{
  "schema": "ferrofinder.endpoint_parent_recovery.v4_variable_cell",
  "status": "complete",
  "input_atom_count": 11,
  "input_formula": "Cs4O5Sb2",
  "input_spacegroup": "Cm",
  "input_pointgroup": "m",
  "input_is_polar_point_group": true,
  "input_energy_eV": -51.53066118063832,
  "input_cartesian_polarization_e_A2": [
    -1.004597131983195e-05,
    -6.533079724593064e-06,
    0.00026687776712491573
  ],
  "input_reduced_polarization": [
    -0.0014021586522413667,
    -0.0014044825669681617,
    0.010253268877531365
  ],
  "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": [
        0.0,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        -0.5,
        0.0
      ]
    },
    {
      "orbit_id": 3,
      "representative_formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        -0.5,
        0.0,
        0.0
      ]
    },
    {
      "orbit_id": 4,
      "representative_formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        -0.5,
        0.5
      ]
    },
    {
      "orbit_id": 5,
      "representative_formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        -0.5,
        0.0,
        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/m",
      "spacegroup_number": 12,
      "pointgroup": "2/m",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 6.635208393392712e-16,
      "parent_symmetrization_rmsd_A": 0.17924768966777616,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -51.4367452866753,
      "reduced_polarization": [
        4.34610569703146e-16,
        -4.971457680697221e-16,
        -6.495877331172403e-17
      ],
      "cartesian_polarization_e_A2": [
        4.5558524464048685e-18,
        -9.450494617729966e-18,
        -1.6907829672345823e-18
      ],
      "ranking_score": 0.1792476896677775
    },
    {
      "candidate_id": "bec_projection_00",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cm",
      "spacegroup_number": 8,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 1.2008626087768988e-05,
      "parent_symmetrization_rmsd_A": 0.004413507574716343,
      "parent_cell_rmsd_A": 0.0029254604065674463,
      "energy_eV": -51.52902958567761,
      "reduced_polarization": [
        5.331340288367569e-06,
        5.881926801660962e-06,
        -9.010374484191939e-06
      ],
      "cartesian_polarization_e_A2": [
        1.3220612717541057e-07,
        9.290063711674934e-08,
        -2.3444758358507838e-07
      ],
      "ranking_score": 0.5051688899285337
    },
    {
      "candidate_id": "inversion_parent_bec_00_00",
      "source": "same_species_inversion_center_projection_after_BEC",
      "spacegroup": "C2/m",
      "spacegroup_number": 12,
      "pointgroup": "2/m",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 4.707624243059053e-16,
      "parent_symmetrization_rmsd_A": 0.179248046512117,
      "parent_cell_rmsd_A": 0.0029254604065674463,
      "energy_eV": -51.43562381181478,
      "reduced_polarization": [
        1.0326477573238981e-16,
        2.6326819436641746e-16,
        3.763555553812893e-16
      ],
      "cartesian_polarization_e_A2": [
        5.466947859412555e-18,
        5.66772656795926e-18,
        9.796894581094944e-18
      ],
      "ranking_score": 0.17997941161375983
    },
    {
      "candidate_id": "bec_projection_01",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.5
      ],
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_residual": 0.0008853581954723098,
      "parent_symmetrization_rmsd_A": 0.24686970900537153,
      "parent_cell_rmsd_A": 0.1659756021036239,
      "energy_eV": -46.97186533769348,
      "reduced_polarization": [
        0.0003130888725636041,
        0.00045725094214609955,
        0.4993095247520198
      ],
      "cartesian_polarization_e_A2": [
        0.0012951309897470237,
        0.0008372031926590701,
        0.013037322384381643
      ],
      "ranking_score": 0.7901343259222221
    },
    {
      "candidate_id": "bec_projection_02",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        -0.5,
        0.0
      ],
      "formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_residual": 3.164078910472966e-06,
      "parent_symmetrization_rmsd_A": 0.25223366960196547,
      "parent_cell_rmsd_A": 0.07179203513564586,
      "energy_eV": -49.24505485952268,
      "reduced_polarization": [
        -2.4963267685095698e-06,
        -0.49999847081343235,
        -1.2005567282890717e-06
      ],
      "cartesian_polarization_e_A2": [
        -0.004215280920868021,
        -0.009403008627927843,
        -5.8830198454205554e-05
      ],
      "ranking_score": 0.7701880065436979
    },
    {
      "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": [
        -0.5,
        0.0,
        0.0
      ],
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_residual": 2.257018172657789e-06,
      "parent_symmetrization_rmsd_A": 0.25223929254292465,
      "parent_cell_rmsd_A": 0.07176597795440011,
      "energy_eV": -49.244177596241194,
      "reduced_polarization": [
        -0.4999994816139254,
        -1.7592079184032884e-06,
        -1.31552058485341e-06
      ],
      "cartesian_polarization_e_A2": [
        -0.010307064242328173,
        6.224599455721003e-06,
        -5.8834179111959605e-05
      ],
      "ranking_score": 0.7701853010678701
    },
    {
      "candidate_id": "bec_projection_04",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        -0.5,
        0.5
      ],
      "formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_residual": 0.00043713976530459554,
      "parent_symmetrization_rmsd_A": 0.27820119263015636,
      "parent_cell_rmsd_A": 0.1476307377380055,
      "energy_eV": -40.84942316965518,
      "reduced_polarization": [
        7.368226049928347e-05,
        -0.4997864587637541,
        0.49962575109977336
      ],
      "cartesian_polarization_e_A2": [
        -0.0027762897182060952,
        -0.008509785192932016,
        0.013262890441180744
      ],
      "ranking_score": 0.8159831565952669
    },
    {
      "candidate_id": "bec_projection_05",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        -0.5,
        0.0,
        0.5
      ],
      "formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_residual": 0.00045253563597417247,
      "parent_symmetrization_rmsd_A": 0.2779244798100298,
      "parent_cell_rmsd_A": 0.1475547442689365,
      "energy_eV": -40.77845723678654,
      "reduced_polarization": [
        -0.49976795329526147,
        6.476883748371205e-05,
        0.49961692321091256
      ],
      "cartesian_polarization_e_A2": [
        -0.008926127512296681,
        0.0009618251775239486,
        0.013262527757351943
      ],
      "ranking_score": 0.8157182371492122
    },
    {
      "candidate_id": "bec_projection_06",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cm",
      "spacegroup_number": 8,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        -0.5,
        -0.5,
        0.0
      ],
      "formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_residual": 1.902172484354947e-05,
      "parent_symmetrization_rmsd_A": 0.38686607461648204,
      "parent_cell_rmsd_A": 0.1138863475855061,
      "energy_eV": -45.99207103461023,
      "reduced_polarization": [
        -0.49998644438292045,
        -0.4999870274990604,
        -3.1281753447861617e-06
      ],
      "cartesian_polarization_e_A2": [
        -0.014548676094312322,
        -0.009413533501279225,
        -0.00023662120204467186
      ],
      "ranking_score": 0.9153757049625457
    },
    {
      "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": 0.08995769095053696,
      "parent_symmetrization_rmsd_A": 0.3825341978458465,
      "parent_cell_rmsd_A": 0.14227805949657324,
      "energy_eV": -30.089788335763668,
      "reduced_polarization": [
        -0.44994810988139117,
        -0.4504317981428278,
        0.4440519185194554
      ],
      "cartesian_polarization_e_A2": [
        -0.011627376519353565,
        -0.007485646171711925,
        0.01176903804281013
      ],
      "ranking_score": 1.0980190946210637
    }
  ],
  "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": [
              -0.0014021586522413667,
              -0.0014044825669681617,
              0.010253268877531365
            ],
            "branch_aligned_reduced_polarization": [
              -0.0014021586522413667,
              -0.0014044825669681617,
              0.010253268877531365
            ],
            "target_residual": 0.010443569449279594,
            "energy_eV": -51.53066118063832,
            "max_atomic_step_A": 0.006005606729969995,
            "max_log_strain_component": 0.0002459182831169192,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.718399915636522,
            "cell_principal_stretches": [
              1.0003776495334094,
              0.9999330460059961,
              0.9997059320115793
            ],
            "cell_volume_ratio": 1.0000165109076637,
            "cell_rmsd_from_input_A": 0.0029254604065674463
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              5.331340288367569e-06,
              5.881926801660962e-06,
              -9.010374484191939e-06
            ],
            "branch_aligned_reduced_polarization": [
              5.331340288367569e-06,
              5.881926801660962e-06,
              -9.010374484191939e-06
            ],
            "target_residual": 1.2008626087768988e-05,
            "energy_eV": -51.52902958567761
          }
        ],
        "iterations": 1
      },
      "parent": {
        "candidate_id": "inversion_parent_endpoint_00",
        "source": "same_species_inversion_center_projection_from_endpoint",
        "spacegroup": "C2/m",
        "spacegroup_number": 12,
        "pointgroup": "2/m",
        "has_inversion": true,
        "is_polar_point_group": false,
        "nonpolar_parent_hypothesis": true,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.0
        ],
        "formal_class": [
          0.0,
          0.0,
          0.0
        ],
        "target_residual": 6.635208393392712e-16,
        "parent_symmetrization_rmsd_A": 0.17924768966777616,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -51.4367452866753,
        "reduced_polarization": [
          4.34610569703146e-16,
          -4.971457680697221e-16,
          -6.495877331172403e-17
        ],
        "cartesian_polarization_e_A2": [
          4.5558524464048685e-18,
          -9.450494617729966e-18,
          -1.6907829672345823e-18
        ],
        "ranking_score": 0.1792476896677775
      },
      "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": [
          -51.53066118063833,
          -51.51614209999076,
