{
  "schema": "ferrofinder.endpoint_parent_recovery.v4_variable_cell",
  "status": "complete",
  "input_atom_count": 16,
  "input_formula": "Mo4O12",
  "input_spacegroup": "Pc",
  "input_pointgroup": "m",
  "input_is_polar_point_group": true,
  "input_energy_eV": -110.95861778358491,
  "input_cartesian_polarization_e_A2": [
    -0.0028950567655400706,
    -3.760818853133067e-17,
    0.0004648784770503524
  ],
  "input_reduced_polarization": [
    -0.08971123919457788,
    -1.5500876478885064e-15,
    0.017428981834154072
  ],
  "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": [
        0.5,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        -0.5,
        0.0,
        0.0
      ]
    },
    {
      "orbit_id": 2,
      "representative_formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.5
      ]
    },
    {
      "orbit_id": 3,
      "representative_formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        -0.5,
        0.0
      ]
    },
    {
      "orbit_id": 4,
      "representative_formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        -0.5,
        0.0,
        0.5
      ]
    },
    {
      "orbit_id": 5,
      "representative_formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        -0.5,
        -0.5,
        0.0
      ]
    },
    {
      "orbit_id": 6,
      "representative_formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        -0.5,
        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": "P2/c",
      "spacegroup_number": 13,
      "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": 8.276489025558611e-16,
      "parent_symmetrization_rmsd_A": 0.0959030061811417,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -111.0250183706618,
      "reduced_polarization": [
        7.909863558363416e-17,
        8.003720534849152e-16,
        -1.9532201041118933e-16
      ],
      "cartesian_polarization_e_A2": [
        2.5502284706702988e-18,
        1.94186071501642e-17,
        -4.916103075990937e-18
      ],
      "ranking_score": 0.09590300618114335
    },
    {
      "candidate_id": "inversion_parent_endpoint_01",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "P2_1/c",
      "spacegroup_number": 14,
      "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": 5.230152793269513e-16,
      "parent_symmetrization_rmsd_A": 0.24527680087046513,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -108.73947088305039,
      "reduced_polarization": [
        3.945951421388275e-16,
        3.3686545289080285e-16,
        6.604031237480397e-17
      ],
      "cartesian_polarization_e_A2": [
        1.2735779531239021e-17,
        8.173021363834932e-18,
        1.528600800190932e-18
      ],
      "ranking_score": 0.2452768008704662
    },
    {
      "candidate_id": "bec_projection_00",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Pc",
      "spacegroup_number": 7,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 0.00020565233414412523,
      "parent_symmetrization_rmsd_A": 0.011240918399942531,
      "parent_cell_rmsd_A": 0.00019578245359412486,
      "energy_eV": -110.95551161554108,
      "reduced_polarization": [
        0.00020558391349679222,
        -2.4721436277287994e-15,
        5.304436847620026e-06
      ],
      "cartesian_polarization_e_A2": [
        6.6347804265976685e-06,
        -5.997310958773669e-17,
        6.771951735579739e-08
      ],
      "ranking_score": 0.5117011686816293
    },
    {
      "candidate_id": "inversion_parent_bec_00_00",
      "source": "same_species_inversion_center_projection_after_BEC",
      "spacegroup": "P2/c",
      "spacegroup_number": 13,
      "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": 2.5821333755816372e-15,
      "parent_symmetrization_rmsd_A": 0.09590303805608531,
      "parent_cell_rmsd_A": 0.00019578245359412486,
      "energy_eV": -111.02493492304467,
      "reduced_polarization": [
        2.4316861785831243e-15,
        -6.483874923357751e-16,
        -5.778483866577361e-16
      ],
      "cartesian_polarization_e_A2": [
        7.846891490116778e-17,
        -1.573065169514405e-17,
        -1.5239068829670798e-17
      ],
      "ranking_score": 0.09595198366948901
    },
    {
      "candidate_id": "bec_projection_01",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Pc",
      "spacegroup_number": 7,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        -0.5,
        0.0,
        0.0
      ],
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_residual": 4.552791508279166e-05,
      "parent_symmetrization_rmsd_A": 0.05206979240436622,
      "parent_cell_rmsd_A": 0.0009717228177274335,
      "energy_eV": -110.94740383012012,
      "reduced_polarization": [
        -0.49995447209126387,
        -3.0324888510668937e-15,
        2.4039558336991552e-08
      ],
      "cartesian_polarization_e_A2": [
        -0.016135770713845286,
        -2.974785901112609e-17,
        0.00015948350877200592
      ],
      "ranking_score": 0.5524037789389636
    },
    {
      "candidate_id": "bec_projection_02",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Pc",
      "spacegroup_number": 7,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.5
      ],
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_residual": 2.6888688227038037e-07,
      "parent_symmetrization_rmsd_A": 0.07104048435397128,
      "parent_cell_rmsd_A": 0.0012201143157704432,
      "energy_eV": -110.61463453158926,
      "reduced_polarization": [
        -1.2821035774170803e-07,
        8.194464566464079e-16,
        0.4999997636480175
      ],
      "cartesian_polarization_e_A2": [
        6.954103283928004e-06,
        -2.901538581267646e-17,
        0.012521111146399148
      ],
      "ranking_score": 0.5713460507066784
    },
    {
      "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,
        -0.5,
        0.0
      ],
      "formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_residual": 8.571828841704486e-07,
      "parent_symmetrization_rmsd_A": 0.07078994678468707,
      "parent_cell_rmsd_A": 0.0029624125919889346,
      "energy_eV": -110.64818890174182,
      "reduced_polarization": [
        -1.6028024596842586e-07,
        -0.5000004912046978,
        -6.839522531001453e-07
      ],
      "cartesian_polarization_e_A2": [
        5.079569450276368e-06,
        -0.012130596121461673,
        -3.7923952683228357e-06
      ],
      "ranking_score": 0.5715322642984526
    },
    {
      "candidate_id": "bec_projection_04",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Pc",
      "spacegroup_number": 7,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        -0.5,
        0.0,
        0.5
      ],
      "formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_residual": 0.00013199377308641924,
      "parent_symmetrization_rmsd_A": 0.08904774022217431,
      "parent_cell_rmsd_A": 0.0013487104636359761,
      "energy_eV": -110.59117151300256,
      "reduced_polarization": [
        -0.49986800753466165,
        -1.128439512473059e-16,
        0.50000058756063
      ],
      "cartesian_polarization_e_A2": [
        -0.0161343985460647,
        5.65694842383216e-18,
        0.01268393223570038
      ],
      "ranking_score": 0.5896489053842562
    },
    {
      "candidate_id": "bec_projection_05",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        -0.5,
        -0.5,
        0.0
      ],
      "formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_residual": 5.400774693979403e-05,
      "parent_symmetrization_rmsd_A": 0.08694448447097868,
      "parent_cell_rmsd_A": 0.0030943307673261416,
      "energy_eV": -110.63681189326809,
      "reduced_polarization": [
        -0.49994603375608904,
        -0.49999849940027513,
        -1.49313365810422e-06
      ],
      "cartesian_polarization_e_A2": [
        -0.016130426420860756,
        -0.012125419762301448,
        0.00015569836432643142
      ],
      "ranking_score": 0.5878260826566898
    },
    {
      "candidate_id": "bec_projection_06",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        -0.5,
        0.5
      ],
      "formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_residual": 4.073398269681374e-06,
      "parent_symmetrization_rmsd_A": 0.09884880361905855,
      "parent_cell_rmsd_A": 0.0031291893039391496,
      "energy_eV": -110.27599201747172,
      "reduced_polarization": [
        -1.2943788269353195e-06,
        -0.4999964385786658,
        0.5000014944681316
      ],
