{
  "schema": "ferrofinder.endpoint_parent_recovery.v4_variable_cell",
  "status": "complete",
  "input_atom_count": 15,
  "input_formula": "H2O10U3",
  "input_spacegroup": "P1",
  "input_pointgroup": "1",
  "input_is_polar_point_group": true,
  "input_energy_eV": -124.43861770192686,
  "input_cartesian_polarization_e_A2": [
    0.009578650524569885,
    -0.00033586134113393817,
    0.009775945618545142
  ],
  "input_reduced_polarization": [
    0.39435960140487847,
    -0.013226645421149498,
    0.19795542222260537
  ],
  "input_formal_targets": [
    {
      "orbit_id": 0,
      "representative_formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.0
      ]
    },
    {
      "orbit_id": 1,
      "representative_formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.5
      ]
    },
    {
      "orbit_id": 2,
      "representative_formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ]
    },
    {
      "orbit_id": 3,
      "representative_formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.5
      ]
    },
    {
      "orbit_id": 4,
      "representative_formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        0.5,
        -0.5,
        0.0
      ]
    },
    {
      "orbit_id": 5,
      "representative_formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "target_reduced_polarization": [
        0.5,
        -0.5,
        0.5
      ]
    },
    {
      "orbit_id": 6,
      "representative_formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        -0.5,
        0.0
      ]
    },
    {
      "orbit_id": 7,
      "representative_formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        -0.5,
        0.5
      ]
    }
  ],
  "parent_candidates": [
    {
      "candidate_id": "inversion_parent_endpoint_00",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "P-1",
      "spacegroup_number": 2,
      "pointgroup": "-1",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 1.295592599325886e-15,
      "parent_symmetrization_rmsd_A": 0.2402156316575608,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -122.70536330877775,
      "reduced_polarization": [
        -7.348226427832688e-16,
        -5.009976062068873e-16,
        9.421238059066267e-16
      ],
      "cartesian_polarization_e_A2": [
        -2.0913103625672572e-17,
        -1.2830124923725505e-17,
        2.251686924113826e-17
      ],
      "ranking_score": 0.24021563165756338
    },
    {
      "candidate_id": "inversion_parent_endpoint_01",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "P-1",
      "spacegroup_number": 2,
      "pointgroup": "-1",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 2.0798464435249693e-15,
      "parent_symmetrization_rmsd_A": 0.9902936720422137,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": "Infinity",
      "reduced_polarization": [
        -3.2796015809837726e-16,
        8.825481607272327e-16,
        -1.854538246394646e-15
      ],
      "cartesian_polarization_e_A2": [
        -2.8867781078382386e-18,
        2.258101986575689e-17,
        -5.914687589837457e-17
      ],
      "ranking_score": 0.9902936720422179
    },
    {
      "candidate_id": "bec_projection_00",
      "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,
        0.0,
        0.0
      ],
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_residual": 8.521366433027468e-05,
      "parent_symmetrization_rmsd_A": 0.07088166588766241,
      "parent_cell_rmsd_A": 0.029604330442941147,
      "energy_eV": -124.2211197483127,
      "reduced_polarization": [
        0.5000801883458936,
        -2.2964430683794972e-05,
        1.7430797308378036e-05
      ],
      "cartesian_polarization_e_A2": [
        0.012176871398599612,
        -2.822806415842712e-05,
        0.00393275197272266
      ],
      "ranking_score": 0.5784531758270582
    },
    {
      "candidate_id": "inversion_parent_bec_00_00",
      "source": "same_species_inversion_center_projection_after_BEC",
      "spacegroup": "P-1",
      "spacegroup_number": 2,
      "pointgroup": "-1",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.0
      ],
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_residual": 0.49999999999999994,
      "parent_symmetrization_rmsd_A": 0.24038907726611874,
      "parent_cell_rmsd_A": 0.029604330442941147,
      "energy_eV": -122.80969801216949,
      "reduced_polarization": [
        4.797991305764916e-17,
        -1.1800548741789495e-15,
        -1.4517325082698162e-15
      ],
      "cartesian_polarization_e_A2": [
        -5.491447784081845e-18,
        -2.988369259244539e-17,
        -5.817103408486698e-17
      ],
      "ranking_score": 1.247790159876854
    },
    {
      "candidate_id": "bec_projection_01",
      "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,
        0.0,
        0.5
      ],
      "formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_residual": 8.979948187269742e-05,
      "parent_symmetrization_rmsd_A": 0.16312396463414122,
      "parent_cell_rmsd_A": 0.09554196000131446,
      "energy_eV": -123.18384445695234,
      "reduced_polarization": [
        0.4999996451613312,
        3.6399916947786724e-05,
        0.4999179093971254
      ],
      "cartesian_polarization_e_A2": [
        0.012537539962887168,
        0.00024152710842887366,
        0.021145156810917755
      ],
      "ranking_score": 0.6871890535982152
    },
    {
      "candidate_id": "bec_projection_02",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 2.7468947662732584e-05,
      "parent_symmetrization_rmsd_A": 0.12689159201103864,
      "parent_cell_rmsd_A": 0.054451376514744014,
      "energy_eV": -123.21653951770517,
      "reduced_polarization": [
        2.2554031453800452e-05,
        -3.0621494747319165e-06,
        -1.5377970980377118e-05
      ],
      "cartesian_polarization_e_A2": [
        5.284822150880718e-07,
        -7.465073178862839e-08,
        -3.67992886474527e-07
      ],
      "ranking_score": 0.6405593740350501
    },
    {
      "candidate_id": "bec_projection_03",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.5
      ],
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_residual": 0.00040991328426049034,
      "parent_symmetrization_rmsd_A": 0.1493967471053204,
      "parent_cell_rmsd_A": 0.05538493153650545,
      "energy_eV": -123.17834658173831,
      "reduced_polarization": [
        0.00020437609114193133,
        -0.0002330328708974317,
        0.4997317557175557
      ],
      "cartesian_polarization_e_A2": [
        8.00502527269232e-05,
        1.6895243871829953e-05,
        0.017071426747197468
      ],
      "ranking_score": 0.6640628065579677
    },
    {
      "candidate_id": "bec_projection_04",
      "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": 0.0002542183170787921,
      "parent_symmetrization_rmsd_A": 0.19050741763957343,
      "parent_cell_rmsd_A": 0.0434939805598882,
      "energy_eV": -122.95506748042263,
      "reduced_polarization": [
        0.4998878344704594,
        -0.4998425597279655,
        -0.00016510120369928738
      ],
      "cartesian_polarization_e_A2": [
        0.009246625378846457,
        -0.012627779134160045,
        2.7152417119259983e-05
      ],
      "ranking_score": 0.7018893494137031
    },
    {
      "candidate_id": "bec_projection_05",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.5,
        -0.5,
        0.5
      ],
      "formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "target_residual": 0.00011966385132244864,
      "parent_symmetrization_rmsd_A": 0.1872803832827564,
      "parent_cell_rmsd_A": 0.11083819341707271,
      "energy_eV": -122.40542366918149,
      "reduced_polarization": [
        0.4999392961106072,
        -0.4999441398073971,
        0.4999133160106578
      ],
      "cartesian_polarization_e_A2": [
        0.009356617462088924,
        -0.012578065420580473,
        0.016968190586813786
      ],
      "ranking_score": 0.7152292593396694
    },
    {
      "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": [
        0.0,
        -0.5,
        0.0
      ],
      "formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_residual": 6.380695757977575e-05,
      "parent_symmetrization_rmsd_A": 0.22953083646968375,
      "parent_cell_rmsd_A": 0.05398004621628453,
      "energy_eV": -120.57280330706465,
      "reduced_polarization": [
        3.670963901492796e-05,
        -0.49996694951606785,
        -4.039054036320393e-05
      ],
      "cartesian_polarization_e_A2": [
        -0.002927558723836867,
        -0.012625388202156649,
        -0.003767521040439592
      ],
      "ranking_score": 0.7431534619389144
    },
    {
      "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": [
        0.0,
        -0.5,
        0.5
      ],
      "formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_residual": 0.00011355228477671616,
      "parent_symmetrization_rmsd_A": 0.1981888474004987,
      "parent_cell_rmsd_A": 0.07006852296246648,
      "energy_eV": -120.79952132584667,
      "reduced_polarization": [
        -9.764316129557935e-05,
        -0.5000404258424457,
        0.4999584586267346
      ],
      "cartesian_polarization_e_A2": [
        -0.0030198614241092395,
        -0.012755840769094754,
        0.0130897108074519
      ],
      "ranking_score": 0.7159330827106687
    }
  ],
  "formal_branches": [
    {
      "orbit_id": 0,
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.0,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              0.39435960140487847,
              -0.013226645421149498,
              0.19795542222260537
            ],
            "branch_aligned_reduced_polarization": [
              0.39435960140487847,
              -0.013226645421149498,
