{
  "schema": "ferrofinder.endpoint_parent_recovery.v4_variable_cell",
  "status": "complete",
  "input_atom_count": 26,
  "input_formula": "B4O18S4",
  "input_spacegroup": "C2",
  "input_pointgroup": "2",
  "input_is_polar_point_group": true,
  "input_energy_eV": -169.2763917932688,
  "input_cartesian_polarization_e_A2": [
    2.6303715765424327e-11,
    -0.002518026840464125,
    2.3245047412343097e-11
  ],
  "input_reduced_polarization": [
    1.0557330114521193e-09,
    -0.17528734402712665,
    7.809481960213832e-10
  ],
  "input_formal_targets": [
    {
      "orbit_id": 0,
      "representative_formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ]
    },
    {
      "orbit_id": 1,
      "representative_formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        -0.5,
        0.0
      ]
    },
    {
      "orbit_id": 2,
      "representative_formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.0
      ]
    },
    {
      "orbit_id": 3,
      "representative_formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.5
      ]
    },
    {
      "orbit_id": 4,
      "representative_formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        0.5,
        -0.5,
        0.0
      ]
    },
    {
      "orbit_id": 5,
      "representative_formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        -0.5,
        0.5
      ]
    },
    {
      "orbit_id": 6,
      "representative_formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.5
      ]
    },
    {
      "orbit_id": 7,
      "representative_formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "target_reduced_polarization": [
        0.5,
        -0.5,
        0.5
      ]
    }
  ],
  "parent_candidates": [
    {
      "candidate_id": "inversion_parent_endpoint_00",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "C2/m",
      "spacegroup_number": 12,
      "pointgroup": "2/m",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 1.6655551327964686e-15,
      "parent_symmetrization_rmsd_A": 0.5130989606187063,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -155.13786093026255,
      "reduced_polarization": [
        9.572586810313111e-17,
        1.3890152731305784e-15,
        9.14082616381336e-16
      ],
      "cartesian_polarization_e_A2": [
        5.944642575915841e-19,
        1.995339571701272e-17,
        2.720781463460989e-17
      ],
      "ranking_score": 0.5130989606187096
    },
    {
      "candidate_id": "inversion_parent_endpoint_01",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "C2/m",
      "spacegroup_number": 12,
      "pointgroup": "2/m",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 3.009136164341044e-15,
      "parent_symmetrization_rmsd_A": 0.8516307010290785,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -119.75910986789803,
      "reduced_polarization": [
        5.059544207185973e-16,
        -1.7703570795201227e-15,
        2.3800727700415847e-15
      ],
      "cartesian_polarization_e_A2": [
        8.346895184681928e-18,
        -2.543142329059125e-17,
        7.084324500178314e-17
      ],
      "ranking_score": 0.8516307010290844
    },
    {
      "candidate_id": "bec_projection_00",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "C2",
      "spacegroup_number": 5,
      "pointgroup": "2",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 9.162656493720434e-05,
      "parent_symmetrization_rmsd_A": 0.0200948124438403,
      "parent_cell_rmsd_A": 0.014869610457645507,
      "energy_eV": -169.18417486049566,
      "reduced_polarization": [
        -1.3937816279082154e-11,
        -9.162656493720316e-05,
        -4.7596870037373015e-12
      ],
      "cartesian_polarization_e_A2": [
        -3.586705947264886e-13,
        -1.316139177301393e-06,
        -1.4149441026247706e-13
      ],
      "ranking_score": 0.523995468188126
    },
    {
      "candidate_id": "inversion_parent_bec_00_00",
      "source": "same_species_inversion_center_projection_after_BEC",
      "spacegroup": "C2/m",
      "spacegroup_number": 12,
      "pointgroup": "2/m",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 6.193674615301526e-16,
      "parent_symmetrization_rmsd_A": 0.5131025296933329,
      "parent_cell_rmsd_A": 0.014869610457645507,
      "energy_eV": -155.13476773528174,
      "reduced_polarization": [
        -1.5556347819606927e-16,
        -8.981277681889685e-17,
        5.927476037690285e-16
      ],
      "cartesian_polarization_e_A2": [
        -5.393268112383947e-18,
        -1.290085624504019e-18,
        1.767745135641115e-17
      ],
      "ranking_score": 0.5168199323077455
    },
    {
      "candidate_id": "inversion_parent_bec_00_01",
      "source": "same_species_inversion_center_projection_after_BEC",
      "spacegroup": "C2/m",
      "spacegroup_number": 12,
      "pointgroup": "2/m",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 2.1949207005691253e-15,
      "parent_symmetrization_rmsd_A": 0.8516362017639619,
      "parent_cell_rmsd_A": 0.014869610457645507,
      "energy_eV": -120.7324856656896,
      "reduced_polarization": [
        1.596892725854043e-16,
        -1.520990385546116e-15,
        -1.5744092432033934e-15
      ],
      "cartesian_polarization_e_A2": [
        7.616196499909372e-18,
        -2.1847758190763827e-17,
        -4.694632477663354e-17
      ],
      "ranking_score": 0.8553536043783777
    },
    {
      "candidate_id": "bec_projection_01",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "C2",
      "spacegroup_number": 5,
      "pointgroup": "2",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        -0.5,
        0.0
      ],
      "formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_residual": 0.000516549618062526,
      "parent_symmetrization_rmsd_A": 0.03717937902904915,
      "parent_cell_rmsd_A": 0.027504216096755543,
      "energy_eV": -168.91995022791775,
      "reduced_polarization": [
        5.058816717383764e-11,
        -0.4994834503819375,
        -2.7205279960467573e-11
      ],
      "cartesian_polarization_e_A2": [
        1.2899678746207274e-12,
        -0.007176047886080424,
        -7.435846680779322e-13
      ],
      "ranking_score": 0.545088532289363
    },
    {
      "candidate_id": "bec_projection_02",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.0
      ],
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_residual": 0.00018952500549829172,
      "parent_symmetrization_rmsd_A": 0.10355324658453356,
      "parent_cell_rmsd_A": 0.07318997398039172,
      "energy_eV": -165.80843260277652,
      "reduced_polarization": [
        0.4998168491765406,
        4.30452203841097e-05,
        -2.2860721278276266e-05
      ],
      "cartesian_polarization_e_A2": [
        0.01322978535841828,
        -0.00018022104700237624,
        -1.2577905968558444e-05
      ],
      "ranking_score": 0.6222297900906281
    },
    {
      "candidate_id": "bec_projection_03",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.5
      ],
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_residual": 8.398048855812422e-05,
      "parent_symmetrization_rmsd_A": 0.14973251010430827,
      "parent_cell_rmsd_A": 0.11989076861937828,
      "energy_eV": -160.12287485829012,
      "reduced_polarization": [
        1.6477438874630666e-05,
        -4.245984162492202e-05,
        0.49992944237592024
      ],
      "cartesian_polarization_e_A2": [
        -0.0010834853236451345,
        0.0003519285665239448,
        0.014921165799480213
      ],
      "ranking_score": 0.6798731632362691
    },
    {
      "candidate_id": "bec_projection_04",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.5,
        -0.5,
        0.0
      ],
      "formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_residual": 2.9119673528109045e-05,
      "parent_symmetrization_rmsd_A": 0.11109154188104577,
      "parent_cell_rmsd_A": 0.08152612101537464,
      "energy_eV": -166.31742259488615,
      "reduced_polarization": [
        0.499974576896896,
        -0.49998606231274706,
        -2.713316971264288e-06
      ],
      "cartesian_polarization_e_A2": [
        0.013369132119927244,
        -0.007375678324878539,
        9.703491577080427e-05
      ],
      "ranking_score": 0.6315313114819456
    },
    {
      "candidate_id": "bec_projection_05",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        -0.5,
        0.5
      ],
      "formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_residual": 0.0009937606639094545,
      "parent_symmetrization_rmsd_A": 0.14941279633764012,
      "parent_cell_rmsd_A": 0.11213764507699309,
      "energy_eV": -158.3501752756162,
      "reduced_polarization": [
        -9.695708190371142e-05,
        -0.5000539408118709,
        0.4990124525478656
      ],
      "cartesian_polarization_e_A2": [
        -0.001011605079113244,
        -0.0068550723646004785,
        0.014661050006177593
      ],
      "ranking_score": 0.6794347289347074
    },
    {
      "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,
        0.0,
        0.5
      ],
      "formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_residual": 0.0002600955977798763,
      "parent_symmetrization_rmsd_A": 0.17096044825759169,
      "parent_cell_rmsd_A": 0.10998637832901746,
      "energy_eV": -157.70787092321763,
      "reduced_polarization": [
        0.49985610184772133,
        -6.717551394714631e-05,
        0.4997940133691688
      ],
      "cartesian_polarization_e_A2": [
