{
  "schema": "ferrofinder.endpoint_parent_recovery.v4_variable_cell",
  "status": "complete",
  "input_atom_count": 8,
  "input_formula": "H2In2O4",
  "input_spacegroup": "Pmn2_1",
  "input_pointgroup": "mm2",
  "input_is_polar_point_group": true,
  "input_energy_eV": -41.67151178004678,
  "input_cartesian_polarization_e_A2": [
    4.999445570633116e-19,
    -1.3854604826791766e-17,
    -0.008235653686587182
  ],
  "input_reduced_polarization": [
    1.2463868489112237e-17,
    -2.4842968079246017e-16,
    -0.12734037037735071
  ],
  "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": [
        0.0,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        -0.5,
        0.0
      ]
    },
    {
      "orbit_id": 3,
      "representative_formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.0
      ]
    },
    {
      "orbit_id": 4,
      "representative_formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        -0.5,
        -0.5
      ]
    },
    {
      "orbit_id": 5,
      "representative_formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        0.5,
        0.0,
        -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": "Pnnm",
      "spacegroup_number": 58,
      "pointgroup": "mmm",
      "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": 2.8353532921354943e-16,
      "parent_symmetrization_rmsd_A": 0.1272265599943764,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -41.63396482136054,
      "reduced_polarization": [
        1.5243579198876283e-18,
        2.454365521082137e-16,
        -1.4195371828310823e-16
      ],
      "cartesian_polarization_e_A2": [
        6.114429446442699e-20,
        1.3687681877071382e-17,
        -9.180762234621049e-18
      ],
      "ranking_score": 0.12722655999437696
    },
    {
      "candidate_id": "inversion_parent_endpoint_01",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "Pmmn",
      "spacegroup_number": 59,
      "pointgroup": "mmm",
      "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": 3.755776693020353e-16,
      "parent_symmetrization_rmsd_A": 0.5148200688013728,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -37.21981267858868,
      "reduced_polarization": [
        9.256768908751907e-18,
        1.0775263263287428e-16,
        -3.596696652046205e-16
      ],
      "cartesian_polarization_e_A2": [
        3.713029575020038e-19,
        6.0092261899337774e-18,
        -2.3261396173250523e-17
      ],
      "ranking_score": 0.5148200688013735
    },
    {
      "candidate_id": "bec_projection_00",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Pmn2_1",
      "spacegroup_number": 31,
      "pointgroup": "mm2",
      "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": 6.439208165140955e-07,
      "parent_symmetrization_rmsd_A": 0.07091220794588086,
      "parent_cell_rmsd_A": 0.005848933767536001,
      "energy_eV": -41.61567052279107,
      "reduced_polarization": [
        -6.12755968896428e-16,
        6.976160247263567e-16,
        6.439208165140955e-07
      ],
      "cartesian_polarization_e_A2": [
        -2.4553190624875947e-17,
        3.885830976008036e-17,
        4.16642154036846e-08
      ],
      "ranking_score": 0.5723757292293978
    },
    {
      "candidate_id": "inversion_parent_bec_00_00",
      "source": "same_species_inversion_center_projection_after_BEC",
      "spacegroup": "Pnnm",
      "spacegroup_number": 58,
      "pointgroup": "mmm",
      "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": 3.0338180270506274e-15,
      "parent_symmetrization_rmsd_A": 0.12724074972362004,
      "parent_cell_rmsd_A": 0.005848933767536001,
      "energy_eV": -41.62067568654678,
      "reduced_polarization": [
        -5.462872499554306e-16,
        2.6287951072334756e-15,
        1.4124653432841584e-15
      ],
      "cartesian_polarization_e_A2": [
        -2.1889711756334048e-17,
        1.4642745051223414e-16,
        9.139207617392291e-17
      ],
      "ranking_score": 0.12870298316551013
    },
    {
      "candidate_id": "bec_projection_01",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Pmn2_1",
      "spacegroup_number": 31,
      "pointgroup": "mm2",
      "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": 4.442588324082841e-05,
      "parent_symmetrization_rmsd_A": 0.24619007957776912,
      "parent_cell_rmsd_A": 0.021781362595158237,
      "energy_eV": -40.009145276772756,
      "reduced_polarization": [
        8.849818120118471e-16,
        -5.729921484193958e-16,
        -0.5000444258832408
      ],
      "cartesian_polarization_e_A2": [
        -1.9435844448182035e-16,
        3.9827403482909977e-16,
        -0.03228462457973201
      ],
      "ranking_score": 0.7517242719930404
    },
    {
      "candidate_id": "bec_projection_02",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Pm",
      "spacegroup_number": 6,
      "pointgroup": "m",
      "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": 0.00021374921623143315,
      "parent_symmetrization_rmsd_A": 0.2846721060392381,
      "parent_cell_rmsd_A": 0.05517055722015407,
      "energy_eV": -40.27252990813565,
      "reduced_polarization": [
        -2.1320192452583247e-15,
        -0.4998438812901583,
        -0.00014599888998519
      ],
      "cartesian_polarization_e_A2": [
        -2.1110167215200533e-18,
        -0.027844381061001695,
        0.00028461284653015284
      ],
      "ranking_score": 0.7988922437767394
    },
    {
      "candidate_id": "bec_projection_03",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Pc",
      "spacegroup_number": 7,
      "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": 2.399684548727727e-06,
      "parent_symmetrization_rmsd_A": 0.19659285067547366,
      "parent_cell_rmsd_A": 0.009939210450446236,
      "energy_eV": -40.894679626045814,
      "reduced_polarization": [
        0.49999772927800684,
        2.946290199885657e-15,
        -7.760847654666985e-07
      ],
      "cartesian_polarization_e_A2": [
        0.020034642208501627,
        7.621468579594111e-17,
        4.265427577975157e-05
      ],
      "ranking_score": 0.6990824526571826
    },
    {
      "candidate_id": "bec_projection_04",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Pm",
      "spacegroup_number": 6,
      "pointgroup": "m",
      "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": 0.0014796549444556209,
      "parent_symmetrization_rmsd_A": 0.4856681950868327,
      "parent_cell_rmsd_A": 0.14326047874672562,
      "energy_eV": -29.264708904172274,
      "reduced_polarization": [
        3.088462005558769e-14,
        -0.5002191795729958,
        -0.501463331496768
      ],
      "cartesian_polarization_e_A2": [
        -1.5689018075898812e-15,
        -0.027368825045043507,
        -0.03154235174366856
      ],
      "ranking_score": 1.0244426246624254
    },
    {
      "candidate_id": "bec_projection_05",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Pc",
      "spacegroup_number": 7,
      "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": 0.0002346764186696127,
      "parent_symmetrization_rmsd_A": 0.34787463405937236,
      "parent_cell_rmsd_A": 0.029081097930440693,
      "energy_eV": -39.06492724182831,
      "reduced_polarization": [
        0.49977843660561,
        -9.984291251061973e-16,
        -0.500077347810221
      ],
      "cartesian_polarization_e_A2": [
        0.02005581310500873,
        5.050540022762527e-16,
        -0.03221774619003463
      ],
      "ranking_score": 0.8556142613793218
    },
    {
      "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": 4.697572471791762e-06,
      "parent_symmetrization_rmsd_A": 0.35737840775298374,
      "parent_cell_rmsd_A": 0.0635335167627976,
      "energy_eV": -38.53170882761725,
      "reduced_polarization": [
        0.5000006697495758,
        -0.49999573857918517,
        -1.8598159243221668e-06
      ],
      "cartesian_polarization_e_A2": [
        0.020031959568942388,
        -0.027851500357816212,
        0.00038400323876006397
      ],
      "ranking_score": 0.8732711820886268
    },
    {
      "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": 0.007396154395432639,
      "parent_symmetrization_rmsd_A": 0.5198551753966713,
      "parent_cell_rmsd_A": 0.16353280570226425,
      "energy_eV": -24.72720967325192,
      "reduced_polarization": [
        0.4983886593110132,
        -0.49901176920524154,
        -0.5071505301147107
      ],
      "cartesian_polarization_e_A2": [
        0.02000450996309144,
        -0.02718122030859688,
        -0.0318208308048377
      ],
      "ranking_score": 1.0755306856131026
    }
  ],
  "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": [
              1.2463868489112237e-17,
              -2.4842968079246017e-16,
              -0.12734037037735071
            ],
            "branch_aligned_reduced_polarization": [
              1.2463868489112237e-17,
              -2.4842968079246017e-16,
              -0.12734037037735071
            ],
            "target_residual": 0.12734037037735071,
            "energy_eV": -41.67151178004678,
            "max_atomic_step_A": 0.059940456595738996,
            "max_log_strain_component": 0.001373770502573482,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.8316443933142786,
            "cell_principal_stretches": [
              1.0013747145575258,
              0.9998550056174202,
              0.9996797311877669
            ],
            "cell_volume_ratio": 1.0009088582596426,
            "cell_rmsd_from_input_A": 0.0059465363914073446
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              1.2570556958723872e-15,
              5.27783362760874e-15,
              0.0022146621805600158
            ],
            "branch_aligned_reduced_polarization": [
              1.2570556958723872e-15,
              5.27783362760874e-15,
              0.0022146621805600158
            ],
            "target_residual": 0.0022146621805600158,
            "energy_eV": -41.61323627467122,
            "max_atomic_step_A": 0.0009782539372056708,
