": 3,
      "representative_formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.0
      ]
    },
    {
      "orbit_id": 4,
      "representative_formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        0.5,
        0.0,
        -0.5
      ]
    },
    {
      "orbit_id": 5,
      "representative_formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        -0.5
      ]
    },
    {
      "orbit_id": 6,
      "representative_formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        0.5,
        0.5,
        0.0
      ]
    },
    {
      "orbit_id": 7,
      "representative_formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "target_reduced_polarization": [
        0.5,
        0.5,
        -0.5
      ]
    }
  ],
  "parent_candidates": [
    {
      "candidate_id": "inversion_parent_endpoint_00",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "C2/c",
      "spacegroup_number": 15,
      "pointgroup": "2/m",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 1.8183053300193245e-15,
      "parent_symmetrization_rmsd_A": 0.03651097669099196,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -121.12940121026642,
      "reduced_polarization": [
        1.4410961255617084e-15,
        1.6981225830658563e-16,
        1.0957372070877831e-15
      ],
      "cartesian_polarization_e_A2": [
        3.782240914512356e-17,
        2.4109395283748907e-18,
        7.16644677238433e-18
      ],
      "ranking_score": 0.036510976690995595
    },
    {
      "candidate_id": "symmetry_projection_00",
      "source": "spglib_refine_cell_from_polar_endpoint",
      "spacegroup": "C2/c",
      "spacegroup_number": 15,
      "pointgroup": "2/m",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 1.4446871858062444e-15,
      "parent_symmetrization_rmsd_A": 1.1784196813653542,
      "parent_cell_rmsd_A": 4.97458097254917e-16,
      "energy_eV": -120.86568023081745,
      "reduced_polarization": [
        -4.529760011420968e-16,
        -1.339778604907078e-15,
        -2.9483401610961507e-16
      ],
      "cartesian_polarization_e_A2": [
        -1.0607043396422656e-17,
        -1.9021743365603463e-17,
        -5.513739117001772e-18
      ],
      "ranking_score": 1.1784196813653574
    },
    {
      "candidate_id": "bec_projection_00",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cc",
      "spacegroup_number": 9,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 1.0549089703718078e-05,
      "parent_symmetrization_rmsd_A": 0.008886684253787861,
      "parent_cell_rmsd_A": 0.00023966724576222057,
      "energy_eV": -121.12226610764354,
      "reduced_polarization": [
        3.003961825806484e-06,
        3.1823481780909194e-16,
        1.0112344284397567e-05
      ],
      "cartesian_polarization_e_A2": [
        7.889244554181978e-08,
        4.51824738389038e-18,
        1.721939867099631e-07
      ],
      "ranking_score": 0.5089676992446358
    },
    {
      "candidate_id": "inversion_parent_bec_00_00",
      "source": "same_species_inversion_center_projection_after_BEC",
      "spacegroup": "C2/c",
      "spacegroup_number": 15,
      "pointgroup": "2/m",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 1.1397487183481447e-15,
      "parent_symmetrization_rmsd_A": 0.0365110150180678,
      "parent_cell_rmsd_A": 0.00023966724576222057,
      "energy_eV": -121.12935741927184,
      "reduced_polarization": [
        -7.289970619045137e-16,
        -3.4363244033546017e-16,
        8.059200770919667e-16
      ],
      "cartesian_polarization_e_A2": [
        -1.9124430970374278e-17,
        -4.878947805293394e-18,
        2.3698623962465186e-17
      ],
      "ranking_score": 0.036570931829510635
    },
    {
      "candidate_id": "symmetry_parent_00_00",
      "source": "spglib_refine_cell_after_MACEField_BEC_backprojection",
      "spacegroup": "C2/c",
      "spacegroup_number": 15,
      "pointgroup": "2/m",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 1.5350762690379127e-15,
      "parent_symmetrization_rmsd_A": 1.1792607583505956,
      "parent_cell_rmsd_A": 0.00023966724576335034,
      "energy_eV": -120.79419504948054,
      "reduced_polarization": [
        -4.062616763088205e-16,
        -2.032378635447088e-16,
        -1.466323624902732e-15
      ],
      "cartesian_polarization_e_A2": [
        -6.983930117415743e-19,
        -2.8856033712241084e-18,
        -2.7422188144454855e-17
      ],
      "ranking_score": 1.1793206751620395
    },
    {
      "candidate_id": "bec_projection_01",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cc",
      "spacegroup_number": 9,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        -0.5
      ],
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_residual": 0.0002551938892276833,
      "parent_symmetrization_rmsd_A": 0.14454544071314235,
      "parent_cell_rmsd_A": 0.0030380703371748843,
      "energy_eV": -120.86157816318678,
      "reduced_polarization": [
        -2.451197438514577e-06,
        4.36179802638097e-16,
        -0.49974481788320835
      ],
      "cartesian_polarization_e_A2": [
        -3.7795655333606522e-06,
        -1.5221653288574733e-17,
        -0.010040439176011641
      ],
      "ranking_score": 0.6458153460758914
    },
    {
      "candidate_id": "bec_projection_02",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cc",
      "spacegroup_number": 9,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.0
      ],
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_residual": 0.0005026303275029681,
      "parent_symmetrization_rmsd_A": 0.2785946851016702,
      "parent_cell_rmsd_A": 0.008463497724797013,
      "energy_eV": -111.78594027891216,
      "reduced_polarization": [
        0.49991241330553554,
        -7.039822819519281e-15,
        0.000494940215660973
      ],
      "cartesian_polarization_e_A2": [
        0.013108481111689172,
        -2.5892474594196107e-16,
        -0.005145881622232331
      ],
      "ranking_score": 0.7817158201878753
    },
    {
      "candidate_id": "bec_projection_03",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.0
      ],
      "formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_residual": 1.6801949156180803e-05,
      "parent_symmetrization_rmsd_A": 0.14280045641466557,
      "parent_cell_rmsd_A": 0.003989275635696312,
      "energy_eV": -118.78713548569159,
      "reduced_polarization": [
        -1.830749709164968e-06,
        0.5000027640653834,
        1.6471605674791457e-05
      ],
      "cartesian_polarization_e_A2": [
        5.270026209441404e-06,
        0.007099123726329184,
        2.62033912072481e-06
      ],
      "ranking_score": 0.643831379221902
    },
    {
      "candidate_id": "symmetry_parent_03_00",
      "source": "spglib_refine_cell_after_MACEField_BEC_backprojection",
      "spacegroup": "C2/c",
      "spacegroup_number": 15,
      "pointgroup": "2/m",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.0
      ],
      "formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_residual": 0.49999999999999717,
      "parent_symmetrization_rmsd_A": 1.1790549020699952,
      "parent_cell_rmsd_A": 0.00023971153761827475,
      "energy_eV": -120.94103586589127,
      "reduced_polarization": [
        -6.617796537313112e-16,
        2.8052145281446327e-15,
        -9.009868144272087e-16
      ],
      "cartesian_polarization_e_A2": [
        -1.2047829214926109e-17,
        3.982886978505534e-17,
        -1.6849622597452745e-17
      ],
      "ranking_score": 2.1791148299543943
    },
    {
      "candidate_id": "bec_projection_04",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cc",
      "spacegroup_number": 9,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.5,
        0.0,
        -0.5
      ],
      "formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_residual": 0.00039740274890051207,
      "parent_symmetrization_rmsd_A": 0.38186973970599114,
      "parent_cell_rmsd_A": 0.012564756945005064,
      "energy_eV": -110.73006069947519,
      "reduced_polarization": [
        0.4997823670775437,
        5.557043046381741e-15,
        -0.4996674870590536
      ],
      "cartesian_polarization_e_A2": [
        0.01310848824858582,
        -7.160431635347949e-16,
        -0.015187909379769654
      ],
      "ranking_score": 0.8858057344400434
    },
    {
      "candidate_id": "bec_projection_05",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.5,
        -0.5
      ],
      "formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_residual": 1.4067020026338444e-05,
      "parent_symmetrization_rmsd_A": 0.20597028845041582,
      "parent_cell_rmsd_A": 0.005114058584143196,
      "energy_eV": -118.44434518629168,
      "reduced_polarization": [
        1.2466292438017912e-07,
        0.4999968959574751,
        -0.4999862802903974
      ],
      "cartesian_polarization_e_A2": [
        1.6077833906893046e-06,
        0.0070907852460077,
        -0.010043115663527183
      ],
      "ranking_score": 0.7072769371365043
    },
    {
      "candidate_id": "bec_projection_06",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.5,
        0.5,
        0.0
      ],
      "formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_residual": 3.910099482673916e-06,
      "parent_symmetrization_rmsd_A": 0.3040987734508237,
      "parent_cell_rmsd_A": 0.009009347645430352,
      "energy_eV": -108.32714832521064,
      "reduced_polarization": [
        0.49999885021971563,
        0.4999978957762389,
        3.0885474944061293e-06
      ],
      "cartesian_polarization_e_A2": [
        0.013115596318194263,
        0.007104200226994902,
        -0.00515453783165674
      ],
      "ranking_score": 0.8063589305611466
    },
    {
      "candidate_id": "bec_projection_07",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.5,
        0.5,
        -0.5
      ],
      "formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "target_residual": 2.903886750829909e-06,
      "parent_symmetrization_rmsd_A": 0.4125770222206545,
      "parent_cell_rmsd_A": 0.014177465670932584,
      "energy_eV": -106.25579520362483,
      "reduced_polarization": [
        0.4999981725257774,
        0.4999990298780265,
        -0.49999796241329414
      ],
      "cartesian_polarization_e_A2": [
        0.013120092794046153,
        0.007094302006228433,
        -0.015195226355007732
      ],
      "ranking_score": 0.9161271964118893
    }
  ],
  "formal_branches": [
    {
