{
  "schema": "ferrofinder.endpoint_parent_recovery.v4_variable_cell",
  "status": "complete",
  "input_atom_count": 32,
  "input_formula": "Na4Nb4S24",
  "input_spacegroup": "Cc",
  "input_pointgroup": "m",
  "input_is_polar_point_group": true,
  "input_energy_eV": -162.43924227520603,
  "input_cartesian_polarization_e_A2": [
    0.00045031783295782044,
    1.792952177291779e-11,
    -0.0005243646538386329
  ],
  "input_reduced_polarization": [
    0.03627402818202208,
    9.821920979113885e-10,
    -0.05171808126921417
  ],
  "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,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        -0.5
      ]
    },
    {
      "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,
        0.5,
        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": [
        0.0,
        0.5,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        -0.5
      ]
    },
    {
      "orbit_id": 6,
      "representative_formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        0.5,
        0.5,
        0.0
      ]
    },
    {
      "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/c",
      "spacegroup_number": 15,
      "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": 6.048840633887996e-15,
      "parent_symmetrization_rmsd_A": 0.6010554455903286,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -107.64400292989492,
      "reduced_polarization": [
        2.0796836827923858e-15,
        5.6107683345464844e-15,
        8.846849663875281e-16
      ],
      "cartesian_polarization_e_A2": [
        2.0974783546818705e-17,
        1.0242231965719264e-16,
        8.969735821042137e-18
      ],
      "ranking_score": 0.6010554455903407
    },
    {
      "candidate_id": "inversion_parent_endpoint_01",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "C2/c",
      "spacegroup_number": 15,
      "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": 2.985151600441803e-15,
      "parent_symmetrization_rmsd_A": 0.815204691362459,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -143.3536230608674,
      "reduced_polarization": [
        -1.2259645221283852e-16,
        -1.1127739630065597e-15,
        -2.767279222409578e-15
      ],
      "cartesian_polarization_e_A2": [
        2.1791982905785666e-18,
        -2.0313241208607355e-17,
        -2.805717799119905e-17
      ],
      "ranking_score": 0.815204691362465
    },
    {
      "candidate_id": "bec_projection_00",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cc",
      "spacegroup_number": 9,
      "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": 0.00015694714215065756,
      "parent_symmetrization_rmsd_A": 0.01332236541339397,
      "parent_cell_rmsd_A": 0.020632659806322954,
      "energy_eV": -162.41147367549527,
      "reduced_polarization": [
        0.00015652244943617692,
        -4.228690636291948e-12,
        1.1538121673744634e-05
      ],
      "cartesian_polarization_e_A2": [
        1.6457771961684133e-06,
        -7.717936748285226e-14,
        1.1567998761150662e-07
      ],
      "ranking_score": 0.518794424649276
    },
    {
      "candidate_id": "inversion_parent_bec_00_00",
      "source": "same_species_inversion_center_projection_after_BEC",
      "spacegroup": "C2/c",
      "spacegroup_number": 15,
      "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": 3.2383927139390275e-15,
      "parent_symmetrization_rmsd_A": 0.6010597478111038,
      "parent_cell_rmsd_A": 0.020632659806322954,
      "energy_eV": -107.31382107323834,
      "reduced_polarization": [
        -2.3273328841156764e-15,
        -2.1281047714264485e-18,
        -2.251822481319802e-15
      ],
      "cartesian_polarization_e_A2": [
        -2.1841892437993665e-17,
        -3.8899185107735824e-20,
        -2.2794922473133192e-17
      ],
      "ranking_score": 0.606217912762691
    },
    {
      "candidate_id": "inversion_parent_bec_00_01",
      "source": "same_species_inversion_center_projection_after_BEC",
      "spacegroup": "C2/c",
      "spacegroup_number": 15,
      "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": 5.035050164642543e-15,
      "parent_symmetrization_rmsd_A": 0.815206421914455,
      "parent_cell_rmsd_A": 0.020632659806322954,
      "energy_eV": -143.22214589794683,
      "reduced_polarization": [
        2.4548182086383147e-15,
        1.7918642307624316e-15,
        4.014326880252632e-15
      ],
      "cartesian_polarization_e_A2": [
        2.096666077306961e-17,
        3.275311386071357e-17,
        4.0649648437583934e-17
      ],
      "ranking_score": 0.8203645868660459
    },
    {
      "candidate_id": "bec_projection_01",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cc",
      "spacegroup_number": 9,
      "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": 0.00032986573377688,
      "parent_symmetrization_rmsd_A": 0.0789981504924039,
      "parent_cell_rmsd_A": 0.09959278402396918,
      "energy_eV": -161.72145101965683,
      "reduced_polarization": [
        -0.00026002102713328936,
        7.934970713644915e-12,
        -0.4997970210164359
      ],
      "cartesian_polarization_e_A2": [
        0.0006225630922511098,
        1.0055839933015838e-12,
        -0.00509476717829615
      ],
      "ranking_score": 0.6045560779659499
    },
    {
      "candidate_id": "bec_projection_02",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cc",
      "spacegroup_number": 9,
      "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": 2.7848949672383276e-05,
      "parent_symmetrization_rmsd_A": 0.17522742325295593,
      "parent_cell_rmsd_A": 0.10204770368951191,
      "energy_eV": -159.91924683886668,
      "reduced_polarization": [
        0.4999735788737042,
        1.312757346812462e-12,
        -8.802731571280122e-06
      ],
      "cartesian_polarization_e_A2": [
        0.00531272656075145,
        1.497814021018757e-12,
        3.383379659634359e-05
      ],
      "ranking_score": 0.7007950470746787
    },
    {
      "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": 0.009145300292898123,
      "parent_symmetrization_rmsd_A": 0.4012278966881886,
      "parent_cell_rmsd_A": 0.917158222780554,
      "energy_eV": -154.2233130566047,
      "reduced_polarization": [
        -0.001782394013151867,
        0.491963428255442,
        0.003984106377060552
      ],
      "cartesian_polarization_e_A2": [
        -0.0006071217647348035,
        0.009039897063005233,
        0.0005508703923479967
      ],
      "ranking_score": 1.1488080529691234
    },
    {
      "candidate_id": "bec_projection_04",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cc",
      "spacegroup_number": 9,
      "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": 3.961943611609451e-05,
      "parent_symmetrization_rmsd_A": 0.1692932668505027,
      "parent_cell_rmsd_A": 0.2251243139219663,
      "energy_eV": -158.9024076534127,
      "reduced_polarization": [
        0.49999607783221023,
        2.3119245777041353e-12,
        -0.4999605751814464
      ],
      "cartesian_polarization_e_A2": [
        0.005962948328939401,
        2.2952284311405195e-12,
        -0.005061056693968992
      ],
      "ranking_score": 0.7256535842032265
    },
    {
      "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": 0.004494624237582614,
      "parent_symmetrization_rmsd_A": 0.3930410515850662,
      "parent_cell_rmsd_A": 0.8750600852457274,
      "energy_eV": -152.161793718264,
      "reduced_polarization": [
        -0.0005945157599781074,
        0.4966622097144988,
        -0.4970491773929603
      ],
      "cartesian_polarization_e_A2": [
        2.611625571445428e-05,
        0.008775159977041527,
        -0.004563876627819419
      ],
      "ranking_score": 1.1207953213716633
    },
    {
      "candidate_id": "bec_projection_06",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.5,
        0.5,
        0.0
      ],
      "formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_residual": 0.00216875108994042,
      "parent_symmetrization_rmsd_A": 0.42593124317917974,
      "parent_cell_rmsd_A": 0.8825445411425834,
      "energy_eV": -151.25378746084522,
      "reduced_polarization": [
        0.4990249510117245,
        0.4983331719751787,
        0.0009871398564797937
      ],
      "cartesian_polarization_e_A2": [
        0.004653629533942558,
        0.0086220532459691,
        0.0005208091852115008
      ],
      "ranking_score": 1.1509048806447064
    },
    {
      "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": 0.0026092765909981937,
      "parent_symmetrization_rmsd_A": 0.4115249424013717,
      "parent_cell_rmsd_A": 0.7892154294561787,
      "energy_eV": -149.1964677656184,
      "reduced_polarization": [
        0.49856587186090773,
        0.49857337309027666,
        -0.4983518687948321
      ],
      "cartesian_polarization_e_A2": [
        0.0053855113015361155,
        0.008281594241802475,
        -0.004592007628766156
      ],
      "ranking_score": 1.1140473529474129
    }
  ],
  "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": [
              0.03627402818202208,
              9.821920979113885e-10,
              -0.05171808126921417
            ],
            "branch_aligned_reduced_polarization": [
              0.03627402818202208,
              9.821920979113885e-10,
              -0.05171808126921417
            ],
            "target_residual": 0.06317091934362816,
            "energy_eV": -162.43924227520603,
            "max_atomic_step_A": 0.02254475525006005,
            "max_log_strain_component": 0.0017118424098717347,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.3912373274709768,
            "cell_principal_stretches": [
              1.001713308448513,
              1.0000859655738148,
              0.9985905287259972
            ],
            "cell_volume_ratio": 1.000387413801225,
            "cell_rmsd_from_input_A": 0.020632659806322954
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.00015652244943617692,
              -4.228690636291948e-12,
              1.1538121673744634e-05
            ],
