{
  "schema": "ferrofinder.endpoint_parent_recovery.v4_variable_cell",
  "status": "complete",
  "input_atom_count": 12,
  "input_formula": "F8Li2V2",
  "input_spacegroup": "P2_1",
  "input_pointgroup": "2",
  "input_is_polar_point_group": true,
  "input_energy_eV": -65.7986521665511,
  "input_cartesian_polarization_e_A2": [
    2.2414677951270715e-17,
    0.01155006724749304,
    1.556947690028385e-17
  ],
  "input_reduced_polarization": [
    7.009601911953609e-16,
    0.33903949892054513,
    6.95995632260154e-16
  ],
  "input_formal_targets": [
    {
      "orbit_id": 0,
      "representative_formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.0
      ]
    },
    {
      "orbit_id": 1,
      "representative_formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ]
    },
    {
      "orbit_id": 2,
      "representative_formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.5
      ]
    },
    {
      "orbit_id": 3,
      "representative_formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        0.5,
        0.5,
        0.0
      ]
    },
    {
      "orbit_id": 4,
      "representative_formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.5
      ]
    },
    {
      "orbit_id": 5,
      "representative_formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.0
      ]
    },
    {
      "orbit_id": 6,
      "representative_formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "target_reduced_polarization": [
        0.5,
        0.5,
        0.5
      ]
    },
    {
      "orbit_id": 7,
      "representative_formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.5
      ]
    }
  ],
  "parent_candidates": [
    {
      "candidate_id": "inversion_parent_endpoint_00",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "P2_1/m",
      "spacegroup_number": 11,
      "pointgroup": "2/m",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 4.892335793721658e-15,
      "parent_symmetrization_rmsd_A": 0.6096763985458233,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -19.773466279128943,
      "reduced_polarization": [
        3.637726510330781e-15,
        -7.401672577356089e-17,
        3.2705377048541303e-15
      ],
      "cartesian_polarization_e_A2": [
        1.1630736345507214e-16,
        -2.5215296826645774e-18,
        6.77587669760866e-17
      ],
      "ranking_score": 0.6096763985458331
    },
    {
      "candidate_id": "inversion_parent_endpoint_01",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "P2_1/m",
      "spacegroup_number": 11,
      "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": 7.680083322128352e-15,
      "parent_symmetrization_rmsd_A": 0.6413584098852111,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -62.68060060365222,
      "reduced_polarization": [
        6.4258880855232044e-15,
        3.6807994750380573e-16,
        4.190007076296005e-15
      ],
      "cartesian_polarization_e_A2": [
        2.053748006216962e-16,
        1.2539388949247412e-17,
        5.90657867870759e-17
      ],
      "ranking_score": 0.6413584098852264
    },
    {
      "candidate_id": "inversion_parent_endpoint_02",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "P2_1/c",
      "spacegroup_number": 14,
      "pointgroup": "2/m",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 1.955249413508466e-15,
      "parent_symmetrization_rmsd_A": 0.863013033747256,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -65.23852901286247,
      "reduced_polarization": [
        -1.2307769432511721e-15,
        -5.253159091359336e-17,
        -1.5183638618402999e-15
      ],
      "cartesian_polarization_e_A2": [
        -3.9371091012212037e-17,
        -1.789595046009638e-18,
        -3.865525299380818e-17
      ],
      "ranking_score": 0.8630130337472599
    },
    {
      "candidate_id": "bec_projection_00",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P2_1",
      "spacegroup_number": 4,
      "pointgroup": "2",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.0
      ],
      "formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_residual": 0.00013817749743938457,
      "parent_symmetrization_rmsd_A": 0.040615766283219154,
      "parent_cell_rmsd_A": 0.024191256457124995,
      "energy_eV": -65.6547692225937,
      "reduced_polarization": [
        1.0298485397184484e-14,
        0.4998618225025606,
        4.759276524381709e-15
      ],
      "cartesian_polarization_e_A2": [
        -8.544949685401602e-16,
        0.01698266328701576,
        -6.145646439009307e-17
      ],
      "ranking_score": 0.5469399353923792
    },
    {
      "candidate_id": "inversion_parent_bec_00_00",
      "source": "same_species_inversion_center_projection_after_BEC",
      "spacegroup": "P2_1/m",
      "spacegroup_number": 11,
      "pointgroup": "2/m",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.0
      ],
      "formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_residual": 0.49999999999999944,
      "parent_symmetrization_rmsd_A": 0.6414066744358291,
      "parent_cell_rmsd_A": 0.024191256457124995,
      "energy_eV": -62.60566144063375,
      "reduced_polarization": [
        1.1272783983189564e-16,
        -5.557467371102206e-16,
        -4.4089422045863326e-17
      ],
      "cartesian_polarization_e_A2": [
        3.594754351642323e-18,
        -1.8881337370293586e-17,
        -3.4300268658901465e-18
      ],
      "ranking_score": 1.6474544885501092
    },
    {
      "candidate_id": "inversion_parent_bec_00_01",
      "source": "same_species_inversion_center_projection_after_BEC",
      "spacegroup": "P2_1/c",
      "spacegroup_number": 14,
      "pointgroup": "2/m",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.0
      ],
      "formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_residual": 0.49999999999999944,
      "parent_symmetrization_rmsd_A": 0.8630227283844802,
      "parent_cell_rmsd_A": 0.024191256457124995,
      "energy_eV": -65.24619087012152,
      "reduced_polarization": [
        2.7773523567916767e-15,
        -5.389856016245206e-16,
        1.9977580989368513e-15
      ],
      "cartesian_polarization_e_A2": [
        8.914760386818732e-17,
        -1.831188255809459e-17,
        3.287206234818931e-17
      ],
      "ranking_score": 1.8690705424987604
    },
    {
      "candidate_id": "bec_projection_01",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P2_1",
      "spacegroup_number": 4,
      "pointgroup": "2",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 0.0004284635673291673,
      "parent_symmetrization_rmsd_A": 0.0697654404703234,
      "parent_cell_rmsd_A": 0.03967108869439243,
      "energy_eV": -65.4860252854925,
      "reduced_polarization": [
        -6.07266856022084e-15,
        -0.0004284635673291673,
        -1.6903864146181027e-15
      ],
      "cartesian_polarization_e_A2": [
        -1.9489738061447342e-16,
        -1.4661499426764471e-05,
        3.212396973295648e-17
      ],
      "ranking_score": 0.5805401397785799
    },
    {
      "candidate_id": "bec_projection_02",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.5
      ],
      "formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_residual": 4.571507026304206e-06,
      "parent_symmetrization_rmsd_A": 0.18184754366592895,
      "parent_cell_rmsd_A": 0.16341900872722115,
      "energy_eV": -57.99777346171371,
      "reduced_polarization": [
        1.7660033010552635e-06,
        0.4999995570779093,
        0.5000041932957031
      ],
      "cartesian_polarization_e_A2": [
        0.0003522619703851559,
        0.016488575026355853,
        0.01855013071012375
      ],
      "ranking_score": 0.7227114388617868
    },
    {
      "candidate_id": "bec_projection_03",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.5,
        0.5,
        0.0
      ],
      "formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_residual": 0.00018336225617248967,
      "parent_symmetrization_rmsd_A": 0.15309985367420198,
      "parent_cell_rmsd_A": 0.0847432933673374,
      "energy_eV": -62.452848790302795,
      "reduced_polarization": [
        0.4998566964164446,
        0.49989043021842317,
        -3.286735301249768e-05
      ],
      "cartesian_polarization_e_A2": [
        0.016070640887468714,
        0.016922076558155173,
        -0.007473960992928155
      ],
      "ranking_score": 0.6746524015283814
    },
    {
      "candidate_id": "bec_projection_04",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.5
      ],
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_residual": 3.3673826978896543e-06,
      "parent_symmetrization_rmsd_A": 0.16875693823372231,
      "parent_cell_rmsd_A": 0.13983858907387026,
      "energy_eV": -60.719416546541964,
      "reduced_polarization": [
        2.375400256662921e-06,
        -1.6030543521160627e-06,
        0.4999982316797239
      ],
      "cartesian_polarization_e_A2": [
        -9.02675685413395e-05,
        -0.0003886032554250151,
        0.01921368771144537
      ],
      "ranking_score": 0.7037233202675857
    },
    {
      "candidate_id": "bec_projection_05",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.0
      ],
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_residual": 0.00018704075754281006,
      "parent_symmetrization_rmsd_A": 0.1404849277106718,
