{
  "schema": "ferrofinder.endpoint_parent_recovery.v4_variable_cell",
  "status": "complete",
  "input_atom_count": 32,
  "input_formula": "Cs4P4Se24",
  "input_spacegroup": "Pc",
  "input_pointgroup": "m",
  "input_is_polar_point_group": true,
  "input_energy_eV": -119.04785247337435,
  "input_cartesian_polarization_e_A2": [
    -0.00020752800554120116,
    1.0029567825685931e-12,
    0.00013498644562545155
  ],
  "input_reduced_polarization": [
    -0.019190800972159087,
    8.323243868625945e-11,
    0.012608662774733815
  ],
  "input_formal_targets": [
    {
      "orbit_id": 0,
      "representative_formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ]
    },
    {
      "orbit_id": 1,
      "representative_formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        -0.5,
        0.0,
        0.0
      ]
    },
    {
      "orbit_id": 2,
      "representative_formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.5
      ]
    },
    {
      "orbit_id": 3,
      "representative_formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.0
      ]
    },
    {
      "orbit_id": 4,
      "representative_formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        -0.5,
        0.0,
        0.5
      ]
    },
    {
      "orbit_id": 5,
      "representative_formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        -0.5,
        0.5,
        0.0
      ]
    },
    {
      "orbit_id": 6,
      "representative_formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.5
      ]
    },
    {
      "orbit_id": 7,
      "representative_formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "target_reduced_polarization": [
        -0.5,
        0.5,
        0.5
      ]
    }
  ],
  "parent_candidates": [
    {
      "candidate_id": "inversion_parent_endpoint_00",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "P2/c",
      "spacegroup_number": 13,
      "pointgroup": "2/m",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 5.4491426668909354e-15,
      "parent_symmetrization_rmsd_A": 0.09089577081975148,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -119.02434831518454,
      "reduced_polarization": [
        5.262401851747757e-15,
        -1.346703575341985e-15,
        4.320555925041967e-16
      ],
      "cartesian_polarization_e_A2": [
        3.222447086690362e-17,
        -1.6227873486801944e-17,
        4.625522134005305e-18
      ],
      "ranking_score": 0.09089577081976237
    },
    {
      "candidate_id": "bec_projection_00",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Pc",
      "spacegroup_number": 7,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 7.651089353803169e-05,
      "parent_symmetrization_rmsd_A": 0.01309732260990413,
      "parent_cell_rmsd_A": 0.0036082987144400555,
      "energy_eV": -119.02884127789615,
      "reduced_polarization": [
        -7.468792006735019e-05,
        4.537028288386931e-15,
        -1.66021512461828e-05
      ],
      "cartesian_polarization_e_A2": [
        -3.907742705664193e-07,
        5.290466996987876e-17,
        -1.7770643852334922e-07
      ],
      "ranking_score": 0.5141524190755902
    },
    {
      "candidate_id": "inversion_parent_bec_00_00",
      "source": "same_species_inversion_center_projection_after_BEC",
      "spacegroup": "P2/c",
      "spacegroup_number": 13,
      "pointgroup": "2/m",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 3.562667253154908e-15,
      "parent_symmetrization_rmsd_A": 0.09089630633244852,
      "parent_cell_rmsd_A": 0.0036082987144400555,
      "energy_eV": -119.01730959081767,
      "reduced_polarization": [
        -3.309178402826781e-17,
        -3.3384904789241206e-15,
        -1.243376134830149e-15
      ],
      "cartesian_polarization_e_A2": [
        7.662321196510825e-18,
        -4.01983081867201e-17,
        -1.3296758391265016e-17
      ],
      "ranking_score": 0.09179838101106566
    },
    {
      "candidate_id": "bec_projection_01",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Pc",
      "spacegroup_number": 7,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        -0.5,
        0.0,
        0.0
      ],
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_residual": 0.00017117770316729786,
      "parent_symmetrization_rmsd_A": 0.1449796469252546,
      "parent_cell_rmsd_A": 0.04168602354425107,
      "energy_eV": -117.90549198707284,
      "reduced_polarization": [
        -0.5001270296752803,
        6.099853999086495e-12,
        0.00011474000026061014
      ],
      "cartesian_polarization_e_A2": [
        -0.0033438027889627813,
        5.019883575261412e-13,
        1.4661366792709608e-05
      ],
      "ranking_score": 0.6557435082176519
    },
    {
      "candidate_id": "bec_projection_02",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Pc",
      "spacegroup_number": 7,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.5
      ],
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_residual": 1.792316360654413e-05,
      "parent_symmetrization_rmsd_A": 0.2951299390171827,
      "parent_cell_rmsd_A": 0.07466707793315587,
      "energy_eV": -114.04634772508854,
      "reduced_polarization": [
        -1.7392186544162847e-05,
        2.888663225344281e-14,
        0.5000043303164873
      ],
      "cartesian_polarization_e_A2": [
        -0.0032401884093771205,
        3.098116440939683e-13,
        0.005471496722046768
      ],
      "ranking_score": 0.8138325548276848
    },
    {
      "candidate_id": "bec_projection_03",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.0
      ],
      "formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_residual": 0.00037706770773229353,
      "parent_symmetrization_rmsd_A": 0.34687567029802974,
      "parent_cell_rmsd_A": 0.23714266510676082,
      "energy_eV": -113.16546011487648,
      "reduced_polarization": [
        -9.588480241719576e-05,
        0.49963572141958223,
        1.6949239768188078e-05
      ],
      "cartesian_polarization_e_A2": [
        0.00011597269970533464,
        0.006010517249632659,
        -2.1054354079357748e-05
      ],
      "ranking_score": 0.9069154719901845
    },
    {
      "candidate_id": "bec_projection_04",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Pc",
      "spacegroup_number": 7,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        -0.5,
        0.0,
        0.5
      ],
      "formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_residual": 2.0093414943678788e-05,
      "parent_symmetrization_rmsd_A": 0.4621340123701779,
      "parent_cell_rmsd_A": 0.138642075835512,
      "energy_eV": -109.4372584289655,
      "reduced_polarization": [
        -0.5000070026418485,
        5.0779408721703294e-14,
        0.4999811662979943
      ],
      "cartesian_polarization_e_A2": [
        -0.006691341470189748,
        2.050413753728412e-12,
        0.00561842091232611
      ],
      "ranking_score": 0.9968347181589433
    },
    {
      "candidate_id": "bec_projection_05",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        -0.5,
        0.5,
        0.0
      ],
      "formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_residual": 0.00011045043807931736,
      "parent_symmetrization_rmsd_A": 0.39021704471545104,
      "parent_cell_rmsd_A": 0.2361291363923609,
      "energy_eV": -111.6856690235101,
      "reduced_polarization": [
        -0.4999335678599615,
        0.49991176145578686,
        -1.7133874730827505e-07
      ],
      "cartesian_polarization_e_A2": [
        -0.0032289391986537927,
        0.006029580730897699,
        -5.891318350376575e-06
      ],
      "ranking_score": 0.9494702296897
    },
    {
      "candidate_id": "bec_projection_06",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.5
      ],
      "formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_residual": 0.0005055221991545578,
      "parent_symmetrization_rmsd_A": 0.5084232163909157,
      "parent_cell_rmsd_A": 0.33591289137588437,
      "energy_eV": -108.13609139000529,
      "reduced_polarization": [
        1.2523221419950192e-05,
        0.49970135069576527,
        0.4995923181928962
      ],
      "cartesian_polarization_e_A2": [
        -0.0031228777893370055,
        0.006024490328308421,
        0.0054540695910272495
      ],
      "ranking_score": 1.093412483633196
    },
    {
      "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": 0.08420497432394365,
      "parent_symmetrization_rmsd_A": 0.6007643623019902,
      "parent_cell_rmsd_A": 0.5324149501680453,
      "energy_eV": -106.75382421605326,
      "reduced_polarization": [
        -0.45001415921916604,
        0.4569217492414864,
        0.44769170492249105
      ],
      "cartesian_polarization_e_A2": [
        -0.006005064616948635,
        0.005527683493352085,
        0.005103430843011731
      ],
      "ranking_score": 1.4022780484918886
    }
  ],
  "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": [
              -0.019190800972159087,
              8.323243868625945e-11,
              0.012608662774733815
            ],
            "branch_aligned_reduced_polarization": [
              -0.019190800972159087,
              8.323243868625945e-11,
              0.012608662774733815
            ],
            "target_residual": 0.022962256398707432,
            "energy_eV": -119.04785247337435,
            "max_atomic_step_A": 0.013374633330307617,
            "max_log_strain_component": 0.0005882707994238619,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.5729724352791663,
            "cell_principal_stretches": [
              1.0007699899376212,
              1.0003230448814462,
              0.9999946879129334
            ],
            "cell_volume_ratio": 1.0010879656656917,
            "cell_rmsd_from_input_A": 0.0036082987144400555
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -7.468792006735019e-05,
              4.537028288386931e-15,
              -1.66021512461828e-05
            ],
            "branch_aligned_reduced_polarization": [
              -7.468792006735019e-05,
              4.537028288386931e-15,
              -1.66021512461828e-05
            ],
            "target_residual": 7.651089353803169e-05,
            "energy_eV": -119.02884127789615
          }
        ],
        "iterations": 1
      },
      "parent": {
        "candidate_id": "inversion_parent_endpoint_00",
        "source": "same_species_inversion_center_projection_from_endpoint",
        "spacegroup": "P2/c",
        "spacegroup_number": 13,
        "pointgroup": "2/m",
        "has_inversion": true,
        "is_polar_point_group": false,
        "nonpolar_parent_hypothesis": true,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.0