              0.19795542222260537
            ],
            "target_residual": 0.22476918639298168,
            "energy_eV": -124.43861770192686,
            "max_atomic_step_A": 0.10655679203106257,
            "max_log_strain_component": 0.0045942510149402,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.1722768687090763,
            "cell_principal_stretches": [
              1.0056426179482365,
              1.0024393548475374,
              0.9969600800566207
            ],
            "cell_volume_ratio": 1.005031206807041,
            "cell_rmsd_from_input_A": 0.031244587768620165
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.49082248828530706,
              -0.0005764091389836832,
              -0.01045292233286304
            ],
            "branch_aligned_reduced_polarization": [
              0.49082248828530706,
              -0.0005764091389836832,
              -0.01045292233286304
            ],
            "target_residual": 0.013922016882107887,
            "energy_eV": -124.20769831032992,
            "max_atomic_step_A": 0.0072165649519626935,
            "max_log_strain_component": 0.0002774193662224631,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.1722768687090763,
            "cell_principal_stretches": [
              1.0052621140583675,
              1.0023904497915097,
              0.9970024982085772
            ],
            "cell_volume_ratio": 1.0046446645990255,
            "cell_rmsd_from_input_A": 0.029604330442941147
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.5000801883458936,
              -2.2964430683794972e-05,
              1.7430797308378036e-05
            ],
            "branch_aligned_reduced_polarization": [
              0.5000801883458936,
              -2.2964430683794972e-05,
              1.7430797308378036e-05
            ],
            "target_residual": 8.521366433027468e-05,
            "energy_eV": -124.2211197483127
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_00",
        "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,
          0.0,
          0.0
        ],
        "formal_class": [
          0.5,
          0.0,
          0.0
        ],
        "target_residual": 8.521366433027468e-05,
        "parent_symmetrization_rmsd_A": 0.07088166588766241,
        "parent_cell_rmsd_A": 0.029604330442941147,
        "energy_eV": -124.2211197483127,
        "reduced_polarization": [
          0.5000801883458936,
          -2.2964430683794972e-05,
          1.7430797308378036e-05
        ],
        "cartesian_polarization_e_A2": [
          0.012176871398599612,
          -2.822806415842712e-05,
          0.00393275197272266
        ],
        "ranking_score": 0.5784531758270582
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 1,
      "formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.0,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              0.39435960140487847,
              -0.013226645421149498,
              0.19795542222260537
            ],
            "branch_aligned_reduced_polarization": [
              0.39435960140487847,
              -0.013226645421149498,
              0.19795542222260537
            ],
            "target_residual": 0.32025890296626813,
            "energy_eV": -124.43861770192686,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.00561467684983483,
            "step_scale": 0.6273107611648339,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.1722768687090763,
            "cell_principal_stretches": [
              1.0017821837142902,
              0.9985659773157194,
              0.9923993303895522
            ],
            "cell_volume_ratio": 0.9927423088956971,
            "cell_rmsd_from_input_A": 0.03598361664182628
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.4519213143621338,
              -0.004984023964875411,
              0.35917968699471514
            ],
            "branch_aligned_reduced_polarization": [
              0.4519213143621338,
              -0.004984023964875411,
              0.35917968699471514
            ],
            "target_residual": 0.14888505990344905,
            "energy_eV": -124.19459259344927,
            "max_atomic_step_A": 0.08810655525944634,
            "max_log_strain_component": 0.007696890283047994,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.1722768687090763,
            "cell_principal_stretches": [
              1.0046222004407825,
              0.9963803091694917,
              0.9821615306683101
            ],
            "cell_volume_ratio": 0.9831297245593927,
            "cell_rmsd_from_input_A": 0.08476688462443706
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.5016382459675945,
              -0.0016701627362676278,
              0.47804915193146424
            ],
            "branch_aligned_reduced_polarization": [
              0.5016382459675945,
              -0.0016701627362676278,
              0.47804915193146424
            ],
            "target_residual": 0.022075167594922052,
            "energy_eV": -123.38620461035462,
            "max_atomic_step_A": 0.016547773159914892,
            "max_log_strain_component": 0.0016448359812893576,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.1722768687090763,
            "cell_principal_stretches": [
              1.0052867583005125,
              0.9957607676028266,
              0.9800980134092032
            ],
            "cell_volume_ratio": 0.9811027257082813,
            "cell_rmsd_from_input_A": 0.09488026991908603
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.5002125944234035,
              0.0002787698818884611,
              0.4985542476712299
            ],
            "branch_aligned_reduced_polarization": [
              0.5002125944234035,
              0.0002787698818884611,
              0.4985542476712299
            ],
            "target_residual": 0.0014876521206432989,
            "energy_eV": -123.19667622384996,
            "max_atomic_step_A": 0.0010240127360476605,
            "max_log_strain_component": 0.00010602451637754371,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.1722768687090763,
            "cell_principal_stretches": [
              1.0053348313325898,
              0.9957211353032775,
              0.979963645749742
            ],
            "cell_volume_ratio": 0.9809760850128525,
            "cell_rmsd_from_input_A": 0.09554196000131446
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              0.4999996451613312,
              3.6399916947786724e-05,
              0.4999179093971254
            ],
            "branch_aligned_reduced_polarization": [
              0.4999996451613312,
              3.6399916947786724e-05,
              0.4999179093971254
            ],
            "target_residual": 8.979948187269742e-05,
            "energy_eV": -123.18384445695234
          }
        ],
        "iterations": 4
      },
      "parent": {
        "candidate_id": "bec_projection_01",
        "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,
          0.0,
          0.5
        ],
        "formal_class": [
          0.5,
          0.0,
          0.5
        ],
        "target_residual": 8.979948187269742e-05,
        "parent_symmetrization_rmsd_A": 0.16312396463414122,
        "parent_cell_rmsd_A": 0.09554196000131446,
        "energy_eV": -123.18384445695234,
        "reduced_polarization": [
          0.4999996451613312,
          3.6399916947786724e-05,
          0.4999179093971254
        ],
        "cartesian_polarization_e_A2": [
          0.012537539962887168,
          0.00024152710842887366,
          0.021145156810917755
        ],
        "ranking_score": 0.6871890535982152
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 2,
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.0,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              0.39435960140487847,
              -0.013226645421149498,
              0.19795542222260537
            ],
            "branch_aligned_reduced_polarization": [
              0.39435960140487847,
              -0.013226645421149498,
              0.19795542222260537
            ],
            "target_residual": 0.4414530423008108,
            "energy_eV": -124.43861770192686,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.0055089580126397066,
            "step_scale": 0.6797793657756512,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.1722768687090763,
            "cell_principal_stretches": [
              1.0088161255305383,
              1.0000783418044397,
              0.9990399236536438
            ],
            "cell_volume_ratio": 1.007926541629005,
            "cell_rmsd_from_input_A": 0.039022925121680783
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.13592915163562802,
              -0.01213140737172948,
              0.04780094197069814
            ],
            "branch_aligned_reduced_polarization": [
              0.13592915163562802,
              -0.01213140737172948,
              0.04780094197069814
            ],
            "target_residual": 0.14459887745928893,
            "energy_eV": -123.8102979292875,
            "max_atomic_step_A": 0.05402204960032474,
            "max_log_strain_component": 0.0019751062622316747,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.1722768687090763,
            "cell_principal_stretches": [
              1.0122861809554269,
              1.0002454940333867,
              0.9981632387551863
            ],
            "cell_volume_ratio": 1.0106749066931549,
            "cell_rmsd_from_input_A": 0.054106490987952026
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.003084999040421902,
              -0.003740212773439594,
              -0.0002283505745047585
            ],
