{
  "schema": "ferrofinder.endpoint_parent_recovery.v4_variable_cell",
  "status": "complete",
  "input_atom_count": 24,
  "input_formula": "Al8Ba2S14",
  "input_spacegroup": "Pmn2_1",
  "input_pointgroup": "mm2",
  "input_is_polar_point_group": true,
  "input_energy_eV": -120.17130256501206,
  "input_cartesian_polarization_e_A2": [
    -9.933472638832225e-18,
    8.635774501218076e-18,
    -0.0030075010681780033
  ],
  "input_reduced_polarization": [
    -3.72102916021988e-16,
    7.762046843457722e-16,
    -0.2858196456807591
  ],
  "input_formal_targets": [
    {
      "orbit_id": 0,
      "representative_formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        -0.5
      ]
    },
    {
      "orbit_id": 1,
      "representative_formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ]
    },
    {
      "orbit_id": 2,
      "representative_formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        -0.5
      ]
    },
    {
      "orbit_id": 3,
      "representative_formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        -0.5,
        0.0,
        -0.5
      ]
    },
    {
      "orbit_id": 4,
      "representative_formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.0
      ]
    },
    {
      "orbit_id": 5,
      "representative_formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        -0.5,
        0.0,
        0.0
      ]
    },
    {
      "orbit_id": 6,
      "representative_formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "target_reduced_polarization": [
        -0.5,
        0.5,
        -0.5
      ]
    },
    {
      "orbit_id": 7,
      "representative_formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        -0.5,
        0.5,
        0.0
      ]
    }
  ],
  "parent_candidates": [
    {
      "candidate_id": "inversion_parent_endpoint_00",
      "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": 9.795214643165859e-16,
      "parent_symmetrization_rmsd_A": 0.35138647025167224,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -115.32253422723007,
      "reduced_polarization": [
        -2.2940940647568514e-16,
        9.48204585990574e-16,
        8.798685347156283e-17
      ],
      "cartesian_polarization_e_A2": [
        -6.1241983445845926e-18,
        1.0549383623647081e-17,
        9.258305361448444e-19
      ],
      "ranking_score": 0.3513864702516742
    },
    {
      "candidate_id": "inversion_parent_endpoint_01",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "Immm",
      "spacegroup_number": 71,
      "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": 7.701202942606424e-16,
      "parent_symmetrization_rmsd_A": 0.6055889855225985,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -99.04933606120754,
      "reduced_polarization": [
        -7.70034204157406e-16,
        8.082133782656978e-18,
        8.201900589990958e-18
      ],
      "cartesian_polarization_e_A2": [
        -2.0556446532954728e-17,
        8.991891732079634e-20,
        8.630346149487286e-20
      ],
      "ranking_score": 0.6055889855226001
    },
    {
      "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,
        -0.5
      ],
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_residual": 2.562290132290812e-05,
      "parent_symmetrization_rmsd_A": 0.03405236988686004,
      "parent_cell_rmsd_A": 0.05720325194848521,
      "energy_eV": -120.07329579958987,
      "reduced_polarization": [
        3.8908154445347857e-16,
        -1.9860582183362956e-15,
        -0.4999743770986771
      ],
      "cartesian_polarization_e_A2": [
        -2.4529443559179878e-18,
        2.3085995569448177e-17,
        -0.005295137906646022
      ],
      "ranking_score": 0.5484044286766272
    },
    {
      "candidate_id": "inversion_parent_bec_00_00",
      "source": "same_species_inversion_center_projection_after_BEC",
      "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,
        -0.5
      ],
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_residual": 0.49999999999999994,
      "parent_symmetrization_rmsd_A": 0.3514010757200542,
      "parent_cell_rmsd_A": 0.05720325194848521,
      "energy_eV": -115.00470603427826,
      "reduced_polarization": [
        1.2961026707046654e-15,
        2.6096424243707674e-16,
        -3.3967918534841176e-17
      ],
      "cartesian_polarization_e_A2": [
        3.4440234064728063e-17,
        2.8918763027546548e-18,
        -3.597480616655143e-19
      ],
      "ranking_score": 1.3657018887071755
    },
    {
      "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,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 2.4419521937252625e-05,
      "parent_symmetrization_rmsd_A": 0.044841754966527134,
      "parent_cell_rmsd_A": 0.07446445174555079,
      "energy_eV": -119.985659277241,
      "reduced_polarization": [
        1.3738207937307251e-15,
        -1.5331293936253557e-15,
        -2.4419521937252625e-05
      ],
      "cartesian_polarization_e_A2": [
        3.6896195788918295e-17,
        -1.7147887719965254e-17,
        -2.5480405857141137e-07
      ],
      "ranking_score": 0.5635067069467894
    },
    {
      "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,
        -0.5
      ],
      "formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_residual": 3.139377776021846e-05,
      "parent_symmetrization_rmsd_A": 0.09092002380397898,
      "parent_cell_rmsd_A": 0.08526966495489005,
      "energy_eV": -119.40276252730983,
      "reduced_polarization": [
        1.4105193286919166e-15,
        0.49998364593455,
        -0.5000267976458913
      ],
      "cartesian_polarization_e_A2": [
        7.998612906657125e-17,
        0.005445526922880994,
        -0.005193152361942859
      ],
      "ranking_score": 0.6123002275982219
    },
    {
      "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,
        -0.5
      ],
      "formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_residual": 0.00021259536502117588,
      "parent_symmetrization_rmsd_A": 0.20242957041121926,
      "parent_cell_rmsd_A": 0.42348935236811497,
      "energy_eV": -114.82741240909711,
      "reduced_polarization": [
        -0.4997919716421031,
        1.7870595552877354e-15,
        -0.49995617088251854
      ],
      "cartesian_polarization_e_A2": [
        -0.013047752111002701,
        8.99047266024523e-16,
        -0.00462742641666909
      ],
      "ranking_score": 0.8087270992332903
    },
    {
      "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,
        0.0
      ],
      "formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_residual": 0.0001527793134637893,
      "parent_symmetrization_rmsd_A": 0.0959605820144034,
      "parent_cell_rmsd_A": 0.10173661626347455,
      "energy_eV": -119.37055356051607,
      "reduced_polarization": [
        -1.2988372712915328e-16,
        0.49984725698489,
        -3.3301587919110072e-06
      ],
      "cartesian_polarization_e_A2": [
        1.407702954970722e-16,
        0.005591918442590154,
        0.0001052203754466752
      ],
      "ranking_score": 0.6217002947071997
    },
    {
      "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,
        0.0
      ],
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_residual": 7.717796034544764e-07,
      "parent_symmetrization_rmsd_A": 0.20555395908083943,
      "parent_cell_rmsd_A": 0.4690766919847925,
      "energy_eV": -114.85658923446655,
      "reduced_polarization": [
        -0.49999956062360346,
        3.192062190733095e-15,
        -6.345014881531356e-07
      ],
      "cartesian_polarization_e_A2": [
        -0.013472562223314668,
        7.176422059688511e-16,
        0.0007124702334358567
      ],
      "ranking_score": 0.8228246756362445
    },
    {
      "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,
        -0.5
      ],
      "formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "target_residual": 0.0004709430103392143,
      "parent_symmetrization_rmsd_A": 0.22181235691662424,
      "parent_cell_rmsd_A": 0.43308518098620125,
      "energy_eV": -113.86474503396647,
      "reduced_polarization": [
        -0.49964032642601697,
        0.4996982980505056,
        -0.499962607850598
      ],
      "cartesian_polarization_e_A2": [
        -0.013047318347539165,
        0.0054505562780266,
        -0.004514467879447582
      ],
      "ranking_score": 0.8310255381838529
    },
    {
      "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,
        0.0
      ],
      "formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_residual": 2.2455033416482573e-06,
      "parent_symmetrization_rmsd_A": 0.22653552637490587,
      "parent_cell_rmsd_A": 0.4841612190754222,
      "energy_eV": -113.78831868399662,
      "reduced_polarization": [
        -0.4999990802140602,
        0.49999998849202665,
        -2.04844981604299e-06
      ],
      "cartesian_polarization_e_A2": [
        -0.013482650602466022,
        0.005610784632681095,
        0.0008386557970035997
      ],
      "ranking_score": 0.8475803221504448
    }
  ],
  "formal_branches": [
    {
      "orbit_id": 0,
      "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": [
              -3.72102916021988e-16,
              7.762046843457722e-16,
              -0.2858196456807591
            ],
            "branch_aligned_reduced_polarization": [
              -3.72102916021988e-16,
              7.762046843457722e-16,
              -0.2858196456807591
            ],
            "target_residual": 0.21418035431924087,
            "energy_eV": -120.17130256501206,
            "max_atomic_step_A": 0.02732500665395823,
            "max_log_strain_component": 0.007425976718146889,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 5.296687313860863,
            "cell_principal_stretches": [
              1.0074536176612277,
              0.9971363670867628,
              0.9964925102942254
            ],
            "cell_volume_ratio": 1.0010451261584559,