      "cartesian_polarization_e_A2": [
        1.1869698913189174e-05,
        -0.012129899189441587,
        0.012517493232814774
      ],
      "ranking_score": 0.5996392477415827
    },
    {
      "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": 0.00015273332814325349,
      "parent_symmetrization_rmsd_A": 0.11223785454795027,
      "parent_cell_rmsd_A": 0.0031624957457244227,
      "energy_eV": -110.2552734786492,
      "reduced_polarization": [
        -0.4998496348051427,
        -0.49997418120556186,
        0.49999284684999407
      ],
      "cartesian_polarization_e_A2": [
        -0.016128970373847588,
        -0.012124508561702664,
        0.01268011542180124
      ],
      "ranking_score": 0.6133339451406679
    }
  ],
  "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": [
              -0.08971123919457788,
              -1.5500876478885064e-15,
              0.017428981834154072
            ],
            "branch_aligned_reduced_polarization": [
              -0.08971123919457788,
              -1.5500876478885064e-15,
              0.017428981834154072
            ],
            "target_residual": 0.09138859800654588,
            "energy_eV": -110.95861778358491,
            "max_atomic_step_A": 0.009536675497492158,
            "max_log_strain_component": 2.925216384545506e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.371188506416751,
            "cell_principal_stretches": [
              1.0000334133964597,
              1.0000234179489114,
              0.999998991937501
            ],
            "cell_volume_ratio": 1.0000558240080555,
            "cell_rmsd_from_input_A": 0.00019578245359412486
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.00020558391349679222,
              -2.4721436277287994e-15,
              5.304436847620026e-06
            ],
            "branch_aligned_reduced_polarization": [
              0.00020558391349679222,
              -2.4721436277287994e-15,
              5.304436847620026e-06
            ],
            "target_residual": 0.00020565233414412523,
            "energy_eV": -110.95551161554108
          }
        ],
        "iterations": 1
      },
      "parent": {
        "candidate_id": "inversion_parent_endpoint_00",
        "source": "same_species_inversion_center_projection_from_endpoint",
        "spacegroup": "P2/c",
        "spacegroup_number": 13,
        "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": 8.276489025558611e-16,
        "parent_symmetrization_rmsd_A": 0.0959030061811417,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -111.0250183706618,
        "reduced_polarization": [
          7.909863558363416e-17,
          8.003720534849152e-16,
          -1.9532201041118933e-16
        ],
        "cartesian_polarization_e_A2": [
          2.5502284706702988e-18,
          1.94186071501642e-17,
          -4.916103075990937e-18
        ],
        "ranking_score": 0.09590300618114335
      },
      "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": [
          -110.95861778358494,
          -110.9745580332976,
          -110.98817239307883,
          -110.99955554146509,
          -111.00878661616073,
          -111.0159199687332,
          -111.02098865803565,
          -111.02401443520063,
          -111.02501837066177
        ],
        "cartesian_polarizations_e_A2": [
          [
            -0.0028950567655400467,
            -9.832206151981874e-18,
            0.00046487847705033126
          ],
          [
            -0.002533938523460814,
            -4.6702979221913905e-17,
            0.0004080054394661359
          ],
          [
            -0.0021724307309627347,
            -3.9328824607927496e-18,
            0.0003506249000668985
          ],
          [
            -0.0018106401060105884,
            1.9172801996364654e-17,
            0.0002928335175459987
          ],
          [
            -0.0014486586636549494,
            1.4748309227972812e-18,
            0.0002347025552171934
          ],
          [
            -0.0010865608862344349,
            -5.45687441434994e-17,
            0.00017629247086128547
          ],
          [
            -0.0007243993750162198,
            -1.6714750458369185e-17,
            0.00011765765206134187
          ],
          [
            -0.0003622059147645466,
            -3.121725453254245e-17,
            5.886812734121368e-05
          ],
          [
            2.7484088759211833e-17,
            -1.9172801996364654e-17,
            -5.899323691189125e-17
          ]
        ],
        "raw_reduced_polarization": [
          [
            -0.08971123919457714,
            -4.0525167265058997e-16,
            0.01742898183415324
          ],
          [
            -0.07852102239334155,
            -1.9249454450903024e-15,
            0.015299449405212523
          ],
          [
            -0.06731872711669339,
            -1.6210066906023596e-16,
            0.013149802930335134
          ],
          [
            -0.05610766159754246,
            7.902407616686504e-16,
            0.010983860567264591
          ],
          [
            -0.04489067808653496,
            6.078775089758849e-17,
            0.008804432088124476
          ],
          [
            -0.03367008540621181,
            -2.249146783210774e-15,
            0.006613902628847087
          ],
          [
            -0.022447514293042335,
            -6.889278435060028e-16,
            0.004414423498638072
          ],
          [
            -0.011223950734153047,
            -1.286674060665623e-15,
            0.002208778787376187
          ],
          [
            8.525517458119213e-16,
            -7.902407616686504e-16,
            -2.3450875838943634e-15
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -0.08971123919457714,
            -4.0525167265058997e-16,
            0.01742898183415324
          ],
          [
            -0.07852102239334155,
            -1.9249454450903024e-15,
            0.015299449405212523
          ],
          [
            -0.06731872711669339,
            -1.62100669060236e-16,
            0.013149802930335134
          ],
          [
            -0.05610766159754246,
            7.902407616686503e-16,
            0.010983860567264591
          ],
          [
            -0.04489067808653496,
            6.078775089758848e-17,
            0.008804432088124476
          ],
          [
            -0.03367008540621181,
            -2.249146783210774e-15,
            0.006613902628847087
          ],
          [
            -0.022447514293042335,
            -6.889278435060027e-16,
            0.004414423498638072
          ],
          [
            -0.011223950734153047,
            -1.286674060665623e-15,
            0.002208778787376187
          ],
          [
            8.517492267046123e-16,
            -7.902407616686504e-16,
            -2.344912458651649e-15
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            -0.08971123919457713,
            -3.885780586188048e-16,
            0.0174289818341532
          ],
          [
            -0.07852102239334158,
            -1.942890293094024e-15,
            0.01529944940521255
          ],
          [
            -0.0673187271166934,
            -1.6653345369377348e-16,
            0.013149802930335186
          ],
          [
            -0.056107661597542435,
            7.771561172376096e-16,
            0.010983860567264636
          ],
          [
            -0.04489067808653496,
            1.1102230246251565e-16,
            0.008804432088124425
          ],
          [
            -0.0336700854062118,
            -2.275957200481571e-15,
            0.00661390262884709
          ],
          [
            -0.022447514293042314,
            -6.661338147750939e-16,
            0.004414423498638076
          ],
          [
            -0.011223950734153054,
            -1.27675647831893e-15,
            0.002208778787376242
          ],
          [
            8.881784197001252e-16,
            -7.771561172376096e-16,
            -2.3314683517128287e-15
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -111.02501837066178,
          -111.02401443520061,
          -111.02098865803565,
          -111.0159199687332,
          -111.00878661616075,
          -110.99955554146506,
          -110.98817239307883,
          -110.9745580332976,
          -110.95861778358494
        ],
        "cartesian_polarizations_e_A2": [
          [
            2.1108517582536086e-17,