            "branch_aligned_reduced_polarization": [
              0.003084999040421902,
              -0.003740212773439594,
              -0.0002283505745047585
            ],
            "target_residual": 0.004853715551500872,
            "energy_eV": -123.22093988558883,
            "max_atomic_step_A": 0.001398291443224794,
            "max_log_strain_component": 6.335529173820768e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.1722768687090763,
            "cell_principal_stretches": [
              1.0123693125898876,
              1.000210797195136,
              0.9981100544944481
            ],
            "cell_volume_ratio": 1.0106689910460487,
            "cell_rmsd_from_input_A": 0.054451376514744014
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              2.2554031453800452e-05,
              -3.0621494747319165e-06,
              -1.5377970980377118e-05
            ],
            "branch_aligned_reduced_polarization": [
              2.2554031453800452e-05,
              -3.0621494747319165e-06,
              -1.5377970980377118e-05
            ],
            "target_residual": 2.7468947662732584e-05,
            "energy_eV": -123.21653951770517
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "inversion_parent_endpoint_00",
        "source": "same_species_inversion_center_projection_from_endpoint",
        "spacegroup": "P-1",
        "spacegroup_number": 2,
        "pointgroup": "-1",
        "has_inversion": true,
        "is_polar_point_group": false,
        "nonpolar_parent_hypothesis": true,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.0
        ],
        "formal_class": [
          0.0,
          0.0,
          0.0
        ],
        "target_residual": 1.295592599325886e-15,
        "parent_symmetrization_rmsd_A": 0.2402156316575608,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -122.70536330877775,
        "reduced_polarization": [
          -7.348226427832688e-16,
          -5.009976062068873e-16,
          9.421238059066267e-16
        ],
        "cartesian_polarization_e_A2": [
          -2.0913103625672572e-17,
          -1.2830124923725505e-17,
          2.251686924113826e-17
        ],
        "ranking_score": 0.24021563165756338
      },
      "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": [
          -124.43861770192684,
          -124.38374417925804,
          -124.22464404640964,
          -123.94521470452284,
          -123.69883103287049,
          -123.36829791788371,
          -122.69619048227959,
          -122.53405413713537,
          -122.70536330877772
        ],
        "cartesian_polarizations_e_A2": [
          [
            0.009578650524569968,
            -0.0003358613411338489,
            0.009775945618545062
          ],
          [
            0.010846570737393986,
            -0.0003897827188792139,
            0.00979403080781187
          ],
          [
            0.012233705758372853,
            -0.0004810123161260355,
            0.009776781660126967
          ],
          [
            0.013725652605444612,
            -0.0004974214251781522,
            0.009646562151807925
          ],
          [
            0.014349836986090802,
            -0.000937443821218009,
            0.009067694767772463
          ],
          [
            0.008493436036806665,
            -0.001449409759032524,
            0.0060932468727456935
          ],
          [
            -0.00023060325804065947,
            -0.0006989001532180633,
            0.002252851920156452
          ],
          [
            -0.0020116274346712055,
            2.3041188126230538e-05,
            0.0006205891403868656
          ],
          [
            -9.109388695845109e-17,
            -7.24902058190491e-17,
            6.447137774172066e-17
          ]
        ],
        "raw_reduced_polarization": [
          [
            0.3943596014048811,
            -0.013226645421146006,
            0.19795542222260165
          ],
          [
            0.44664670972564224,
            -0.015375226463805647,
            0.1868640260663284
          ],
          [
            0.504149753384193,
            -0.018988299776374992,
            0.17385975376070792
          ],
          [
            0.5652377598008014,
            -0.019678825161559166,
            0.15606030971110746
          ],
          [
            0.5948218112942949,
            -0.036931026897670895,
            0.13613969566723846
          ],
          [
            0.36038421121801917,
            -0.056852454598627,
            0.10778763472782059
          ],
          [
            -0.0029164884063173587,
            -0.027296716647891812,
            0.0727838546315184
          ],
          [
            -0.08237422574582393,
            0.0009764756128045955,
            0.037022445145712
          ],
          [
            -3.046424868601402e-15,
            -2.8328106048321595e-15,
            3.2301120693588537e-15
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            0.3943596014048811,
            -0.013226645421146006,
            0.19795542222260165
          ],
          [
            0.44664670972564224,
            -0.015375226463805647,
            0.1868640260663284
          ],
          [
            0.504149753384193,
            -0.018988299776374992,
            0.17385975376070792
          ],
          [
            0.5652377598008014,
            -0.019678825161559166,
            0.15606030971110746
          ],
          [
            0.5948218112942949,
            -0.036931026897670895,
            0.13613969566723846
          ],
          [
            0.36038421121801917,
            -0.056852454598627,
            0.10778763472782059
          ],
          [
            -0.0029164884063173635,
            -0.027296716647891812,
            0.0727838546315184
          ],
          [
            -0.08237422574582393,
            0.0009764756128045962,
            0.037022445145712
          ],
          [
            -3.0531133177191805e-15,
            -2.832803436270126e-15,
            3.2335245592207684e-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": [
          [
            0.39435960140488113,
            -0.013226645421145988,
            0.19795542222260165
          ],
          [
            0.44664670972564224,
            -0.015375226463805625,
            0.18686402606632835
          ],
          [
            -0.495850246615807,
            -0.018988299776375006,
            0.17385975376070795
          ],
          [
            -0.4347622401991986,
            -0.019678825161559166,
            0.15606030971110751
          ],
          [
            -0.4051781887057051,
            -0.036931026897670916,
            0.1361396956672385
          ],
          [
            0.3603842112180191,
            -0.05685245459862698,
            0.1077876347278206
          ],
          [
            -0.0029164884063173635,
            -0.027296716647891794,
            0.07278385463151837
          ],
          [
            -0.08237422574582393,
            0.0009764756128045615,
            0.03702244514571196
          ],
          [
            -3.0531133177191805e-15,
            -2.831068712794149e-15,
            3.219646771412954e-15
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -122.70536330877772,
          -122.53405413713536,
          -122.69619048227956,
          -123.36829791788367,
          -123.69883103287049,
          -123.94521470452284,
          -124.22464404640961,
          -124.38374417925807,
          -124.43861770192683
        ],
        "cartesian_polarizations_e_A2": [
          [
            -2.242705836667218e-16,
            1.860368113940198e-17,
            1.2387485613856974e-16
          ],
          [
            0.0020116274346711266,
            -2.3041188126238493e-05,
            -0.0006205891403868627
          ],
          [
            0.0002306032580404352,
            0.0006989001532181041,
            -0.0022528519201565123
          ],
          [
            -0.008493436036806802,
            0.0014494097590324754,
            -0.006093246872745692
          ],
          [
            -0.014349836986090879,
            0.0009374438212181028,
            -0.009067694767772501
          ],
          [
            -0.013725652605444455,
            0.0004974214251781425,
            -0.009646562151807826
          ],
          [
            -0.012233705758372801,
            0.00048101231612612014,
            -0.009776781660126885
          ],
          [
            -0.010846570737394028,
            0.0003897827188792333,
            -0.009794030807811901
          ],
          [
            -0.00957865052456975,
            0.00033586134113377993,
            -0.009775945618545046
          ]
        ],
        "raw_reduced_polarization": [
          [
            -9.332674126312748e-15,
            7.37580411467868e-16,
            5.622081933039846e-15
          ],
          [
            0.08237422574582076,
            -0.0009764756128049042,
            -0.037022445145711104
          ],
          [
            0.00291648840630782,
            0.027296716647893418,
            -0.0727838546315183
          ],
          [
            -0.36038421121802433,
            0.05685245459862511,
            -0.1077876347278189
          ],
          [
            -0.5948218112942989,
            0.036931026897674565,
            -0.1361396956672395
          ],
          [
            -0.5652377598007948,
            0.019678825161558784,
            -0.156060309711106
          ],
          [
            -0.5041497533841918,
            0.018988299776378302,
            -0.17385975376070656
          ],