      "orbit_id": 0,
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.0,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              0.006522297247876223,
              7.394187310515106e-16,
              -0.02428302766870887
            ],
            "branch_aligned_reduced_polarization": [
              0.006522297247876223,
              7.394187310515106e-16,
              -0.02428302766870887
            ],
            "target_residual": 0.025143702872666436,
            "energy_eV": -121.1230623072979,
            "max_atomic_step_A": 0.008093619060283934,
            "max_log_strain_component": 2.247936369143742e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.16220932376333472,
            "cell_principal_stretches": [
              1.0000098636381676,
              0.9999926299296958,
              0.9999734396807448
            ],
            "cell_volume_ratio": 0.9999759331096844,
            "cell_rmsd_from_input_A": 0.00023966724576222057
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              3.003961825806484e-06,
              3.1823481780909194e-16,
              1.0112344284397567e-05
            ],
            "branch_aligned_reduced_polarization": [
              3.003961825806484e-06,
              3.1823481780909194e-16,
              1.0112344284397567e-05
            ],
            "target_residual": 1.0549089703718078e-05,
            "energy_eV": -121.12226610764354
          }
        ],
        "iterations": 1
      },
      "parent": {
        "candidate_id": "inversion_parent_endpoint_00",
        "source": "same_species_inversion_center_projection_from_endpoint",
        "spacegroup": "C2/c",
        "spacegroup_number": 15,
        "pointgroup": "2/m",
        "has_inversion": true,
        "is_polar_point_group": false,
        "nonpolar_parent_hypothesis": true,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.0
        ],
        "formal_class": [
          0.0,
          0.0,
          0.0
        ],
        "target_residual": 1.8183053300193245e-15,
        "parent_symmetrization_rmsd_A": 0.03651097669099196,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -121.12940121026642,
        "reduced_polarization": [
          1.4410961255617084e-15,
          1.6981225830658563e-16,
          1.0957372070877831e-15
        ],
        "cartesian_polarization_e_A2": [
          3.782240914512356e-17,
          2.4109395283748907e-18,
          7.16644677238433e-18
        ],
        "ranking_score": 0.036510976690995595
      },
      "branch_status": "sampled",
      "incoming": {
        "reached": true,
        "construction": "variable_cell_linear_interpolation",
        "continuation_fractions": [
          0.0,
          0.125,
          0.25,
          0.375,
          0.5,
          0.625,
          0.75,
          0.875,
          1.0
        ],
        "energies_eV": [
          -121.12306230729789,
          -121.12455983749983,
          -121.12585203950796,
          -121.12694118756568,
          -121.12782930544522,
          -121.12851813272127,
          -121.12900909169954,
          -121.12930323521202,
          -121.12940121026645
        ],
        "cartesian_polarizations_e_A2": [
          [
            0.00017099709345204514,
            2.391955752560915e-17,
            -0.0005549840288170407
          ],
          [
            0.00014962495048007575,
            2.3350044251189884e-17,
            -0.00048556216938063835
          ],
          [
            0.00012825528006760067,
            9.814612095825341e-18,
            -0.0004161557881757726
          ],
          [
            0.00010688542996051835,
            1.4313766963737538e-17,
            -0.0003467654912760788
          ],
          [
            8.551362994358043e-05,
            2.7260702068868843e-17,
            -0.00027739066822023845
          ],
          [
            6.413897885457067e-05,
            5.638181416750729e-18,
            -0.00020802962901007215
          ],
          [
            4.2761361338817706e-05,
            -9.264082597220051e-18,
            -0.00013867979491164636
          ],
          [
            2.1381345810725762e-05,
            -1.469344248001705e-17,
            -6.933785791861529e-05
          ],
          [
            -1.8240786157733003e-17,
            -2.171743953118799e-17,
            2.466790893060959e-17
          ]
        ],
        "raw_reduced_polarization": [
          [
            0.006522297247875782,
            1.6847515391047077e-15,
            -0.024283027668710135
          ],
          [
            0.005707104527583774,
            1.6446384072212622e-15,
            -0.021245168695351282
          ],
          [
            0.004892006206634866,
            6.912829727913761e-16,
            -0.018208031835340508
          ],
          [
            0.0040769012310149285,
            1.008176714670595e-15,
            -0.015171699079435117
          ],
          [
            0.0032617221412910608,
            1.9200819128209207e-15,
            -0.012136174631068317
          ],
          [
            0.002446434579439722,
            3.971200056461097e-16,
            -0.009101391979136753
          ],
          [
            0.0016310341191501116,
            -6.525069453040455e-16,
            -0.006067225021656687
          ],
          [
            0.0008155423796665115,
            -1.034918802592892e-15,
            -0.00303349799679377
          ],
          [
            -6.953404306063286e-16,
            -1.5296474291553854e-15,
            8.714252835580446e-16
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            0.006522297247875782,
            1.6847515391047077e-15,
            -0.024283027668710135
          ],
          [
            0.005707104527583774,
            1.6446384072212622e-15,
            -0.021245168695351282
          ],
          [
            0.004892006206634866,
            6.9128297279137615e-16,
            -0.018208031835340508
          ],
          [
            0.0040769012310149285,
            1.008176714670595e-15,
            -0.015171699079435117
          ],
          [
            0.0032617221412910608,
            1.9200819128209207e-15,
            -0.012136174631068317
          ],
          [
            0.002446434579439722,
            3.9712000564610965e-16,
            -0.009101391979136753
          ],
          [
            0.0016310341191501116,
            -6.525069453040455e-16,
            -0.006067225021656687
          ],
          [
            0.0008155423796665115,
            -1.034918802592892e-15,
            -0.00303349799679377
          ],
          [
            -6.95298853214954e-16,
            -1.5296474291553854e-15,
            8.712648658093514e-16
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            0.006522297247875786,
            1.6653345369377348e-15,
            -0.024283027668710155
          ],
          [
            0.005707104527583828,
            1.6653345369377348e-15,
            -0.021245168695351258
          ],
          [
            0.00489200620663488,
            6.661338147750939e-16,
            -0.018208031835340532
          ],
          [
            0.0040769012310148955,
            9.992007221626409e-16,
            -0.015171699079435108
          ],
          [
            0.003261722141291057,
            1.887379141862766e-15,
            -0.012136174631068308
          ],
          [
            0.0024464345794397158,
            4.440892098500626e-16,
            -0.00910139197913673
          ],
          [
            0.0016310341191501099,
            -6.661338147750939e-16,
            -0.006067225021656686
          ],
          [
            0.0008155423796665229,
            -1.0547118733938987e-15,
            -0.0030334979967937548
          ],
          [
            -7.216449660063518e-16,
            -1.5543122344752192e-15,
            8.881784197001252e-16
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -121.12940121026644,
          -121.129303235212,
          -121.12900909169954,
          -121.12851813272127,
          -121.12782930544527,
          -121.12694118756569,
          -121.12585203950798,
          -121.12455983749983,
          -121.12306230729789
        ],
        "cartesian_polarizations_e_A2": [
          [
            1.537762898619655e-18,
            -1.1333314160943384e-17,
            2.728319071441451e-17
          ],
          [
            -2.138134581074573e-05,
            5.752084071634581e-18,
            6.933785791865414e-05
          ],
          [
            -4.276136133881277e-05,
            -4.442203540470271e-17,
            0.00013867979491170678
          ],
          [
            -6.41389788546178e-05,
            -2.6653221242821626e-17,
            0.00020802962901011793
          ],
          [
            -8.551362994364441e-05,
            -2.429923304188866e-18,
            0.0002773906682203104
          ],
          [
            -0.00010688542996053204,
            -2.904517699538254e-17,
            0.0003467654912761445
          ],
          [
            -0.00012825528006762496,
            -1.4123929205597784e-17,
            0.00041615578817581566
          ],
          [
            -0.00014962495048018957,
            -4.115682596469892e-17,
            0.000485562169380731
          ],
          [
            -0.00017099709345207989,
            -5.547059292843646e-17,
            0.0005549840288170916
          ]
        ],
        "raw_reduced_polarization": [
          [
            5.82684306424079e-17,
            -7.982513244805639e-16,
            1.3880622213170249e-15
          ],
          [
            -0.0008155423796672728,
            4.0514263202279874e-16,
            0.003033497996795314
          ],
          [
            -0.001631034119149924,
            -3.1288242869087427e-15,
            0.00606722502165979
          ],
          [
            -0.0024464345794415186,
            -1.877294572145246e-15,
            0.00910139197913811
          ],
          [
            -0.0032617221412934994,
            -1.7114936270270047e-16,
            0.012136174631070645
          ],
          [
            -0.0040769012310154515,
            -2.0457697260557165e-15,
            0.01517169907943812
          ],
          [
            -0.004892006206635793,
            -9.948056707094464e-16,