            "cell_rmsd_from_input_A": 0.05630328738281934
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -5.322477902073646e-15,
              -8.386876871978761e-15,
              -0.4966995843496017
            ],
            "branch_aligned_reduced_polarization": [
              -5.322477902073646e-15,
              -8.386876871978761e-15,
              -0.4966995843496017
            ],
            "target_residual": 0.0033004156503982918,
            "energy_eV": -120.07623273912702,
            "max_atomic_step_A": 0.00041399397630260124,
            "max_log_strain_component": 0.00011899226575896829,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 5.296687313860863,
            "cell_principal_stretches": [
              1.0075735039824716,
              0.9970905476604793,
              0.9964364072889037
            ],
            "cell_volume_ratio": 1.001061881925406,
            "cell_rmsd_from_input_A": 0.05720325194848521
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              3.8908154445347857e-16,
              -1.9860582183362956e-15,
              -0.4999743770986771
            ],
            "branch_aligned_reduced_polarization": [
              3.8908154445347857e-16,
              -1.9860582183362956e-15,
              -0.4999743770986771
            ],
            "target_residual": 2.562290132290812e-05,
            "energy_eV": -120.07329579958987
          }
        ],
        "iterations": 2
      },
      "parent": {
        "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,
          -0.5
        ],
        "formal_class": [
          0.0,
          0.0,
          0.5
        ],
        "target_residual": 2.562290132290812e-05,
        "parent_symmetrization_rmsd_A": 0.03405236988686004,
        "parent_cell_rmsd_A": 0.05720325194848521,
        "energy_eV": -120.07329579958987,
        "reduced_polarization": [
          3.8908154445347857e-16,
          -1.9860582183362956e-15,
          -0.4999743770986771
        ],
        "cartesian_polarization_e_A2": [
          -2.4529443559179878e-18,
          2.3085995569448177e-17,
          -0.005295137906646022
        ],
        "ranking_score": 0.5484044286766272
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 1,
      "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": [
              -3.72102916021988e-16,
              7.762046843457722e-16,
              -0.2858196456807591
            ],
            "branch_aligned_reduced_polarization": [
              -3.72102916021988e-16,
              7.762046843457722e-16,
              -0.2858196456807591
            ],
            "target_residual": 0.2858196456807591,
            "energy_eV": -120.17130256501206,
            "max_atomic_step_A": 0.036464706321373,
            "max_log_strain_component": 0.009909825955608836,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 5.296687313860863,
            "cell_principal_stretches": [
              1.004699916985843,
              1.003834278357707,
              0.9901391145721719
            ],
            "cell_volume_ratio": 0.9986069982822569,
            "cell_rmsd_from_input_A": 0.07556852804604633
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              9.954755312534648e-15,
              7.316832482666544e-15,
              0.0042747773215228504
            ],
            "branch_aligned_reduced_polarization": [
              9.954755312534648e-15,
              7.316832482666544e-15,
              0.0042747773215228504
            ],
            "target_residual": 0.0042747773215228504,
            "energy_eV": -119.97983113866127,
            "max_atomic_step_A": 0.0005568034366435528,
            "max_log_strain_component": 0.0001443125394806227,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 5.296687313860863,
            "cell_principal_stretches": [
              1.0046313158688527,
              1.0037783360568704,
              0.9902820143731033
            ],
            "cell_volume_ratio": 0.9986272700382217,
            "cell_rmsd_from_input_A": 0.07446445174555079
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              1.3738207937307251e-15,
              -1.5331293936253557e-15,
              -2.4419521937252625e-05
            ],
            "branch_aligned_reduced_polarization": [
              1.3738207937307251e-15,
              -1.5331293936253557e-15,
              -2.4419521937252625e-05
            ],
            "target_residual": 2.4419521937252625e-05,
            "energy_eV": -119.985659277241
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "inversion_parent_endpoint_00",
        "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": 9.795214643165859e-16,
        "parent_symmetrization_rmsd_A": 0.35138647025167224,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -115.32253422723007,
        "reduced_polarization": [
          -2.2940940647568514e-16,
          9.48204585990574e-16,
          8.798685347156283e-17
        ],
        "cartesian_polarization_e_A2": [
          -6.1241983445845926e-18,
          1.0549383623647081e-17,
          9.258305361448444e-19
        ],
        "ranking_score": 0.3513864702516742
      },
      "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": [
          -120.17130256501206,
          -119.94766822644506,
          -119.38629732843455,
          -118.5958055333661,
          -117.68554572999258,
          -116.78142625893096,
          -116.01616779654785,
          -115.50342136535222,
          -115.32253422723005
        ],
        "cartesian_polarizations_e_A2": [
          [
            -7.168746656760121e-18,
            4.219753449458833e-18,
            -0.0030075010681779894
          ],
          [
            2.6745585677379377e-18,
            -2.6054524205379536e-17,
            -0.0058510114898394855
          ],
          [
            -2.7207247149174822e-17,
            -6.5258977764886596e-18,
            -0.008441280767305463
          ],
          [
            -1.3697121751891171e-17,
            -6.869366080514379e-19,
            -0.010441015865817006
          ],
          [
            -5.334045507291951e-18,
            9.911513916170746e-18,
            -0.011352069057056121
          ],
          [
            -5.460328712527482e-18,
            1.0843785027097698e-17,
            -0.01070780622385328
          ],
          [
            9.714936898194618e-18,
            1.3689665260453654e-17,
            -0.008355820951010723
          ],
          [
            6.488608096358194e-18,
            1.3444330757578142e-17,
            -0.00457787190615494
          ],
          [
            -1.3920721806083556e-18,
            9.469911810994821e-18,
            -2.810052444114469e-17
          ]
        ],
        "raw_reduced_polarization": [
          [
            -2.6853766373457387e-16,
            3.7928183439622966e-16,
            -0.28581964568075774
          ],
          [
            1.0018762605097133e-16,
            -2.3418448147023018e-15,
            -0.5560543431205168
          ],
          [
            -1.0191698683058971e-15,
            -5.865637671476574e-16,
            -0.8022221183996785
          ],
          [
            -5.130873291040822e-16,
            -6.174355443659552e-17,
            -0.9922681281449753
          ],
          [
            -1.9981067644946505e-16,
            8.908712854423068e-16,
            -1.0788506078892108
          ],
          [
            -2.0454118214684302e-16,
            9.746661093205435e-16,
            -1.0176227078695859
          ],
          [
            3.6391667649600505e-16,
            1.2304608348435822e-15,
            -0.794100394131064
          ],
          [
            2.4306001348815354e-16,
            1.208409565401941e-15,
            -0.4350607685675023
          ],
          [
            -5.2146327528250165e-17,
            8.511790004473525e-16,
            -2.670549987228174e-15
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -2.6853766373457387e-16,
            3.7928183439622966e-16,
            -0.28581964568075774
          ],
          [
            1.0018762605097132e-16,
            -2.3418448147023018e-15,
            -0.5560543431205168
          ],
          [
            -1.0191698683058971e-15,
            -5.865637671476574e-16,
            -0.8022221183996785
          ],
          [
            -5.130873291040822e-16,
            -6.174355443659549e-17,
            -0.9922681281449753
          ],
          [
            -1.9981067644946502e-16,
            8.908712854423068e-16,
            -1.0788506078892108
          ],
          [
            -2.0454118214684302e-16,
            9.746661093205435e-16,
            -1.0176227078695859
          ],
          [
            3.639166764960051e-16,
            1.2304608348435822e-15,
            -0.794100394131064
          ],
          [
            2.4306001348815354e-16,
            1.208409565401941e-15,
            -0.4350607685675023
          ],
          [
            -5.2146327528250184e-17,
            8.511790004473525e-16,
            -2.6645352591003757e-15
          ]
        ],
        "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": [
          [
            -2.7755575615628914e-16,
            3.3306690738754696e-16,
            -0.28581964568075774
          ],
          [
            1.1102230246251565e-16,
            -2.3314683517128287e-15,
            0.4439456568794832
          ],
          [
            -9.992007221626409e-16,
            -6.106226635438361e-16,
            0.1977778816003215
          ],
          [
            -4.996003610813204e-16,
            -5.551115123125783e-17,
            0.0077318718550246635
          ],
          [
            -2.220446049250313e-16,
            8.881784197001252e-16,
            -0.07885060788921083
          ],
