{
  "schema": "ferrofinder.endpoint_parent_recovery.v4_variable_cell",
  "status": "complete",
  "input_atom_count": 10,
  "input_formula": "Ba2O6Ti2",
  "input_spacegroup": "Amm2",
  "input_pointgroup": "mm2",
  "input_is_polar_point_group": true,
  "input_energy_eV": -77.09364059380064,
  "input_cartesian_polarization_e_A2": [
    1.474515553189884e-19,
    -1.9215961107207124e-17,
    0.031143548517256557
  ],
  "input_reduced_polarization": [
    5.015106977600827e-18,
    -4.488792417905308e-16,
    0.7213208851942755
  ],
  "input_formal_targets": [
    {
      "orbit_id": 0,
      "representative_formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.5
      ]
    },
    {
      "orbit_id": 1,
      "representative_formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        1.0
      ]
    },
    {
      "orbit_id": 2,
      "representative_formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        -0.5,
        0.5
      ]
    },
    {
      "orbit_id": 3,
      "representative_formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.5
      ]
    },
    {
      "orbit_id": 4,
      "representative_formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        -0.5,
        1.0
      ]
    },
    {
      "orbit_id": 5,
      "representative_formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        0.5,
        0.0,
        1.0
      ]
    },
    {
      "orbit_id": 6,
      "representative_formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "target_reduced_polarization": [
        0.5,
        -0.5,
        0.5
      ]
    },
    {
      "orbit_id": 7,
      "representative_formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        0.5,
        -0.5,
        1.0
      ]
    }
  ],
  "parent_candidates": [
    {
      "candidate_id": "inversion_parent_endpoint_00",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "Cmmm",
      "spacegroup_number": 65,
      "pointgroup": "mmm",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 9.312548916339031e-16,
      "parent_symmetrization_rmsd_A": 0.12551661495758457,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -76.81287619380225,
      "reduced_polarization": [
        7.57306375778424e-18,
        -6.346810440734804e-16,
        6.814384008780176e-16
      ],
      "cartesian_polarization_e_A2": [
        2.226592642195934e-19,
        -2.7169904782740802e-17,
        2.9421593544390956e-17
      ],
      "ranking_score": 0.12551661495758643
    },
    {
      "candidate_id": "bec_projection_00",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Amm2",
      "spacegroup_number": 38,
      "pointgroup": "mm2",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.5
      ],
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_residual": 0.00010487960915678274,
      "parent_symmetrization_rmsd_A": 0.04998173265508226,
      "parent_cell_rmsd_A": 0.01060891100900724,
      "energy_eV": -76.99031468836958,
      "reduced_polarization": [
        4.2331642212499914e-16,
        4.69270329008133e-16,
        0.4998951203908432
      ],
      "cartesian_polarization_e_A2": [
        -1.219217219935429e-17,
        1.946038070659356e-17,
        0.021560385292464637
      ],
      "ranking_score": 0.5528437196256476
    },
    {
      "candidate_id": "inversion_parent_bec_00_00",
      "source": "same_species_inversion_center_projection_after_BEC",
      "spacegroup": "Cmmm",
      "spacegroup_number": 65,
      "pointgroup": "mmm",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.5
      ],
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_residual": 0.4999999999999991,
      "parent_symmetrization_rmsd_A": 0.1255166149575845,
      "parent_cell_rmsd_A": 0.01060891100900724,
      "energy_eV": -76.79036489566136,
      "reduced_polarization": [
        -1.3322564345996737e-16,
        8.012619482936084e-16,
        8.862933627664678e-16
      ],
      "cartesian_polarization_e_A2": [
        -3.9035868773284715e-18,
        3.427665465935969e-17,
        3.822567095365711e-17
      ],
      "ranking_score": 1.1281688427098346
    },
    {
      "candidate_id": "bec_projection_01",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Amm2",
      "spacegroup_number": 38,
      "pointgroup": "mm2",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        1.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 1.4533120280768586e-05,
      "parent_symmetrization_rmsd_A": 0.07396601313097592,
      "parent_cell_rmsd_A": 0.01562490980930621,
      "energy_eV": -76.86471637724412,
      "reduced_polarization": [
        -1.6809051417957863e-15,
        7.528262472922363e-16,
        1.0000145331202808
      ],
      "cartesian_polarization_e_A2": [
        2.330677933600595e-17,
        3.296954070996891e-17,
        0.043244326997819736
      ],
      "ranking_score": 0.577901306823864
    },
    {
      "candidate_id": "bec_projection_02",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Pm",
      "spacegroup_number": 6,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        -0.5,
        0.5
      ],
      "formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_residual": 0.00011037687966879493,
      "parent_symmetrization_rmsd_A": 0.10202843932585856,
      "parent_cell_rmsd_A": 0.047166278125465116,
      "energy_eV": -76.88753777462156,
      "reduced_polarization": [
        3.4214405891486113e-15,
        -0.5000116334095752,
        0.4998902378965805
      ],
      "cartesian_polarization_e_A2": [
        -1.0857489972080566e-16,
        -0.02122788917319535,
        0.02140005277790968
      ],
      "ranking_score": 0.6140407626165625
    },
    {
      "candidate_id": "bec_projection_03",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cm",
      "spacegroup_number": 8,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.5
      ],
      "formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_residual": 0.00029086999274710584,
      "parent_symmetrization_rmsd_A": 0.07206041089430196,
      "parent_cell_rmsd_A": 0.011727842137458094,
      "energy_eV": -77.01615152261469,
      "reduced_polarization": [
        0.49983793639376345,
        4.602747958044173e-16,
        0.4997584617210165
      ],
      "cartesian_polarization_e_A2": [
        0.014678073831624413,
        3.612617716269869e-17,
        0.02157616744212139
      ],
      "ranking_score": 0.5755741114141607
    },
    {
      "candidate_id": "bec_projection_04",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Pm",
      "spacegroup_number": 6,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        -0.5,
        1.0
      ],
      "formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_residual": 4.653171145669663e-05,
      "parent_symmetrization_rmsd_A": 0.12584491912417162,
      "parent_cell_rmsd_A": 0.05152689321309781,
      "energy_eV": -75.68437392740866,
      "reduced_polarization": [
        -1.5081499126396715e-15,
        -0.4999760111208762,
        0.999960128533392
      ],
      "cartesian_polarization_e_A2": [
        6.590615649664522e-17,
        -0.021077647720133093,
        0.04307431622575528
      ],
      "ranking_score": 0.6388197058503595
    },
    {
      "candidate_id": "bec_projection_05",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cm",
      "spacegroup_number": 8,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.5,
        0.0,
        1.0
      ],
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_residual": 9.104443872743326e-06,
      "parent_symmetrization_rmsd_A": 0.10321865455457656,
      "parent_cell_rmsd_A": 0.018724891618721155,
      "energy_eV": -76.80267698063545,
      "reduced_polarization": [
        0.4999916534418686,
        -8.385256490684798e-17,
        1.0000036367383176
      ],
      "cartesian_polarization_e_A2": [
        0.014858520869758782,
        -5.4142768725816444e-17,
        0.043276744134885
      ],
      "ranking_score": 0.6079180863470023
    },
    {
      "candidate_id": "bec_projection_06",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.5,
        -0.5,
        0.5
      ],
      "formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "target_residual": 5.728860271216236e-05,
      "parent_symmetrization_rmsd_A": 0.11717121614517091,
      "parent_cell_rmsd_A": 0.04876054285904521,
      "energy_eV": -76.88244935196471,
      "reduced_polarization": [
        0.49999909959507305,
        -0.4999642650513166,
        0.5000447681439673
      ],
      "cartesian_polarization_e_A2": [
        0.014688461683956709,
        -0.021221964912702306,
        0.021425557230688043
      ],
      "ranking_score": 0.6294759290653565
    },
    {
      "candidate_id": "bec_projection_07",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.5,
        -0.5,
        1.0
      ],
      "formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_residual": 6.275510515513984e-05,
      "parent_symmetrization_rmsd_A": 0.14961812564004007,
      "parent_cell_rmsd_A": 0.054677937209734684,
      "energy_eV": -75.59831573131319,
      "reduced_polarization": [
        0.4999423320992248,
        -0.5000175219707973,
        1.0000174813324032
      ],
      "cartesian_polarization_e_A2": [
        0.014871129952134349,
        -0.021067560810572712,
        0.04310668375292377
      ],
      "ranking_score": 0.663413120152784
    }
  ],
  "formal_branches": [
    {
      "orbit_id": 0,