            "branch_aligned_reduced_polarization": [
              0.00015652244943617692,
              -4.228690636291948e-12,
              1.1538121673744634e-05
            ],
            "target_residual": 0.00015694714215065756,
            "energy_eV": -162.41147367549527
          }
        ],
        "iterations": 1
      },
      "parent": {
        "candidate_id": "bec_projection_00",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cc",
        "spacegroup_number": 9,
        "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": 0.00015694714215065756,
        "parent_symmetrization_rmsd_A": 0.01332236541339397,
        "parent_cell_rmsd_A": 0.020632659806322954,
        "energy_eV": -162.41147367549527,
        "reduced_polarization": [
          0.00015652244943617692,
          -4.228690636291948e-12,
          1.1538121673744634e-05
        ],
        "cartesian_polarization_e_A2": [
          1.6457771961684133e-06,
          -7.717936748285226e-14,
          1.1567998761150662e-07
        ],
        "ranking_score": 0.518794424649276
      },
      "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": [
          -162.43924227520603,
          -162.43891106920165,
          -162.43768725213897,
          -162.43556850755294,
          -162.4325525691989,
          -162.42863723128556,
          -162.42382034883406,
          -162.41809983787945,
          -162.41147367549527
        ],
        "cartesian_polarizations_e_A2": [
          [
            0.0004503178329578138,
            1.7929555122434484e-11,
            -0.0005243646538386265
          ],
          [
            0.0003940268645807537,
            1.5703258342204757e-11,
            -0.0004588235284896463
          ],
          [
            0.00033779032578906595,
            1.3469919746899456e-11,
            -0.0003932846373408196
          ],
          [
            0.00028161076054655267,
            1.1229474269269067e-11,
            -0.00032774427100240095
          ],
          [
            0.0002254905137724994,
            8.98184611651082e-12,
            -0.00026219857932566676
          ],
          [
            0.0001694318158314607,
            6.7272442161889734e-12,
            -0.00019664367165217746
          ],
          [
            0.00011343679076162715,
            4.465894417195045e-12,
            -0.00013107562554738283
          ],
          [
            5.75074650715929e-05,
            2.1976218826757138e-12,
            -6.549049524004931e-05
          ],
          [
            1.6457771961109787e-06,
            -7.716497478436239e-14,
            1.1567998761524093e-07
          ]
        ],
        "raw_reduced_polarization": [
          [
            0.03627402818202153,
            9.821939248218986e-10,
            -0.051718081269213546
          ],
          [
            0.031741135674248105,
            8.59707156209724e-10,
            -0.04525521162086156
          ],
          [
            0.027212906443058262,
            7.369854899049021e-10,
            -0.03879214697042892
          ],
          [
            0.022689625969137834,
            6.140254383808649e-10,
            -0.032328519875689035
          ],
          [
            0.018171562934020367,
            4.908229306875263e-10,
            -0.02586394875844816
          ],
          [
            0.013658975997465855,
            3.673894846562901e-10,
            -0.019398047794943873
          ],
          [
            0.00915211446377456,
            2.437375386668615e-10,
            -0.012930427780184542
          ],
          [
            0.004651219005375359,
            1.1985760084392944e-10,
            -0.0064606969633448225
          ],
          [
            0.00015652244943080597,
            -4.227903237520483e-12,
            1.153812167410914e-05
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            0.03627402818202153,
            9.821939248218986e-10,
            -0.051718081269213546
          ],
          [
            0.031741135674248105,
            8.59707156209724e-10,
            -0.04525521162086156
          ],
          [
            0.027212906443058262,
            7.369854899049021e-10,
            -0.03879214697042892
          ],
          [
            0.022689625969137834,
            6.140254383808649e-10,
            -0.032328519875689035
          ],
          [
            0.018171562934020367,
            4.908229306875263e-10,
            -0.02586394875844816
          ],
          [
            0.013658975997465855,
            3.673894846562901e-10,
            -0.019398047794943873
          ],
          [
            0.00915211446377456,
            2.437375386668615e-10,
            -0.012930427780184542
          ],
          [
            0.004651219005375359,
            1.1985760084392944e-10,
            -0.0064606969633448225
          ],
          [
            0.00015652244943080602,
            -4.227903237520472e-12,
            1.153812167410933e-05
          ]
        ],
        "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": [
          [
            0.03627402818202152,
            9.821938817822229e-10,
            -0.05171808126921357
          ],
          [
            0.03174113567424808,
            8.597071943228229e-10,
            -0.045255211620861546
          ],
          [
            0.027212906443058293,
            7.369854726491099e-10,
            -0.03879214697042893
          ],
          [
            0.022689625969137817,
            6.140253860920097e-10,
            -0.03232851987568902
          ],
          [
            0.018171562934020336,
            4.90822937848634e-10,
            -0.025863948758448163
          ],
          [
            0.013658975997465905,
            3.673894521938337e-10,
            -0.019398047794943862
          ],
          [
            0.009152114463774508,
            2.4373758567008963e-10,
            -0.01293042778018455
          ],
          [
            0.004651219005375351,
            1.198575683147851e-10,
            -0.006460696963344836
          ],
          [
            0.00015652244943076266,
            -4.22789581122629e-12,
            1.153812167409285e-05
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -162.41147367549524,
          -162.40527136021853,
          -162.3981784960672,
          -162.39019204543834,
          -162.3813090380936,
          -162.37152657095896,
          -162.36084180783996,
          -162.3492519790574,
          -162.33675438100948
        ],
        "cartesian_polarizations_e_A2": [
          [
            1.645777196158883e-06,
            -7.71443971154404e-14,
            1.1567998762261233e-07
          ],
          [
            -5.0817581078156334e-05,
            -1.8326152182401403e-12,
            6.08864354606196e-05
          ],
          [
            -0.00010327926961815674,
            -3.575002848384807e-12,
            0.00012162520233780668
          ],
          [
            -0.0001557387353454781,
            -5.3041692467767946e-12,
            0.0001823366934878275
          ],
          [
            -0.00020819543041570118,
            -7.0200967623899625e-12,
            0.00024302561723809607
          ],
          [
            -0.00026064879872132637,
            -8.72293006765904e-12,
            0.0003036966684228791
          ],
          [
            -0.000313098262375201,
            -1.0412628104559543e-11,
            0.0003643545193628656
          ],
          [
            -0.00036554320827770776,
            -1.2089198175377366e-11,
            0.00042500381077758106
          ],
          [
            -0.0004179829748674481,
            -1.375272187131136e-11,
            0.0004856491426360031
          ]
        ],
        "raw_reduced_polarization": [
          [
            0.00015652244943540903,
            -4.226777470088293e-12,
            1.1538121674840271e-05
          ],
          [
            -0.004074713784302232,
            -9.992232519828683e-11,
            0.00600666905741518
          ],
          [
            -0.008305754341277255,
            -1.9503628079249567e-10,
            0.011998263556672805
          ],
          [
            -0.012536490995889143,
            -2.8956071084869283e-10,
            0.017986787728776075
          ],
          [
            -0.016766816289742175,
            -3.834942739784838e-10,
            0.023972707009118036
          ],
          [
            -0.02099662236428542,
            -4.768445223134497e-10,
            0.029956485276892084
          ],
          [
            -0.025225799793129385,
            -5.696088485070253e-10,
            0.035938583965924975
          ],
          [
            -0.029454236423749013,
            -6.617872987664664e-10,
            0.04191946116874426
          ],
          [
            -0.0336818162378869,
            -7.533839952819293e-10,
            0.0478995707344195
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            0.00015652244943540903,
            -4.226777470088293e-12,
            1.1538121674840271e-05
          ],
          [
            -0.004074713784302232,
            -9.992232519828683e-11,
            0.00600666905741518
          ],
          [
            -0.008305754341277255,
            -1.9503628079249567e-10,
            0.011998263556672805
          ],
          [
            -0.012536490995889143,
            -2.8956071084869283e-10,
            0.017986787728776075
          ],
          [
            -0.016766816289742175,
            -3.834942739784838e-10,
            0.023972707009118036
          ],
          [
            -0.02099662236428542,
            -4.768445223134497e-10,
            0.029956485276892084
          ],
          [
            -0.025225799793129385,
            -5.696088485070253e-10,
            0.035938583965924975
          ],
          [
            -0.029454236423749013,
            -6.617872987664664e-10,
            0.04191946116874426
          ],
          [
            -0.0336818162378869,