      "parent_cell_rmsd_A": 0.07274168429118678,
      "energy_eV": -63.450085521857595,
      "reduced_polarization": [
        0.4999372648219075,
        9.64508380411273e-05,
        0.0001474644982802713
      ],
      "cartesian_polarization_e_A2": [
        0.0159410029788442,
        -4.241973846458587e-05,
        -0.0079631365215069
      ],
      "ranking_score": 0.6590444302985541
    },
    {
      "candidate_id": "bec_projection_06",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.5,
        0.5,
        0.5
      ],
      "formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "target_residual": 0.0005262700639780417,
      "parent_symmetrization_rmsd_A": 0.2184970789502984,
      "parent_cell_rmsd_A": 0.10881062134768725,
      "energy_eV": -54.21384841585188,
      "reduced_polarization": [
        0.5002998977436234,
        0.4996788305586349,
        0.5002896061351945
      ],
      "cartesian_polarization_e_A2": [
        0.016551190865716884,
        0.017108847240696928,
        0.01125013116345768
      ],
      "ranking_score": 0.7467522744151763
    },
    {
      "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,
        0.0,
        0.5
      ],
      "formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_residual": 0.00044642171857566253,
      "parent_symmetrization_rmsd_A": 0.17596293416927478,
      "parent_cell_rmsd_A": 0.07347343283194702,
      "energy_eV": -59.89345309786425,
      "reduced_polarization": [
        0.5003801417119913,
        -1.7684265229784037e-05,
        0.500233392151504
      ],
      "cartesian_polarization_e_A2": [
        0.01588591968469858,
        0.00013986008853367264,
        0.011219323332678426
      ],
      "ranking_score": 0.6952241358144129
    }
  ],
  "formal_branches": [
    {
      "orbit_id": 0,
      "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": [
              7.009601911953609e-16,
              0.33903949892054513,
              6.95995632260154e-16
            ],
            "branch_aligned_reduced_polarization": [
              7.009601911953609e-16,
              0.33903949892054513,
              6.95995632260154e-16
            ],
            "target_residual": 0.16096050107945487,
            "energy_eV": -65.7986521665511,
            "max_atomic_step_A": 0.07867596885294319,
            "max_log_strain_component": 0.004126017506868218,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.7060488239940996,
            "cell_principal_stretches": [
              1.0056429960355493,
              0.9990989293368991,
              0.9968326574360057
            ],
            "cell_volume_ratio": 1.0015544948733153,
            "cell_rmsd_from_input_A": 0.02188671319660407
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              9.269832591656433e-14,
              0.4876183197723233,
              3.028115529135775e-14
            ],
            "branch_aligned_reduced_polarization": [
              9.269832591656433e-14,
              0.4876183197723233,
              3.028115529135775e-14
            ],
            "target_residual": 0.012381680227676717,
            "energy_eV": -65.6782349490075,
            "max_atomic_step_A": 0.006935467503232832,
            "max_log_strain_component": 0.00043460300706463803,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.7060488239940996,
            "cell_principal_stretches": [
              1.0062392365226402,
              0.9990040647491196,
              0.9964996184421187
            ],
            "cell_volume_ratio": 1.001718374034148,
            "cell_rmsd_from_input_A": 0.024191256457124995
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              1.0298485397184484e-14,
              0.4998618225025606,
              4.759276524381709e-15
            ],
            "branch_aligned_reduced_polarization": [
              1.0298485397184484e-14,
              0.4998618225025606,
              4.759276524381709e-15
            ],
            "target_residual": 0.00013817749743938457,
            "energy_eV": -65.6547692225937
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_00",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P2_1",
        "spacegroup_number": 4,
        "pointgroup": "2",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.5,
          0.0
        ],
        "formal_class": [
          0.0,
          0.5,
          0.0
        ],
        "target_residual": 0.00013817749743938457,
        "parent_symmetrization_rmsd_A": 0.040615766283219154,
        "parent_cell_rmsd_A": 0.024191256457124995,
        "energy_eV": -65.6547692225937,
        "reduced_polarization": [
          1.0298485397184484e-14,
          0.4998618225025606,
          4.759276524381709e-15
        ],
        "cartesian_polarization_e_A2": [
          -8.544949685401602e-16,
          0.01698266328701576,
          -6.145646439009307e-17
        ],
        "ranking_score": 0.5469399353923792
      },
      "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": [
          -65.7986521665511,
          -65.79414384127617,
          -65.78618063210386,
          -65.77462184672714,
          -65.75927945620816,
          -65.73991970449242,
          -65.7162655690324,
          -65.68799993573057,
          -65.6547692225937
        ],
        "cartesian_polarizations_e_A2": [
          [
            1.3869361606574693e-18,
            0.011550067247492921,
            -4.15186050674236e-17
          ],
          [
            -1.6908044119205237e-16,
            0.012285277820654576,
            4.58038020583761e-17
          ],
          [
            -3.4027962981102363e-16,
            0.013004019444165415,
            -6.08201204551179e-18
          ],
          [
            -4.672307883261846e-16,
            0.013706500642509736,
            -9.890090945239429e-17
          ],
          [
            -9.192413519202782e-16,
            0.014392958436254138,
            -1.1550863904697524e-16
          ],
          [
            -1.8211946493209166e-16,
            0.015063626842500654,
            -3.8077493036108487e-17
          ],
          [
            -6.068750370219229e-16,
            0.01571870970596889,
            3.2528716459428647e-17
          ],
          [
            -6.467715602544876e-16,
            0.01635835939562003,
            -6.968943459020588e-18
          ],
          [
            -8.759779331997786e-16,
            0.016982663287015837,
            -1.132656930910436e-16
          ]
        ],
        "raw_reduced_polarization": [
          [
            4.5065421745336637e-17,
            0.33903949892054164,
            -1.0684432868637226e-15
          ],
          [
            -1.951183378042906e-15,
            0.36074312647237466,
            5.851810447345043e-16
          ],
          [
            -3.5686673904633376e-15,
            0.3819776838786677,
            -1.2264547777696263e-15
          ],
          [
            -3.4164422864446472e-15,
            0.4027488135385636,
            -3.3621662525814347e-15
          ],
          [
            -1.3061604525205535e-14,
            0.4230630034412823,
            -7.49455015416476e-15
          ],
          [
            1.4798964681545155e-14,
            0.4429266623898155,
            6.227605083946798e-15
          ],
          [
            6.69142430465738e-15,
            0.4623453207207253,
            5.0578533078719516e-15
          ],
          [
            1.0949664077311018e-14,
            0.4813230019830602,
            6.079507963774625e-15
          ],
          [
            9.63597605024451e-15,
            0.49986182250256284,
            3.127526365610454e-15
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            4.5065421745336637e-17,
            0.33903949892054164,
            -1.0684432868637226e-15
          ],
          [
            -1.951183378042906e-15,
            0.36074312647237466,
            5.851810447345043e-16
          ],
          [
            -3.5686673904633376e-15,
            0.3819776838786677,
            -1.2264547777696261e-15
          ],
          [
            -3.4164422864446472e-15,
            0.4027488135385636,
            -3.3621662525814344e-15
          ],
          [
            -1.3061604525205535e-14,
            0.4230630034412823,
            -7.49455015416476e-15
          ],
          [
            1.479896468154516e-14,
            0.4429266623898155,
            6.2276050839467984e-15
          ],
          [
            6.69142430465738e-15,
            0.4623453207207253,
            5.0578533078719516e-15
          ],
          [
            1.0949664077311018e-14,
            0.4813230019830602,
            6.079507963774625e-15
          ],
          [
            9.63597605024451e-15,
            0.49986182250256284,
            3.127526365610454e-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": [
          [
            0.0,
            0.33903949892054164,
            -1.0547118733938987e-15
          ],
          [
            -1.942890293094024e-15,
            0.3607431264723746,
            5.551115123125783e-16
          ],
          [
            -3.552713678800501e-15,
            0.3819776838786677,
            -1.2212453270876722e-15