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.0,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              5.015106977600827e-18,
              -4.488792417905308e-16,
              0.7213208851942755
            ],
            "branch_aligned_reduced_polarization": [
              5.015106977600827e-18,
              -4.488792417905308e-16,
              0.7213208851942755
            ],
            "target_residual": 0.2213208851942755,
            "energy_eV": -77.09364059380064,
            "max_atomic_step_A": 0.05401171154122747,
            "max_log_strain_component": 0.0020007638462084198,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.242186718405806,
            "cell_principal_stretches": [
              1.002002766709722,
              1.0016295304626617,
              0.9991224054148549
            ],
            "cell_volume_ratio": 1.002754775608181,
            "cell_rmsd_from_input_A": 0.011199028397585206
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -4.474779160185826e-16,
              3.652572569431858e-15,
              0.48462323463779683
            ],
            "branch_aligned_reduced_polarization": [
              -4.474779160185826e-16,
              3.652572569431858e-15,
              0.48462323463779683
            ],
            "target_residual": 0.01537676536220317,
            "energy_eV": -76.98034528304252,
            "max_atomic_step_A": 0.0034656958131965604,
            "max_log_strain_component": 0.00010524970069816278,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.242186718405806,
            "cell_principal_stretches": [
              1.0018973117680752,
              1.00154374327409,
              0.9991685518691946
            ],
            "cell_volume_ratio": 1.0026096723795774,
            "cell_rmsd_from_input_A": 0.01060891100900724
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              4.2331642212499914e-16,
              4.69270329008133e-16,
              0.4998951203908432
            ],
            "branch_aligned_reduced_polarization": [
              4.2331642212499914e-16,
              4.69270329008133e-16,
              0.4998951203908432
            ],
            "target_residual": 0.00010487960915678274,
            "energy_eV": -76.99031468836958
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_00",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Amm2",
        "spacegroup_number": 38,
        "pointgroup": "mm2",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.5
        ],
        "formal_class": [
          0.0,
          0.0,
          0.5
        ],
        "target_residual": 0.00010487960915678274,
        "parent_symmetrization_rmsd_A": 0.04998173265508226,
        "parent_cell_rmsd_A": 0.01060891100900724,
        "energy_eV": -76.99031468836958,
        "reduced_polarization": [
          4.2331642212499914e-16,
          4.69270329008133e-16,
          0.4998951203908432
        ],
        "cartesian_polarization_e_A2": [
          -1.219217219935429e-17,
          1.946038070659356e-17,
          0.021560385292464637
        ],
        "ranking_score": 0.5528437196256476
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 1,
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.0,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        1.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              5.015106977600827e-18,
              -4.488792417905308e-16,
              0.7213208851942755
            ],
            "branch_aligned_reduced_polarization": [
              5.015106977600827e-18,
              -4.488792417905308e-16,
              0.7213208851942755
            ],
            "target_residual": 0.2786791148057245,
            "energy_eV": -77.09364059380064,
            "max_atomic_step_A": 0.06800955973151297,
            "max_log_strain_component": 0.0025192882140663004,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.242186718405806,
            "cell_principal_stretches": [
              1.0011061312918403,
              0.997951925333245,
              0.9974838825292554
            ],
            "cell_volume_ratio": 0.9965420494551579,
            "cell_rmsd_from_input_A": 0.014044766147809336
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              1.774131331442657e-15,
              -5.03557064499269e-15,
              0.9775294388417597
            ],
            "branch_aligned_reduced_polarization": [
              1.774131331442657e-15,
              -5.03557064499269e-15,
              0.9775294388417597
            ],
            "target_residual": 0.02247056115824031,
            "energy_eV": -76.90849398419542,
            "max_atomic_step_A": 0.005724913433805388,
            "max_log_strain_component": 0.0002841476410565927,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.242186718405806,
            "cell_principal_stretches": [
              1.0012309673346393,
              0.9977211887228626,
              0.9972004901015945
            ],
            "cell_volume_ratio": 0.9961527823193649,
            "cell_rmsd_from_input_A": 0.01562490980930621
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -1.6809051417957863e-15,
              7.528262472922363e-16,
              1.0000145331202808
            ],
            "branch_aligned_reduced_polarization": [
              -1.6809051417957863e-15,
              7.528262472922363e-16,
              1.0000145331202808
            ],
            "target_residual": 1.4533120280768586e-05,
            "energy_eV": -76.86471637724412
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "inversion_parent_endpoint_00",
        "source": "same_species_inversion_center_projection_from_endpoint",
        "spacegroup": "Cmmm",
        "spacegroup_number": 65,
        "pointgroup": "mmm",
        "has_inversion": true,
        "is_polar_point_group": false,
        "nonpolar_parent_hypothesis": true,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.0
        ],
        "formal_class": [
          0.0,
          0.0,
          0.0
        ],
        "target_residual": 9.312548916339031e-16,
        "parent_symmetrization_rmsd_A": 0.12551661495758457,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -76.81287619380225,
        "reduced_polarization": [
          7.57306375778424e-18,
          -6.346810440734804e-16,
          6.814384008780176e-16
        ],
        "cartesian_polarization_e_A2": [
          2.226592642195934e-19,
          -2.7169904782740802e-17,
          2.9421593544390956e-17
        ],
        "ranking_score": 0.12551661495758643
      },
      "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": [
          -77.09364059380064,
          -77.0725893524893,
          -77.03366639656889,
          -76.98466650409638,
          -76.93290390017364,
          -76.88496182017099,
          -76.8464059059219,
          -76.82148667876587,
          -76.81287619380225
        ],
        "cartesian_polarizations_e_A2": [
          [
            1.0883230279578785e-17,
            -6.603879555124036e-17,
            0.031143548517256595
          ],
          [
            -5.25071602527153e-17,
            -4.583752462919496e-17,
            0.027863802917421118
          ],
          [
            -3.1067669529708405e-17,
            -1.5783319902746887e-17,
            0.024385632230494936
          ],
          [
            6.085004510524731e-18,
            -2.3763437562789e-17,
            0.020708855849733625
          ],
          [
            1.3835184935931899e-17,
            -6.415047957850756e-17,
            0.016841557115955794
          ],
          [
            -2.3575731710175045e-17,
            -3.864018141180545e-17,
            0.012802211477821854
          ],
          [
            -1.277343627667435e-17,
            -5.263458749881788e-17,
            0.008620540889603016
          ],
          [
            -1.5097952836313132e-17,
            -6.732804506645335e-18,
            0.004336906045959756
          ],
          [
            -1.812449258973819e-18,
            -5.235418988750858e-17,
            -1.2007060329241937e-17
          ]
        ],
        "raw_reduced_polarization": [
          [
            3.701592973765224e-16,
            -1.5426469855146932e-15,
            0.7213208851942763
          ],
          [
            -1.785868078418882e-15,
            -1.0707511940888963e-15,
            0.6453581541659063
          ],
          [
            -1.056670347757076e-15,
            -3.686937453378377e-16,
            0.5647996668323189
          ],
          [
            2.0696254111017298e-16,
            -5.551069642579897e-16,
            0.47964124013079473
          ],
          [
            4.705608724064419e-16,
            -1.498536475643639e-15,
            0.3900700936567943
          ],
          [
            -8.018553371374171e-16,
            -9.026233576354646e-16,
            0.2965141403366402
          ],
          [
            -4.3444878733564345e-16,
            -1.2295285984714737e-15,
            0.19966177527574994
          ],
          [
            -5.135100030181332e-16,
            -1.5727634778222555e-16,
            0.10044779920768224
          ],
          [
            -6.164483586194164e-17,
            -1.2229785921271546e-15,
            -2.780975128916622e-16
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            3.701592973765224e-16,
            -1.5426469855146932e-15,