        ],
        "formal_class": [
          0.0,
          0.0,
          0.0
        ],
        "target_residual": 5.4491426668909354e-15,
        "parent_symmetrization_rmsd_A": 0.09089577081975148,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -119.02434831518454,
        "reduced_polarization": [
          5.262401851747757e-15,
          -1.346703575341985e-15,
          4.320555925041967e-16
        ],
        "cartesian_polarization_e_A2": [
          3.222447086690362e-17,
          -1.6227873486801944e-17,
          4.625522134005305e-18
        ],
        "ranking_score": 0.09089577081976237
      },
      "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": [
          -119.04785247337433,
          -119.04247116257244,
          -119.03773542905596,
          -119.03368227120771,
          -119.03033931677174,
          -119.02772552468112,
          -119.02585221238739,
          -119.02472485947273,
          -119.02434831518455
        ],
        "cartesian_polarizations_e_A2": [
          [
            -0.00020752800554119831,
            1.0029329225835852e-12,
            0.00013498644562547497
          ],
          [
            -0.000179908666860437,
            9.117815610958307e-13,
            0.00011878746816388688
          ],
          [
            -0.0001529367691386442,
            8.052134242761445e-13,
            0.00010240786782256141
          ],
          [
            -0.00012653231544302768,
            6.853971239336923e-13,
            8.582776770824755e-05
          ],
          [
            -0.00010061282352621261,
            5.55632520407546e-13,
            6.903112216772172e-05
          ],
          [
            -7.509289413710774e-05,
            4.1964357017310286e-13,
            5.201588271218064e-05
          ],
          [
            -4.988275016535324e-05,
            2.8044999396085783e-13,
            3.480332391224491e-05
          ],
          [
            -2.4886568841019968e-05,
            1.403336003855336e-13,
            1.744205266934758e-05
          ],
          [
            3.237865493803713e-18,
            -6.514277005390804e-18,
            2.0095323937734157e-17
          ]
        ],
        "raw_reduced_polarization": [
          [
            -0.019190800972156564,
            8.323045861615699e-11,
            0.012608662774736002
          ],
          [
            -0.016479205746092736,
            7.566607474832095e-11,
            0.011095566825270043
          ],
          [
            -0.013881163202954058,
            6.682229795961688e-11,
            0.009565599456088883
          ],
          [
            -0.011386407056355494,
            5.687909497700426e-11,
            0.008016904028602997
          ],
          [
            -0.008983955199735242,
            4.611031152157349e-11,
            0.006447981768401672
          ],
          [
            -0.006661137843346982,
            3.482498780761478e-11,
            0.004858641332536371
          ],
          [
            -0.0044025457007071025,
            2.3273721592597648e-11,
            0.0032508699122794442
          ],
          [
            -0.002189421321768708,
            1.1645873474026917e-11,
            0.0016292077266569906
          ],
          [
            2.2799846617880136e-15,
            -5.406007226432196e-16,
            1.87704151854601e-15
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -0.019190800972156564,
            8.323045861615699e-11,
            0.012608662774736002
          ],
          [
            -0.016479205746092736,
            7.566607474832095e-11,
            0.011095566825270043
          ],
          [
            -0.013881163202954058,
            6.682229795961688e-11,
            0.009565599456088883
          ],
          [
            -0.011386407056355494,
            5.687909497700426e-11,
            0.008016904028602997
          ],
          [
            -0.008983955199735242,
            4.611031152157349e-11,
            0.006447981768401672
          ],
          [
            -0.006661137843346982,
            3.482498780761478e-11,
            0.004858641332536371
          ],
          [
            -0.0044025457007071025,
            2.3273721592597648e-11,
            0.0032508699122794442
          ],
          [
            -0.002189421321768708,
            1.1645873474026917e-11,
            0.0016292077266569906
          ],
          [
            2.2798603283025187e-15,
            -5.406007226426927e-16,
            1.8769708010069053e-15
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            -0.019190800972156585,
            8.32304225539815e-11,
            0.012608662774736046
          ],
          [
            -0.01647920574609274,
            7.566602899800046e-11,
            0.01109556682527002
          ],
          [
            -0.013881163202954072,
            6.682232545074385e-11,
            0.009565599456088925
          ],
          [
            -0.011386407056355519,
            5.687905701989848e-11,
            0.008016904028603
          ],
          [
            -0.008983955199735216,
            4.6110337770244314e-11,
            0.006447981768401667
          ],
          [
            -0.006661137843346987,
            3.482503174723206e-11,
            0.004858641332536329
          ],
          [
            -0.004402545700707083,
            2.327371628751962e-11,
            0.0032508699122794082
          ],
          [
            -0.002189421321768692,
            1.1645906461410505e-11,
            0.0016292077266569782
          ],
          [
            2.3314683517128287e-15,
            -5.551115123125783e-16,
            1.887379141862766e-15
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -119.02434831518455,
          -119.02472485947271,
          -119.02585221238739,
          -119.02772552468114,
          -119.03033931677172,
          -119.03368227120774,
          -119.03773542905607,
          -119.04247116257248,
          -119.04785247337433
        ],
        "cartesian_polarizations_e_A2": [
          [
            3.237865493803713e-18,
            -6.514277005390804e-18,
            2.0095323937734157e-17
          ],
          [
            2.4886568841035194e-05,
            -1.4032969438906487e-13,
            -1.744205266932386e-05
          ],
          [
            4.9882750165385486e-05,
            -2.804765264697654e-13,
            -3.480332391216728e-05
          ],
          [
            7.50928941371244e-05,
            -4.1961201383321084e-13,
            -5.2015882712148e-05
          ],
          [
            0.00010061282352621539,
            -5.556449450739448e-13,
            -6.903112216770425e-05
          ],
          [
            0.00012653231544304191,
            -6.853829775451658e-13,
            -8.582776770821997e-05
          ],
          [
            0.00015293676913868224,
            -8.051797093592567e-13,
            -0.00010240786782253177
          ],
          [
            0.00017990866686043926,
            -9.117495679010703e-13,
            -0.00011878746816385373
          ],
          [
            0.00020752800554122282,
            -1.0029662391916227e-12,
            -0.0001349864456254032
          ]
        ],
        "raw_reduced_polarization": [
          [
            2.2799846617880136e-15,
            -5.406007226432196e-16,
            1.87704151854601e-15
          ],
          [
            0.002189421321773116,
            -1.1645549326848053e-11,
            -0.0016292077266547751
          ],
          [
            0.004402545700718881,
            -2.3275923447611968e-11,
            -0.0032508699122721935
          ],
          [
            0.006661137843352399,
            -3.482236903961712e-11,
            -0.0048586413325333215
          ],
          [
            0.008983955199737218,
            -4.6111342608158885e-11,
            -0.00644798176840004
          ],
          [
            0.011386407056360097,
            -5.68779210097545e-11,
            -0.00801690402860042
          ],
          [
            0.013881163202962432,
            -6.681950005765196e-11,
            -0.009565599456086116
          ],
          [
            0.016479205746096036,
            -7.566341972702038e-11,
            -0.011095566825266946
          ],
          [
            0.01919080097216666,
            -8.323322346363986e-11,
            -0.0126086627747293
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            2.2799846617880136e-15,
            -5.406007226432196e-16,
            1.87704151854601e-15
          ],
          [
            0.002189421321773116,
            -1.1645549326848053e-11,
            -0.0016292077266547751
          ],
          [
            0.004402545700718881,
            -2.3275923447611968e-11,
            -0.0032508699122721935
          ],
          [
            0.006661137843352399,
            -3.482236903961712e-11,
            -0.0048586413325333215
          ],
          [
            0.008983955199737218,
            -4.6111342608158885e-11,
            -0.00644798176840004
          ],
          [
            0.011386407056360097,
            -5.68779210097545e-11,
            -0.00801690402860042
          ],
          [
            0.013881163202962432,
            -6.681950005765196e-11,
            -0.009565599456086116
          ],
          [
            0.016479205746096036,
            -7.566341972702038e-11,
            -0.011095566825266946
          ],
          [
            0.01919080097216666,
            -8.323322346363986e-11,
            -0.0126086627747293
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          0.019190800972161127,
          -8.323153981760228e-11,
          -0.012608662774732248
        ],
        "actual_opposite_endpoint_branch_residual": 6.492613374234759e-15
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            -0.019190800972156564,
            8.323045861615699e-11,
            0.012608662774736002
          ],
          [
            -0.016479205746092736,
            7.566607474832095e-11,
            0.011095566825270043
          ],
          [
            -0.013881163202954058,
            6.682229795961688e-11,
            0.009565599456088883
          ],
          [
            -0.011386407056355494,
            5.687909497700426e-11,
            0.008016904028602997
          ],
          [
            -0.008983955199735242,
            4.611031152157349e-11,
            0.006447981768401672
          ],
          [