            -7.533839952819293e-10,
            0.0478995707344195
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          -0.03596140691336791,
          -9.906482304557735e-10,
          0.051740900301567874
        ],
        "actual_opposite_endpoint_branch_residual": 0.004466804953340624
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            0.03627402818202153,
            9.821939248218986e-10,
            -0.051718081269213546
          ],
          [
            0.031741135674248105,
            8.59707156209724e-10,
            -0.04525521162086156
          ],
          [
            0.027212906443058262,
            7.369854899049021e-10,
            -0.03879214697042892
          ],
          [
            0.022689625969137834,
            6.140254383808649e-10,
            -0.032328519875689035
          ],
          [
            0.018171562934020367,
            4.908229306875263e-10,
            -0.02586394875844816
          ],
          [
            0.013658975997465855,
            3.673894846562901e-10,
            -0.019398047794943873
          ],
          [
            0.00915211446377456,
            2.437375386668615e-10,
            -0.012930427780184542
          ],
          [
            0.004651219005375359,
            1.1985760084392944e-10,
            -0.0064606969633448225
          ],
          [
            0.00015652244943080597,
            -4.227903237520483e-12,
            1.153812167410914e-05
          ],
          [
            -0.004074713784302232,
            -9.992232519828683e-11,
            0.00600666905741518
          ],
          [
            -0.008305754341277255,
            -1.9503628079249567e-10,
            0.011998263556672805
          ],
          [
            -0.012536490995889143,
            -2.8956071084869283e-10,
            0.017986787728776075
          ],
          [
            -0.016766816289742175,
            -3.834942739784838e-10,
            0.023972707009118036
          ],
          [
            -0.02099662236428542,
            -4.768445223134497e-10,
            0.029956485276892084
          ],
          [
            -0.025225799793129385,
            -5.696088485070253e-10,
            0.035938583965924975
          ],
          [
            -0.029454236423749013,
            -6.617872987664664e-10,
            0.04191946116874426
          ],
          [
            -0.0336818162378869,
            -7.533839952819293e-10,
            0.0478995707344195
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            0.03627402818202153,
            9.821939248218986e-10,
            -0.051718081269213546
          ],
          [
            0.031741135674248105,
            8.59707156209724e-10,
            -0.04525521162086156
          ],
          [
            0.027212906443058262,
            7.369854899049021e-10,
            -0.03879214697042892
          ],
          [
            0.022689625969137834,
            6.140254383808649e-10,
            -0.032328519875689035
          ],
          [
            0.018171562934020367,
            4.908229306875263e-10,
            -0.02586394875844816
          ],
          [
            0.013658975997465855,
            3.673894846562901e-10,
            -0.019398047794943873
          ],
          [
            0.00915211446377456,
            2.437375386668615e-10,
            -0.012930427780184542
          ],
          [
            0.004651219005375359,
            1.1985760084392944e-10,
            -0.0064606969633448225
          ],
          [
            0.00015652244943080602,
            -4.227903237520472e-12,
            1.153812167410933e-05
          ],
          [
            -0.004074713784302232,
            -9.992232519828683e-11,
            0.00600666905741518
          ],
          [
            -0.008305754341277255,
            -1.9503628079249567e-10,
            0.011998263556672805
          ],
          [
            -0.012536490995889143,
            -2.8956071084869283e-10,
            0.017986787728776075
          ],
          [
            -0.016766816289742175,
            -3.834942739784838e-10,
            0.023972707009118036
          ],
          [
            -0.02099662236428542,
            -4.768445223134497e-10,
            0.029956485276892084
          ],
          [
            -0.025225799793129385,
            -5.696088485070253e-10,
            0.035938583965924975
          ],
          [
            -0.029454236423749013,
            -6.617872987664664e-10,
            0.04191946116874426
          ],
          [
            -0.0336818162378869,
            -7.533839952819293e-10,
            0.0478995707344195
          ]
        ],
        "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": [
          [
            0.03627402818202152,
            9.821938817822229e-10,
            -0.05171808126921357
          ],
          [
            0.03174113567424808,
            8.597071943228229e-10,
            -0.045255211620861546
          ],
          [
            0.027212906443058293,
            7.369854726491099e-10,
            -0.03879214697042893
          ],
          [
            0.022689625969137817,
            6.140253860920097e-10,
            -0.03232851987568902
          ],
          [
            0.018171562934020336,
            4.90822937848634e-10,
            -0.025863948758448163
          ],
          [
            0.013658975997465905,
            3.673894521938337e-10,
            -0.019398047794943862
          ],
          [
            0.009152114463774508,
            2.4373758567008963e-10,
            -0.01293042778018455
          ],
          [
            0.004651219005375351,
            1.198575683147851e-10,
            -0.006460696963344836
          ],
          [
            0.00015652244943076266,
            -4.22789581122629e-12,
            1.153812167409285e-05
          ],
          [
            -0.004074713784302242,
            -9.992234817346457e-11,
            0.006006669057415204
          ],
          [
            -0.008305754341277227,
            -1.9503626491612636e-10,
            0.011998263556672772
          ],
          [
            -0.01253649099588916,
            -2.895607087438634e-10,
            0.017986787728776044
          ],
          [
            -0.016766816289742192,
            -3.8349429187789497e-10,
            0.02397270700911802
          ],
          [
            -0.0209966223642854,
            -4.768445083236372e-10,
            0.029956485276892098
          ],
          [
            -0.02522579979312939,
            -5.696088600792848e-10,
            0.035938583965924975
          ],
          [
            -0.029454236423749003,
            -6.617872916336864e-10,
            0.04191946116874423
          ],
          [
            -0.03368181623788691,
            -7.533840218343357e-10,
            0.04789957073441953
          ]
        ]
      },
      "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,
        0.0,
        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": [
              0.03627402818202208,
              9.821920979113885e-10,
              -0.05171808126921417
            ],
            "branch_aligned_reduced_polarization": [
              0.03627402818202208,
              9.821920979113885e-10,
              -0.05171808126921418
            ],
            "target_residual": 0.4497471331554043,
            "energy_eV": -162.43924227520603,
            "max_atomic_step_A": 0.11999999999999998,
            "max_log_strain_component": 0.007517184062981933,
            "step_scale": 0.8504749507336763,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.3912373274709768,
            "cell_principal_stretches": [
              1.0032338208000553,
              0.9987540934802824,
              0.9925109993010749
            ],
            "cell_volume_ratio": 0.9944800272250308,
            "cell_rmsd_from_input_A": 0.08819933148828543
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.003838938201074967,
              1.1865084159534266e-10,
              -0.442718468529767
            ],
            "branch_aligned_reduced_polarization": [
              0.003838938201074967,
              1.1865084159534266e-10,
              -0.442718468529767
            ],
            "target_residual": 0.05741002781820409,
            "energy_eV": -161.9058620682911,
            "max_atomic_step_A": 0.017219646441457598,
            "max_log_strain_component": 0.0009793565136316136,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.3912373274709768,
            "cell_principal_stretches": [
              1.003647186404045,
              0.9985871311506702,
              0.9915394530118058
            ],
            "cell_volume_ratio": 0.9937497576189699,
            "cell_rmsd_from_input_A": 0.09959278402396918
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.00026002102713328936,
              7.934970713644915e-12,
              -0.4997970210164359
            ],
            "branch_aligned_reduced_polarization": [
              -0.00026002102713328936,
              7.934970713644915e-12,
              -0.4997970210164359
            ],
            "target_residual": 0.00032986573377688,
            "energy_eV": -161.72145101965683
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_01",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cc",
        "spacegroup_number": 9,
        "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": 0.00032986573377688,
        "parent_symmetrization_rmsd_A": 0.0789981504924039,
        "parent_cell_rmsd_A": 0.09959278402396918,
        "energy_eV": -161.72145101965683,
        "reduced_polarization": [
          -0.00026002102713328936,
          7.934970713644915e-12,
          -0.4997970210164359
        ],
        "cartesian_polarization_e_A2": [
          0.0006225630922511098,
          1.0055839933015838e-12,
          -0.00509476717829615
        ],
        "ranking_score": 0.6045560779659499
      },