            0.7213208851942763
          ],
          [
            -1.7858680784188825e-15,
            -1.0707511940888963e-15,
            0.6453581541659063
          ],
          [
            -1.056670347757076e-15,
            -3.6869374533783777e-16,
            0.5647996668323189
          ],
          [
            2.0696254111017288e-16,
            -5.551069642579897e-16,
            0.47964124013079473
          ],
          [
            4.705608724064419e-16,
            -1.498536475643639e-15,
            0.3900700936567943
          ],
          [
            -8.018553371374172e-16,
            -9.026233576354646e-16,
            0.2965141403366402
          ],
          [
            -4.3444878733564345e-16,
            -1.2295285984714737e-15,
            0.19966177527574994
          ],
          [
            -5.135100030181332e-16,
            -1.5727634778222557e-16,
            0.10044779920768224
          ],
          [
            -6.164483586194164e-17,
            -1.2229785921271546e-15,
            -2.7755575615628914e-16
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            3.3306690738754696e-16,
            -1.5543122344752192e-15,
            -0.2786791148057237
          ],
          [
            -1.7763568394002505e-15,
            -1.0547118733938987e-15,
            -0.35464184583409386
          ],
          [
            -1.0547118733938987e-15,
            -3.885780586188048e-16,
            -0.43520033316768103
          ],
          [
            2.220446049250313e-16,
            -5.551115123125783e-16,
            0.4796412401307948
          ],
          [
            4.440892098500626e-16,
            -1.4988010832439613e-15,
            0.39007009365679424
          ],
          [
            -7.771561172376096e-16,
            -8.881784197001252e-16,
            0.29651414033664025
          ],
          [
            -4.440892098500626e-16,
            -1.2212453270876722e-15,
            0.1996617752757499
          ],
          [
            -4.996003610813204e-16,
            -1.6653345369377348e-16,
            0.10044779920768221
          ],
          [
            -5.551115123125783e-17,
            -1.2212453270876722e-15,
            -2.7755575615628914e-16
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -76.81287619380224,
          -76.82148667876587,
          -76.84640590592193,
          -76.88496182017097,
          -76.93290390017366,
          -76.98466650409637,
          -77.03366639656888,
          -77.0725893524893,
          -77.09364059380063
        ],
        "cartesian_polarizations_e_A2": [
          [
            -1.3169379885524516e-18,
            -5.179344996691205e-17,
            1.0229927070180308e-17
          ],
          [
            -1.628565155005054e-17,
            -5.787250527687978e-17,
            -0.00433690604595979
          ],
          [
            -4.445890994264452e-18,
            -2.769276324381978e-17,
            -0.008620540889603028
          ],
          [
            -2.371985226754864e-17,
            -1.9232927918615794e-17,
            -0.012802211477821861
          ],
          [
            2.647696313114173e-18,
            -1.044199839246018e-17,
            -0.016841557115955842
          ],
          [
            9.651868418234494e-18,
            -7.672180815018749e-17,
            -0.020708855849733636
          ],
          [
            -3.852338816293903e-17,
            -2.4742646419911907e-17,
            -0.024385632230494954
          ],
          [
            -4.680188731248052e-17,
            -6.217780083182283e-17,
            -0.027863802917421146
          ],
          [
            1.6634307963908178e-17,
            -7.21058659611533e-17,
            -0.031143548517256595
          ]
        ],
        "raw_reduced_polarization": [
          [
            -4.479155802167709e-17,
            -1.2098798712776078e-15,
            2.369370351502053e-16
          ],
          [
            -5.539058882542448e-16,
            -1.3518848286730292e-15,
            -0.10044779920768303
          ],
          [
            -1.5121318251783155e-16,
            -6.468948650873493e-16,
            -0.19966177527575024
          ],
          [
            -8.06757150559028e-16,
            -4.49275581551953e-16,
            -0.29651414033664036
          ],
          [
            9.005317187560996e-17,
            -2.4392203413793813e-16,
            -0.39007009365679546
          ],
          [
            3.282783457011076e-16,
            -1.792199041157412e-15,
            -0.47964124013079495
          ],
          [
            -1.3102534751757956e-15,
            -5.779809973020641e-16,
            -0.5647996668323192
          ],
          [
            -1.5918209280189432e-15,
            -1.4524552760009099e-15,
            -0.6453581541659068
          ],
          [
            5.657643539729685e-16,
            -1.68437197914356e-15,
            -0.7213208851942763
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -4.479155802167709e-17,
            -1.2098798712776078e-15,
            2.369370351502053e-16
          ],
          [
            -5.539058882542448e-16,
            -1.3518848286730292e-15,
            -0.10044779920768303
          ],
          [
            -1.5121318251783157e-16,
            -6.468948650873493e-16,
            -0.19966177527575024
          ],
          [
            -8.06757150559028e-16,
            -4.49275581551953e-16,
            -0.29651414033664036
          ],
          [
            9.005317187560996e-17,
            -2.4392203413793813e-16,
            -0.39007009365679546
          ],
          [
            3.282783457011076e-16,
            -1.792199041157412e-15,
            -0.47964124013079495
          ],
          [
            -1.3102534751757956e-15,
            -5.779809973020641e-16,
            -0.5647996668323192
          ],
          [
            -1.5918209280189432e-15,
            -1.4524552760009099e-15,
            -0.6453581541659068
          ],
          [
            5.657643539729685e-16,
            -1.68437197914356e-15,
            -0.7213208851942763
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          -4.934489691004057e-16,
          -9.033101987396163e-16,
          -0.721320885194277
        ],
        "actual_opposite_endpoint_branch_residual": 1.4750337717390535e-15
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            3.701592973765224e-16,
            -1.5426469855146932e-15,
            0.7213208851942763
          ],
          [
            -1.785868078418882e-15,
            -1.0707511940888963e-15,
            0.6453581541659063
          ],
          [
            -1.056670347757076e-15,
            -3.686937453378377e-16,
            0.5647996668323189
          ],
          [
            2.0696254111017298e-16,
            -5.551069642579897e-16,
            0.47964124013079473
          ],
          [
            4.705608724064419e-16,
            -1.498536475643639e-15,
            0.3900700936567943
          ],
          [
            -8.018553371374171e-16,
            -9.026233576354646e-16,
            0.2965141403366402
          ],
          [
            -4.3444878733564345e-16,
            -1.2295285984714737e-15,
            0.19966177527574994
          ],
          [
            -5.135100030181332e-16,
            -1.5727634778222555e-16,
            0.10044779920768224
          ],
          [
            -6.164483586194164e-17,
            -1.2229785921271546e-15,
            -2.780975128916622e-16
          ],
          [
            -5.539058882542448e-16,
            -1.3518848286730292e-15,
            -0.10044779920768303
          ],
          [
            -1.5121318251783155e-16,
            -6.468948650873493e-16,
            -0.19966177527575024
          ],
          [
            -8.06757150559028e-16,
            -4.49275581551953e-16,
            -0.29651414033664036
          ],
          [
            9.005317187560996e-17,
            -2.4392203413793813e-16,
            -0.39007009365679546
          ],
          [
            3.282783457011076e-16,
            -1.792199041157412e-15,
            -0.47964124013079495
          ],
          [
            -1.3102534751757956e-15,
            -5.779809973020641e-16,
            -0.5647996668323192
          ],
          [
            -1.5918209280189432e-15,
            -1.4524552760009099e-15,
            -0.6453581541659068
          ],
          [
            5.657643539729685e-16,
            -1.68437197914356e-15,
            -0.7213208851942763
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            3.701592973765224e-16,
            -1.5426469855146932e-15,
            0.7213208851942763
          ],
          [
            -1.7858680784188825e-15,
            -1.0707511940888963e-15,
            0.6453581541659063
          ],
          [
            -1.056670347757076e-15,
            -3.6869374533783777e-16,
            0.5647996668323189
          ],
          [
            2.0696254111017288e-16,
            -5.551069642579897e-16,
            0.47964124013079473
          ],
          [
            4.705608724064419e-16,
            -1.498536475643639e-15,
            0.3900700936567943
          ],
          [
            -8.018553371374172e-16,
            -9.026233576354646e-16,
            0.2965141403366402