          ],
          [
            -3.4416913763379853e-15,
            0.4027488135385636,
            -3.3861802251067274e-15
          ],
          [
            -1.304512053934559e-14,
            0.42306300344128234,
            -7.494005416219807e-15
          ],
          [
            1.4765966227514582e-14,
            0.4429266623898155,
            6.217248937900877e-15
          ],
          [
            6.661338147750939e-15,
            0.4623453207207253,
            5.10702591327572e-15
          ],
          [
            1.099120794378905e-14,
            0.4813230019830602,
            6.106226635438361e-15
          ],
          [
            9.658940314238862e-15,
            0.49986182250256284,
            3.1086244689504383e-15
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -65.6547692225937,
          -65.62213732773951,
          -65.58385251672287,
          -65.539511636514,
          -65.48869238503968,
          -65.43095680670888,
          -65.36585410873207,
          -65.29292299995704,
          -65.2116937167504
        ],
        "cartesian_polarizations_e_A2": [
          [
            -8.395328205963513e-16,
            0.016982663287015757,
            -8.360937597256847e-17
          ],
          [
            -6.055386447886158e-16,
            0.017540599209071462,
            3.502340815302654e-17
          ],
          [
            -2.867710195557872e-16,
            0.01808440096928587,
            2.854305504709206e-16
          ],
          [
            -3.0126805229625273e-16,
            0.018614009596723356,
            3.7326669229762686e-16
          ],
          [
            2.4643929066020686e-16,
            0.019129304586814336,
            6.6372765966311465e-16
          ],
          [
            -2.6768523729271456e-16,
            0.01963012448689225,
            7.092965766513486e-16
          ],
          [
            7.076152690892137e-16,
            0.020116291888989595,
            8.645401239987788e-16
          ],
          [
            7.077447832701717e-16,
            0.020587640351080367,
            1.1128892531371067e-15
          ],
          [
            8.479548726755167e-16,
            0.021044040935818915,
            1.1603734278326492e-15
          ]
        ],
        "raw_reduced_polarization": [
          [
            1.076890036953066e-14,
            0.49986182250256056,
            4.3693208863732826e-15
          ],
          [
            1.448188569368907e-14,
            0.5161088385276894,
            8.755162684916912e-15
          ],
          [
            2.0518019944521464e-14,
            0.5319290401432661,
            1.7573853779224438e-14
          ],
          [
            1.585849026346612e-14,
            0.5473211219695887,
            1.7729666353147333e-14
          ],
          [
            2.8449704791520816e-14,
            0.5622819719853928,
            3.024927688320574e-14
          ],
          [
            7.589277364630211e-15,
            0.5768072794736706,
            2.2613550514364276e-14
          ],
          [
            3.301663768725205e-14,
            0.590892271191665,
            3.682841202959658e-14
          ],
          [
            2.768422146766719e-14,
            0.6045325026717089,
            4.0842004829842537e-14
          ],
          [
            2.6494796250518678e-14,
            0.6177246366848727,
            4.1279339357043943e-14
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            1.076890036953066e-14,
            0.49986182250256056,
            4.3693208863732826e-15
          ],
          [
            1.448188569368907e-14,
            0.5161088385276894,
            8.755162684916912e-15
          ],
          [
            2.0518019944521464e-14,
            0.5319290401432661,
            1.7573853779224438e-14
          ],
          [
            1.585849026346612e-14,
            0.5473211219695887,
            1.7729666353147333e-14
          ],
          [
            2.8449704791520816e-14,
            0.5622819719853928,
            3.024927688320574e-14
          ],
          [
            7.58927736463021e-15,
            0.5768072794736706,
            2.2613550514364276e-14
          ],
          [
            3.301663768725205e-14,
            0.590892271191665,
            3.682841202959658e-14
          ],
          [
            2.768422146766719e-14,
            0.6045325026717089,
            4.0842004829842537e-14
          ],
          [
            2.6494796250518678e-14,
            0.6177246366848727,
            4.1279339357043943e-14
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          -5.487234539449312e-14,
          0.6579752418232278,
          -2.741838036496855e-14
        ],
        "actual_opposite_endpoint_branch_residual": 0.0402506051383551
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            4.5065421745336637e-17,
            0.33903949892054164,
            -1.0684432868637226e-15
          ],
          [
            -1.951183378042906e-15,
            0.36074312647237466,
            5.851810447345043e-16
          ],
          [
            -3.5686673904633376e-15,
            0.3819776838786677,
            -1.2264547777696263e-15
          ],
          [
            -3.4164422864446472e-15,
            0.4027488135385636,
            -3.3621662525814347e-15
          ],
          [
            -1.3061604525205535e-14,
            0.4230630034412823,
            -7.49455015416476e-15
          ],
          [
            1.4798964681545155e-14,
            0.4429266623898155,
            6.227605083946798e-15
          ],
          [
            6.69142430465738e-15,
            0.4623453207207253,
            5.0578533078719516e-15
          ],
          [
            1.0949664077311018e-14,
            0.4813230019830602,
            6.079507963774625e-15
          ],
          [
            9.63597605024451e-15,
            0.49986182250256284,
            3.127526365610454e-15
          ],
          [
            1.448188569368907e-14,
            0.5161088385276894,
            8.755162684916912e-15
          ],
          [
            2.0518019944521464e-14,
            0.5319290401432661,
            1.7573853779224438e-14
          ],
          [
            1.585849026346612e-14,
            0.5473211219695887,
            1.7729666353147333e-14
          ],
          [
            2.8449704791520816e-14,
            0.5622819719853928,
            3.024927688320574e-14
          ],
          [
            7.589277364630211e-15,
            0.5768072794736706,
            2.2613550514364276e-14
          ],
          [
            3.301663768725205e-14,
            0.590892271191665,
            3.682841202959658e-14
          ],
          [
            2.768422146766719e-14,
            0.6045325026717089,
            4.0842004829842537e-14
          ],
          [
            2.6494796250518678e-14,
            0.6177246366848727,
            4.1279339357043943e-14
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            4.5065421745336637e-17,
            0.33903949892054164,
            -1.0684432868637226e-15
          ],
          [
            -1.951183378042906e-15,
            0.36074312647237466,
            5.851810447345043e-16
          ],
          [
            -3.5686673904633376e-15,
            0.3819776838786677,
            -1.2264547777696261e-15
          ],
          [
            -3.4164422864446472e-15,
            0.4027488135385636,
            -3.3621662525814344e-15
          ],
          [
            -1.3061604525205535e-14,
            0.4230630034412823,
            -7.49455015416476e-15
          ],
          [
            1.479896468154516e-14,
            0.4429266623898155,
            6.2276050839467984e-15
          ],
          [
            6.69142430465738e-15,
            0.4623453207207253,
            5.0578533078719516e-15
          ],
          [
            1.0949664077311018e-14,
            0.4813230019830602,
            6.079507963774625e-15
          ],
          [
            9.63597605024451e-15,
            0.49986182250256284,
            3.127526365610454e-15
          ],
          [
            1.448188569368907e-14,
            0.5161088385276894,
            8.755162684916912e-15
          ],
          [
            2.0518019944521464e-14,
            0.5319290401432661,
            1.7573853779224438e-14
          ],
          [
            1.585849026346612e-14,
            0.5473211219695887,
            1.7729666353147333e-14
          ],
          [
            2.8449704791520816e-14,
            0.5622819719853928,
            3.024927688320574e-14
          ],
          [
            7.58927736463021e-15,
            0.5768072794736706,
            2.2613550514364276e-14
          ],
          [
            3.301663768725205e-14,
            0.590892271191665,
            3.682841202959658e-14
          ],
          [
            2.768422146766719e-14,
            0.6045325026717089,
            4.0842004829842537e-14
          ],
          [
            2.6494796250518678e-14,
            0.6177246366848727,
            4.1279339357043943e-14
          ]
        ],