            -0.006661137843346982,
            3.482498780761478e-11,
            0.004858641332536371
          ],
          [
            -0.0044025457007071025,
            2.3273721592597648e-11,
            0.0032508699122794442
          ],
          [
            -0.002189421321768708,
            1.1645873474026917e-11,
            0.0016292077266569906
          ],
          [
            2.2799846617880136e-15,
            -5.406007226432196e-16,
            1.87704151854601e-15
          ],
          [
            0.002189421321773116,
            -1.1645549326848053e-11,
            -0.0016292077266547751
          ],
          [
            0.004402545700718881,
            -2.3275923447611968e-11,
            -0.0032508699122721935
          ],
          [
            0.006661137843352399,
            -3.482236903961712e-11,
            -0.0048586413325333215
          ],
          [
            0.008983955199737218,
            -4.6111342608158885e-11,
            -0.00644798176840004
          ],
          [
            0.011386407056360097,
            -5.68779210097545e-11,
            -0.00801690402860042
          ],
          [
            0.013881163202962432,
            -6.681950005765196e-11,
            -0.009565599456086116
          ],
          [
            0.016479205746096036,
            -7.566341972702038e-11,
            -0.011095566825266946
          ],
          [
            0.01919080097216666,
            -8.323322346363986e-11,
            -0.0126086627747293
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -0.019190800972156564,
            8.323045861615699e-11,
            0.012608662774736002
          ],
          [
            -0.016479205746092736,
            7.566607474832095e-11,
            0.011095566825270043
          ],
          [
            -0.013881163202954058,
            6.682229795961688e-11,
            0.009565599456088883
          ],
          [
            -0.011386407056355494,
            5.687909497700426e-11,
            0.008016904028602997
          ],
          [
            -0.008983955199735242,
            4.611031152157349e-11,
            0.006447981768401672
          ],
          [
            -0.006661137843346982,
            3.482498780761478e-11,
            0.004858641332536371
          ],
          [
            -0.0044025457007071025,
            2.3273721592597648e-11,
            0.0032508699122794442
          ],
          [
            -0.002189421321768708,
            1.1645873474026917e-11,
            0.0016292077266569906
          ],
          [
            2.2798603283025187e-15,
            -5.406007226426927e-16,
            1.8769708010069053e-15
          ],
          [
            0.002189421321773116,
            -1.1645549326848053e-11,
            -0.0016292077266547751
          ],
          [
            0.004402545700718881,
            -2.3275923447611968e-11,
            -0.0032508699122721935
          ],
          [
            0.006661137843352399,
            -3.482236903961712e-11,
            -0.0048586413325333215
          ],
          [
            0.008983955199737218,
            -4.6111342608158885e-11,
            -0.00644798176840004
          ],
          [
            0.011386407056360097,
            -5.68779210097545e-11,
            -0.00801690402860042
          ],
          [
            0.013881163202962432,
            -6.681950005765196e-11,
            -0.009565599456086116
          ],
          [
            0.016479205746096036,
            -7.566341972702038e-11,
            -0.011095566825266946
          ],
          [
            0.01919080097216666,
            -8.323322346363986e-11,
            -0.0126086627747293
          ]
        ],
        "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": [
          [
            -0.019190800972156585,
            8.32304225539815e-11,
            0.012608662774736046
          ],
          [
            -0.01647920574609274,
            7.566602899800046e-11,
            0.01109556682527002
          ],
          [
            -0.013881163202954072,
            6.682232545074385e-11,
            0.009565599456088925
          ],
          [
            -0.011386407056355519,
            5.687905701989848e-11,
            0.008016904028603
          ],
          [
            -0.008983955199735216,
            4.6110337770244314e-11,
            0.006447981768401667
          ],
          [
            -0.006661137843346987,
            3.482503174723206e-11,
            0.004858641332536329
          ],
          [
            -0.004402545700707083,
            2.327371628751962e-11,
            0.0032508699122794082
          ],
          [
            -0.002189421321768692,
            1.1645906461410505e-11,
            0.0016292077266569782
          ],
          [
            2.3314683517128287e-15,
            -5.551115123125783e-16,
            1.887379141862766e-15
          ],
          [
            0.002189421321773133,
            -1.1645573394503117e-11,
            -0.0016292077266547578
          ],
          [
            0.004402545700718852,
            -2.327593673356887e-11,
            -0.003250869912272192
          ],
          [
            0.006661137843352427,
            -3.482236721197296e-11,
            -0.004858641332533331
          ],
          [
            0.00898395519973727,
            -4.6111336970966477e-11,
            -0.006447981768400057
          ],
          [
            0.01138640705636007,
            -5.687794679687386e-11,
            -0.008016904028600447
          ],
          [
            0.013881163202962399,
            -6.681949438203105e-11,
            -0.009565599456086094
          ],
          [
            0.01647920574609607,
            -7.566341997389259e-11,
            -0.011095566825266967
          ],
          [
            0.019190800972166633,
            -8.323319811154306e-11,
            -0.012608662774729273
          ]
        ]
      },
      "incoming_structure_ids": [
        "incoming_00_000",
        "incoming_00_001",
        "incoming_00_002",
        "incoming_00_003",
        "incoming_00_004",
        "incoming_00_005",
        "incoming_00_006",
        "incoming_00_007",
        "incoming_00_008"
      ],
      "reflected_structure_ids": [
        "reflected_00_001",
        "reflected_00_002",
        "reflected_00_003",
        "reflected_00_004",
        "reflected_00_005",
        "reflected_00_006",
        "reflected_00_007",
        "reflected_00_008"
      ]
    },
    {
      "orbit_id": 1,
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.0,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        -0.5,
        0.0,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -0.019190800972159087,
              8.323243868625945e-11,
              0.012608662774733815
            ],
            "branch_aligned_reduced_polarization": [
              -0.019190800972159083,
              8.323243868625945e-11,
              0.012608662774733815
            ],
            "target_residual": 0.4809744943827696,
            "energy_eV": -119.04785247337435,
            "max_atomic_step_A": 0.11999999999999998,
            "max_log_strain_component": 0.00584355378288932,
            "step_scale": 0.8132862298045465,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.5729724352791663,
            "cell_principal_stretches": [
              0.9999048101769887,
              0.9971136049906079,
              0.9924385962390735
            ],
            "cell_volume_ratio": 0.9894798290513265,
            "cell_rmsd_from_input_A": 0.03305691698301348
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.40645348364555994,
              6.239709750638866e-11,
              0.00122310527421881
            ],
            "branch_aligned_reduced_polarization": [
              -0.40645348364555994,
              6.239709750638866e-11,
              0.00122310527421881
            ],
            "target_residual": 0.09355451196261645,
            "energy_eV": -118.31899220206928,
            "max_atomic_step_A": 0.030828168378037677,
            "max_log_strain_component": 0.0015422860209375726,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.5729724352791663,
            "cell_principal_stretches": [
              0.9998767812794873,
              0.9963594144287639,
              0.9904535545332006
            ],
            "cell_volume_ratio": 0.9867261254997405,
            "cell_rmsd_from_input_A": 0.04168602354425107
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.5001270296752803,
              6.099853999086495e-12,
              0.00011474000026061014
            ],
            "branch_aligned_reduced_polarization": [
              -0.5001270296752803,
              6.099853999086495e-12,
              0.00011474000026061014
            ],
            "target_residual": 0.00017117770316729786,
            "energy_eV": -117.90549198707284
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_01",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Pc",
        "spacegroup_number": 7,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          -0.5,
          0.0,
          0.0
        ],
        "formal_class": [
          0.5,
          0.0,
          0.0
        ],
        "target_residual": 0.00017117770316729786,
        "parent_symmetrization_rmsd_A": 0.1449796469252546,
        "parent_cell_rmsd_A": 0.04168602354425107,
        "energy_eV": -117.90549198707284,
        "reduced_polarization": [
          -0.5001270296752803,
          6.099853999086495e-12,
          0.00011474000026061014
        ],
        "cartesian_polarization_e_A2": [
          -0.0033438027889627813,
          5.019883575261412e-13,
          1.4661366792709608e-05
        ],
        "ranking_score": 0.6557435082176519
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 2,
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.0,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -0.019190800972159087,
              8.323243868625945e-11,
              0.012608662774733815
            ],
            "branch_aligned_reduced_polarization": [
              -0.019190800972159087,
              8.323243868625945e-11,
              0.012608662774733825
            ],
            "target_residual": 0.48776900521064903,
            "energy_eV": -119.04785247337435,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.004744655667156299,
            "step_scale": 0.43495341331389853,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.5729724352791663,
            "cell_principal_stretches": [
              1.0001633169165152,