          ],
          [
            -4.3444878733564345e-16,
            -1.2295285984714737e-15,
            0.19966177527574994
          ],
          [
            -5.135100030181332e-16,
            -1.5727634778222557e-16,
            0.10044779920768224
          ],
          [
            -6.164483586194164e-17,
            -1.2229785921271546e-15,
            -2.7755575615628914e-16
          ],
          [
            -5.539058882542448e-16,
            -1.3518848286730292e-15,
            -0.10044779920768303
          ],
          [
            -1.5121318251783157e-16,
            -6.468948650873493e-16,
            -0.19966177527575024
          ],
          [
            -8.06757150559028e-16,
            -4.49275581551953e-16,
            -0.29651414033664036
          ],
          [
            9.005317187560996e-17,
            -2.4392203413793813e-16,
            -0.39007009365679546
          ],
          [
            3.282783457011076e-16,
            -1.792199041157412e-15,
            -0.47964124013079495
          ],
          [
            -1.3102534751757956e-15,
            -5.779809973020641e-16,
            -0.5647996668323192
          ],
          [
            -1.5918209280189432e-15,
            -1.4524552760009099e-15,
            -0.6453581541659068
          ],
          [
            5.657643539729685e-16,
            -1.68437197914356e-15,
            -0.7213208851942763
          ]
        ],
        "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": [
          [
            3.3306690738754696e-16,
            -1.5543122344752192e-15,
            -0.2786791148057237
          ],
          [
            -1.7763568394002505e-15,
            -1.0547118733938987e-15,
            -0.35464184583409386
          ],
          [
            -1.0547118733938987e-15,
            -3.885780586188048e-16,
            -0.43520033316768103
          ],
          [
            2.220446049250313e-16,
            -5.551115123125783e-16,
            0.4796412401307948
          ],
          [
            4.440892098500626e-16,
            -1.4988010832439613e-15,
            0.39007009365679424
          ],
          [
            -7.771561172376096e-16,
            -8.881784197001252e-16,
            0.29651414033664025
          ],
          [
            -4.440892098500626e-16,
            -1.2212453270876722e-15,
            0.1996617752757499
          ],
          [
            -4.996003610813204e-16,
            -1.6653345369377348e-16,
            0.10044779920768221
          ],
          [
            -5.551115123125783e-17,
            -1.2212453270876722e-15,
            -2.7755575615628914e-16
          ],
          [
            -5.551115123125783e-16,
            -1.3322676295501878e-15,
            -0.10044779920768304
          ],
          [
            -1.6653345369377348e-16,
            -6.661338147750939e-16,
            -0.19966177527575024
          ],
          [
            -8.326672684688674e-16,
            -4.440892098500626e-16,
            -0.29651414033664036
          ],
          [
            1.1102230246251565e-16,
            -2.220446049250313e-16,
            -0.39007009365679546
          ],
          [
            3.3306690738754696e-16,
            -1.7763568394002505e-15,
            -0.47964124013079495
          ],
          [
            -1.3322676295501878e-15,
            -5.551115123125783e-16,
            0.4352003331676808
          ],
          [
            -1.609823385706477e-15,
            -1.4432899320127035e-15,
            0.3546418458340932
          ],
          [
            5.551115123125783e-16,
            -1.6653345369377348e-15,
            0.2786791148057237
          ]
        ]
      },
      "incoming_structure_ids": [
        "incoming_01_000",
        "incoming_01_001",
        "incoming_01_002",
        "incoming_01_003",
        "incoming_01_004",
        "incoming_01_005",
        "incoming_01_006",
        "incoming_01_007",
        "incoming_01_008"
      ],
      "reflected_structure_ids": [
        "reflected_01_001",
        "reflected_01_002",
        "reflected_01_003",
        "reflected_01_004",
        "reflected_01_005",
        "reflected_01_006",
        "reflected_01_007",
        "reflected_01_008"
      ]
    },
    {
      "orbit_id": 2,
      "formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.5,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        -0.5,
        0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              5.015106977600827e-18,
              -4.488792417905308e-16,
              0.7213208851942755
            ],
            "branch_aligned_reduced_polarization": [
              5.015106977600827e-18,
              -4.440892098500626e-16,
              0.7213208851942755
            ],
            "target_residual": 0.5467933194756289,
            "energy_eV": -77.09364059380064,
            "max_atomic_step_A": 0.11892692566459431,
            "max_log_strain_component": 0.007440966474950419,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.242186718405806,
            "cell_principal_stretches": [
              1.0093007676507786,
              0.9991224054148564,
              0.9943869983154714
            ],
            "cell_volume_ratio": 1.0027547756081938,
            "cell_rmsd_from_input_A": 0.046721172143600526
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              1.1454229921467518e-14,
              -0.4956812861927811,
              0.4751473350313184
            ],
            "branch_aligned_reduced_polarization": [
              1.1454229921467518e-14,
              -0.4956812861927811,
              0.4751473350313184
            ],
            "target_residual": 0.025225111397062187,
            "energy_eV": -76.9010924143791,
            "max_atomic_step_A": 0.005784250283331129,
            "max_log_strain_component": 0.0001814532351739536,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.242186718405806,
            "cell_principal_stretches": [
              1.0092530677802507,
              0.9992019644386039,
              0.9941067630037167
            ],
            "cell_volume_ratio": 1.0025046269540485,
            "cell_rmsd_from_input_A": 0.047166278125465116
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              3.4214405891486113e-15,
              -0.5000116334095752,
              0.4998902378965805
            ],
            "branch_aligned_reduced_polarization": [
              3.4214405891486113e-15,
              -0.5000116334095752,
              0.4998902378965805
            ],
            "target_residual": 0.00011037687966879493,
            "energy_eV": -76.88753777462156
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_02",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Pm",
        "spacegroup_number": 6,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          -0.5,
          0.5
        ],
        "formal_class": [
          0.0,
          0.5,
          0.5
        ],
        "target_residual": 0.00011037687966879493,
        "parent_symmetrization_rmsd_A": 0.10202843932585856,
        "parent_cell_rmsd_A": 0.047166278125465116,
        "energy_eV": -76.88753777462156,
        "reduced_polarization": [
          3.4214405891486113e-15,
          -0.5000116334095752,
          0.4998902378965805
        ],
        "cartesian_polarization_e_A2": [
          -1.0857489972080566e-16,
          -0.02122788917319535,
          0.02140005277790968
        ],
        "ranking_score": 0.6140407626165625
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 3,
      "formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.0,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              5.015106977600827e-18,
              -4.488792417905308e-16,
              0.7213208851942755
            ],
            "branch_aligned_reduced_polarization": [
              0.0,
              -4.488792417905308e-16,
              0.7213208851942755
            ],
            "target_residual": 0.5467933194756294,
            "energy_eV": -77.09364059380064,
            "max_atomic_step_A": 0.08878885730697743,
            "max_log_strain_component": 0.002000763846208438,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.242186718405806,
            "cell_principal_stretches": [
              1.0022889805177155,
              1.0020027667097222,
              0.9984650387889982
            ],
            "cell_volume_ratio": 1.002754775608181,
            "cell_rmsd_from_input_A": 0.012715799638544136
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.5174194669205934,
              6.138454182852451e-15,
              0.472341802466465
            ],
            "branch_aligned_reduced_polarization": [
              0.5174194669205934,
              6.138454182852451e-15,
              0.472341802466465
            ],
            "target_residual": 0.03268659845566203,
            "energy_eV": -77.00064482845004,
            "max_atomic_step_A": 0.006551510108484333,
            "max_log_strain_component": 0.00018748402685020172,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.242186718405806,
            "cell_principal_stretches": [
              1.002151970442821,
              1.0018149248053332,
              0.9985313448927973
            ],
            "cell_volume_ratio": 1.0024963140684484,
            "cell_rmsd_from_input_A": 0.011727842137458094