            -4.522814829911662e-17,
            -8.848985536783687e-18
          ],
          [
            0.0003622059147646134,
            -7.865764921585499e-17,
            -5.886812734125251e-05
          ],
          [
            0.0007243993750163046,
            -5.973065237328989e-17,
            -0.00011765765206132171
          ],
          [
            0.001086560886234607,
            -8.086989560005092e-17,
            -0.00017629247086134545
          ],
          [
            0.0014486586636550216,
            -6.5629976064479e-17,
            -0.000234702555217274
          ],
          [
            0.0018106401060107118,
            -6.907124821767267e-17,
            -0.00029283351754600317
          ],
          [
            0.002172430730962847,
            -3.613335760853339e-17,
            -0.0003506249000669059
          ],
          [
            0.0025339385234609394,
            -3.9328824607927496e-18,
            -0.00040800543946616444
          ],
          [
            0.0028950567655401586,
            -6.784222244867494e-17,
            -0.00046487847705034015
          ]
        ],
        "raw_reduced_polarization": [
          [
            6.541933009830714e-16,
            -1.864157694192714e-15,
            -3.4509950507565705e-16
          ],
          [
            0.011223950734155117,
            -3.2420133812047198e-15,
            -0.0022087787873777114
          ],
          [
            0.02244751429304496,
            -2.461903911352334e-15,
            -0.004414423498637234
          ],
          [
            0.033670085406217146,
            -3.3331950075511027e-15,
            -0.006613902628849415
          ],
          [
            0.044890678086537204,
            -2.7050549149426876e-15,
            -0.008804432088127666
          ],
          [
            0.05610766159754628,
            -2.8468930003703945e-15,
            -0.010983860567264721
          ],
          [
            0.06731872711669687,
            -1.489299896990918e-15,
            -0.013149802930335385
          ],
          [
            0.07852102239334542,
            -1.6210066906023596e-16,
            -0.01529944940521361
          ],
          [
            0.0897112391945806,
            -2.796236541289071e-15,
            -0.017428981834153548
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            6.541933009830714e-16,
            -1.864157694192714e-15,
            -3.4509950507565705e-16
          ],
          [
            0.011223950734155117,
            -3.2420133812047198e-15,
            -0.0022087787873777114
          ],
          [
            0.02244751429304496,
            -2.461903911352334e-15,
            -0.004414423498637234
          ],
          [
            0.033670085406217146,
            -3.3331950075511027e-15,
            -0.006613902628849415
          ],
          [
            0.044890678086537204,
            -2.7050549149426876e-15,
            -0.008804432088127666
          ],
          [
            0.05610766159754628,
            -2.8468930003703945e-15,
            -0.010983860567264721
          ],
          [
            0.06731872711669687,
            -1.489299896990918e-15,
            -0.013149802930335385
          ],
          [
            0.07852102239334542,
            -1.62100669060236e-16,
            -0.01529944940521361
          ],
          [
            0.0897112391945806,
            -2.796236541289071e-15,
            -0.017428981834153548
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          0.08971123919457884,
          -1.1752298506867107e-15,
          -0.01742898183415793
        ],
        "actual_opposite_endpoint_branch_residual": 4.993510137658059e-15
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            -0.08971123919457714,
            -4.0525167265058997e-16,
            0.01742898183415324
          ],
          [
            -0.07852102239334155,
            -1.9249454450903024e-15,
            0.015299449405212523
          ],
          [
            -0.06731872711669339,
            -1.6210066906023596e-16,
            0.013149802930335134
          ],
          [
            -0.05610766159754246,
            7.902407616686504e-16,
            0.010983860567264591
          ],
          [
            -0.04489067808653496,
            6.078775089758849e-17,
            0.008804432088124476
          ],
          [
            -0.03367008540621181,
            -2.249146783210774e-15,
            0.006613902628847087
          ],
          [
            -0.022447514293042335,
            -6.889278435060028e-16,
            0.004414423498638072
          ],
          [
            -0.011223950734153047,
            -1.286674060665623e-15,
            0.002208778787376187
          ],
          [
            8.525517458119213e-16,
            -7.902407616686504e-16,
            -2.3450875838943634e-15
          ],
          [
            0.011223950734155117,
            -3.2420133812047198e-15,
            -0.0022087787873777114
          ],
          [
            0.02244751429304496,
            -2.461903911352334e-15,
            -0.004414423498637234
          ],
          [
            0.033670085406217146,
            -3.3331950075511027e-15,
            -0.006613902628849415
          ],
          [
            0.044890678086537204,
            -2.7050549149426876e-15,
            -0.008804432088127666
          ],
          [
            0.05610766159754628,
            -2.8468930003703945e-15,
            -0.010983860567264721
          ],
          [
            0.06731872711669687,
            -1.489299896990918e-15,
            -0.013149802930335385
          ],
          [
            0.07852102239334542,
            -1.6210066906023596e-16,
            -0.01529944940521361
          ],
          [
            0.0897112391945806,
            -2.796236541289071e-15,
            -0.017428981834153548
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -0.08971123919457714,
            -4.0525167265058997e-16,
            0.01742898183415324
          ],
          [
            -0.07852102239334155,
            -1.9249454450903024e-15,
            0.015299449405212523
          ],
          [
            -0.06731872711669339,
            -1.62100669060236e-16,
            0.013149802930335134
          ],
          [
            -0.05610766159754246,
            7.902407616686503e-16,
            0.010983860567264591
          ],
          [
            -0.04489067808653496,
            6.078775089758848e-17,
            0.008804432088124476
          ],
          [
            -0.03367008540621181,
            -2.249146783210774e-15,
            0.006613902628847087
          ],
          [
            -0.022447514293042335,
            -6.889278435060027e-16,
            0.004414423498638072
          ],
          [
            -0.011223950734153047,
            -1.286674060665623e-15,
            0.002208778787376187
          ],
          [
            8.517492267046123e-16,
            -7.902407616686504e-16,
            -2.344912458651649e-15
          ],
          [
            0.011223950734155117,
            -3.2420133812047198e-15,
            -0.0022087787873777114
          ],
          [
            0.02244751429304496,
            -2.461903911352334e-15,
            -0.004414423498637234
          ],
          [
            0.033670085406217146,
            -3.3331950075511027e-15,
            -0.006613902628849415
          ],
          [
            0.044890678086537204,
            -2.7050549149426876e-15,
            -0.008804432088127666
          ],
          [
            0.05610766159754628,
            -2.8468930003703945e-15,
            -0.010983860567264721
          ],
          [
            0.06731872711669687,
            -1.489299896990918e-15,
            -0.013149802930335385
          ],
          [
            0.07852102239334542,
            -1.62100669060236e-16,
            -0.01529944940521361
          ],
          [
            0.0897112391945806,
            -2.796236541289071e-15,
            -0.017428981834153548
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            -0.08971123919457713,
            -3.885780586188048e-16,
            0.0174289818341532
          ],
          [
            -0.07852102239334158,
            -1.942890293094024e-15,
            0.01529944940521255
          ],
          [
            -0.0673187271166934,