              0.9971402844053098,
              0.993766348508357
            ],
            "cell_volume_ratio": 0.9910862941112553,
            "cell_rmsd_from_input_A": 0.031237296137391752
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.014470514461612178,
              -5.1102088901980706e-12,
              0.22074885570761682
            ],
            "branch_aligned_reduced_polarization": [
              -0.014470514461612178,
              -5.1102088901980706e-12,
              0.22074885570761682
            ],
            "target_residual": 0.2796258167218992,
            "energy_eV": -118.20295318826142,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.004722271441080665,
            "step_scale": 0.7504781984570761,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.5729724352791663,
            "cell_principal_stretches": [
              1.000345892926171,
              0.9942594787236506,
              0.9875932703222874
            ],
            "cell_volume_ratio": 0.9822636106969316,
            "cell_rmsd_from_input_A": 0.06248791544731858
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.025682964984745645,
              -1.0676343240833877e-10,
              0.41569652082003133
            ],
            "branch_aligned_reduced_polarization": [
              -0.025682964984745645,
              -1.0676343240833877e-10,
              0.41569652082003133
            ],
            "target_residual": 0.08812883348969894,
            "energy_eV": -115.55079649403967,
            "max_atomic_step_A": 0.04484920910698442,
            "max_log_strain_component": 0.0016930075606599237,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.5729724352791663,
            "cell_principal_stretches": [
              1.0004576702934815,
              0.9931299475346134,
              0.9853723371134031
            ],
            "cell_volume_ratio": 0.9790506548798549,
            "cell_rmsd_from_input_A": 0.07452050430166922
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -0.00468607636066554,
              5.164989880308332e-11,
              0.4968116169831029
            ],
            "branch_aligned_reduced_polarization": [
              -0.00468607636066554,
              5.164989880308332e-11,
              0.4968116169831029
            ],
            "target_residual": 0.005667900662540437,
            "energy_eV": -114.08483009840246,
            "max_atomic_step_A": 0.001295042385419018,
            "max_log_strain_component": 1.54443491856738e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.5729724352791663,
            "cell_principal_stretches": [
              1.000462873956408,
              0.9931146094073607,
              0.9853600360040579
            ],
            "cell_volume_ratio": 0.9790284043707193,
            "cell_rmsd_from_input_A": 0.07466707793315587
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              -1.7392186544162847e-05,
              2.888663225344281e-14,
              0.5000043303164873
            ],
            "branch_aligned_reduced_polarization": [
              -1.7392186544162847e-05,
              2.888663225344281e-14,
              0.5000043303164873
            ],
            "target_residual": 1.792316360654413e-05,
            "energy_eV": -114.04634772508854
          }
        ],
        "iterations": 4
      },
      "parent": {
        "candidate_id": "bec_projection_02",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Pc",
        "spacegroup_number": 7,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.5
        ],
        "formal_class": [
          0.0,
          0.0,
          0.5
        ],
        "target_residual": 1.792316360654413e-05,
        "parent_symmetrization_rmsd_A": 0.2951299390171827,
        "parent_cell_rmsd_A": 0.07466707793315587,
        "energy_eV": -114.04634772508854,
        "reduced_polarization": [
          -1.7392186544162847e-05,
          2.888663225344281e-14,
          0.5000043303164873
        ],
        "cartesian_polarization_e_A2": [
          -0.0032401884093771205,
          3.098116440939683e-13,
          0.005471496722046768
        ],
        "ranking_score": 0.8138325548276848
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 3,
      "formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.5,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -0.019190800972159087,
              8.323243868625945e-11,
              0.012608662774733815
            ],
            "branch_aligned_reduced_polarization": [
              -0.019190800972159087,
              8.323242095542582e-11,
              0.012608662774733815
            ],
            "target_residual": 0.5005269874199467,
            "energy_eV": -119.04785247337435,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.006484723543541174,
            "step_scale": 0.38809329491980965,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.5729724352791663,
            "cell_principal_stretches": [
              1.0067681155970358,
              1.0001185090138187,
              0.993578890051847
            ],
            "cell_volume_ratio": 1.0004220918213473,
            "cell_rmsd_from_input_A": 0.07902044141350265
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.013628363959147283,
              0.19127167168281464,
              0.006776980807626966
            ],
            "branch_aligned_reduced_polarization": [
              -0.013628363959147283,
              0.19127167168281467,
              0.006776980807626966
            ],
            "target_residual": 0.30910328448367175,
            "energy_eV": -118.23004514787856,
            "max_atomic_step_A": 0.12000000000000001,
            "max_log_strain_component": 0.006622584921805982,
            "step_scale": 0.6095261343667209,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.5729724352791663,
            "cell_principal_stretches": [
              1.0138448237838948,
              1.0003371647829342,
              0.9871720012668976
            ],
            "cell_volume_ratio": 1.0011766714084327,
            "cell_rmsd_from_input_A": 0.15985250050778257
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.008639029475853622,
              0.37034376497659316,
              0.0019101047717178037
            ],
            "branch_aligned_reduced_polarization": [
              -0.008639029475853622,
              0.37034376497659316,
              0.0019101047717178037
            ],
            "target_residual": 0.12995776471980625,
            "energy_eV": -115.85249636538427,
            "max_atomic_step_A": 0.09006147800088757,
            "max_log_strain_component": 0.005633047437725401,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.5729724352791663,
            "cell_principal_stretches": [
              1.0201058191405634,
              1.000684284578979,
              0.981934549030184
            ],
            "cell_volume_ratio": 1.0023625797059916,
            "cell_rmsd_from_input_A": 0.22885270944285116
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -0.0027510499531471977,
              0.48865712828815583,
              0.0003698430082569113
            ],
            "branch_aligned_reduced_polarization": [
              -0.0027510499531471977,
              0.48865712828815583,
              0.0003698430082569113
            ],
            "target_residual": 0.011677576733501794,
            "energy_eV": -113.39216143412233,
            "max_atomic_step_A": 0.00953283796977485,
            "max_log_strain_component": 0.0006736519398635955,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.5729724352791663,
            "cell_principal_stretches": [
              1.0208933871615589,
              1.0007536618159405,
              0.9813415634549524
            ],
            "cell_volume_ratio": 1.0026001650848586,
            "cell_rmsd_from_input_A": 0.23714266510676082
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              -9.588480241719576e-05,
              0.49963572141958223,
              1.6949239768188078e-05
            ],
            "branch_aligned_reduced_polarization": [
              -9.588480241719576e-05,
              0.49963572141958223,
              1.6949239768188078e-05
            ],
            "target_residual": 0.00037706770773229353,
            "energy_eV": -113.16546011487648
          }
        ],
        "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": [
          0.0,
          0.5,
          0.0
        ],
        "formal_class": [
          0.0,
          0.5,
          0.0
        ],
        "target_residual": 0.00037706770773229353,
        "parent_symmetrization_rmsd_A": 0.34687567029802974,
        "parent_cell_rmsd_A": 0.23714266510676082,
        "energy_eV": -113.16546011487648,
        "reduced_polarization": [
          -9.588480241719576e-05,
          0.49963572141958223,
          1.6949239768188078e-05
        ],
        "cartesian_polarization_e_A2": [
          0.00011597269970533464,
          0.006010517249632659,
          -2.1054354079357748e-05
        ],
        "ranking_score": 0.9069154719901845
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 4,
      "formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.0,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        -0.5,
        0.0,
        0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -0.019190800972159087,
              8.323243868625945e-11,
              0.012608662774733815
            ],
            "branch_aligned_reduced_polarization": [
              -0.019190800972159083,
              8.323243868625945e-11,
              0.012608662774733825
            ],
            "target_residual": 0.6846369851768359,
            "energy_eV": -119.04785247337435,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.005167337568788249,
            "step_scale": 0.27659731261798715,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.5729724352791663,
            "cell_principal_stretches": [
              1.000072935858003,
              0.9971105987740985,
              0.9932520559711224
            ],
            "cell_volume_ratio": 0.9904543866349959,
            "cell_rmsd_from_input_A": 0.03204355152782445
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.15317961146273137,
              6.275824340112082e-11,
              0.14532577087774806
            ],
            "branch_aligned_reduced_polarization": [
              -0.1531796114627314,
              6.275824340112082e-11,
              0.14532577087774806
            ],
            "target_residual": 0.49606268828506506,