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.49983793639376345,
              4.602747958044173e-16,
              0.4997584617210165
            ],
            "branch_aligned_reduced_polarization": [
              0.49983793639376345,
              4.602747958044173e-16,
              0.4997584617210165
            ],
            "target_residual": 0.00029086999274710584,
            "energy_eV": -77.01615152261469
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_03",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cm",
        "spacegroup_number": 8,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.5,
          0.0,
          0.5
        ],
        "formal_class": [
          0.5,
          0.0,
          0.5
        ],
        "target_residual": 0.00029086999274710584,
        "parent_symmetrization_rmsd_A": 0.07206041089430196,
        "parent_cell_rmsd_A": 0.011727842137458094,
        "energy_eV": -77.01615152261469,
        "reduced_polarization": [
          0.49983793639376345,
          4.602747958044173e-16,
          0.4997584617210165
        ],
        "cartesian_polarization_e_A2": [
          0.014678073831624413,
          3.612617716269869e-17,
          0.02157616744212139
        ],
        "ranking_score": 0.5755741114141607
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 4,
      "formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.5,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        -0.5,
        1.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              5.015106977600827e-18,
              -4.488792417905308e-16,
              0.7213208851942755
            ],
            "branch_aligned_reduced_polarization": [
              5.015106977600827e-18,
              -4.440892098500626e-16,
              0.7213208851942755
            ],
            "target_residual": 0.5724177224972177,
            "energy_eV": -77.09364059380064,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.007092075852597869,
            "step_scale": 0.9531121899920889,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.242186718405806,
            "cell_principal_stretches": [
              1.0049301062348543,
              1.0010542398892368,
              0.9907696595637842
            ],
            "cell_volume_ratio": 0.9967039176756837,
            "cell_rmsd_from_input_A": 0.044766279649401344
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              7.199808864178053e-15,
              -0.45090908034986416,
              0.9558774380936054
            ],
            "branch_aligned_reduced_polarization": [
              7.199808864178053e-15,
              -0.45090908034986416,
              0.9558774380936054
            ],
            "target_residual": 0.06600544569412224,
            "energy_eV": -76.09735794777308,
            "max_atomic_step_A": 0.015681786956994556,
            "max_log_strain_component": 0.001014092943540415,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.242186718405806,
            "cell_principal_stretches": [
              1.0054086207804387,
              1.0013155085931478,
              0.9892305248913252
            ],
            "cell_volume_ratio": 0.9958892773823556,
            "cell_rmsd_from_input_A": 0.05152689321309781
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -1.5081499126396715e-15,
              -0.4999760111208762,
              0.999960128533392
            ],
            "branch_aligned_reduced_polarization": [
              -1.5081499126396715e-15,
              -0.4999760111208762,
              0.999960128533392
            ],
            "target_residual": 4.653171145669663e-05,
            "energy_eV": -75.68437392740866
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_04",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Pm",
        "spacegroup_number": 6,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          -0.5,
          1.0
        ],
        "formal_class": [
          0.0,
          0.5,
          0.0
        ],
        "target_residual": 4.653171145669663e-05,
        "parent_symmetrization_rmsd_A": 0.12584491912417162,
        "parent_cell_rmsd_A": 0.05152689321309781,
        "energy_eV": -75.68437392740866,
        "reduced_polarization": [
          -1.5081499126396715e-15,
          -0.4999760111208762,
          0.999960128533392
        ],
        "cartesian_polarization_e_A2": [
          6.590615649664522e-17,
          -0.021077647720133093,
          0.04307431622575528
        ],
        "ranking_score": 0.6388197058503595
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 5,
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.0,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.5,
        0.0,
        1.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              5.015106977600827e-18,
              -4.488792417905308e-16,
              0.7213208851942755
            ],
            "branch_aligned_reduced_polarization": [
              0.0,
              -4.488792417905308e-16,
              0.7213208851942755
            ],
            "target_residual": 0.5724177224972181,
            "energy_eV": -77.09364059380064,
            "max_atomic_step_A": 0.097936185412442,
            "max_log_strain_component": 0.0025192882140662822,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.242186718405806,
            "cell_principal_stretches": [
              1.001667342915152,
              0.9974838825292554,
              0.9973927953746172
            ],
            "cell_volume_ratio": 0.9965420494551579,
            "cell_rmsd_from_input_A": 0.015269364891979567
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.44571728539031863,
              -1.840350524607206e-15,
              0.961729102379098
            ],
            "branch_aligned_reduced_polarization": [
              0.44571728539031863,
              -1.840350524607206e-15,
              0.961729102379098
            ],
            "target_residual": 0.06641742775887723,
            "energy_eV": -76.89584319668367,
            "max_atomic_step_A": 0.013630395222905076,
            "max_log_strain_component": 0.0005760002967674819,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.242186718405806,
            "cell_principal_stretches": [
              1.0020154962785248,
              0.9969094969559088,
              0.9968309271669857
            ],
            "cell_volume_ratio": 0.9957531180186011,
            "cell_rmsd_from_input_A": 0.018670280475585912
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.4983190939847571,
              -2.159169859821664e-15,
              0.9996122388995305
            ],
            "branch_aligned_reduced_polarization": [
              0.4983190939847571,
              -2.159169859821664e-15,
              0.9996122388995305
            ],
            "target_residual": 0.0017250517972272734,
            "energy_eV": -76.80402719726541,
            "max_atomic_step_A": 0.0002947037730242833,
            "max_log_strain_component": 8.205580085197677e-06,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.242186718405806,
            "cell_principal_stretches": [
              1.0020230475285545,
              0.9969013167687554,
              0.9968203479855912
            ],
            "cell_volume_ratio": 0.9957418835792273,
            "cell_rmsd_from_input_A": 0.018724891618721155
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.4999916534418686,
              -8.385256490684798e-17,
              1.0000036367383176
            ],
            "branch_aligned_reduced_polarization": [
              0.4999916534418686,
              -8.385256490684798e-17,
              1.0000036367383176
            ],
            "target_residual": 9.104443872743326e-06,
            "energy_eV": -76.80267698063545
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_05",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cm",
        "spacegroup_number": 8,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.5,
          0.0,
          1.0
        ],
        "formal_class": [
          0.5,
          0.0,
          0.0
        ],
        "target_residual": 9.104443872743326e-06,
        "parent_symmetrization_rmsd_A": 0.10321865455457656,
        "parent_cell_rmsd_A": 0.018724891618721155,
        "energy_eV": -76.80267698063545,
        "reduced_polarization": [
          0.4999916534418686,
          -8.385256490684798e-17,
          1.0000036367383176
        ],
        "cartesian_polarization_e_A2": [
          0.014858520869758782,
          -5.4142768725816444e-17,
          0.043276744134885
        ],
        "ranking_score": 0.6079180863470023
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 6,
      "formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.5,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.5,
        -0.5,
        0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              5.015106977600827e-18,
              -4.488792417905308e-16,
              0.7213208851942755
            ],
            "branch_aligned_reduced_polarization": [
              0.0,
              -4.440892098500626e-16,
              0.7213208851942755
            ],
            "target_residual": 0.7409338258057714,
            "energy_eV": -77.09364059380064,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.006459254717854794,