            "max_log_strain_component": 2.251888701844074e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.8316443933142786,
            "cell_principal_stretches": [
              1.0013521649673622,
              0.9998573822001687,
              0.9996849802166896
            ],
            "cell_volume_ratio": 1.0008939535708907,
            "cell_rmsd_from_input_A": 0.005848933767536001
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -6.12755968896428e-16,
              6.976160247263567e-16,
              6.439208165140955e-07
            ],
            "branch_aligned_reduced_polarization": [
              -6.12755968896428e-16,
              6.976160247263567e-16,
              6.439208165140955e-07
            ],
            "target_residual": 6.439208165140955e-07,
            "energy_eV": -41.61567052279107
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "inversion_parent_endpoint_00",
        "source": "same_species_inversion_center_projection_from_endpoint",
        "spacegroup": "Pnnm",
        "spacegroup_number": 58,
        "pointgroup": "mmm",
        "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": 2.8353532921354943e-16,
        "parent_symmetrization_rmsd_A": 0.1272265599943764,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -41.63396482136054,
        "reduced_polarization": [
          1.5243579198876283e-18,
          2.454365521082137e-16,
          -1.4195371828310823e-16
        ],
        "cartesian_polarization_e_A2": [
          6.114429446442699e-20,
          1.3687681877071382e-17,
          -9.180762234621049e-18
        ],
        "ranking_score": 0.12722655999437696
      },
      "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": [
          -41.67151178004677,
          -41.69194288407848,
          -41.69890669805774,
          -41.69620371079013,
          -41.686077729822514,
          -41.670632565844116,
          -41.653330525307084,
          -41.63936943764025,
          -41.63396482136054
        ],
        "cartesian_polarizations_e_A2": [
          [
            -1.844598733040633e-17,
            -1.0599607307244303e-16,
            -0.008235653686587154
          ],
          [
            -2.5409627325112987e-18,
            -1.0683068782104493e-17,
            -0.0075291458353706495
          ],
          [
            -2.650719657935397e-18,
            6.059303074849892e-17,
            -0.006647483209934289
          ],
          [
            -6.221581125387195e-18,
            1.2686144178749087e-17,
            -0.005627393944866682
          ],
          [
            1.4902298333130301e-19,
            8.513070435739519e-17,
            -0.004518743862191423
          ],
          [
            3.118128437349229e-17,
            -4.5403042323944097e-17,
            -0.003373443193060597
          ],
          [
            -2.1423407811031007e-17,
            -2.5038442458057408e-17,
            -0.0022308896121966564
          ],
          [
            1.3250256977040526e-17,
            -8.41291666590729e-17,
            -0.0011078271152802025
          ],
          [
            -1.4022538382659296e-17,
            6.3430720893745436e-18,
            -2.6039980156379704e-17
          ]
        ],
        "raw_reduced_polarization": [
          [
            -4.598677133090581e-16,
            -1.9006367144965327e-15,
            -0.1273403703773503
          ],
          [
            -6.334747500760465e-17,
            -1.915602357917765e-16,
            -0.11641628652533759
          ],
          [
            -6.608377019259656e-17,
            1.0865057123814823e-15,
            -0.10278394481410442
          ],
          [
            -1.5510713707269914e-16,
            2.274777800027346e-16,
            -0.08701123875153347
          ],
          [
            3.715217697352208e-18,
            1.5264956289657192e-15,
            -0.0698691978742354
          ],
          [
            7.773650543086164e-16,
            -8.141310021150502e-16,
            -0.05216046254481388
          ],
          [
            -5.340962988251833e-16,
            -4.489693026369762e-16,
            -0.034494202925357466
          ],
          [
            3.303355503635595e-16,
            -1.5085368568602401e-15,
            -0.01712931608617849
          ],
          [
            -3.4958891304193366e-16,
            1.137388900013673e-16,
            -4.0263236458481606e-16
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -4.598677133090581e-16,
            -1.9006367144965327e-15,
            -0.1273403703773503
          ],
          [
            -6.334747500760466e-17,
            -1.915602357917764e-16,
            -0.11641628652533759
          ],
          [
            -6.608377019259656e-17,
            1.0865057123814823e-15,
            -0.10278394481410442
          ],
          [
            -1.5510713707269914e-16,
            2.274777800027346e-16,
            -0.08701123875153347
          ],
          [
            3.7152176973522046e-18,
            1.5264956289657192e-15,
            -0.0698691978742354
          ],
          [
            7.773650543086164e-16,
            -8.141310021150504e-16,
            -0.05216046254481388
          ],
          [
            -5.340962988251832e-16,
            -4.489693026369762e-16,
            -0.034494202925357466
          ],
          [
            3.3033555036355954e-16,
            -1.5085368568602401e-15,
            -0.01712931608617849
          ],
          [
            -3.4958891304193366e-16,
            1.1373889000136725e-16,
            -4.0245584642661925e-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": [
          [
            -4.440892098500626e-16,
            -1.887379141862766e-15,
            -0.1273403703773503
          ],
          [
            -5.551115123125783e-17,
            -1.6653345369377348e-16,
            -0.11641628652533759
          ],
          [
            -5.551115123125783e-17,
            1.1102230246251565e-15,
            -0.10278394481410441
          ],
          [
            -1.6653345369377348e-16,
            2.220446049250313e-16,
            -0.08701123875153349
          ],
          [
            0.0,
            1.5543122344752192e-15,
            -0.0698691978742354
          ],
          [
            7.771561172376096e-16,
            -8.326672684688674e-16,
            -0.05216046254481388
          ],
          [
            -5.551115123125783e-16,
            -4.440892098500626e-16,
            -0.03449420292535749
          ],
          [
            3.3306690738754696e-16,
            -1.4988010832439613e-15,
            -0.017129316086178514
          ],
          [
            -3.3306690738754696e-16,
            1.1102230246251565e-16,
            -3.885780586188048e-16
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -41.63396482136054,
          -41.63936943764025,
          -41.653330525307084,
          -41.6706325658441,
          -41.686077729822514,
          -41.696203710790144,
          -41.69890669805774,
          -41.691942884078486,
          -41.671511780046785
        ],
        "cartesian_polarizations_e_A2": [
          [
            -1.4022538382659296e-17,
            6.3430720893745436e-18,
            -2.6039980156379704e-17
          ],
          [
            -6.627295550331684e-18,
            1.6358449072597507e-17,
            0.0011078271152802398
          ],
          [
            -3.4070435939547254e-17,
            5.1412268513877875e-17,
            0.0022308896121964986
          ],
          [
            -3.091467469729695e-18,
            2.6741056545205313e-16,
            0.003373443193060493
          ],
          [
            1.4152804457932022e-17,
            -6.676917988815309e-17,
            0.0045187438621912
          ],
          [
            -1.9634844467310785e-17,
            3.872612433512879e-17,
            0.005627393944866491
          ],
          [
            -9.491341056974596e-18,
            1.382122023684769e-16,
            0.006647483209934151
          ],
          [
            -1.7477027011233047e-18,
            4.673842592170716e-18,
            0.007529145835370648
          ],
          [
            8.556652184568659e-18,
            7.010763888256074e-18,
            0.00823565368658704
          ]
        ],
        "raw_reduced_polarization": [
          [
            -3.4958891304193366e-16,
            1.137388900013673e-16,
            -4.0263236458481606e-16
          ],
          [
            -1.6522180111934365e-16,
            2.933266110561578e-16,
            0.017129316086179066
          ],
          [
            -8.493930515248388e-16,
            9.218836347479245e-16,
            0.03449420292535502
          ],
          [
            -7.707183413980032e-17,
            4.794992152162906e-15,
            0.052160462544812276
          ],
          [
            3.5283651161632207e-16,
            -1.1972514736986032e-15,
            0.06986919787423194
          ],
          [
            -4.895065178472244e-16,
            6.944058547451899e-16,
            0.08701123875153051
          ],
          [
            -2.366238916857772e-16,
            2.478310550556109e-15,
            0.1027839448141023
          ],
          [
            -4.3571104669729494e-17,
            8.380760315890222e-17,
            0.11641628652533757
          ],
          [
            2.133216294262665e-16,
            1.2571140473835332e-16,
            0.12734037037734852
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -3.4958891304193366e-16,
            1.137388900013673e-16,
            -4.0263236458481606e-16
          ],
          [
            -1.6522180111934365e-16,
            2.933266110561578e-16,
            0.017129316086179066
          ],
          [
            -8.493930515248388e-16,
            9.218836347479245e-16,
            0.03449420292535502
          ],
          [
            -7.707183413980029e-17,
            4.794992152162906e-15,
            0.052160462544812276
          ],
          [
            3.5283651161632207e-16,
            -1.1972514736986036e-15,