          [
            -2.220446049250313e-16,
            9.992007221626409e-16,
            -0.017622707869585863
          ],
          [
            3.3306690738754696e-16,
            1.2212453270876722e-15,
            0.20589960586893596
          ],
          [
            2.220446049250313e-16,
            1.2212453270876722e-15,
            -0.4350607685675023
          ],
          [
            -5.551115123125783e-17,
            8.881784197001252e-16,
            -2.6645352591003757e-15
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -115.32253422723005,
          -115.50342136535221,
          -116.01616779654785,
          -116.78142625893096,
          -117.6855457299926,
          -118.5958055333661,
          -119.38629732843457,
          -119.94766822644507,
          -120.17130256501206
        ],
        "cartesian_polarizations_e_A2": [
          [
            -3.7030988633301647e-19,
            1.1089119529973212e-17,
            1.9395075658680907e-17
          ],
          [
            6.989294182930858e-18,
            1.614301028920879e-17,
            0.004577871906154938
          ],
          [
            1.0981904018397646e-17,
            1.3984066663904272e-17,
            0.008355820951010716
          ],
          [
            3.532200980006178e-19,
            -2.3895580580075017e-17,
            0.010707806223853283
          ],
          [
            -9.926893157905923e-18,
            -1.4229401166779785e-18,
            0.011352069057056116
          ],
          [
            -1.1627583887569394e-17,
            7.2619012851152e-18,
            0.010441015865817013
          ],
          [
            -3.199940537531778e-17,
            -2.8949471339310597e-18,
            0.008441280767305485
          ],
          [
            -6.3764194975246954e-18,
            3.2580421981868197e-17,
            0.005851011489839493
          ],
          [
            -1.6261592940289524e-17,
            3.140281636806573e-18,
            0.003007501068178008
          ]
        ],
        "raw_reduced_polarization": [
          [
            -1.387162310163521e-17,
            9.967173787621848e-16,
            1.8432225050127874e-15
          ],
          [
            2.618154638325789e-16,
            1.4509735292599946e-15,
            0.43506076856750214
          ],
          [
            4.113766310428724e-16,
            1.2569223581735518e-15,
            0.7941003941310634
          ],
          [
            1.3231448179541531e-17,
            -2.1477936436158582e-15,
            1.0176227078695863
          ],
          [
            -3.7185645195774755e-16,
            -1.278973627615193e-16,
            1.0788506078892104
          ],
          [
            -4.3556347595310795e-16,
            6.527175754725812e-16,
            0.992268128144976
          ],
          [
            -1.1986817182722129e-15,
            -2.6020497941136684e-16,
            0.8022221183996807
          ],
          [
            -2.3885748469603987e-16,
            2.9284085818499593e-15,
            0.5560543431205175
          ],
          [
            -6.091511369940873e-16,
            2.822562488530081e-16,
            0.2858196456807595
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -1.387162310163521e-17,
            9.967173787621848e-16,
            1.8432225050127874e-15
          ],
          [
            2.618154638325789e-16,
            1.4509735292599946e-15,
            0.43506076856750214
          ],
          [
            4.113766310428724e-16,
            1.2569223581735518e-15,
            0.7941003941310634
          ],
          [
            1.3231448179541553e-17,
            -2.1477936436158582e-15,
            1.0176227078695863
          ],
          [
            -3.7185645195774755e-16,
            -1.2789736276151927e-16,
            1.0788506078892104
          ],
          [
            -4.3556347595310795e-16,
            6.527175754725812e-16,
            0.992268128144976
          ],
          [
            -1.1986817182722129e-15,
            -2.6020497941136694e-16,
            0.8022221183996807
          ],
          [
            -2.388574846960398e-16,
            2.9284085818499593e-15,
            0.5560543431205175
          ],
          [
            -6.091511369940873e-16,
            2.8225624885300794e-16,
            0.2858196456807595
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          1.6424500867807358e-16,
          1.3230761664984753e-15,
          0.2858196456807524
        ],
        "actual_opposite_endpoint_branch_residual": 7.222779633441189e-15
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            -2.6853766373457387e-16,
            3.7928183439622966e-16,
            -0.28581964568075774
          ],
          [
            1.0018762605097133e-16,
            -2.3418448147023018e-15,
            -0.5560543431205168
          ],
          [
            -1.0191698683058971e-15,
            -5.865637671476574e-16,
            -0.8022221183996785
          ],
          [
            -5.130873291040822e-16,
            -6.174355443659552e-17,
            -0.9922681281449753
          ],
          [
            -1.9981067644946505e-16,
            8.908712854423068e-16,
            -1.0788506078892108
          ],
          [
            -2.0454118214684302e-16,
            9.746661093205435e-16,
            -1.0176227078695859
          ],
          [
            3.6391667649600505e-16,
            1.2304608348435822e-15,
            -0.794100394131064
          ],
          [
            2.4306001348815354e-16,
            1.208409565401941e-15,
            -0.4350607685675023
          ],
          [
            -5.2146327528250165e-17,
            8.511790004473525e-16,
            -2.670549987228174e-15
          ],
          [
            2.618154638325789e-16,
            1.4509735292599946e-15,
            0.43506076856750214
          ],
          [
            4.113766310428724e-16,
            1.2569223581735518e-15,
            0.7941003941310634
          ],
          [
            1.3231448179541531e-17,
            -2.1477936436158582e-15,
            1.0176227078695863
          ],
          [
            -3.7185645195774755e-16,
            -1.278973627615193e-16,
            1.0788506078892104
          ],
          [
            -4.3556347595310795e-16,
            6.527175754725812e-16,
            0.992268128144976
          ],
          [
            -1.1986817182722129e-15,
            -2.6020497941136684e-16,
            0.8022221183996807
          ],
          [
            -2.3885748469603987e-16,
            2.9284085818499593e-15,
            0.5560543431205175
          ],
          [
            -6.091511369940873e-16,
            2.822562488530081e-16,
            0.2858196456807595
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -2.6853766373457387e-16,
            3.7928183439622966e-16,
            -0.28581964568075774
          ],
          [
            1.0018762605097132e-16,
            -2.3418448147023018e-15,
            -0.5560543431205168
          ],
          [
            -1.0191698683058971e-15,
            -5.865637671476574e-16,
            -0.8022221183996785
          ],
          [
            -5.130873291040822e-16,
            -6.174355443659549e-17,
            -0.9922681281449753
          ],
          [
            -1.9981067644946502e-16,
            8.908712854423068e-16,
            -1.0788506078892108
          ],
          [
            -2.0454118214684302e-16,
            9.746661093205435e-16,
            -1.0176227078695859
          ],
          [
            3.639166764960051e-16,
            1.2304608348435822e-15,
            -0.794100394131064
          ],
          [
            2.4306001348815354e-16,
            1.208409565401941e-15,
            -0.4350607685675023
          ],
          [
            -5.2146327528250184e-17,
            8.511790004473525e-16,
            -2.6645352591003757e-15
          ],
          [
            2.618154638325789e-16,
            1.4509735292599946e-15,
            0.43506076856750214
          ],
          [
            4.113766310428724e-16,
            1.2569223581735518e-15,
            0.7941003941310634
          ],
          [
            1.3231448179541553e-17,
            -2.1477936436158582e-15,
            1.0176227078695863
          ],
          [
            -3.7185645195774755e-16,
            -1.2789736276151927e-16,
            1.0788506078892104
          ],
          [
            -4.3556347595310795e-16,
            6.527175754725812e-16,
            0.992268128144976
          ],
          [
            -1.1986817182722129e-15,
            -2.6020497941136694e-16,
            0.8022221183996807
          ],
          [
            -2.388574846960398e-16,
            2.9284085818499593e-15,
            0.5560543431205175
          ],
          [
            -6.091511369940873e-16,
            2.8225624885300794e-16,
            0.2858196456807595
          ]
        ],
        "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": [
          [
            -2.7755575615628914e-16,
            3.3306690738754696e-16,
            -0.28581964568075774
          ],
          [
            1.1102230246251565e-16,
            -2.3314683517128287e-15,
            0.4439456568794832
          ],
          [
            -9.992007221626409e-16,
            -6.106226635438361e-16,
            0.1977778816003215
          ],
          [
            -4.996003610813204e-16,
            -5.551115123125783e-17,
            0.0077318718550246635
          ],
          [
            -2.220446049250313e-16,
            8.881784197001252e-16,
            -0.07885060788921083
          ],
          [
            -2.220446049250313e-16,
            9.992007221626409e-16,
            -0.017622707869585863
          ],