            -1.6653345369377348e-16,
            0.013149802930335186
          ],
          [
            -0.056107661597542435,
            7.771561172376096e-16,
            0.010983860567264636
          ],
          [
            -0.04489067808653496,
            1.1102230246251565e-16,
            0.008804432088124425
          ],
          [
            -0.0336700854062118,
            -2.275957200481571e-15,
            0.00661390262884709
          ],
          [
            -0.022447514293042314,
            -6.661338147750939e-16,
            0.004414423498638076
          ],
          [
            -0.011223950734153054,
            -1.27675647831893e-15,
            0.002208778787376242
          ],
          [
            8.881784197001252e-16,
            -7.771561172376096e-16,
            -2.3314683517128287e-15
          ],
          [
            0.011223950734155164,
            -3.219646771412954e-15,
            -0.0022087787873776854
          ],
          [
            0.022447514293044923,
            -2.4424906541753444e-15,
            -0.004414423498637243
          ],
          [
            0.03367008540621719,
            -3.3306690738754696e-15,
            -0.006613902628849422
          ],
          [
            0.04489067808653724,
            -2.7200464103316335e-15,
            -0.008804432088127645
          ],
          [
            0.05610766159754632,
            -2.831068712794149e-15,
            -0.010983860567264747
          ],
          [
            0.06731872711669684,
            -1.4988010832439613e-15,
            -0.013149802930335408
          ],
          [
            0.07852102239334546,
            -1.6653345369377348e-16,
            -0.015299449405213605
          ],
          [
            0.08971123919458057,
            -2.7755575615628914e-15,
            -0.017428981834153534
          ]
        ]
      },
      "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": [
        0.5,
        0.0,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.0,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        -0.5,
        0.0,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -0.08971123919457788,
              -1.5500876478885064e-15,
              0.017428981834154072
            ],
            "branch_aligned_reduced_polarization": [
              -0.08971123919457791,
              -1.5500876478885064e-15,
              0.017428981834154072
            ],
            "target_residual": 0.41065878372564263,
            "energy_eV": -110.95861778358491,
            "max_atomic_step_A": 0.04252963641736623,
            "max_log_strain_component": 0.00014270864237924587,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.371188506416751,
            "cell_principal_stretches": [
              1.0000605008217418,
              0.9999230474113967,
              0.9998420071565111
            ],
            "cell_volume_ratio": 0.999825553333952,
            "cell_rmsd_from_input_A": 0.000930408645178824
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.4848049169572741,
              3.7077014391893085e-16,
              0.00020279778265196196
            ],
            "branch_aligned_reduced_polarization": [
              -0.4848049169572741,
              3.7077014391893085e-16,
              0.00020279778265196196
            ],
            "target_residual": 0.015196436280127786,
            "energy_eV": -110.94989671778632,
            "max_atomic_step_A": 0.0017368108943135849,
            "max_log_strain_component": 6.342820892525632e-06,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.371188506416751,
            "cell_principal_stretches": [
              1.0000628899282484,
              0.9999194305838706,
              0.9998349659195838
            ],
            "cell_volume_ratio": 0.9998172842832523,
            "cell_rmsd_from_input_A": 0.0009717228177274335
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.49995447209126387,
              -3.0324888510668937e-15,
              2.4039558336991552e-08
            ],
            "branch_aligned_reduced_polarization": [
              -0.49995447209126387,
              -3.0324888510668937e-15,
              2.4039558336991552e-08
            ],
            "target_residual": 4.552791508279166e-05,
            "energy_eV": -110.94740383012012
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_01",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Pc",
        "spacegroup_number": 7,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          -0.5,
          0.0,
          0.0
        ],
        "formal_class": [
          0.5,
          0.0,
          0.0
        ],
        "target_residual": 4.552791508279166e-05,
        "parent_symmetrization_rmsd_A": 0.05206979240436622,
        "parent_cell_rmsd_A": 0.0009717228177274335,
        "energy_eV": -110.94740383012012,
        "reduced_polarization": [
          -0.49995447209126387,
          -3.0324888510668937e-15,
          2.4039558336991552e-08
        ],
        "cartesian_polarization_e_A2": [
          -0.016135770713845286,
          -2.974785901112609e-17,
          0.00015948350877200592
        ],
        "ranking_score": 0.5524037789389636
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 2,
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.0,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -0.08971123919457788,
              -1.5500876478885064e-15,
              0.017428981834154072
            ],
            "branch_aligned_reduced_polarization": [
              -0.08971123919457788,
              -1.5500876478885064e-15,
              0.01742898183415409
            ],
            "target_residual": 0.4908389695322163,
            "energy_eV": -110.95861778358491,
            "max_atomic_step_A": 0.06111725091292065,
            "max_log_strain_component": 0.0003037291197690561,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.371188506416751,
            "cell_principal_stretches": [
              1.000078234149164,
              0.9998682692092491,
              0.9996932817378745
            ],
            "cell_volume_ratio": 0.9996397912019994,
            "cell_rmsd_from_input_A": 0.0012281337468093405
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.0003122133477106424,
              8.641913530122745e-15,
              0.5034931327724502
            ],
            "branch_aligned_reduced_polarization": [
              0.0003122133477106424,
              8.641913530122745e-15,
              0.5034931327724502
            ],
            "target_residual": 0.003507057704180882,
            "energy_eV": -110.6096899634454,
            "max_atomic_step_A": 0.0004913552886299146,
            "max_log_strain_component": 2.0190134266207225e-06,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.371188506416751,
            "cell_principal_stretches": [
              1.0000778082905968,
              0.9998692100474837,
              0.9996953149537172
            ],
            "cell_volume_ratio": 0.9996423392610757,
            "cell_rmsd_from_input_A": 0.0012201143157704432
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -1.2821035774170803e-07,
              8.194464566464079e-16,
              0.4999997636480175
            ],
            "branch_aligned_reduced_polarization": [
              -1.2821035774170803e-07,
              8.194464566464079e-16,
              0.4999997636480175
            ],
            "target_residual": 2.6888688227038037e-07,
            "energy_eV": -110.61463453158926
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_02",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Pc",
        "spacegroup_number": 7,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.5
        ],
        "formal_class": [
          0.0,
          0.0,
          0.5
        ],
        "target_residual": 2.6888688227038037e-07,
        "parent_symmetrization_rmsd_A": 0.07104048435397128,
        "parent_cell_rmsd_A": 0.0012201143157704432,
        "energy_eV": -110.61463453158926,
        "reduced_polarization": [
          -1.2821035774170803e-07,
          8.194464566464079e-16,
          0.4999997636480175
        ],
        "cartesian_polarization_e_A2": [
          6.954103283928004e-06,
          -2.901538581267646e-17,
          0.012521111146399148
        ],
        "ranking_score": 0.5713460507066784
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 3,