            0.06986919787423194
          ],
          [
            -4.895065178472244e-16,
            6.944058547451898e-16,
            0.08701123875153051
          ],
          [
            -2.366238916857772e-16,
            2.478310550556109e-15,
            0.1027839448141023
          ],
          [
            -4.357110466972949e-17,
            8.38076031589021e-17,
            0.11641628652533757
          ],
          [
            2.133216294262665e-16,
            1.2571140473835332e-16,
            0.12734037037734852
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          -2.3931011277480923e-16,
          2.1281144944992675e-15,
          0.1273403703773495
        ],
        "actual_opposite_endpoint_branch_residual": 2.271166946897956e-15
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            -4.598677133090581e-16,
            -1.9006367144965327e-15,
            -0.1273403703773503
          ],
          [
            -6.334747500760465e-17,
            -1.915602357917765e-16,
            -0.11641628652533759
          ],
          [
            -6.608377019259656e-17,
            1.0865057123814823e-15,
            -0.10278394481410442
          ],
          [
            -1.5510713707269914e-16,
            2.274777800027346e-16,
            -0.08701123875153347
          ],
          [
            3.715217697352208e-18,
            1.5264956289657192e-15,
            -0.0698691978742354
          ],
          [
            7.773650543086164e-16,
            -8.141310021150502e-16,
            -0.05216046254481388
          ],
          [
            -5.340962988251833e-16,
            -4.489693026369762e-16,
            -0.034494202925357466
          ],
          [
            3.303355503635595e-16,
            -1.5085368568602401e-15,
            -0.01712931608617849
          ],
          [
            -3.4958891304193366e-16,
            1.137388900013673e-16,
            -4.0263236458481606e-16
          ],
          [
            -1.6522180111934365e-16,
            2.933266110561578e-16,
            0.017129316086179066
          ],
          [
            -8.493930515248388e-16,
            9.218836347479245e-16,
            0.03449420292535502
          ],
          [
            -7.707183413980032e-17,
            4.794992152162906e-15,
            0.052160462544812276
          ],
          [
            3.5283651161632207e-16,
            -1.1972514736986032e-15,
            0.06986919787423194
          ],
          [
            -4.895065178472244e-16,
            6.944058547451899e-16,
            0.08701123875153051
          ],
          [
            -2.366238916857772e-16,
            2.478310550556109e-15,
            0.1027839448141023
          ],
          [
            -4.3571104669729494e-17,
            8.380760315890222e-17,
            0.11641628652533757
          ],
          [
            2.133216294262665e-16,
            1.2571140473835332e-16,
            0.12734037037734852
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -4.598677133090581e-16,
            -1.9006367144965327e-15,
            -0.1273403703773503
          ],
          [
            -6.334747500760466e-17,
            -1.915602357917764e-16,
            -0.11641628652533759
          ],
          [
            -6.608377019259656e-17,
            1.0865057123814823e-15,
            -0.10278394481410442
          ],
          [
            -1.5510713707269914e-16,
            2.274777800027346e-16,
            -0.08701123875153347
          ],
          [
            3.7152176973522046e-18,
            1.5264956289657192e-15,
            -0.0698691978742354
          ],
          [
            7.773650543086164e-16,
            -8.141310021150504e-16,
            -0.05216046254481388
          ],
          [
            -5.340962988251832e-16,
            -4.489693026369762e-16,
            -0.034494202925357466
          ],
          [
            3.3033555036355954e-16,
            -1.5085368568602401e-15,
            -0.01712931608617849
          ],
          [
            -3.4958891304193366e-16,
            1.1373889000136725e-16,
            -4.0245584642661925e-16
          ],
          [
            -1.6522180111934365e-16,
            2.933266110561578e-16,
            0.017129316086179066
          ],
          [
            -8.493930515248388e-16,
            9.218836347479245e-16,
            0.03449420292535502
          ],
          [
            -7.707183413980029e-17,
            4.794992152162906e-15,
            0.052160462544812276
          ],
          [
            3.5283651161632207e-16,
            -1.1972514736986036e-15,
            0.06986919787423194
          ],
          [
            -4.895065178472244e-16,
            6.944058547451898e-16,
            0.08701123875153051
          ],
          [
            -2.366238916857772e-16,
            2.478310550556109e-15,
            0.1027839448141023
          ],
          [
            -4.357110466972949e-17,
            8.38076031589021e-17,
            0.11641628652533757
          ],
          [
            2.133216294262665e-16,
            1.2571140473835332e-16,
            0.12734037037734852
          ]
        ],
        "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": [
          [
            -4.440892098500626e-16,
            -1.887379141862766e-15,
            -0.1273403703773503
          ],
          [
            -5.551115123125783e-17,
            -1.6653345369377348e-16,
            -0.11641628652533759
          ],
          [
            -5.551115123125783e-17,
            1.1102230246251565e-15,
            -0.10278394481410441
          ],
          [
            -1.6653345369377348e-16,
            2.220446049250313e-16,
            -0.08701123875153349
          ],
          [
            0.0,
            1.5543122344752192e-15,
            -0.0698691978742354
          ],
          [
            7.771561172376096e-16,
            -8.326672684688674e-16,
            -0.05216046254481388
          ],
          [
            -5.551115123125783e-16,
            -4.440892098500626e-16,
            -0.03449420292535749
          ],
          [
            3.3306690738754696e-16,
            -1.4988010832439613e-15,
            -0.017129316086178514
          ],
          [
            -3.3306690738754696e-16,
            1.1102230246251565e-16,
            -3.885780586188048e-16
          ],
          [
            -1.6653345369377348e-16,
            3.3306690738754696e-16,
            0.01712931608617907
          ],
          [
            -8.326672684688674e-16,
            8.881784197001252e-16,
            0.03449420292535499
          ],
          [
            -5.551115123125783e-17,
            4.773959005888173e-15,
            0.052160462544812325
          ],
          [
            3.3306690738754696e-16,
            -1.2212453270876722e-15,
            0.06986919787423196
          ],
          [
            -4.996003610813204e-16,
            6.661338147750939e-16,
            0.0870112387515305
          ],
          [
            -2.220446049250313e-16,
            2.4424906541753444e-15,
            0.10278394481410236
          ],
          [
            -5.551115123125783e-17,
            1.1102230246251565e-16,
            0.11641628652533753
          ],
          [
            2.220446049250313e-16,
            1.1102230246251565e-16,
            0.12734037037734858
          ]
        ]
      },
      "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": [
              1.2463868489112237e-17,
              -2.4842968079246017e-16,
              -0.12734037037735071
            ],
            "branch_aligned_reduced_polarization": [
              1.2463868489112237e-17,
              -2.4842968079246017e-16,
              -0.1273403703773507
            ],
            "target_residual": 0.3726596296226493,
            "energy_eV": -41.67151178004678,
            "max_atomic_step_A": 0.11999999999999998,
            "max_log_strain_component": 0.002750270346131077,
            "step_scale": 0.6840927060430215,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.8316443933142786,
            "cell_principal_stretches": [
              1.0006414822768375,
              1.0002903400198029,
              0.9972535081825719
            ],
            "cell_volume_ratio": 0.9981829569733475,
            "cell_rmsd_from_input_A": 0.011857749063727987
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              3.848161830307464e-15,
              -1.1717590178114191e-14,
              -0.3618680813093833
            ],
            "branch_aligned_reduced_polarization": [
              3.848161830307464e-15,
              -1.1717590178114191e-14,
              -0.3618680813093833
            ],
            "target_residual": 0.1381319186906167,
            "energy_eV": -41.13973090800717,
            "max_atomic_step_A": 0.0797228961591564,
            "max_log_strain_component": 0.0021551476949302514,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.8316443933142786,
            "cell_principal_stretches": [
              1.0011444437065382,
              1.0005179131524757,
              0.995106593872838
            ],
            "cell_volume_ratio": 0.9967614059666287,
            "cell_rmsd_from_input_A": 0.021105890840648758
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -3.934907751824622e-16,
              -9.869221430569358e-15,
              -0.4920352981640941
            ],
            "branch_aligned_reduced_polarization": [
              -3.934907751824622e-16,
              -9.869221430569358e-15,
              -0.4920352981640941
            ],
            "target_residual": 0.007964701835905919,
            "energy_eV": -40.10651825590694,
            "max_atomic_step_A": 0.004852279869386865,
            "max_log_strain_component": 0.00015775967648912916,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.8316443933142786,
            "cell_principal_stretches": [
              1.001181271080596,
              1.000534573841894,