          [
            3.3306690738754696e-16,
            1.2212453270876722e-15,
            0.20589960586893596
          ],
          [
            2.220446049250313e-16,
            1.2212453270876722e-15,
            -0.4350607685675023
          ],
          [
            -5.551115123125783e-17,
            8.881784197001252e-16,
            -2.6645352591003757e-15
          ],
          [
            2.220446049250313e-16,
            1.4432899320127035e-15,
            0.4350607685675021
          ],
          [
            4.440892098500626e-16,
            1.2212453270876722e-15,
            -0.20589960586893663
          ],
          [
            0.0,
            -2.1649348980190553e-15,
            0.017622707869586307
          ],
          [
            -3.885780586188048e-16,
            -1.1102230246251565e-16,
            0.07885060788921039
          ],
          [
            -4.440892098500626e-16,
            6.661338147750939e-16,
            -0.007731871855023886
          ],
          [
            -1.2212453270876722e-15,
            -2.7755575615628914e-16,
            -0.19777788160031928
          ],
          [
            -2.220446049250313e-16,
            2.886579864025407e-15,
            -0.4439456568794826
          ],
          [
            -6.106226635438361e-16,
            3.3306690738754696e-16,
            0.28581964568075957
          ]
        ]
      },
      "incoming_structure_ids": [
        "incoming_01_000",
        "incoming_01_001",
        "incoming_01_002",
        "incoming_01_003",
        "incoming_01_004",
        "incoming_01_005",
        "incoming_01_006",
        "incoming_01_007",
        "incoming_01_008"
      ],
      "reflected_structure_ids": [
        "reflected_01_001",
        "reflected_01_002",
        "reflected_01_003",
        "reflected_01_004",
        "reflected_01_005",
        "reflected_01_006",
        "reflected_01_007",
        "reflected_01_008"
      ]
    },
    {
      "orbit_id": 2,
      "formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.5,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        -0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -3.72102916021988e-16,
              7.762046843457722e-16,
              -0.2858196456807591
            ],
            "branch_aligned_reduced_polarization": [
              -3.72102916021988e-16,
              7.771561172376096e-16,
              -0.2858196456807591
            ],
            "target_residual": 0.5439422985724817,
            "energy_eV": -120.17130256501206,
            "max_atomic_step_A": 0.0731697420390138,
            "max_log_strain_component": 0.018524700924862463,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 5.296687313860863,
            "cell_principal_stretches": [
              1.0217384346179104,
              0.9964925102942046,
              0.9831955090334007
            ],
            "cell_volume_ratio": 1.0010451261584477,
            "cell_rmsd_from_input_A": 0.08639686297690466
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -1.5227495469997835e-14,
              0.5045445965896074,
              -0.5039404528092695
            ],
            "branch_aligned_reduced_polarization": [
              -1.5227495469997835e-14,
              0.5045445965896074,
              -0.5039404528092695
            ],
            "target_residual": 0.0060150250626535735,
            "energy_eV": -119.38618662702159,
            "max_atomic_step_A": 0.0008802932090267651,
            "max_log_strain_component": 0.0001639444895959939,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 5.296687313860863,
            "cell_principal_stretches": [
              1.021507504118001,
              0.9965577568041885,
              0.9833342515236912
            ],
            "cell_volume_ratio": 1.001025641124501,
            "cell_rmsd_from_input_A": 0.08526966495489005
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              1.4105193286919166e-15,
              0.49998364593455,
              -0.5000267976458913
            ],
            "branch_aligned_reduced_polarization": [
              1.4105193286919166e-15,
              0.49998364593455,
              -0.5000267976458913
            ],
            "target_residual": 3.139377776021846e-05,
            "energy_eV": -119.40276252730983
          }
        ],
        "iterations": 2
      },
      "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,
          -0.5
        ],
        "formal_class": [
          0.0,
          0.5,
          0.5
        ],
        "target_residual": 3.139377776021846e-05,
        "parent_symmetrization_rmsd_A": 0.09092002380397898,
        "parent_cell_rmsd_A": 0.08526966495489005,
        "energy_eV": -119.40276252730983,
        "reduced_polarization": [
          1.4105193286919166e-15,
          0.49998364593455,
          -0.5000267976458913
        ],
        "cartesian_polarization_e_A2": [
          7.998612906657125e-17,
          0.005445526922880994,
          -0.005193152361942859
        ],
        "ranking_score": 0.6123002275982219
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 3,
      "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": [
              -3.72102916021988e-16,
              7.762046843457722e-16,
              -0.2858196456807591
            ],
            "branch_aligned_reduced_polarization": [
              -3.885780586188048e-16,
              7.762046843457722e-16,
              -0.2858196456807591
            ],
            "target_residual": 0.543942298572482,
            "energy_eV": -120.17130256501206,
            "max_atomic_step_A": 0.06302655419510622,
            "max_log_strain_component": 0.02,
            "step_scale": 0.4078897695344756,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 5.296687313860863,
            "cell_principal_stretches": [
              1.0211423548381418,
              0.9988309616613642,
              0.9808593924907081
            ],
            "cell_volume_ratio": 1.000426164438594,
            "cell_rmsd_from_input_A": 0.1698768793597817
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.204261833160575,
              -1.9696470605149127e-14,
              -0.38015969673903854
            ],
            "branch_aligned_reduced_polarization": [
              -0.204261833160575,
              -1.9696470605149127e-14,
              -0.38015969673903854
            ],
            "target_residual": 0.31909679034929633,
            "energy_eV": -119.41619143200938,
            "max_atomic_step_A": 0.06223070161497891,
            "max_log_strain_component": 0.02,
            "step_scale": 0.6908848424546871,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 5.296687313860863,
            "cell_principal_stretches": [
              1.0424979314786762,
              0.9979168845165053,
              0.961967289103909
            ],
            "cell_volume_ratio": 1.000759858950946,
            "cell_rmsd_from_input_A": 0.339322904092102
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.40563327177023784,
              -4.000098831270751e-14,
              -0.4688611891867595
            ],
            "branch_aligned_reduced_polarization": [
              -0.40563327177023784,
              -4.000098831270751e-14,
              -0.4688611891867595
            ],
            "target_residual": 0.09937154993081558,
            "energy_eV": -116.88743178118887,
            "max_atomic_step_A": 0.028707603620154613,
            "max_log_strain_component": 0.009504982373312843,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 5.296687313860863,
            "cell_principal_stretches": [
              1.0525937024148162,
              0.9977150486999988,
              0.9530036981269969
            ],
            "cell_volume_ratio": 1.0008335976747318,
            "cell_rmsd_from_input_A": 0.4199210468445843
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -0.4960602792208061,
              -1.8134293012068623e-14,
              -0.5005728216086308
            ],
            "branch_aligned_reduced_polarization": [
              -0.4960602792208061,
              -1.8134293012068623e-14,
              -0.5005728216086308
            ],
            "target_residual": 0.0039811461180577976,
            "energy_eV": -114.92125367986202,
            "max_atomic_step_A": 0.0012461918464068333,
            "max_log_strain_component": 0.00042378676310603203,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 5.296687313860863,
            "cell_principal_stretches": [
              1.0530166959589151,
              0.9977390579458579,
              0.9525896061490288
            ],
            "cell_volume_ratio": 1.0008248250673062,
            "cell_rmsd_from_input_A": 0.42348935236811497
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              -0.4997919716421031,
              1.7870595552877354e-15,
              -0.49995617088251854
            ],
            "branch_aligned_reduced_polarization": [
              -0.4997919716421031,
              1.7870595552877354e-15,
              -0.49995617088251854
            ],
            "target_residual": 0.00021259536502117588,
            "energy_eV": -114.82741240909711
          }
        ],
        "iterations": 4
      },
      "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,
          -0.5
        ],
        "formal_class": [
          0.5,
          0.0,
          0.5
        ],
        "target_residual": 0.00021259536502117588,
        "parent_symmetrization_rmsd_A": 0.20242957041121926,
        "parent_cell_rmsd_A": 0.42348935236811497,
        "energy_eV": -114.82741240909711,
        "reduced_polarization": [
          -0.4997919716421031,
          1.7870595552877354e-15,
          -0.49995617088251854
        ],
        "cartesian_polarization_e_A2": [
          -0.013047752111002701,