      "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": [
              0.03627402818202208,
              9.821920979113885e-10,
              -0.05171808126921417
            ],
            "branch_aligned_reduced_polarization": [
              0.03627402818202208,
              9.821920979113885e-10,
              -0.05171808126921417
            ],
            "target_residual": 0.4666010467934005,
            "energy_eV": -162.43924227520603,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.006181241253369459,
            "step_scale": 0.9035005877471194,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.3912373274709768,
            "cell_principal_stretches": [
              1.0104596960772163,
              1.0001849711460171,
              0.9938378233172183
            ],
            "cell_volume_ratio": 1.004418819040041,
            "cell_rmsd_from_input_A": 0.07999701032545266
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.42558271092996414,
              1.1170182984868535e-10,
              -0.001102333819908061
            ],
            "branch_aligned_reduced_polarization": [
              0.42558271092996414,
              1.1170182984868535e-10,
              -0.001102333819908061
            ],
            "target_residual": 0.07442545298742757,
            "energy_eV": -160.5961366301987,
            "max_atomic_step_A": 0.02895515671500734,
            "max_log_strain_component": 0.0017108265654557303,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.3912373274709768,
            "cell_principal_stretches": [
              1.01319170116222,
              1.0002253616349481,
              0.9921389927838983
            ],
            "cell_volume_ratio": 1.0054535334869266,
            "cell_rmsd_from_input_A": 0.10178796725974441
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.5011478842019392,
              2.510247086353523e-11,
              0.0025551260133825433
            ],
            "branch_aligned_reduced_polarization": [
              0.5011478842019392,
              2.510247086353523e-11,
              0.0025551260133825433
            ],
            "target_residual": 0.0028011260388147185,
            "energy_eV": -159.907406167929,
            "max_atomic_step_A": 0.0008252948989738226,
            "max_log_strain_component": 2.844127335318742e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.3912373274709768,
            "cell_principal_stretches": [
              1.0131668595542196,
              1.0002218175120798,
              0.99211077548887
            ],
            "cell_volume_ratio": 1.00539672387433,
            "cell_rmsd_from_input_A": 0.10204770368951191
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.4999735788737042,
              1.312757346812462e-12,
              -8.802731571280122e-06
            ],
            "branch_aligned_reduced_polarization": [
              0.4999735788737042,
              1.312757346812462e-12,
              -8.802731571280122e-06
            ],
            "target_residual": 2.7848949672383276e-05,
            "energy_eV": -159.91924683886668
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_02",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cc",
        "spacegroup_number": 9,
        "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": 2.7848949672383276e-05,
        "parent_symmetrization_rmsd_A": 0.17522742325295593,
        "parent_cell_rmsd_A": 0.10204770368951191,
        "energy_eV": -159.91924683886668,
        "reduced_polarization": [
          0.4999735788737042,
          1.312757346812462e-12,
          -8.802731571280122e-06
        ],
        "cartesian_polarization_e_A2": [
          0.00531272656075145,
          1.497814021018757e-12,
          3.383379659634359e-05
        ],
        "ranking_score": 0.7007950470746787
      },
      "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": false,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              0.03627402818202208,
              9.821920979113885e-10,
              -0.05171808126921417
            ],
            "branch_aligned_reduced_polarization": [
              0.03627402818202208,
              9.821921054253835e-10,
              -0.05171808126921417
            ],
            "target_residual": 0.5039747653092633,
            "energy_eV": -162.43924227520603,
            "max_atomic_step_A": 0.105745360677967,
            "max_log_strain_component": 0.02,
            "step_scale": 0.4632281867358472,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.3912373274709768,
            "cell_principal_stretches": [
              1.0265083053978976,
              0.9993786836032537,
              0.9749568037297281
            ],
            "cell_volume_ratio": 1.000179442202248,
            "cell_rmsd_from_input_A": 0.25903568567791163
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.018224263093996225,
              0.20999779229954982,
              -0.03843598321296976
            ],
            "branch_aligned_reduced_polarization": [
              0.018224263093996225,
              0.20999779229954985,
              -0.03843598321296976
            ],
            "target_residual": 0.29310532073301215,
            "energy_eV": -160.9159354422976,
            "max_atomic_step_A": 0.08852894320252182,
            "max_log_strain_component": 0.02,
            "step_scale": 0.5573988514711684,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.3912373274709768,
            "cell_principal_stretches": [
              1.0539522656585838,
              0.9984810229861522,
              0.9507429694420694
            ],
            "cell_volume_ratio": 1.0005156344589499,
            "cell_rmsd_from_input_A": 0.521258086348641
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.009007504078424782,
              0.3332820493585476,
              -0.02013315554527641
            ],
            "branch_aligned_reduced_polarization": [
              0.009007504078424782,
              0.3332820493585476,
              -0.02013315554527641
            ],
            "target_residual": 0.16817061023858745,
            "energy_eV": -157.66437256361303,
            "max_atomic_step_A": 0.08174290762473924,
            "max_log_strain_component": 0.02,
            "step_scale": 0.6381807850774216,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.3912373274709768,
            "cell_principal_stretches": [
              1.0825917624619894,
              0.9968356519676725,
              0.9275054444642495
            ],
            "cell_volume_ratio": 1.0009324010919156,
            "cell_rmsd_from_input_A": 0.7900323698839344
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.010476111588663734,
              0.40119652116455323,
              -0.002831699560930218
            ],
            "branch_aligned_reduced_polarization": [
              0.010476111588663734,
              0.40119652116455323,
              -0.002831699560930218
            ],
            "target_residual": 0.09939766026626624,
            "energy_eV": -155.01858905786537,
            "max_atomic_step_A": 0.07507061087226104,
            "max_log_strain_component": 0.02,
            "step_scale": 0.8865848670755684,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.3912373274709768,
            "cell_principal_stretches": [
              1.112449287813592,
              0.994235624543443,
              0.9051661784486883
            ],
            "cell_volume_ratio": 1.0011470242253069,
            "cell_rmsd_from_input_A": 1.0684384035978087
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              0.013526071767876083,
              0.4455354336922996,
              -7.861441991280396e-06
            ],
            "branch_aligned_reduced_polarization": [
              0.013526071767876083,
              0.4455354336922996,
              -7.861441991280396e-06
            ],
            "target_residual": 0.05611901337655448,
            "energy_eV": -153.10554494077283,
            "max_atomic_step_A": 0.044609294511664094,
            "max_log_strain_component": 0.01424711230539116,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": true,
            "strain_jacobian_frobenius_norm": 2.2618991328916334,
            "cell_principal_stretches": [
              1.0981645601294487,
              0.9970719452129648,
              0.9222618447070702
            ],
            "cell_volume_ratio": 1.0098297529694695,
            "cell_rmsd_from_input_A": 0.917158222780554
          },
          {
            "iteration": 5,
            "reduced_polarization": [
              -0.001782394013151867,
              0.491963428255442,
              0.003984106377060552
            ],
            "branch_aligned_reduced_polarization": [
              -0.001782394013151867,
              0.491963428255442,
              0.003984106377060552
            ],
            "target_residual": 0.009145300292898123,
            "energy_eV": -154.2233130566047
          }
        ],
        "iterations": 5
      },
      "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": 0.009145300292898123,
        "parent_symmetrization_rmsd_A": 0.4012278966881886,
        "parent_cell_rmsd_A": 0.917158222780554,
        "energy_eV": -154.2233130566047,
        "reduced_polarization": [
          -0.001782394013151867,
          0.491963428255442,
          0.003984106377060552
        ],
        "cartesian_polarization_e_A2": [
          -0.0006071217647348035,
          0.009039897063005233,
          0.0005508703923479967
        ],
        "ranking_score": 1.1488080529691234
      },
      "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": [
              0.03627402818202208,
              9.821920979113885e-10,
              -0.05171808126921417
            ],
            "branch_aligned_reduced_polarization": [
              0.03627402818202208,
              9.821920979113885e-10,
              -0.05171808126921418
            ],
            "target_residual": 0.6449794226170963,