          -51.50007150379838,
          -51.4837780808312,
          -51.468593178276116,
          -51.45558717379806,
          -51.445507681173126,
          -51.43901043848576,
          -51.436745286675304
        ],
        "cartesian_polarizations_e_A2": [
          [
            -1.0045971319828181e-05,
            -6.5330797245976265e-06,
            0.00026687776712490836
          ],
          [
            -1.0268179254578883e-05,
            -6.672881099897539e-06,
            0.0001939873623422159
          ],
          [
            -8.693610726904802e-06,
            -5.649788651800562e-06,
            0.00013628159542665262
          ],
          [
            -7.284525036468566e-06,
            -4.733851244934958e-06,
            9.216812291699906e-05
          ],
          [
            -6.689032042742493e-06,
            -4.344550001579057e-06,
            5.978651817688737e-05
          ],
          [
            -6.189215878788224e-06,
            -4.017218841610916e-06,
            3.6768449768522384e-05
          ],
          [
            -4.769539218765741e-06,
            -3.0945551006580766e-06,
            2.0505344452911734e-05
          ],
          [
            -2.5016939312512e-06,
            -1.6229491884797663e-06,
            8.921187115178605e-06
          ],
          [
            3.246085723589034e-19,
            -5.646918412246214e-18,
            -8.240291135264727e-18
          ]
        ],
        "raw_reduced_polarization": [
          [
            -0.001402158652241055,
            -0.001404482566968376,
            0.010253268877531082
          ],
          [
            -0.0011214465287497576,
            -0.001123468318394676,
            0.00745286730462962
          ],
          [
            -0.0008388267820765477,
            -0.0008405503380667183,
            0.0052358495652220375
          ],
          [
            -0.0006157084269725079,
            -0.00061713735097345,
            0.0035410388672917083
          ],
          [
            -0.00046709276886444,
            -0.0004682305492991288,
            0.0022969588389583472
          ],
          [
            -0.00035883429472168064,
            -0.00035968425392446737,
            0.0014126197387967783
          ],
          [
            -0.0002455669345327073,
            -0.00024613192294513164,
            0.0007878018928556587
          ],
          [
            -0.00012154883735082828,
            -0.00012183084606511703,
            0.00034274616122623744
          ],
          [
            1.7168894312953179e-16,
            -2.6844452392103964e-16,
            -3.1658658399768754e-16
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -0.001402158652241055,
            -0.001404482566968376,
            0.010253268877531082
          ],
          [
            -0.0011214465287497576,
            -0.001123468318394676,
            0.00745286730462962
          ],
          [
            -0.0008388267820765477,
            -0.0008405503380667183,
            0.0052358495652220375
          ],
          [
            -0.0006157084269725079,
            -0.00061713735097345,
            0.0035410388672917083
          ],
          [
            -0.00046709276886444,
            -0.0004682305492991288,
            0.0022969588389583472
          ],
          [
            -0.00035883429472168064,
            -0.00035968425392446737,
            0.0014126197387967783
          ],
          [
            -0.0002455669345327073,
            -0.00024613192294513164,
            0.0007878018928556587
          ],
          [
            -0.00012154883735082829,
            -0.00012183084606511702,
            0.00034274616122623744
          ],
          [
            1.7168341401307963e-16,
            -2.684484579074109e-16,
            -3.165870343657673e-16
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            -0.0014021586522410812,
            -0.0014044825669684013,
            0.010253268877531085
          ],
          [
            -0.0011214465287497366,
            -0.0011234683183946603,
            0.0074528673046295735
          ],
          [
            -0.0008388267820765294,
            -0.0008405503380667367,
            0.0052358495652220505
          ],
          [
            -0.0006157084269725055,
            -0.0006171373509734623,
            0.0035410388672917348
          ],
          [
            -0.00046709276886441886,
            -0.0004682305492991201,
            0.0022969588389583073
          ],
          [
            -0.00035883429472166606,
            -0.0003596842539244638,
            0.0014126197387968054
          ],
          [
            -0.00024556693453270384,
            -0.0002461319229451475,
            0.0007878018928556552
          ],
          [
            -0.00012154883735082667,
            -0.00012183084606509631,
            0.00034274616122620394
          ],
          [
            2.220446049250313e-16,
            -2.7755575615628914e-16,
            -3.3306690738754696e-16
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -51.436745286675304,
          -51.43901043848576,
          -51.44550768117313,
          -51.455587173798065,
          -51.46859317827613,
          -51.483778080831215,
          -51.50007150379838,
          -51.516142099990766,
          -51.53066118063833
        ],
        "cartesian_polarizations_e_A2": [
          [
            -9.315639808080983e-18,
            -1.3503024162228997e-17,
            -8.943842364302942e-18
          ],
          [
            2.5016939312480195e-06,
            1.6229491884594062e-06,
            -8.921187115189579e-06
          ],
          [
            4.7695392187538225e-06,
            3.0945551006246e-06,
            -2.050534445293079e-05
          ],
          [
            6.189215878755654e-06,
            4.017218841592123e-06,
            -3.6768449768520494e-05
          ],
          [
            6.6890320427186674e-06,
            4.344550001532341e-06,
            -5.978651817689166e-05
          ],
          [
            7.284525036468264e-06,
            4.733851244901833e-06,
            -9.216812291698722e-05
          ],
          [
            8.693610726872589e-06,
            5.649788651757584e-06,
            -0.00013628159542662693
          ],
          [
            1.0268179254559603e-05,
            6.672881099871328e-06,
            -0.00019398736234222985
          ],
          [
            1.0045971319872149e-05,
            6.533079724571257e-06,
            -0.00026687776712490743
          ]
        ],
        "raw_reduced_polarization": [
          [
            -1.2288378587877002e-16,
            -6.844951678424893e-16,
            -3.4361656104733067e-16
          ],
          [
            0.00012154883735116152,
            0.00012183084606407499,
            -0.00034274616122665903
          ],
          [
            0.0002455669345329339,
            0.00024613192294342234,
            -0.0007878018928563908
          ],
          [
            0.00035883429472049946,
            0.000359684253923458,
            -0.0014126197387967058
          ],
          [
            0.0004670927688643181,
            0.0004682305492966551,
            -0.002296958838958512
          ],
          [
            0.0006157084269731697,
            0.0006171373509716371,
            -0.0035410388672912534
          ],
          [
            0.0008388267820758177,
            0.0008405503380643253,
            -0.00523584956522105
          ],
          [
            0.0011214465287494471,
            0.0011234683183933337,
            -0.007452867304630157
          ],
          [
            0.0014021586522437652,
            0.0014044825669669665,
            -0.010253268877531046
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -1.2288378587877002e-16,
            -6.844951678424893e-16,
            -3.4361656104733067e-16
          ],
          [
            0.00012154883735116152,
            0.00012183084606407499,
            -0.00034274616122665903
          ],
          [
            0.0002455669345329339,
            0.00024613192294342234,
            -0.0007878018928563908
          ],
          [
            0.00035883429472049946,
            0.000359684253923458,
            -0.0014126197387967058
          ],
          [
            0.0004670927688643181,
            0.0004682305492966551,
            -0.002296958838958512
          ],
          [
            0.0006157084269731697,
            0.0006171373509716371,
            -0.0035410388672912534
          ],
          [
            0.0008388267820758177,
            0.0008405503380643253,
            -0.00523584956522105
          ],
          [
            0.0011214465287494471,
            0.0011234683183933337,
            -0.007452867304630157
          ],
          [
            0.0014021586522437652,
            0.0014044825669669665,
            -0.010253268877531046
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          0.0014021586522413986,
          0.001404482566967839,
          -0.010253268877531715
        ],
        "actual_opposite_endpoint_branch_residual": 2.6096970698539538e-15
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            -0.001402158652241055,
            -0.001404482566968376,
            0.010253268877531082
          ],
          [
            -0.0011214465287497576,
            -0.001123468318394676,
            0.00745286730462962
          ],
          [
            -0.0008388267820765477,
            -0.0008405503380667183,
            0.0052358495652220375
          ],
          [
            -0.0006157084269725079,
            -0.00061713735097345,
            0.0035410388672917083
          ],
          [
            -0.00046709276886444,
            -0.0004682305492991288,
            0.0022969588389583472
          ],
          [
            -0.00035883429472168064,
            -0.00035968425392446737,
            0.0014126197387967783
          ],
          [
            -0.0002455669345327073,
            -0.00024613192294513164,
            0.0007878018928556587
          ],
          [
            -0.00012154883735082828,
            -0.00012183084606511703,
            0.00034274616122623744
          ],
          [
            1.7168894312953179e-16,
            -2.6844452392103964e-16,
            -3.1658658399768754e-16
          ],
          [
            0.00012154883735116152,
            0.00012183084606407499,
            -0.00034274616122665903
          ],
          [
            0.0002455669345329339,
            0.00024613192294342234,