          8.99047266024523e-16,
          -0.00462742641666909
        ],
        "ranking_score": 0.8087270992332903
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 4,
      "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": [
              -3.72102916021988e-16,
              7.762046843457722e-16,
              -0.2858196456807591
            ],
            "branch_aligned_reduced_polarization": [
              -3.72102916021988e-16,
              7.771561172376096e-16,
              -0.2858196456807591
            ],
            "target_residual": 0.575927833896812,
            "energy_eV": -120.17130256501206,
            "max_atomic_step_A": 0.07775630673836773,
            "max_log_strain_component": 0.018524700924882783,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 5.296687313860863,
            "cell_principal_stretches": [
              1.016856052540334,
              1.0046999169858222,
              0.9774594752789583
            ],
            "cell_volume_ratio": 0.9986069982822491,
            "cell_rmsd_from_input_A": 0.09940481361661496
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -4.459432735412097e-15,
              0.48897773008376044,
              -0.006287824530927861
            ],
            "branch_aligned_reduced_polarization": [
              -4.459432735412097e-15,
              0.48897773008376044,
              -0.006287824530927861
            ],
            "target_residual": 0.012689648199937528,
            "energy_eV": -119.40619763036541,
            "max_atomic_step_A": 0.0017101483873393308,
            "max_log_strain_component": 0.0004329368988424601,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 5.296687313860863,
            "cell_principal_stretches": [
              1.01725323814533,
              1.0048109634040412,
              0.976937745918452
            ],
            "cell_volume_ratio": 0.9985741876674842,
            "cell_rmsd_from_input_A": 0.10173661626347455
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -1.2988372712915328e-16,
              0.49984725698489,
              -3.3301587919110072e-06
            ],
            "branch_aligned_reduced_polarization": [
              -1.2988372712915328e-16,
              0.49984725698489,
              -3.3301587919110072e-06
            ],
            "target_residual": 0.0001527793134637893,
            "energy_eV": -119.37055356051607
          }
        ],
        "iterations": 2
      },
      "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,
          0.0
        ],
        "formal_class": [
          0.0,
          0.5,
          0.0
        ],
        "target_residual": 0.0001527793134637893,
        "parent_symmetrization_rmsd_A": 0.0959605820144034,
        "parent_cell_rmsd_A": 0.10173661626347455,
        "energy_eV": -119.37055356051607,
        "reduced_polarization": [
          -1.2988372712915328e-16,
          0.49984725698489,
          -3.3301587919110072e-06
        ],
        "cartesian_polarization_e_A2": [
          1.407702954970722e-16,
          0.005591918442590154,
          0.0001052203754466752
        ],
        "ranking_score": 0.6217002947071997
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 5,
      "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": [
              -3.72102916021988e-16,
              7.762046843457722e-16,
              -0.2858196456807591
            ],
            "branch_aligned_reduced_polarization": [
              -3.885780586188048e-16,
              7.762046843457722e-16,
              -0.2858196456807591
            ],
            "target_residual": 0.5759278338968123,
            "energy_eV": -120.17130256501206,
            "max_atomic_step_A": 0.06379142374940909,
            "max_log_strain_component": 0.02,
            "step_scale": 0.40788976953443973,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 5.296687313860863,
            "cell_principal_stretches": [
              1.0193402652291763,
              1.0015621911747319,
              0.9789397519700291
            ],
            "cell_volume_ratio": 0.999431574351983,
            "cell_rmsd_from_input_A": 0.17217824900319292
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.20139747631653626,
              -1.1826547895506186e-14,
              -0.1774026881965991
            ],
            "branch_aligned_reduced_polarization": [
              -0.20139747631653626,
              -1.1826547895506186e-14,
              -0.1774026881965991
            ],
            "target_residual": 0.3473257562138363,
            "energy_eV": -119.4606766342493,
            "max_atomic_step_A": 0.06300783604551781,
            "max_log_strain_component": 0.02,
            "step_scale": 0.6659339388335378,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 5.296687313860863,
            "cell_principal_stretches": [
              1.0389444512082526,
              1.0033999628606858,
              0.9580687056785103
            ],
            "cell_volume_ratio": 0.9987644212364005,
            "cell_rmsd_from_input_A": 0.3477457759016907
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.39119139506639616,
              -2.5968939187072255e-14,
              -0.07090355003715776
            ],
            "branch_aligned_reduced_polarization": [
              -0.39119139506639616,
              -2.5968939187072255e-14,
              -0.07090355003715776
            ],
            "target_residual": 0.12987157470158284,
            "energy_eV": -117.25575747003424,
            "max_atomic_step_A": 0.03616694038547639,
            "max_log_strain_component": 0.012030063579006031,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 5.296687313860863,
            "cell_principal_stretches": [
              1.0508139915020753,
              1.0047834271006058,
              0.9454679058133896
            ],
            "cell_volume_ratio": 0.9982632909275531,
            "cell_rmsd_from_input_A": 0.4562763690761467
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -0.48928032093452084,
              -1.4938034688362823e-14,
              -0.006182337182844138
            ],
            "branch_aligned_reduced_polarization": [
              -0.48928032093452084,
              -1.4938034688362823e-14,
              -0.006182337182844138
            ],
            "target_residual": 0.012374684331701125,
            "energy_eV": -115.15236778289442,
            "max_atomic_step_A": 0.00375880327888363,
            "max_log_strain_component": 0.001360013437742223,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 5.296687313860863,
            "cell_principal_stretches": [
              1.0521629563226689,
              1.0049449220272995,
              0.9440487248843856
            ],
            "cell_volume_ratio": 0.9982048542033399,
            "cell_rmsd_from_input_A": 0.46866806720632537
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              -0.49887481537850215,
              -1.911011125678004e-15,
              -0.00023252988533168
            ],
            "branch_aligned_reduced_polarization": [
              -0.49887481537850215,
              -1.911011125678004e-15,
              -0.00023252988533168
            ],
            "target_residual": 0.0011489606520797978,
            "energy_eV": -114.88572580562521,
            "max_atomic_step_A": 0.0004301705947620739,
            "max_log_strain_component": 8.221903386845552e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": true,
            "strain_jacobian_frobenius_norm": 5.201135812636413,
            "cell_principal_stretches": [
              1.0521972488370679,
              1.0049326569151797,
              0.9439302214511458
            ],
            "cell_volume_ratio": 0.9980999008110724,
            "cell_rmsd_from_input_A": 0.4690766919847925
          },
          {
            "iteration": 5,
            "reduced_polarization": [
              -0.49999956062360346,
              3.192062190733095e-15,
              -6.345014881531356e-07
            ],
            "branch_aligned_reduced_polarization": [
              -0.49999956062360346,
              3.192062190733095e-15,
              -6.345014881531356e-07
            ],
            "target_residual": 7.717796034544764e-07,
            "energy_eV": -114.85658923446655
          }
        ],
        "iterations": 5
      },
      "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,
          0.0
        ],
        "formal_class": [
          0.5,
          0.0,
          0.0
        ],
        "target_residual": 7.717796034544764e-07,
        "parent_symmetrization_rmsd_A": 0.20555395908083943,
        "parent_cell_rmsd_A": 0.4690766919847925,
        "energy_eV": -114.85658923446655,
        "reduced_polarization": [
          -0.49999956062360346,
          3.192062190733095e-15,
          -6.345014881531356e-07
        ],
        "cartesian_polarization_e_A2": [
          -0.013472562223314668,
          7.176422059688511e-16,
          0.0007124702334358567
        ],
        "ranking_score": 0.8228246756362445
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 6,
      "formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.5,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        -0.5,
        0.5,
        -0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -3.72102916021988e-16,
              7.762046843457722e-16,
              -0.2858196456807591
            ],
            "branch_aligned_reduced_polarization": [
              -3.885780586188048e-16,
              7.771561172376096e-16,
              -0.2858196456807591
            ],
            "target_residual": 0.7388323383395684,
            "energy_eV": -120.17130256501206,
            "max_atomic_step_A": 0.06943803766609506,
            "max_log_strain_component": 0.02,