              0.9949496185610293
            ],
            "cell_volume_ratio": 0.9966574260995924,
            "cell_rmsd_from_input_A": 0.021781362595158237
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              8.849818120118471e-16,
              -5.729921484193958e-16,
              -0.5000444258832408
            ],
            "branch_aligned_reduced_polarization": [
              8.849818120118471e-16,
              -5.729921484193958e-16,
              -0.5000444258832408
            ],
            "target_residual": 4.442588324082841e-05,
            "energy_eV": -40.009145276772756
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_01",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Pmn2_1",
        "spacegroup_number": 31,
        "pointgroup": "mm2",
        "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": 4.442588324082841e-05,
        "parent_symmetrization_rmsd_A": 0.24619007957776912,
        "parent_cell_rmsd_A": 0.021781362595158237,
        "energy_eV": -40.009145276772756,
        "reduced_polarization": [
          8.849818120118471e-16,
          -5.729921484193958e-16,
          -0.5000444258832408
        ],
        "cartesian_polarization_e_A2": [
          -1.9435844448182035e-16,
          3.9827403482909977e-16,
          -0.03228462457973201
        ],
        "ranking_score": 0.7517242719930404
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 2,
      "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": [
              1.2463868489112237e-17,
              -2.4842968079246017e-16,
              -0.12734037037735071
            ],
            "branch_aligned_reduced_polarization": [
              1.2463868489112237e-17,
              -2.220446049250313e-16,
              -0.12734037037735071
            ],
            "target_residual": 0.5159608220861741,
            "energy_eV": -41.67151178004678,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.004568872592183177,
            "step_scale": 0.5738649766255911,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.8316443933142786,
            "cell_principal_stretches": [
              1.0049089364406982,
              0.9999167902313002,
              0.9957168105197185
            ],
            "cell_volume_ratio": 1.0005214609680957,
            "cell_rmsd_from_input_A": 0.023982294406229714
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              2.7109815797672975e-17,
              -0.28053823049730553,
              -0.03898017425391312
            ],
            "branch_aligned_reduced_polarization": [
              2.7109815797672975e-17,
              -0.28053823049730553,
              -0.03898017425391312
            ],
            "target_residual": 0.22289666273436942,
            "energy_eV": -41.29428305796588,
            "max_atomic_step_A": 0.10174914867910732,
            "max_log_strain_component": 0.0041077848879312725,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.8316443933142786,
            "cell_principal_stretches": [
              1.009105217649965,
              0.9998988952476697,
              0.9917051348237518
            ],
            "cell_volume_ratio": 1.0006336468741868,
            "cell_rmsd_from_input_A": 0.045284744673394745
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -3.812238776150112e-15,
              -0.4584216203127161,
              -0.010403898550581284
            ],
            "branch_aligned_reduced_polarization": [
              -3.812238776150112e-15,
              -0.4584216203127161,
              -0.010403898550581284
            ],
            "target_residual": 0.042860270209959354,
            "energy_eV": -40.54114624224789,
            "max_atomic_step_A": 0.036215521850790286,
            "max_log_strain_component": 0.0016822138505162558,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.8316443933142786,
            "cell_principal_stretches": [
              1.0109273265087977,
              0.9998677531478696,
              0.990141687869149
            ],
            "cell_volume_ratio": 1.0008289154028422,
            "cell_rmsd_from_input_A": 0.05413341364638993
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -3.3370265816210704e-15,
              -0.4965659615975372,
              -0.002064824327850184
            ],
            "branch_aligned_reduced_polarization": [
              -3.3370265816210704e-15,
              -0.4965659615975372,
              -0.002064824327850184
            ],
            "target_residual": 0.004007008766458007,
            "energy_eV": -40.29710487760192,
            "max_atomic_step_A": 0.003906918130535226,
            "max_log_strain_component": 0.00019447063237245824,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.8316443933142786,
            "cell_principal_stretches": [
              1.0111495546061415,
              0.9998613988871567,
              0.9899697821973881
            ],
            "cell_volume_ratio": 1.0008687635883617,
            "cell_rmsd_from_input_A": 0.05517055722015407
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              -2.1320192452583247e-15,
              -0.4998438812901583,
              -0.00014599888998519
            ],
            "branch_aligned_reduced_polarization": [
              -2.1320192452583247e-15,
              -0.4998438812901583,
              -0.00014599888998519
            ],
            "target_residual": 0.00021374921623143315,
            "energy_eV": -40.27252990813565
          }
        ],
        "iterations": 4
      },
      "parent": {
        "candidate_id": "bec_projection_02",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Pm",
        "spacegroup_number": 6,
        "pointgroup": "m",
        "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": 0.00021374921623143315,
        "parent_symmetrization_rmsd_A": 0.2846721060392381,
        "parent_cell_rmsd_A": 0.05517055722015407,
        "energy_eV": -40.27252990813565,
        "reduced_polarization": [
          -2.1320192452583247e-15,
          -0.4998438812901583,
          -0.00014599888998519
        ],
        "cartesian_polarization_e_A2": [
          -2.1110167215200533e-18,
          -0.027844381061001695,
          0.00028461284653015284
        ],
        "ranking_score": 0.7988922437767394
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 3,
      "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": [
              1.2463868489112237e-17,
              -2.4842968079246017e-16,
              -0.12734037037735071
            ],
            "branch_aligned_reduced_polarization": [
              0.0,
              -2.4842968079246017e-16,
              -0.12734037037735071
            ],
            "target_residual": 0.5159608220861743,
            "energy_eV": -41.67151178004678,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.001521570666860826,
            "step_scale": 0.731880110770609,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.8316443933142786,
            "cell_principal_stretches": [
              1.0020716955593059,
              0.9997655915609183,
              0.9988304410193007
            ],
            "cell_volume_ratio": 1.0006650942689157,
            "cell_rmsd_from_input_A": 0.007164542883496857
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.3622252749140511,
              9.654849931310818e-15,
              -0.03344224260583095
            ],
            "branch_aligned_reduced_polarization": [
              0.3622252749140511,
              9.654849931310818e-15,
              -0.03344224260583095
            ],
            "target_residual": 0.14177538031342413,
            "energy_eV": -41.29086043847789,
            "max_atomic_step_A": 0.04523798618375125,
            "max_log_strain_component": 0.0006015185954895728,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.8316443933142786,
            "cell_principal_stretches": [
              1.0028698293291254,
              0.9996810109437282,
              0.9983594827146283
            ],
            "cell_volume_ratio": 1.0009052243475747,
            "cell_rmsd_from_input_A": 0.009912879239355852
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.4984874005092025,
              -3.0680900811445485e-15,
              -0.00019279294306014984
            ],
            "branch_aligned_reduced_polarization": [
              0.4984874005092025,
              -3.0680900811445485e-15,
              -0.00019279294306014984
            ],
            "target_residual": 0.0015248364956462388,
            "energy_eV": -40.89971284835985,
            "max_atomic_step_A": 0.00048093845136896004,
            "max_log_strain_component": 6.863863205268559e-06,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.8316443933142786,
            "cell_principal_stretches": [
              1.0028777082474565,
              0.9996804987907814,
              0.9983536013296822
            ],
            "cell_volume_ratio": 1.0009066786217395,
            "cell_rmsd_from_input_A": 0.009939210450446236
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.49999772927800684,
              2.946290199885657e-15,
              -7.760847654666985e-07
            ],
            "branch_aligned_reduced_polarization": [
              0.49999772927800684,
              2.946290199885657e-15,
              -7.760847654666985e-07
            ],
            "target_residual": 2.399684548727727e-06,
            "energy_eV": -40.894679626045814
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_03",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Pc",
        "spacegroup_number": 7,
        "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": 2.399684548727727e-06,
        "parent_symmetrization_rmsd_A": 0.19659285067547366,
        "parent_cell_rmsd_A": 0.009939210450446236,
        "energy_eV": -40.894679626045814,
        "reduced_polarization": [
          0.49999772927800684,
          2.946290199885657e-15,
          -7.760847654666985e-07
        ],
        "cartesian_polarization_e_A2": [
          0.020034642208501627,