          [
            -0.4466467097256442,
            0.01537522646380641,
            -0.18686402606632904
          ],
          [
            -0.39435960140487153,
            0.0132266454211433,
            -0.1979554222226028
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -9.332674126312748e-15,
            7.37580411467868e-16,
            5.622081933039846e-15
          ],
          [
            0.08237422574582076,
            -0.0009764756128049042,
            -0.037022445145711104
          ],
          [
            0.0029164884063078156,
            0.027296716647893418,
            -0.0727838546315183
          ],
          [
            -0.36038421121802433,
            0.05685245459862511,
            -0.1077876347278189
          ],
          [
            -0.5948218112942989,
            0.036931026897674565,
            -0.1361396956672395
          ],
          [
            -0.5652377598007948,
            0.019678825161558784,
            -0.156060309711106
          ],
          [
            -0.5041497533841918,
            0.018988299776378302,
            -0.17385975376070656
          ],
          [
            -0.4466467097256442,
            0.01537522646380641,
            -0.18686402606632904
          ],
          [
            -0.39435960140487153,
            0.0132266454211433,
            -0.1979554222226028
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          -0.3943596014048872,
          0.013226645421140344,
          -0.1979554222225952
        ],
        "actual_opposite_endpoint_branch_residual": 1.76410047710074e-14
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            0.3943596014048811,
            -0.013226645421146006,
            0.19795542222260165
          ],
          [
            0.44664670972564224,
            -0.015375226463805647,
            0.1868640260663284
          ],
          [
            0.504149753384193,
            -0.018988299776374992,
            0.17385975376070792
          ],
          [
            0.5652377598008014,
            -0.019678825161559166,
            0.15606030971110746
          ],
          [
            0.5948218112942949,
            -0.036931026897670895,
            0.13613969566723846
          ],
          [
            0.36038421121801917,
            -0.056852454598627,
            0.10778763472782059
          ],
          [
            -0.0029164884063173587,
            -0.027296716647891812,
            0.0727838546315184
          ],
          [
            -0.08237422574582393,
            0.0009764756128045955,
            0.037022445145712
          ],
          [
            -3.046424868601402e-15,
            -2.8328106048321595e-15,
            3.2301120693588537e-15
          ],
          [
            0.08237422574582076,
            -0.0009764756128049042,
            -0.037022445145711104
          ],
          [
            0.00291648840630782,
            0.027296716647893418,
            -0.0727838546315183
          ],
          [
            -0.36038421121802433,
            0.05685245459862511,
            -0.1077876347278189
          ],
          [
            -0.5948218112942989,
            0.036931026897674565,
            -0.1361396956672395
          ],
          [
            -0.5652377598007948,
            0.019678825161558784,
            -0.156060309711106
          ],
          [
            -0.5041497533841918,
            0.018988299776378302,
            -0.17385975376070656
          ],
          [
            -0.4466467097256442,
            0.01537522646380641,
            -0.18686402606632904
          ],
          [
            -0.39435960140487153,
            0.0132266454211433,
            -0.1979554222226028
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            0.3943596014048811,
            -0.013226645421146006,
            0.19795542222260165
          ],
          [
            0.44664670972564224,
            -0.015375226463805647,
            0.1868640260663284
          ],
          [
            0.504149753384193,
            -0.018988299776374992,
            0.17385975376070792
          ],
          [
            0.5652377598008014,
            -0.019678825161559166,
            0.15606030971110746
          ],
          [
            0.5948218112942949,
            -0.036931026897670895,
            0.13613969566723846
          ],
          [
            0.36038421121801917,
            -0.056852454598627,
            0.10778763472782059
          ],
          [
            -0.0029164884063173635,
            -0.027296716647891812,
            0.0727838546315184
          ],
          [
            -0.08237422574582393,
            0.0009764756128045962,
            0.037022445145712
          ],
          [
            -3.0531133177191805e-15,
            -2.832803436270126e-15,
            3.2335245592207684e-15
          ],
          [
            0.08237422574582076,
            -0.0009764756128049042,
            -0.037022445145711104
          ],
          [
            0.0029164884063078156,
            0.027296716647893418,
            -0.0727838546315183
          ],
          [
            -0.36038421121802433,
            0.05685245459862511,
            -0.1077876347278189
          ],
          [
            -0.5948218112942989,
            0.036931026897674565,
            -0.1361396956672395
          ],
          [
            -0.5652377598007948,
            0.019678825161558784,
            -0.156060309711106
          ],
          [
            -0.5041497533841918,
            0.018988299776378302,
            -0.17385975376070656
          ],
          [
            -0.4466467097256442,
            0.01537522646380641,
            -0.18686402606632904
          ],
          [
            -0.39435960140487153,
            0.0132266454211433,
            -0.1979554222226028
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            0.39435960140488113,
            -0.013226645421145988,
            0.19795542222260165
          ],
          [
            0.44664670972564224,
            -0.015375226463805625,
            0.18686402606632835
          ],
          [
            -0.495850246615807,
            -0.018988299776375006,
            0.17385975376070795
          ],
          [
            -0.4347622401991986,
            -0.019678825161559166,
            0.15606030971110751
          ],
          [
            -0.4051781887057051,
            -0.036931026897670916,
            0.1361396956672385
          ],
          [
            0.3603842112180191,
            -0.05685245459862698,
            0.1077876347278206
          ],
          [
            -0.0029164884063173635,
            -0.027296716647891794,
            0.07278385463151837
          ],
          [
            -0.08237422574582393,
            0.0009764756128045615,
            0.03702244514571196
          ],
          [
            -3.0531133177191805e-15,
            -2.831068712794149e-15,
            3.219646771412954e-15
          ],
          [
            0.08237422574582076,
            -0.0009764756128048946,
            -0.037022445145711125
          ],
          [
            0.00291648840630776,
            0.02729671664789346,
            -0.07278385463151832
          ],
          [
            -0.36038421121802433,
            0.05685245459862509,
            -0.10778763472781888
          ],
          [
            0.4051781887057011,
            0.03693102689767458,
            -0.1361396956672395
          ],
          [
            0.4347622401992052,
            0.019678825161558833,
            -0.15606030971110596
          ],
          [
            0.49585024661580823,
            0.01898829977637828,
            -0.17385975376070656
          ],
          [
            -0.4466467097256442,
            0.015375226463806402,
            -0.18686402606632901
          ],
          [
            -0.39435960140487153,
            0.013226645421143268,
            -0.19795542222260276
          ]
        ]
      },
      "incoming_structure_ids": [
        "incoming_02_000",
        "incoming_02_001",
        "incoming_02_002",
        "incoming_02_003",
        "incoming_02_004",
        "incoming_02_005",
        "incoming_02_006",
        "incoming_02_007",
        "incoming_02_008"
      ],
      "reflected_structure_ids": [
        "reflected_02_001",
        "reflected_02_002",
        "reflected_02_003",
        "reflected_02_004",
        "reflected_02_005",
        "reflected_02_006",
        "reflected_02_007",
        "reflected_02_008"
      ]
    },
    {
      "orbit_id": 3,
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.0,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              0.39435960140487847,
              -0.013226645421149498,
              0.19795542222260537
            ],
            "branch_aligned_reduced_polarization": [
              0.39435960140487847,
              -0.013226645421149498,
              0.19795542222260537
            ],
            "target_residual": 0.49691585437982966,
            "energy_eV": -124.43861770192686,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.0042012683189054404,
            "step_scale": 0.7722062140053968,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.1722768687090763,
            "cell_principal_stretches": [
              1.0042354708945338,
              0.9976179951881368,
              0.9943013714349486
            ],
            "cell_volume_ratio": 0.9961342438837674,
            "cell_rmsd_from_input_A": 0.032585281302891886
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.09054666786533254,
              -0.009051060978591376,