            "step_scale": 0.8680666334943895,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.242186718405806,
            "cell_principal_stretches": [
              1.0081561591549013,
              0.9993404070441112,
              0.9949376313722408
            ],
            "cell_volume_ratio": 1.0023908946788391,
            "cell_rmsd_from_input_A": 0.04086428717470908
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.4357593849258858,
              -0.42697091443419555,
              0.5008229284087192
            ],
            "branch_aligned_reduced_polarization": [
              0.4357593849258858,
              -0.42697091443419555,
              0.5008229284087192
            ],
            "target_residual": 0.09726654704904444,
            "energy_eV": -76.93581343403982,
            "max_atomic_step_A": 0.018983877142466906,
            "max_log_strain_component": 0.001291347554548861,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.242186718405806,
            "cell_principal_stretches": [
              1.0094078702094202,
              0.9993638022675394,
              0.9935731782687725
            ],
            "cell_volume_ratio": 1.0022825299709794,
            "cell_rmsd_from_input_A": 0.0485040937518352
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.4982663432121329,
              -0.497712376754292,
              0.5011178612217561
            ],
            "branch_aligned_reduced_polarization": [
              0.4982663432121329,
              -0.497712376754292,
              0.5011178612217561
            ],
            "target_residual": 0.003080324606843775,
            "energy_eV": -76.88382894948862,
            "max_atomic_step_A": 0.0006235534447329217,
            "max_log_strain_component": 4.1511610299137456e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.242186718405806,
            "cell_principal_stretches": [
              1.009455512422471,
              0.9993613508736859,
              0.9935366906152575
            ],
            "cell_volume_ratio": 1.0022905680717202,
            "cell_rmsd_from_input_A": 0.04876054285904521
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.49999909959507305,
              -0.4999642650513166,
              0.5000447681439673
            ],
            "branch_aligned_reduced_polarization": [
              0.49999909959507305,
              -0.4999642650513166,
              0.5000447681439673
            ],
            "target_residual": 5.728860271216236e-05,
            "energy_eV": -76.88244935196471
          }
        ],
        "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": [
          0.5,
          -0.5,
          0.5
        ],
        "formal_class": [
          0.5,
          0.5,
          0.5
        ],
        "target_residual": 5.728860271216236e-05,
        "parent_symmetrization_rmsd_A": 0.11717121614517091,
        "parent_cell_rmsd_A": 0.04876054285904521,
        "energy_eV": -76.88244935196471,
        "reduced_polarization": [
          0.49999909959507305,
          -0.4999642650513166,
          0.5000447681439673
        ],
        "cartesian_polarization_e_A2": [
          0.014688461683956709,
          -0.021221964912702306,
          0.021425557230688043
        ],
        "ranking_score": 0.6294759290653565
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 7,
      "formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.5,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.5,
        -0.5,
        1.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              5.015106977600827e-18,
              -4.488792417905308e-16,
              0.7213208851942755
            ],
            "branch_aligned_reduced_polarization": [
              0.0,
              -4.440892098500626e-16,
              0.7213208851942755
            ],
            "target_residual": 0.7600408206332747,
            "energy_eV": -77.09364059380064,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.006188604200320742,
            "step_scale": 0.8316936007109033,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.242186718405806,
            "cell_principal_stretches": [
              1.0045122732086014,
              1.0007863839403524,
              0.9918641391134883
            ],
            "cell_volume_ratio": 0.9971232066350597,
            "cell_rmsd_from_input_A": 0.03941025731478165
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.3698595187455285,
              -0.39352114574142183,
              0.9186708871988045
            ],
            "branch_aligned_reduced_polarization": [
              0.3698595187455285,
              -0.39352114574142183,
              0.9186708871988045
            ],
            "target_residual": 0.1867852131577726,
            "energy_eV": -76.40582038303097,
            "max_atomic_step_A": 0.0385974071613958,
            "max_log_strain_component": 0.0022128667831364216,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.242186718405806,
            "cell_principal_stretches": [
              1.0058270807740575,
              1.0011699664051683,
              0.9885180063709028
            ],
            "cell_volume_ratio": 0.9954414527093776,
            "cell_rmsd_from_input_A": 0.05431067956792925
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.49127927749955935,
              -0.4985547342554189,
              0.997688291664702
            ],
            "branch_aligned_reduced_polarization": [
              0.49127927749955935,
              -0.4985547342554189,
              0.997688291664702
            ],
            "target_residual": 0.009136946395248126,
            "energy_eV": -75.61991572357289,
            "max_atomic_step_A": 0.0015754809871330738,
            "max_log_strain_component": 4.774029318710483e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.242186718405806,
            "cell_principal_stretches": [
              1.0058506157087934,
              1.0011753413199935,
              0.9884246864165147
            ],
            "cell_volume_ratio": 0.9953761126625581,
            "cell_rmsd_from_input_A": 0.054677937209734684
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.4999423320992248,
              -0.5000175219707973,
              1.0000174813324032
            ],
            "branch_aligned_reduced_polarization": [
              0.4999423320992248,
              -0.5000175219707973,
              1.0000174813324032
            ],
            "target_residual": 6.275510515513984e-05,
            "energy_eV": -75.59831573131319
          }
        ],
        "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": [
          0.5,
          -0.5,
          1.0
        ],
        "formal_class": [
          0.5,
          0.5,
          0.0
        ],
        "target_residual": 6.275510515513984e-05,
        "parent_symmetrization_rmsd_A": 0.14961812564004007,
        "parent_cell_rmsd_A": 0.054677937209734684,
        "energy_eV": -75.59831573131319,
        "reduced_polarization": [
          0.4999423320992248,
          -0.5000175219707973,
          1.0000174813324032
        ],
        "cartesian_polarization_e_A2": [
          0.014871129952134349,
          -0.021067560810572712,
          0.04310668375292377
        ],
        "ranking_score": 0.663413120152784
      },
      "branch_status": "awaiting_branch_sampling"
    }
  ],
  "sampled_polarization_branches": [
    {
      "orbit_id": 1,
      "candidate_id": "inversion_parent_endpoint_00",
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "construction": "MACEField-BEC-parent plus variable-cell P-N-P path and symmetric log-strain continuation beyond both polar endpoints",
      "geometry_diagnostics": {
        "collision_aware": false,
        "permutations_tested": 1,
        "selected_order": [
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9
        ],
        "endpoint_rmsd_A": 0.12551661495758457,
        "minimum_distance_A_by_image": [
          1.8537818431521502,
          1.8791614100486729,
          1.904739177568977,
          1.9305072677021082,
          1.9564581603677778,
          1.9825846772390758,
          1.9950581219991306,
          1.9944138151946864,
          1.994199
        ],
        "minimum_distance_A": 1.8537818431521502,
        "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": [
          135.65297833568087,
          135.65297833568087,
          135.65297833568087,
          135.65297833568087,
          135.65297833568087,
          135.65297833568087,
          135.65297833568087,
          135.65297833568087,
          135.65297833568087
        ],
        "cell_deformation_log_strain_norm": 0.0
      },
      "parent_reduced_polarization": [
        -6.164483586194164e-17,
        -1.2229785921271546e-15,
        -2.780975128916622e-16
      ],
      "incoming": {
        "reached": true,
        "construction": "variable_cell_linear_interpolation",
        "continuation_fractions": [
          0.0,
          0.125,
          0.25,
          0.375,
          0.5,
          0.625,
          0.75,
          0.875,
          1.0
        ],
        "energies_eV": [
          -77.09364059380064,
          -77.0725893524893,
          -77.03366639656889,
          -76.98466650409638,
          -76.93290390017364,
          -76.88496182017099,
          -76.8464059059219,
          -76.82148667876587,
          -76.81287619380225
        ],
        "cartesian_polarizations_e_A2": [