            -0.0007878018928563908
          ],
          [
            0.00035883429472049946,
            0.000359684253923458,
            -0.0014126197387967058
          ],
          [
            0.0004670927688643181,
            0.0004682305492966551,
            -0.002296958838958512
          ],
          [
            0.0006157084269731697,
            0.0006171373509716371,
            -0.0035410388672912534
          ],
          [
            0.0008388267820758177,
            0.0008405503380643253,
            -0.00523584956522105
          ],
          [
            0.0011214465287494471,
            0.0011234683183933337,
            -0.007452867304630157
          ],
          [
            0.0014021586522437652,
            0.0014044825669669665,
            -0.010253268877531046
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -0.001402158652241055,
            -0.001404482566968376,
            0.010253268877531082
          ],
          [
            -0.0011214465287497576,
            -0.001123468318394676,
            0.00745286730462962
          ],
          [
            -0.0008388267820765477,
            -0.0008405503380667183,
            0.0052358495652220375
          ],
          [
            -0.0006157084269725079,
            -0.00061713735097345,
            0.0035410388672917083
          ],
          [
            -0.00046709276886444,
            -0.0004682305492991288,
            0.0022969588389583472
          ],
          [
            -0.00035883429472168064,
            -0.00035968425392446737,
            0.0014126197387967783
          ],
          [
            -0.0002455669345327073,
            -0.00024613192294513164,
            0.0007878018928556587
          ],
          [
            -0.00012154883735082829,
            -0.00012183084606511702,
            0.00034274616122623744
          ],
          [
            1.7168341401307963e-16,
            -2.684484579074109e-16,
            -3.165870343657673e-16
          ],
          [
            0.00012154883735116152,
            0.00012183084606407499,
            -0.00034274616122665903
          ],
          [
            0.0002455669345329339,
            0.00024613192294342234,
            -0.0007878018928563908
          ],
          [
            0.00035883429472049946,
            0.000359684253923458,
            -0.0014126197387967058
          ],
          [
            0.0004670927688643181,
            0.0004682305492966551,
            -0.002296958838958512
          ],
          [
            0.0006157084269731697,
            0.0006171373509716371,
            -0.0035410388672912534
          ],
          [
            0.0008388267820758177,
            0.0008405503380643253,
            -0.00523584956522105
          ],
          [
            0.0011214465287494471,
            0.0011234683183933337,
            -0.007452867304630157
          ],
          [
            0.0014021586522437652,
            0.0014044825669669665,
            -0.010253268877531046
          ]
        ],
        "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": [
          [
            -0.0014021586522410812,
            -0.0014044825669684013,
            0.010253268877531085
          ],
          [
            -0.0011214465287497366,
            -0.0011234683183946603,
            0.0074528673046295735
          ],
          [
            -0.0008388267820765294,
            -0.0008405503380667367,
            0.0052358495652220505
          ],
          [
            -0.0006157084269725055,
            -0.0006171373509734623,
            0.0035410388672917348
          ],
          [
            -0.00046709276886441886,
            -0.0004682305492991201,
            0.0022969588389583073
          ],
          [
            -0.00035883429472166606,
            -0.0003596842539244638,
            0.0014126197387968054
          ],
          [
            -0.00024556693453270384,
            -0.0002461319229451475,
            0.0007878018928556552
          ],
          [
            -0.00012154883735082667,
            -0.00012183084606509631,
            0.00034274616122620394
          ],
          [
            2.220446049250313e-16,
            -2.7755575615628914e-16,
            -3.3306690738754696e-16
          ],
          [
            0.00012154883735115973,
            0.00012183084606409711,
            -0.00034274616122664803
          ],
          [
            0.0002455669345329259,
            0.0002461319229434267,
            -0.0007878018928563768
          ],
          [
            0.0003588342947205003,
            0.0003596842539234091,
            -0.0014126197387966943
          ],
          [
            0.00046709276886436335,
            0.0004682305492966776,
            -0.0022969588389585294
          ],
          [
            0.0006157084269731161,
            0.000617137350971686,
            -0.003541038867291235
          ],
          [
            0.0008388267820758077,
            0.0008405503380642942,
            -0.005235849565221051
          ],
          [
            0.001121446528749459,
            0.0011234683183933836,
            -0.007452867304630184
          ],
          [
            0.0014021586522438012,
            0.0014044825669670136,
            -0.01025326887753103
          ]
        ]
      },
      "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": [
              -0.0014021586522413667,
              -0.0014044825669681617,
              0.010253268877531365
            ],
            "branch_aligned_reduced_polarization": [
              -0.0014021586522413667,
              -0.0014044825669681617,
              0.010253268877531363
            ],
            "target_residual": 0.48975075218452757,
            "energy_eV": -51.53066118063832,
            "max_atomic_step_A": 0.11999999999999998,
            "max_log_strain_component": 0.007117430938975287,
            "step_scale": 0.5286408913297255,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.718399915636522,
            "cell_principal_stretches": [
              1.0085433887548922,
              1.0019958267432236,
              0.9900381624959107
            ],
            "cell_volume_ratio": 1.0004892693050444,
            "cell_rmsd_from_input_A": 0.07968637672874344
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.0003348779000490636,
              0.0002633871325615917,
              0.26501909026299464
            ],
            "branch_aligned_reduced_polarization": [
              -0.0003348779000490636,
              0.0002633871325615917,
              0.26501909026299464
            ],
            "target_residual": 0.23498129597229692,
            "energy_eV": -50.48646943892017,
            "max_atomic_step_A": 0.11291628671111503,
            "max_log_strain_component": 0.006946967698756805,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.718399915636522,
            "cell_principal_stretches": [
              1.016954852898547,
              1.0039463533131185,
              0.9803450087001334
            ],
            "cell_volume_ratio": 1.0009009966131404,
            "cell_rmsd_from_input_A": 0.15719721008497448
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.004329113722953717,
              0.005355128702478728,
              0.4761751749142722
            ],
            "branch_aligned_reduced_polarization": [
              0.004329113722953717,
              0.005355128702478728,
              0.4761751749142722
            ],
            "target_residual": 0.02480001853652337,
            "energy_eV": -47.33516261734654,
            "max_atomic_step_A": 0.016006888578043447,
            "max_log_strain_component": 0.0007297193567903993,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.718399915636522,
            "cell_principal_stretches": [
              1.01783969110156,
              1.004143782441487,
              0.979193872966262
            ],
            "cell_volume_ratio": 1.0007923412969306,
            "cell_rmsd_from_input_A": 0.1659756021036239
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.0003130888725636041,
              0.00045725094214609955,
              0.4993095247520198
            ],
            "branch_aligned_reduced_polarization": [
              0.0003130888725636041,
              0.00045725094214609955,
              0.4993095247520198
            ],
            "target_residual": 0.0008853581954723098,
            "energy_eV": -46.97186533769348
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_01",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.5
        ],
        "formal_class": [
          0.0,
          0.0,
          0.5
        ],
        "target_residual": 0.0008853581954723098,
        "parent_symmetrization_rmsd_A": 0.24686970900537153,
        "parent_cell_rmsd_A": 0.1659756021036239,
        "energy_eV": -46.97186533769348,
        "reduced_polarization": [
          0.0003130888725636041,
          0.00045725094214609955,
          0.4993095247520198
        ],
        "cartesian_polarization_e_A2": [
          0.0012951309897470237,
          0.0008372031926590701,
          0.013037322384381643
        ],
        "ranking_score": 0.7901343259222221
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 2,
      "formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.5,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        -0.5,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -0.0014021586522413667,
              -0.0014044825669681617,
              0.010253268877531365
            ],
            "branch_aligned_reduced_polarization": [
              -0.0014021586522413667,
              -0.0014044825669681793,
              0.010253268877531365
            ],
            "target_residual": 0.4987029031155461,
            "energy_eV": -51.53066118063832,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.0032649627706266044,
            "step_scale": 0.40432712757679096,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.718399915636522,
            "cell_principal_stretches": [
              1.0027999806223498,
              0.9989360184739589,
              0.9957525482384678
            ],
            "cell_volume_ratio": 0.9974782072884028,
            "cell_rmsd_from_input_A": 0.028033462074053127
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.002293960989465193,
              -0.20486956051531305,
              0.012544620058761002
            ],
            "branch_aligned_reduced_polarization": [
              0.002293960989465193,
              -0.20486956051531302,
              0.012544620058761002