        0.012151302755105738,
        -1.2807048400448118e-05,
        0.014888025435951207
      ],
      "ranking_score": 0.6989772340354058
    },
    {
      "candidate_id": "bec_projection_07",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.5,
        -0.5,
        0.5
      ],
      "formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "target_residual": 0.00038252439901186996,
      "parent_symmetrization_rmsd_A": 0.17202768427855925,
      "parent_cell_rmsd_A": 0.10947019635578696,
      "energy_eV": -157.58426417541534,
      "reduced_polarization": [
        0.4996319193039564,
        -0.4999758727836036,
        0.49989871133099695
      ],
      "cartesian_polarization_e_A2": [
        0.01235448855669922,
        -0.007231622550277368,
        0.014770483188123662
      ],
      "ranking_score": 0.7001602821655297
    }
  ],
  "formal_branches": [
    {
      "orbit_id": 0,
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.0,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              1.0557330114521193e-09,
              -0.17528734402712665,
              7.809481960213832e-10
            ],
            "branch_aligned_reduced_polarization": [
              1.0557330114521193e-09,
              -0.17528734402712665,
              7.809481960213832e-10
            ],
            "target_residual": 0.17528734402712665,
            "energy_eV": -169.2763917932688,
            "max_atomic_step_A": 0.021073221904246438,
            "max_log_strain_component": 0.001239091028263552,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.0084026645189437,
            "cell_principal_stretches": [
              1.0016403906631597,
              0.9995569458320042,
              0.9984298437853393
            ],
            "cell_volume_ratio": 0.9996245746344049,
            "cell_rmsd_from_input_A": 0.014869610457645507
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -1.3937816279082154e-11,
              -9.162656493720316e-05,
              -4.7596870037373015e-12
            ],
            "branch_aligned_reduced_polarization": [
              -1.3937816279082154e-11,
              -9.162656493720316e-05,
              -4.7596870037373015e-12
            ],
            "target_residual": 9.162656493720434e-05,
            "energy_eV": -169.18417486049566
          }
        ],
        "iterations": 1
      },
      "parent": {
        "candidate_id": "inversion_parent_endpoint_00",
        "source": "same_species_inversion_center_projection_from_endpoint",
        "spacegroup": "C2/m",
        "spacegroup_number": 12,
        "pointgroup": "2/m",
        "has_inversion": true,
        "is_polar_point_group": false,
        "nonpolar_parent_hypothesis": true,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.0
        ],
        "formal_class": [
          0.0,
          0.0,
          0.0
        ],
        "target_residual": 1.6655551327964686e-15,
        "parent_symmetrization_rmsd_A": 0.5130989606187063,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -155.13786093026255,
        "reduced_polarization": [
          9.572586810313111e-17,
          1.3890152731305784e-15,
          9.14082616381336e-16
        ],
        "cartesian_polarization_e_A2": [
          5.944642575915841e-19,
          1.995339571701272e-17,
          2.720781463460989e-17
        ],
        "ranking_score": 0.5130989606187096
      },
      "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": [
          -169.2763917932688,
          -168.64870775511008,
          -167.0347193969657,
          -164.71976600522936,
          -162.04390210610066,
          -159.38823195092283,
          -157.14775603117124,
          -155.65854762382554,
          -155.13786093026255
        ],
        "cartesian_polarizations_e_A2": [
          [
            2.630370195442685e-11,
            -0.0025180268404641315,
            2.3245053092002703e-11
          ],
          [
            1.503208992597809e-11,
            -0.0022123276034625963,
            1.613391863637153e-11
          ],
          [
            6.173592594454435e-12,
            -0.0019381959429709938,
            1.0567096171892766e-11
          ],
          [
            -4.1216095191422667e-13,
            -0.0016659734360570263,
            6.433828402953758e-12
          ],
          [
            -4.820969615108774e-12,
            -0.001376667107965327,
            3.695636321583407e-12
          ],
          [
            -6.9849717283370304e-12,
            -0.0010655491485713506,
            2.02976590117746e-12
          ],
          [
            -6.7925009199548244e-12,
            -0.0007333512143034696,
            1.1188748191732849e-12
          ],
          [
            -4.217633191297854e-12,
            -0.0003772645973623073,
            5.457643927497075e-13
          ],
          [
            -1.5880555598950303e-17,
            -1.0866272085828839e-17,
            2.758827096934479e-18
          ]
        ],
        "raw_reduced_polarization": [
          [
            1.0557325053006017e-09,
            -0.1752873440271271,
            7.809483868370802e-10
          ],
          [
            6.110076288947086e-10,
            -0.15400671013394696,
            5.420403938234027e-10
          ],
          [
            2.6155192403807635e-10,
            -0.13492358921198647,
            3.5501561026036577e-10
          ],
          [
            1.767223624500699e-12,
            -0.11597337015373359,
            2.1615299791257371e-10
          ],
          [
            -1.720671017745592e-10,
            -0.09583389544817913,
            1.2415980347534785e-10
          ],
          [
            -2.5825816418232503e-10,
            -0.07417604815880806,
            6.819267737989408e-11
          ],
          [
            -2.5344460609393307e-10,
            -0.05105076106759428,
            3.759008343184321e-11
          ],
          [
            -1.5777131746544268e-10,
            -0.026262511663661652,
            1.8335678581764078e-11
          ],
          [
            -5.921568467759461e-16,
            -7.564335466138093e-16,
            9.268645515181239e-17
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            1.0557325053006017e-09,
            -0.1752873440271271,
            7.809483868370802e-10
          ],
          [
            6.110076288947086e-10,
            -0.15400671013394696,
            5.420403938234027e-10
          ],
          [
            2.6155192403807635e-10,
            -0.13492358921198647,
            3.5501561026036577e-10
          ],
          [
            1.7672236245006736e-12,
            -0.11597337015373359,
            2.1615299791257371e-10
          ],
          [
            -1.720671017745592e-10,
            -0.09583389544817913,
            1.2415980347534785e-10
          ],
          [
            -2.5825816418232503e-10,
            -0.07417604815880806,
            6.819267737989408e-11
          ],
          [
            -2.5344460609393307e-10,
            -0.05105076106759428,
            3.759008343184321e-11
          ],
          [
            -1.5777131746544268e-10,
            -0.026262511663661652,
            1.8335678581764078e-11
          ],
          [
            -5.921568467881263e-16,
            -7.563394355258879e-16,
            9.268645515192769e-17
          ]
        ],
        "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": [
          [
            1.0557325014204366e-09,
            -0.1752873440271271,
            7.809484170451242e-10
          ],
          [
            6.110075778664736e-10,
            -0.15400671013394696,
            5.420404125544565e-10
          ],
          [
            2.615518912563175e-10,
            -0.13492358921198644,
            3.5501557249517646e-10
          ],
          [
            1.7672530105983242e-12,
            -0.1159733701537336,
            2.16152984400253e-10
          ],
          [
            -1.7206708280426142e-10,
            -0.09583389544817911,
            1.2415979355751006e-10
          ],
          [
            -2.582581370980108e-10,
            -0.07417604815880807,
            6.819267373003868e-11
          ],
          [
            -2.5344459864129476e-10,
            -0.051050761067594264,
            3.759004219006101e-11
          ],
          [
            -1.577712960276756e-10,
            -0.02626251166366167,
            1.8335666318591848e-11
          ],
          [
            -6.106226635438361e-16,
            -7.771561172376096e-16,
            1.1102230246251565e-16
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -155.13786093026255,
          -155.65854762382554,
          -157.14775603117124,
          -159.38823195092283,
          -162.04390210610063,
          -164.7197660052294,
          -167.03471939696564,
          -168.64870775511005,
          -169.2763917932687
        ],
        "cartesian_polarizations_e_A2": [
          [
            -3.905733983764193e-17,
            2.070791032557181e-18,
            2.4148178267581712e-18
          ],
          [
            4.217484059137153e-12,
            0.0003772645973622731,
            -5.456368267615148e-13
          ],
          [
            6.792424122688475e-12,
            0.0007333512143034113,
            -1.118850076223642e-12
          ],
          [
            6.984966962887557e-12,