            "energy_eV": -162.43924227520603,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.009165497857803625,
            "step_scale": 0.5269924614234579,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.3912373274709768,
            "cell_principal_stretches": [
              1.0084682773425706,
              0.9996706310063107,
              0.9908763772845222
            ],
            "cell_volume_ratio": 0.9989382655638241,
            "cell_rmsd_from_input_A": 0.1101143417962877
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.2769144032171073,
              4.914300259789272e-10,
              -0.2868249274729215
            ],
            "branch_aligned_reduced_polarization": [
              0.2769144032171073,
              4.914300259789272e-10,
              -0.2868249274729215
            ],
            "target_residual": 0.30856246537598275,
            "energy_eV": -161.49449739159098,
            "max_atomic_step_A": 0.11263040083831947,
            "max_log_strain_component": 0.008714283983423068,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.3912373274709768,
            "cell_principal_stretches": [
              1.01693565206811,
              0.9994034017866102,
              0.9822791130468095
            ],
            "cell_volume_ratio": 0.9983186996434201,
            "cell_rmsd_from_input_A": 0.2135102796290011
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.48601444579655195,
              9.615684654099143e-11,
              -0.4778573722575807
            ],
            "branch_aligned_reduced_polarization": [
              0.48601444579655195,
              9.615684654099143e-11,
              -0.4778573722575807
            ],
            "target_residual": 0.02618953397288583,
            "energy_eV": -159.1493664862983,
            "max_atomic_step_A": 0.010434224101169752,
            "max_log_strain_component": 0.0009586437032674073,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.3912373274709768,
            "cell_principal_stretches": [
              1.0177881913667217,
              0.9993632163262521,
              0.981337908572188
            ],
            "cell_volume_ratio": 0.9981581192866306,
            "cell_rmsd_from_input_A": 0.22471792652079745
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.5000614296169189,
              1.9793835408100823e-11,
              -0.4984763109503265
            ],
            "branch_aligned_reduced_polarization": [
              0.5000614296169189,
              1.9793835408100823e-11,
              -0.4984763109503265
            ],
            "target_residual": 0.0015249268565835162,
            "energy_eV": -158.90813509594682,
            "max_atomic_step_A": 0.0004926965642169729,
            "max_log_strain_component": 3.57364380930526e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.3912373274709768,
            "cell_principal_stretches": [
              1.017807555196714,
              0.9993601058371059,
              0.9813028396773923
            ],
            "cell_volume_ratio": 0.9981383323030912,
            "cell_rmsd_from_input_A": 0.2251243139219663
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              0.49999607783221023,
              2.3119245777041353e-12,
              -0.4999605751814464
            ],
            "branch_aligned_reduced_polarization": [
              0.49999607783221023,
              2.3119245777041353e-12,
              -0.4999605751814464
            ],
            "target_residual": 3.961943611609451e-05,
            "energy_eV": -158.9024076534127
          }
        ],
        "iterations": 4
      },
      "parent": {
        "candidate_id": "bec_projection_04",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cc",
        "spacegroup_number": 9,
        "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": 3.961943611609451e-05,
        "parent_symmetrization_rmsd_A": 0.1692932668505027,
        "parent_cell_rmsd_A": 0.2251243139219663,
        "energy_eV": -158.9024076534127,
        "reduced_polarization": [
          0.49999607783221023,
          2.3119245777041353e-12,
          -0.4999605751814464
        ],
        "cartesian_polarization_e_A2": [
          0.005962948328939401,
          2.2952284311405195e-12,
          -0.005061056693968992
        ],
        "ranking_score": 0.7256535842032265
      },
      "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": false,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              0.03627402818202208,
              9.821920979113885e-10,
              -0.05171808126921417
            ],
            "branch_aligned_reduced_polarization": [
              0.03627402818202208,
              9.821921054253835e-10,
              -0.05171808126921418
            ],
            "target_residual": 0.6725120688874757,
            "energy_eV": -162.43924227520603,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.018034615216207063,
            "step_scale": 0.4177071049808331,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.3912373274709768,
            "cell_principal_stretches": [
              1.0216421596088963,
              1.0010888923331005,
              0.9750971087284921
            ],
            "cell_volume_ratio": 0.9972850708760809,
            "cell_rmsd_from_input_A": 0.23494909218736837
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.016691509206342898,
              0.18947248461946464,
              -0.24328107950527522
            ],
            "branch_aligned_reduced_polarization": [
              0.016691509206342898,
              0.18947248461946464,
              -0.24328107950527522
            ],
            "target_residual": 0.4032499825517304,
            "energy_eV": -161.00474036430865,
            "max_atomic_step_A": 0.09855176991678617,
            "max_log_strain_component": 0.02,
            "step_scale": 0.5743569519120715,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.3912373274709768,
            "cell_principal_stretches": [
              1.0469262431566242,
              1.0017106561942846,
              0.9489916622729654
            ],
            "cell_volume_ratio": 0.9952238542269144,
            "cell_rmsd_from_input_A": 0.49080977178269747
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.0004527089462655828,
              0.3266964149347083,
              -0.3805553848897254
            ],
            "branch_aligned_reduced_polarization": [
              -0.0004527089462655828,
              0.3266964149347083,
              -0.3805553848897254
            ],
            "target_residual": 0.21047886739697758,
            "energy_eV": -156.86668779564354,
            "max_atomic_step_A": 0.08392948260187483,
            "max_log_strain_component": 0.02,
            "step_scale": 0.7449917955738917,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.3912373274709768,
            "cell_principal_stretches": [
              1.0738706763326722,
              1.001082186738453,
              0.9245817604597665
            ],
            "cell_volume_ratio": 0.9939557233410343,
            "cell_rmsd_from_input_A": 0.74708237662391
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -0.002373976597846839,
              0.4097569026258075,
              -0.449743448871982
            ],
            "branch_aligned_reduced_polarization": [
              -0.002373976597846839,
              0.4097569026258075,
              -0.449743448871982
            ],
            "target_residual": 0.10332073034903598,
            "energy_eV": -152.86506377705825,
            "max_atomic_step_A": 0.06749962537593365,
            "max_log_strain_component": 0.01767475059980277,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.3912373274709768,
            "cell_principal_stretches": [
              1.0990726502616948,
              0.9991544754863116,
              0.9042334917420397
            ],
            "cell_volume_ratio": 0.9929780024893181,
            "cell_rmsd_from_input_A": 0.9790761581991266
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              -0.0010109996973235178,
              0.45649179927180855,
              -0.4805699418532565
            ],
            "branch_aligned_reduced_polarization": [
              -0.0010109996973235178,
              0.45649179927180855,
              -0.4805699418532565
            ],
            "target_residual": 0.04766039037375187,
            "energy_eV": -151.0599904733001,
            "max_atomic_step_A": 0.027403920513135574,
            "max_log_strain_component": 0.009021938391320955,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": true,
            "strain_jacobian_frobenius_norm": 2.857166118788059,
            "cell_principal_stretches": [
              1.0895283861049059,
              1.000989296667451,
              0.9159016797986539
            ],
            "cell_volume_ratio": 0.9988880990358623,
            "cell_rmsd_from_input_A": 0.8750600852457274
          },
          {
            "iteration": 5,
            "reduced_polarization": [
              -0.0005945157599781074,
              0.4966622097144988,
              -0.4970491773929603
            ],
            "branch_aligned_reduced_polarization": [
              -0.0005945157599781074,
              0.4966622097144988,
              -0.4970491773929603
            ],
            "target_residual": 0.004494624237582614,
            "energy_eV": -152.161793718264
          }
        ],
        "iterations": 5
      },
      "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": 0.004494624237582614,
        "parent_symmetrization_rmsd_A": 0.3930410515850662,
        "parent_cell_rmsd_A": 0.8750600852457274,
        "energy_eV": -152.161793718264,
        "reduced_polarization": [
          -0.0005945157599781074,
          0.4966622097144988,
          -0.4970491773929603
        ],
        "cartesian_polarization_e_A2": [
          2.611625571445428e-05,
          0.008775159977041527,
          -0.004563876627819419
        ],
        "ranking_score": 1.1207953213716633