        "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": [
          [
            0.0,
            0.33903949892054164,
            -1.0547118733938987e-15
          ],
          [
            -1.942890293094024e-15,
            0.3607431264723746,
            5.551115123125783e-16
          ],
          [
            -3.552713678800501e-15,
            0.3819776838786677,
            -1.2212453270876722e-15
          ],
          [
            -3.4416913763379853e-15,
            0.4027488135385636,
            -3.3861802251067274e-15
          ],
          [
            -1.304512053934559e-14,
            0.42306300344128234,
            -7.494005416219807e-15
          ],
          [
            1.4765966227514582e-14,
            0.4429266623898155,
            6.217248937900877e-15
          ],
          [
            6.661338147750939e-15,
            0.4623453207207253,
            5.10702591327572e-15
          ],
          [
            1.099120794378905e-14,
            0.4813230019830602,
            6.106226635438361e-15
          ],
          [
            9.658940314238862e-15,
            0.49986182250256284,
            3.1086244689504383e-15
          ],
          [
            1.4432899320127035e-14,
            -0.4838911614723105,
            8.770761894538737e-15
          ],
          [
            2.0539125955565396e-14,
            -0.46807095985673386,
            1.7541523789077473e-14
          ],
          [
            1.587618925213974e-14,
            -0.4526788780304112,
            1.7763568394002505e-14
          ],
          [
            2.842170943040401e-14,
            -0.43771802801460735,
            3.019806626980426e-14
          ],
          [
            7.549516567451064e-15,
            -0.4231927205263295,
            2.2648549702353193e-14
          ],
          [
            3.297362383136715e-14,
            -0.4091077288083351,
            3.68594044175552e-14
          ],
          [
            2.7644553313166398e-14,
            -0.395467497328291,
            4.085620730620576e-14
          ],
          [
            2.653433028854124e-14,
            -0.38227536331512724,
            4.1300296516055823e-14
          ]
        ]
      },
      "incoming_structure_ids": [
        "incoming_00_000",
        "incoming_00_001",
        "incoming_00_002",
        "incoming_00_003",
        "incoming_00_004",
        "incoming_00_005",
        "incoming_00_006",
        "incoming_00_007",
        "incoming_00_008"
      ],
      "reflected_structure_ids": [
        "reflected_00_001",
        "reflected_00_002",
        "reflected_00_003",
        "reflected_00_004",
        "reflected_00_005",
        "reflected_00_006",
        "reflected_00_007",
        "reflected_00_008"
      ]
    },
    {
      "orbit_id": 1,
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "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": [
              7.009601911953609e-16,
              0.33903949892054513,
              6.95995632260154e-16
            ],
            "branch_aligned_reduced_polarization": [
              7.009601911953609e-16,
              0.33903949892054513,
              6.95995632260154e-16
            ],
            "target_residual": 0.33903949892054513,
            "energy_eV": -65.7986521665511,
            "max_atomic_step_A": 0.12000000000000001,
            "max_log_strain_component": 0.006293180853605261,
            "step_scale": 0.7241160341149472,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.7060488239940996,
            "cell_principal_stretches": [
              1.004850360208839,
              1.0013759173295111,
              0.9914539778395949
            ],
            "cell_volume_ratio": 0.9976336621332439,
            "cell_rmsd_from_input_A": 0.03341450713210553
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -2.697257754100491e-14,
              0.06643431887220524,
              -1.0042999509287239e-14
            ],
            "branch_aligned_reduced_polarization": [
              -2.697257754100491e-14,
              0.06643431887220524,
              -1.0042999509287239e-14
            ],
            "target_residual": 0.06643431887220524,
            "energy_eV": -65.60788278200626,
            "max_atomic_step_A": 0.027246859358442285,
            "max_log_strain_component": 0.0011774216138794127,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.7060488239940996,
            "cell_principal_stretches": [
              1.0057604466641086,
              1.0016335545061283,
              0.9898631905699998
            ],
            "cell_volume_ratio": 0.997191554775641,
            "cell_rmsd_from_input_A": 0.03967108869439243
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -6.07266856022084e-15,
              -0.0004284635673291673,
              -1.6903864146181027e-15
            ],
            "branch_aligned_reduced_polarization": [
              -6.07266856022084e-15,
              -0.0004284635673291673,
              -1.6903864146181027e-15
            ],
            "target_residual": 0.0004284635673291673,
            "energy_eV": -65.4860252854925
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_01",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P2_1",
        "spacegroup_number": 4,
        "pointgroup": "2",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.0
        ],
        "formal_class": [
          0.0,
          0.0,
          0.0
        ],
        "target_residual": 0.0004284635673291673,
        "parent_symmetrization_rmsd_A": 0.0697654404703234,
        "parent_cell_rmsd_A": 0.03967108869439243,
        "energy_eV": -65.4860252854925,
        "reduced_polarization": [
          -6.07266856022084e-15,
          -0.0004284635673291673,
          -1.6903864146181027e-15
        ],
        "cartesian_polarization_e_A2": [
          -1.9489738061447342e-16,
          -1.4661499426764471e-05,
          3.212396973295648e-17
        ],
        "ranking_score": 0.5805401397785799
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 2,
      "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": [
              7.009601911953609e-16,
              0.33903949892054513,
              6.95995632260154e-16
            ],
            "branch_aligned_reduced_polarization": [
              7.009601911953609e-16,
              0.33903949892054513,
              7.216449660063518e-16
            ],
            "target_residual": 0.5252697239587948,
            "energy_eV": -65.7986521665511,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.006341445502839518,
            "step_scale": 0.3887911411917838,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.7060488239940996,
            "cell_principal_stretches": [
              1.0062666306383588,
              1.0021887107195029,
              0.9922010792673284
            ],
            "cell_volume_ratio": 1.0006040869610635,
            "cell_rmsd_from_input_A": 0.04383864012035461
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.002841076377616823,
              0.38161397262940566,
              0.19096234926559907
            ],
            "branch_aligned_reduced_polarization": [
              0.002841076377616823,
              0.38161397262940566,
              0.19096234926559907
            ],
            "target_residual": 0.3309495320483353,
            "energy_eV": -65.41106579436521,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.006844941570331694,
            "step_scale": 0.5515311848071702,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.7060488239940996,
            "cell_principal_stretches": [
              1.0122996750394542,
              1.0064797425929966,
              0.9832414556805694
            ],
            "cell_volume_ratio": 1.0017845207038976,
            "cell_rmsd_from_input_A": 0.09180971822608282
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.007917940746324707,
              0.4307094203210461,
              0.35417294013328054
            ],
            "branch_aligned_reduced_polarization": [
              0.007917940746324707,
              0.4307094203210461,
              0.35417294013328054
            ],
            "target_residual": 0.16164593903738983,
            "energy_eV": -63.70464621733632,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.008261283873570162,
            "step_scale": 0.9688395889461006,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.7060488239940996,
            "cell_principal_stretches": [
              1.0189157030737466,
              1.0130332869971421,
              0.9722878826459272
            ],
            "cell_volume_ratio": 1.0035912003683056,
            "cell_rmsd_from_input_A": 0.14912521809183898
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -0.0019927865811375355,
              0.4884003843154327,
              0.47552014436590573
            ],
            "branch_aligned_reduced_polarization": [
              -0.0019927865811375355,
              0.4884003843154327,
              0.47552014436590573
            ],
            "target_residual": 0.027162209303621062,
            "energy_eV": -59.45313113602084,
            "max_atomic_step_A": 0.02119076695688502,