            0.0010655491485713202,
            -2.0297447474310017e-12
          ],
          [
            4.82086069011715e-12,
            0.0013766671079653255,
            -3.695556476424132e-12
          ],
          [
            4.1215600589939083e-13,
            0.001665973436057015,
            -6.433790590741498e-12
          ],
          [
            -6.173655654316097e-12,
            0.0019381959429710107,
            -1.056701799335647e-11
          ],
          [
            -1.5032111801547936e-11,
            0.002212327603462573,
            -1.6133854771363045e-11
          ],
          [
            -2.6303703482880678e-11,
            0.002518026840464162,
            -2.3244988479302823e-11
          ]
        ],
        "raw_reduced_polarization": [
          [
            -1.4681477918777824e-15,
            1.4415392810714994e-16,
            8.112900748594248e-17
          ],
          [
            1.577660304053023e-10,
            0.026262511663659272,
            -1.8331392833209317e-11
          ],
          [
            2.5344177317300784e-10,
            0.05105076106759022,
            -3.75892521596352e-11
          ],
          [
            2.5825804123292935e-10,
            0.07417604815880594,
            -6.819196669172715e-11
          ],
          [
            1.7206320424853297e-10,
            0.09583389544817902,
            -1.2415712097132922e-10
          ],
          [
            -1.7673085236055345e-12,
            0.1159733701537328,
            -2.161517275611553e-10
          ],
          [
            -2.6155409436569923e-10,
            0.13492358921198763,
            -3.550129837487564e-10
          ],
          [
            -6.110082828170376e-10,
            0.15400671013394532,
            -5.420382481937433e-10
          ],
          [
            -1.0557323889818773e-09,
            0.17528734402712923,
            -7.809462160877367e-10
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -1.4681477918777824e-15,
            1.4415392810714994e-16,
            8.112900748594248e-17
          ],
          [
            1.577660304053023e-10,
            0.026262511663659272,
            -1.8331392833209317e-11
          ],
          [
            2.5344177317300784e-10,
            0.05105076106759022,
            -3.75892521596352e-11
          ],
          [
            2.5825804123292935e-10,
            0.07417604815880594,
            -6.819196669172715e-11
          ],
          [
            1.7206320424853297e-10,
            0.09583389544817902,
            -1.2415712097132922e-10
          ],
          [
            -1.767308523605542e-12,
            0.1159733701537328,
            -2.161517275611553e-10
          ],
          [
            -2.6155409436569923e-10,
            0.13492358921198763,
            -3.550129837487564e-10
          ],
          [
            -6.110082828170376e-10,
            0.15400671013394532,
            -5.420382481937433e-10
          ],
          [
            -1.0557323889818773e-09,
            0.17528734402712923,
            -7.809462160877367e-10
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          -1.0557336896142953e-09,
          0.1752873440271256,
          -7.809482014641699e-10
        ],
        "actual_opposite_endpoint_branch_residual": 4.342086799987132e-15
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            1.0557325053006017e-09,
            -0.1752873440271271,
            7.809483868370802e-10
          ],
          [
            6.110076288947086e-10,
            -0.15400671013394696,
            5.420403938234027e-10
          ],
          [
            2.6155192403807635e-10,
            -0.13492358921198647,
            3.5501561026036577e-10
          ],
          [
            1.767223624500699e-12,
            -0.11597337015373359,
            2.1615299791257371e-10
          ],
          [
            -1.720671017745592e-10,
            -0.09583389544817913,
            1.2415980347534785e-10
          ],
          [
            -2.5825816418232503e-10,
            -0.07417604815880806,
            6.819267737989408e-11
          ],
          [
            -2.5344460609393307e-10,
            -0.05105076106759428,
            3.759008343184321e-11
          ],
          [
            -1.5777131746544268e-10,
            -0.026262511663661652,
            1.8335678581764078e-11
          ],
          [
            -5.921568467759461e-16,
            -7.564335466138093e-16,
            9.268645515181239e-17
          ],
          [
            1.577660304053023e-10,
            0.026262511663659272,
            -1.8331392833209317e-11
          ],
          [
            2.5344177317300784e-10,
            0.05105076106759022,
            -3.75892521596352e-11
          ],
          [
            2.5825804123292935e-10,
            0.07417604815880594,
            -6.819196669172715e-11
          ],
          [
            1.7206320424853297e-10,
            0.09583389544817902,
            -1.2415712097132922e-10
          ],
          [
            -1.7673085236055345e-12,
            0.1159733701537328,
            -2.161517275611553e-10
          ],
          [
            -2.6155409436569923e-10,
            0.13492358921198763,
            -3.550129837487564e-10
          ],
          [
            -6.110082828170376e-10,
            0.15400671013394532,
            -5.420382481937433e-10
          ],
          [
            -1.0557323889818773e-09,
            0.17528734402712923,
            -7.809462160877367e-10
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            1.0557325053006017e-09,
            -0.1752873440271271,
            7.809483868370802e-10
          ],
          [
            6.110076288947086e-10,
            -0.15400671013394696,
            5.420403938234027e-10
          ],
          [
            2.6155192403807635e-10,
            -0.13492358921198647,
            3.5501561026036577e-10
          ],
          [
            1.7672236245006736e-12,
            -0.11597337015373359,
            2.1615299791257371e-10
          ],
          [
            -1.720671017745592e-10,
            -0.09583389544817913,
            1.2415980347534785e-10
          ],
          [
            -2.5825816418232503e-10,
            -0.07417604815880806,
            6.819267737989408e-11
          ],
          [
            -2.5344460609393307e-10,
            -0.05105076106759428,
            3.759008343184321e-11
          ],
          [
            -1.5777131746544268e-10,
            -0.026262511663661652,
            1.8335678581764078e-11
          ],
          [
            -5.921568467881263e-16,
            -7.563394355258879e-16,
            9.268645515192769e-17
          ],
          [
            1.577660304053023e-10,
            0.026262511663659272,
            -1.8331392833209317e-11
          ],
          [
            2.5344177317300784e-10,
            0.05105076106759022,
            -3.75892521596352e-11
          ],
          [
            2.5825804123292935e-10,
            0.07417604815880594,
            -6.819196669172715e-11
          ],
          [
            1.7206320424853297e-10,
            0.09583389544817902,
            -1.2415712097132922e-10
          ],
          [
            -1.767308523605542e-12,
            0.1159733701537328,
            -2.161517275611553e-10
          ],
          [
            -2.6155409436569923e-10,
            0.13492358921198763,
            -3.550129837487564e-10
          ],
          [
            -6.110082828170376e-10,
            0.15400671013394532,
            -5.420382481937433e-10
          ],
          [
            -1.0557323889818773e-09,
            0.17528734402712923,
            -7.809462160877367e-10
          ]
        ],
        "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": [
          [
            1.0557325014204366e-09,
            -0.1752873440271271,
            7.809484170451242e-10
          ],
          [
            6.110075778664736e-10,
            -0.15400671013394696,
            5.420404125544565e-10
          ],
          [
            2.615518912563175e-10,
            -0.13492358921198644,
            3.5501557249517646e-10
          ],
          [
            1.7672530105983242e-12,
            -0.1159733701537336,
            2.16152984400253e-10
          ],
          [
            -1.7206708280426142e-10,
            -0.09583389544817911,
            1.2415979355751006e-10
          ],
          [
            -2.582581370980108e-10,
            -0.07417604815880807,
            6.819267373003868e-11
          ],
          [
            -2.5344459864129476e-10,
            -0.051050761067594264,
            3.759004219006101e-11
          ],
          [
            -1.577712960276756e-10,
            -0.02626251166366167,
            1.8335666318591848e-11
          ],
          [
            -6.106226635438361e-16,
            -7.771561172376096e-16,
            1.1102230246251565e-16
          ],
          [
            1.5776602246830862e-10,
            0.026262511663659227,
            -1.833139195994704e-11
          ],
          [
            2.534418230837332e-10,
            0.05105076106759021,
            -3.7589265033943775e-11
          ],
          [
            2.582580815868596e-10,
            0.07417604815880596,
            -6.819195208507267e-11
          ],
          [