            0.018208031835342177
          ],
          [
            -0.005707104527588112,
            -2.8988423307769893e-15,
            0.02124516869535367
          ],
          [
            -0.006522297247877106,
            -3.907019045447584e-15,
            0.02428302766871199
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            5.82684306424079e-17,
            -7.982513244805639e-16,
            1.3880622213170249e-15
          ],
          [
            -0.0008155423796672728,
            4.0514263202279874e-16,
            0.003033497996795314
          ],
          [
            -0.001631034119149924,
            -3.1288242869087427e-15,
            0.00606722502165979
          ],
          [
            -0.0024464345794415186,
            -1.877294572145246e-15,
            0.00910139197913811
          ],
          [
            -0.0032617221412934994,
            -1.7114936270270052e-16,
            0.012136174631070645
          ],
          [
            -0.0040769012310154515,
            -2.045769726055716e-15,
            0.01517169907943812
          ],
          [
            -0.004892006206635793,
            -9.948056707094464e-16,
            0.018208031835342177
          ],
          [
            -0.005707104527588112,
            -2.8988423307769893e-15,
            0.02124516869535367
          ],
          [
            -0.006522297247877106,
            -3.907019045447584e-15,
            0.02428302766871199
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          -0.006522297247877172,
          -4.744046397415478e-15,
          0.02428302766871188
        ],
        "actual_opposite_endpoint_branch_residual": 8.469274579463618e-16
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            0.006522297247875782,
            1.6847515391047077e-15,
            -0.024283027668710135
          ],
          [
            0.005707104527583774,
            1.6446384072212622e-15,
            -0.021245168695351282
          ],
          [
            0.004892006206634866,
            6.912829727913761e-16,
            -0.018208031835340508
          ],
          [
            0.0040769012310149285,
            1.008176714670595e-15,
            -0.015171699079435117
          ],
          [
            0.0032617221412910608,
            1.9200819128209207e-15,
            -0.012136174631068317
          ],
          [
            0.002446434579439722,
            3.971200056461097e-16,
            -0.009101391979136753
          ],
          [
            0.0016310341191501116,
            -6.525069453040455e-16,
            -0.006067225021656687
          ],
          [
            0.0008155423796665115,
            -1.034918802592892e-15,
            -0.00303349799679377
          ],
          [
            -6.953404306063286e-16,
            -1.5296474291553854e-15,
            8.714252835580446e-16
          ],
          [
            -0.0008155423796672728,
            4.0514263202279874e-16,
            0.003033497996795314
          ],
          [
            -0.001631034119149924,
            -3.1288242869087427e-15,
            0.00606722502165979
          ],
          [
            -0.0024464345794415186,
            -1.877294572145246e-15,
            0.00910139197913811
          ],
          [
            -0.0032617221412934994,
            -1.7114936270270047e-16,
            0.012136174631070645
          ],
          [
            -0.0040769012310154515,
            -2.0457697260557165e-15,
            0.01517169907943812
          ],
          [
            -0.004892006206635793,
            -9.948056707094464e-16,
            0.018208031835342177
          ],
          [
            -0.005707104527588112,
            -2.8988423307769893e-15,
            0.02124516869535367
          ],
          [
            -0.006522297247877106,
            -3.907019045447584e-15,
            0.02428302766871199
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            0.006522297247875782,
            1.6847515391047077e-15,
            -0.024283027668710135
          ],
          [
            0.005707104527583774,
            1.6446384072212622e-15,
            -0.021245168695351282
          ],
          [
            0.004892006206634866,
            6.9128297279137615e-16,
            -0.018208031835340508
          ],
          [
            0.0040769012310149285,
            1.008176714670595e-15,
            -0.015171699079435117
          ],
          [
            0.0032617221412910608,
            1.9200819128209207e-15,
            -0.012136174631068317
          ],
          [
            0.002446434579439722,
            3.9712000564610965e-16,
            -0.009101391979136753
          ],
          [
            0.0016310341191501116,
            -6.525069453040455e-16,
            -0.006067225021656687
          ],
          [
            0.0008155423796665115,
            -1.034918802592892e-15,
            -0.00303349799679377
          ],
          [
            -6.95298853214954e-16,
            -1.5296474291553854e-15,
            8.712648658093514e-16
          ],
          [
            -0.0008155423796672728,
            4.0514263202279894e-16,
            0.003033497996795314
          ],
          [
            -0.001631034119149924,
            -3.1288242869087423e-15,
            0.00606722502165979
          ],
          [
            -0.0024464345794415186,
            -1.877294572145246e-15,
            0.00910139197913811
          ],
          [
            -0.0032617221412934994,
            -1.7114936270270052e-16,
            0.012136174631070645
          ],
          [
            -0.0040769012310154515,
            -2.045769726055716e-15,
            0.01517169907943812
          ],
          [
            -0.004892006206635793,
            -9.948056707094464e-16,
            0.018208031835342177
          ],
          [
            -0.005707104527588112,
            -2.8988423307769893e-15,
            0.02124516869535367
          ],
          [
            -0.006522297247877106,
            -3.907019045447584e-15,
            0.02428302766871199
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            0.006522297247875786,
            1.6653345369377348e-15,
            -0.024283027668710155
          ],
          [
            0.005707104527583828,
            1.6653345369377348e-15,
            -0.021245168695351258
          ],
          [
            0.00489200620663488,
            6.661338147750939e-16,
            -0.018208031835340532
          ],
          [
            0.0040769012310148955,
            9.992007221626409e-16,
            -0.015171699079435108
          ],
          [
            0.003261722141291057,
            1.887379141862766e-15,
            -0.012136174631068308
          ],
          [
            0.0024464345794397158,
            4.440892098500626e-16,
            -0.00910139197913673
          ],
          [
            0.0016310341191501099,
            -6.661338147750939e-16,
            -0.006067225021656686
          ],
          [
            0.0008155423796665229,
            -1.0547118733938987e-15,
            -0.0030334979967937548
          ],
          [
            -7.216449660063518e-16,
            -1.5543122344752192e-15,
            8.881784197001252e-16
          ],
          [
            -0.0008155423796673,
            4.440892098500626e-16,
            0.003033497996795309
          ],
          [
            -0.0016310341191499433,
            -3.1086244689504383e-15,
            0.0060672250216597945
          ],
          [
            -0.002446434579441492,
            -1.887379141862766e-15,
            0.009101391979138063
          ],
          [
            -0.0032617221412934994,
            -1.6653345369377348e-16,
            0.01213617463107064
          ],
          [
            -0.004076901231015451,
            -2.0539125955565396e-15,
            0.015171699079438161
          ],
          [
            -0.004892006206635768,
            -9.992007221626409e-16,
            0.018208031835342142
          ],
          [
            -0.005707104527588103,
            -2.886579864025407e-15,
            0.021245168695353644
          ],
          [
            -0.006522297247877118,
            -3.885780586188048e-15,
            0.024283027668712043
          ]
        ]
      },
      "incoming_structure_ids": [
        "incoming_00_000",
        "incoming_00_001",
        "incoming_00_002",
        "incoming_00_003",
        "incoming_00_004",
        "incoming_00_005",
        "incoming_00_006",
        "incoming_00_007",
        "incoming_00_008"
      ],
      "reflected_structure_ids": [
        "reflected_00_001",
        "reflected_00_002",
        "reflected_00_003",
        "reflected_00_004",
        "reflected_00_005",
        "reflected_00_006",
        "reflected_00_007",
        "reflected_00_008"
      ]
    },
    {
      "orbit_id": 1,
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.0,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        -0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              0.006522297247876223,
              7.394187310515106e-16,
              -0.02428302766870887
            ],
            "branch_aligned_reduced_polarization": [
              0.006522297247876223,
              7.394187310515106e-16,
              -0.02428302766870888
            ],
            "target_residual": 0.4757616820693319,
            "energy_eV": -121.1230623072979,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.0003833121885664295,
            "step_scale": 0.9440679858971077,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.16220932376333472,
            "cell_principal_stretches": [
              1.000361547521952,
              1.0002195986226774,
              0.9996167612661649
            ],
            "cell_volume_ratio": 1.0001977640579924,
            "cell_rmsd_from_input_A": 0.002742713631401588
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.0005652783797161179,
              1.2043875403608937e-15,
              -0.4590483126412718
            ],
            "branch_aligned_reduced_polarization": [
              0.0005652783797161179,
              1.2043875403608937e-15,
              -0.4590483126412718
            ],
            "target_residual": 0.0409555885951306,
            "energy_eV": -120.93442797627701,