            "max_log_strain_component": 0.0019658942420309844,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.7060488239940996,
            "cell_principal_stretches": [
              1.0205184723071319,
              1.0146711481632975,
              0.9696287782596831
            ],
            "cell_volume_ratio": 1.004041533876019,
            "cell_rmsd_from_input_A": 0.16306955310480684
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              -0.001137256373039942,
              0.4989454502553128,
              0.4978815410256946
            ],
            "branch_aligned_reduced_polarization": [
              -0.001137256373039942,
              0.4989454502553128,
              0.4978815410256946
            ],
            "target_residual": 0.0026255086455494563,
            "energy_eV": -58.12811272279701,
            "max_atomic_step_A": 0.0018352477407732252,
            "max_log_strain_component": 8.794605358762112e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": true,
            "strain_jacobian_frobenius_norm": 1.6238088943850602,
            "cell_principal_stretches": [
              1.0205310078388703,
              1.0146282001435736,
              0.9695440616780057
            ],
            "cell_volume_ratio": 1.0039236477990203,
            "cell_rmsd_from_input_A": 0.16341900872722115
          },
          {
            "iteration": 5,
            "reduced_polarization": [
              1.7660033010552635e-06,
              0.4999995570779093,
              0.5000041932957031
            ],
            "branch_aligned_reduced_polarization": [
              1.7660033010552635e-06,
              0.4999995570779093,
              0.5000041932957031
            ],
            "target_residual": 4.571507026304206e-06,
            "energy_eV": -57.99777346171371
          }
        ],
        "iterations": 5
      },
      "parent": {
        "candidate_id": "bec_projection_02",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.5,
          0.5
        ],
        "formal_class": [
          0.0,
          0.5,
          0.5
        ],
        "target_residual": 4.571507026304206e-06,
        "parent_symmetrization_rmsd_A": 0.18184754366592895,
        "parent_cell_rmsd_A": 0.16341900872722115,
        "energy_eV": -57.99777346171371,
        "reduced_polarization": [
          1.7660033010552635e-06,
          0.4999995570779093,
          0.5000041932957031
        ],
        "cartesian_polarization_e_A2": [
          0.0003522619703851559,
          0.016488575026355853,
          0.01855013071012375
        ],
        "ranking_score": 0.7227114388617868
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 3,
      "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": [
              7.009601911953609e-16,
              0.33903949892054513,
              6.95995632260154e-16
            ],
            "branch_aligned_reduced_polarization": [
              7.216449660063518e-16,
              0.33903949892054513,
              6.95995632260154e-16
            ],
            "target_residual": 0.5252697239587948,
            "energy_eV": -65.7986521665511,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.004851049876821591,
            "step_scale": 0.44867541886011314,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.7060488239940996,
            "cell_principal_stretches": [
              1.0055683171211214,
              1.0005756631630776,
              0.9945832768484502
            ],
            "cell_volume_ratio": 1.0006971650042766,
            "cell_rmsd_from_input_A": 0.02765664574297359
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.21731312702426978,
              0.39216185350791744,
              -0.0026709301440043225
            ],
            "branch_aligned_reduced_polarization": [
              0.21731312702426975,
              0.39216185350791744,
              -0.0026709301440043225
            ],
            "target_residual": 0.30256911253377905,
            "energy_eV": -65.56889887211682,
            "max_atomic_step_A": 0.11999999999999998,
            "max_log_strain_component": 0.005101080981278516,
            "step_scale": 0.7064497612406101,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.7060488239940996,
            "cell_principal_stretches": [
              1.0123443043106415,
              1.0012476775690335,
              0.9884791975220234
            ],
            "cell_volume_ratio": 1.0019298131346954,
            "cell_rmsd_from_input_A": 0.0593948451958494
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.39722268294752466,
              0.4579428177875584,
              -0.0029286157023891554
            ],
            "branch_aligned_reduced_polarization": [
              0.39722268294752466,
              0.4579428177875584,
              -0.0029286157023891554
            ],
            "target_residual": 0.11108807436483824,
            "energy_eV": -64.38950374391351,
            "max_atomic_step_A": 0.0745561363607773,
            "max_log_strain_component": 0.0038921679499907117,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.7060488239940996,
            "cell_principal_stretches": [
              1.0175131496170355,
              1.0017233523523967,
              0.9838732265774014
            ],
            "cell_volume_ratio": 1.0028292004382884,
            "cell_rmsd_from_input_A": 0.08341272205694769
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.4937578417114223,
              0.4987661150637863,
              -0.00030384770425104273
            ],
            "branch_aligned_reduced_polarization": [
              0.4937578417114223,
              0.4987661150637863,
              -0.00030384770425104273
            ],
            "target_residual": 0.00637019117160962,
            "energy_eV": -62.58538144446473,
            "max_atomic_step_A": 0.004261305746916419,
            "max_log_strain_component": 0.00024148729621792307,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.7060488239940996,
            "cell_principal_stretches": [
              1.0177857757386215,
              1.0017526684055877,
              0.9836117488665573
            ],
            "cell_volume_ratio": 1.0028606537847204,
            "cell_rmsd_from_input_A": 0.0847432933673374
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              0.4998566964164446,
              0.49989043021842317,
              -3.286735301249768e-05
            ],
            "branch_aligned_reduced_polarization": [
              0.4998566964164446,
              0.49989043021842317,
              -3.286735301249768e-05
            ],
            "target_residual": 0.00018336225617248967,
            "energy_eV": -62.452848790302795
          }
        ],
        "iterations": 4
      },
      "parent": {
        "candidate_id": "bec_projection_03",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.5,
          0.5,
          0.0
        ],
        "formal_class": [
          0.5,
          0.5,
          0.0
        ],
        "target_residual": 0.00018336225617248967,
        "parent_symmetrization_rmsd_A": 0.15309985367420198,
        "parent_cell_rmsd_A": 0.0847432933673374,
        "energy_eV": -62.452848790302795,
        "reduced_polarization": [
          0.4998566964164446,
          0.49989043021842317,
          -3.286735301249768e-05
        ],
        "cartesian_polarization_e_A2": [
          0.016070640887468714,
          0.016922076558155173,
          -0.007473960992928155
        ],
        "ranking_score": 0.6746524015283814
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 4,
      "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": [
              7.009601911953609e-16,
              0.33903949892054513,
              6.95995632260154e-16
            ],
            "branch_aligned_reduced_polarization": [
              7.009601911953609e-16,
              0.33903949892054513,
              7.216449660063518e-16
            ],
            "target_residual": 0.6041090810675614,
            "energy_eV": -65.7986521665511,
            "max_atomic_step_A": 0.12000000000000001,
            "max_log_strain_component": 0.005697200724524999,
            "step_scale": 0.34929278668346025,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.7060488239940996,
            "cell_principal_stretches": [
              1.007894609765034,
              0.9958787067636246,
              0.9951352640171411
            ],
            "cell_volume_ratio": 0.9988578466343387,
            "cell_rmsd_from_input_A": 0.04214263657661948
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.0011991409279486856,
              0.2031404561699958,
              0.17369146905556165
            ],
            "branch_aligned_reduced_polarization": [
              0.0011991409279486856,
              0.2031404561699958,
              0.17369146905556165
            ],
            "target_residual": 0.3843757799849472,
            "energy_eV": -65.50335949644224,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.006171273628660542,
            "step_scale": 0.5626584493841995,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.7060488239940996,
            "cell_principal_stretches": [
              1.0157513697782836,
              0.9931512223887623,