            1.7206325253482646e-10,
            0.095833895448179,
            -1.2415712902225096e-10
          ],
          [
            -1.7673085217495554e-12,
            0.11597337015373277,
            -2.1615170764377467e-10
          ],
          [
            -2.6155411170236675e-10,
            0.13492358921198766,
            -3.550129634710686e-10
          ],
          [
            -6.110082995114396e-10,
            0.1540067101339453,
            -5.420382476195584e-10
          ],
          [
            -1.0557323903981342e-09,
            0.1752873440271292,
            -7.809461965990749e-10
          ]
        ]
      },
      "incoming_structure_ids": [
        "incoming_00_000",
        "incoming_00_001",
        "incoming_00_002",
        "incoming_00_003",
        "incoming_00_004",
        "incoming_00_005",
        "incoming_00_006",
        "incoming_00_007",
        "incoming_00_008"
      ],
      "reflected_structure_ids": [
        "reflected_00_001",
        "reflected_00_002",
        "reflected_00_003",
        "reflected_00_004",
        "reflected_00_005",
        "reflected_00_006",
        "reflected_00_007",
        "reflected_00_008"
      ]
    },
    {
      "orbit_id": 1,
      "formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.5,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        -0.5,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              1.0557330114521193e-09,
              -0.17528734402712665,
              7.809481960213832e-10
            ],
            "branch_aligned_reduced_polarization": [
              1.0557330114521193e-09,
              -0.17528734402712665,
              7.809481960213832e-10
            ],
            "target_residual": 0.32471265597287335,
            "energy_eV": -169.2763917932688,
            "max_atomic_step_A": 0.03903728412644253,
            "max_log_strain_component": 0.002295365595346981,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.0084026645189437,
            "cell_principal_stretches": [
              1.0029151771509388,
              1.0008212586951069,
              0.9969683376467336
            ],
            "cell_volume_ratio": 1.0006958327373248,
            "cell_rmsd_from_input_A": 0.027504216096755543
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              5.058816717383764e-11,
              -0.4994834503819375,
              -2.7205279960467573e-11
            ],
            "branch_aligned_reduced_polarization": [
              5.058816717383764e-11,
              -0.4994834503819375,
              -2.7205279960467573e-11
            ],
            "target_residual": 0.000516549618062526,
            "energy_eV": -168.91995022791775
          }
        ],
        "iterations": 1
      },
      "parent": {
        "candidate_id": "bec_projection_01",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "C2",
        "spacegroup_number": 5,
        "pointgroup": "2",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          -0.5,
          0.0
        ],
        "formal_class": [
          0.0,
          0.5,
          0.0
        ],
        "target_residual": 0.000516549618062526,
        "parent_symmetrization_rmsd_A": 0.03717937902904915,
        "parent_cell_rmsd_A": 0.027504216096755543,
        "energy_eV": -168.91995022791775,
        "reduced_polarization": [
          5.058816717383764e-11,
          -0.4994834503819375,
          -2.7205279960467573e-11
        ],
        "cartesian_polarization_e_A2": [
          1.2899678746207274e-12,
          -0.007176047886080424,
          -7.435846680779322e-13
        ],
        "ranking_score": 0.545088532289363
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 2,
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.0,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              1.0557330114521193e-09,
              -0.17528734402712665,
              7.809481960213832e-10
            ],
            "branch_aligned_reduced_polarization": [
              1.0557330010207977e-09,
              -0.17528734402712665,
              7.809481960213832e-10
            ],
            "target_residual": 0.5298354951495334,
            "energy_eV": -169.2763917932688,
            "max_atomic_step_A": 0.11368717590032824,
            "max_log_strain_component": 0.013408219618544336,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.0084026645189437,
            "cell_principal_stretches": [
              1.0154824493375278,
              1.0014546299195277,
              0.9829540663413653
            ],
            "cell_volume_ratio": 0.9996245746076068,
            "cell_rmsd_from_input_A": 0.07221703324390574
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.4920648527923683,
              0.014601246285731163,
              -0.0004771012455922141
            ],
            "branch_aligned_reduced_polarization": [
              0.4920648527923683,
              0.014601246285731163,
              -0.0004771012455922141
            ],
            "target_residual": 0.016624998643666386,
            "energy_eV": -165.8746775928364,
            "max_atomic_step_A": 0.0028145626034488426,
            "max_log_strain_component": 0.00026306663085171365,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.0084026645189437,
            "cell_principal_stretches": [
              1.0158558989407263,
              1.0013229435495967,
              0.9827564154114863
            ],
            "cell_volume_ratio": 0.9996596478280722,
            "cell_rmsd_from_input_A": 0.07318997398039172
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.4998168491765406,
              4.30452203841097e-05,
              -2.2860721278276266e-05
            ],
            "branch_aligned_reduced_polarization": [
              0.4998168491765406,
              4.30452203841097e-05,
              -2.2860721278276266e-05
            ],
            "target_residual": 0.00018952500549829172,
            "energy_eV": -165.80843260277652
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_02",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.5,
          0.0,
          0.0
        ],
        "formal_class": [
          0.5,
          0.0,
          0.0
        ],
        "target_residual": 0.00018952500549829172,
        "parent_symmetrization_rmsd_A": 0.10355324658453356,
        "parent_cell_rmsd_A": 0.07318997398039172,
        "energy_eV": -165.80843260277652,
        "reduced_polarization": [
          0.4998168491765406,
          4.30452203841097e-05,
          -2.2860721278276266e-05
        ],
        "cartesian_polarization_e_A2": [
          0.01322978535841828,
          -0.00018022104700237624,
          -1.2577905968558444e-05
        ],
        "ranking_score": 0.6222297900906281
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 3,
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.0,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              1.0557330114521193e-09,
              -0.17528734402712665,
              7.809481960213832e-10
            ],
            "branch_aligned_reduced_polarization": [
              1.0557330114521193e-09,
              -0.17528734402712665,
              7.809481950005193e-10
            ],
            "target_residual": 0.5298354954088449,
            "energy_eV": -169.2763917932688,
            "max_atomic_step_A": 0.11376439874271262,
            "max_log_strain_component": 0.02,
            "step_scale": 0.8800200855456003,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.0084026645189437,
            "cell_principal_stretches": [
              1.020983491706002,
              0.9987274237208622,
              0.980371764635141
            ],
            "cell_volume_ratio": 0.9996696106155613,
            "cell_rmsd_from_input_A": 0.10135098480382926
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.0022724852328178074,
              -0.06997315206911141,
              0.4323058564328774
            ],
            "branch_aligned_reduced_polarization": [
              -0.0022724852328178074,
              -0.06997315206911141,
              0.4323058564328774
            ],
            "target_residual": 0.09738533397235219,
            "energy_eV": -162.419654455007,
            "max_atomic_step_A": 0.02528400654855581,
            "max_log_strain_component": 0.0032647298244534093,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.0084026645189437,
            "cell_principal_stretches": [
              1.0247165758933652,
              0.9979328377871398,
              0.9773774222323833
            ],
            "cell_volume_ratio": 0.9994645104780432,
            "cell_rmsd_from_input_A": 0.11920946959198134
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.00017688708389542422,
              -0.0032077303840202507,
              0.4977532647367185
            ],
            "branch_aligned_reduced_polarization": [
              0.00017688708389542422,
              -0.0032077303840202507,
              0.4977532647367185
            ],
            "target_residual": 0.003920286035519392,
            "energy_eV": -160.20394517002026,
            "max_atomic_step_A": 0.0009560839184131447,
            "max_log_strain_component": 0.00012191035218730424,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.0084026645189437,
            "cell_principal_stretches": [
              1.024857922956101,