            "energy_eV": -118.33316578981868,
            "max_atomic_step_A": 0.12000000000000001,
            "max_log_strain_component": 0.005247571866924557,
            "step_scale": 0.3770312233206541,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.5729724352791663,
            "cell_principal_stretches": [
              1.0001469666874347,
              0.994184968928692,
              0.9864459503130734
            ],
            "cell_volume_ratio": 0.9808538681231397,
            "cell_rmsd_from_input_A": 0.0643371662882367
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.2914630666360118,
              -5.355134305414125e-11,
              0.2747933824228882
            ],
            "branch_aligned_reduced_polarization": [
              -0.2914630666360118,
              -5.355134305414125e-11,
              0.2747933824228882
            ],
            "target_residual": 0.30692942703067744,
            "energy_eV": -116.15605834764148,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.005553987189310816,
            "step_scale": 0.6176915994843057,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.5729724352791663,
            "cell_principal_stretches": [
              1.0002441722686637,
              0.9910577453555827,
              0.9792862878957602
            ],
            "cell_volume_ratio": 0.9707662368709605,
            "cell_rmsd_from_input_A": 0.09859183911352871
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -0.4344838083826768,
              1.432972310775753e-11,
              0.39744314967299865
            ],
            "branch_aligned_reduced_polarization": [
              -0.4344838083826768,
              1.432972310775753e-11,
              0.39744314967299865
            ],
            "target_residual": 0.12169748934564249,
            "energy_eV": -112.61894269788596,
            "max_atomic_step_A": 0.09195222740576378,
            "max_log_strain_component": 0.004729628767274146,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.5729724352791663,
            "cell_principal_stretches": [
              1.0003847714830263,
              0.9882797484189235,
              0.9732091621573877
            ],
            "cell_volume_ratio": 0.9621729802663903,
            "cell_rmsd_from_input_A": 0.12859760700690903
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              -0.5050724643149047,
              1.4073026076708316e-10,
              0.4920600056719495
            ],
            "branch_aligned_reduced_polarization": [
              -0.5050724643149047,
              1.4073026076708316e-10,
              0.4920600056719495
            ],
            "target_residual": 0.009421963922423794,
            "energy_eV": -109.54746219809611,
            "max_atomic_step_A": 0.0033919117139089502,
            "max_log_strain_component": 0.0011105258066124264,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": true,
            "strain_jacobian_frobenius_norm": 3.265782074246615,
            "cell_principal_stretches": [
              0.9998304185011136,
              0.9871828474353078,
              0.9724150409471831
            ],
            "cell_volume_ratio": 0.95978865900558,
            "cell_rmsd_from_input_A": 0.138642075835512
          },
          {
            "iteration": 5,
            "reduced_polarization": [
              -0.5000070026418485,
              5.0779408721703294e-14,
              0.4999811662979943
            ],
            "branch_aligned_reduced_polarization": [
              -0.5000070026418485,
              5.0779408721703294e-14,
              0.4999811662979943
            ],
            "target_residual": 2.0093414943678788e-05,
            "energy_eV": -109.4372584289655
          }
        ],
        "iterations": 5
      },
      "parent": {
        "candidate_id": "bec_projection_04",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Pc",
        "spacegroup_number": 7,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          -0.5,
          0.0,
          0.5
        ],
        "formal_class": [
          0.5,
          0.0,
          0.5
        ],
        "target_residual": 2.0093414943678788e-05,
        "parent_symmetrization_rmsd_A": 0.4621340123701779,
        "parent_cell_rmsd_A": 0.138642075835512,
        "energy_eV": -109.4372584289655,
        "reduced_polarization": [
          -0.5000070026418485,
          5.0779408721703294e-14,
          0.4999811662979943
        ],
        "cartesian_polarization_e_A2": [
          -0.006691341470189748,
          2.050413753728412e-12,
          0.00561842091232611
        ],
        "ranking_score": 0.9968347181589433
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 5,
      "formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.5,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        -0.5,
        0.5,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -0.019190800972159087,
              8.323243868625945e-11,
              0.012608662774733815
            ],
            "branch_aligned_reduced_polarization": [
              -0.019190800972159083,
              8.323242095542582e-11,
              0.012608662774733815
            ],
            "target_residual": 0.6937841625199644,
            "energy_eV": -119.04785247337435,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.005853432400575032,
            "step_scale": 0.35031221743898927,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.5729724352791663,
            "cell_principal_stretches": [
              1.0045628528141044,
              0.9986754685551956,
              0.9922477123653676
            ],
            "cell_volume_ratio": 0.9954549325459804,
            "cell_rmsd_from_input_A": 0.07248181490400948
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.18289401022831664,
              0.17311566778602566,
              0.007027150642477549
            ],
            "branch_aligned_reduced_polarization": [
              -0.18289401022831664,
              0.17311566778602566,
              0.007027150642477549
            ],
            "target_residual": 0.4554766253521765,
            "energy_eV": -118.23858622817167,
            "max_atomic_step_A": 0.12000000000000001,
            "max_log_strain_component": 0.005826386155231775,
            "step_scale": 0.5066292809708198,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.5729724352791663,
            "cell_principal_stretches": [
              1.0090516852453721,
              0.9972749098596889,
              0.98446568166522
            ],
            "cell_volume_ratio": 0.9906697139494491,
            "cell_rmsd_from_input_A": 0.14432951076432685
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.33279493062518417,
              0.33231220139657547,
              0.004637271686399657
            ],
            "branch_aligned_reduced_polarization": [
              -0.33279493062518417,
              0.33231220139657547,
              0.004637271686399657
            ],
            "target_residual": 0.23685066458381138,
            "energy_eV": -115.91016086053575,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.006473272565038325,
            "step_scale": 0.939136026472619,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.5729724352791663,
            "cell_principal_stretches": [
              1.0140599540397324,
              0.9957034985046272,
              0.975881499926405
            ],
            "cell_volume_ratio": 0.9853505209914486,
            "cell_rmsd_from_input_A": 0.22361479279854382
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -0.4772805652853201,
              0.47989983047063445,
              0.002940802382498248
            ],
            "branch_aligned_reduced_polarization": [
              -0.4772805652853201,
              0.47989983047063445,
              0.002940802382498248
            ],
            "target_residual": 0.03047684116697046,
            "energy_eV": -112.21173194479417,
            "max_atomic_step_A": 0.01830250662102257,
            "max_log_strain_component": 0.0010289351861333762,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.5729724352791663,
            "cell_principal_stretches": [
              1.0148753415508598,
              0.9954668179198142,
              0.9745507403024586
            ],
            "cell_volume_ratio": 0.984563982949733,
            "cell_rmsd_from_input_A": 0.2361291363923609
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              -0.4999335678599615,
              0.49991176145578686,
              -1.7133874730827505e-07
            ],
            "branch_aligned_reduced_polarization": [
              -0.4999335678599615,
              0.49991176145578686,
              -1.7133874730827505e-07
            ],
            "target_residual": 0.00011045043807931736,
            "energy_eV": -111.6856690235101
          }
        ],
        "iterations": 4
      },
      "parent": {
        "candidate_id": "bec_projection_05",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          -0.5,
          0.5,
          0.0
        ],
        "formal_class": [
          0.5,
          0.5,
          0.0
        ],
        "target_residual": 0.00011045043807931736,
        "parent_symmetrization_rmsd_A": 0.39021704471545104,
        "parent_cell_rmsd_A": 0.2361291363923609,
        "energy_eV": -111.6856690235101,
        "reduced_polarization": [
          -0.4999335678599615,
          0.49991176145578686,
          -1.7133874730827505e-07
        ],
        "cartesian_polarization_e_A2": [
          -0.0032289391986537927,
          0.006029580730897699,
          -5.891318350376575e-06
        ],
        "ranking_score": 0.9494702296897
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 6,
      "formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.5,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -0.019190800972159087,
              8.323243868625945e-11,
              0.012608662774733815
            ],
            "branch_aligned_reduced_polarization": [
              -0.019190800972159087,
              8.323242095542582e-11,
              0.012608662774733825
            ],
            "target_residual": 0.6985117052426206,
            "energy_eV": -119.04785247337435,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.004836793245184727,
            "step_scale": 0.2894690926738732,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.5729724352791663,
            "cell_principal_stretches": [
              1.0032057441081512,
              0.998347354238075,
              0.992522667517383
            ],