              0.989403063062956
            ],
            "cell_volume_ratio": 0.9981045805659763,
            "cell_rmsd_from_input_A": 0.08520370778116174
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.01162713203685334,
              0.0899792746748226,
              0.3502536295104408
            ],
            "branch_aligned_reduced_polarization": [
              0.01162713203685334,
              0.0899792746748226,
              0.3502536295104408
            ],
            "target_residual": 0.17508693710613,
            "energy_eV": -64.1299721415894,
            "max_atomic_step_A": 0.11019752422010441,
            "max_log_strain_component": 0.00684900342455707,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.7060488239940996,
            "cell_principal_stretches": [
              1.024085951427913,
              0.9905164241687571,
              0.9832324126371372
            ],
            "cell_volume_ratio": 0.9973653507466317,
            "cell_rmsd_from_input_A": 0.13101662844626857
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.016818889118016427,
              0.012166739663677616,
              0.4906541537097977
            ],
            "branch_aligned_reduced_polarization": [
              0.016818889118016427,
              0.012166739663677616,
              0.4906541537097977
            ],
            "target_residual": 0.022765092314504798,
            "energy_eV": -61.17730038779679,
            "max_atomic_step_A": 0.017435082678864896,
            "max_log_strain_component": 0.0014918649213423994,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.7060488239940996,
            "cell_principal_stretches": [
              1.025756297103798,
              0.9900156526901349,
              0.9819777590468518
            ],
            "cell_volume_ratio": 0.9972129377417595,
            "cell_rmsd_from_input_A": 0.14008914432877093
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              0.001232309323392141,
              0.0005502913975868893,
              0.4988346171780113
            ],
            "branch_aligned_reduced_polarization": [
              0.001232309323392141,
              0.0005502913975868893,
              0.4988346171780113
            ],
            "target_residual": 0.0017831219847681918,
            "energy_eV": -60.768823358556276,
            "max_atomic_step_A": 0.0016139500925419724,
            "max_log_strain_component": 0.00010517984941795324,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": true,
            "strain_jacobian_frobenius_norm": 2.249170219867178,
            "cell_principal_stretches": [
              1.0257050039211169,
              0.9900149247002488,
              0.9819738517303521
            ],
            "cell_volume_ratio": 0.9971583708944454,
            "cell_rmsd_from_input_A": 0.13983858907387026
          },
          {
            "iteration": 5,
            "reduced_polarization": [
              2.375400256662921e-06,
              -1.6030543521160627e-06,
              0.4999982316797239
            ],
            "branch_aligned_reduced_polarization": [
              2.375400256662921e-06,
              -1.6030543521160627e-06,
              0.4999982316797239
            ],
            "target_residual": 3.3673826978896543e-06,
            "energy_eV": -60.719416546541964
          }
        ],
        "iterations": 5
      },
      "parent": {
        "candidate_id": "bec_projection_04",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.5
        ],
        "formal_class": [
          0.0,
          0.0,
          0.5
        ],
        "target_residual": 3.3673826978896543e-06,
        "parent_symmetrization_rmsd_A": 0.16875693823372231,
        "parent_cell_rmsd_A": 0.13983858907387026,
        "energy_eV": -60.719416546541964,
        "reduced_polarization": [
          2.375400256662921e-06,
          -1.6030543521160627e-06,
          0.4999982316797239
        ],
        "cartesian_polarization_e_A2": [
          -9.02675685413395e-05,
          -0.0003886032554250151,
          0.01921368771144537
        ],
        "ranking_score": 0.7037233202675857
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 5,
      "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": [
              7.009601911953609e-16,
              0.33903949892054513,
              6.95995632260154e-16
            ],
            "branch_aligned_reduced_polarization": [
              7.216449660063518e-16,
              0.33903949892054513,
              6.95995632260154e-16
            ],
            "target_residual": 0.6041090810675614,
            "energy_eV": -65.7986521665511,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.00425043859021236,
            "step_scale": 0.3931246561518428,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.7060488239940996,
            "cell_principal_stretches": [
              1.005485208957475,
              0.9994873138367212,
              0.9937758345431443
            ],
            "cell_volume_ratio": 0.9987146128455361,
            "cell_rmsd_from_input_A": 0.029109585875273607
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.20220709979185642,
              0.1842202891024656,
              0.004649828252756308
            ],
            "branch_aligned_reduced_polarization": [
              0.20220709979185642,
              0.1842202891024656,
              0.004649828252756308
            ],
            "target_residual": 0.35019901089830835,
            "energy_eV": -65.59251575123884,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.004581801406347835,
            "step_scale": 0.720710438968913,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.7060488239940996,
            "cell_principal_stretches": [
              1.0107193773916234,
              0.9986156351674794,
              0.9887427778415734
            ],
            "cell_volume_ratio": 0.9979580316132353,
            "cell_rmsd_from_input_A": 0.05563165357098277
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.4078401349121823,
              0.045552527850246,
              0.007908770305967178
            ],
            "branch_aligned_reduced_polarization": [
              0.4078401349121823,
              0.045552527850246,
              0.007908770305967178
            ],
            "target_residual": 0.10310684833853058,
            "energy_eV": -64.52514025059634,
            "max_atomic_step_A": 0.05938641155447112,
            "max_log_strain_component": 0.0029904043502860687,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.7060488239940996,
            "cell_principal_stretches": [
              1.013866910895767,
              0.9979213506936784,
              0.9861702641913631
            ],
            "cell_volume_ratio": 0.9977670714271241,
            "cell_rmsd_from_input_A": 0.07137118048001172
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.4972550546921663,
              0.0005867243200456552,
              0.003317158137741689
            ],
            "branch_aligned_reduced_polarization": [
              0.4972550546921663,
              0.0005867243200456552,
              0.003317158137741689
            ],
            "target_residual": 0.004345400819431643,
            "energy_eV": -63.496353222695035,
            "max_atomic_step_A": 0.003371678485314085,
            "max_log_strain_component": 0.0002656828238887862,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.7060488239940996,
            "cell_principal_stretches": [
              1.0141357393380965,
              0.9978059504288016,
              0.9860251704581029
            ],
            "cell_volume_ratio": 0.9977693960557634,
            "cell_rmsd_from_input_A": 0.07274168429118678
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              0.4999372648219075,
              9.64508380411273e-05,
              0.0001474644982802713
            ],
            "branch_aligned_reduced_polarization": [
              0.4999372648219075,
              9.64508380411273e-05,
              0.0001474644982802713
            ],
            "target_residual": 0.00018704075754281006,
            "energy_eV": -63.450085521857595
          }
        ],
        "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,
          0.0,
          0.0
        ],
        "formal_class": [
          0.5,
          0.0,
          0.0
        ],
        "target_residual": 0.00018704075754281006,
        "parent_symmetrization_rmsd_A": 0.1404849277106718,
        "parent_cell_rmsd_A": 0.07274168429118678,
        "energy_eV": -63.450085521857595,
        "reduced_polarization": [
          0.4999372648219075,
          9.64508380411273e-05,
          0.0001474644982802713
        ],
        "cartesian_polarization_e_A2": [
          0.0159410029788442,
          -4.241973846458587e-05,
          -0.0079631365215069
        ],
        "ranking_score": 0.6590444302985541
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 6,
      "formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.5,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.5,
        0.5,
        0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              7.009601911953609e-16,
              0.33903949892054513,