      "formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.5,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        -0.5,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -0.08971123919457788,
              -1.5500876478885064e-15,
              0.017428981834154072
            ],
            "branch_aligned_reduced_polarization": [
              -0.08971123919457788,
              -1.5543122344752192e-15,
              0.017428981834154072
            ],
            "target_residual": 0.50828326339316,
            "energy_eV": -110.95861778358491,
            "max_atomic_step_A": 0.0620640337056372,
            "max_log_strain_component": 0.00042115119380891795,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.371188506416751,
            "cell_principal_stretches": [
              1.0005413045491984,
              1.0000231692684927,
              0.9994916246197071
            ],
            "cell_volume_ratio": 1.0000558240080608,
            "cell_rmsd_from_input_A": 0.002976329050918862
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.0002540266727602726,
              -0.5025171999631936,
              0.001885335533762964
            ],
            "branch_aligned_reduced_polarization": [
              -0.0002540266727602726,
              -0.5025171999631936,
              0.001885335533762964
            ],
            "target_residual": 0.0031552044751560152,
            "energy_eV": -110.64525565854566,
            "max_atomic_step_A": 0.00043187987344396047,
            "max_log_strain_component": 1.9828936093239208e-06,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.371188506416751,
            "cell_principal_stretches": [
              1.0005393113592258,
              1.0000237889637549,
              0.999494598223837
            ],
            "cell_volume_ratio": 1.0000574267780884,
            "cell_rmsd_from_input_A": 0.0029624125919889346
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -1.6028024596842586e-07,
              -0.5000004912046978,
              -6.839522531001453e-07
            ],
            "branch_aligned_reduced_polarization": [
              -1.6028024596842586e-07,
              -0.5000004912046978,
              -6.839522531001453e-07
            ],
            "target_residual": 8.571828841704486e-07,
            "energy_eV": -110.64818890174182
          }
        ],
        "iterations": 2
      },
      "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,
          -0.5,
          0.0
        ],
        "formal_class": [
          0.0,
          0.5,
          0.0
        ],
        "target_residual": 8.571828841704486e-07,
        "parent_symmetrization_rmsd_A": 0.07078994678468707,
        "parent_cell_rmsd_A": 0.0029624125919889346,
        "energy_eV": -110.64818890174182,
        "reduced_polarization": [
          -1.6028024596842586e-07,
          -0.5000004912046978,
          -6.839522531001453e-07
        ],
        "cartesian_polarization_e_A2": [
          5.079569450276368e-06,
          -0.012130596121461673,
          -3.7923952683228357e-06
        ],
        "ranking_score": 0.5715322642984526
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 4,
      "formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.0,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        -0.5,
        0.0,
        0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -0.08971123919457788,
              -1.5500876478885064e-15,
              0.017428981834154072
            ],
            "branch_aligned_reduced_polarization": [
              -0.08971123919457791,
              -1.5500876478885064e-15,
              0.01742898183415409
            ],
            "target_residual": 0.633412704969572,
            "energy_eV": -110.95861778358491,
            "max_atomic_step_A": 0.07413431321516041,
            "max_log_strain_component": 0.0002616794228136114,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.371188506416751,
            "cell_principal_stretches": [
              0.9999095665339756,
              0.9997679142437319,
              0.9997320281362241
            ],
            "cell_volume_ratio": 0.9994096163227034,
            "cell_rmsd_from_input_A": 0.0013081699111162865
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.471436175197802,
              4.006974601418334e-15,
              0.5018018873741977
            ],
            "branch_aligned_reduced_polarization": [
              -0.471436175197802,
              4.006974601418334e-15,
              0.5018018873741977
            ],
            "target_residual": 0.02862060246465742,
            "energy_eV": -110.59421273777636,
            "max_atomic_step_A": 0.003372502528528603,
            "max_log_strain_component": 1.225624255531438e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.371188506416751,
            "cell_principal_stretches": [
              0.9998999577910956,
              0.9997609423066472,
              0.9997326714449511
            ],
            "cell_volume_ratio": 0.9993936861032474,
            "cell_rmsd_from_input_A": 0.0013487104636359761
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.49986800753466165,
              -1.128439512473059e-16,
              0.50000058756063
            ],
            "branch_aligned_reduced_polarization": [
              -0.49986800753466165,
              -1.128439512473059e-16,
              0.50000058756063
            ],
            "target_residual": 0.00013199377308641924,
            "energy_eV": -110.59117151300256
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_04",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Pc",
        "spacegroup_number": 7,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          -0.5,
          0.0,
          0.5
        ],
        "formal_class": [
          0.5,
          0.0,
          0.5
        ],
        "target_residual": 0.00013199377308641924,
        "parent_symmetrization_rmsd_A": 0.08904774022217431,
        "parent_cell_rmsd_A": 0.0013487104636359761,
        "energy_eV": -110.59117151300256,
        "reduced_polarization": [
          -0.49986800753466165,
          -1.128439512473059e-16,
          0.50000058756063
        ],
        "cartesian_polarization_e_A2": [
          -0.0161343985460647,
          5.65694842383216e-18,
          0.01268393223570038
        ],
        "ranking_score": 0.5896489053842562
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 5,
      "formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.5,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        -0.5,
        -0.5,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -0.08971123919457788,
              -1.5500876478885064e-15,
              0.017428981834154072
            ],
            "branch_aligned_reduced_polarization": [
              -0.08971123919457791,
              -1.5543122344752192e-15,
              0.017428981834154072
            ],
            "target_residual": 0.6470244482637596,
            "energy_eV": -110.95861778358491,
            "max_atomic_step_A": 0.07513272115113616,
            "max_log_strain_component": 0.0004211511938121227,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.371188506416751,
            "cell_principal_stretches": [
              1.0004862522707971,
              0.999924977368013,
              0.9994146008871836
            ],
            "cell_volume_ratio": 0.9998255533339582,
            "cell_rmsd_from_input_A": 0.003111476568280194
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.4830967898306686,
              -0.505890172886274,
              0.002038148469114889
            ],
            "branch_aligned_reduced_polarization": [
              -0.4830967898306686,
              -0.505890172886274,
              0.002038148469114889
            ],
            "target_residual": 0.01801573478493012,
            "energy_eV": -110.63251245575123,
            "max_atomic_step_A": 0.0020960893145289213,
            "max_log_strain_component": 7.2525137110413825e-06,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.371188506416751,
            "cell_principal_stretches": [
              1.000479515445489,
              0.9999215454699687,
              0.9994169058263197
            ],
            "cell_volume_ratio": 0.9998176952872717,
            "cell_rmsd_from_input_A": 0.0030943307673261416
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.49994603375608904,