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 6,
      "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": false,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              0.03627402818202208,
              9.821920979113885e-10,
              -0.05171808126921417
            ],
            "branch_aligned_reduced_polarization": [
              0.03627402818202208,
              9.821921054253835e-10,
              -0.05171808126921417
            ],
            "target_residual": 0.6838980449500532,
            "energy_eV": -162.43924227520603,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.019976219456753576,
            "step_scale": 0.4626773977873363,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.3912373274709768,
            "cell_principal_stretches": [
              1.0245464686160324,
              1.0053344311880898,
              0.9730571798084285
            ],
            "cell_volume_ratio": 1.002260417417827,
            "cell_rmsd_from_input_A": 0.25943980332341576
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.2307165496712193,
              0.2079782740104991,
              -0.03753588370976068
            ],
            "branch_aligned_reduced_polarization": [
              0.2307165496712193,
              0.20797827401049906,
              -0.03753588370976068
            ],
            "target_residual": 0.39899775392442094,
            "energy_eV": -160.15594851732078,
            "max_atomic_step_A": 0.10527560253908529,
            "max_log_strain_component": 0.02,
            "step_scale": 0.5813503930535094,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.3912373274709768,
            "cell_principal_stretches": [
              1.050020782410044,
              1.0102117024849004,
              0.9471108960983801
            ],
            "cell_volume_ratio": 1.0046415205754833,
            "cell_rmsd_from_input_A": 0.5165618916039861
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.36424340196422866,
              0.3351472694301179,
              -0.017636374831869046
            ],
            "branch_aligned_reduced_polarization": [
              0.36424340196422866,
              0.3351472694301179,
              -0.017636374831869046
            ],
            "target_residual": 0.21428326673775142,
            "energy_eV": -155.55221858467743,
            "max_atomic_step_A": 0.08795928424262757,
            "max_log_strain_component": 0.02,
            "step_scale": 0.8102844970044968,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.3912373274709768,
            "cell_principal_stretches": [
              1.076789686320932,
              1.0138463886915223,
              0.9224847015656211
            ],
            "cell_volume_ratio": 1.00707593511472,
            "cell_rmsd_from_input_A": 0.7739478417306898
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.4545951212981481,
              0.4250056590019811,
              -0.004708747326522457
            ],
            "branch_aligned_reduced_polarization": [
              0.4545951212981481,
              0.4250056590019811,
              -0.004708747326522457
            ],
            "target_residual": 0.08779479764224103,
            "energy_eV": -152.10937617721896,
            "max_atomic_step_A": 0.04333407404490146,
            "max_log_strain_component": 0.012395948773425647,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.3912373274709768,
            "cell_principal_stretches": [
              1.0944658215511487,
              1.01466962807068,
              0.9082075766491123
            ],
            "cell_volume_ratio": 1.0085837933804478,
            "cell_rmsd_from_input_A": 0.9363355085641968
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              0.4835319157308149,
              0.4678148566038532,
              -0.0003494480917497561
            ],
            "branch_aligned_reduced_polarization": [
              0.4835319157308149,
              0.4678148566038532,
              -0.0003494480917497561
            ],
            "target_residual": 0.03615526751244336,
            "energy_eV": -150.71983236766226,
            "max_atomic_step_A": 0.012742526449004978,
            "max_log_strain_component": 0.005998731984391309,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": true,
            "strain_jacobian_frobenius_norm": 3.10489538296897,
            "cell_principal_stretches": [
              1.0920912727259247,
              1.0145761682137082,
              0.9180402112257907
            ],
            "cell_volume_ratio": 1.0171975313898989,
            "cell_rmsd_from_input_A": 0.8825445411425834
          },
          {
            "iteration": 5,
            "reduced_polarization": [
              0.4990249510117245,
              0.4983331719751787,
              0.0009871398564797937
            ],
            "branch_aligned_reduced_polarization": [
              0.4990249510117245,
              0.4983331719751787,
              0.0009871398564797937
            ],
            "target_residual": 0.00216875108994042,
            "energy_eV": -151.25378746084522
          }
        ],
        "iterations": 5
      },
      "parent": {
        "candidate_id": "bec_projection_06",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.5,
          0.5,
          0.0
        ],
        "formal_class": [
          0.5,
          0.5,
          0.0
        ],
        "target_residual": 0.00216875108994042,
        "parent_symmetrization_rmsd_A": 0.42593124317917974,
        "parent_cell_rmsd_A": 0.8825445411425834,
        "energy_eV": -151.25378746084522,
        "reduced_polarization": [
          0.4990249510117245,
          0.4983331719751787,
          0.0009871398564797937
        ],
        "cartesian_polarization_e_A2": [
          0.004653629533942558,
          0.0086220532459691,
          0.0005208091852115008
        ],
        "ranking_score": 1.1509048806447064
      },
      "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": false,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              0.03627402818202208,
              9.821920979113885e-10,
              -0.05171808126921417
            ],
            "branch_aligned_reduced_polarization": [
              0.03627402818202208,
              9.821921054253835e-10,
              -0.05171808126921418
            ],
            "target_residual": 0.8160872837002736,
            "energy_eV": -162.43924227520603,
            "max_atomic_step_A": 0.12000000000000001,
            "max_log_strain_component": 0.015078541351189552,
            "step_scale": 0.34924026967846344,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.3912373274709768,
            "cell_principal_stretches": [
              1.0167951283168548,
              1.0053773194169764,
              0.9775336599187456
            ],
            "cell_volume_ratio": 0.9992962576735681,
            "cell_rmsd_from_input_A": 0.20540723751566195
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.18822073404768608,
              0.16148412226333198,
              -0.21009971511423625
            ],
            "branch_aligned_reduced_polarization": [
              0.18822073404768608,
              0.16148412226333198,
              -0.21009971511423625
            ],
            "target_residual": 0.5439131229658257,
            "energy_eV": -161.00088461912446,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.018035095348226463,
            "step_scale": 0.5242331397751944,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.3912373274709768,
            "cell_principal_stretches": [
              1.0376201666021159,
              1.011490330534745,
              0.951804458948802
            ],
            "cell_volume_ratio": 0.9989594838565677,
            "cell_rmsd_from_input_A": 0.4421805209823445
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.32268485845095646,
              0.29945231344934764,
              -0.3418325690667313
            ],
            "branch_aligned_reduced_polarization": [
              0.32268485845095646,
              0.29945231344934764,
              -0.3418325690667313
            ],
            "target_residual": 0.310929204500649,
            "energy_eV": -156.20370390196697,
            "max_atomic_step_A": 0.09896423995342929,
            "max_log_strain_component": 0.02,
            "step_scale": 0.8013876610759854,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.3912373274709768,
            "cell_principal_stretches": [
              1.0612931831822037,
              1.0182913752594935,
              0.9241560015035643
            ],
            "cell_volume_ratio": 0.9987406539452051,
            "cell_rmsd_from_input_A": 0.6987641542184618
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.4278704537972787,
              0.4107431436549175,
              -0.4288283438514609
            ],
            "branch_aligned_reduced_polarization": [
              0.4278704537972787,
              0.4107431436549175,
              -0.4288283438514609
            ],
            "target_residual": 0.13503652275937456,
            "energy_eV": -150.39290144303774,
            "max_atomic_step_A": 0.052707569006372704,
            "max_log_strain_component": 0.010940535058795404,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.3912373274709768,
            "cell_principal_stretches": [
              1.0739380597483816,
              1.0228700081738107,
              0.9087393520834394
            ],
            "cell_volume_ratio": 0.9982492985612486,
            "cell_rmsd_from_input_A": 0.8397075136164903
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              0.4754877808626306,
              0.46682352461233,
              -0.48044620828404955
            ],
            "branch_aligned_reduced_polarization": [
              0.4754877808626306,
              0.46682352461233,
              -0.48044620828404955
            ],
            "target_residual": 0.04564951452817285,
            "energy_eV": -148.69987476793568,