              6.95995632260154e-16
            ],
            "branch_aligned_reduced_polarization": [
              7.216449660063518e-16,
              0.33903949892054513,
              7.216449660063518e-16
            ],
            "target_residual": 0.7251953412065936,
            "energy_eV": -65.7986521665511,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.003993652181065747,
            "step_scale": 0.3532235666325903,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.7060488239940996,
            "cell_principal_stretches": [
              1.0046913815121201,
              1.0006091210513348,
              0.995270530329559
            ],
            "cell_volume_ratio": 1.0005488084311174,
            "cell_rmsd_from_input_A": 0.0253270591561506
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.17178386331516096,
              0.37366536004524986,
              0.17302840300709055
            ],
            "branch_aligned_reduced_polarization": [
              0.17178386331516093,
              0.37366536004524986,
              0.17302840300709055
            ],
            "target_residual": 0.4802048509468755,
            "energy_eV": -65.43075264868048,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.0042132615765854056,
            "step_scale": 0.48345268453317086,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.7060488239940996,
            "cell_principal_stretches": [
              1.0105746437197323,
              1.0013116951941405,
              0.9899439659009477
            ],
            "cell_volume_ratio": 1.0017245066104101,
            "cell_rmsd_from_input_A": 0.05400535750160527
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.3156329715367391,
              0.4168483180265228,
              0.32411443653459354
            ],
            "branch_aligned_reduced_polarization": [
              0.3156329715367391,
              0.4168483180265228,
              0.32411443653459354
            ],
            "target_residual": 0.2680319660692259,
            "energy_eV": -63.815526879002896,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.004683620385787608,
            "step_scale": 0.7300444151496049,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.7060488239940996,
            "cell_principal_stretches": [
              1.0185053003713647,
              1.0009031904239787,
              0.9843707069865285
            ],
            "cell_volume_ratio": 1.0034923093773354,
            "cell_rmsd_from_input_A": 0.08578972320427944
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.4276649156967392,
              0.4592017300795666,
              0.43634901854695796
            ],
            "branch_aligned_reduced_polarization": [
              0.4276649156967392,
              0.4592017300795666,
              0.43634901854695796
            ],
            "target_residual": 0.10463417553359844,
            "energy_eV": -60.02558840412895,
            "max_atomic_step_A": 0.07780121910023616,
            "max_log_strain_component": 0.004912474042371578,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.7060488239940996,
            "cell_principal_stretches": [
              1.0264991349182306,
              1.0000063754025683,
              0.9793904349853572
            ],
            "cell_volume_ratio": 1.0053498437287711,
            "cell_rmsd_from_input_A": 0.11610910521356253
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              0.4905298664714625,
              0.4841140163224165,
              0.48859713968040247
            ],
            "branch_aligned_reduced_polarization": [
              0.4905298664714625,
              0.4841140163224165,
              0.48859713968040247
            ],
            "target_residual": 0.021727243955942284,
            "energy_eV": -55.437809185850924,
            "max_atomic_step_A": 0.014015431212924083,
            "max_log_strain_component": 0.0023568140979859597,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": true,
            "strain_jacobian_frobenius_norm": 3.1123370580290004,
            "cell_principal_stretches": [
              1.0230662904497274,
              0.9984752919028325,
              0.9802779211183097
            ],
            "cell_volume_ratio": 1.001360182937545,
            "cell_rmsd_from_input_A": 0.10881062134768725
          },
          {
            "iteration": 5,
            "reduced_polarization": [
              0.5002998977436234,
              0.4996788305586349,
              0.5002896061351945
            ],
            "branch_aligned_reduced_polarization": [
              0.5002998977436234,
              0.4996788305586349,
              0.5002896061351945
            ],
            "target_residual": 0.0005262700639780417,
            "energy_eV": -54.21384841585188
          }
        ],
        "iterations": 5
      },
      "parent": {
        "candidate_id": "bec_projection_06",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.5,
          0.5,
          0.5
        ],
        "formal_class": [
          0.5,
          0.5,
          0.5
        ],
        "target_residual": 0.0005262700639780417,
        "parent_symmetrization_rmsd_A": 0.2184970789502984,
        "parent_cell_rmsd_A": 0.10881062134768725,
        "energy_eV": -54.21384841585188,
        "reduced_polarization": [
          0.5002998977436234,
          0.4996788305586349,
          0.5002896061351945
        ],
        "cartesian_polarization_e_A2": [
          0.016551190865716884,
          0.017108847240696928,
          0.01125013116345768
        ],
        "ranking_score": 0.7467522744151763
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 7,
      "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": [
              7.009601911953609e-16,
              0.33903949892054513,
              6.95995632260154e-16
            ],
            "branch_aligned_reduced_polarization": [
              7.216449660063518e-16,
              0.33903949892054513,
              7.216449660063518e-16
            ],
            "target_residual": 0.7841860632708878,
            "energy_eV": -65.7986521665511,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.0036450150247479,
            "step_scale": 0.32238791689300145,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.7060488239940996,
            "cell_principal_stretches": [
              1.0049225672813595,
              0.9993164131397297,
              0.994732472348228
            ],
            "cell_volume_ratio": 0.9989457765456651,
            "cell_rmsd_from_input_A": 0.026643288818900265
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.1632708414404542,
              0.2096294153001602,
              0.16375107396325378
            ],
            "branch_aligned_reduced_polarization": [
              0.16327084144045423,
              0.2096294153001602,
              0.16375107396325378
            ],
            "target_residual": 0.5199945752064842,
            "energy_eV": -65.48642586007111,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.0037758185274065557,
            "step_scale": 0.5123617977109427,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.7060488239940996,
            "cell_principal_stretches": [
              1.0094585558484979,
              0.9986274082480051,
              0.9903333386272337
            ],
            "cell_volume_ratio": 0.9983282812109097,
            "cell_rmsd_from_input_A": 0.050705654405697485
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.32822818080631494,
              0.0977543249569805,
              0.33318684866581105
            ],
            "branch_aligned_reduced_polarization": [
              0.32822818080631494,
              0.0977543249569805,
              0.33318684866581105
            ],
            "target_residual": 0.25862732526735455,
            "energy_eV": -63.99309382130885,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.00402092025424002,
            "step_scale": 0.9507384620256908,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.7060488239940996,
            "cell_principal_stretches": [
              1.0135664432766247,
              0.9986905997703146,
              0.9857133360647375
            ],
            "cell_volume_ratio": 0.9977777567398083,
            "cell_rmsd_from_input_A": 0.07249179976642271
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.4819526282211206,
              0.009318007156325395,
              0.49148906927786173
            ],
            "branch_aligned_reduced_polarization": [
              0.4819526282211206,
              0.009318007156325395,
              0.49148906927786173
            ],
            "target_residual": 0.022022007793283976,
            "energy_eV": -60.30549935050275,
            "max_atomic_step_A": 0.012522549043329067,
            "max_log_strain_component": 0.00038513126552272776,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.7060488239940996,
            "cell_principal_stretches": [
              1.0137432391047987,
              0.9989626388465733,
              0.985200277453679
            ],
            "cell_volume_ratio": 0.9977040662295332,
            "cell_rmsd_from_input_A": 0.07347343283194702