              0.9978965117203958,
              0.9772688735744981
            ],
            "cell_volume_ratio": 0.9994549745431149,
            "cell_rmsd_from_input_A": 0.11989076861937828
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              1.6477438874630666e-05,
              -4.245984162492202e-05,
              0.49992944237592024
            ],
            "branch_aligned_reduced_polarization": [
              1.6477438874630666e-05,
              -4.245984162492202e-05,
              0.49992944237592024
            ],
            "target_residual": 8.398048855812422e-05,
            "energy_eV": -160.12287485829012
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_03",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.5
        ],
        "formal_class": [
          0.0,
          0.0,
          0.5
        ],
        "target_residual": 8.398048855812422e-05,
        "parent_symmetrization_rmsd_A": 0.14973251010430827,
        "parent_cell_rmsd_A": 0.11989076861937828,
        "energy_eV": -160.12287485829012,
        "reduced_polarization": [
          1.6477438874630666e-05,
          -4.245984162492202e-05,
          0.49992944237592024
        ],
        "cartesian_polarization_e_A2": [
          -0.0010834853236451345,
          0.0003519285665239448,
          0.014921165799480213
        ],
        "ranking_score": 0.6798731632362691
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 4,
      "formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.5,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.5,
        -0.5,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              1.0557330114521193e-09,
              -0.17528734402712665,
              7.809481960213832e-10
            ],
            "branch_aligned_reduced_polarization": [
              1.0557330010207977e-09,
              -0.17528734402712665,
              7.809481960213832e-10
            ],
            "target_residual": 0.5961864707398388,
            "energy_eV": -169.2763917932688,
            "max_atomic_step_A": 0.11891756435407708,
            "max_log_strain_component": 0.013408219647935505,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.0084026645189437,
            "cell_principal_stretches": [
              1.0181872119847775,
              0.9973302286388359,
              0.9854519892881826
            ],
            "cell_volume_ratio": 1.0006958327104973,
            "cell_rmsd_from_input_A": 0.076583021288851
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.473772607451504,
              -0.4736023438218115,
              -0.008084214582284838
            ],
            "branch_aligned_reduced_polarization": [
              0.473772607451504,
              -0.4736023438218115,
              -0.008084214582284838
            ],
            "target_residual": 0.03807974391992656,
            "energy_eV": -166.6191211086995,
            "max_atomic_step_A": 0.008406541487574155,
            "max_log_strain_component": 0.000979128482299975,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.0084026645189437,
            "cell_principal_stretches": [
              1.019344744336705,
              0.9969668490017389,
              0.9847668721604269
            ],
            "cell_volume_ratio": 1.0007722071935419,
            "cell_rmsd_from_input_A": 0.0813575150980957
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.49910649698807374,
              -0.4993800935411531,
              -0.00010906761473476257
            ],
            "branch_aligned_reduced_polarization": [
              0.49910649698807374,
              -0.4993800935411531,
              -0.00010906761473476257
            ],
            "target_residual": 0.0010929443694101427,
            "energy_eV": -166.32802394950525,
            "max_atomic_step_A": 0.0002654232103651169,
            "max_log_strain_component": 3.211282210095832e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.0084026645189437,
            "cell_principal_stretches": [
              1.0193852827481449,
              0.996957933891981,
              0.9847384856697741
            ],
            "cell_volume_ratio": 1.0007742087548197,
            "cell_rmsd_from_input_A": 0.08152612101537464
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.499974576896896,
              -0.49998606231274706,
              -2.713316971264288e-06
            ],
            "branch_aligned_reduced_polarization": [
              0.499974576896896,
              -0.49998606231274706,
              -2.713316971264288e-06
            ],
            "target_residual": 2.9119673528109045e-05,
            "energy_eV": -166.31742259488615
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_04",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.5,
          -0.5,
          0.0
        ],
        "formal_class": [
          0.5,
          0.5,
          0.0
        ],
        "target_residual": 2.9119673528109045e-05,
        "parent_symmetrization_rmsd_A": 0.11109154188104577,
        "parent_cell_rmsd_A": 0.08152612101537464,
        "energy_eV": -166.31742259488615,
        "reduced_polarization": [
          0.499974576896896,
          -0.49998606231274706,
          -2.713316971264288e-06
        ],
        "cartesian_polarization_e_A2": [
          0.013369132119927244,
          -0.007375678324878539,
          9.703491577080427e-05
        ],
        "ranking_score": 0.6315313114819456
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 5,
      "formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.5,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        -0.5,
        0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              1.0557330114521193e-09,
              -0.17528734402712665,
              7.809481960213832e-10
            ],
            "branch_aligned_reduced_polarization": [
              1.0557330114521193e-09,
              -0.17528734402712665,
              7.809481950005193e-10
            ],
            "target_residual": 0.5961864709702909,
            "energy_eV": -169.2763917932688,
            "max_atomic_step_A": 0.11416587876719742,
            "max_log_strain_component": 0.02,
            "step_scale": 0.880020085094575,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.0084026645189437,
            "cell_principal_stretches": [
              1.0196764647351932,
              1.0023587459453012,
              0.9789945334694831
            ],
            "cell_volume_ratio": 1.0006123211498266,
            "cell_rmsd_from_input_A": 0.10229393661012809
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.010167195481448236,
              -0.5048101183094627,
              0.44695765000838505
            ],
            "branch_aligned_reduced_polarization": [
              -0.010167195481448236,
              -0.5048101183094627,
              0.44695765000838505
            ],
            "target_residual": 0.05422176679841762,
            "energy_eV": -160.3845700583138,
            "max_atomic_step_A": 0.015372621834253497,
            "max_log_strain_component": 0.0020174788946335552,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.0084026645189437,
            "cell_principal_stretches": [
              1.0218614771016192,
              1.0022129013866035,
              0.9769980373578844
            ],
            "cell_volume_ratio": 1.0005659224117944,
            "cell_rmsd_from_input_A": 0.11213764507699309
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -9.695708190371142e-05,
              -0.5000539408118709,
              0.4990124525478656
            ],
            "branch_aligned_reduced_polarization": [
              -9.695708190371142e-05,
              -0.5000539408118709,
              0.4990124525478656
            ],
            "target_residual": 0.0009937606639094545,
            "energy_eV": -158.3501752756162
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_05",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          -0.5,
          0.5
        ],
        "formal_class": [
          0.0,
          0.5,
          0.5
        ],
        "target_residual": 0.0009937606639094545,
        "parent_symmetrization_rmsd_A": 0.14941279633764012,
        "parent_cell_rmsd_A": 0.11213764507699309,
        "energy_eV": -158.3501752756162,
        "reduced_polarization": [
          -9.695708190371142e-05,
          -0.5000539408118709,
          0.4990124525478656
        ],
        "cartesian_polarization_e_A2": [
          -0.001011605079113244,
          -0.0068550723646004785,
          0.014661050006177593
        ],
        "ranking_score": 0.6794347289347074
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 6,
      "formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.0,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              1.0557330114521193e-09,
              -0.17528734402712665,
              7.809481960213832e-10
            ],
            "branch_aligned_reduced_polarization": [
              1.0557330010207977e-09,
              -0.17528734402712665,
              7.809481950005193e-10
            ],
            "target_residual": 0.7285091977040531,
            "energy_eV": -169.2763917932688,
            "max_atomic_step_A": 0.11999999999999998,
            "max_log_strain_component": 0.01279516067390714,
            "step_scale": 0.7460681025917021,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.0084026645189437,