            ],
            "target_residual": 0.29540583281286836,
            "energy_eV": -51.07984334641912,
            "max_atomic_step_A": 0.11999999999999998,
            "max_log_strain_component": 0.004079882650847253,
            "step_scale": 0.7210842507022729,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.718399915636522,
            "cell_principal_stretches": [
              1.006398423699095,
              0.9977845601520389,
              0.9906920659497132
            ],
            "cell_volume_ratio": 0.9948220714831699,
            "cell_rmsd_from_input_A": 0.06312881274807602
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.0009364698078265311,
              -0.4372821294259184,
              0.008821496699396372
            ],
            "branch_aligned_reduced_polarization": [
              -0.0009364698078265311,
              -0.4372821294259184,
              0.008821496699396372
            ],
            "target_residual": 0.06334214291501106,
            "energy_eV": -49.65035319903275,
            "max_atomic_step_A": 0.03542819762235514,
            "max_log_strain_component": 0.001034225055151311,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.718399915636522,
            "cell_principal_stretches": [
              1.0073553989000001,
              0.9975325512454021,
              0.9895030326158609
            ],
            "cell_volume_ratio": 0.994321715548351,
            "cell_rmsd_from_input_A": 0.07194372673508949
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -0.0011376807778279154,
              -0.5010796536661136,
              0.00030660780054010954
            ],
            "branch_aligned_reduced_polarization": [
              -0.0011376807778279154,
              -0.5010796536661136,
              0.00030660780054010954
            ],
            "target_residual": 0.001598116996450435,
            "energy_eV": -49.23383968817271,
            "max_atomic_step_A": 0.000993239158565552,
            "max_log_strain_component": 1.4023793731044713e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.718399915636522,
            "cell_principal_stretches": [
              1.0073422976965978,
              0.9975378336868174,
              0.989525634564521
            ],
            "cell_volume_ratio": 0.9943367610655423,
            "cell_rmsd_from_input_A": 0.07179203513564586
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              -2.4963267685095698e-06,
              -0.49999847081343235,
              -1.2005567282890717e-06
            ],
            "branch_aligned_reduced_polarization": [
              -2.4963267685095698e-06,
              -0.49999847081343235,
              -1.2005567282890717e-06
            ],
            "target_residual": 3.164078910472966e-06,
            "energy_eV": -49.24505485952268
          }
        ],
        "iterations": 4
      },
      "parent": {
        "candidate_id": "bec_projection_02",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          -0.5,
          0.0
        ],
        "formal_class": [
          0.0,
          0.5,
          0.0
        ],
        "target_residual": 3.164078910472966e-06,
        "parent_symmetrization_rmsd_A": 0.25223366960196547,
        "parent_cell_rmsd_A": 0.07179203513564586,
        "energy_eV": -49.24505485952268,
        "reduced_polarization": [
          -2.4963267685095698e-06,
          -0.49999847081343235,
          -1.2005567282890717e-06
        ],
        "cartesian_polarization_e_A2": [
          -0.004215280920868021,
          -0.009403008627927843,
          -5.8830198454205554e-05
        ],
        "ranking_score": 0.7701880065436979
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 3,
      "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": [
              -0.0014021586522413667,
              -0.0014044825669681617,
              0.010253268877531365
            ],
            "branch_aligned_reduced_polarization": [
              -0.0014021586522413587,
              -0.0014044825669681617,
              0.010253268877531365
            ],
            "target_residual": 0.49870523306919545,
            "energy_eV": -51.53066118063832,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.0026781882987405342,
            "step_scale": 0.40432658738538263,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.718399915636522,
            "cell_principal_stretches": [
              1.002741299215831,
              0.9990609609116823,
              0.9956863136580704
            ],
            "cell_volume_ratio": 0.9974782363178063,
            "cell_rmsd_from_input_A": 0.027993396875350473
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.20473455903739932,
              0.0021871131259043027,
              0.012555599702598431
            ],
            "branch_aligned_reduced_polarization": [
              -0.20473455903739934,
              0.0021871131259043027,
              0.012555599702598431
            ],
            "target_residual": 0.2955403647127688,
            "energy_eV": -51.07995946087405,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.0031579286381520928,
            "step_scale": 0.7199813308737935,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.718399915636522,
            "cell_principal_stretches": [
              1.0063238149496962,
              0.9979390262310167,
              0.9906151844159201
            ],
            "cell_volume_ratio": 0.9948251087158924,
            "cell_rmsd_from_input_A": 0.06304190740421561
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.43681718731243563,
              -0.0009903346305361377,
              0.008833548291530352
            ],
            "branch_aligned_reduced_polarization": [
              -0.43681718731243563,
              -0.0009903346305361377,
              0.008833548291530352
            ],
            "target_residual": 0.06380501670880655,
            "energy_eV": -49.65253573453637,
            "max_atomic_step_A": 0.035718237246799796,
            "max_log_strain_component": 0.0007911014299888218,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.718399915636522,
            "cell_principal_stretches": [
              1.0072974291251469,
              0.9976635419973865,
              0.9894293088089983
            ],
            "cell_volume_ratio": 0.9943209691328396,
            "cell_rmsd_from_input_A": 0.07192036197943283
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -0.5011213182130121,
              -0.001132762318696176,
              0.00031045885398656566
            ],
            "branch_aligned_reduced_polarization": [
              -0.5011213182130121,
              -0.001132762318696176,
              0.00031045885398656566
            ],
            "target_residual": 0.0016238502718875334,
            "energy_eV": -49.23267532183056,
            "max_atomic_step_A": 0.0010083725179041959,
            "max_log_strain_component": 1.6628821303486443e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.718399915636522,
            "cell_principal_stretches": [
              1.0072842018389008,
              0.9976685708754284,
              0.9894525197786739
            ],
            "cell_volume_ratio": 0.9943362497440829,
            "cell_rmsd_from_input_A": 0.07176597795440011
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              -0.4999994816139254,
              -1.7592079184032884e-06,
              -1.31552058485341e-06
            ],
            "branch_aligned_reduced_polarization": [
              -0.4999994816139254,
              -1.7592079184032884e-06,
              -1.31552058485341e-06
            ],
            "target_residual": 2.257018172657789e-06,
            "energy_eV": -49.244177596241194
          }
        ],
        "iterations": 4
      },
      "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": [
          -0.5,
          0.0,
          0.0
        ],
        "formal_class": [
          0.5,
          0.0,
          0.0
        ],
        "target_residual": 2.257018172657789e-06,
        "parent_symmetrization_rmsd_A": 0.25223929254292465,
        "parent_cell_rmsd_A": 0.07176597795440011,
        "energy_eV": -49.244177596241194,
        "reduced_polarization": [
          -0.4999994816139254,
          -1.7592079184032884e-06,
          -1.31552058485341e-06
        ],
        "cartesian_polarization_e_A2": [
          -0.010307064242328173,
          6.224599455721003e-06,
          -5.8834179111959605e-05
        ],
        "ranking_score": 0.7701853010678701
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 4,
      "formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.5,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        -0.5,
        0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -0.0014021586522413667,
              -0.0014044825669681617,
              0.010253268877531365
            ],
            "branch_aligned_reduced_polarization": [
              -0.0014021586522413667,
              -0.0014044825669681793,
              0.010253268877531363
            ],
            "target_residual": 0.6988929221979161,
            "energy_eV": -51.53066118063832,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.0018847679574972582,
            "step_scale": 0.2501153466274855,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.718399915636522,
            "cell_principal_stretches": [
              1.0025406205827148,
              1.0003500941058447,
              0.9957868277911451
            ],
            "cell_volume_ratio": 0.9986662491097733,
            "cell_rmsd_from_input_A": 0.02945498973915989
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.0019450428939986686,
              -0.12830077616823576,
              0.13379545992807396
            ],
            "branch_aligned_reduced_polarization": [
              -0.0019450428939986686,
              -0.12830077616823576,
              0.13379545992807396
            ],
            "target_residual": 0.5217948460441961,
            "energy_eV": -51.19016939417566,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.0018571820135206277,
            "step_scale": 0.35078168491687095,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.718399915636522,
            "cell_principal_stretches": [
              1.0051768853086687,
              1.0007556294242332,
              0.9916065680032286
            ],
            "cell_volume_ratio": 0.9974931675505303,
            "cell_rmsd_from_input_A": 0.05903189121194494
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.0007989693960097626,