            "cell_volume_ratio": 0.9940588944860863,
            "cell_rmsd_from_input_A": 0.06223203729689217
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.014512396047613554,
              0.14209833257821197,
              0.14964580450794865
            ],
            "branch_aligned_reduced_polarization": [
              -0.014512396047613554,
              0.14209833257821197,
              0.14964580450794862
            ],
            "target_residual": 0.5010511705217557,
            "energy_eV": -118.19924846697344,
            "max_atomic_step_A": 0.11999999999999998,
            "max_log_strain_component": 0.004843232907764397,
            "step_scale": 0.374346893529343,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.5729724352791663,
            "cell_principal_stretches": [
              1.0064604477771237,
              0.9967510553944513,
              0.9851720381097375
            ],
            "cell_volume_ratio": 0.9883152428312557,
            "cell_rmsd_from_input_A": 0.1239101577171466
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.017979616769272615,
              0.27104014876068255,
              0.2727527721437413
            ],
            "branch_aligned_reduced_polarization": [
              -0.017979616769272615,
              0.27104014876068255,
              0.2727527721437413
            ],
            "target_residual": 0.3230900534944625,
            "energy_eV": -115.79746430687304,
            "max_atomic_step_A": 0.12000000000000001,
            "max_log_strain_component": 0.005212263460549261,
            "step_scale": 0.5478758567228245,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.5729724352791663,
            "cell_principal_stretches": [
              1.010061413132665,
              0.9951698345955504,
              0.9775170500258501
            ],
            "cell_volume_ratio": 0.9825831782163713,
            "cell_rmsd_from_input_A": 0.18944193771253037
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -0.024437758055721792,
              0.39161583348225704,
              0.37916111167272987
            ],
            "branch_aligned_reduced_polarization": [
              -0.024437758055721792,
              0.39161583348225704,
              0.37916111167272987
            ],
            "target_residual": 0.1641534906808451,
            "energy_eV": -112.27265181339199,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.00503491764650806,
            "step_scale": 0.8784772194141908,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.5729724352791663,
            "cell_principal_stretches": [
              1.0134659882902268,
              0.9935667640285838,
              0.9700009898091229
            ],
            "cell_volume_ratio": 0.9767387354498526,
            "cell_rmsd_from_input_A": 0.2528127878477712
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              -0.015108753331622463,
              0.48464626022002666,
              0.4686126291738935
            ],
            "branch_aligned_reduced_polarization": [
              -0.015108753331622463,
              0.48464626022002666,
              0.4686126291738935
            ],
            "target_residual": 0.03806808111584388,
            "energy_eV": -108.87620097073176,
            "max_atomic_step_A": 0.027977047095700622,
            "max_log_strain_component": 0.0049572753085576,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": true,
            "strain_jacobian_frobenius_norm": 2.43550772024871,
            "cell_principal_stretches": [
              1.0162919064593132,
              0.9884784197064573,
              0.965140758557957
            ],
            "cell_volume_ratio": 0.9695636296399669,
            "cell_rmsd_from_input_A": 0.33591289137588437
          },
          {
            "iteration": 5,
            "reduced_polarization": [
              1.2523221419950192e-05,
              0.49970135069576527,
              0.4995923181928962
            ],
            "branch_aligned_reduced_polarization": [
              1.2523221419950192e-05,
              0.49970135069576527,
              0.4995923181928962
            ],
            "target_residual": 0.0005055221991545578,
            "energy_eV": -108.13609139000529
          }
        ],
        "iterations": 5
      },
      "parent": {
        "candidate_id": "bec_projection_06",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.5,
          0.5
        ],
        "formal_class": [
          0.0,
          0.5,
          0.5
        ],
        "target_residual": 0.0005055221991545578,
        "parent_symmetrization_rmsd_A": 0.5084232163909157,
        "parent_cell_rmsd_A": 0.33591289137588437,
        "energy_eV": -108.13609139000529,
        "reduced_polarization": [
          1.2523221419950192e-05,
          0.49970135069576527,
          0.4995923181928962
        ],
        "cartesian_polarization_e_A2": [
          -0.0031228777893370055,
          0.006024490328308421,
          0.0054540695910272495
        ],
        "ranking_score": 1.093412483633196
      },
      "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": [
              -0.019190800972159087,
              8.323243868625945e-11,
              0.012608662774733815
            ],
            "branch_aligned_reduced_polarization": [
              -0.019190800972159083,
              8.323242095542582e-11,
              0.012608662774733825
            ],
            "target_residual": 0.8477781557629299,
            "energy_eV": -119.04785247337435,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.0042057287167847355,
            "step_scale": 0.22512430260877458,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.5729724352791663,
            "cell_principal_stretches": [
              1.0019413233668912,
              0.9977665640737718,
              0.9925180685986323
            ],
            "cell_volume_ratio": 0.9922238382243918,
            "cell_rmsd_from_input_A": 0.05249977823218921
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.12652811508926137,
              0.110691835621727,
              0.11959641299183837
            ],
            "branch_aligned_reduced_polarization": [
              -0.12652811508926137,
              0.11069183562172702,
              0.11959641299183837
            ],
            "target_residual": 0.6601128575319802,
            "energy_eV": -118.28256429969043,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.004175087164714101,
            "step_scale": 0.2729403827036418,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.5729724352791663,
            "cell_principal_stretches": [
              1.003987772714835,
              0.9955562648823849,
              0.9850273262511524
            ],
            "cell_volume_ratio": 0.9845607355438636,
            "cell_rmsd_from_input_A": 0.10560230370689853
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.23047833086124114,
              0.21237493933725538,
              0.21923220385358094
            ],
            "branch_aligned_reduced_polarization": [
              -0.23047833086124114,
              0.21237493933725538,
              0.21923220385358094
            ],
            "target_residual": 0.483942828244729,
            "energy_eV": -116.09846503023188,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.004309893231327943,
            "step_scale": 0.34908034942887123,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.5729724352791663,
            "cell_principal_stretches": [
              1.0063705798293598,
              0.9933066245686981,
              0.9771372301956985
            ],
            "cell_volume_ratio": 0.9767801487968932,
            "cell_rmsd_from_input_A": 0.16304235096194425
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -0.3272613629023535,
              0.3092042971740553,
              0.3050593217860203
            ],
            "branch_aligned_reduced_polarization": [
              -0.3272613629023535,
              0.3092042971740553,
              0.3050593217860203
            ],
            "target_residual": 0.3228676276521463,
            "energy_eV": -112.93497027026442,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.004783621285450849,
            "step_scale": 0.42520291829501766,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.5729724352791663,
            "cell_principal_stretches": [
              1.008707354287296,
              0.9907730837233485,
              0.9686812593320903
            ],
            "cell_volume_ratio": 0.9681001435521113,
            "cell_rmsd_from_input_A": 0.22268007163305806
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              -0.39401295802910025,
              0.3918799929606811,
              0.37568228924081976
            ],
            "branch_aligned_reduced_polarization": [
              -0.39401295802910025,
              0.3918799929606811,
              0.37568228924081976
            ],
            "target_residual": 0.19590324702854425,
            "energy_eV": -109.77333273238077,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.01766795884970863,
            "step_scale": 0.6271996771554738,
            "strain_jacobian_refreshed": true,
            "strain_jacobian_frobenius_norm": 2.769549267685631,
            "cell_principal_stretches": [
              1.0158267324303476,
              0.9673337583324063,
              0.941627413439278
            ],
            "cell_volume_ratio": 0.9252840486656969,
            "cell_rmsd_from_input_A": 0.5324149501680453
          },
          {
            "iteration": 5,
            "reduced_polarization": [
              -0.45001415921916604,
              0.4569217492414864,
              0.44769170492249105
            ],
            "branch_aligned_reduced_polarization": [
              -0.45001415921916604,
              0.4569217492414864,
              0.44769170492249105
            ],
            "target_residual": 0.08420497432394365,
            "energy_eV": -106.75382421605326
          }
        ],
        "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": 0.08420497432394365,
        "parent_symmetrization_rmsd_A": 0.6007643623019902,
        "parent_cell_rmsd_A": 0.5324149501680453,
        "energy_eV": -106.75382421605326,
        "reduced_polarization": [
          -0.45001415921916604,
          0.4569217492414864,
          0.44769170492249105
        ],
        "cartesian_polarization_e_A2": [
          -0.006005064616948635,
          0.005527683493352085,
          0.005103430843011731
        ],
        "ranking_score": 1.4022780484918886