              0.4080402554615887
            ],
            "branch_aligned_reduced_polarization": [
              0.09054666786533254,
              -0.009051060978591376,
              0.4080402554615887
            ],
            "target_residual": 0.1293723903385993,
            "energy_eV": -123.79220871969497,
            "max_atomic_step_A": 0.05333681689774265,
            "max_log_strain_component": 0.003192509627298613,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.1722768687090763,
            "cell_principal_stretches": [
              1.006171122737752,
              0.9956620907354998,
              0.9906630055239475
            ],
            "cell_volume_ratio": 0.9924525824718288,
            "cell_rmsd_from_input_A": 0.052972093829165505
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.00294195071056527,
              -0.005523571219266608,
              0.492957730535262
            ],
            "branch_aligned_reduced_polarization": [
              0.00294195071056527,
              -0.005523571219266608,
              0.492957730535262
            ],
            "target_residual": 0.009421171488285699,
            "energy_eV": -123.22090356554939,
            "max_atomic_step_A": 0.005213376115631845,
            "max_log_strain_component": 0.0004361670001592332,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.1722768687090763,
            "cell_principal_stretches": [
              1.0062853188474594,
              0.9954496895055089,
              0.9901593409564666
            ],
            "cell_volume_ratio": 0.9918489569758305,
            "cell_rmsd_from_input_A": 0.05538493153650545
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.00020437609114193133,
              -0.0002330328708974317,
              0.4997317557175557
            ],
            "branch_aligned_reduced_polarization": [
              0.00020437609114193133,
              -0.0002330328708974317,
              0.4997317557175557
            ],
            "target_residual": 0.00040991328426049034,
            "energy_eV": -123.17834658173831
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_03",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.5
        ],
        "formal_class": [
          0.0,
          0.0,
          0.5
        ],
        "target_residual": 0.00040991328426049034,
        "parent_symmetrization_rmsd_A": 0.1493967471053204,
        "parent_cell_rmsd_A": 0.05538493153650545,
        "energy_eV": -123.17834658173831,
        "reduced_polarization": [
          0.00020437609114193133,
          -0.0002330328708974317,
          0.4997317557175557
        ],
        "cartesian_polarization_e_A2": [
          8.00502527269232e-05,
          1.6895243871829953e-05,
          0.017071426747197468
        ],
        "ranking_score": 0.6640628065579677
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 4,
      "formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.5,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.5,
        -0.5,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              0.39435960140487847,
              -0.013226645421149498,
              0.19795542222260537
            ],
            "branch_aligned_reduced_polarization": [
              0.39435960140487847,
              -0.013226645421149485,
              0.19795542222260537
            ],
            "target_residual": 0.5359986396723535,
            "energy_eV": -124.43861770192686,
            "max_atomic_step_A": 0.12000000000000001,
            "max_log_strain_component": 0.0036023098404015116,
            "step_scale": 0.6429927724705569,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.1722768687090763,
            "cell_principal_stretches": [
              1.0057611728918345,
              1.0021630949080702,
              0.9995009741029004
            ],
            "cell_volume_ratio": 1.0074337432328622,
            "cell_rmsd_from_input_A": 0.0254097498270059
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.44023703530293395,
              -0.312609003995069,
              0.060823463449851074
            ],
            "branch_aligned_reduced_polarization": [
              0.44023703530293395,
              -0.312609003995069,
              0.060823463449851074
            ],
            "target_residual": 0.20587979754977948,
            "energy_eV": -123.87008103379988,
            "max_atomic_step_A": 0.06920398398636936,
            "max_log_strain_component": 0.0021296282969485514,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.1722768687090763,
            "cell_principal_stretches": [
              1.009411357765707,
              1.0037903899089886,
              0.9977417993810451
            ],
            "cell_volume_ratio": 1.0109493270203274,
            "cell_rmsd_from_input_A": 0.04115599873417602
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.4826184783631452,
              -0.4858886410998987,
              0.005156416797987951
            ],
            "branch_aligned_reduced_polarization": [
              0.4826184783631452,
              -0.4858886410998987,
              0.005156416797987951
            ],
            "target_residual": 0.022974689956874104,
            "energy_eV": -123.03563381908987,
            "max_atomic_step_A": 0.007482541227803707,
            "max_log_strain_component": 0.0004127851138401343,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.1722768687090763,
            "cell_principal_stretches": [
              1.0100108194236668,
              1.0038800578591356,
              0.9973299235659601
            ],
            "cell_volume_ratio": 1.0112224499906621,
            "cell_rmsd_from_input_A": 0.0434939805598882
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.4998878344704594,
              -0.4998425597279655,
              -0.00016510120369928738
            ],
            "branch_aligned_reduced_polarization": [
              0.4998878344704594,
              -0.4998425597279655,
              -0.00016510120369928738
            ],
            "target_residual": 0.0002542183170787921,
            "energy_eV": -122.95506748042263
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_04",
        "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": 0.0002542183170787921,
        "parent_symmetrization_rmsd_A": 0.19050741763957343,
        "parent_cell_rmsd_A": 0.0434939805598882,
        "energy_eV": -122.95506748042263,
        "reduced_polarization": [
          0.4998878344704594,
          -0.4998425597279655,
          -0.00016510120369928738
        ],
        "cartesian_polarization_e_A2": [
          0.009246625378846457,
          -0.012627779134160045,
          2.7152417119259983e-05
        ],
        "ranking_score": 0.7018893494137031
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 5,
      "formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.5,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.5,
        -0.5,
        0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              0.39435960140487847,
              -0.013226645421149498,
              0.19795542222260537
            ],
            "branch_aligned_reduced_polarization": [
              0.39435960140487847,
              -0.013226645421149485,
              0.19795542222260537
            ],
            "target_residual": 0.5825282134867015,
            "energy_eV": -124.43861770192686,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.004699480632272226,
            "step_scale": 0.5478183205511805,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.1722768687090763,
            "cell_principal_stretches": [
              1.0050666507566564,
              1.0003394647739918,
              0.9918398131284302
            ],
            "cell_volume_ratio": 0.9972035196604436,
            "cell_rmsd_from_input_A": 0.04118038188565517
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.43401065789720206,
              -0.2730773990085696,
              0.34191677431961975
            ],
            "branch_aligned_reduced_polarization": [
              0.43401065789720206,
              -0.2730773990085696,
              0.34191677431961975
            ],
            "target_residual": 0.2843215896716077,
            "energy_eV": -123.96960569100693,
            "max_atomic_step_A": 0.10332600566267618,
            "max_log_strain_component": 0.007101469092376253,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.1722768687090763,
            "cell_principal_stretches": [
              1.0110833276003206,
              1.0006102099943146,
              0.979571634099619
            ],
            "cell_volume_ratio": 0.9910329168266218,
            "cell_rmsd_from_input_A": 0.09985277940662791
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.47576315440964867,
              -0.48927972792882996,
              0.4821494234676772
            ],
            "branch_aligned_reduced_polarization": [
              0.47576315440964867,
              -0.48927972792882996,
              0.4821494234676772
            ],
            "target_residual": 0.03195296543337965,
            "energy_eV": -122.5839064910461,
            "max_atomic_step_A": 0.01585854823625248,
            "max_log_strain_component": 0.001463023778819684,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.1722768687090763,
            "cell_principal_stretches": [
              1.0117612529696967,
              1.0006510593686393,
              0.9772359454973727
            ],
            "cell_volume_ratio": 0.9893731862444671,
            "cell_rmsd_from_input_A": 0.11014096832893457
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.4992057623211576,