              -0.2647441864457024,
              0.2593910820673356
            ],
            "branch_aligned_reduced_polarization": [
              -0.0007989693960097626,
              -0.2647441864457024,
              0.2593910820673356
            ],
            "target_residual": 0.3365094167358736,
            "energy_eV": -49.73746980582333,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.0024081056368919023,
            "step_scale": 0.5761303105133014,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.718399915636522,
            "cell_principal_stretches": [
              1.008626544820466,
              1.0014853058931186,
              0.9864286838171047
            ],
            "cell_volume_ratio": 0.9964159425752609,
            "cell_rmsd_from_input_A": 0.09660884727803595
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.007360442438018575,
              -0.39619504509081116,
              0.3766090085488058
            ],
            "branch_aligned_reduced_polarization": [
              0.007360442438018575,
              -0.39619504509081116,
              0.3766090085488058
            ],
            "target_residual": 0.16141555547062617,
            "energy_eV": -45.439064864888174,
            "max_atomic_step_A": 0.10351807346279593,
            "max_log_strain_component": 0.003539665144082809,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.718399915636522,
            "cell_principal_stretches": [
              1.0131680233236373,
              1.0025882228729641,
              0.9799977366256671
            ],
            "cell_volume_ratio": 0.9954722223024882,
            "cell_rmsd_from_input_A": 0.14435886779637522
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              -0.02386527176001162,
              -0.5025701760212132,
              0.4999386375939577
            ],
            "branch_aligned_reduced_polarization": [
              -0.02386527176001162,
              -0.5025701760212132,
              0.4999386375939577
            ],
            "target_residual": 0.024003349064330645,
            "energy_eV": -39.975488267180936,
            "max_atomic_step_A": 0.011223918988903204,
            "max_log_strain_component": 0.0012350979725118001,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": true,
            "strain_jacobian_frobenius_norm": 1.9308528564728693,
            "cell_principal_stretches": [
              1.0137408588449446,
              1.0018341966694628,
              0.9798833431539121
            ],
            "cell_volume_ratio": 0.9951697770498019,
            "cell_rmsd_from_input_A": 0.1476307377380055
          },
          {
            "iteration": 5,
            "reduced_polarization": [
              7.368226049928347e-05,
              -0.4997864587637541,
              0.49962575109977336
            ],
            "branch_aligned_reduced_polarization": [
              7.368226049928347e-05,
              -0.4997864587637541,
              0.49962575109977336
            ],
            "target_residual": 0.00043713976530459554,
            "energy_eV": -40.84942316965518
          }
        ],
        "iterations": 5
      },
      "parent": {
        "candidate_id": "bec_projection_04",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          -0.5,
          0.5
        ],
        "formal_class": [
          0.0,
          0.5,
          0.5
        ],
        "target_residual": 0.00043713976530459554,
        "parent_symmetrization_rmsd_A": 0.27820119263015636,
        "parent_cell_rmsd_A": 0.1476307377380055,
        "energy_eV": -40.84942316965518,
        "reduced_polarization": [
          7.368226049928347e-05,
          -0.4997864587637541,
          0.49962575109977336
        ],
        "cartesian_polarization_e_A2": [
          -0.0027762897182060952,
          -0.008509785192932016,
          0.013262890441180744
        ],
        "ranking_score": 0.8159831565952669
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 5,
      "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": [
              -0.0014021586522413667,
              -0.0014044825669681617,
              0.010253268877531365
            ],
            "branch_aligned_reduced_polarization": [
              -0.0014021586522413587,
              -0.0014044825669681617,
              0.010253268877531363
            ],
            "target_residual": 0.6988945847644473,
            "energy_eV": -51.53066118063832,
            "max_atomic_step_A": 0.11999999999999998,
            "max_log_strain_component": 0.0021878833801574345,
            "step_scale": 0.25011510425403727,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.718399915636522,
            "cell_principal_stretches": [
              1.0026865808975682,
              1.0001254827170067,
              0.995865493451454
            ],
            "cell_volume_ratio": 0.9986662662962477,
            "cell_rmsd_from_input_A": 0.029382693519230563
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.1281548127606711,
              -0.0020280970406538227,
              0.1338260033100852
            ],
            "branch_aligned_reduced_polarization": [
              -0.1281548127606711,
              -0.0020280970406538227,
              0.1338260033100852
            ],
            "target_residual": 0.5218777177677963,
            "energy_eV": -51.1891942727451,
            "max_atomic_step_A": 0.12000000000000001,
            "max_log_strain_component": 0.0023207300604796625,
            "step_scale": 0.35064506236367826,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.718399915636522,
            "cell_principal_stretches": [
              1.005469715153308,
              1.0002964615235577,
              0.9917708489080025
            ],
            "cell_volume_ratio": 0.9974911830617961,
            "cell_rmsd_from_input_A": 0.05885881848844986
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.2644531698608857,
              -0.0008842166850286619,
              0.25941555725270343
            ],
            "branch_aligned_reduced_polarization": [
              -0.2644531698608857,
              -0.0008842166850286619,
              0.25941555725270343
            ],
            "target_residual": 0.3366956565204815,
            "energy_eV": -49.73042695351039,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.0030949179464162158,
            "step_scale": 0.575360867019058,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.718399915636522,
            "cell_principal_stretches": [
              1.0090616718667536,
              1.0007899314840483,
              0.9866827241562484
            ],
            "cell_volume_ratio": 0.9964101937612393,
            "cell_rmsd_from_input_A": 0.0962755726875893
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -0.39573904334449383,
              0.007375219745097732,
              0.37657574644672753
            ],
            "branch_aligned_reduced_polarization": [
              -0.39573904334449383,
              0.007375219745097732,
              0.37657574644672753
            ],
            "target_residual": 0.16173523831927383,
            "energy_eV": -45.41468794734503,
            "max_atomic_step_A": 0.1036002256435932,
            "max_log_strain_component": 0.004033324962298982,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.718399915636522,
            "cell_principal_stretches": [
              1.0137136321962785,
              1.0017030864209269,
              0.9803238435916001
            ],
            "cell_volume_ratio": 0.9954601163962778,
            "cell_rmsd_from_input_A": 0.14387151372954773
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              -0.5024732518259449,
              -0.023990345143737976,
              0.5001646473908425
            ],
            "branch_aligned_reduced_polarization": [
              -0.5024732518259449,
              -0.023990345143737976,
              0.5001646473908425
            ],
            "target_residual": 0.024118058451573658,
            "energy_eV": -39.897230712242276,
            "max_atomic_step_A": 0.011300244371490435,
            "max_log_strain_component": 0.001117238798659355,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": true,
            "strain_jacobian_frobenius_norm": 1.9044665814826667,
            "cell_principal_stretches": [
              1.0140940103628318,
              1.0013308408763704,
              0.9800430325816847
            ],
            "cell_volume_ratio": 0.9951784331218312,
            "cell_rmsd_from_input_A": 0.1475547442689365
          },
          {
            "iteration": 5,
            "reduced_polarization": [
              -0.49976795329526147,
              6.476883748371205e-05,
              0.49961692321091256
            ],
            "branch_aligned_reduced_polarization": [
              -0.49976795329526147,
              6.476883748371205e-05,
              0.49961692321091256
            ],
            "target_residual": 0.00045253563597417247,
            "energy_eV": -40.77845723678654
          }
        ],
        "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": [
          -0.5,
          0.0,
          0.5
        ],
        "formal_class": [
          0.5,
          0.0,
          0.5
        ],
        "target_residual": 0.00045253563597417247,
        "parent_symmetrization_rmsd_A": 0.2779244798100298,
        "parent_cell_rmsd_A": 0.1475547442689365,
        "energy_eV": -40.77845723678654,
        "reduced_polarization": [
          -0.49976795329526147,
          6.476883748371205e-05,
          0.49961692321091256
        ],
        "cartesian_polarization_e_A2": [
          -0.008926127512296681,
          0.0009618251775239486,
          0.013262527757351943
        ],
        "ranking_score": 0.8157182371492122
      },
      "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": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -0.0014021586522413667,
              -0.0014044825669681617,
              0.010253268877531365
            ],
            "branch_aligned_reduced_polarization": [
              -0.0014021586522413587,
              -0.0014044825669681793,
              0.010253268877531365
            ],
            "target_residual": 0.7051967292349224,
            "energy_eV": -51.53066118063832,
            "max_atomic_step_A": 0.12000000000000001,
            "max_log_strain_component": 0.0025792001063647475,
            "step_scale": 0.2016388398433674,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.718399915636522,
            "cell_principal_stretches": [