            "max_atomic_step_A": 0.01190214225214864,
            "max_log_strain_component": 4.119063545109733e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.16220932376333472,
            "cell_principal_stretches": [
              1.0004004295502713,
              1.0002432491532924,
              0.9995755872645583
            ],
            "cell_volume_ratio": 1.0002190901454924,
            "cell_rmsd_from_input_A": 0.0030380703371748843
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -2.451197438514577e-06,
              4.36179802638097e-16,
              -0.49974481788320835
            ],
            "branch_aligned_reduced_polarization": [
              -2.451197438514577e-06,
              4.36179802638097e-16,
              -0.49974481788320835
            ],
            "target_residual": 0.0002551938892276833,
            "energy_eV": -120.86157816318678
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_01",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cc",
        "spacegroup_number": 9,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          -0.5
        ],
        "formal_class": [
          0.0,
          0.0,
          0.5
        ],
        "target_residual": 0.0002551938892276833,
        "parent_symmetrization_rmsd_A": 0.14454544071314235,
        "parent_cell_rmsd_A": 0.0030380703371748843,
        "energy_eV": -120.86157816318678,
        "reduced_polarization": [
          -2.451197438514577e-06,
          4.36179802638097e-16,
          -0.49974481788320835
        ],
        "cartesian_polarization_e_A2": [
          -3.7795655333606522e-06,
          -1.5221653288574733e-17,
          -0.010040439176011641
        ],
        "ranking_score": 0.6458153460758914
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 2,
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.0,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              0.006522297247876223,
              7.394187310515106e-16,
              -0.02428302766870887
            ],
            "branch_aligned_reduced_polarization": [
              0.00652229724787623,
              7.394187310515106e-16,
              -0.02428302766870887
            ],
            "target_residual": 0.49407480055784336,
            "energy_eV": -121.1230623072979,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.00036965160026942615,
            "step_scale": 0.4608582411639898,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.16220932376333472,
            "cell_principal_stretches": [
              1.0003989987411814,
              1.0003697199298414,
              0.9996699834827887
            ],
            "cell_volume_ratio": 1.0004385959330562,
            "cell_rmsd_from_input_A": 0.0039903604725070995
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.2377390371818558,
              4.670178720038166e-15,
              -0.005827542506752991
            ],
            "branch_aligned_reduced_polarization": [
              0.2377390371818558,
              4.670178720038166e-15,
              -0.005827542506752991
            ],
            "target_residual": 0.26232569997994487,
            "energy_eV": -119.07958300092798,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.00033340675772550247,
            "step_scale": 0.9004827507480856,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.16220932376333472,
            "cell_principal_stretches": [
              1.0008005791159627,
              1.0006940116438845,
              0.9993795116368903
            ],
            "cell_volume_ratio": 1.0008737302870414,
            "cell_rmsd_from_input_A": 0.007932537253324188
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.47798222515828465,
              7.565824402793866e-15,
              0.021874861087367834
            ],
            "branch_aligned_reduced_polarization": [
              0.47798222515828465,
              7.565824402793866e-15,
              0.021874861087367834
            ],
            "target_residual": 0.031036945026405433,
            "energy_eV": -112.57633832345927,
            "max_atomic_step_A": 0.015071507436928398,
            "max_log_strain_component": 4.057102665187113e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.16220932376333472,
            "cell_principal_stretches": [
              1.0008612831083632,
              1.0006994083603271,
              0.9993733977199633
            ],
            "cell_volume_ratio": 1.0009337132669693,
            "cell_rmsd_from_input_A": 0.008463497724797013
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.49991241330553554,
              -7.039822819519281e-15,
              0.000494940215660973
            ],
            "branch_aligned_reduced_polarization": [
              0.49991241330553554,
              -7.039822819519281e-15,
              0.000494940215660973
            ],
            "target_residual": 0.0005026303275029681,
            "energy_eV": -111.78594027891216
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_02",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cc",
        "spacegroup_number": 9,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.5,
          0.0,
          0.0
        ],
        "formal_class": [
          0.5,
          0.0,
          0.0
        ],
        "target_residual": 0.0005026303275029681,
        "parent_symmetrization_rmsd_A": 0.2785946851016702,
        "parent_cell_rmsd_A": 0.008463497724797013,
        "energy_eV": -111.78594027891216,
        "reduced_polarization": [
          0.49991241330553554,
          -7.039822819519281e-15,
          0.000494940215660973
        ],
        "cartesian_polarization_e_A2": [
          0.013108481111689172,
          -2.5892474594196107e-16,
          -0.005145881622232331
        ],
        "ranking_score": 0.7817158201878753
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 3,
      "formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.5,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              0.006522297247876223,
              7.394187310515106e-16,
              -0.02428302766870887
            ],
            "branch_aligned_reduced_polarization": [
              0.006522297247876223,
              7.216449660063518e-16,
              -0.02428302766870887
            ],
            "target_residual": 0.5006318066145501,
            "energy_eV": -121.1230623072979,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.0006889931110264288,
            "step_scale": 0.9182245002355972,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.16220932376333472,
            "cell_principal_stretches": [
              1.0007505867504751,
              0.9999757127156218,
              0.9992521630734804
            ],
            "cell_volume_ratio": 0.999977901169936,
            "cell_rmsd_from_input_A": 0.0036690582982820447
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.0005681373021488667,
              0.4595678534619174,
              -0.0021333959333185654
            ],
            "branch_aligned_reduced_polarization": [
              0.0005681373021488667,
              0.4595678534619174,
              -0.0021333959333185654
            ],
            "target_residual": 0.040492377454026784,
            "energy_eV": -119.16033143390634,
            "max_atomic_step_A": 0.010525799266091847,
            "max_log_strain_component": 6.011518735549763e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.16220932376333472,
            "cell_principal_stretches": [
              1.0008161484501847,
              0.9999734082462394,
              0.9991869792880249
            ],
            "cell_volume_ratio": 0.9999758723733276,
            "cell_rmsd_from_input_A": 0.003989275635696312
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -1.830749709164968e-06,
              0.5000027640653834,
              1.6471605674791457e-05
            ],
            "branch_aligned_reduced_polarization": [
              -1.830749709164968e-06,
              0.5000027640653834,
              1.6471605674791457e-05
            ],
            "target_residual": 1.6801949156180803e-05,
            "energy_eV": -118.78713548569159
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_03",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.5,
          0.0
        ],
        "formal_class": [
          0.0,
          0.5,
          0.0
        ],
        "target_residual": 1.6801949156180803e-05,
        "parent_symmetrization_rmsd_A": 0.14280045641466557,
        "parent_cell_rmsd_A": 0.003989275635696312,
        "energy_eV": -118.78713548569159,
        "reduced_polarization": [
          -1.830749709164968e-06,
          0.5000027640653834,
          1.6471605674791457e-05
        ],
        "cartesian_polarization_e_A2": [
          5.270026209441404e-06,
          0.007099123726329184,
          2.62033912072481e-06
        ],
        "ranking_score": 0.643831379221902
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 4,
      "formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.0,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.5,
        0.0,
        -0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              0.006522297247876223,
              7.394187310515106e-16,
              -0.02428302766870887
            ],
            "branch_aligned_reduced_polarization": [
              0.00652229724787623,
              7.394187310515106e-16,
              -0.02428302766870888
            ],
            "target_residual": 0.6854391883147358,
            "energy_eV": -121.1230623072979,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.0002713760955493382,
            "step_scale": 0.3774025614185971,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.16220932376333472,
            "cell_principal_stretches": [
              1.000439283333613,
              1.00014576671511,
              0.9998622932162338
            ],
            "cell_volume_ratio": 1.000447326723667,
            "cell_rmsd_from_input_A": 0.004075953185071218
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.19509557276794356,
              2.40913260891832e-15,
              -0.19354319378989943
            ],
            "branch_aligned_reduced_polarization": [
              0.19509557276794354,
              2.40913260891832e-15,
              -0.19354319378989943
            ],
            "target_residual": 0.43229906756573455,