          7.621468579594111e-17,
          4.265427577975157e-05
        ],
        "ranking_score": 0.6990824526571826
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 4,
      "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": false,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              1.2463868489112237e-17,
              -2.4842968079246017e-16,
              -0.12734037037735071
            ],
            "branch_aligned_reduced_polarization": [
              1.2463868489112237e-17,
              -2.220446049250313e-16,
              -0.1273403703773507
            ],
            "target_residual": 0.6235985884769865,
            "energy_eV": -41.67151178004678,
            "max_atomic_step_A": 0.11999999999999998,
            "max_log_strain_component": 0.0034119996707194385,
            "step_scale": 0.42855804616444054,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.8316443933142786,
            "cell_principal_stretches": [
              1.0029172006643499,
              1.0001818771113078,
              0.9957747932062961
            ],
            "cell_volume_ratio": 0.9988613050677353,
            "cell_rmsd_from_input_A": 0.019168473065293085
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              8.496505151848189e-15,
              -0.1945533007611172,
              -0.26528057203281313
            ],
            "branch_aligned_reduced_polarization": [
              8.496505151848189e-15,
              -0.1945533007611172,
              -0.26528057203281313
            ],
            "target_residual": 0.38521538902433783,
            "energy_eV": -41.13437513873163,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.004139478712867134,
            "step_scale": 0.5517083658087698,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.8316443933142786,
            "cell_principal_stretches": [
              1.0064279992441698,
              1.000423919730555,
              0.9905583328257448
            ],
            "cell_volume_ratio": 0.997348257489588,
            "cell_rmsd_from_input_A": 0.04264584927400472
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              1.2019292969490148e-14,
              -0.3469424565527868,
              -0.37602150102962956
            ],
            "branch_aligned_reduced_polarization": [
              1.2019292969490148e-14,
              -0.3469424565527868,
              -0.37602150102962956
            ],
            "target_residual": 0.19697025108640567,
            "energy_eV": -39.445841747249005,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.005852323739883471,
            "step_scale": 0.8039961338591054,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.8316443933142786,
            "cell_principal_stretches": [
              1.011444342203305,
              1.0007491456917261,
              0.9833208587493611
            ],
            "cell_volume_ratio": 0.9953194002188317,
            "cell_rmsd_from_input_A": 0.07535011840521723
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              1.3212259108946233e-14,
              -0.43028036974655737,
              -0.4501885760695548
            ],
            "branch_aligned_reduced_polarization": [
              1.3212259108946233e-14,
              -0.43028036974655737,
              -0.4501885760695548
            ],
            "target_residual": 0.08568549933714152,
            "energy_eV": -34.9226317894706,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.01560981333828844,
            "step_scale": 0.8408855747762378,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.8316443933142786,
            "cell_principal_stretches": [
              1.0252026116283859,
              1.0014851727067253,
              0.9649568109501563
            ],
            "cell_volume_ratio": 0.9907454887697604,
            "cell_rmsd_from_input_A": 0.15960247617127102
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              1.3789861169813447e-14,
              -0.5147318068952972,
              -0.5687429044210487
            ],
            "branch_aligned_reduced_polarization": [
              1.3789861169813447e-14,
              -0.5147318068952972,
              -0.5687429044210487
            ],
            "target_residual": 0.0703037199772655,
            "energy_eV": -25.590461093153213,
            "max_atomic_step_A": 0.0333779378630437,
            "max_log_strain_component": 0.0030420401239059204,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": true,
            "strain_jacobian_frobenius_norm": 2.7907683422480343,
            "cell_principal_stretches": [
              1.0232959174674159,
              1.0014021296683446,
              0.9690649758392046
            ],
            "cell_volume_ratio": 0.9930306417286839,
            "cell_rmsd_from_input_A": 0.14326047874672562
          },
          {
            "iteration": 5,
            "reduced_polarization": [
              3.088462005558769e-14,
              -0.5002191795729958,
              -0.501463331496768
            ],
            "branch_aligned_reduced_polarization": [
              3.088462005558769e-14,
              -0.5002191795729958,
              -0.501463331496768
            ],
            "target_residual": 0.0014796549444556209,
            "energy_eV": -29.264708904172274
          }
        ],
        "iterations": 5
      },
      "parent": {
        "candidate_id": "bec_projection_04",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Pm",
        "spacegroup_number": 6,
        "pointgroup": "m",
        "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": 0.0014796549444556209,
        "parent_symmetrization_rmsd_A": 0.4856681950868327,
        "parent_cell_rmsd_A": 0.14326047874672562,
        "energy_eV": -29.264708904172274,
        "reduced_polarization": [
          3.088462005558769e-14,
          -0.5002191795729958,
          -0.501463331496768
        ],
        "cartesian_polarization_e_A2": [
          -1.5689018075898812e-15,
          -0.027368825045043507,
          -0.03154235174366856
        ],
        "ranking_score": 1.0244426246624254
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 5,
      "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": [
              1.2463868489112237e-17,
              -2.4842968079246017e-16,
              -0.12734037037735071
            ],
            "branch_aligned_reduced_polarization": [
              0.0,
              -2.4842968079246017e-16,
              -0.1273403703773507
            ],
            "target_residual": 0.6235985884769867,
            "energy_eV": -41.67151178004678,
            "max_atomic_step_A": 0.11999999999999998,
            "max_log_strain_component": 0.0020749155586629567,
            "step_scale": 0.5161072988090992,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.8316443933142786,
            "cell_principal_stretches": [
              1.0006428649381658,
              1.0004839221547805,
              0.9975045573597251
            ],
            "cell_volume_ratio": 0.9986288429403752,
            "cell_rmsd_from_input_A": 0.009799646611745079
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.25492931472573466,
              -7.953461728359258e-15,
              -0.3069781841162341
            ],
            "branch_aligned_reduced_polarization": [
              0.25492931472573466,
              -7.953461728359258e-15,
              -0.3069781841162341
            ],
            "target_residual": 0.3119568274422992,
            "energy_eV": -41.228836909859936,
            "max_atomic_step_A": 0.11999999999999998,
            "max_log_strain_component": 0.002535091081441841,
            "step_scale": 0.8870783084855597,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.8316443933142786,
            "cell_principal_stretches": [
              1.0012357047437275,
              1.0010754865963007,
              0.9946559794989522
            ],
            "cell_volume_ratio": 0.9969561416668495,
            "cell_rmsd_from_input_A": 0.02129284334284216
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.44807589695858147,
              -1.2209516736907987e-14,
              -0.45229109686691593
            ],
            "branch_aligned_reduced_polarization": [
              0.44807589695858147,
              -1.2209516736907987e-14,
              -0.45229109686691593
            ],
            "target_residual": 0.07051419654805582,
            "energy_eV": -39.98474124152687,
            "max_atomic_step_A": 0.044727502584977354,
            "max_log_strain_component": 0.001483509847947191,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.8316443933142786,
            "cell_principal_stretches": [
              1.0015457700868344,
              1.0014218263888899,
              0.9930295001489675
            ],
            "cell_volume_ratio": 0.9959785934907195,
            "cell_rmsd_from_input_A": 0.02791472398900603
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.4914967550649929,
              -6.776892081949727e-15,
              -0.4959630115603097
            ],
            "branch_aligned_reduced_polarization": [
              0.4914967550649929,
              -6.776892081949727e-15,
              -0.4959630115603097
            ],
            "target_residual": 0.009412887446842065,
            "energy_eV": -39.18718749865624,
            "max_atomic_step_A": 0.006217192047333873,
            "max_log_strain_component": 0.0002529302908463739,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.8316443933142786,
            "cell_principal_stretches": [
              1.00161761918559,
              1.0014808873784848,
              0.9927336527130511
            ],
            "cell_volume_ratio": 0.9958120225575746,
            "cell_rmsd_from_input_A": 0.029081097930440693
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              0.49977843660561,
              -9.984291251061973e-16,
              -0.500077347810221
            ],
            "branch_aligned_reduced_polarization": [
              0.49977843660561,