              -0.49926793599005015,
              0.498553531546364
            ],
            "branch_aligned_reduced_polarization": [
              0.4992057623211576,
              -0.49926793599005015,
              0.498553531546364
            ],
            "target_residual": 0.0018052706701547367,
            "energy_eV": -122.41880063928669,
            "max_atomic_step_A": 0.0010291329725890608,
            "max_log_strain_component": 0.0001013661709934831,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.1722768687090763,
            "cell_principal_stretches": [
              1.0118131144163902,
              1.000642256407466,
              0.9770827614047096
            ],
            "cell_volume_ratio": 0.9892601026978298,
            "cell_rmsd_from_input_A": 0.11083819341707271
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              0.4999392961106072,
              -0.4999441398073971,
              0.4999133160106578
            ],
            "branch_aligned_reduced_polarization": [
              0.4999392961106072,
              -0.4999441398073971,
              0.4999133160106578
            ],
            "target_residual": 0.00011966385132244864,
            "energy_eV": -122.40542366918149
          }
        ],
        "iterations": 4
      },
      "parent": {
        "candidate_id": "bec_projection_05",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.5,
          -0.5,
          0.5
        ],
        "formal_class": [
          0.5,
          0.5,
          0.5
        ],
        "target_residual": 0.00011966385132244864,
        "parent_symmetrization_rmsd_A": 0.1872803832827564,
        "parent_cell_rmsd_A": 0.11083819341707271,
        "energy_eV": -122.40542366918149,
        "reduced_polarization": [
          0.4999392961106072,
          -0.4999441398073971,
          0.4999133160106578
        ],
        "cartesian_polarization_e_A2": [
          0.009356617462088924,
          -0.012578065420580473,
          0.016968190586813786
        ],
        "ranking_score": 0.7152292593396694
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 6,
      "formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.5,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        -0.5,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              0.39435960140487847,
              -0.013226645421149498,
              0.19795542222260537
            ],
            "branch_aligned_reduced_polarization": [
              0.39435960140487847,
              -0.013226645421149485,
              0.19795542222260537
            ],
            "target_residual": 0.6570039140944991,
            "energy_eV": -124.43861770192686,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.004541724421099757,
            "step_scale": 0.4984224701444423,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.1722768687090763,
            "cell_principal_stretches": [
              1.0062734313260269,
              1.0024850555934524,
              1.0002928091449153
            ],
            "cell_volume_ratio": 1.0090694550199109,
            "cell_rmsd_from_input_A": 0.02972876561434841
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.20694959994359705,
              -0.25111603359960377,
              0.07888174789443204
            ],
            "branch_aligned_reduced_polarization": [
              0.20694959994359705,
              -0.25111603359960377,
              0.07888174789443204
            ],
            "target_residual": 0.3331571638114498,
            "energy_eV": -123.44564975633517,
            "max_atomic_step_A": 0.11796461251725311,
            "max_log_strain_component": 0.002844210493635174,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.1722768687090763,
            "cell_principal_stretches": [
              1.0111769757577163,
              1.0055144742285043,
              0.9996829776481461
            ],
            "cell_volume_ratio": 1.0164307516766857,
            "cell_rmsd_from_input_A": 0.05381898625354334
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.002884926981400155,
              -0.4971013477631864,
              -0.0010369412404858346
            ],
            "branch_aligned_reduced_polarization": [
              0.002884926981400155,
              -0.4971013477631864,
              -0.0010369412404858346
            ],
            "target_residual": 0.004219032544815878,
            "energy_eV": -120.62121723200029,
            "max_atomic_step_A": 0.0014679485924166968,
            "max_log_strain_component": 5.561098222407732e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.1722768687090763,
            "cell_principal_stretches": [
              1.0112084997213315,
              1.0055530330170983,
              0.9996513601837488
            ],
            "cell_volume_ratio": 1.0164692686537593,
            "cell_rmsd_from_input_A": 0.05398004621628453
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              3.670963901492796e-05,
              -0.49996694951606785,
              -4.039054036320393e-05
            ],
            "branch_aligned_reduced_polarization": [
              3.670963901492796e-05,
              -0.49996694951606785,
              -4.039054036320393e-05
            ],
            "target_residual": 6.380695757977575e-05,
            "energy_eV": -120.57280330706465
          }
        ],
        "iterations": 3
      },
      "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": [
          0.0,
          -0.5,
          0.0
        ],
        "formal_class": [
          0.0,
          0.5,
          0.0
        ],
        "target_residual": 6.380695757977575e-05,
        "parent_symmetrization_rmsd_A": 0.22953083646968375,
        "parent_cell_rmsd_A": 0.05398004621628453,
        "energy_eV": -120.57280330706465,
        "reduced_polarization": [
          3.670963901492796e-05,
          -0.49996694951606785,
          -4.039054036320393e-05
        ],
        "cartesian_polarization_e_A2": [
          -0.002927558723836867,
          -0.012625388202156649,
          -0.003767521040439592
        ],
        "ranking_score": 0.7431534619389144
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 7,
      "formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.5,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        -0.5,
        0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              0.39435960140487847,
              -0.013226645421149498,
              0.19795542222260537
            ],
            "branch_aligned_reduced_polarization": [
              0.39435960140487847,
              -0.013226645421149485,
              0.19795542222260537
            ],
            "target_residual": 0.6954845224107339,
            "energy_eV": -124.43861770192686,
            "max_atomic_step_A": 0.11999999999999998,
            "max_log_strain_component": 0.005012384936253896,
            "step_scale": 0.6190614511175553,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.1722768687090763,
            "cell_principal_stretches": [
              1.007480241871099,
              0.9981616429904844,
              0.9953173238106467
            ],
            "cell_volume_ratio": 1.000919102590392,
            "cell_rmsd_from_input_A": 0.038608316963206275
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.15876272515062576,
              -0.3070630994948554,
              0.3653134481262581
            ],
            "branch_aligned_reduced_polarization": [
              0.15876272515062576,
              -0.3070630994948554,
              0.3653134481262581
            ],
            "target_residual": 0.28384981544722443,
            "energy_eV": -123.11762218535883,
            "max_atomic_step_A": 0.09782939246997545,
            "max_log_strain_component": 0.003715609600078082,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.1722768687090763,
            "cell_principal_stretches": [
              1.0129871910644266,
              0.9964625041397721,
              0.9912225377292229
            ],
            "cell_volume_ratio": 1.0005437497110237,
            "cell_rmsd_from_input_A": 0.06930412351804956
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.0027088015622004943,
              -0.5006921266677846,
              0.496363362434168
            ],
            "branch_aligned_reduced_polarization": [
              -0.0027088015622004943,
              -0.5006921266677846,
              0.496363362434168
            ],
            "target_residual": 0.004587131784989277,
            "energy_eV": -120.76885843623668,
            "max_atomic_step_A": 0.002642382493873703,
            "max_log_strain_component": 0.00017432696064257356,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.1722768687090763,
            "cell_principal_stretches": [
              1.0130210390685952,
              0.9964264845454799,
              0.9909937174724943
            ],
            "cell_volume_ratio": 1.0003100422056603,
            "cell_rmsd_from_input_A": 0.07006852296246648
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -9.764316129557935e-05,
              -0.5000404258424457,
              0.4999584586267346
            ],
            "branch_aligned_reduced_polarization": [
              -9.764316129557935e-05,
              -0.5000404258424457,
              0.4999584586267346
            ],
            "target_residual": 0.00011355228477671616,
            "energy_eV": -120.79952132584667
          }
        ],
        "iterations": 3
      },
      "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": [
          0.0,
          -0.5,
          0.5
        ],