          [
            1.0883230279578785e-17,
            -6.603879555124036e-17,
            0.031143548517256595
          ],
          [
            -5.25071602527153e-17,
            -4.583752462919496e-17,
            0.027863802917421118
          ],
          [
            -3.1067669529708405e-17,
            -1.5783319902746887e-17,
            0.024385632230494936
          ],
          [
            6.085004510524731e-18,
            -2.3763437562789e-17,
            0.020708855849733625
          ],
          [
            1.3835184935931899e-17,
            -6.415047957850756e-17,
            0.016841557115955794
          ],
          [
            -2.3575731710175045e-17,
            -3.864018141180545e-17,
            0.012802211477821854
          ],
          [
            -1.277343627667435e-17,
            -5.263458749881788e-17,
            0.008620540889603016
          ],
          [
            -1.5097952836313132e-17,
            -6.732804506645335e-18,
            0.004336906045959756
          ],
          [
            -1.812449258973819e-18,
            -5.235418988750858e-17,
            -1.2007060329241937e-17
          ]
        ],
        "raw_reduced_polarization": [
          [
            3.701592973765224e-16,
            -1.5426469855146932e-15,
            0.7213208851942763
          ],
          [
            -1.785868078418882e-15,
            -1.0707511940888963e-15,
            0.6453581541659063
          ],
          [
            -1.056670347757076e-15,
            -3.686937453378377e-16,
            0.5647996668323189
          ],
          [
            2.0696254111017298e-16,
            -5.551069642579897e-16,
            0.47964124013079473
          ],
          [
            4.705608724064419e-16,
            -1.498536475643639e-15,
            0.3900700936567943
          ],
          [
            -8.018553371374171e-16,
            -9.026233576354646e-16,
            0.2965141403366402
          ],
          [
            -4.3444878733564345e-16,
            -1.2295285984714737e-15,
            0.19966177527574994
          ],
          [
            -5.135100030181332e-16,
            -1.5727634778222555e-16,
            0.10044779920768224
          ],
          [
            -6.164483586194164e-17,
            -1.2229785921271546e-15,
            -2.780975128916622e-16
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            3.701592973765224e-16,
            -1.5426469855146932e-15,
            0.7213208851942763
          ],
          [
            -1.7858680784188825e-15,
            -1.0707511940888963e-15,
            0.6453581541659063
          ],
          [
            -1.056670347757076e-15,
            -3.6869374533783777e-16,
            0.5647996668323189
          ],
          [
            2.0696254111017288e-16,
            -5.551069642579897e-16,
            0.47964124013079473
          ],
          [
            4.705608724064419e-16,
            -1.498536475643639e-15,
            0.3900700936567943
          ],
          [
            -8.018553371374172e-16,
            -9.026233576354646e-16,
            0.2965141403366402
          ],
          [
            -4.3444878733564345e-16,
            -1.2295285984714737e-15,
            0.19966177527574994
          ],
          [
            -5.135100030181332e-16,
            -1.5727634778222557e-16,
            0.10044779920768224
          ],
          [
            -6.164483586194164e-17,
            -1.2229785921271546e-15,
            -2.7755575615628914e-16
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            3.3306690738754696e-16,
            -1.5543122344752192e-15,
            -0.2786791148057237
          ],
          [
            -1.7763568394002505e-15,
            -1.0547118733938987e-15,
            -0.35464184583409386
          ],
          [
            -1.0547118733938987e-15,
            -3.885780586188048e-16,
            -0.43520033316768103
          ],
          [
            2.220446049250313e-16,
            -5.551115123125783e-16,
            0.4796412401307948
          ],
          [
            4.440892098500626e-16,
            -1.4988010832439613e-15,
            0.39007009365679424
          ],
          [
            -7.771561172376096e-16,
            -8.881784197001252e-16,
            0.29651414033664025
          ],
          [
            -4.440892098500626e-16,
            -1.2212453270876722e-15,
            0.1996617752757499
          ],
          [
            -4.996003610813204e-16,
            -1.6653345369377348e-16,
            0.10044779920768221
          ],
          [
            -5.551115123125783e-17,
            -1.2212453270876722e-15,
            -2.7755575615628914e-16
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -76.81287619380224,
          -76.82148667876587,
          -76.84640590592193,
          -76.88496182017097,
          -76.93290390017366,
          -76.98466650409637,
          -77.03366639656888,
          -77.0725893524893,
          -77.09364059380063
        ],
        "cartesian_polarizations_e_A2": [
          [
            -1.3169379885524516e-18,
            -5.179344996691205e-17,
            1.0229927070180308e-17
          ],
          [
            -1.628565155005054e-17,
            -5.787250527687978e-17,
            -0.00433690604595979
          ],
          [
            -4.445890994264452e-18,
            -2.769276324381978e-17,
            -0.008620540889603028
          ],
          [
            -2.371985226754864e-17,
            -1.9232927918615794e-17,
            -0.012802211477821861
          ],
          [
            2.647696313114173e-18,
            -1.044199839246018e-17,
            -0.016841557115955842
          ],
          [
            9.651868418234494e-18,
            -7.672180815018749e-17,
            -0.020708855849733636
          ],
          [
            -3.852338816293903e-17,
            -2.4742646419911907e-17,
            -0.024385632230494954
          ],
          [
            -4.680188731248052e-17,
            -6.217780083182283e-17,
            -0.027863802917421146
          ],
          [
            1.6634307963908178e-17,
            -7.21058659611533e-17,
            -0.031143548517256595
          ]
        ],
        "raw_reduced_polarization": [
          [
            -4.479155802167709e-17,
            -1.2098798712776078e-15,
            2.369370351502053e-16
          ],
          [
            -5.539058882542448e-16,
            -1.3518848286730292e-15,
            -0.10044779920768303
          ],
          [
            -1.5121318251783155e-16,
            -6.468948650873493e-16,
            -0.19966177527575024
          ],
          [
            -8.06757150559028e-16,
            -4.49275581551953e-16,
            -0.29651414033664036
          ],
          [
            9.005317187560996e-17,
            -2.4392203413793813e-16,
            -0.39007009365679546
          ],
          [
            3.282783457011076e-16,
            -1.792199041157412e-15,
            -0.47964124013079495
          ],
          [
            -1.3102534751757956e-15,
            -5.779809973020641e-16,
            -0.5647996668323192
          ],
          [
            -1.5918209280189432e-15,
            -1.4524552760009099e-15,
            -0.6453581541659068
          ],
          [
            5.657643539729685e-16,
            -1.68437197914356e-15,
            -0.7213208851942763
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -4.479155802167709e-17,
            -1.2098798712776078e-15,
            2.369370351502053e-16
          ],
          [
            -5.539058882542448e-16,
            -1.3518848286730292e-15,
            -0.10044779920768303
          ],
          [
            -1.5121318251783157e-16,
            -6.468948650873493e-16,
            -0.19966177527575024
          ],
          [
            -8.06757150559028e-16,
            -4.49275581551953e-16,
            -0.29651414033664036
          ],
          [
            9.005317187560996e-17,
            -2.4392203413793813e-16,
            -0.39007009365679546
          ],
          [
            3.282783457011076e-16,
            -1.792199041157412e-15,
            -0.47964124013079495
          ],
          [
            -1.3102534751757956e-15,
            -5.779809973020641e-16,
            -0.5647996668323192
          ],
          [
            -1.5918209280189432e-15,
            -1.4524552760009099e-15,
            -0.6453581541659068
          ],
          [
            5.657643539729685e-16,
            -1.68437197914356e-15,
            -0.7213208851942763
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          -4.934489691004057e-16,
          -9.033101987396163e-16,
          -0.721320885194277
        ],
        "actual_opposite_endpoint_branch_residual": 1.4750337717390535e-15
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            3.701592973765224e-16,
            -1.5426469855146932e-15,
            0.7213208851942763
          ],
          [
            -1.785868078418882e-15,
            -1.0707511940888963e-15,
            0.6453581541659063
          ],
          [
            -1.056670347757076e-15,
            -3.686937453378377e-16,
            0.5647996668323189
          ],
          [
            2.0696254111017298e-16,
            -5.551069642579897e-16,
            0.47964124013079473