              1.0024610501504694,
              0.999128941363154,
              0.9959000986579645
            ],
            "cell_volume_ratio": 0.997481436433295,
            "cell_rmsd_from_input_A": 0.026859387526720367
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.1012467673861433,
              -0.10137571216998897,
              0.015441625691019128
            ],
            "branch_aligned_reduced_polarization": [
              -0.1012467673861433,
              -0.10137571216998897,
              0.015441625691019128
            ],
            "target_residual": 0.5640424692981597,
            "energy_eV": -51.22547836813413,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.0038928367442630325,
            "step_scale": 0.30143872933668603,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.718399915636522,
            "cell_principal_stretches": [
              1.006300267041772,
              0.9978639020475858,
              0.990362298303101
            ],
            "cell_volume_ratio": 0.9944730060895014,
            "cell_rmsd_from_input_A": 0.06543622533733649
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.23268423232096905,
              -0.23284235201720432,
              0.01682895898558221
            ],
            "branch_aligned_reduced_polarization": [
              -0.23268423232096902,
              -0.23284235201720432,
              0.01682895898558221
            ],
            "target_residual": 0.3783042986618939,
            "energy_eV": -49.91652704626087,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.0029368775900288726,
            "step_scale": 0.46491160414933397,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.718399915636522,
            "cell_principal_stretches": [
              1.0093028312201062,
              0.9969329475050396,
              0.9864342763926643
            ],
            "cell_volume_ratio": 0.9925573170563562,
            "cell_rmsd_from_input_A": 0.09412480885899606
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -0.37577051891522867,
              -0.37587164606997003,
              0.009201588362660766
            ],
            "branch_aligned_reduced_polarization": [
              -0.37577051891522867,
              -0.37587164606997003,
              0.009201588362660766
            ],
            "target_residual": 0.17585642282375186,
            "energy_eV": -48.04211230603071,
            "max_atomic_step_A": 0.111638566367103,
            "max_log_strain_component": 0.001951432747479012,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.718399915636522,
            "cell_principal_stretches": [
              1.0113373854694347,
              0.9963203188230516,
              0.9838781303719564
            ],
            "cell_volume_ratio": 0.991371332761857,
            "cell_rmsd_from_input_A": 0.11319328487307076
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              -0.4972302511018576,
              -0.4972301007773703,
              0.005028668685618529
            ],
            "branch_aligned_reduced_polarization": [
              -0.4972302511018576,
              -0.4972301007773703,
              0.005028668685618529
            ],
            "target_residual": 0.006374273245790939,
            "energy_eV": -45.98072494719487,
            "max_atomic_step_A": 0.003928502210138219,
            "max_log_strain_component": 0.00019753854384736713,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": true,
            "strain_jacobian_frobenius_norm": 1.977934033867009,
            "cell_principal_stretches": [
              1.011282724074436,
              0.9962007928085967,
              0.9836178995553281
            ],
            "cell_volume_ratio": 0.9909366575320548,
            "cell_rmsd_from_input_A": 0.1138863475855061
          },
          {
            "iteration": 5,
            "reduced_polarization": [
              -0.49998644438292045,
              -0.4999870274990604,
              -3.1281753447861617e-06
            ],
            "branch_aligned_reduced_polarization": [
              -0.49998644438292045,
              -0.4999870274990604,
              -3.1281753447861617e-06
            ],
            "target_residual": 1.902172484354947e-05,
            "energy_eV": -45.99207103461023
          }
        ],
        "iterations": 5
      },
      "parent": {
        "candidate_id": "bec_projection_06",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cm",
        "spacegroup_number": 8,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          -0.5,
          -0.5,
          0.0
        ],
        "formal_class": [
          0.5,
          0.5,
          0.0
        ],
        "target_residual": 1.902172484354947e-05,
        "parent_symmetrization_rmsd_A": 0.38686607461648204,
        "parent_cell_rmsd_A": 0.1138863475855061,
        "energy_eV": -45.99207103461023,
        "reduced_polarization": [
          -0.49998644438292045,
          -0.4999870274990604,
          -3.1281753447861617e-06
        ],
        "cartesian_polarization_e_A2": [
          -0.014548676094312322,
          -0.009413533501279225,
          -0.00023662120204467186
        ],
        "ranking_score": 0.9153757049625457
      },
      "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": [
              -0.0014021586522413667,
              -0.0014044825669681617,
              0.010253268877531365
            ],
            "branch_aligned_reduced_polarization": [
              -0.0014021586522413587,
              -0.0014044825669681793,
              0.010253268877531363
            ],
            "target_residual": 0.8585156714039068,
            "energy_eV": -51.53066118063832,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.0017898884859803203,
            "step_scale": 0.15664039035702587,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.718399915636522,
            "cell_principal_stretches": [
              1.001145911327009,
              0.9999501932760054,
              0.9970921614477721
            ],
            "cell_volume_ratio": 0.9981850218474374,
            "cell_rmsd_from_input_A": 0.01787992185269689
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.08087176372339858,
              -0.0810564950376391,
              0.0903574701002407
            ],
            "branch_aligned_reduced_polarization": [
              -0.08087176372339855,
              -0.08105649503763912,
              0.0903574701002407
            ],
            "target_residual": 0.7204090095891067,
            "energy_eV": -51.29752511893703,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.001693776928705324,
            "step_scale": 0.20214137573399726,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.718399915636522,
            "cell_principal_stretches": [
              1.0021783555788304,
              0.9998524265629086,
              0.9943924337075604
            ],
            "cell_volume_ratio": 0.9964115084390436,
            "cell_rmsd_from_input_A": 0.03418949354266951
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.17014296542005655,
              -0.17051807539868044,
              0.175128559192364
            ],
            "branch_aligned_reduced_polarization": [
              -0.17014296542005658,
              -0.17051807539868047,
              0.17512855919236403
            ],
            "target_residual": 0.5682477056295898,
            "energy_eV": -50.14067749347822,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.0017169671129178142,
            "step_scale": 0.2981714325353801,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.718399915636522,
            "cell_principal_stretches": [
              1.0033412154097299,
              0.9998619161115148,
              0.9915678792813816
            ],
            "cell_volume_ratio": 0.9947435441332564,
            "cell_rmsd_from_input_A": 0.051802338602515166
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -0.267125022595198,
              -0.2676694070285241,
              0.2560489315769163
            ],
            "branch_aligned_reduced_polarization": [
              -0.267125022595198,
              -0.2676694070285241,
              0.2560489315769163
            ],
            "target_residual": 0.4095367911635397,
            "energy_eV": -46.70492117849159,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.00278086431060744,
            "step_scale": 0.48150341436044336,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.718399915636522,
            "cell_principal_stretches": [
              1.006421289570318,
              1.000510318267851,
              0.9859647750861984
            ],
            "cell_volume_ratio": 0.9928023271586677,
            "cell_rmsd_from_input_A": 0.09071376488968969
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              -0.3916899532205664,
              -0.39270946759065334,
              0.3729854021252429
            ],
            "branch_aligned_reduced_polarization": [
              -0.3916899532205664,
              -0.39270946759065334,
              0.3729854021252429
            ],
            "target_residual": 0.19843143060344653,
            "energy_eV": -38.41369134399224,
            "max_atomic_step_A": 0.1188459591208126,
            "max_log_strain_component": 0.007108750220382936,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": true,
            "strain_jacobian_frobenius_norm": 1.510154634924857,
            "cell_principal_stretches": [
              1.0043638109196653,
              1.0022287798656822,
              0.9736800980934749
            ],
            "cell_volume_ratio": 0.9801086425232787,
            "cell_rmsd_from_input_A": 0.14227805949657324
          },
          {
            "iteration": 5,
            "reduced_polarization": [
              -0.44994810988139117,
              -0.4504317981428278,
              0.4440519185194554
            ],
            "branch_aligned_reduced_polarization": [
              -0.44994810988139117,
              -0.4504317981428278,
              0.4440519185194554
            ],
            "target_residual": 0.08995769095053696,
            "energy_eV": -30.089788335763668
          }
        ],
        "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": 0.08995769095053696,
        "parent_symmetrization_rmsd_A": 0.3825341978458465,
        "parent_cell_rmsd_A": 0.14227805949657324,
        "energy_eV": -30.089788335763668,
        "reduced_polarization": [
          -0.44994810988139117,
          -0.4504317981428278,
          0.4440519185194554
        ],