            "cell_principal_stretches": [
              1.0166059042368756,
              0.9994656011588912,
              0.9839156199146284
            ],
            "cell_volume_ratio": 0.9997198936687054,
            "cell_rmsd_from_input_A": 0.07848639234852471
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.3631921409583799,
              -0.052594003796669765,
              0.3667235821957623
            ],
            "branch_aligned_reduced_polarization": [
              0.3631921409583799,
              -0.052594003796669765,
              0.3667235821957623
            ],
            "target_residual": 0.19810381892746448,
            "energy_eV": -163.4268389356136,
            "max_atomic_step_A": 0.05173466741194954,
            "max_log_strain_component": 0.005056261920275817,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.0084026645189437,
            "cell_principal_stretches": [
              1.0230289373096066,
              0.9992932167359757,
              0.9778020619739402
            ],
            "cell_volume_ratio": 0.9996127950639481,
            "cell_rmsd_from_input_A": 0.10855080143774835
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.494673521295516,
              -0.0024681816220218098,
              0.49413371650663657
            ],
            "branch_aligned_reduced_polarization": [
              0.494673521295516,
              -0.0024681816220218098,
              0.49413371650663657
            ],
            "target_residual": 0.008299191402366618,
            "energy_eV": -157.99486074535017,
            "max_atomic_step_A": 0.002262476367984972,
            "max_log_strain_component": 0.00021938016975430247,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.0084026645189437,
            "cell_principal_stretches": [
              1.0233337409074272,
              0.999279930277901,
              0.9775181573297267
            ],
            "cell_volume_ratio": 0.9996070073350675,
            "cell_rmsd_from_input_A": 0.10998637832901746
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.49985610184772133,
              -6.717551394714631e-05,
              0.4997940133691688
            ],
            "branch_aligned_reduced_polarization": [
              0.49985610184772133,
              -6.717551394714631e-05,
              0.4997940133691688
            ],
            "target_residual": 0.0002600955977798763,
            "energy_eV": -157.70787092321763
          }
        ],
        "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,
          0.0,
          0.5
        ],
        "formal_class": [
          0.5,
          0.0,
          0.5
        ],
        "target_residual": 0.0002600955977798763,
        "parent_symmetrization_rmsd_A": 0.17096044825759169,
        "parent_cell_rmsd_A": 0.10998637832901746,
        "energy_eV": -157.70787092321763,
        "reduced_polarization": [
          0.49985610184772133,
          -6.717551394714631e-05,
          0.4997940133691688
        ],
        "cartesian_polarization_e_A2": [
          0.012151302755105738,
          -1.2807048400448118e-05,
          0.014888025435951207
        ],
        "ranking_score": 0.6989772340354058
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 7,
      "formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.5,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.5,
        -0.5,
        0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              1.0557330114521193e-09,
              -0.17528734402712665,
              7.809481960213832e-10
            ],
            "branch_aligned_reduced_polarization": [
              1.0557330010207977e-09,
              -0.17528734402712665,
              7.809481950005193e-10
            ],
            "target_residual": 0.77809916277572,
            "energy_eV": -169.2763917932688,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.012527324069864697,
            "step_scale": 0.7304509198073358,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.0084026645189437,
            "cell_principal_stretches": [
              1.0159947529911315,
              1.0009662050697534,
              0.9838067155257393
            ],
            "cell_volume_ratio": 1.000508223924776,
            "cell_rmsd_from_input_A": 0.07826054591491806
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.3412387252504895,
              -0.4241589313018575,
              0.36570775152560486
            ],
            "branch_aligned_reduced_polarization": [
              0.3412387252504895,
              -0.4241589313018575,
              0.36570775152560486
            ],
            "target_residual": 0.2213400507402007,
            "energy_eV": -163.37737203320097,
            "max_atomic_step_A": 0.05421353953713712,
            "max_log_strain_component": 0.0060512769630588865,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.0084026645189437,
            "cell_principal_stretches": [
              1.0227055873715358,
              1.00088246554876,
              0.977598719464964
            ],
            "cell_volume_ratio": 1.0006779578409501,
            "cell_rmsd_from_input_A": 0.10836499443202928
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.49030194667194243,
              -0.49815642128768656,
              0.4972070215590353
            ],
            "branch_aligned_reduced_polarization": [
              0.49030194667194243,
              -0.49815642128768656,
              0.4972070215590353
            ],
            "target_residual": 0.010259227524235798,
            "energy_eV": -157.79436529629783,
            "max_atomic_step_A": 0.002782416930410705,
            "max_log_strain_component": 0.00034961437782365506,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.0084026645189437,
            "cell_principal_stretches": [
              1.0229983187390324,
              1.0008334800140786,
              0.9773763178333215
            ],
            "cell_volume_ratio": 1.0006876885198108,
            "cell_rmsd_from_input_A": 0.10947019635578696
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.4996319193039564,
              -0.4999758727836036,
              0.49989871133099695
            ],
            "branch_aligned_reduced_polarization": [
              0.4996319193039564,
              -0.4999758727836036,
              0.49989871133099695
            ],
            "target_residual": 0.00038252439901186996,
            "energy_eV": -157.58426417541534
          }
        ],
        "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,
          0.5
        ],
        "formal_class": [
          0.5,
          0.5,
          0.5
        ],
        "target_residual": 0.00038252439901186996,
        "parent_symmetrization_rmsd_A": 0.17202768427855925,
        "parent_cell_rmsd_A": 0.10947019635578696,
        "energy_eV": -157.58426417541534,
        "reduced_polarization": [
          0.4996319193039564,
          -0.4999758727836036,
          0.49989871133099695
        ],
        "cartesian_polarization_e_A2": [
          0.01235448855669922,
          -0.007231622550277368,
          0.014770483188123662
        ],
        "ranking_score": 0.7001602821655297
      },
      "branch_status": "awaiting_branch_sampling"
    }
  ],
  "sampled_polarization_branches": [
    {
      "orbit_id": 0,
      "candidate_id": "inversion_parent_endpoint_00",
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "construction": "MACEField-BEC-parent plus variable-cell P-N-P path and symmetric log-strain continuation beyond both polar endpoints",
      "geometry_diagnostics": {
        "collision_aware": false,
        "permutations_tested": 1,
        "selected_order": [
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          10,
          11,
          12,
          13,
          14,
          15,
          16,
          17,
          18,
          19,
          20,
          21,
          22,
          23,
          24,
          25
        ],
        "endpoint_rmsd_A": 0.5130989606187063,
        "minimum_distance_A_by_image": [
          1.3867579635564147,
          1.3593974900611008,
          1.33523165443469,
          1.3144366681385107,
          1.297174655400128,
          1.2835881610549793,
          1.273794801493263,
          1.2678824763931043,
          1.2659055652381248
        ],
        "minimum_distance_A": 1.2659055652381248,
        "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": [
          297.1559394846886,
          297.1559394846886,
          297.1559394846886,
          297.1559394846886,
          297.1559394846886,
          297.1559394846886,
          297.1559394846886,
          297.1559394846886,
          297.1559394846886
        ],
        "cell_deformation_log_strain_norm": 0.0
      },
      "parent_reduced_polarization": [
        -5.921568467759461e-16,
        -7.564335466138093e-16,
        9.268645515181239e-17
      ],
      "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": [
          -169.2763917932688,
          -168.64870775511008,
          -167.0347193969657,
          -164.71976600522936,
          -162.04390210610066,
          -159.38823195092283,
          -157.14775603117124,
          -155.65854762382554,
          -155.13786093026255
        ],
        "cartesian_polarizations_e_A2": [
          [
            2.630370195442685e-11,