            "max_atomic_step_A": 0.009941917621285904,
            "max_log_strain_component": 0.005614326944517228,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": true,
            "strain_jacobian_frobenius_norm": 3.5640491265389915,
            "cell_principal_stretches": [
              1.0742145322289918,
              1.0234238561455524,
              0.9180973936872648
            ],
            "cell_volume_ratio": 1.009334955389663,
            "cell_rmsd_from_input_A": 0.7892154294561787
          },
          {
            "iteration": 5,
            "reduced_polarization": [
              0.49856587186090773,
              0.49857337309027666,
              -0.4983518687948321
            ],
            "branch_aligned_reduced_polarization": [
              0.49856587186090773,
              0.49857337309027666,
              -0.4983518687948321
            ],
            "target_residual": 0.0026092765909981937,
            "energy_eV": -149.1964677656184
          }
        ],
        "iterations": 5
      },
      "parent": {
        "candidate_id": "bec_projection_07",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.5,
          0.5,
          -0.5
        ],
        "formal_class": [
          0.5,
          0.5,
          0.5
        ],
        "target_residual": 0.0026092765909981937,
        "parent_symmetrization_rmsd_A": 0.4115249424013717,
        "parent_cell_rmsd_A": 0.7892154294561787,
        "energy_eV": -149.1964677656184,
        "reduced_polarization": [
          0.49856587186090773,
          0.49857337309027666,
          -0.4983518687948321
        ],
        "cartesian_polarization_e_A2": [
          0.0053855113015361155,
          0.008281594241802475,
          -0.004592007628766156
        ],
        "ranking_score": 1.1140473529474129
      },
      "branch_status": "awaiting_branch_sampling"
    }
  ],
  "sampled_polarization_branches": [
    {
      "orbit_id": 0,
      "candidate_id": "bec_projection_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,
          26,
          27,
          28,
          29,
          30,
          31
        ],
        "endpoint_rmsd_A": 0.01332236541339397,
        "minimum_distance_A_by_image": [
          2.0645955447030095,
          2.063312218606206,
          2.062029090112179,
          2.060746159021515,
          2.059463425134848,
          2.0581808882528523,
          2.056898548176246,
          2.0556164047057957,
          2.054334457642304
        ],
        "minimum_distance_A": 2.054334457642304,
        "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": [
          713.2495657669397,
          713.2841002546791,
          713.3186364145279,
          713.3531742465658,
          713.3877137508744,
          713.4222549275346,
          713.456797776628,
          713.4913422982345,
          713.5258884924349
        ],
        "cell_deformation_log_strain_norm": 0.0022197312549477543
      },
      "parent_reduced_polarization": [
        0.00015652244943080597,
        -4.227903237520483e-12,
        1.153812167410914e-05
      ],
      "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": [
          -162.43924227520603,
          -162.43891106920165,
          -162.43768725213897,
          -162.43556850755294,
          -162.4325525691989,
          -162.42863723128556,
          -162.42382034883406,
          -162.41809983787945,
          -162.41147367549527
        ],
        "cartesian_polarizations_e_A2": [
          [
            0.0004503178329578138,
            1.7929555122434484e-11,
            -0.0005243646538386265
          ],
          [
            0.0003940268645807537,
            1.5703258342204757e-11,
            -0.0004588235284896463
          ],
          [
            0.00033779032578906595,
            1.3469919746899456e-11,
            -0.0003932846373408196
          ],
          [
            0.00028161076054655267,
            1.1229474269269067e-11,
            -0.00032774427100240095
          ],
          [
            0.0002254905137724994,
            8.98184611651082e-12,
            -0.00026219857932566676
          ],
          [
            0.0001694318158314607,
            6.7272442161889734e-12,
            -0.00019664367165217746
          ],
          [
            0.00011343679076162715,
            4.465894417195045e-12,
            -0.00013107562554738283
          ],
          [
            5.75074650715929e-05,
            2.1976218826757138e-12,
            -6.549049524004931e-05
          ],
          [
            1.6457771961109787e-06,
            -7.716497478436239e-14,
            1.1567998761524093e-07
          ]
        ],
        "raw_reduced_polarization": [
          [
            0.03627402818202153,
            9.821939248218986e-10,
            -0.051718081269213546
          ],
          [
            0.031741135674248105,
            8.59707156209724e-10,
            -0.04525521162086156
          ],
          [
            0.027212906443058262,
            7.369854899049021e-10,
            -0.03879214697042892
          ],
          [
            0.022689625969137834,
            6.140254383808649e-10,
            -0.032328519875689035
          ],
          [
            0.018171562934020367,
            4.908229306875263e-10,
            -0.02586394875844816
          ],
          [
            0.013658975997465855,
            3.673894846562901e-10,
            -0.019398047794943873
          ],
          [
            0.00915211446377456,
            2.437375386668615e-10,
            -0.012930427780184542
          ],
          [
            0.004651219005375359,
            1.1985760084392944e-10,
            -0.0064606969633448225
          ],
          [
            0.00015652244943080597,
            -4.227903237520483e-12,
            1.153812167410914e-05
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            0.03627402818202153,
            9.821939248218986e-10,
            -0.051718081269213546
          ],
          [
            0.031741135674248105,
            8.59707156209724e-10,
            -0.04525521162086156
          ],
          [
            0.027212906443058262,
            7.369854899049021e-10,
            -0.03879214697042892
          ],
          [
            0.022689625969137834,
            6.140254383808649e-10,
            -0.032328519875689035
          ],
          [
            0.018171562934020367,
            4.908229306875263e-10,
            -0.02586394875844816
          ],
          [
            0.013658975997465855,
            3.673894846562901e-10,
            -0.019398047794943873
          ],
          [
            0.00915211446377456,
            2.437375386668615e-10,
            -0.012930427780184542
          ],
          [
            0.004651219005375359,
            1.1985760084392944e-10,
            -0.0064606969633448225
          ],
          [
            0.00015652244943080602,
            -4.227903237520472e-12,
            1.153812167410933e-05
          ]
        ],
        "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": [
          [
            0.03627402818202152,
            9.821938817822229e-10,
            -0.05171808126921357
          ],
          [
            0.03174113567424808,
            8.597071943228229e-10,
            -0.045255211620861546
          ],
          [
            0.027212906443058293,
            7.369854726491099e-10,
            -0.03879214697042893
          ],
          [
            0.022689625969137817,
            6.140253860920097e-10,
            -0.03232851987568902
          ],
          [
            0.018171562934020336,
            4.90822937848634e-10,
            -0.025863948758448163
          ],
          [
            0.013658975997465905,
            3.673894521938337e-10,
            -0.019398047794943862
          ],
          [
            0.009152114463774508,
            2.4373758567008963e-10,
            -0.01293042778018455
          ],
          [
            0.004651219005375351,
            1.198575683147851e-10,
            -0.006460696963344836
          ],
          [
            0.00015652244943076266,
            -4.22789581122629e-12,
            1.153812167409285e-05
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -162.41147367549524,
          -162.40527136021853,
          -162.3981784960672,
          -162.39019204543834,
          -162.3813090380936,
          -162.37152657095896,
          -162.36084180783996,
          -162.3492519790574,
          -162.33675438100948
        ],
        "cartesian_polarizations_e_A2": [
          [
            1.645777196158883e-06,
            -7.71443971154404e-14,
            1.1567998762261233e-07
          ],
          [
            -5.0817581078156334e-05,
            -1.8326152182401403e-12,
            6.08864354606196e-05
          ],
          [
            -0.00010327926961815674,
            -3.575002848384807e-12,
            0.00012162520233780668
          ],
          [
            -0.0001557387353454781,
            -5.3041692467767946e-12,
            0.0001823366934878275
          ],
          [
            -0.00020819543041570118,
            -7.0200967623899625e-12,
            0.00024302561723809607
          ],
          [
            -0.00026064879872132637,
            -8.72293006765904e-12,
            0.0003036966684228791
          ],
          [
            -0.000313098262375201,
            -1.0412628104559543e-11,
            0.0003643545193628656
          ],
          [
            -0.00036554320827770776,
            -1.2089198175377366e-11,
            0.00042500381077758106
          ],
          [
            -0.0004179829748674481,
            -1.375272187131136e-11,
            0.0004856491426360031
          ]
        ],
        "raw_reduced_polarization": [
          [
            0.00015652244943540903,
            -4.226777470088293e-12,
            1.1538121674840271e-05
          ],
          [
            -0.004074713784302232,
            -9.992232519828683e-11,
            0.00600666905741518