              -9.984291251061973e-16,
              -0.500077347810221
            ],
            "target_residual": 0.0002346764186696127,
            "energy_eV": -39.06492724182831
          }
        ],
        "iterations": 4
      },
      "parent": {
        "candidate_id": "bec_projection_05",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Pc",
        "spacegroup_number": 7,
        "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": 0.0002346764186696127,
        "parent_symmetrization_rmsd_A": 0.34787463405937236,
        "parent_cell_rmsd_A": 0.029081097930440693,
        "energy_eV": -39.06492724182831,
        "reduced_polarization": [
          0.49977843660561,
          -9.984291251061973e-16,
          -0.500077347810221
        ],
        "cartesian_polarization_e_A2": [
          0.02005581310500873,
          5.050540022762527e-16,
          -0.03221774619003463
        ],
        "ranking_score": 0.8556142613793218
      },
      "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": [
              1.2463868489112237e-17,
              -2.4842968079246017e-16,
              -0.12734037037735071
            ],
            "branch_aligned_reduced_polarization": [
              0.0,
              -2.220446049250313e-16,
              -0.12734037037735071
            ],
            "target_residual": 0.7184814332519948,
            "energy_eV": -41.67151178004678,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.0036905305890113705,
            "step_scale": 0.46354241828115317,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.8316443933142786,
            "cell_principal_stretches": [
              1.0040893058030056,
              0.9999276182626219,
              0.9964189473813392
            ],
            "cell_volume_ratio": 1.0004211916994228,
            "cell_rmsd_from_input_A": 0.019699918802323007
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.22677489446561339,
              -0.22755573642243213,
              -0.057366613643768154
            ],
            "branch_aligned_reduced_polarization": [
              0.22677489446561339,
              -0.2275557364224321,
              -0.057366613643768154
            ],
            "target_residual": 0.3900881482582538,
            "energy_eV": -41.27878118798707,
            "max_atomic_step_A": 0.11999999999999998,
            "max_log_strain_component": 0.0039331154735357575,
            "step_scale": 0.8097821410306122,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.8316443933142786,
            "cell_principal_stretches": [
              1.0082568325806633,
              0.9999036088283068,
              0.99246305031413
            ],
            "cell_volume_ratio": 1.00056119699957,
            "cell_rmsd_from_input_A": 0.04046973841581223
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.4380816637857383,
              -0.40734811669987514,
              -0.01669421687279889
            ],
            "branch_aligned_reduced_polarization": [
              0.4380816637857383,
              -0.40734811669987514,
              -0.01669421687279889
            ],
            "target_residual": 0.11268073799722093,
            "energy_eV": -39.979211090858456,
            "max_atomic_step_A": 0.07372437182347699,
            "max_log_strain_component": 0.0035375140385986094,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.8316443933142786,
            "cell_principal_stretches": [
              1.0119535484678734,
              0.9998726743939831,
              0.9890618710405272
            ],
            "cell_volume_ratio": 1.000757231806569,
            "cell_rmsd_from_input_A": 0.0589325759933288
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.4956958197381931,
              -0.48590358269804285,
              -0.006485412653371765
            ],
            "branch_aligned_reduced_polarization": [
              0.4956958197381931,
              -0.48590358269804285,
              -0.006485412653371765
            ],
            "target_residual": 0.0161026558604958,
            "energy_eV": -38.803377890823356,
            "max_atomic_step_A": 0.014358645291974035,
            "max_log_strain_component": 0.0009461888686307581,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.8316443933142786,
            "cell_principal_stretches": [
              1.0129875782183757,
              0.9998516633184179,
              0.9882007702707074
            ],
            "cell_volume_ratio": 1.0008866148444242,
            "cell_rmsd_from_input_A": 0.06390956549607357
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              0.49956221482504193,
              -0.49890095631872106,
              -0.0010659891331940578
            ],
            "branch_aligned_reduced_polarization": [
              0.49956221482504193,
              -0.49890095631872106,
              -0.0010659891331940578
            ],
            "target_residual": 0.0015924464527449773,
            "energy_eV": -38.55392726300148,
            "max_atomic_step_A": 0.001276634245496608,
            "max_log_strain_component": 0.0001327776324769146,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": true,
            "strain_jacobian_frobenius_norm": 2.166123272581322,
            "cell_principal_stretches": [
              1.012882186410637,
              0.9998741285509233,
              0.988246594061214
            ],
            "cell_volume_ratio": 1.0008513764334188,
            "cell_rmsd_from_input_A": 0.0635335167627976
          },
          {
            "iteration": 5,
            "reduced_polarization": [
              0.5000006697495758,
              -0.49999573857918517,
              -1.8598159243221668e-06
            ],
            "branch_aligned_reduced_polarization": [
              0.5000006697495758,
              -0.49999573857918517,
              -1.8598159243221668e-06
            ],
            "target_residual": 4.697572471791762e-06,
            "energy_eV": -38.53170882761725
          }
        ],
        "iterations": 5
      },
      "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": 4.697572471791762e-06,
        "parent_symmetrization_rmsd_A": 0.35737840775298374,
        "parent_cell_rmsd_A": 0.0635335167627976,
        "energy_eV": -38.53170882761725,
        "reduced_polarization": [
          0.5000006697495758,
          -0.49999573857918517,
          -1.8598159243221668e-06
        ],
        "cartesian_polarization_e_A2": [
          0.020031959568942388,
          -0.027851500357816212,
          0.00038400323876006397
        ],
        "ranking_score": 0.8732711820886268
      },
      "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": false,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              1.2463868489112237e-17,
              -2.4842968079246017e-16,
              -0.12734037037735071
            ],
            "branch_aligned_reduced_polarization": [
              0.0,
              -2.220446049250313e-16,
              -0.1273403703773507
            ],
            "target_residual": 0.7992966905664567,
            "energy_eV": -41.67151178004678,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.002995918866925245,
            "step_scale": 0.3762969695146437,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.8316443933142786,
            "cell_principal_stretches": [
              1.0026499342179542,
              1.0001716420896938,
              0.9961888193988645
            ],
            "cell_volume_ratio": 0.9990000952763926,
            "cell_rmsd_from_input_A": 0.01708526117124736
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.18442675897265703,
              -0.1718119596851036,
              -0.2503151011322048
            ],
            "branch_aligned_reduced_polarization": [
              0.18442675897265703,
              -0.1718119596851036,
              -0.2503151011322048
            ],
            "target_residual": 0.519265258784809,
            "energy_eV": -41.18524474001308,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.0037972465185328553,
            "step_scale": 0.4793437063632217,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.8316443933142786,
            "cell_principal_stretches": [
              1.005936456150705,
              1.000398366760197,
              0.9913571700532846
            ],
            "cell_volume_ratio": 0.9976395866145146,
            "cell_rmsd_from_input_A": 0.03873109701396601
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.31782164008912456,
              -0.3118599450213942,
              -0.34999281626009165
            ],
            "branch_aligned_reduced_polarization": [
              0.31782164008912456,
              -0.3118599450213942,
              -0.34999281626009165
            ],
            "target_residual": 0.3018075384756781,
            "energy_eV": -39.63715947647193,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.005400450846352849,
            "step_scale": 0.6123134594061505,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.8316443933142786,
            "cell_principal_stretches": [
              1.0106207968823686,
              1.0007222891744805,
              0.9845187150702552
            ],
            "cell_volume_ratio": 0.9956937481051148,
            "cell_rmsd_from_input_A": 0.06934991969363946
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.4133305437220598,
              -0.4011630834468987,
              -0.4256874429258862
            ],
            "branch_aligned_reduced_polarization": [
              0.4133305437220598,
              -0.4011630834468987,
              -0.4256874429258862
            ],
            "target_residual": 0.15100558553951546,
            "energy_eV": -35.78225279057233,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.01083844865588134,
            "step_scale": 0.7618448972878717,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.8316443933142786,
            "cell_principal_stretches": [
              1.0201255380498544,
              1.0012789164042366,