            -0.0025180268404641315,
            2.3245053092002703e-11
          ],
          [
            1.503208992597809e-11,
            -0.0022123276034625963,
            1.613391863637153e-11
          ],
          [
            6.173592594454435e-12,
            -0.0019381959429709938,
            1.0567096171892766e-11
          ],
          [
            -4.1216095191422667e-13,
            -0.0016659734360570263,
            6.433828402953758e-12
          ],
          [
            -4.820969615108774e-12,
            -0.001376667107965327,
            3.695636321583407e-12
          ],
          [
            -6.9849717283370304e-12,
            -0.0010655491485713506,
            2.02976590117746e-12
          ],
          [
            -6.7925009199548244e-12,
            -0.0007333512143034696,
            1.1188748191732849e-12
          ],
          [
            -4.217633191297854e-12,
            -0.0003772645973623073,
            5.457643927497075e-13
          ],
          [
            -1.5880555598950303e-17,
            -1.0866272085828839e-17,
            2.758827096934479e-18
          ]
        ],
        "raw_reduced_polarization": [
          [
            1.0557325053006017e-09,
            -0.1752873440271271,
            7.809483868370802e-10
          ],
          [
            6.110076288947086e-10,
            -0.15400671013394696,
            5.420403938234027e-10
          ],
          [
            2.6155192403807635e-10,
            -0.13492358921198647,
            3.5501561026036577e-10
          ],
          [
            1.767223624500699e-12,
            -0.11597337015373359,
            2.1615299791257371e-10
          ],
          [
            -1.720671017745592e-10,
            -0.09583389544817913,
            1.2415980347534785e-10
          ],
          [
            -2.5825816418232503e-10,
            -0.07417604815880806,
            6.819267737989408e-11
          ],
          [
            -2.5344460609393307e-10,
            -0.05105076106759428,
            3.759008343184321e-11
          ],
          [
            -1.5777131746544268e-10,
            -0.026262511663661652,
            1.8335678581764078e-11
          ],
          [
            -5.921568467759461e-16,
            -7.564335466138093e-16,
            9.268645515181239e-17
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            1.0557325053006017e-09,
            -0.1752873440271271,
            7.809483868370802e-10
          ],
          [
            6.110076288947086e-10,
            -0.15400671013394696,
            5.420403938234027e-10
          ],
          [
            2.6155192403807635e-10,
            -0.13492358921198647,
            3.5501561026036577e-10
          ],
          [
            1.7672236245006736e-12,
            -0.11597337015373359,
            2.1615299791257371e-10
          ],
          [
            -1.720671017745592e-10,
            -0.09583389544817913,
            1.2415980347534785e-10
          ],
          [
            -2.5825816418232503e-10,
            -0.07417604815880806,
            6.819267737989408e-11
          ],
          [
            -2.5344460609393307e-10,
            -0.05105076106759428,
            3.759008343184321e-11
          ],
          [
            -1.5777131746544268e-10,
            -0.026262511663661652,
            1.8335678581764078e-11
          ],
          [
            -5.921568467881263e-16,
            -7.563394355258879e-16,
            9.268645515192769e-17
          ]
        ],
        "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": [
          [
            1.0557325014204366e-09,
            -0.1752873440271271,
            7.809484170451242e-10
          ],
          [
            6.110075778664736e-10,
            -0.15400671013394696,
            5.420404125544565e-10
          ],
          [
            2.615518912563175e-10,
            -0.13492358921198644,
            3.5501557249517646e-10
          ],
          [
            1.7672530105983242e-12,
            -0.1159733701537336,
            2.16152984400253e-10
          ],
          [
            -1.7206708280426142e-10,
            -0.09583389544817911,
            1.2415979355751006e-10
          ],
          [
            -2.582581370980108e-10,
            -0.07417604815880807,
            6.819267373003868e-11
          ],
          [
            -2.5344459864129476e-10,
            -0.051050761067594264,
            3.759004219006101e-11
          ],
          [
            -1.577712960276756e-10,
            -0.02626251166366167,
            1.8335666318591848e-11
          ],
          [
            -6.106226635438361e-16,
            -7.771561172376096e-16,
            1.1102230246251565e-16
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -155.13786093026255,
          -155.65854762382554,
          -157.14775603117124,
          -159.38823195092283,
          -162.04390210610063,
          -164.7197660052294,
          -167.03471939696564,
          -168.64870775511005,
          -169.2763917932687
        ],
        "cartesian_polarizations_e_A2": [
          [
            -3.905733983764193e-17,
            2.070791032557181e-18,
            2.4148178267581712e-18
          ],
          [
            4.217484059137153e-12,
            0.0003772645973622731,
            -5.456368267615148e-13
          ],
          [
            6.792424122688475e-12,
            0.0007333512143034113,
            -1.118850076223642e-12
          ],
          [
            6.984966962887557e-12,
            0.0010655491485713202,
            -2.0297447474310017e-12
          ],
          [
            4.82086069011715e-12,
            0.0013766671079653255,
            -3.695556476424132e-12
          ],
          [
            4.1215600589939083e-13,
            0.001665973436057015,
            -6.433790590741498e-12
          ],
          [
            -6.173655654316097e-12,
            0.0019381959429710107,
            -1.056701799335647e-11
          ],
          [
            -1.5032111801547936e-11,
            0.002212327603462573,
            -1.6133854771363045e-11
          ],
          [
            -2.6303703482880678e-11,
            0.002518026840464162,
            -2.3244988479302823e-11
          ]
        ],
        "raw_reduced_polarization": [
          [
            -1.4681477918777824e-15,
            1.4415392810714994e-16,
            8.112900748594248e-17
          ],
          [
            1.577660304053023e-10,
            0.026262511663659272,
            -1.8331392833209317e-11
          ],
          [
            2.5344177317300784e-10,
            0.05105076106759022,
            -3.75892521596352e-11
          ],
          [
            2.5825804123292935e-10,
            0.07417604815880594,
            -6.819196669172715e-11
          ],
          [
            1.7206320424853297e-10,
            0.09583389544817902,
            -1.2415712097132922e-10
          ],
          [
            -1.7673085236055345e-12,
            0.1159733701537328,
            -2.161517275611553e-10
          ],
          [
            -2.6155409436569923e-10,
            0.13492358921198763,
            -3.550129837487564e-10
          ],
          [
            -6.110082828170376e-10,
            0.15400671013394532,
            -5.420382481937433e-10
          ],
          [
            -1.0557323889818773e-09,
            0.17528734402712923,
            -7.809462160877367e-10
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -1.4681477918777824e-15,
            1.4415392810714994e-16,
            8.112900748594248e-17
          ],
          [
            1.577660304053023e-10,
            0.026262511663659272,
            -1.8331392833209317e-11
          ],
          [
            2.5344177317300784e-10,
            0.05105076106759022,
            -3.75892521596352e-11
          ],
          [
            2.5825804123292935e-10,
            0.07417604815880594,
            -6.819196669172715e-11
          ],
          [
            1.7206320424853297e-10,
            0.09583389544817902,
            -1.2415712097132922e-10
          ],
          [
            -1.767308523605542e-12,
            0.1159733701537328,
            -2.161517275611553e-10
          ],
          [
            -2.6155409436569923e-10,
            0.13492358921198763,
            -3.550129837487564e-10
          ],
          [
            -6.110082828170376e-10,
            0.15400671013394532,
            -5.420382481937433e-10
          ],
          [
            -1.0557323889818773e-09,
            0.17528734402712923,
            -7.809462160877367e-10
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          -1.0557336896142953e-09,
          0.1752873440271256,
          -7.809482014641699e-10
        ],
        "actual_opposite_endpoint_branch_residual": 4.342086799987132e-15
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            1.0557325053006017e-09,
            -0.1752873440271271,
            7.809483868370802e-10
          ],
          [
            6.110076288947086e-10,
            -0.15400671013394696,
            5.420403938234027e-10
          ],
          [
            2.6155192403807635e-10,
            -0.13492358921198647,
            3.5501561026036577e-10
          ],
          [
            1.767223624500699e-12,
            -0.11597337015373359,
            2.1615299791257371e-10