              -0.49999849940027513,
              -1.49313365810422e-06
            ],
            "branch_aligned_reduced_polarization": [
              -0.49994603375608904,
              -0.49999849940027513,
              -1.49313365810422e-06
            ],
            "target_residual": 5.400774693979403e-05,
            "energy_eV": -110.63681189326809
          }
        ],
        "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": [
          -0.5,
          -0.5,
          0.0
        ],
        "formal_class": [
          0.5,
          0.5,
          0.0
        ],
        "target_residual": 5.400774693979403e-05,
        "parent_symmetrization_rmsd_A": 0.08694448447097868,
        "parent_cell_rmsd_A": 0.0030943307673261416,
        "energy_eV": -110.63681189326809,
        "reduced_polarization": [
          -0.49994603375608904,
          -0.49999849940027513,
          -1.49313365810422e-06
        ],
        "cartesian_polarization_e_A2": [
          -0.016130426420860756,
          -0.012125419762301448,
          0.00015569836432643142
        ],
        "ranking_score": 0.5878260826566898
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 6,
      "formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.5,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        -0.5,
        0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -0.08971123919457788,
              -1.5500876478885064e-15,
              0.017428981834154072
            ],
            "branch_aligned_reduced_polarization": [
              -0.08971123919457788,
              -1.5543122344752192e-15,
              0.01742898183415409
            ],
            "target_residual": 0.70065889990169,
            "energy_eV": -110.95861778358491,
            "max_atomic_step_A": 0.08650401662135503,
            "max_log_strain_component": 0.00042115119380978466,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.371188506416751,
            "cell_principal_stretches": [
              1.0004465968184246,
              0.9998640945152395,
              0.9993293688818706
            ],
            "cell_volume_ratio": 0.9996397912020054,
            "cell_rmsd_from_input_A": 0.003212993704593355
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -5.923186302718788e-05,
              -0.5173968072843893,
              0.49914413158687265
            ],
            "branch_aligned_reduced_polarization": [
              -5.923186302718788e-05,
              -0.5173968072843893,
              0.49914413158687265
            ],
            "target_residual": 0.017417948296064252,
            "energy_eV": -110.258566823888,
            "max_atomic_step_A": 0.0021779177751024485,
            "max_log_strain_component": 1.3209647563311857e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.371188506416751,
            "cell_principal_stretches": [
              1.0004308686044945,
              0.9998634367576185,
              0.9993439229500922
            ],
            "cell_volume_ratio": 0.999637976423002,
            "cell_rmsd_from_input_A": 0.0031291893039391496
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -1.2943788269353195e-06,
              -0.4999964385786658,
              0.5000014944681316
            ],
            "branch_aligned_reduced_polarization": [
              -1.2943788269353195e-06,
              -0.4999964385786658,
              0.5000014944681316
            ],
            "target_residual": 4.073398269681374e-06,
            "energy_eV": -110.27599201747172
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_06",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          -0.5,
          0.5
        ],
        "formal_class": [
          0.0,
          0.5,
          0.5
        ],
        "target_residual": 4.073398269681374e-06,
        "parent_symmetrization_rmsd_A": 0.09884880361905855,
        "parent_cell_rmsd_A": 0.0031291893039391496,
        "energy_eV": -110.27599201747172,
        "reduced_polarization": [
          -1.2943788269353195e-06,
          -0.4999964385786658,
          0.5000014944681316
        ],
        "cartesian_polarization_e_A2": [
          1.1869698913189174e-05,
          -0.012129899189441587,
          0.012517493232814774
        ],
        "ranking_score": 0.5996392477415827
      },
      "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": [
              -0.08971123919457788,
              -1.5500876478885064e-15,
              0.017428981834154072
            ],
            "branch_aligned_reduced_polarization": [
              -0.08971123919457791,
              -1.5543122344752192e-15,
              0.01742898183415409
            ],
            "target_residual": 0.806976861388769,
            "energy_eV": -110.95861778358491,
            "max_atomic_step_A": 0.09672618969511101,
            "max_log_strain_component": 0.0004211511938129894,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.371188506416751,
            "cell_principal_stretches": [
              1.0003539382590376,
              0.9997654848483494,
              0.9992903609076098
            ],
            "cell_volume_ratio": 0.9994096163227092,
            "cell_rmsd_from_input_A": 0.0032437242580286413
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.4701037497285373,
              -0.5207741438629948,
              0.49809411889154737
            ],
            "branch_aligned_reduced_polarization": [
              -0.4701037497285373,
              -0.5207741438629948,
              0.49809411889154737
            ],
            "target_residual": 0.036455222072206535,
            "energy_eV": -110.23945599397905,
            "max_atomic_step_A": 0.0043036361293545605,
            "max_log_strain_component": 1.6031006553187154e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.371188506416751,
            "cell_principal_stretches": [
              1.0003274302381633,
              0.9997566251097761,
              0.999304562606391
            ],
            "cell_volume_ratio": 0.9993884798662188,
            "cell_rmsd_from_input_A": 0.0031624957457244227
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.4998496348051427,
              -0.49997418120556186,
              0.49999284684999407
            ],
            "branch_aligned_reduced_polarization": [
              -0.4998496348051427,
              -0.49997418120556186,
              0.49999284684999407
            ],
            "target_residual": 0.00015273332814325349,
            "energy_eV": -110.2552734786492
          }
        ],
        "iterations": 2
      },
      "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": 0.00015273332814325349,
        "parent_symmetrization_rmsd_A": 0.11223785454795027,
        "parent_cell_rmsd_A": 0.0031624957457244227,
        "energy_eV": -110.2552734786492,
        "reduced_polarization": [
          -0.4998496348051427,
          -0.49997418120556186,
          0.49999284684999407
        ],
        "cartesian_polarization_e_A2": [
          -0.016128970373847588,
          -0.012124508561702664,
          0.01268011542180124
        ],
        "ranking_score": 0.6133339451406679
      },
      "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
        ],
        "endpoint_rmsd_A": 0.0959030061811417,
        "minimum_distance_A_by_image": [
          1.7648694241612204,
          1.7640515568359805,
          1.7633635832930512,
          1.7628056556141267,
          1.7623778973076594,
          1.7620804031724437,
          1.7619132391927057,
          1.7618764424649875,
          1.761970021157001
        ],
        "minimum_distance_A": 1.7618764424649875,
        "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": [
          225.83395983847834,
          225.83395983847834,
          225.83395983847834,
          225.83395983847834,
          225.83395983847834,
          225.83395983847834,
          225.83395983847834,
          225.83395983847834,
          225.83395983847834
        ],
        "cell_deformation_log_strain_norm": 0.0
      },
      "parent_reduced_polarization": [
        8.525517458119213e-16,
        -7.902407616686504e-16,
        -2.3450875838943634e-15
      ],
      "incoming": {
        "reached": true,
        "construction": "variable_cell_linear_interpolation",
        "continuation_fractions": [
          0.0,
          0.125,
          0.25,
          0.375,
          0.5,
          0.625,