        "cartesian_polarization_e_A2": [
          -0.011627376519353565,
          -0.007485646171711925,
          0.01176903804281013
        ],
        "ranking_score": 1.0980190946210637
      },
      "branch_status": "awaiting_branch_sampling"
    }
  ],
  "sampled_polarization_branches": [
    {
      "orbit_id": 0,
      "candidate_id": "inversion_parent_endpoint_00",
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "construction": "MACEField-BEC-parent plus variable-cell P-N-P path and symmetric log-strain continuation beyond both polar endpoints",
      "geometry_diagnostics": {
        "collision_aware": false,
        "permutations_tested": 1,
        "selected_order": [
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          10
        ],
        "endpoint_rmsd_A": 0.17924768966777616,
        "minimum_distance_A_by_image": [
          1.9385047380191511,
          1.9363034489432613,
          1.9344102706727495,
          1.93282610857952,
          1.931551722982553,
          1.930587727334573,
          1.9299345867517517,
          1.9295926168946178,
          1.9295619832064403
        ],
        "minimum_distance_A": 1.9295619832064403,
        "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": [
          315.63080369652465,
          315.63080369652465,
          315.63080369652465,
          315.63080369652465,
          315.63080369652465,
          315.63080369652465,
          315.63080369652465,
          315.63080369652465,
          315.63080369652465
        ],
        "cell_deformation_log_strain_norm": 0.0
      },
      "parent_reduced_polarization": [
        1.7168894312953179e-16,
        -2.6844452392103964e-16,
        -3.1658658399768754e-16
      ],
      "incoming": {
        "reached": true,
        "construction": "variable_cell_linear_interpolation",
        "continuation_fractions": [
          0.0,
          0.125,
          0.25,
          0.375,
          0.5,
          0.625,
          0.75,
          0.875,
          1.0
        ],
        "energies_eV": [
          -51.53066118063833,
          -51.51614209999076,
          -51.50007150379838,
          -51.4837780808312,
          -51.468593178276116,
          -51.45558717379806,
          -51.445507681173126,
          -51.43901043848576,
          -51.436745286675304
        ],
        "cartesian_polarizations_e_A2": [
          [
            -1.0045971319828181e-05,
            -6.5330797245976265e-06,
            0.00026687776712490836
          ],
          [
            -1.0268179254578883e-05,
            -6.672881099897539e-06,
            0.0001939873623422159
          ],
          [
            -8.693610726904802e-06,
            -5.649788651800562e-06,
            0.00013628159542665262
          ],
          [
            -7.284525036468566e-06,
            -4.733851244934958e-06,
            9.216812291699906e-05
          ],
          [
            -6.689032042742493e-06,
            -4.344550001579057e-06,
            5.978651817688737e-05
          ],
          [
            -6.189215878788224e-06,
            -4.017218841610916e-06,
            3.6768449768522384e-05
          ],
          [
            -4.769539218765741e-06,
            -3.0945551006580766e-06,
            2.0505344452911734e-05
          ],
          [
            -2.5016939312512e-06,
            -1.6229491884797663e-06,
            8.921187115178605e-06
          ],
          [
            3.246085723589034e-19,
            -5.646918412246214e-18,
            -8.240291135264727e-18
          ]
        ],
        "raw_reduced_polarization": [
          [
            -0.001402158652241055,
            -0.001404482566968376,
            0.010253268877531082
          ],
          [
            -0.0011214465287497576,
            -0.001123468318394676,
            0.00745286730462962
          ],
          [
            -0.0008388267820765477,
            -0.0008405503380667183,
            0.0052358495652220375
          ],
          [
            -0.0006157084269725079,
            -0.00061713735097345,
            0.0035410388672917083
          ],
          [
            -0.00046709276886444,
            -0.0004682305492991288,
            0.0022969588389583472
          ],
          [
            -0.00035883429472168064,
            -0.00035968425392446737,
            0.0014126197387967783
          ],
          [
            -0.0002455669345327073,
            -0.00024613192294513164,
            0.0007878018928556587
          ],
          [
            -0.00012154883735082828,
            -0.00012183084606511703,
            0.00034274616122623744
          ],
          [
            1.7168894312953179e-16,
            -2.6844452392103964e-16,
            -3.1658658399768754e-16
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -0.001402158652241055,
            -0.001404482566968376,
            0.010253268877531082
          ],
          [
            -0.0011214465287497576,
            -0.001123468318394676,
            0.00745286730462962
          ],
          [
            -0.0008388267820765477,
            -0.0008405503380667183,
            0.0052358495652220375
          ],
          [
            -0.0006157084269725079,
            -0.00061713735097345,
            0.0035410388672917083
          ],
          [
            -0.00046709276886444,
            -0.0004682305492991288,
            0.0022969588389583472
          ],
          [
            -0.00035883429472168064,
            -0.00035968425392446737,
            0.0014126197387967783
          ],
          [
            -0.0002455669345327073,
            -0.00024613192294513164,
            0.0007878018928556587
          ],
          [
            -0.00012154883735082829,
            -0.00012183084606511702,
            0.00034274616122623744
          ],
          [
            1.7168341401307963e-16,
            -2.684484579074109e-16,
            -3.165870343657673e-16
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            -0.0014021586522410812,
            -0.0014044825669684013,
            0.010253268877531085
          ],
          [
            -0.0011214465287497366,
            -0.0011234683183946603,
            0.0074528673046295735
          ],
          [
            -0.0008388267820765294,
            -0.0008405503380667367,
            0.0052358495652220505
          ],
          [
            -0.0006157084269725055,
            -0.0006171373509734623,
            0.0035410388672917348
          ],
          [
            -0.00046709276886441886,
            -0.0004682305492991201,
            0.0022969588389583073
          ],
          [
            -0.00035883429472166606,
            -0.0003596842539244638,
            0.0014126197387968054
          ],
          [
            -0.00024556693453270384,
            -0.0002461319229451475,
            0.0007878018928556552
          ],
          [
            -0.00012154883735082667,
            -0.00012183084606509631,
            0.00034274616122620394
          ],
          [
            2.220446049250313e-16,
            -2.7755575615628914e-16,
            -3.3306690738754696e-16
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -51.436745286675304,
          -51.43901043848576,
          -51.44550768117313,
          -51.455587173798065,
          -51.46859317827613,
          -51.483778080831215,
          -51.50007150379838,
          -51.516142099990766,
          -51.53066118063833
        ],
        "cartesian_polarizations_e_A2": [
          [
            -9.315639808080983e-18,
            -1.3503024162228997e-17,
            -8.943842364302942e-18
          ],
          [
            2.5016939312480195e-06,
            1.6229491884594062e-06,
            -8.921187115189579e-06
          ],
          [
            4.7695392187538225e-06,
            3.0945551006246e-06,
            -2.050534445293079e-05
          ],
          [
            6.189215878755654e-06,
            4.017218841592123e-06,
            -3.6768449768520494e-05
          ],
          [
            6.6890320427186674e-06,
            4.344550001532341e-06,
            -5.978651817689166e-05
          ],
          [
            7.284525036468264e-06,
            4.733851244901833e-06,
            -9.216812291698722e-05
          ],
          [
            8.693610726872589e-06,
            5.649788651757584e-06,
            -0.00013628159542662693
          ],
          [
            1.0268179254559603e-05,
            6.672881099871328e-06,
            -0.00019398736234222985
          ],
          [
            1.0045971319872149e-05,
            6.533079724571257e-06,
            -0.00026687776712490743
          ]
        ],
        "raw_reduced_polarization": [
          [
            -1.2288378587877002e-16,
            -6.844951678424893e-16,
            -3.4361656104733067e-16
          ],
          [
            0.00012154883735116152,
            0.00012183084606407499,
            -0.00034274616122665903
          ],
          [
            0.0002455669345329339,
            0.00024613192294342234,
            -0.0007878018928563908
          ],
          [
            0.00035883429472049946,
            0.000359684253923458,
            -0.0014126197387967058
          ],
          [
            0.0004670927688643181,
            0.0004682305492966551,
            -0.002296958838958512
          ],
          [
            0.0006157084269731697,
            0.0006171373509716371,
            -0.0035410388672912534
          ],
          [
            0.0008388267820758177,
            0.0008405503380643253,
            -0.00523584956522105
          ],
          [
            0.0011214465287494471,
            0.0011234683183933337,
            -0.007452867304630157
          ],
          [
            0.0014021586522437652,
            0.0014044825669669665,
            -0.010253268877531046
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -1.2288378587877002e-16,
            -6.844951678424893e-16,
            -3.4361656104733067e-16
          ],
          [
            0.00012154883735116152,
            0.00012183084606407499,
            -0.00034274616122665903
          ],
          [
            0.0002455669345329339,
            0.00024613192294342234,
            -0.0007878018928563908
          ],
          [
            0.00035883429472049946,
            0.000359684253923458,
            -0.0014126197387967058
          ],
          [
            0.0004670927688643181,
            0.0004682305492966551,
            -0.002296958838958512
          ],
          [
            0.0006157084269731697,
            0.0006171373509716371,