            "energy_eV": -119.75222313799303,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.00027739889038584973,
            "step_scale": 0.5976130029950809,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.16220932376333472,
            "cell_principal_stretches": [
              1.000888300307912,
              1.0002375224340327,
              0.999770617866495
            ],
            "cell_volume_ratio": 1.000896393307671,
            "cell_rmsd_from_input_A": 0.008200657116450362
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.37786603872389435,
              8.820325272687695e-15,
              -0.34659814068401523
            ],
            "branch_aligned_reduced_polarization": [
              0.37786603872389435,
              8.820325272687695e-15,
              -0.34659814068401523
            ],
            "target_residual": 0.19608374470769996,
            "energy_eV": -115.80035704019701,
            "max_atomic_step_A": 0.09737252922626186,
            "max_log_strain_component": 0.0002993545423137149,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.16220932376333472,
            "cell_principal_stretches": [
              1.0013043961793657,
              1.000218703369416,
              0.9997743074067982
            ],
            "cell_volume_ratio": 1.0012973484147474,
            "cell_rmsd_from_input_A": 0.01196068842877902
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.4919696579181682,
              5.719720182578775e-15,
              -0.47630933050777385
            ],
            "branch_aligned_reduced_polarization": [
              0.4919696579181682,
              5.719720182578775e-15,
              -0.47630933050777385
            ],
            "target_residual": 0.02501467998878125,
            "energy_eV": -111.26905018398186,
            "max_atomic_step_A": 0.012586718406673723,
            "max_log_strain_component": 5.447107905102699e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.16220932376333472,
            "cell_principal_stretches": [
              1.0013719927036018,
              1.0002012273838914,
              0.9997871603005766
            ],
            "cell_volume_ratio": 1.001360321568119,
            "cell_rmsd_from_input_A": 0.012564756945005064
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              0.4997823670775437,
              5.557043046381741e-15,
              -0.4996674870590536
            ],
            "branch_aligned_reduced_polarization": [
              0.4997823670775437,
              5.557043046381741e-15,
              -0.4996674870590536
            ],
            "target_residual": 0.00039740274890051207,
            "energy_eV": -110.73006069947519
          }
        ],
        "iterations": 4
      },
      "parent": {
        "candidate_id": "bec_projection_04",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cc",
        "spacegroup_number": 9,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.5,
          0.0,
          -0.5
        ],
        "formal_class": [
          0.5,
          0.0,
          0.5
        ],
        "target_residual": 0.00039740274890051207,
        "parent_symmetrization_rmsd_A": 0.38186973970599114,
        "parent_cell_rmsd_A": 0.012564756945005064,
        "energy_eV": -110.73006069947519,
        "reduced_polarization": [
          0.4997823670775437,
          5.557043046381741e-15,
          -0.4996674870590536
        ],
        "cartesian_polarization_e_A2": [
          0.01310848824858582,
          -7.160431635347949e-16,
          -0.015187909379769654
        ],
        "ranking_score": 0.8858057344400434
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 5,
      "formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.5,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        -0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              0.006522297247876223,
              7.394187310515106e-16,
              -0.02428302766870887
            ],
            "branch_aligned_reduced_polarization": [
              0.006522297247876223,
              7.216449660063518e-16,
              -0.02428302766870888
            ],
            "target_residual": 0.6901805402396096,
            "energy_eV": -121.1230623072979,
            "max_atomic_step_A": 0.12000000000000001,
            "max_log_strain_component": 0.0004937152126382651,
            "step_scale": 0.6579766867506218,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.16220932376333472,
            "cell_principal_stretches": [
              1.0005596846780023,
              1.0001969981173089,
              0.9993815043328655
            ],
            "cell_volume_ratio": 1.0001378293117809,
            "cell_rmsd_from_input_A": 0.0032469524870757816
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.0027973515228429144,
              0.3291024552331836,
              -0.32840734637951474
            ],
            "branch_aligned_reduced_polarization": [
              0.0027973515228429144,
              0.3291024552331836,
              -0.32840734637951474
            ],
            "target_residual": 0.24219379587303264,
            "energy_eV": -120.06402377867681,
            "max_atomic_step_A": 0.06681911004968873,
            "max_log_strain_component": 0.00026150102791869706,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.16220932376333472,
            "cell_principal_stretches": [
              1.0008646779340413,
              1.000316936262225,
              0.9990403796686176
            ],
            "cell_volume_ratio": 1.000221133748688,
            "cell_rmsd_from_input_A": 0.005068134501319351
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.00033135063927080204,
              0.4991454913917942,
              -0.49204538210070337
            ],
            "branch_aligned_reduced_polarization": [
              0.00033135063927080204,
              0.4991454913917942,
              -0.49204538210070337
            ],
            "target_residual": 0.008007241980323399,
            "energy_eV": -118.47098218347173,
            "max_atomic_step_A": 0.00250656960863171,
            "max_log_strain_component": 9.071733613500553e-06,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.16220932376333472,
            "cell_principal_stretches": [
              1.0008696314911882,
              1.0003226938477878,
              0.9990337146134382
            ],
            "cell_volume_ratio": 1.0002251681794314,
            "cell_rmsd_from_input_A": 0.005114058584143196
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              1.2466292438017912e-07,
              0.4999968959574751,
              -0.4999862802903974
            ],
            "branch_aligned_reduced_polarization": [
              1.2466292438017912e-07,
              0.4999968959574751,
              -0.4999862802903974
            ],
            "target_residual": 1.4067020026338444e-05,
            "energy_eV": -118.44434518629168
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_05",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.5,
          -0.5
        ],
        "formal_class": [
          0.0,
          0.5,
          0.5
        ],
        "target_residual": 1.4067020026338444e-05,
        "parent_symmetrization_rmsd_A": 0.20597028845041582,
        "parent_cell_rmsd_A": 0.005114058584143196,
        "energy_eV": -118.44434518629168,
        "reduced_polarization": [
          1.2466292438017912e-07,
          0.4999968959574751,
          -0.4999862802903974
        ],
        "cartesian_polarization_e_A2": [
          1.6077833906893046e-06,
          0.0070907852460077,
          -0.010043115663527183
        ],
        "ranking_score": 0.7072769371365043
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 6,
      "formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.5,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.5,
        0.5,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              0.006522297247876223,
              7.394187310515106e-16,
              -0.02428302766870887
            ],
            "branch_aligned_reduced_polarization": [
              0.00652229724787623,
              7.216449660063518e-16,
              -0.02428302766870887
            ],
            "target_residual": 0.7029295189037603,
            "energy_eV": -121.1230623072979,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.0003281923316177081,
            "step_scale": 0.40916944658665116,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.16220932376333472,
            "cell_principal_stretches": [
              1.0005054677750502,
              1.0003160877580466,
              0.9995680340989936
            ],
            "cell_volume_ratio": 1.000389394451274,
            "cell_rmsd_from_input_A": 0.003900696231201466
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.21272401522125384,
              0.20984048194113614,
              -0.008546111089290943
            ],
            "branch_aligned_reduced_polarization": [
              0.21272401522125384,
              0.20984048194113614,
              -0.008546111089290943
            ],
            "target_residual": 0.40840307707643564,
            "energy_eV": -119.075995406612,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.00028881642294717626,
            "step_scale": 0.7274736227610498,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.16220932376333472,
            "cell_principal_stretches": [
              1.0009544759218028,
              1.0006207998888186,
              0.9991895730978925
            ],
            "cell_volume_ratio": 1.0007641643209555,
            "cell_rmsd_from_input_A": 0.007589938700907498
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.4273395299459621,
              0.4307897982371303,
              0.014827143806331154
            ],
            "branch_aligned_reduced_polarization": [
              0.4273395299459621,
              0.4307897982371303,
              0.014827143806331154
            ],
            "target_residual": 0.10143687756424927,
            "energy_eV": -112.14011283747382,
            "max_atomic_step_A": 0.04222480339042859,
            "max_log_strain_component": 9.615933261546104e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.16220932376333472,
            "cell_principal_stretches": [
              1.0010812196492382,