              0.9714526376990142
            ],
            "cell_volume_ratio": 0.9922710555405513,
            "cell_rmsd_from_input_A": 0.12874825553859628
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              0.48150059803527423,
              -0.45922431767237765,
              -0.47371127285732095
            ],
            "branch_aligned_reduced_polarization": [
              0.48150059803527423,
              -0.45922431767237765,
              -0.47371127285732095
            ],
            "target_residual": 0.05192284003324455,
            "energy_eV": -27.34554911347522,
            "max_atomic_step_A": 0.036578656840833945,
            "max_log_strain_component": 0.006778367549764905,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": true,
            "strain_jacobian_frobenius_norm": 2.461410895685404,
            "cell_principal_stretches": [
              1.024926532491443,
              1.0011712810159992,
              0.9629373875876437
            ],
            "cell_volume_ratio": 0.9880960618434719,
            "cell_rmsd_from_input_A": 0.16353280570226425
          },
          {
            "iteration": 5,
            "reduced_polarization": [
              0.4983886593110132,
              -0.49901176920524154,
              -0.5071505301147107
            ],
            "branch_aligned_reduced_polarization": [
              0.4983886593110132,
              -0.49901176920524154,
              -0.5071505301147107
            ],
            "target_residual": 0.007396154395432639,
            "energy_eV": -24.72720967325192
          }
        ],
        "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": 0.007396154395432639,
        "parent_symmetrization_rmsd_A": 0.5198551753966713,
        "parent_cell_rmsd_A": 0.16353280570226425,
        "energy_eV": -24.72720967325192,
        "reduced_polarization": [
          0.4983886593110132,
          -0.49901176920524154,
          -0.5071505301147107
        ],
        "cartesian_polarization_e_A2": [
          0.02000450996309144,
          -0.02718122030859688,
          -0.0318208308048377
        ],
        "ranking_score": 1.0755306856131026
      },
      "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
        ],
        "endpoint_rmsd_A": 0.1272265599943764,
        "minimum_distance_A_by_image": [
          1.0491718062114122,
          1.0779410208543243,
          1.106725594020544,
          1.1355243577343084,
          1.1643362590264983,
          1.193160346176426,
          1.221995756874792,
          1.2508417080031606,
          1.2796974867790645
        ],
        "minimum_distance_A": 1.0491718062114122,
        "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": [
          83.13888432394425,
          83.13888432394425,
          83.13888432394425,
          83.13888432394425,
          83.13888432394425,
          83.13888432394425,
          83.13888432394425,
          83.13888432394425,
          83.13888432394425
        ],
        "cell_deformation_log_strain_norm": 0.0
      },
      "parent_reduced_polarization": [
        -3.4958891304193366e-16,
        1.137388900013673e-16,
        -4.0263236458481606e-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": [
          -41.67151178004677,
          -41.69194288407848,
          -41.69890669805774,
          -41.69620371079013,
          -41.686077729822514,
          -41.670632565844116,
          -41.653330525307084,
          -41.63936943764025,
          -41.63396482136054
        ],
        "cartesian_polarizations_e_A2": [
          [
            -1.844598733040633e-17,
            -1.0599607307244303e-16,
            -0.008235653686587154
          ],
          [
            -2.5409627325112987e-18,
            -1.0683068782104493e-17,
            -0.0075291458353706495
          ],
          [
            -2.650719657935397e-18,
            6.059303074849892e-17,
            -0.006647483209934289
          ],
          [
            -6.221581125387195e-18,
            1.2686144178749087e-17,
            -0.005627393944866682
          ],
          [
            1.4902298333130301e-19,
            8.513070435739519e-17,
            -0.004518743862191423
          ],
          [
            3.118128437349229e-17,
            -4.5403042323944097e-17,
            -0.003373443193060597
          ],
          [
            -2.1423407811031007e-17,
            -2.5038442458057408e-17,
            -0.0022308896121966564
          ],
          [
            1.3250256977040526e-17,
            -8.41291666590729e-17,
            -0.0011078271152802025
          ],
          [
            -1.4022538382659296e-17,
            6.3430720893745436e-18,
            -2.6039980156379704e-17
          ]
        ],
        "raw_reduced_polarization": [
          [
            -4.598677133090581e-16,
            -1.9006367144965327e-15,
            -0.1273403703773503
          ],
          [
            -6.334747500760465e-17,
            -1.915602357917765e-16,
            -0.11641628652533759
          ],
          [
            -6.608377019259656e-17,
            1.0865057123814823e-15,
            -0.10278394481410442
          ],
          [
            -1.5510713707269914e-16,
            2.274777800027346e-16,
            -0.08701123875153347
          ],
          [
            3.715217697352208e-18,
            1.5264956289657192e-15,
            -0.0698691978742354
          ],
          [
            7.773650543086164e-16,
            -8.141310021150502e-16,
            -0.05216046254481388
          ],
          [
            -5.340962988251833e-16,
            -4.489693026369762e-16,
            -0.034494202925357466
          ],
          [
            3.303355503635595e-16,
            -1.5085368568602401e-15,
            -0.01712931608617849
          ],
          [
            -3.4958891304193366e-16,
            1.137388900013673e-16,
            -4.0263236458481606e-16
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -4.598677133090581e-16,
            -1.9006367144965327e-15,
            -0.1273403703773503
          ],
          [
            -6.334747500760466e-17,
            -1.915602357917764e-16,
            -0.11641628652533759
          ],
          [
            -6.608377019259656e-17,
            1.0865057123814823e-15,
            -0.10278394481410442
          ],
          [
            -1.5510713707269914e-16,
            2.274777800027346e-16,
            -0.08701123875153347
          ],
          [
            3.7152176973522046e-18,
            1.5264956289657192e-15,
            -0.0698691978742354
          ],
          [
            7.773650543086164e-16,
            -8.141310021150504e-16,
            -0.05216046254481388
          ],
          [
            -5.340962988251832e-16,
            -4.489693026369762e-16,
            -0.034494202925357466
          ],
          [
            3.3033555036355954e-16,
            -1.5085368568602401e-15,
            -0.01712931608617849
          ],
          [
            -3.4958891304193366e-16,
            1.1373889000136725e-16,
            -4.0245584642661925e-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": [
          [
            -4.440892098500626e-16,
            -1.887379141862766e-15,
            -0.1273403703773503
          ],
          [
            -5.551115123125783e-17,
            -1.6653345369377348e-16,
            -0.11641628652533759
          ],
          [
            -5.551115123125783e-17,
            1.1102230246251565e-15,
            -0.10278394481410441
          ],
          [
            -1.6653345369377348e-16,
            2.220446049250313e-16,
            -0.08701123875153349
          ],
          [
            0.0,
            1.5543122344752192e-15,
            -0.0698691978742354
          ],
          [
            7.771561172376096e-16,
            -8.326672684688674e-16,
            -0.05216046254481388
          ],
          [
            -5.551115123125783e-16,
            -4.440892098500626e-16,
            -0.03449420292535749
          ],
          [
            3.3306690738754696e-16,
            -1.4988010832439613e-15,
            -0.017129316086178514
          ],
          [
            -3.3306690738754696e-16,
            1.1102230246251565e-16,
            -3.885780586188048e-16
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -41.63396482136054,
          -41.63936943764025,
          -41.653330525307084,
          -41.6706325658441,
          -41.686077729822514,
          -41.696203710790144,
          -41.69890669805774,
          -41.691942884078486,
          -41.671511780046785
        ],
        "cartesian_polarizations_e_A2": [
          [
            -1.4022538382659296e-17,
            6.3430720893745436e-18,
            -2.6039980156379704e-17
          ],
          [
            -6.627295550331684e-18,
            1.6358449072597507e-17,
            0.0011078271152802398
          ],
          [
            -3.4070435939547254e-17,
            5.1412268513877875e-17,
            0.0022308896121964986
          ],
          [
            -3.091467469729695e-18,
            2.6741056545205313e-16,
            0.003373443193060493
          ],
          [
            1.4152804457932022e-17,
            -6.676917988815309e-17,
            0.0045187438621912
          ],
          [
            -1.9634844467310785e-17,
            3.872612433512879e-17,
            0.005627393944866491
          ],
          [
            -9.491341056974596e-18,
            1.382122023684769e-16,
            0.006647483209934151
          ],
          [
            -1.7477027011233047e-18,
            4.673842592170716e-18,
            0.007529145835370648
          ],
          [
            8.556652184568659e-18,
            7.010763888256074e-18,
            0.00823565368658704
          ]
        ],
        "raw_reduced_polarization": [
          [
            -3.4958891304193366e-16,
            1.137388900013673e-16,
            -4.0263236458481606e-16
          ],
          [
            -1.6522180111934365e-16,