          ],
          [
            4.705608724064419e-16,
            -1.498536475643639e-15,
            0.3900700936567943
          ],
          [
            -8.018553371374171e-16,
            -9.026233576354646e-16,
            0.2965141403366402
          ],
          [
            -4.3444878733564345e-16,
            -1.2295285984714737e-15,
            0.19966177527574994
          ],
          [
            -5.135100030181332e-16,
            -1.5727634778222555e-16,
            0.10044779920768224
          ],
          [
            -6.164483586194164e-17,
            -1.2229785921271546e-15,
            -2.780975128916622e-16
          ],
          [
            -5.539058882542448e-16,
            -1.3518848286730292e-15,
            -0.10044779920768303
          ],
          [
            -1.5121318251783155e-16,
            -6.468948650873493e-16,
            -0.19966177527575024
          ],
          [
            -8.06757150559028e-16,
            -4.49275581551953e-16,
            -0.29651414033664036
          ],
          [
            9.005317187560996e-17,
            -2.4392203413793813e-16,
            -0.39007009365679546
          ],
          [
            3.282783457011076e-16,
            -1.792199041157412e-15,
            -0.47964124013079495
          ],
          [
            -1.3102534751757956e-15,
            -5.779809973020641e-16,
            -0.5647996668323192
          ],
          [
            -1.5918209280189432e-15,
            -1.4524552760009099e-15,
            -0.6453581541659068
          ],
          [
            5.657643539729685e-16,
            -1.68437197914356e-15,
            -0.7213208851942763
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            3.701592973765224e-16,
            -1.5426469855146932e-15,
            0.7213208851942763
          ],
          [
            -1.7858680784188825e-15,
            -1.0707511940888963e-15,
            0.6453581541659063
          ],
          [
            -1.056670347757076e-15,
            -3.6869374533783777e-16,
            0.5647996668323189
          ],
          [
            2.0696254111017288e-16,
            -5.551069642579897e-16,
            0.47964124013079473
          ],
          [
            4.705608724064419e-16,
            -1.498536475643639e-15,
            0.3900700936567943
          ],
          [
            -8.018553371374172e-16,
            -9.026233576354646e-16,
            0.2965141403366402
          ],
          [
            -4.3444878733564345e-16,
            -1.2295285984714737e-15,
            0.19966177527574994
          ],
          [
            -5.135100030181332e-16,
            -1.5727634778222557e-16,
            0.10044779920768224
          ],
          [
            -6.164483586194164e-17,
            -1.2229785921271546e-15,
            -2.7755575615628914e-16
          ],
          [
            -5.539058882542448e-16,
            -1.3518848286730292e-15,
            -0.10044779920768303
          ],
          [
            -1.5121318251783157e-16,
            -6.468948650873493e-16,
            -0.19966177527575024
          ],
          [
            -8.06757150559028e-16,
            -4.49275581551953e-16,
            -0.29651414033664036
          ],
          [
            9.005317187560996e-17,
            -2.4392203413793813e-16,
            -0.39007009365679546
          ],
          [
            3.282783457011076e-16,
            -1.792199041157412e-15,
            -0.47964124013079495
          ],
          [
            -1.3102534751757956e-15,
            -5.779809973020641e-16,
            -0.5647996668323192
          ],
          [
            -1.5918209280189432e-15,
            -1.4524552760009099e-15,
            -0.6453581541659068
          ],
          [
            5.657643539729685e-16,
            -1.68437197914356e-15,
            -0.7213208851942763
          ]
        ],
        "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": [
          [
            3.3306690738754696e-16,
            -1.5543122344752192e-15,
            -0.2786791148057237
          ],
          [
            -1.7763568394002505e-15,
            -1.0547118733938987e-15,
            -0.35464184583409386
          ],
          [
            -1.0547118733938987e-15,
            -3.885780586188048e-16,
            -0.43520033316768103
          ],
          [
            2.220446049250313e-16,
            -5.551115123125783e-16,
            0.4796412401307948
          ],
          [
            4.440892098500626e-16,
            -1.4988010832439613e-15,
            0.39007009365679424
          ],
          [
            -7.771561172376096e-16,
            -8.881784197001252e-16,
            0.29651414033664025
          ],
          [
            -4.440892098500626e-16,
            -1.2212453270876722e-15,
            0.1996617752757499
          ],
          [
            -4.996003610813204e-16,
            -1.6653345369377348e-16,
            0.10044779920768221
          ],
          [
            -5.551115123125783e-17,
            -1.2212453270876722e-15,
            -2.7755575615628914e-16
          ],
          [
            -5.551115123125783e-16,
            -1.3322676295501878e-15,
            -0.10044779920768304
          ],
          [
            -1.6653345369377348e-16,
            -6.661338147750939e-16,
            -0.19966177527575024
          ],
          [
            -8.326672684688674e-16,
            -4.440892098500626e-16,
            -0.29651414033664036
          ],
          [
            1.1102230246251565e-16,
            -2.220446049250313e-16,
            -0.39007009365679546
          ],
          [
            3.3306690738754696e-16,
            -1.7763568394002505e-15,
            -0.47964124013079495
          ],
          [
            -1.3322676295501878e-15,
            -5.551115123125783e-16,
            0.4352003331676808
          ],
          [
            -1.609823385706477e-15,
            -1.4432899320127035e-15,
            0.3546418458340932
          ],
          [
            5.551115123125783e-16,
            -1.6653345369377348e-15,
            0.2786791148057237
          ]
        ]
      },
      "incoming_structure_ids": [
        "incoming_01_000",
        "incoming_01_001",
        "incoming_01_002",
        "incoming_01_003",
        "incoming_01_004",
        "incoming_01_005",
        "incoming_01_006",
        "incoming_01_007",
        "incoming_01_008"
      ],
      "reflected_structure_ids": [
        "reflected_01_001",
        "reflected_01_002",
        "reflected_01_003",
        "reflected_01_004",
        "reflected_01_005",
        "reflected_01_006",
        "reflected_01_007",
        "reflected_01_008"
      ],
      "positive_extension_structure_ids": [
        "extension_plus_01_000",
        "extension_plus_01_001",
        "extension_plus_01_002",
        "extension_plus_01_003"
      ],
      "negative_extension_structure_ids": [
        "extension_minus_01_000",
        "extension_minus_01_001",
        "extension_minus_01_002",
        "extension_minus_01_003"
      ],
      "extension": {
        "enabled": true,
        "fraction_beyond_polar_endpoint": 0.35,
        "images_per_side": 4,
        "construction": "continue fractional atomic displacements and symmetric log strain beyond +P; reflect these structures about N for the -P side",
        "positive_path_coordinates": [
          1.35,
          1.2625,
          1.175,
          1.0875
        ],
        "negative_path_coordinates": [
          -1.0875,
          -1.175,
          -1.2625,
          -1.35
        ]
      },
      "branch_coordinates": [
        1.35,
        1.2625,
        1.175,
        1.0875,
        1.0,
        0.875,
        0.75,
        0.625,
        0.5,
        0.375,
        0.25,
        0.125,
        0.0,
        -0.125,
        -0.25,
        -0.375,
        -0.5,
        -0.625,
        -0.75,
        -0.875,
        -1.0,
        -1.0875,
        -1.175,
        -1.2625,
        -1.35
      ],
      "parent": {
        "candidate_id": "inversion_parent_endpoint_00",
        "source": "same_species_inversion_center_projection_from_endpoint",
        "spacegroup": "Cmmm",
        "spacegroup_number": 65,
        "pointgroup": "mmm",
        "has_inversion": true,
        "is_polar_point_group": false,
        "nonpolar_parent_hypothesis": true,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.0
        ],
        "formal_class": [
          0.0,
          0.0,
          0.0
        ],
        "target_residual": 9.312548916339031e-16,
        "parent_symmetrization_rmsd_A": 0.12551661495758457,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -76.81287619380225,
        "reduced_polarization": [
          7.57306375778424e-18,
          -6.346810440734804e-16,
          6.814384008780176e-16
        ],
        "cartesian_polarization_e_A2": [
          2.226592642195934e-19,
          -2.7169904782740802e-17,
          2.9421593544390956e-17
        ],
        "ranking_score": 0.12551661495758643
      }
    }
  ],
  "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": 52,
      "full_response": 20,
      "energy_polarization": 32
    },
    "model_evaluations_for_recovery_and_path_properties": {
      "total": 77,
      "full_response": 45,
      "energy_polarization": 32
    },
    "elapsed_seconds": 134.5088133320096
  }
}