              1.000738988847922,
              0.9990930157672496
            ],
            "cell_volume_ratio": 1.0009123716485766,
            "cell_rmsd_from_input_A": 0.008963765970661874
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.49878056037270807,
              0.4991700563308824,
              0.0033744480325819033
            ],
            "branch_aligned_reduced_polarization": [
              0.49878056037270807,
              0.4991700563308824,
              0.0033744480325819033
            ],
            "target_residual": 0.0036827624174136093,
            "energy_eV": -108.38902578991123,
            "max_atomic_step_A": 0.0014745717336059592,
            "max_log_strain_component": 4.862113173717311e-06,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.16220932376333472,
            "cell_principal_stretches": [
              1.001082454073397,
              1.0007429243911603,
              0.9990932684646191
            ],
            "cell_volume_ratio": 1.0009177952533148,
            "cell_rmsd_from_input_A": 0.009009347645430352
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              0.49999885021971563,
              0.4999978957762389,
              3.0885474944061293e-06
            ],
            "branch_aligned_reduced_polarization": [
              0.49999885021971563,
              0.4999978957762389,
              3.0885474944061293e-06
            ],
            "target_residual": 3.910099482673916e-06,
            "energy_eV": -108.32714832521064
          }
        ],
        "iterations": 4
      },
      "parent": {
        "candidate_id": "bec_projection_06",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.5,
          0.5,
          0.0
        ],
        "formal_class": [
          0.5,
          0.5,
          0.0
        ],
        "target_residual": 3.910099482673916e-06,
        "parent_symmetrization_rmsd_A": 0.3040987734508237,
        "parent_cell_rmsd_A": 0.009009347645430352,
        "energy_eV": -108.32714832521064,
        "reduced_polarization": [
          0.49999885021971563,
          0.4999978957762389,
          3.0885474944061293e-06
        ],
        "cartesian_polarization_e_A2": [
          0.013115596318194263,
          0.007104200226994902,
          -0.00515453783165674
        ],
        "ranking_score": 0.8063589305611466
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 7,
      "formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.5,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.5,
        0.5,
        -0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              0.006522297247876223,
              7.394187310515106e-16,
              -0.02428302766870887
            ],
            "branch_aligned_reduced_polarization": [
              0.00652229724787623,
              7.216449660063518e-16,
              -0.02428302766870888
            ],
            "target_residual": 0.8484261198699409,
            "energy_eV": -121.1230623072979,
            "max_atomic_step_A": 0.12000000000000001,
            "max_log_strain_component": 0.00026077791538704753,
            "step_scale": 0.3475400075807709,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.16220932376333472,
            "cell_principal_stretches": [
              1.00042702776744,
              1.0002892111772586,
              0.9996957795109116
            ],
            "cell_volume_ratio": 1.0004119240246803,
            "cell_rmsd_from_input_A": 0.00400124308371086
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.18090024240389044,
              0.17756228483477743,
              -0.18045879484401875
            ],
            "branch_aligned_reduced_polarization": [
              0.18090024240389047,
              0.17756228483477743,
              -0.18045879484401872
            ],
            "target_residual": 0.5548849585737587,
            "energy_eV": -119.64877299550783,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.000255882102435455,
            "step_scale": 0.5347481711282203,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.16220932376333472,
            "cell_principal_stretches": [
              1.0008474226801103,
              1.000540060722027,
              0.999436536765219
            ],
            "cell_volume_ratio": 1.0008236957732997,
            "cell_rmsd_from_input_A": 0.007976951820617733
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.35362920453190405,
              0.3578780131027621,
              -0.32204665358403906
            ],
            "branch_aligned_reduced_polarization": [
              0.35362920453190405,
              0.3578780131027621,
              -0.32204665358403906
            ],
            "target_residual": 0.27072211292434323,
            "energy_eV": -115.00684130964251,
            "max_atomic_step_A": 0.11979595886663841,
            "max_log_strain_component": 0.000347153541614983,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.16220932376333472,
            "cell_principal_stretches": [
              1.001315711504363,
              1.0007119445212058,
              0.999253886185236
            ],
            "cell_volume_ratio": 1.001280965363335,
            "cell_rmsd_from_input_A": 0.01235712124615449
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.4868552728522064,
              0.4970118899882961,
              -0.4601562170026197
            ],
            "branch_aligned_reduced_polarization": [
              0.4868552728522064,
              0.4970118899882961,
              -0.4601562170026197
            ],
            "target_residual": 0.04206233109058884,
            "energy_eV": -107.50782697607933,
            "max_atomic_step_A": 0.024121827842497577,
            "max_log_strain_component": 0.00010548304289380108,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.16220932376333472,
            "cell_principal_stretches": [
              1.0014435205476977,
              1.0007308424907833,
              0.9992294402745729
            ],
            "cell_volume_ratio": 1.0014031820096911,
            "cell_rmsd_from_input_A": 0.013522751481427881
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              0.49916646798099773,
              0.49963376530299797,
              -0.498991692806713
            ],
            "branch_aligned_reduced_polarization": [
              0.49916646798099773,
              0.49963376530299797,
              -0.498991692806713
            ],
            "target_residual": 0.0013585237855939238,
            "energy_eV": -106.3259273678054,
            "max_atomic_step_A": 0.0009702804488877018,
            "max_log_strain_component": 6.678939617122399e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": true,
            "strain_jacobian_frobenius_norm": 1.3381083094277475,
            "cell_principal_stretches": [
              1.0015032306570952,
              1.0006751861763201,
              0.9992420825235826
            ],
            "cell_volume_ratio": 1.001419862488112,
            "cell_rmsd_from_input_A": 0.014177465670932584
          },
          {
            "iteration": 5,
            "reduced_polarization": [
              0.4999981725257774,
              0.4999990298780265,
              -0.49999796241329414
            ],
            "branch_aligned_reduced_polarization": [
              0.4999981725257774,
              0.4999990298780265,
              -0.49999796241329414
            ],
            "target_residual": 2.903886750829909e-06,
            "energy_eV": -106.25579520362483
          }
        ],
        "iterations": 5
      },
      "parent": {
        "candidate_id": "bec_projection_07",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.5,
          0.5,
          -0.5
        ],
        "formal_class": [
          0.5,
          0.5,
          0.5
        ],
        "target_residual": 2.903886750829909e-06,
        "parent_symmetrization_rmsd_A": 0.4125770222206545,
        "parent_cell_rmsd_A": 0.014177465670932584,
        "energy_eV": -106.25579520362483,
        "reduced_polarization": [
          0.4999981725257774,
          0.4999990298780265,
          -0.49999796241329414
        ],
        "cartesian_polarization_e_A2": [
          0.013120092794046153,
          0.007094302006228433,
          -0.015195226355007732
        ],
        "ranking_score": 0.9161271964118893
      },
      "branch_status": "awaiting_branch_sampling"
    }
  ],
  "sampled_polarization_branches": [
    {
      "orbit_id": 0,
      "candidate_id": "inversion_parent_endpoint_00",
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "construction": "MACEField-BEC-parent plus variable-cell P-N-P path and symmetric log-strain continuation beyond both polar endpoints",
      "geometry_diagnostics": {
        "collision_aware": false,
        "permutations_tested": 1,
        "selected_order": [
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          10,
          11,
          12,
          13,
          14,
          15,
          16,
          17,
          18,
          19,
          20,
          21,
          22,
          23
        ],
        "endpoint_rmsd_A": 0.03651097669099196,
        "minimum_distance_A_by_image": [
          1.769240845541052,
          1.769431659522213,
          1.7696249216557463,
          1.769820631139644,
          1.7700187871621025,
          1.7702193889015363,
          1.7704224355265923,
          1.7706279261961697,
          1.7708358600594338
        ],
        "minimum_distance_A": 1.769240845541052,
        "minimum_distance_floor_A": 0.0,
        "geometry_valid": true,
        "parameters": [
          0.0,
          0.125,
          0.25,
          0.375,
          0.5,
          0.625,
          0.75,
          0.875,
          1.0
        ],
        "cell_mode": "variable_cell",
        "cell_volume_A3_by_image": [
          365.5170589824885,
          365.5170589824885,
          365.5170589824885,
          365.5170589824885,
          365.5170589824885,
          365.5170589824885,
          365.5170589824885,
          365.5170589824885,
          365.5170589824885
        ],
        "cell_deformation_log_strain_norm": 0.0
      },
      "parent_reduced_polarization": [
        -6.953404306063286e-16,
        -1.5296474291553854e-15,
        8.714252835580446e-16
      ],
      "incoming": {
        "reached": true,