            "step_scale": 0.4078897695344707,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 5.296687313860863,
            "cell_principal_stretches": [
              1.0225593398548698,
              0.9987981627639657,
              0.9795323572753771
            ],
            "cell_volume_ratio": 1.0004261644385906,
            "cell_rmsd_from_input_A": 0.17196341306396828
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.20407848236038204,
              0.2042653576172899,
              -0.3814611977145361
            ],
            "branch_aligned_reduced_polarization": [
              -0.20407848236038206,
              0.20426535761728992,
              -0.3814611977145361
            ],
            "target_residual": 0.43483326799433875,
            "energy_eV": -119.3045474305393,
            "max_atomic_step_A": 0.07216027547041517,
            "max_log_strain_component": 0.02,
            "step_scale": 0.689282347948107,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 5.296687313860863,
            "cell_principal_stretches": [
              1.0453442967853541,
              0.9979122042855694,
              0.959334146296384
            ],
            "cell_volume_ratio": 1.000740765015788,
            "cell_rmsd_from_input_A": 0.34351657194819324
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.4038775086857583,
              0.4044216428581357,
              -0.47030255074206545
            ],
            "branch_aligned_reduced_polarization": [
              -0.4038775086857583,
              0.4044216428581357,
              -0.47030255074206545
            ],
            "target_residual": 0.13876849131853325,
            "energy_eV": -116.38345689531755,
            "max_atomic_step_A": 0.035923005576033236,
            "max_log_strain_component": 0.009847588360773122,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 5.296687313860863,
            "cell_principal_stretches": [
              1.0564792281291027,
              0.997787505591894,
              0.9493837382702576
            ],
            "cell_volume_ratio": 1.000785057824476,
            "cell_rmsd_from_input_A": 0.42809682803449994
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -0.49476206982184767,
              0.4953012206868541,
              -0.5014200470596343
            ],
            "branch_aligned_reduced_polarization": [
              -0.49476206982184767,
              0.4953012206868541,
              -0.5014200470596343
            ],
            "target_residual": 0.007178507730470348,
            "energy_eV": -114.01334803837042,
            "max_atomic_step_A": 0.002069306680683851,
            "max_log_strain_component": 0.0005858981961750341,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 5.296687313860863,
            "cell_principal_stretches": [
              1.0570893998722377,
              0.997836942961026,
              0.9487721054788011
            ],
            "cell_volume_ratio": 1.0007675257979174,
            "cell_rmsd_from_input_A": 0.43308518098620125
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              -0.49964032642601697,
              0.4996982980505056,
              -0.499962607850598
            ],
            "branch_aligned_reduced_polarization": [
              -0.49964032642601697,
              0.4996982980505056,
              -0.499962607850598
            ],
            "target_residual": 0.0004709430103392143,
            "energy_eV": -113.86474503396647
          }
        ],
        "iterations": 4
      },
      "parent": {
        "candidate_id": "bec_projection_06",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          -0.5,
          0.5,
          -0.5
        ],
        "formal_class": [
          0.5,
          0.5,
          0.5
        ],
        "target_residual": 0.0004709430103392143,
        "parent_symmetrization_rmsd_A": 0.22181235691662424,
        "parent_cell_rmsd_A": 0.43308518098620125,
        "energy_eV": -113.86474503396647,
        "reduced_polarization": [
          -0.49964032642601697,
          0.4996982980505056,
          -0.499962607850598
        ],
        "cartesian_polarization_e_A2": [
          -0.013047318347539165,
          0.0054505562780266,
          -0.004514467879447582
        ],
        "ranking_score": 0.8310255381838529
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 7,
      "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": [
              -3.72102916021988e-16,
              7.762046843457722e-16,
              -0.2858196456807591
            ],
            "branch_aligned_reduced_polarization": [
              -3.885780586188048e-16,
              7.771561172376096e-16,
              -0.2858196456807591
            ],
            "target_residual": 0.7626879242895311,
            "energy_eV": -120.17130256501206,
            "max_atomic_step_A": 0.07001012578652611,
            "max_log_strain_component": 0.02,
            "step_scale": 0.40788976953443484,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 5.296687313860863,
            "cell_principal_stretches": [
              1.0207082172464383,
              1.0016060091200762,
              0.9775850090502465
            ],
            "cell_volume_ratio": 0.9994315743519798,
            "cell_rmsd_from_input_A": 0.17421304588203096
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.20118593151229136,
              0.20177018260847715,
              -0.17892158933106242
            ],
            "branch_aligned_reduced_polarization": [
              -0.20118593151229136,
              0.20177018260847712,
              -0.17892158933106242
            ],
            "target_residual": 0.4585235071796336,
            "energy_eV": -119.357001231171,
            "max_atomic_step_A": 0.07016703952030519,
            "max_log_strain_component": 0.02,
            "step_scale": 0.6639068084491633,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 5.296687313860863,
            "cell_principal_stretches": [
              1.0416912156618208,
              1.0035531573636725,
              0.9553769714011422
            ],
            "cell_volume_ratio": 0.9987439286726922,
            "cell_rmsd_from_input_A": 0.35206826948499237
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.3889921588253795,
              0.3907786957793566,
              -0.0737448503702768
            ],
            "branch_aligned_reduced_polarization": [
              -0.3889921588253795,
              0.3907786957793566,
              -0.0737448503702768
            ],
            "target_residual": 0.17230884206575883,
            "energy_eV": -116.81311454262796,
            "max_atomic_step_A": 0.043396410447870806,
            "max_log_strain_component": 0.012568982395855428,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 5.296687313860863,
            "cell_principal_stretches": [
              1.0549343621951952,
              1.0051303444852668,
              0.9413789697490943
            ],
            "cell_volume_ratio": 0.9981879323503223,
            "cell_rmsd_from_input_A": 0.46724449223992603
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -0.48668259411017006,
              0.48843129305592314,
              -0.008246473696179885
            ],
            "branch_aligned_reduced_polarization": [
              -0.48668259411017006,
              0.48843129305592314,
              -0.008246473696179885
            ],
            "target_residual": 0.01947286852043622,
            "energy_eV": -114.25064514888315,
            "max_atomic_step_A": 0.0056699515389474825,
            "max_log_strain_component": 0.0017862786458065828,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 5.296687313860863,
            "cell_principal_stretches": [
              1.0567992465814458,
              1.0053729524380812,
              0.9394103179296435
            ],
            "cell_volume_ratio": 0.9981022120893709,
            "cell_rmsd_from_input_A": 0.4838202932284564
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              -0.498218787449793,
              0.49853318658385426,
              -0.0004341897488733986
            ],
            "branch_aligned_reduced_polarization": [
              -0.498218787449793,
              0.49853318658385426,
              -0.0004341897488733986
            ],
            "target_residual": 0.002347931107342566,
            "energy_eV": -113.84518073590046,
            "max_atomic_step_A": 0.0008300055893409839,
            "max_log_strain_component": 0.00011124181753606136,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": true,
            "strain_jacobian_frobenius_norm": 5.170819660204182,
            "cell_principal_stretches": [
              1.0567852794406825,
              1.0053922980748817,
              0.9392020524625713
            ],
            "cell_volume_ratio": 0.9978869475121159,
            "cell_rmsd_from_input_A": 0.4841612190754222
          },
          {
            "iteration": 5,
            "reduced_polarization": [
              -0.4999990802140602,
              0.49999998849202665,
              -2.04844981604299e-06
            ],
            "branch_aligned_reduced_polarization": [
              -0.4999990802140602,
              0.49999998849202665,
              -2.04844981604299e-06
            ],
            "target_residual": 2.2455033416482573e-06,
            "energy_eV": -113.78831868399662
          }
        ],
        "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,
          0.0
        ],
        "formal_class": [
          0.5,
          0.5,
          0.0
        ],
        "target_residual": 2.2455033416482573e-06,
        "parent_symmetrization_rmsd_A": 0.22653552637490587,
        "parent_cell_rmsd_A": 0.4841612190754222,
        "energy_eV": -113.78831868399662,
        "reduced_polarization": [
          -0.4999990802140602,
          0.49999998849202665,