      },
      "branch_status": "awaiting_branch_sampling"
    }
  ],
  "sampled_polarization_branches": [
    {
      "orbit_id": 0,
      "candidate_id": "inversion_parent_endpoint_00",
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "construction": "MACEField-BEC-parent plus variable-cell P-N-P path and symmetric log-strain continuation beyond both polar endpoints",
      "geometry_diagnostics": {
        "collision_aware": false,
        "permutations_tested": 1,
        "selected_order": [
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          10,
          11,
          12,
          13,
          14,
          15,
          16,
          17,
          18,
          19,
          20,
          21,
          22,
          23,
          24,
          25,
          26,
          27,
          28,
          29,
          30,
          31
        ],
        "endpoint_rmsd_A": 0.09089577081975148,
        "minimum_distance_A_by_image": [
          2.1728206836109822,
          2.1730428150745142,
          2.1732654522152064,
          2.1734885948776643,
          2.173712242906205,
          2.173936396144858,
          2.174161054437361,
          2.174386217627169,
          2.1746118855574483
        ],
        "minimum_distance_A": 2.1728206836109822,
        "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": [
          1080.0950608546964,
          1080.0950608546964,
          1080.0950608546964,
          1080.0950608546964,
          1080.0950608546964,
          1080.0950608546964,
          1080.0950608546964,
          1080.0950608546964,
          1080.0950608546964
        ],
        "cell_deformation_log_strain_norm": 0.0
      },
      "parent_reduced_polarization": [
        2.2799846617880136e-15,
        -5.406007226432196e-16,
        1.87704151854601e-15
      ],
      "incoming": {
        "reached": true,
        "construction": "variable_cell_linear_interpolation",
        "continuation_fractions": [
          0.0,
          0.125,
          0.25,
          0.375,
          0.5,
          0.625,
          0.75,
          0.875,
          1.0
        ],
        "energies_eV": [
          -119.04785247337433,
          -119.04247116257244,
          -119.03773542905596,
          -119.03368227120771,
          -119.03033931677174,
          -119.02772552468112,
          -119.02585221238739,
          -119.02472485947273,
          -119.02434831518455
        ],
        "cartesian_polarizations_e_A2": [
          [
            -0.00020752800554119831,
            1.0029329225835852e-12,
            0.00013498644562547497
          ],
          [
            -0.000179908666860437,
            9.117815610958307e-13,
            0.00011878746816388688
          ],
          [
            -0.0001529367691386442,
            8.052134242761445e-13,
            0.00010240786782256141
          ],
          [
            -0.00012653231544302768,
            6.853971239336923e-13,
            8.582776770824755e-05
          ],
          [
            -0.00010061282352621261,
            5.55632520407546e-13,
            6.903112216772172e-05
          ],
          [
            -7.509289413710774e-05,
            4.1964357017310286e-13,
            5.201588271218064e-05
          ],
          [
            -4.988275016535324e-05,
            2.8044999396085783e-13,
            3.480332391224491e-05
          ],
          [
            -2.4886568841019968e-05,
            1.403336003855336e-13,
            1.744205266934758e-05
          ],
          [
            3.237865493803713e-18,
            -6.514277005390804e-18,
            2.0095323937734157e-17
          ]
        ],
        "raw_reduced_polarization": [
          [
            -0.019190800972156564,
            8.323045861615699e-11,
            0.012608662774736002
          ],
          [
            -0.016479205746092736,
            7.566607474832095e-11,
            0.011095566825270043
          ],
          [
            -0.013881163202954058,
            6.682229795961688e-11,
            0.009565599456088883
          ],
          [
            -0.011386407056355494,
            5.687909497700426e-11,
            0.008016904028602997
          ],
          [
            -0.008983955199735242,
            4.611031152157349e-11,
            0.006447981768401672
          ],
          [
            -0.006661137843346982,
            3.482498780761478e-11,
            0.004858641332536371
          ],
          [
            -0.0044025457007071025,
            2.3273721592597648e-11,
            0.0032508699122794442
          ],
          [
            -0.002189421321768708,
            1.1645873474026917e-11,
            0.0016292077266569906
          ],
          [
            2.2799846617880136e-15,
            -5.406007226432196e-16,
            1.87704151854601e-15
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -0.019190800972156564,
            8.323045861615699e-11,
            0.012608662774736002
          ],
          [
            -0.016479205746092736,
            7.566607474832095e-11,
            0.011095566825270043
          ],
          [
            -0.013881163202954058,
            6.682229795961688e-11,
            0.009565599456088883
          ],
          [
            -0.011386407056355494,
            5.687909497700426e-11,
            0.008016904028602997
          ],
          [
            -0.008983955199735242,
            4.611031152157349e-11,
            0.006447981768401672
          ],
          [
            -0.006661137843346982,
            3.482498780761478e-11,
            0.004858641332536371
          ],
          [
            -0.0044025457007071025,
            2.3273721592597648e-11,
            0.0032508699122794442
          ],
          [
            -0.002189421321768708,
            1.1645873474026917e-11,
            0.0016292077266569906
          ],
          [
            2.2798603283025187e-15,
            -5.406007226426927e-16,
            1.8769708010069053e-15
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            -0.019190800972156585,
            8.32304225539815e-11,
            0.012608662774736046
          ],
          [
            -0.01647920574609274,
            7.566602899800046e-11,
            0.01109556682527002
          ],
          [
            -0.013881163202954072,
            6.682232545074385e-11,
            0.009565599456088925
          ],
          [
            -0.011386407056355519,
            5.687905701989848e-11,
            0.008016904028603
          ],
          [
            -0.008983955199735216,
            4.6110337770244314e-11,
            0.006447981768401667
          ],
          [
            -0.006661137843346987,
            3.482503174723206e-11,
            0.004858641332536329
          ],
          [
            -0.004402545700707083,
            2.327371628751962e-11,
            0.0032508699122794082
          ],
          [
            -0.002189421321768692,
            1.1645906461410505e-11,
            0.0016292077266569782
          ],
          [
            2.3314683517128287e-15,
            -5.551115123125783e-16,
            1.887379141862766e-15
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -119.02434831518455,
          -119.02472485947271,
          -119.02585221238739,
          -119.02772552468114,
          -119.03033931677172,
          -119.03368227120774,
          -119.03773542905607,
          -119.04247116257248,
          -119.04785247337433
        ],
        "cartesian_polarizations_e_A2": [
          [
            3.237865493803713e-18,
            -6.514277005390804e-18,
            2.0095323937734157e-17
          ],
          [
            2.4886568841035194e-05,
            -1.4032969438906487e-13,
            -1.744205266932386e-05
          ],
          [
            4.9882750165385486e-05,
            -2.804765264697654e-13,
            -3.480332391216728e-05
          ],
          [
            7.50928941371244e-05,
            -4.1961201383321084e-13,
            -5.2015882712148e-05
          ],
          [
            0.00010061282352621539,
            -5.556449450739448e-13,
            -6.903112216770425e-05
          ],
          [
            0.00012653231544304191,
            -6.853829775451658e-13,
            -8.582776770821997e-05
          ],
          [
            0.00015293676913868224,
            -8.051797093592567e-13,
            -0.00010240786782253177
          ],
          [
            0.00017990866686043926,
            -9.117495679010703e-13,
            -0.00011878746816385373
          ],
          [
            0.00020752800554122282,
            -1.0029662391916227e-12,
            -0.0001349864456254032
          ]
        ],
        "raw_reduced_polarization": [
          [
            2.2799846617880136e-15,
            -5.406007226432196e-16,
            1.87704151854601e-15
          ],
          [
            0.002189421321773116,
            -1.1645549326848053e-11,
            -0.0016292077266547751
          ],
          [
            0.004402545700718881,
            -2.3275923447611968e-11,
            -0.0032508699122721935
          ],
          [
            0.006661137843352399,
            -3.482236903961712e-11,
            -0.0048586413325333215
          ],
          [
            0.008983955199737218,
            -4.6111342608158885e-11,
            -0.00644798176840004
          ],
          [
            0.011386407056360097,
            -5.68779210097545e-11,
            -0.00801690402860042
          ],
          [
            0.013881163202962432,
            -6.681950005765196e-11,
            -0.009565599456086116
          ],
          [
            0.016479205746096036,
            -7.566341972702038e-11,
            -0.011095566825266946
          ],
          [
            0.01919080097216666,
            -8.323322346363986e-11,
            -0.0126086627747293
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            2.2799846617880136e-15,
            -5.406007226432196e-16,
            1.87704151854601e-15
          ],
          [
            0.002189421321773116,
            -1.1645549326848053e-11,
            -0.0016292077266547751
          ],
          [
            0.004402545700718881,
            -2.3275923447611968e-11,
            -0.0032508699122721935
          ],
          [
            0.006661137843352399,
            -3.482236903961712e-11,
            -0.0048586413325333215
          ],
          [
            0.008983955199737218,
            -4.6111342608158885e-11,
            -0.00644798176840004
          ],