            -0.0035410388672912534
          ],
          [
            0.0008388267820758177,
            0.0008405503380643253,
            -0.00523584956522105
          ],
          [
            0.0011214465287494471,
            0.0011234683183933337,
            -0.007452867304630157
          ],
          [
            0.0014021586522437652,
            0.0014044825669669665,
            -0.010253268877531046
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          0.0014021586522413986,
          0.001404482566967839,
          -0.010253268877531715
        ],
        "actual_opposite_endpoint_branch_residual": 2.6096970698539538e-15
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            -0.001402158652241055,
            -0.001404482566968376,
            0.010253268877531082
          ],
          [
            -0.0011214465287497576,
            -0.001123468318394676,
            0.00745286730462962
          ],
          [
            -0.0008388267820765477,
            -0.0008405503380667183,
            0.0052358495652220375
          ],
          [
            -0.0006157084269725079,
            -0.00061713735097345,
            0.0035410388672917083
          ],
          [
            -0.00046709276886444,
            -0.0004682305492991288,
            0.0022969588389583472
          ],
          [
            -0.00035883429472168064,
            -0.00035968425392446737,
            0.0014126197387967783
          ],
          [
            -0.0002455669345327073,
            -0.00024613192294513164,
            0.0007878018928556587
          ],
          [
            -0.00012154883735082828,
            -0.00012183084606511703,
            0.00034274616122623744
          ],
          [
            1.7168894312953179e-16,
            -2.6844452392103964e-16,
            -3.1658658399768754e-16
          ],
          [
            0.00012154883735116152,
            0.00012183084606407499,
            -0.00034274616122665903
          ],
          [
            0.0002455669345329339,
            0.00024613192294342234,
            -0.0007878018928563908
          ],
          [
            0.00035883429472049946,
            0.000359684253923458,
            -0.0014126197387967058
          ],
          [
            0.0004670927688643181,
            0.0004682305492966551,
            -0.002296958838958512
          ],
          [
            0.0006157084269731697,
            0.0006171373509716371,
            -0.0035410388672912534
          ],
          [
            0.0008388267820758177,
            0.0008405503380643253,
            -0.00523584956522105
          ],
          [
            0.0011214465287494471,
            0.0011234683183933337,
            -0.007452867304630157
          ],
          [
            0.0014021586522437652,
            0.0014044825669669665,
            -0.010253268877531046
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -0.001402158652241055,
            -0.001404482566968376,
            0.010253268877531082
          ],
          [
            -0.0011214465287497576,
            -0.001123468318394676,
            0.00745286730462962
          ],
          [
            -0.0008388267820765477,
            -0.0008405503380667183,
            0.0052358495652220375
          ],
          [
            -0.0006157084269725079,
            -0.00061713735097345,
            0.0035410388672917083
          ],
          [
            -0.00046709276886444,
            -0.0004682305492991288,
            0.0022969588389583472
          ],
          [
            -0.00035883429472168064,
            -0.00035968425392446737,
            0.0014126197387967783
          ],
          [
            -0.0002455669345327073,
            -0.00024613192294513164,
            0.0007878018928556587
          ],
          [
            -0.00012154883735082829,
            -0.00012183084606511702,
            0.00034274616122623744
          ],
          [
            1.7168341401307963e-16,
            -2.684484579074109e-16,
            -3.165870343657673e-16
          ],
          [
            0.00012154883735116152,
            0.00012183084606407499,
            -0.00034274616122665903
          ],
          [
            0.0002455669345329339,
            0.00024613192294342234,
            -0.0007878018928563908
          ],
          [
            0.00035883429472049946,
            0.000359684253923458,
            -0.0014126197387967058
          ],
          [
            0.0004670927688643181,
            0.0004682305492966551,
            -0.002296958838958512
          ],
          [
            0.0006157084269731697,
            0.0006171373509716371,
            -0.0035410388672912534
          ],
          [
            0.0008388267820758177,
            0.0008405503380643253,
            -0.00523584956522105
          ],
          [
            0.0011214465287494471,
            0.0011234683183933337,
            -0.007452867304630157
          ],
          [
            0.0014021586522437652,
            0.0014044825669669665,
            -0.010253268877531046
          ]
        ],
        "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": [
          [
            -0.0014021586522410812,
            -0.0014044825669684013,
            0.010253268877531085
          ],
          [
            -0.0011214465287497366,
            -0.0011234683183946603,
            0.0074528673046295735
          ],
          [
            -0.0008388267820765294,
            -0.0008405503380667367,
            0.0052358495652220505
          ],
          [
            -0.0006157084269725055,
            -0.0006171373509734623,
            0.0035410388672917348
          ],
          [
            -0.00046709276886441886,
            -0.0004682305492991201,
            0.0022969588389583073
          ],
          [
            -0.00035883429472166606,
            -0.0003596842539244638,
            0.0014126197387968054
          ],
          [
            -0.00024556693453270384,
            -0.0002461319229451475,
            0.0007878018928556552
          ],
          [
            -0.00012154883735082667,
            -0.00012183084606509631,
            0.00034274616122620394
          ],
          [
            2.220446049250313e-16,
            -2.7755575615628914e-16,
            -3.3306690738754696e-16
          ],
          [
            0.00012154883735115973,
            0.00012183084606409711,
            -0.00034274616122664803
          ],
          [
            0.0002455669345329259,
            0.0002461319229434267,
            -0.0007878018928563768
          ],
          [
            0.0003588342947205003,
            0.0003596842539234091,
            -0.0014126197387966943
          ],
          [
            0.00046709276886436335,
            0.0004682305492966776,
            -0.0022969588389585294
          ],
          [
            0.0006157084269731161,
            0.000617137350971686,
            -0.003541038867291235
          ],
          [
            0.0008388267820758077,
            0.0008405503380642942,
            -0.005235849565221051
          ],
          [
            0.001121446528749459,
            0.0011234683183933836,
            -0.007452867304630184
          ],
          [
            0.0014021586522438012,
            0.0014044825669670136,
            -0.01025326887753103
          ]
        ]
      },
      "incoming_structure_ids": [
        "incoming_00_000",
        "incoming_00_001",
        "incoming_00_002",
        "incoming_00_003",
        "incoming_00_004",
        "incoming_00_005",
        "incoming_00_006",
        "incoming_00_007",
        "incoming_00_008"
      ],
      "reflected_structure_ids": [
        "reflected_00_001",
        "reflected_00_002",
        "reflected_00_003",
        "reflected_00_004",
        "reflected_00_005",
        "reflected_00_006",
        "reflected_00_007",
        "reflected_00_008"
      ],
      "positive_extension_structure_ids": [
        "extension_plus_00_000",
        "extension_plus_00_001",
        "extension_plus_00_002",
        "extension_plus_00_003"
      ],
      "negative_extension_structure_ids": [
        "extension_minus_00_000",
        "extension_minus_00_001",
        "extension_minus_00_002",
        "extension_minus_00_003"
      ],
      "extension": {
        "enabled": true,
        "fraction_beyond_polar_endpoint": 0.35,
        "images_per_side": 4,
        "construction": "continue fractional atomic displacements and symmetric log strain beyond +P; reflect these structures about N for the -P side",
        "positive_path_coordinates": [
          1.35,
          1.2625,
          1.175,
          1.0875
        ],
        "negative_path_coordinates": [
          -1.0875,
          -1.175,
          -1.2625,
          -1.35
        ]
      },
      "branch_coordinates": [
        1.35,
        1.2625,
        1.175,
        1.0875,
        1.0,
        0.875,
        0.75,
        0.625,
        0.5,
        0.375,
        0.25,
        0.125,
        0.0,
        -0.125,
        -0.25,
        -0.375,
        -0.5,
        -0.625,
        -0.75,
        -0.875,
        -1.0,
        -1.0875,
        -1.175,
        -1.2625,
        -1.35
      ],
      "parent": {
        "candidate_id": "inversion_parent_endpoint_00",
        "source": "same_species_inversion_center_projection_from_endpoint",
        "spacegroup": "C2/m",
        "spacegroup_number": 12,
        "pointgroup": "2/m",
        "has_inversion": true,
        "is_polar_point_group": false,
        "nonpolar_parent_hypothesis": true,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.0
        ],
        "formal_class": [
          0.0,
          0.0,
          0.0
        ],
        "target_residual": 6.635208393392712e-16,
        "parent_symmetrization_rmsd_A": 0.17924768966777616,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -51.4367452866753,
        "reduced_polarization": [
          4.34610569703146e-16,
          -4.971457680697221e-16,
          -6.495877331172403e-17
        ],
        "cartesian_polarization_e_A2": [
          4.5558524464048685e-18,
          -9.450494617729966e-18,
          -1.6907829672345823e-18
        ],
        "ranking_score": 0.1792476896677775
      }
    }
  ],
  "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": 33,
      "energy_polarization": 80
    },
    "model_evaluations_for_recovery_and_path_properties": {
      "total": 138,
      "full_response": 58,
      "energy_polarization": 80
    },
    "elapsed_seconds": 187.54327656596433
  }
}