          0.75,
          0.875,
          1.0
        ],
        "energies_eV": [
          -110.95861778358494,
          -110.9745580332976,
          -110.98817239307883,
          -110.99955554146509,
          -111.00878661616073,
          -111.0159199687332,
          -111.02098865803565,
          -111.02401443520063,
          -111.02501837066177
        ],
        "cartesian_polarizations_e_A2": [
          [
            -0.0028950567655400467,
            -9.832206151981874e-18,
            0.00046487847705033126
          ],
          [
            -0.002533938523460814,
            -4.6702979221913905e-17,
            0.0004080054394661359
          ],
          [
            -0.0021724307309627347,
            -3.9328824607927496e-18,
            0.0003506249000668985
          ],
          [
            -0.0018106401060105884,
            1.9172801996364654e-17,
            0.0002928335175459987
          ],
          [
            -0.0014486586636549494,
            1.4748309227972812e-18,
            0.0002347025552171934
          ],
          [
            -0.0010865608862344349,
            -5.45687441434994e-17,
            0.00017629247086128547
          ],
          [
            -0.0007243993750162198,
            -1.6714750458369185e-17,
            0.00011765765206134187
          ],
          [
            -0.0003622059147645466,
            -3.121725453254245e-17,
            5.886812734121368e-05
          ],
          [
            2.7484088759211833e-17,
            -1.9172801996364654e-17,
            -5.899323691189125e-17
          ]
        ],
        "raw_reduced_polarization": [
          [
            -0.08971123919457714,
            -4.0525167265058997e-16,
            0.01742898183415324
          ],
          [
            -0.07852102239334155,
            -1.9249454450903024e-15,
            0.015299449405212523
          ],
          [
            -0.06731872711669339,
            -1.6210066906023596e-16,
            0.013149802930335134
          ],
          [
            -0.05610766159754246,
            7.902407616686504e-16,
            0.010983860567264591
          ],
          [
            -0.04489067808653496,
            6.078775089758849e-17,
            0.008804432088124476
          ],
          [
            -0.03367008540621181,
            -2.249146783210774e-15,
            0.006613902628847087
          ],
          [
            -0.022447514293042335,
            -6.889278435060028e-16,
            0.004414423498638072
          ],
          [
            -0.011223950734153047,
            -1.286674060665623e-15,
            0.002208778787376187
          ],
          [
            8.525517458119213e-16,
            -7.902407616686504e-16,
            -2.3450875838943634e-15
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -0.08971123919457714,
            -4.0525167265058997e-16,
            0.01742898183415324
          ],
          [
            -0.07852102239334155,
            -1.9249454450903024e-15,
            0.015299449405212523
          ],
          [
            -0.06731872711669339,
            -1.62100669060236e-16,
            0.013149802930335134
          ],
          [
            -0.05610766159754246,
            7.902407616686503e-16,
            0.010983860567264591
          ],
          [
            -0.04489067808653496,
            6.078775089758848e-17,
            0.008804432088124476
          ],
          [
            -0.03367008540621181,
            -2.249146783210774e-15,
            0.006613902628847087
          ],
          [
            -0.022447514293042335,
            -6.889278435060027e-16,
            0.004414423498638072
          ],
          [
            -0.011223950734153047,
            -1.286674060665623e-15,
            0.002208778787376187
          ],
          [
            8.517492267046123e-16,
            -7.902407616686504e-16,
            -2.344912458651649e-15
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            -0.08971123919457713,
            -3.885780586188048e-16,
            0.0174289818341532
          ],
          [
            -0.07852102239334158,
            -1.942890293094024e-15,
            0.01529944940521255
          ],
          [
            -0.0673187271166934,
            -1.6653345369377348e-16,
            0.013149802930335186
          ],
          [
            -0.056107661597542435,
            7.771561172376096e-16,
            0.010983860567264636
          ],
          [
            -0.04489067808653496,
            1.1102230246251565e-16,
            0.008804432088124425
          ],
          [
            -0.0336700854062118,
            -2.275957200481571e-15,
            0.00661390262884709
          ],
          [
            -0.022447514293042314,
            -6.661338147750939e-16,
            0.004414423498638076
          ],
          [
            -0.011223950734153054,
            -1.27675647831893e-15,
            0.002208778787376242
          ],
          [
            8.881784197001252e-16,
            -7.771561172376096e-16,
            -2.3314683517128287e-15
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -111.02501837066178,
          -111.02401443520061,
          -111.02098865803565,
          -111.0159199687332,
          -111.00878661616075,
          -110.99955554146506,
          -110.98817239307883,
          -110.9745580332976,
          -110.95861778358494
        ],
        "cartesian_polarizations_e_A2": [
          [
            2.1108517582536086e-17,
            -4.522814829911662e-17,
            -8.848985536783687e-18
          ],
          [
            0.0003622059147646134,
            -7.865764921585499e-17,
            -5.886812734125251e-05
          ],
          [
            0.0007243993750163046,
            -5.973065237328989e-17,
            -0.00011765765206132171
          ],
          [
            0.001086560886234607,
            -8.086989560005092e-17,
            -0.00017629247086134545
          ],
          [
            0.0014486586636550216,
            -6.5629976064479e-17,
            -0.000234702555217274
          ],
          [
            0.0018106401060107118,
            -6.907124821767267e-17,
            -0.00029283351754600317
          ],
          [
            0.002172430730962847,
            -3.613335760853339e-17,
            -0.0003506249000669059
          ],
          [
            0.0025339385234609394,
            -3.9328824607927496e-18,
            -0.00040800543946616444
          ],
          [
            0.0028950567655401586,
            -6.784222244867494e-17,
            -0.00046487847705034015
          ]
        ],
        "raw_reduced_polarization": [
          [
            6.541933009830714e-16,
            -1.864157694192714e-15,
            -3.4509950507565705e-16
          ],
          [
            0.011223950734155117,
            -3.2420133812047198e-15,
            -0.0022087787873777114
          ],
          [
            0.02244751429304496,
            -2.461903911352334e-15,
            -0.004414423498637234
          ],
          [
            0.033670085406217146,
            -3.3331950075511027e-15,
            -0.006613902628849415
          ],
          [
            0.044890678086537204,
            -2.7050549149426876e-15,
            -0.008804432088127666
          ],
          [
            0.05610766159754628,
            -2.8468930003703945e-15,
            -0.010983860567264721
          ],
          [
            0.06731872711669687,
            -1.489299896990918e-15,
            -0.013149802930335385
          ],
          [
            0.07852102239334542,
            -1.6210066906023596e-16,
            -0.01529944940521361
          ],
          [
            0.0897112391945806,
            -2.796236541289071e-15,
            -0.017428981834153548
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            6.541933009830714e-16,
            -1.864157694192714e-15,
            -3.4509950507565705e-16
          ],
          [
            0.011223950734155117,
            -3.2420133812047198e-15,
            -0.0022087787873777114
          ],
          [
            0.02244751429304496,
            -2.461903911352334e-15,
            -0.004414423498637234
          ],
          [
            0.033670085406217146,
            -3.3331950075511027e-15,
            -0.006613902628849415
          ],
          [
            0.044890678086537204,