          [
            0.011386407056360097,
            -5.68779210097545e-11,
            -0.00801690402860042
          ],
          [
            0.013881163202962432,
            -6.681950005765196e-11,
            -0.009565599456086116
          ],
          [
            0.016479205746096036,
            -7.566341972702038e-11,
            -0.011095566825266946
          ],
          [
            0.01919080097216666,
            -8.323322346363986e-11,
            -0.0126086627747293
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          0.019190800972161127,
          -8.323153981760228e-11,
          -0.012608662774732248
        ],
        "actual_opposite_endpoint_branch_residual": 6.492613374234759e-15
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            -0.019190800972156564,
            8.323045861615699e-11,
            0.012608662774736002
          ],
          [
            -0.016479205746092736,
            7.566607474832095e-11,
            0.011095566825270043
          ],
          [
            -0.013881163202954058,
            6.682229795961688e-11,
            0.009565599456088883
          ],
          [
            -0.011386407056355494,
            5.687909497700426e-11,
            0.008016904028602997
          ],
          [
            -0.008983955199735242,
            4.611031152157349e-11,
            0.006447981768401672
          ],
          [
            -0.006661137843346982,
            3.482498780761478e-11,
            0.004858641332536371
          ],
          [
            -0.0044025457007071025,
            2.3273721592597648e-11,
            0.0032508699122794442
          ],
          [
            -0.002189421321768708,
            1.1645873474026917e-11,
            0.0016292077266569906
          ],
          [
            2.2799846617880136e-15,
            -5.406007226432196e-16,
            1.87704151854601e-15
          ],
          [
            0.002189421321773116,
            -1.1645549326848053e-11,
            -0.0016292077266547751
          ],
          [
            0.004402545700718881,
            -2.3275923447611968e-11,
            -0.0032508699122721935
          ],
          [
            0.006661137843352399,
            -3.482236903961712e-11,
            -0.0048586413325333215
          ],
          [
            0.008983955199737218,
            -4.6111342608158885e-11,
            -0.00644798176840004
          ],
          [
            0.011386407056360097,
            -5.68779210097545e-11,
            -0.00801690402860042
          ],
          [
            0.013881163202962432,
            -6.681950005765196e-11,
            -0.009565599456086116
          ],
          [
            0.016479205746096036,
            -7.566341972702038e-11,
            -0.011095566825266946
          ],
          [
            0.01919080097216666,
            -8.323322346363986e-11,
            -0.0126086627747293
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -0.019190800972156564,
            8.323045861615699e-11,
            0.012608662774736002
          ],
          [
            -0.016479205746092736,
            7.566607474832095e-11,
            0.011095566825270043
          ],
          [
            -0.013881163202954058,
            6.682229795961688e-11,
            0.009565599456088883
          ],
          [
            -0.011386407056355494,
            5.687909497700426e-11,
            0.008016904028602997
          ],
          [
            -0.008983955199735242,
            4.611031152157349e-11,
            0.006447981768401672
          ],
          [
            -0.006661137843346982,
            3.482498780761478e-11,
            0.004858641332536371
          ],
          [
            -0.0044025457007071025,
            2.3273721592597648e-11,
            0.0032508699122794442
          ],
          [
            -0.002189421321768708,
            1.1645873474026917e-11,
            0.0016292077266569906
          ],
          [
            2.2798603283025187e-15,
            -5.406007226426927e-16,
            1.8769708010069053e-15
          ],
          [
            0.002189421321773116,
            -1.1645549326848053e-11,
            -0.0016292077266547751
          ],
          [
            0.004402545700718881,
            -2.3275923447611968e-11,
            -0.0032508699122721935
          ],
          [
            0.006661137843352399,
            -3.482236903961712e-11,
            -0.0048586413325333215
          ],
          [
            0.008983955199737218,
            -4.6111342608158885e-11,
            -0.00644798176840004
          ],
          [
            0.011386407056360097,
            -5.68779210097545e-11,
            -0.00801690402860042
          ],
          [
            0.013881163202962432,
            -6.681950005765196e-11,
            -0.009565599456086116
          ],
          [
            0.016479205746096036,
            -7.566341972702038e-11,
            -0.011095566825266946
          ],
          [
            0.01919080097216666,
            -8.323322346363986e-11,
            -0.0126086627747293
          ]
        ],
        "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": [
          [
            -0.019190800972156585,
            8.32304225539815e-11,
            0.012608662774736046
          ],
          [
            -0.01647920574609274,
            7.566602899800046e-11,
            0.01109556682527002
          ],
          [
            -0.013881163202954072,
            6.682232545074385e-11,
            0.009565599456088925
          ],
          [
            -0.011386407056355519,
            5.687905701989848e-11,
            0.008016904028603
          ],
          [
            -0.008983955199735216,
            4.6110337770244314e-11,
            0.006447981768401667
          ],
          [
            -0.006661137843346987,
            3.482503174723206e-11,
            0.004858641332536329
          ],
          [
            -0.004402545700707083,
            2.327371628751962e-11,
            0.0032508699122794082
          ],
          [
            -0.002189421321768692,
            1.1645906461410505e-11,
            0.0016292077266569782
          ],
          [
            2.3314683517128287e-15,
            -5.551115123125783e-16,
            1.887379141862766e-15
          ],
          [
            0.002189421321773133,
            -1.1645573394503117e-11,
            -0.0016292077266547578
          ],
          [
            0.004402545700718852,
            -2.327593673356887e-11,
            -0.003250869912272192
          ],
          [
            0.006661137843352427,
            -3.482236721197296e-11,
            -0.004858641332533331
          ],
          [
            0.00898395519973727,
            -4.6111336970966477e-11,
            -0.006447981768400057
          ],
          [
            0.01138640705636007,
            -5.687794679687386e-11,
            -0.008016904028600447
          ],
          [
            0.013881163202962399,
            -6.681949438203105e-11,
            -0.009565599456086094
          ],
          [
            0.01647920574609607,
            -7.566341997389259e-11,
            -0.011095566825266967
          ],
          [
            0.019190800972166633,
            -8.323319811154306e-11,
            -0.012608662774729273
          ]
        ]
      },
      "incoming_structure_ids": [
        "incoming_00_000",
        "incoming_00_001",
        "incoming_00_002",
        "incoming_00_003",
        "incoming_00_004",
        "incoming_00_005",
        "incoming_00_006",
        "incoming_00_007",
        "incoming_00_008"
      ],
      "reflected_structure_ids": [
        "reflected_00_001",
        "reflected_00_002",
        "reflected_00_003",
        "reflected_00_004",
        "reflected_00_005",
        "reflected_00_006",
        "reflected_00_007",
        "reflected_00_008"
      ],
      "positive_extension_structure_ids": [
        "extension_plus_00_000",
        "extension_plus_00_001",
        "extension_plus_00_002",
        "extension_plus_00_003"
      ],
      "negative_extension_structure_ids": [
        "extension_minus_00_000",
        "extension_minus_00_001",
        "extension_minus_00_002",
        "extension_minus_00_003"
      ],
      "extension": {
        "enabled": true,
        "fraction_beyond_polar_endpoint": 0.35,
        "images_per_side": 4,
        "construction": "continue fractional atomic displacements and symmetric log strain beyond +P; reflect these structures about N for the -P side",
        "positive_path_coordinates": [
          1.35,
          1.2625,
          1.175,
          1.0875
        ],
        "negative_path_coordinates": [
          -1.0875,
          -1.175,
          -1.2625,
          -1.35
        ]
      },
      "branch_coordinates": [
        1.35,
        1.2625,
        1.175,
        1.0875,
        1.0,
        0.875,
        0.75,
        0.625,
        0.5,
        0.375,
        0.25,
        0.125,
        0.0,
        -0.125,
        -0.25,
        -0.375,
        -0.5,
        -0.625,
        -0.75,
        -0.875,
        -1.0,
        -1.0875,
        -1.175,
        -1.2625,
        -1.35
      ],
      "parent": {
        "candidate_id": "inversion_parent_endpoint_00",
        "source": "same_species_inversion_center_projection_from_endpoint",
        "spacegroup": "P2/c",
        "spacegroup_number": 13,
        "pointgroup": "2/m",
        "has_inversion": true,
        "is_polar_point_group": false,
        "nonpolar_parent_hypothesis": true,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.0
        ],
        "formal_class": [
          0.0,
          0.0,
          0.0
        ],
        "target_residual": 5.4491426668909354e-15,
        "parent_symmetrization_rmsd_A": 0.09089577081975148,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -119.02434831518454,
        "reduced_polarization": [
          5.262401851747757e-15,
          -1.346703575341985e-15,
          4.320555925041967e-16
        ],
        "cartesian_polarization_e_A2": [
          3.222447086690362e-17,
          -1.6227873486801944e-17,
          4.625522134005305e-18
        ],
        "ranking_score": 0.09089577081976237
      }
    }
  ],
  "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": 99,
      "full_response": 31,
      "energy_polarization": 68
    },
    "model_evaluations_for_recovery_and_path_properties": {
      "total": 124,
      "full_response": 56,
      "energy_polarization": 68
    },
    "elapsed_seconds": 444.34477944200626
  }
}