        "construction": "variable_cell_linear_interpolation",
        "continuation_fractions": [
          0.0,
          0.125,
          0.25,
          0.375,
          0.5,
          0.625,
          0.75,
          0.875,
          1.0
        ],
        "energies_eV": [
          -121.12306230729789,
          -121.12455983749983,
          -121.12585203950796,
          -121.12694118756568,
          -121.12782930544522,
          -121.12851813272127,
          -121.12900909169954,
          -121.12930323521202,
          -121.12940121026645
        ],
        "cartesian_polarizations_e_A2": [
          [
            0.00017099709345204514,
            2.391955752560915e-17,
            -0.0005549840288170407
          ],
          [
            0.00014962495048007575,
            2.3350044251189884e-17,
            -0.00048556216938063835
          ],
          [
            0.00012825528006760067,
            9.814612095825341e-18,
            -0.0004161557881757726
          ],
          [
            0.00010688542996051835,
            1.4313766963737538e-17,
            -0.0003467654912760788
          ],
          [
            8.551362994358043e-05,
            2.7260702068868843e-17,
            -0.00027739066822023845
          ],
          [
            6.413897885457067e-05,
            5.638181416750729e-18,
            -0.00020802962901007215
          ],
          [
            4.2761361338817706e-05,
            -9.264082597220051e-18,
            -0.00013867979491164636
          ],
          [
            2.1381345810725762e-05,
            -1.469344248001705e-17,
            -6.933785791861529e-05
          ],
          [
            -1.8240786157733003e-17,
            -2.171743953118799e-17,
            2.466790893060959e-17
          ]
        ],
        "raw_reduced_polarization": [
          [
            0.006522297247875782,
            1.6847515391047077e-15,
            -0.024283027668710135
          ],
          [
            0.005707104527583774,
            1.6446384072212622e-15,
            -0.021245168695351282
          ],
          [
            0.004892006206634866,
            6.912829727913761e-16,
            -0.018208031835340508
          ],
          [
            0.0040769012310149285,
            1.008176714670595e-15,
            -0.015171699079435117
          ],
          [
            0.0032617221412910608,
            1.9200819128209207e-15,
            -0.012136174631068317
          ],
          [
            0.002446434579439722,
            3.971200056461097e-16,
            -0.009101391979136753
          ],
          [
            0.0016310341191501116,
            -6.525069453040455e-16,
            -0.006067225021656687
          ],
          [
            0.0008155423796665115,
            -1.034918802592892e-15,
            -0.00303349799679377
          ],
          [
            -6.953404306063286e-16,
            -1.5296474291553854e-15,
            8.714252835580446e-16
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            0.006522297247875782,
            1.6847515391047077e-15,
            -0.024283027668710135
          ],
          [
            0.005707104527583774,
            1.6446384072212622e-15,
            -0.021245168695351282
          ],
          [
            0.004892006206634866,
            6.9128297279137615e-16,
            -0.018208031835340508
          ],
          [
            0.0040769012310149285,
            1.008176714670595e-15,
            -0.015171699079435117
          ],
          [
            0.0032617221412910608,
            1.9200819128209207e-15,
            -0.012136174631068317
          ],
          [
            0.002446434579439722,
            3.9712000564610965e-16,
            -0.009101391979136753
          ],
          [
            0.0016310341191501116,
            -6.525069453040455e-16,
            -0.006067225021656687
          ],
          [
            0.0008155423796665115,
            -1.034918802592892e-15,
            -0.00303349799679377
          ],
          [
            -6.95298853214954e-16,
            -1.5296474291553854e-15,
            8.712648658093514e-16
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            0.006522297247875786,
            1.6653345369377348e-15,
            -0.024283027668710155
          ],
          [
            0.005707104527583828,
            1.6653345369377348e-15,
            -0.021245168695351258
          ],
          [
            0.00489200620663488,
            6.661338147750939e-16,
            -0.018208031835340532
          ],
          [
            0.0040769012310148955,
            9.992007221626409e-16,
            -0.015171699079435108
          ],
          [
            0.003261722141291057,
            1.887379141862766e-15,
            -0.012136174631068308
          ],
          [
            0.0024464345794397158,
            4.440892098500626e-16,
            -0.00910139197913673
          ],
          [
            0.0016310341191501099,
            -6.661338147750939e-16,
            -0.006067225021656686
          ],
          [
            0.0008155423796665229,
            -1.0547118733938987e-15,
            -0.0030334979967937548
          ],
          [
            -7.216449660063518e-16,
            -1.5543122344752192e-15,
            8.881784197001252e-16
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -121.12940121026644,
          -121.129303235212,
          -121.12900909169954,
          -121.12851813272127,
          -121.12782930544527,
          -121.12694118756569,
          -121.12585203950798,
          -121.12455983749983,
          -121.12306230729789
        ],
        "cartesian_polarizations_e_A2": [
          [
            1.537762898619655e-18,
            -1.1333314160943384e-17,
            2.728319071441451e-17
          ],
          [
            -2.138134581074573e-05,
            5.752084071634581e-18,
            6.933785791865414e-05
          ],
          [
            -4.276136133881277e-05,
            -4.442203540470271e-17,
            0.00013867979491170678
          ],
          [
            -6.41389788546178e-05,
            -2.6653221242821626e-17,
            0.00020802962901011793
          ],
          [
            -8.551362994364441e-05,
            -2.429923304188866e-18,
            0.0002773906682203104
          ],
          [
            -0.00010688542996053204,
            -2.904517699538254e-17,
            0.0003467654912761445
          ],
          [
            -0.00012825528006762496,
            -1.4123929205597784e-17,
            0.00041615578817581566
          ],
          [
            -0.00014962495048018957,
            -4.115682596469892e-17,
            0.000485562169380731
          ],
          [
            -0.00017099709345207989,
            -5.547059292843646e-17,
            0.0005549840288170916
          ]
        ],
        "raw_reduced_polarization": [
          [
            5.82684306424079e-17,
            -7.982513244805639e-16,
            1.3880622213170249e-15
          ],
          [
            -0.0008155423796672728,
            4.0514263202279874e-16,
            0.003033497996795314
          ],
          [
            -0.001631034119149924,
            -3.1288242869087427e-15,
            0.00606722502165979
          ],
          [
            -0.0024464345794415186,
            -1.877294572145246e-15,
            0.00910139197913811
          ],
          [
            -0.0032617221412934994,
            -1.7114936270270047e-16,
            0.012136174631070645
          ],
          [
            -0.0040769012310154515,
            -2.0457697260557165e-15,
            0.01517169907943812
          ],
          [
            -0.004892006206635793,
            -9.948056707094464e-16,
            0.018208031835342177
          ],
          [
            -0.005707104527588112,
            -2.8988423307769893e-15,
            0.02124516869535367
          ],
          [
            -0.006522297247877106,
            -3.907019045447584e-15,
            0.02428302766871199
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            5.82684306424079e-17,
            -7.982513244805639e-16,
            1.3880622213170249e-15
          ],
          [
            -0.0008155423796672728,
            4.0514263202279874e-16,
            0.003033497996795314
          ],
          [
            -0.001631034119149924,
            -3.1288242869087427e-15,
            0.00606722502165979
          ],
          [
            -0.0024464345794415186,
            -1.877294572145246e-15,
            0.00910139197913811
          ],
          [
            -0.0032617221412934994,
            -1.7114936270270052e-16,
            0.012136174631070645
          ],
          [
            -0.0040769012310154515,
            -2.045769726055716e-15,
            0.01517169907943812
          ],
          [
            -0.004892006206635793,
            -9.948056707094464e-16,
            0.018208031835342177
          ],
          [
            -0.005707104527588112,
            -2.8988423307769893e-15,
            0.02124516869535367
          ],
          [
            -0.006522297247877106,
            -3.907019045447584e-15,
            0.02428302766871199
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          -0.006522297247877172,
          -4.744046397415478e-15,
          0.02428302766871188
        ],
        "actual_opposite_endpoint_branch_residual": 8.469274579463618e-16
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            0.006522297247875782,
            1.6847515391047077e-15,
            -0.024283027668710135
          ],
          [
            0.005707104527583774,
            1.6446384072212622e-15,
            -0.021245168695351282
          ],
          [
            0.004892006206634866,
            6.912829727913761e-16,
            -0.018208031835340508
          ],
          [
            0.0040769012310149285,
            1.008176714670595e-15,
            -0.015171699079435117
          ],
          [
            0.0032617221412910608,
            1.9200819128209207e-15,
            -0.012136174631068317
          ],
          [
            0.002446434579439722,
            3.971200056461097e-16,
            -0.009101391979136753
          ],
          [
            0.0016310341191501116,
            -6.525069453040455e-16,
            -0.006067225021656687