            2.933266110561578e-16,
            0.017129316086179066
          ],
          [
            -8.493930515248388e-16,
            9.218836347479245e-16,
            0.03449420292535502
          ],
          [
            -7.707183413980032e-17,
            4.794992152162906e-15,
            0.052160462544812276
          ],
          [
            3.5283651161632207e-16,
            -1.1972514736986032e-15,
            0.06986919787423194
          ],
          [
            -4.895065178472244e-16,
            6.944058547451899e-16,
            0.08701123875153051
          ],
          [
            -2.366238916857772e-16,
            2.478310550556109e-15,
            0.1027839448141023
          ],
          [
            -4.3571104669729494e-17,
            8.380760315890222e-17,
            0.11641628652533757
          ],
          [
            2.133216294262665e-16,
            1.2571140473835332e-16,
            0.12734037037734852
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -3.4958891304193366e-16,
            1.137388900013673e-16,
            -4.0263236458481606e-16
          ],
          [
            -1.6522180111934365e-16,
            2.933266110561578e-16,
            0.017129316086179066
          ],
          [
            -8.493930515248388e-16,
            9.218836347479245e-16,
            0.03449420292535502
          ],
          [
            -7.707183413980029e-17,
            4.794992152162906e-15,
            0.052160462544812276
          ],
          [
            3.5283651161632207e-16,
            -1.1972514736986036e-15,
            0.06986919787423194
          ],
          [
            -4.895065178472244e-16,
            6.944058547451898e-16,
            0.08701123875153051
          ],
          [
            -2.366238916857772e-16,
            2.478310550556109e-15,
            0.1027839448141023
          ],
          [
            -4.357110466972949e-17,
            8.38076031589021e-17,
            0.11641628652533757
          ],
          [
            2.133216294262665e-16,
            1.2571140473835332e-16,
            0.12734037037734852
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          -2.3931011277480923e-16,
          2.1281144944992675e-15,
          0.1273403703773495
        ],
        "actual_opposite_endpoint_branch_residual": 2.271166946897956e-15
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            -4.598677133090581e-16,
            -1.9006367144965327e-15,
            -0.1273403703773503
          ],
          [
            -6.334747500760465e-17,
            -1.915602357917765e-16,
            -0.11641628652533759
          ],
          [
            -6.608377019259656e-17,
            1.0865057123814823e-15,
            -0.10278394481410442
          ],
          [
            -1.5510713707269914e-16,
            2.274777800027346e-16,
            -0.08701123875153347
          ],
          [
            3.715217697352208e-18,
            1.5264956289657192e-15,
            -0.0698691978742354
          ],
          [
            7.773650543086164e-16,
            -8.141310021150502e-16,
            -0.05216046254481388
          ],
          [
            -5.340962988251833e-16,
            -4.489693026369762e-16,
            -0.034494202925357466
          ],
          [
            3.303355503635595e-16,
            -1.5085368568602401e-15,
            -0.01712931608617849
          ],
          [
            -3.4958891304193366e-16,
            1.137388900013673e-16,
            -4.0263236458481606e-16
          ],
          [
            -1.6522180111934365e-16,
            2.933266110561578e-16,
            0.017129316086179066
          ],
          [
            -8.493930515248388e-16,
            9.218836347479245e-16,
            0.03449420292535502
          ],
          [
            -7.707183413980032e-17,
            4.794992152162906e-15,
            0.052160462544812276
          ],
          [
            3.5283651161632207e-16,
            -1.1972514736986032e-15,
            0.06986919787423194
          ],
          [
            -4.895065178472244e-16,
            6.944058547451899e-16,
            0.08701123875153051
          ],
          [
            -2.366238916857772e-16,
            2.478310550556109e-15,
            0.1027839448141023
          ],
          [
            -4.3571104669729494e-17,
            8.380760315890222e-17,
            0.11641628652533757
          ],
          [
            2.133216294262665e-16,
            1.2571140473835332e-16,
            0.12734037037734852
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -4.598677133090581e-16,
            -1.9006367144965327e-15,
            -0.1273403703773503
          ],
          [
            -6.334747500760466e-17,
            -1.915602357917764e-16,
            -0.11641628652533759
          ],
          [
            -6.608377019259656e-17,
            1.0865057123814823e-15,
            -0.10278394481410442
          ],
          [
            -1.5510713707269914e-16,
            2.274777800027346e-16,
            -0.08701123875153347
          ],
          [
            3.7152176973522046e-18,
            1.5264956289657192e-15,
            -0.0698691978742354
          ],
          [
            7.773650543086164e-16,
            -8.141310021150504e-16,
            -0.05216046254481388
          ],
          [
            -5.340962988251832e-16,
            -4.489693026369762e-16,
            -0.034494202925357466
          ],
          [
            3.3033555036355954e-16,
            -1.5085368568602401e-15,
            -0.01712931608617849
          ],
          [
            -3.4958891304193366e-16,
            1.1373889000136725e-16,
            -4.0245584642661925e-16
          ],
          [
            -1.6522180111934365e-16,
            2.933266110561578e-16,
            0.017129316086179066
          ],
          [
            -8.493930515248388e-16,
            9.218836347479245e-16,
            0.03449420292535502
          ],
          [
            -7.707183413980029e-17,
            4.794992152162906e-15,
            0.052160462544812276
          ],
          [
            3.5283651161632207e-16,
            -1.1972514736986036e-15,
            0.06986919787423194
          ],
          [
            -4.895065178472244e-16,
            6.944058547451898e-16,
            0.08701123875153051
          ],
          [
            -2.366238916857772e-16,
            2.478310550556109e-15,
            0.1027839448141023
          ],
          [
            -4.357110466972949e-17,
            8.38076031589021e-17,
            0.11641628652533757
          ],
          [
            2.133216294262665e-16,
            1.2571140473835332e-16,
            0.12734037037734852
          ]
        ],
        "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": [
          [
            -4.440892098500626e-16,
            -1.887379141862766e-15,
            -0.1273403703773503
          ],
          [
            -5.551115123125783e-17,
            -1.6653345369377348e-16,
            -0.11641628652533759
          ],
          [
            -5.551115123125783e-17,
            1.1102230246251565e-15,
            -0.10278394481410441
          ],
          [
            -1.6653345369377348e-16,
            2.220446049250313e-16,
            -0.08701123875153349
          ],
          [
            0.0,
            1.5543122344752192e-15,
            -0.0698691978742354
          ],
          [
            7.771561172376096e-16,
            -8.326672684688674e-16,
            -0.05216046254481388
          ],
          [
            -5.551115123125783e-16,
            -4.440892098500626e-16,
            -0.03449420292535749
          ],
          [
            3.3306690738754696e-16,
            -1.4988010832439613e-15,
            -0.017129316086178514
          ],
          [
            -3.3306690738754696e-16,
            1.1102230246251565e-16,
            -3.885780586188048e-16
          ],
          [
            -1.6653345369377348e-16,
            3.3306690738754696e-16,
            0.01712931608617907
          ],
          [
            -8.326672684688674e-16,
            8.881784197001252e-16,
            0.03449420292535499
          ],
          [
            -5.551115123125783e-17,
            4.773959005888173e-15,
            0.052160462544812325
          ],
          [
            3.3306690738754696e-16,
            -1.2212453270876722e-15,
            0.06986919787423196
          ],
          [
            -4.996003610813204e-16,
            6.661338147750939e-16,
            0.0870112387515305
          ],
          [
            -2.220446049250313e-16,
            2.4424906541753444e-15,
            0.10278394481410236
          ],
          [
            -5.551115123125783e-17,
            1.1102230246251565e-16,
            0.11641628652533753
          ],
          [
            2.220446049250313e-16,
            1.1102230246251565e-16,
            0.12734037037734858
          ]
        ]
      },
      "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": "Pnnm",
        "spacegroup_number": 58,
        "pointgroup": "mmm",
        "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": 2.8353532921354943e-16,
        "parent_symmetrization_rmsd_A": 0.1272265599943764,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -41.63396482136054,
        "reduced_polarization": [
          1.5243579198876283e-18,
          2.454365521082137e-16,
          -1.4195371828310823e-16
        ],
        "cartesian_polarization_e_A2": [
          6.114429446442699e-20,
          1.3687681877071382e-17,
          -9.180762234621049e-18
        ],
        "ranking_score": 0.12722655999437696
      }
    }
  ],
  "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": 101,
      "full_response": 32,
      "energy_polarization": 69
    },
    "model_evaluations_for_recovery_and_path_properties": {
      "total": 126,
      "full_response": 57,
      "energy_polarization": 69
    },
    "elapsed_seconds": 218.53808765596477
  }
}