          -2.04844981604299e-06
        ],
        "cartesian_polarization_e_A2": [
          -0.013482650602466022,
          0.005610784632681095,
          0.0008386557970035997
        ],
        "ranking_score": 0.8475803221504448
      },
      "branch_status": "awaiting_branch_sampling"
    }
  ],
  "sampled_polarization_branches": [
    {
      "orbit_id": 1,
      "candidate_id": "inversion_parent_endpoint_00",
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "construction": "MACEField-BEC-parent plus variable-cell P-N-P path and symmetric log-strain continuation beyond both polar endpoints",
      "geometry_diagnostics": {
        "collision_aware": false,
        "permutations_tested": 1,
        "selected_order": [
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          10,
          11,
          12,
          13,
          14,
          15,
          16,
          17,
          18,
          19,
          20,
          21,
          22,
          23
        ],
        "endpoint_rmsd_A": 0.35138647025167224,
        "minimum_distance_A_by_image": [
          2.223038945840053,
          2.2025632109300526,
          2.184662346704232,
          2.16940009394668,
          2.1568324676869026,
          2.147006787894433,
          2.1399608240351164,
          2.1357220879808367,
          2.1343073052672805
        ],
        "minimum_distance_A": 2.1343073052672805,
        "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": [
          565.6680020606906,
          565.6680020606906,
          565.6680020606906,
          565.6680020606906,
          565.6680020606906,
          565.6680020606906,
          565.6680020606906,
          565.6680020606906,
          565.6680020606906
        ],
        "cell_deformation_log_strain_norm": 0.0
      },
      "parent_reduced_polarization": [
        -5.2146327528250165e-17,
        8.511790004473525e-16,
        -2.670549987228174e-15
      ],
      "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": [
          -120.17130256501206,
          -119.94766822644506,
          -119.38629732843455,
          -118.5958055333661,
          -117.68554572999258,
          -116.78142625893096,
          -116.01616779654785,
          -115.50342136535222,
          -115.32253422723005
        ],
        "cartesian_polarizations_e_A2": [
          [
            -7.168746656760121e-18,
            4.219753449458833e-18,
            -0.0030075010681779894
          ],
          [
            2.6745585677379377e-18,
            -2.6054524205379536e-17,
            -0.0058510114898394855
          ],
          [
            -2.7207247149174822e-17,
            -6.5258977764886596e-18,
            -0.008441280767305463
          ],
          [
            -1.3697121751891171e-17,
            -6.869366080514379e-19,
            -0.010441015865817006
          ],
          [
            -5.334045507291951e-18,
            9.911513916170746e-18,
            -0.011352069057056121
          ],
          [
            -5.460328712527482e-18,
            1.0843785027097698e-17,
            -0.01070780622385328
          ],
          [
            9.714936898194618e-18,
            1.3689665260453654e-17,
            -0.008355820951010723
          ],
          [
            6.488608096358194e-18,
            1.3444330757578142e-17,
            -0.00457787190615494
          ],
          [
            -1.3920721806083556e-18,
            9.469911810994821e-18,
            -2.810052444114469e-17
          ]
        ],
        "raw_reduced_polarization": [
          [
            -2.6853766373457387e-16,
            3.7928183439622966e-16,
            -0.28581964568075774
          ],
          [
            1.0018762605097133e-16,
            -2.3418448147023018e-15,
            -0.5560543431205168
          ],
          [
            -1.0191698683058971e-15,
            -5.865637671476574e-16,
            -0.8022221183996785
          ],
          [
            -5.130873291040822e-16,
            -6.174355443659552e-17,
            -0.9922681281449753
          ],
          [
            -1.9981067644946505e-16,
            8.908712854423068e-16,
            -1.0788506078892108
          ],
          [
            -2.0454118214684302e-16,
            9.746661093205435e-16,
            -1.0176227078695859
          ],
          [
            3.6391667649600505e-16,
            1.2304608348435822e-15,
            -0.794100394131064
          ],
          [
            2.4306001348815354e-16,
            1.208409565401941e-15,
            -0.4350607685675023
          ],
          [
            -5.2146327528250165e-17,
            8.511790004473525e-16,
            -2.670549987228174e-15
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -2.6853766373457387e-16,
            3.7928183439622966e-16,
            -0.28581964568075774
          ],
          [
            1.0018762605097132e-16,
            -2.3418448147023018e-15,
            -0.5560543431205168
          ],
          [
            -1.0191698683058971e-15,
            -5.865637671476574e-16,
            -0.8022221183996785
          ],
          [
            -5.130873291040822e-16,
            -6.174355443659549e-17,
            -0.9922681281449753
          ],
          [
            -1.9981067644946502e-16,
            8.908712854423068e-16,
            -1.0788506078892108
          ],
          [
            -2.0454118214684302e-16,
            9.746661093205435e-16,
            -1.0176227078695859
          ],
          [
            3.639166764960051e-16,
            1.2304608348435822e-15,
            -0.794100394131064
          ],
          [
            2.4306001348815354e-16,
            1.208409565401941e-15,
            -0.4350607685675023
          ],
          [
            -5.2146327528250184e-17,
            8.511790004473525e-16,
            -2.6645352591003757e-15
          ]
        ],
        "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": [
          [
            -2.7755575615628914e-16,
            3.3306690738754696e-16,
            -0.28581964568075774
          ],
          [
            1.1102230246251565e-16,
            -2.3314683517128287e-15,
            0.4439456568794832
          ],
          [
            -9.992007221626409e-16,
            -6.106226635438361e-16,
            0.1977778816003215
          ],
          [
            -4.996003610813204e-16,
            -5.551115123125783e-17,
            0.0077318718550246635
          ],
          [
            -2.220446049250313e-16,
            8.881784197001252e-16,
            -0.07885060788921083
          ],
          [
            -2.220446049250313e-16,
            9.992007221626409e-16,
            -0.017622707869585863
          ],
          [
            3.3306690738754696e-16,
            1.2212453270876722e-15,
            0.20589960586893596
          ],
          [
            2.220446049250313e-16,
            1.2212453270876722e-15,
            -0.4350607685675023
          ],
          [
            -5.551115123125783e-17,
            8.881784197001252e-16,
            -2.6645352591003757e-15
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -115.32253422723005,
          -115.50342136535221,
          -116.01616779654785,
          -116.78142625893096,
          -117.6855457299926,
          -118.5958055333661,
          -119.38629732843457,
          -119.94766822644507,
          -120.17130256501206
        ],
        "cartesian_polarizations_e_A2": [
          [
            -3.7030988633301647e-19,
            1.1089119529973212e-17,
            1.9395075658680907e-17
          ],
          [
            6.989294182930858e-18,
            1.614301028920879e-17,
            0.004577871906154938
          ],
          [
            1.0981904018397646e-17,
            1.3984066663904272e-17,
            0.008355820951010716
          ],
          [
            3.532200980006178e-19,
            -2.3895580580075017e-17,
            0.010707806223853283
          ],
          [
            -9.926893157905923e-18,
            -1.4229401166779785e-18,
            0.011352069057056116
          ],
          [
            -1.1627583887569394e-17,
            7.2619012851152e-18,
            0.010441015865817013
          ],
          [
            -3.199940537531778e-17,
            -2.8949471339310597e-18,
            0.008441280767305485
          ],
          [
            -6.3764194975246954e-18,
            3.2580421981868197e-17,
            0.005851011489839493
          ],
          [
            -1.6261592940289524e-17,
            3.140281636806573e-18,
            0.003007501068178008
          ]
        ],
        "raw_reduced_polarization": [
          [
            -1.387162310163521e-17,
            9.967173787621848e-16,
            1.8432225050127874e-15
          ],
          [
            2.618154638325789e-16,
            1.4509735292599946e-15,
            0.43506076856750214
          ],
          [
            4.113766310428724e-16,
            1.2569223581735518e-15,
            0.7941003941310634
          ],
          [
            1.3231448179541531e-17,
            -2.1477936436158582e-15,
            1.0176227078695863
          ],
          [
            -3.7185645195774755e-16,
            -1.278973627615193e-16,
            1.0788506078892104
          ],
          [
            -4.3556347595310795e-16,
            6.527175754725812e-16,
            0.992268128144976
          ],
          [
            -1.1986817182722129e-15,
            -2.6020497941136684e-16,
            0.8022221183996807
          ],
          [
            -2.3885748469603987e-16,
            2.9284085818499593e-15,
            0.5560543431205175
          ],
          [
            -6.091511369940873e-16,
            2.822562488530081e-16,
            0.2858196456807595
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -1.387162310163521e-17,