            -2.7050549149426876e-15,
            -0.008804432088127666
          ],
          [
            0.05610766159754628,
            -2.8468930003703945e-15,
            -0.010983860567264721
          ],
          [
            0.06731872711669687,
            -1.489299896990918e-15,
            -0.013149802930335385
          ],
          [
            0.07852102239334542,
            -1.62100669060236e-16,
            -0.01529944940521361
          ],
          [
            0.0897112391945806,
            -2.796236541289071e-15,
            -0.017428981834153548
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          0.08971123919457884,
          -1.1752298506867107e-15,
          -0.01742898183415793
        ],
        "actual_opposite_endpoint_branch_residual": 4.993510137658059e-15
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            -0.08971123919457714,
            -4.0525167265058997e-16,
            0.01742898183415324
          ],
          [
            -0.07852102239334155,
            -1.9249454450903024e-15,
            0.015299449405212523
          ],
          [
            -0.06731872711669339,
            -1.6210066906023596e-16,
            0.013149802930335134
          ],
          [
            -0.05610766159754246,
            7.902407616686504e-16,
            0.010983860567264591
          ],
          [
            -0.04489067808653496,
            6.078775089758849e-17,
            0.008804432088124476
          ],
          [
            -0.03367008540621181,
            -2.249146783210774e-15,
            0.006613902628847087
          ],
          [
            -0.022447514293042335,
            -6.889278435060028e-16,
            0.004414423498638072
          ],
          [
            -0.011223950734153047,
            -1.286674060665623e-15,
            0.002208778787376187
          ],
          [
            8.525517458119213e-16,
            -7.902407616686504e-16,
            -2.3450875838943634e-15
          ],
          [
            0.011223950734155117,
            -3.2420133812047198e-15,
            -0.0022087787873777114
          ],
          [
            0.02244751429304496,
            -2.461903911352334e-15,
            -0.004414423498637234
          ],
          [
            0.033670085406217146,
            -3.3331950075511027e-15,
            -0.006613902628849415
          ],
          [
            0.044890678086537204,
            -2.7050549149426876e-15,
            -0.008804432088127666
          ],
          [
            0.05610766159754628,
            -2.8468930003703945e-15,
            -0.010983860567264721
          ],
          [
            0.06731872711669687,
            -1.489299896990918e-15,
            -0.013149802930335385
          ],
          [
            0.07852102239334542,
            -1.6210066906023596e-16,
            -0.01529944940521361
          ],
          [
            0.0897112391945806,
            -2.796236541289071e-15,
            -0.017428981834153548
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -0.08971123919457714,
            -4.0525167265058997e-16,
            0.01742898183415324
          ],
          [
            -0.07852102239334155,
            -1.9249454450903024e-15,
            0.015299449405212523
          ],
          [
            -0.06731872711669339,
            -1.62100669060236e-16,
            0.013149802930335134
          ],
          [
            -0.05610766159754246,
            7.902407616686503e-16,
            0.010983860567264591
          ],
          [
            -0.04489067808653496,
            6.078775089758848e-17,
            0.008804432088124476
          ],
          [
            -0.03367008540621181,
            -2.249146783210774e-15,
            0.006613902628847087
          ],
          [
            -0.022447514293042335,
            -6.889278435060027e-16,
            0.004414423498638072
          ],
          [
            -0.011223950734153047,
            -1.286674060665623e-15,
            0.002208778787376187
          ],
          [
            8.517492267046123e-16,
            -7.902407616686504e-16,
            -2.344912458651649e-15
          ],
          [
            0.011223950734155117,
            -3.2420133812047198e-15,
            -0.0022087787873777114
          ],
          [
            0.02244751429304496,
            -2.461903911352334e-15,
            -0.004414423498637234
          ],
          [
            0.033670085406217146,
            -3.3331950075511027e-15,
            -0.006613902628849415
          ],
          [
            0.044890678086537204,
            -2.7050549149426876e-15,
            -0.008804432088127666
          ],
          [
            0.05610766159754628,
            -2.8468930003703945e-15,
            -0.010983860567264721
          ],
          [
            0.06731872711669687,
            -1.489299896990918e-15,
            -0.013149802930335385
          ],
          [
            0.07852102239334542,
            -1.62100669060236e-16,
            -0.01529944940521361
          ],
          [
            0.0897112391945806,
            -2.796236541289071e-15,
            -0.017428981834153548
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            -0.08971123919457713,
            -3.885780586188048e-16,
            0.0174289818341532
          ],
          [
            -0.07852102239334158,
            -1.942890293094024e-15,
            0.01529944940521255
          ],
          [
            -0.0673187271166934,
            -1.6653345369377348e-16,
            0.013149802930335186
          ],
          [
            -0.056107661597542435,
            7.771561172376096e-16,
            0.010983860567264636
          ],
          [
            -0.04489067808653496,
            1.1102230246251565e-16,
            0.008804432088124425
          ],
          [
            -0.0336700854062118,
            -2.275957200481571e-15,
            0.00661390262884709
          ],
          [
            -0.022447514293042314,
            -6.661338147750939e-16,
            0.004414423498638076
          ],
          [
            -0.011223950734153054,
            -1.27675647831893e-15,
            0.002208778787376242
          ],
          [
            8.881784197001252e-16,
            -7.771561172376096e-16,
            -2.3314683517128287e-15
          ],
          [
            0.011223950734155164,
            -3.219646771412954e-15,
            -0.0022087787873776854
          ],
          [
            0.022447514293044923,
            -2.4424906541753444e-15,
            -0.004414423498637243
          ],
          [
            0.03367008540621719,
            -3.3306690738754696e-15,
            -0.006613902628849422
          ],
          [
            0.04489067808653724,
            -2.7200464103316335e-15,
            -0.008804432088127645
          ],
          [
            0.05610766159754632,
            -2.831068712794149e-15,
            -0.010983860567264747
          ],
          [
            0.06731872711669684,
            -1.4988010832439613e-15,
            -0.013149802930335408
          ],
          [
            0.07852102239334546,
            -1.6653345369377348e-16,
            -0.015299449405213605
          ],
          [
            0.08971123919458057,
            -2.7755575615628914e-15,
            -0.017428981834153534
          ]
        ]
      },
      "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": "P2/c",
        "spacegroup_number": 13,
        "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": 8.276489025558611e-16,
        "parent_symmetrization_rmsd_A": 0.0959030061811417,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -111.0250183706618,
        "reduced_polarization": [
          7.909863558363416e-17,
          8.003720534849152e-16,
          -1.9532201041118933e-16
        ],
        "cartesian_polarization_e_A2": [
          2.5502284706702988e-18,
          1.94186071501642e-17,
          -4.916103075990937e-18
        ],
        "ranking_score": 0.09590300618114335
      }
    }
  ],
  "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": 49,
      "full_response": 16,
      "energy_polarization": 33
    },
    "model_evaluations_for_recovery_and_path_properties": {
      "total": 74,
      "full_response": 41,
      "energy_polarization": 33
    },
    "elapsed_seconds": 302.6211354759871
  }
}