        "formal_class": [
          0.0,
          0.5,
          0.5
        ],
        "target_residual": 0.00011355228477671616,
        "parent_symmetrization_rmsd_A": 0.1981888474004987,
        "parent_cell_rmsd_A": 0.07006852296246648,
        "energy_eV": -120.79952132584667,
        "reduced_polarization": [
          -9.764316129557935e-05,
          -0.5000404258424457,
          0.4999584586267346
        ],
        "cartesian_polarization_e_A2": [
          -0.0030198614241092395,
          -0.012755840769094754,
          0.0130897108074519
        ],
        "ranking_score": 0.7159330827106687
      },
      "branch_status": "awaiting_branch_sampling"
    }
  ],
  "sampled_polarization_branches": [
    {
      "orbit_id": 2,
      "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
        ],
        "endpoint_rmsd_A": 0.2402156316575608,
        "minimum_distance_A_by_image": [
          0.9791118870314347,
          1.0088605760430378,
          1.0424613757288268,
          1.0795546587847746,
          1.1197934122624151,
          1.1628511488636946,
          1.2084265745612528,
          1.256245700976924,
          1.3060621040995994
        ],
        "minimum_distance_A": 0.9791118870314347,
        "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": [
          216.331296699249,
          216.331296699249,
          216.331296699249,
          216.331296699249,
          216.331296699249,
          216.331296699249,
          216.331296699249,
          216.331296699249,
          216.331296699249
        ],
        "cell_deformation_log_strain_norm": 0.0
      },
      "parent_reduced_polarization": [
        -3.046424868601402e-15,
        -2.8328106048321595e-15,
        3.2301120693588537e-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": [
          -124.43861770192684,
          -124.38374417925804,
          -124.22464404640964,
          -123.94521470452284,
          -123.69883103287049,
          -123.36829791788371,
          -122.69619048227959,
          -122.53405413713537,
          -122.70536330877772
        ],
        "cartesian_polarizations_e_A2": [
          [
            0.009578650524569968,
            -0.0003358613411338489,
            0.009775945618545062
          ],
          [
            0.010846570737393986,
            -0.0003897827188792139,
            0.00979403080781187
          ],
          [
            0.012233705758372853,
            -0.0004810123161260355,
            0.009776781660126967
          ],
          [
            0.013725652605444612,
            -0.0004974214251781522,
            0.009646562151807925
          ],
          [
            0.014349836986090802,
            -0.000937443821218009,
            0.009067694767772463
          ],
          [
            0.008493436036806665,
            -0.001449409759032524,
            0.0060932468727456935
          ],
          [
            -0.00023060325804065947,
            -0.0006989001532180633,
            0.002252851920156452
          ],
          [
            -0.0020116274346712055,
            2.3041188126230538e-05,
            0.0006205891403868656
          ],
          [
            -9.109388695845109e-17,
            -7.24902058190491e-17,
            6.447137774172066e-17
          ]
        ],
        "raw_reduced_polarization": [
          [
            0.3943596014048811,
            -0.013226645421146006,
            0.19795542222260165
          ],
          [
            0.44664670972564224,
            -0.015375226463805647,
            0.1868640260663284
          ],
          [
            0.504149753384193,
            -0.018988299776374992,
            0.17385975376070792
          ],
          [
            0.5652377598008014,
            -0.019678825161559166,
            0.15606030971110746
          ],
          [
            0.5948218112942949,
            -0.036931026897670895,
            0.13613969566723846
          ],
          [
            0.36038421121801917,
            -0.056852454598627,
            0.10778763472782059
          ],
          [
            -0.0029164884063173587,
            -0.027296716647891812,
            0.0727838546315184
          ],
          [
            -0.08237422574582393,
            0.0009764756128045955,
            0.037022445145712
          ],
          [
            -3.046424868601402e-15,
            -2.8328106048321595e-15,
            3.2301120693588537e-15
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            0.3943596014048811,
            -0.013226645421146006,
            0.19795542222260165
          ],
          [
            0.44664670972564224,
            -0.015375226463805647,
            0.1868640260663284
          ],
          [
            0.504149753384193,
            -0.018988299776374992,
            0.17385975376070792
          ],
          [
            0.5652377598008014,
            -0.019678825161559166,
            0.15606030971110746
          ],
          [
            0.5948218112942949,
            -0.036931026897670895,
            0.13613969566723846
          ],
          [
            0.36038421121801917,
            -0.056852454598627,
            0.10778763472782059
          ],
          [
            -0.0029164884063173635,
            -0.027296716647891812,
            0.0727838546315184
          ],
          [
            -0.08237422574582393,
            0.0009764756128045962,
            0.037022445145712
          ],
          [
            -3.0531133177191805e-15,
            -2.832803436270126e-15,
            3.2335245592207684e-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": [
          [
            0.39435960140488113,
            -0.013226645421145988,
            0.19795542222260165
          ],
          [
            0.44664670972564224,
            -0.015375226463805625,
            0.18686402606632835
          ],
          [
            -0.495850246615807,
            -0.018988299776375006,
            0.17385975376070795
          ],
          [
            -0.4347622401991986,
            -0.019678825161559166,
            0.15606030971110751
          ],
          [
            -0.4051781887057051,
            -0.036931026897670916,
            0.1361396956672385
          ],
          [
            0.3603842112180191,
            -0.05685245459862698,
            0.1077876347278206
          ],
          [
            -0.0029164884063173635,
            -0.027296716647891794,
            0.07278385463151837
          ],
          [
            -0.08237422574582393,
            0.0009764756128045615,
            0.03702244514571196
          ],
          [
            -3.0531133177191805e-15,
            -2.831068712794149e-15,
            3.219646771412954e-15
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -122.70536330877772,
          -122.53405413713536,
          -122.69619048227956,
          -123.36829791788367,
          -123.69883103287049,
          -123.94521470452284,
          -124.22464404640961,
          -124.38374417925807,
          -124.43861770192683
        ],
        "cartesian_polarizations_e_A2": [
          [
            -2.242705836667218e-16,
            1.860368113940198e-17,
            1.2387485613856974e-16
          ],
          [
            0.0020116274346711266,
            -2.3041188126238493e-05,
            -0.0006205891403868627
          ],
          [
            0.0002306032580404352,
            0.0006989001532181041,
            -0.0022528519201565123
          ],
          [
            -0.008493436036806802,
            0.0014494097590324754,
            -0.006093246872745692
          ],
          [
            -0.014349836986090879,
            0.0009374438212181028,
            -0.009067694767772501
          ],
          [
            -0.013725652605444455,
            0.0004974214251781425,
            -0.009646562151807826
          ],
          [
            -0.012233705758372801,
            0.00048101231612612014,
            -0.009776781660126885
          ],
          [
            -0.010846570737394028,
            0.0003897827188792333,
            -0.009794030807811901
          ],
          [
            -0.00957865052456975,
            0.00033586134113377993,
            -0.009775945618545046
          ]
        ],
        "raw_reduced_polarization": [
          [
            -9.332674126312748e-15,
            7.37580411467868e-16,
            5.622081933039846e-15
          ],
          [
            0.08237422574582076,
            -0.0009764756128049042,
            -0.037022445145711104
          ],
          [
            0.00291648840630782,
            0.027296716647893418,
            -0.0727838546315183
          ],
          [
            -0.36038421121802433,
            0.05685245459862511,
            -0.1077876347278189
          ],
          [
            -0.5948218112942989,
            0.036931026897674565,
            -0.1361396956672395
          ],
          [
            -0.5652377598007948,
            0.019678825161558784,
            -0.156060309711106
          ],
          [
            -0.5041497533841918,
            0.018988299776378302,
            -0.17385975376070656
          ],
          [
            -0.4466467097256442,
            0.01537522646380641,
            -0.18686402606632904
          ],
          [
            -0.39435960140487153,
            0.0132266454211433,
            -0.1979554222226028
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -9.332674126312748e-15,
            7.37580411467868e-16,
            5.622081933039846e-15
          ],
          [
            0.08237422574582076,
            -0.0009764756128049042,
            -0.037022445145711104