          ],
          [
            -0.008305754341277255,
            -1.9503628079249567e-10,
            0.011998263556672805
          ],
          [
            -0.012536490995889143,
            -2.8956071084869283e-10,
            0.017986787728776075
          ],
          [
            -0.016766816289742175,
            -3.834942739784838e-10,
            0.023972707009118036
          ],
          [
            -0.02099662236428542,
            -4.768445223134497e-10,
            0.029956485276892084
          ],
          [
            -0.025225799793129385,
            -5.696088485070253e-10,
            0.035938583965924975
          ],
          [
            -0.029454236423749013,
            -6.617872987664664e-10,
            0.04191946116874426
          ],
          [
            -0.0336818162378869,
            -7.533839952819293e-10,
            0.0478995707344195
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            0.00015652244943540903,
            -4.226777470088293e-12,
            1.1538121674840271e-05
          ],
          [
            -0.004074713784302232,
            -9.992232519828683e-11,
            0.00600666905741518
          ],
          [
            -0.008305754341277255,
            -1.9503628079249567e-10,
            0.011998263556672805
          ],
          [
            -0.012536490995889143,
            -2.8956071084869283e-10,
            0.017986787728776075
          ],
          [
            -0.016766816289742175,
            -3.834942739784838e-10,
            0.023972707009118036
          ],
          [
            -0.02099662236428542,
            -4.768445223134497e-10,
            0.029956485276892084
          ],
          [
            -0.025225799793129385,
            -5.696088485070253e-10,
            0.035938583965924975
          ],
          [
            -0.029454236423749013,
            -6.617872987664664e-10,
            0.04191946116874426
          ],
          [
            -0.0336818162378869,
            -7.533839952819293e-10,
            0.0478995707344195
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          -0.03596140691336791,
          -9.906482304557735e-10,
          0.051740900301567874
        ],
        "actual_opposite_endpoint_branch_residual": 0.004466804953340624
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            0.03627402818202153,
            9.821939248218986e-10,
            -0.051718081269213546
          ],
          [
            0.031741135674248105,
            8.59707156209724e-10,
            -0.04525521162086156
          ],
          [
            0.027212906443058262,
            7.369854899049021e-10,
            -0.03879214697042892
          ],
          [
            0.022689625969137834,
            6.140254383808649e-10,
            -0.032328519875689035
          ],
          [
            0.018171562934020367,
            4.908229306875263e-10,
            -0.02586394875844816
          ],
          [
            0.013658975997465855,
            3.673894846562901e-10,
            -0.019398047794943873
          ],
          [
            0.00915211446377456,
            2.437375386668615e-10,
            -0.012930427780184542
          ],
          [
            0.004651219005375359,
            1.1985760084392944e-10,
            -0.0064606969633448225
          ],
          [
            0.00015652244943080597,
            -4.227903237520483e-12,
            1.153812167410914e-05
          ],
          [
            -0.004074713784302232,
            -9.992232519828683e-11,
            0.00600666905741518
          ],
          [
            -0.008305754341277255,
            -1.9503628079249567e-10,
            0.011998263556672805
          ],
          [
            -0.012536490995889143,
            -2.8956071084869283e-10,
            0.017986787728776075
          ],
          [
            -0.016766816289742175,
            -3.834942739784838e-10,
            0.023972707009118036
          ],
          [
            -0.02099662236428542,
            -4.768445223134497e-10,
            0.029956485276892084
          ],
          [
            -0.025225799793129385,
            -5.696088485070253e-10,
            0.035938583965924975
          ],
          [
            -0.029454236423749013,
            -6.617872987664664e-10,
            0.04191946116874426
          ],
          [
            -0.0336818162378869,
            -7.533839952819293e-10,
            0.0478995707344195
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            0.03627402818202153,
            9.821939248218986e-10,
            -0.051718081269213546
          ],
          [
            0.031741135674248105,
            8.59707156209724e-10,
            -0.04525521162086156
          ],
          [
            0.027212906443058262,
            7.369854899049021e-10,
            -0.03879214697042892
          ],
          [
            0.022689625969137834,
            6.140254383808649e-10,
            -0.032328519875689035
          ],
          [
            0.018171562934020367,
            4.908229306875263e-10,
            -0.02586394875844816
          ],
          [
            0.013658975997465855,
            3.673894846562901e-10,
            -0.019398047794943873
          ],
          [
            0.00915211446377456,
            2.437375386668615e-10,
            -0.012930427780184542
          ],
          [
            0.004651219005375359,
            1.1985760084392944e-10,
            -0.0064606969633448225
          ],
          [
            0.00015652244943080602,
            -4.227903237520472e-12,
            1.153812167410933e-05
          ],
          [
            -0.004074713784302232,
            -9.992232519828683e-11,
            0.00600666905741518
          ],
          [
            -0.008305754341277255,
            -1.9503628079249567e-10,
            0.011998263556672805
          ],
          [
            -0.012536490995889143,
            -2.8956071084869283e-10,
            0.017986787728776075
          ],
          [
            -0.016766816289742175,
            -3.834942739784838e-10,
            0.023972707009118036
          ],
          [
            -0.02099662236428542,
            -4.768445223134497e-10,
            0.029956485276892084
          ],
          [
            -0.025225799793129385,
            -5.696088485070253e-10,
            0.035938583965924975
          ],
          [
            -0.029454236423749013,
            -6.617872987664664e-10,
            0.04191946116874426
          ],
          [
            -0.0336818162378869,
            -7.533839952819293e-10,
            0.0478995707344195
          ]
        ],
        "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": [
          [
            0.03627402818202152,
            9.821938817822229e-10,
            -0.05171808126921357
          ],
          [
            0.03174113567424808,
            8.597071943228229e-10,
            -0.045255211620861546
          ],
          [
            0.027212906443058293,
            7.369854726491099e-10,
            -0.03879214697042893
          ],
          [
            0.022689625969137817,
            6.140253860920097e-10,
            -0.03232851987568902
          ],
          [
            0.018171562934020336,
            4.90822937848634e-10,
            -0.025863948758448163
          ],
          [
            0.013658975997465905,
            3.673894521938337e-10,
            -0.019398047794943862
          ],
          [
            0.009152114463774508,
            2.4373758567008963e-10,
            -0.01293042778018455
          ],
          [
            0.004651219005375351,
            1.198575683147851e-10,
            -0.006460696963344836
          ],
          [
            0.00015652244943076266,
            -4.22789581122629e-12,
            1.153812167409285e-05
          ],
          [
            -0.004074713784302242,
            -9.992234817346457e-11,
            0.006006669057415204
          ],
          [
            -0.008305754341277227,
            -1.9503626491612636e-10,
            0.011998263556672772
          ],
          [
            -0.01253649099588916,
            -2.895607087438634e-10,
            0.017986787728776044
          ],
          [
            -0.016766816289742192,
            -3.8349429187789497e-10,
            0.02397270700911802
          ],
          [
            -0.0209966223642854,
            -4.768445083236372e-10,
            0.029956485276892098
          ],
          [
            -0.02522579979312939,
            -5.696088600792848e-10,
            0.035938583965924975
          ],
          [
            -0.029454236423749003,
            -6.617872916336864e-10,
            0.04191946116874423
          ],
          [
            -0.03368181623788691,
            -7.533840218343357e-10,
            0.04789957073441953
          ]
        ]
      },
      "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": "bec_projection_00",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cc",
        "spacegroup_number": 9,
        "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": 0.00015694714215065756,
        "parent_symmetrization_rmsd_A": 0.01332236541339397,
        "parent_cell_rmsd_A": 0.020632659806322954,
        "energy_eV": -162.41147367549527,
        "reduced_polarization": [
          0.00015652244943617692,
          -4.228690636291948e-12,
          1.1538121673744634e-05
        ],
        "cartesian_polarization_e_A2": [
          1.6457771961684133e-06,
          -7.717936748285226e-14,
          1.1567998761150662e-07
        ],
        "ranking_score": 0.518794424649276
      }
    }
  ],
  "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": 113,
      "full_response": 31,
      "energy_polarization": 82
    },
    "model_evaluations_for_recovery_and_path_properties": {
      "total": 138,
      "full_response": 56,
      "energy_polarization": 82
    },
    "elapsed_seconds": 672.8448037769995
  }
}