          ],
          [
            0.0008155423796665115,
            -1.034918802592892e-15,
            -0.00303349799679377
          ],
          [
            -6.953404306063286e-16,
            -1.5296474291553854e-15,
            8.714252835580446e-16
          ],
          [
            -0.0008155423796672728,
            4.0514263202279874e-16,
            0.003033497996795314
          ],
          [
            -0.001631034119149924,
            -3.1288242869087427e-15,
            0.00606722502165979
          ],
          [
            -0.0024464345794415186,
            -1.877294572145246e-15,
            0.00910139197913811
          ],
          [
            -0.0032617221412934994,
            -1.7114936270270047e-16,
            0.012136174631070645
          ],
          [
            -0.0040769012310154515,
            -2.0457697260557165e-15,
            0.01517169907943812
          ],
          [
            -0.004892006206635793,
            -9.948056707094464e-16,
            0.018208031835342177
          ],
          [
            -0.005707104527588112,
            -2.8988423307769893e-15,
            0.02124516869535367
          ],
          [
            -0.006522297247877106,
            -3.907019045447584e-15,
            0.02428302766871199
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            0.006522297247875782,
            1.6847515391047077e-15,
            -0.024283027668710135
          ],
          [
            0.005707104527583774,
            1.6446384072212622e-15,
            -0.021245168695351282
          ],
          [
            0.004892006206634866,
            6.9128297279137615e-16,
            -0.018208031835340508
          ],
          [
            0.0040769012310149285,
            1.008176714670595e-15,
            -0.015171699079435117
          ],
          [
            0.0032617221412910608,
            1.9200819128209207e-15,
            -0.012136174631068317
          ],
          [
            0.002446434579439722,
            3.9712000564610965e-16,
            -0.009101391979136753
          ],
          [
            0.0016310341191501116,
            -6.525069453040455e-16,
            -0.006067225021656687
          ],
          [
            0.0008155423796665115,
            -1.034918802592892e-15,
            -0.00303349799679377
          ],
          [
            -6.95298853214954e-16,
            -1.5296474291553854e-15,
            8.712648658093514e-16
          ],
          [
            -0.0008155423796672728,
            4.0514263202279894e-16,
            0.003033497996795314
          ],
          [
            -0.001631034119149924,
            -3.1288242869087423e-15,
            0.00606722502165979
          ],
          [
            -0.0024464345794415186,
            -1.877294572145246e-15,
            0.00910139197913811
          ],
          [
            -0.0032617221412934994,
            -1.7114936270270052e-16,
            0.012136174631070645
          ],
          [
            -0.0040769012310154515,
            -2.045769726055716e-15,
            0.01517169907943812
          ],
          [
            -0.004892006206635793,
            -9.948056707094464e-16,
            0.018208031835342177
          ],
          [
            -0.005707104527588112,
            -2.8988423307769893e-15,
            0.02124516869535367
          ],
          [
            -0.006522297247877106,
            -3.907019045447584e-15,
            0.02428302766871199
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            0.006522297247875786,
            1.6653345369377348e-15,
            -0.024283027668710155
          ],
          [
            0.005707104527583828,
            1.6653345369377348e-15,
            -0.021245168695351258
          ],
          [
            0.00489200620663488,
            6.661338147750939e-16,
            -0.018208031835340532
          ],
          [
            0.0040769012310148955,
            9.992007221626409e-16,
            -0.015171699079435108
          ],
          [
            0.003261722141291057,
            1.887379141862766e-15,
            -0.012136174631068308
          ],
          [
            0.0024464345794397158,
            4.440892098500626e-16,
            -0.00910139197913673
          ],
          [
            0.0016310341191501099,
            -6.661338147750939e-16,
            -0.006067225021656686
          ],
          [
            0.0008155423796665229,
            -1.0547118733938987e-15,
            -0.0030334979967937548
          ],
          [
            -7.216449660063518e-16,
            -1.5543122344752192e-15,
            8.881784197001252e-16
          ],
          [
            -0.0008155423796673,
            4.440892098500626e-16,
            0.003033497996795309
          ],
          [
            -0.0016310341191499433,
            -3.1086244689504383e-15,
            0.0060672250216597945
          ],
          [
            -0.002446434579441492,
            -1.887379141862766e-15,
            0.009101391979138063
          ],
          [
            -0.0032617221412934994,
            -1.6653345369377348e-16,
            0.01213617463107064
          ],
          [
            -0.004076901231015451,
            -2.0539125955565396e-15,
            0.015171699079438161
          ],
          [
            -0.004892006206635768,
            -9.992007221626409e-16,
            0.018208031835342142
          ],
          [
            -0.005707104527588103,
            -2.886579864025407e-15,
            0.021245168695353644
          ],
          [
            -0.006522297247877118,
            -3.885780586188048e-15,
            0.024283027668712043
          ]
        ]
      },
      "incoming_structure_ids": [
        "incoming_00_000",
        "incoming_00_001",
        "incoming_00_002",
        "incoming_00_003",
        "incoming_00_004",
        "incoming_00_005",
        "incoming_00_006",
        "incoming_00_007",
        "incoming_00_008"
      ],
      "reflected_structure_ids": [
        "reflected_00_001",
        "reflected_00_002",
        "reflected_00_003",
        "reflected_00_004",
        "reflected_00_005",
        "reflected_00_006",
        "reflected_00_007",
        "reflected_00_008"
      ],
      "positive_extension_structure_ids": [
        "extension_plus_00_000",
        "extension_plus_00_001",
        "extension_plus_00_002",
        "extension_plus_00_003"
      ],
      "negative_extension_structure_ids": [
        "extension_minus_00_000",
        "extension_minus_00_001",
        "extension_minus_00_002",
        "extension_minus_00_003"
      ],
      "extension": {
        "enabled": true,
        "fraction_beyond_polar_endpoint": 0.35,
        "images_per_side": 4,
        "construction": "continue fractional atomic displacements and symmetric log strain beyond +P; reflect these structures about N for the -P side",
        "positive_path_coordinates": [
          1.35,
          1.2625,
          1.175,
          1.0875
        ],
        "negative_path_coordinates": [
          -1.0875,
          -1.175,
          -1.2625,
          -1.35
        ]
      },
      "branch_coordinates": [
        1.35,
        1.2625,
        1.175,
        1.0875,
        1.0,
        0.875,
        0.75,
        0.625,
        0.5,
        0.375,
        0.25,
        0.125,
        0.0,
        -0.125,
        -0.25,
        -0.375,
        -0.5,
        -0.625,
        -0.75,
        -0.875,
        -1.0,
        -1.0875,
        -1.175,
        -1.2625,
        -1.35
      ],
      "parent": {
        "candidate_id": "inversion_parent_endpoint_00",
        "source": "same_species_inversion_center_projection_from_endpoint",
        "spacegroup": "C2/c",
        "spacegroup_number": 15,
        "pointgroup": "2/m",
        "has_inversion": true,
        "is_polar_point_group": false,
        "nonpolar_parent_hypothesis": true,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.0
        ],
        "formal_class": [
          0.0,
          0.0,
          0.0
        ],
        "target_residual": 1.8183053300193245e-15,
        "parent_symmetrization_rmsd_A": 0.03651097669099196,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -121.12940121026642,
        "reduced_polarization": [
          1.4410961255617084e-15,
          1.6981225830658563e-16,
          1.0957372070877831e-15
        ],
        "cartesian_polarization_e_A2": [
          3.782240914512356e-17,
          2.4109395283748907e-18,
          7.16644677238433e-18
        ],
        "ranking_score": 0.036510976690995595
      }
    }
  ],
  "path_sampling": {
    "num_images": 17,
    "images_per_leg_including_parent": 9,
    "extension_fraction_beyond_polar_endpoint": 0.35,
    "extension_images_per_side": 4,
    "total_images_per_sampled_branch": 25,
    "construction": "linear polar-to-parent interpolation plus parent-reflected second leg and symmetric log-strain continuation beyond both polar endpoints"
  },
  "branch_folding": "componentwise integer unwrap with per-image shifts, then reduced-coordinate fold [-0.5, 0.5)",
  "bec_backprojection_settings": {
    "variable_cell": true,
    "max_strain_step_log_component": 0.02,
    "strain_response_refresh_iterations": 4,
    "cell_principal_stretch_bounds": [
      0.85,
      1.15
    ],
    "cell_volume_ratio_bounds": [
      0.7,
      1.3
    ],
    "strain_jacobian": "branch-matched finite differences of reduced polarization in six symmetric log-strain coordinates at fixed fractional positions"
  },
  "model_input_contract": "one polar endpoint structure; no reference parent or path frame",
  "run": {
    "model_file": "MACEField-MH-0-omat-dielectric.model",
    "model_sha256": "f92e043aaf2cd8879919db8452503553fe7b608cb749d8d169dd96d4aa094aa2",
    "model_head": "mp-ferroelectric",
    "device": "cpu",
    "dtype": "float64",
    "num_images": 17,
    "compute_becs_for_every_image": true,
    "compute_polarizability_for_every_image": true,
    "initial_structure_relaxation": {
      "enabled": false
    },
    "model_evaluations_for_recovery": {
      "total": 72,
      "full_response": 25,
      "energy_polarization": 47
    },
    "model_evaluations_for_recovery_and_path_properties": {
      "total": 97,
      "full_response": 50,
      "energy_polarization": 47
    },
    "elapsed_seconds": 539.9699376140488
  }
}