          ],
          [
            0.0029164884063078156,
            0.027296716647893418,
            -0.0727838546315183
          ],
          [
            -0.36038421121802433,
            0.05685245459862511,
            -0.1077876347278189
          ],
          [
            -0.5948218112942989,
            0.036931026897674565,
            -0.1361396956672395
          ],
          [
            -0.5652377598007948,
            0.019678825161558784,
            -0.156060309711106
          ],
          [
            -0.5041497533841918,
            0.018988299776378302,
            -0.17385975376070656
          ],
          [
            -0.4466467097256442,
            0.01537522646380641,
            -0.18686402606632904
          ],
          [
            -0.39435960140487153,
            0.0132266454211433,
            -0.1979554222226028
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          -0.3943596014048872,
          0.013226645421140344,
          -0.1979554222225952
        ],
        "actual_opposite_endpoint_branch_residual": 1.76410047710074e-14
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            0.3943596014048811,
            -0.013226645421146006,
            0.19795542222260165
          ],
          [
            0.44664670972564224,
            -0.015375226463805647,
            0.1868640260663284
          ],
          [
            0.504149753384193,
            -0.018988299776374992,
            0.17385975376070792
          ],
          [
            0.5652377598008014,
            -0.019678825161559166,
            0.15606030971110746
          ],
          [
            0.5948218112942949,
            -0.036931026897670895,
            0.13613969566723846
          ],
          [
            0.36038421121801917,
            -0.056852454598627,
            0.10778763472782059
          ],
          [
            -0.0029164884063173587,
            -0.027296716647891812,
            0.0727838546315184
          ],
          [
            -0.08237422574582393,
            0.0009764756128045955,
            0.037022445145712
          ],
          [
            -3.046424868601402e-15,
            -2.8328106048321595e-15,
            3.2301120693588537e-15
          ],
          [
            0.08237422574582076,
            -0.0009764756128049042,
            -0.037022445145711104
          ],
          [
            0.00291648840630782,
            0.027296716647893418,
            -0.0727838546315183
          ],
          [
            -0.36038421121802433,
            0.05685245459862511,
            -0.1077876347278189
          ],
          [
            -0.5948218112942989,
            0.036931026897674565,
            -0.1361396956672395
          ],
          [
            -0.5652377598007948,
            0.019678825161558784,
            -0.156060309711106
          ],
          [
            -0.5041497533841918,
            0.018988299776378302,
            -0.17385975376070656
          ],
          [
            -0.4466467097256442,
            0.01537522646380641,
            -0.18686402606632904
          ],
          [
            -0.39435960140487153,
            0.0132266454211433,
            -0.1979554222226028
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            0.3943596014048811,
            -0.013226645421146006,
            0.19795542222260165
          ],
          [
            0.44664670972564224,
            -0.015375226463805647,
            0.1868640260663284
          ],
          [
            0.504149753384193,
            -0.018988299776374992,
            0.17385975376070792
          ],
          [
            0.5652377598008014,
            -0.019678825161559166,
            0.15606030971110746
          ],
          [
            0.5948218112942949,
            -0.036931026897670895,
            0.13613969566723846
          ],
          [
            0.36038421121801917,
            -0.056852454598627,
            0.10778763472782059
          ],
          [
            -0.0029164884063173635,
            -0.027296716647891812,
            0.0727838546315184
          ],
          [
            -0.08237422574582393,
            0.0009764756128045962,
            0.037022445145712
          ],
          [
            -3.0531133177191805e-15,
            -2.832803436270126e-15,
            3.2335245592207684e-15
          ],
          [
            0.08237422574582076,
            -0.0009764756128049042,
            -0.037022445145711104
          ],
          [
            0.0029164884063078156,
            0.027296716647893418,
            -0.0727838546315183
          ],
          [
            -0.36038421121802433,
            0.05685245459862511,
            -0.1077876347278189
          ],
          [
            -0.5948218112942989,
            0.036931026897674565,
            -0.1361396956672395
          ],
          [
            -0.5652377598007948,
            0.019678825161558784,
            -0.156060309711106
          ],
          [
            -0.5041497533841918,
            0.018988299776378302,
            -0.17385975376070656
          ],
          [
            -0.4466467097256442,
            0.01537522646380641,
            -0.18686402606632904
          ],
          [
            -0.39435960140487153,
            0.0132266454211433,
            -0.1979554222226028
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            0.39435960140488113,
            -0.013226645421145988,
            0.19795542222260165
          ],
          [
            0.44664670972564224,
            -0.015375226463805625,
            0.18686402606632835
          ],
          [
            -0.495850246615807,
            -0.018988299776375006,
            0.17385975376070795
          ],
          [
            -0.4347622401991986,
            -0.019678825161559166,
            0.15606030971110751
          ],
          [
            -0.4051781887057051,
            -0.036931026897670916,
            0.1361396956672385
          ],
          [
            0.3603842112180191,
            -0.05685245459862698,
            0.1077876347278206
          ],
          [
            -0.0029164884063173635,
            -0.027296716647891794,
            0.07278385463151837
          ],
          [
            -0.08237422574582393,
            0.0009764756128045615,
            0.03702244514571196
          ],
          [
            -3.0531133177191805e-15,
            -2.831068712794149e-15,
            3.219646771412954e-15
          ],
          [
            0.08237422574582076,
            -0.0009764756128048946,
            -0.037022445145711125
          ],
          [
            0.00291648840630776,
            0.02729671664789346,
            -0.07278385463151832
          ],
          [
            -0.36038421121802433,
            0.05685245459862509,
            -0.10778763472781888
          ],
          [
            0.4051781887057011,
            0.03693102689767458,
            -0.1361396956672395
          ],
          [
            0.4347622401992052,
            0.019678825161558833,
            -0.15606030971110596
          ],
          [
            0.49585024661580823,
            0.01898829977637828,
            -0.17385975376070656
          ],
          [
            -0.4466467097256442,
            0.015375226463806402,
            -0.18686402606632901
          ],
          [
            -0.39435960140487153,
            0.013226645421143268,
            -0.19795542222260276
          ]
        ]
      },
      "incoming_structure_ids": [
        "incoming_02_000",
        "incoming_02_001",
        "incoming_02_002",
        "incoming_02_003",
        "incoming_02_004",
        "incoming_02_005",
        "incoming_02_006",
        "incoming_02_007",
        "incoming_02_008"
      ],
      "reflected_structure_ids": [
        "reflected_02_001",
        "reflected_02_002",
        "reflected_02_003",
        "reflected_02_004",
        "reflected_02_005",
        "reflected_02_006",
        "reflected_02_007",
        "reflected_02_008"
      ],
      "positive_extension_structure_ids": [
        "extension_plus_02_000",
        "extension_plus_02_001",
        "extension_plus_02_002",
        "extension_plus_02_003"
      ],
      "negative_extension_structure_ids": [
        "extension_minus_02_000",
        "extension_minus_02_001",
        "extension_minus_02_002",
        "extension_minus_02_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": "P-1",
        "spacegroup_number": 2,
        "pointgroup": "-1",
        "has_inversion": true,
        "is_polar_point_group": false,
        "nonpolar_parent_hypothesis": true,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.0
        ],
        "formal_class": [
          0.0,
          0.0,
          0.0
        ],
        "target_residual": 1.295592599325886e-15,
        "parent_symmetrization_rmsd_A": 0.2402156316575608,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -122.70536330877775,
        "reduced_polarization": [
          -7.348226427832688e-16,
          -5.009976062068873e-16,
          9.421238059066267e-16
        ],
        "cartesian_polarization_e_A2": [
          -2.0913103625672572e-17,
          -1.2830124923725505e-17,
          2.251686924113826e-17
        ],
        "ranking_score": 0.24021563165756338
      }
    }
  ],
  "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": 59,
      "full_response": 26,
      "energy_polarization": 33
    },
    "model_evaluations_for_recovery_and_path_properties": {
      "total": 84,
      "full_response": 51,
      "energy_polarization": 33
    },
    "elapsed_seconds": 215.56913850002456
  }
}