          ],
          [
            -1.720671017745592e-10,
            -0.09583389544817913,
            1.2415980347534785e-10
          ],
          [
            -2.5825816418232503e-10,
            -0.07417604815880806,
            6.819267737989408e-11
          ],
          [
            -2.5344460609393307e-10,
            -0.05105076106759428,
            3.759008343184321e-11
          ],
          [
            -1.5777131746544268e-10,
            -0.026262511663661652,
            1.8335678581764078e-11
          ],
          [
            -5.921568467759461e-16,
            -7.564335466138093e-16,
            9.268645515181239e-17
          ],
          [
            1.577660304053023e-10,
            0.026262511663659272,
            -1.8331392833209317e-11
          ],
          [
            2.5344177317300784e-10,
            0.05105076106759022,
            -3.75892521596352e-11
          ],
          [
            2.5825804123292935e-10,
            0.07417604815880594,
            -6.819196669172715e-11
          ],
          [
            1.7206320424853297e-10,
            0.09583389544817902,
            -1.2415712097132922e-10
          ],
          [
            -1.7673085236055345e-12,
            0.1159733701537328,
            -2.161517275611553e-10
          ],
          [
            -2.6155409436569923e-10,
            0.13492358921198763,
            -3.550129837487564e-10
          ],
          [
            -6.110082828170376e-10,
            0.15400671013394532,
            -5.420382481937433e-10
          ],
          [
            -1.0557323889818773e-09,
            0.17528734402712923,
            -7.809462160877367e-10
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            1.0557325053006017e-09,
            -0.1752873440271271,
            7.809483868370802e-10
          ],
          [
            6.110076288947086e-10,
            -0.15400671013394696,
            5.420403938234027e-10
          ],
          [
            2.6155192403807635e-10,
            -0.13492358921198647,
            3.5501561026036577e-10
          ],
          [
            1.7672236245006736e-12,
            -0.11597337015373359,
            2.1615299791257371e-10
          ],
          [
            -1.720671017745592e-10,
            -0.09583389544817913,
            1.2415980347534785e-10
          ],
          [
            -2.5825816418232503e-10,
            -0.07417604815880806,
            6.819267737989408e-11
          ],
          [
            -2.5344460609393307e-10,
            -0.05105076106759428,
            3.759008343184321e-11
          ],
          [
            -1.5777131746544268e-10,
            -0.026262511663661652,
            1.8335678581764078e-11
          ],
          [
            -5.921568467881263e-16,
            -7.563394355258879e-16,
            9.268645515192769e-17
          ],
          [
            1.577660304053023e-10,
            0.026262511663659272,
            -1.8331392833209317e-11
          ],
          [
            2.5344177317300784e-10,
            0.05105076106759022,
            -3.75892521596352e-11
          ],
          [
            2.5825804123292935e-10,
            0.07417604815880594,
            -6.819196669172715e-11
          ],
          [
            1.7206320424853297e-10,
            0.09583389544817902,
            -1.2415712097132922e-10
          ],
          [
            -1.767308523605542e-12,
            0.1159733701537328,
            -2.161517275611553e-10
          ],
          [
            -2.6155409436569923e-10,
            0.13492358921198763,
            -3.550129837487564e-10
          ],
          [
            -6.110082828170376e-10,
            0.15400671013394532,
            -5.420382481937433e-10
          ],
          [
            -1.0557323889818773e-09,
            0.17528734402712923,
            -7.809462160877367e-10
          ]
        ],
        "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": [
          [
            1.0557325014204366e-09,
            -0.1752873440271271,
            7.809484170451242e-10
          ],
          [
            6.110075778664736e-10,
            -0.15400671013394696,
            5.420404125544565e-10
          ],
          [
            2.615518912563175e-10,
            -0.13492358921198644,
            3.5501557249517646e-10
          ],
          [
            1.7672530105983242e-12,
            -0.1159733701537336,
            2.16152984400253e-10
          ],
          [
            -1.7206708280426142e-10,
            -0.09583389544817911,
            1.2415979355751006e-10
          ],
          [
            -2.582581370980108e-10,
            -0.07417604815880807,
            6.819267373003868e-11
          ],
          [
            -2.5344459864129476e-10,
            -0.051050761067594264,
            3.759004219006101e-11
          ],
          [
            -1.577712960276756e-10,
            -0.02626251166366167,
            1.8335666318591848e-11
          ],
          [
            -6.106226635438361e-16,
            -7.771561172376096e-16,
            1.1102230246251565e-16
          ],
          [
            1.5776602246830862e-10,
            0.026262511663659227,
            -1.833139195994704e-11
          ],
          [
            2.534418230837332e-10,
            0.05105076106759021,
            -3.7589265033943775e-11
          ],
          [
            2.582580815868596e-10,
            0.07417604815880596,
            -6.819195208507267e-11
          ],
          [
            1.7206325253482646e-10,
            0.095833895448179,
            -1.2415712902225096e-10
          ],
          [
            -1.7673085217495554e-12,
            0.11597337015373277,
            -2.1615170764377467e-10
          ],
          [
            -2.6155411170236675e-10,
            0.13492358921198766,
            -3.550129634710686e-10
          ],
          [
            -6.110082995114396e-10,
            0.1540067101339453,
            -5.420382476195584e-10
          ],
          [
            -1.0557323903981342e-09,
            0.1752873440271292,
            -7.809461965990749e-10
          ]
        ]
      },
      "incoming_structure_ids": [
        "incoming_00_000",
        "incoming_00_001",
        "incoming_00_002",
        "incoming_00_003",
        "incoming_00_004",
        "incoming_00_005",
        "incoming_00_006",
        "incoming_00_007",
        "incoming_00_008"
      ],
      "reflected_structure_ids": [
        "reflected_00_001",
        "reflected_00_002",
        "reflected_00_003",
        "reflected_00_004",
        "reflected_00_005",
        "reflected_00_006",
        "reflected_00_007",
        "reflected_00_008"
      ],
      "positive_extension_structure_ids": [
        "extension_plus_00_000",
        "extension_plus_00_001",
        "extension_plus_00_002",
        "extension_plus_00_003"
      ],
      "negative_extension_structure_ids": [
        "extension_minus_00_000",
        "extension_minus_00_001",
        "extension_minus_00_002",
        "extension_minus_00_003"
      ],
      "extension": {
        "enabled": true,
        "fraction_beyond_polar_endpoint": 0.35,
        "images_per_side": 4,
        "construction": "continue fractional atomic displacements and symmetric log strain beyond +P; reflect these structures about N for the -P side",
        "positive_path_coordinates": [
          1.35,
          1.2625,
          1.175,
          1.0875
        ],
        "negative_path_coordinates": [
          -1.0875,
          -1.175,
          -1.2625,
          -1.35
        ]
      },
      "branch_coordinates": [
        1.35,
        1.2625,
        1.175,
        1.0875,
        1.0,
        0.875,
        0.75,
        0.625,
        0.5,
        0.375,
        0.25,
        0.125,
        0.0,
        -0.125,
        -0.25,
        -0.375,
        -0.5,
        -0.625,
        -0.75,
        -0.875,
        -1.0,
        -1.0875,
        -1.175,
        -1.2625,
        -1.35
      ],
      "parent": {
        "candidate_id": "inversion_parent_endpoint_00",
        "source": "same_species_inversion_center_projection_from_endpoint",
        "spacegroup": "C2/m",
        "spacegroup_number": 12,
        "pointgroup": "2/m",
        "has_inversion": true,
        "is_polar_point_group": false,
        "nonpolar_parent_hypothesis": true,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.0
        ],
        "formal_class": [
          0.0,
          0.0,
          0.0
        ],
        "target_residual": 1.6655551327964686e-15,
        "parent_symmetrization_rmsd_A": 0.5130989606187063,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -155.13786093026255,
        "reduced_polarization": [
          9.572586810313111e-17,
          1.3890152731305784e-15,
          9.14082616381336e-16
        ],
        "cartesian_polarization_e_A2": [
          5.944642575915841e-19,
          1.995339571701272e-17,
          2.720781463460989e-17
        ],
        "ranking_score": 0.5130989606187096
      }
    }
  ],
  "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": 53,
      "full_response": 19,
      "energy_polarization": 34
    },
    "model_evaluations_for_recovery_and_path_properties": {
      "total": 78,
      "full_response": 44,
      "energy_polarization": 34
    },
    "elapsed_seconds": 637.8043806540081
  }
}