            9.967173787621848e-16,
            1.8432225050127874e-15
          ],
          [
            2.618154638325789e-16,
            1.4509735292599946e-15,
            0.43506076856750214
          ],
          [
            4.113766310428724e-16,
            1.2569223581735518e-15,
            0.7941003941310634
          ],
          [
            1.3231448179541553e-17,
            -2.1477936436158582e-15,
            1.0176227078695863
          ],
          [
            -3.7185645195774755e-16,
            -1.2789736276151927e-16,
            1.0788506078892104
          ],
          [
            -4.3556347595310795e-16,
            6.527175754725812e-16,
            0.992268128144976
          ],
          [
            -1.1986817182722129e-15,
            -2.6020497941136694e-16,
            0.8022221183996807
          ],
          [
            -2.388574846960398e-16,
            2.9284085818499593e-15,
            0.5560543431205175
          ],
          [
            -6.091511369940873e-16,
            2.8225624885300794e-16,
            0.2858196456807595
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          1.6424500867807358e-16,
          1.3230761664984753e-15,
          0.2858196456807524
        ],
        "actual_opposite_endpoint_branch_residual": 7.222779633441189e-15
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            -2.6853766373457387e-16,
            3.7928183439622966e-16,
            -0.28581964568075774
          ],
          [
            1.0018762605097133e-16,
            -2.3418448147023018e-15,
            -0.5560543431205168
          ],
          [
            -1.0191698683058971e-15,
            -5.865637671476574e-16,
            -0.8022221183996785
          ],
          [
            -5.130873291040822e-16,
            -6.174355443659552e-17,
            -0.9922681281449753
          ],
          [
            -1.9981067644946505e-16,
            8.908712854423068e-16,
            -1.0788506078892108
          ],
          [
            -2.0454118214684302e-16,
            9.746661093205435e-16,
            -1.0176227078695859
          ],
          [
            3.6391667649600505e-16,
            1.2304608348435822e-15,
            -0.794100394131064
          ],
          [
            2.4306001348815354e-16,
            1.208409565401941e-15,
            -0.4350607685675023
          ],
          [
            -5.2146327528250165e-17,
            8.511790004473525e-16,
            -2.670549987228174e-15
          ],
          [
            2.618154638325789e-16,
            1.4509735292599946e-15,
            0.43506076856750214
          ],
          [
            4.113766310428724e-16,
            1.2569223581735518e-15,
            0.7941003941310634
          ],
          [
            1.3231448179541531e-17,
            -2.1477936436158582e-15,
            1.0176227078695863
          ],
          [
            -3.7185645195774755e-16,
            -1.278973627615193e-16,
            1.0788506078892104
          ],
          [
            -4.3556347595310795e-16,
            6.527175754725812e-16,
            0.992268128144976
          ],
          [
            -1.1986817182722129e-15,
            -2.6020497941136684e-16,
            0.8022221183996807
          ],
          [
            -2.3885748469603987e-16,
            2.9284085818499593e-15,
            0.5560543431205175
          ],
          [
            -6.091511369940873e-16,
            2.822562488530081e-16,
            0.2858196456807595
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -2.6853766373457387e-16,
            3.7928183439622966e-16,
            -0.28581964568075774
          ],
          [
            1.0018762605097132e-16,
            -2.3418448147023018e-15,
            -0.5560543431205168
          ],
          [
            -1.0191698683058971e-15,
            -5.865637671476574e-16,
            -0.8022221183996785
          ],
          [
            -5.130873291040822e-16,
            -6.174355443659549e-17,
            -0.9922681281449753
          ],
          [
            -1.9981067644946502e-16,
            8.908712854423068e-16,
            -1.0788506078892108
          ],
          [
            -2.0454118214684302e-16,
            9.746661093205435e-16,
            -1.0176227078695859
          ],
          [
            3.639166764960051e-16,
            1.2304608348435822e-15,
            -0.794100394131064
          ],
          [
            2.4306001348815354e-16,
            1.208409565401941e-15,
            -0.4350607685675023
          ],
          [
            -5.2146327528250184e-17,
            8.511790004473525e-16,
            -2.6645352591003757e-15
          ],
          [
            2.618154638325789e-16,
            1.4509735292599946e-15,
            0.43506076856750214
          ],
          [
            4.113766310428724e-16,
            1.2569223581735518e-15,
            0.7941003941310634
          ],
          [
            1.3231448179541553e-17,
            -2.1477936436158582e-15,
            1.0176227078695863
          ],
          [
            -3.7185645195774755e-16,
            -1.2789736276151927e-16,
            1.0788506078892104
          ],
          [
            -4.3556347595310795e-16,
            6.527175754725812e-16,
            0.992268128144976
          ],
          [
            -1.1986817182722129e-15,
            -2.6020497941136694e-16,
            0.8022221183996807
          ],
          [
            -2.388574846960398e-16,
            2.9284085818499593e-15,
            0.5560543431205175
          ],
          [
            -6.091511369940873e-16,
            2.8225624885300794e-16,
            0.2858196456807595
          ]
        ],
        "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": [
          [
            -2.7755575615628914e-16,
            3.3306690738754696e-16,
            -0.28581964568075774
          ],
          [
            1.1102230246251565e-16,
            -2.3314683517128287e-15,
            0.4439456568794832
          ],
          [
            -9.992007221626409e-16,
            -6.106226635438361e-16,
            0.1977778816003215
          ],
          [
            -4.996003610813204e-16,
            -5.551115123125783e-17,
            0.0077318718550246635
          ],
          [
            -2.220446049250313e-16,
            8.881784197001252e-16,
            -0.07885060788921083
          ],
          [
            -2.220446049250313e-16,
            9.992007221626409e-16,
            -0.017622707869585863
          ],
          [
            3.3306690738754696e-16,
            1.2212453270876722e-15,
            0.20589960586893596
          ],
          [
            2.220446049250313e-16,
            1.2212453270876722e-15,
            -0.4350607685675023
          ],
          [
            -5.551115123125783e-17,
            8.881784197001252e-16,
            -2.6645352591003757e-15
          ],
          [
            2.220446049250313e-16,
            1.4432899320127035e-15,
            0.4350607685675021
          ],
          [
            4.440892098500626e-16,
            1.2212453270876722e-15,
            -0.20589960586893663
          ],
          [
            0.0,
            -2.1649348980190553e-15,
            0.017622707869586307
          ],
          [
            -3.885780586188048e-16,
            -1.1102230246251565e-16,
            0.07885060788921039
          ],
          [
            -4.440892098500626e-16,
            6.661338147750939e-16,
            -0.007731871855023886
          ],
          [
            -1.2212453270876722e-15,
            -2.7755575615628914e-16,
            -0.19777788160031928
          ],
          [
            -2.220446049250313e-16,
            2.886579864025407e-15,
            -0.4439456568794826
          ],
          [
            -6.106226635438361e-16,
            3.3306690738754696e-16,
            0.28581964568075957
          ]
        ]
      },
      "incoming_structure_ids": [
        "incoming_01_000",
        "incoming_01_001",
        "incoming_01_002",
        "incoming_01_003",
        "incoming_01_004",
        "incoming_01_005",
        "incoming_01_006",
        "incoming_01_007",
        "incoming_01_008"
      ],
      "reflected_structure_ids": [
        "reflected_01_001",
        "reflected_01_002",
        "reflected_01_003",
        "reflected_01_004",
        "reflected_01_005",
        "reflected_01_006",
        "reflected_01_007",
        "reflected_01_008"
      ],
      "positive_extension_structure_ids": [
        "extension_plus_01_000",
        "extension_plus_01_001",
        "extension_plus_01_002",
        "extension_plus_01_003"
      ],
      "negative_extension_structure_ids": [
        "extension_minus_01_000",
        "extension_minus_01_001",
        "extension_minus_01_002",
        "extension_minus_01_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": "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": 9.795214643165859e-16,
        "parent_symmetrization_rmsd_A": 0.35138647025167224,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -115.32253422723007,
        "reduced_polarization": [
          -2.2940940647568514e-16,
          9.48204585990574e-16,
          8.798685347156283e-17
        ],
        "cartesian_polarization_e_A2": [
          -6.1241983445845926e-18,
          1.0549383623647081e-17,
          9.258305361448444e-19
        ],
        "ranking_score": 0.3513864702516742
      }
    }
  ],
  "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": 84,
      "full_response": 27,
      "energy_polarization": 57
    },
    "model_evaluations_for_recovery_and_path_properties": {
      "total": 109,
      "full_response": 52,
      "energy_polarization": 57
    },
    "elapsed_seconds": 297.97077524801716
  }
}