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              0.5003801417119913,
              -1.7684265229784037e-05,
              0.500233392151504
            ],
            "branch_aligned_reduced_polarization": [
              0.5003801417119913,
              -1.7684265229784037e-05,
              0.500233392151504
            ],
            "target_residual": 0.00044642171857566253,
            "energy_eV": -59.89345309786425
          }
        ],
        "iterations": 4
      },
      "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,
          0.0,
          0.5
        ],
        "formal_class": [
          0.5,
          0.0,
          0.5
        ],
        "target_residual": 0.00044642171857566253,
        "parent_symmetrization_rmsd_A": 0.17596293416927478,
        "parent_cell_rmsd_A": 0.07347343283194702,
        "energy_eV": -59.89345309786425,
        "reduced_polarization": [
          0.5003801417119913,
          -1.7684265229784037e-05,
          0.500233392151504
        ],
        "cartesian_polarization_e_A2": [
          0.01588591968469858,
          0.00013986008853367264,
          0.011219323332678426
        ],
        "ranking_score": 0.6952241358144129
      },
      "branch_status": "awaiting_branch_sampling"
    }
  ],
  "sampled_polarization_branches": [
    {
      "orbit_id": 0,
      "candidate_id": "bec_projection_00",
      "formal_class": [
        0.0,
        0.5,
        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
        ],
        "endpoint_rmsd_A": 0.040615766283219154,
        "minimum_distance_A_by_image": [
          1.8881509029351362,
          1.890291986965646,
          1.892435973053238,
          1.8945828601458738,
          1.894086775880626,
          1.881545319602687,
          1.8690369748668119,
          1.856562323427873,
          1.8441219610021358
        ],
        "minimum_distance_A": 1.8441219610021358,
        "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": [
          155.0941688038146,
          155.12745750986488,
          155.16075336085157,
          155.19405635830793,
          155.227366503768,
          155.26068379876614,
          155.2940082448366,
          155.32733984351438,
          155.36067859633485
        ],
        "cell_deformation_log_strain_norm": 0.007209379038789962
      },
      "parent_reduced_polarization": [
        9.63597605024451e-15,
        0.49986182250256284,
        3.127526365610454e-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": [
          -65.7986521665511,
          -65.79414384127617,
          -65.78618063210386,
          -65.77462184672714,
          -65.75927945620816,
          -65.73991970449242,
          -65.7162655690324,
          -65.68799993573057,
          -65.6547692225937
        ],
        "cartesian_polarizations_e_A2": [
          [
            1.3869361606574693e-18,
            0.011550067247492921,
            -4.15186050674236e-17
          ],
          [
            -1.6908044119205237e-16,
            0.012285277820654576,
            4.58038020583761e-17
          ],
          [
            -3.4027962981102363e-16,
            0.013004019444165415,
            -6.08201204551179e-18
          ],
          [
            -4.672307883261846e-16,
            0.013706500642509736,
            -9.890090945239429e-17
          ],
          [
            -9.192413519202782e-16,
            0.014392958436254138,
            -1.1550863904697524e-16
          ],
          [
            -1.8211946493209166e-16,
            0.015063626842500654,
            -3.8077493036108487e-17
          ],
          [
            -6.068750370219229e-16,
            0.01571870970596889,
            3.2528716459428647e-17
          ],
          [
            -6.467715602544876e-16,
            0.01635835939562003,
            -6.968943459020588e-18
          ],
          [
            -8.759779331997786e-16,
            0.016982663287015837,
            -1.132656930910436e-16
          ]
        ],
        "raw_reduced_polarization": [
          [
            4.5065421745336637e-17,
            0.33903949892054164,
            -1.0684432868637226e-15
          ],
          [
            -1.951183378042906e-15,
            0.36074312647237466,
            5.851810447345043e-16
          ],
          [
            -3.5686673904633376e-15,
            0.3819776838786677,
            -1.2264547777696263e-15
          ],
          [
            -3.4164422864446472e-15,
            0.4027488135385636,
            -3.3621662525814347e-15
          ],
          [
            -1.3061604525205535e-14,
            0.4230630034412823,
            -7.49455015416476e-15
          ],
          [
            1.4798964681545155e-14,
            0.4429266623898155,
            6.227605083946798e-15
          ],
          [
            6.69142430465738e-15,
            0.4623453207207253,
            5.0578533078719516e-15
          ],
          [
            1.0949664077311018e-14,
            0.4813230019830602,
            6.079507963774625e-15
          ],
          [
            9.63597605024451e-15,
            0.49986182250256284,
            3.127526365610454e-15
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            4.5065421745336637e-17,
            0.33903949892054164,
            -1.0684432868637226e-15
          ],
          [
            -1.951183378042906e-15,
            0.36074312647237466,
            5.851810447345043e-16
          ],
          [
            -3.5686673904633376e-15,
            0.3819776838786677,
            -1.2264547777696261e-15
          ],
          [
            -3.4164422864446472e-15,
            0.4027488135385636,
            -3.3621662525814344e-15
          ],
          [
            -1.3061604525205535e-14,
            0.4230630034412823,
            -7.49455015416476e-15
          ],
          [
            1.479896468154516e-14,
            0.4429266623898155,
            6.2276050839467984e-15
          ],
          [
            6.69142430465738e-15,
            0.4623453207207253,
            5.0578533078719516e-15
          ],
          [
            1.0949664077311018e-14,
            0.4813230019830602,
            6.079507963774625e-15
          ],
          [
            9.63597605024451e-15,
            0.49986182250256284,
            3.127526365610454e-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": [
          [
            0.0,
            0.33903949892054164,
            -1.0547118733938987e-15
          ],
          [
            -1.942890293094024e-15,
            0.3607431264723746,
            5.551115123125783e-16
          ],
          [
            -3.552713678800501e-15,
            0.3819776838786677,
            -1.2212453270876722e-15
          ],
          [
            -3.4416913763379853e-15,
            0.4027488135385636,
            -3.3861802251067274e-15
          ],
          [
            -1.304512053934559e-14,
            0.42306300344128234,
            -7.494005416219807e-15
          ],
          [
            1.4765966227514582e-14,
            0.4429266623898155,
            6.217248937900877e-15
          ],
          [
            6.661338147750939e-15,
            0.4623453207207253,
            5.10702591327572e-15
          ],
          [
            1.099120794378905e-14,
            0.4813230019830602,
            6.106226635438361e-15
          ],
          [
            9.658940314238862e-15,
            0.49986182250256284,
            3.1086244689504383e-15
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -65.6547692225937,
          -65.62213732773951,
          -65.58385251672287,
          -65.539511636514,
          -65.48869238503968,
          -65.43095680670888,
          -65.36585410873207,
          -65.29292299995704,
          -65.2116937167504
        ],
        "cartesian_polarizations_e_A2": [
          [
            -8.395328205963513e-16,
            0.016982663287015757,
            -8.360937597256847e-17
          ],
          [
            -6.055386447886158e-16,
            0.017540599209071462,
            3.502340815302654e-17
          ],
          [
            -2.867710195557872e-16,
            0.01808440096928587,
            2.854305504709206e-16
          ],
          [
            -3.0126805229625273e-16,
            0.018614009596723356,
            3.7326669229762686e-16
          ],
          [
            2.4643929066020686e-16,
            0.019129304586814336,
            6.6372765966311465e-16
          ],
          [
            -2.6768523729271456e-16,
            0.01963012448689225,
            7.092965766513486e-16
          ],
          [
            7.076152690892137e-16,
            0.020116291888989595,
            8.645401239987788e-16
          ],
          [
            7.077447832701717e-16,
            0.020587640351080367,
            1.1128892531371067e-15
          ],
          [
            8.479548726755167e-16,
            0.021044040935818915,
            1.1603734278326492e-15
          ]
        ],
        "raw_reduced_polarization": [
          [
            1.076890036953066e-14,
            0.49986182250256056,
            4.3693208863732826e-15
          ],
          [
            1.448188569368907e-14,
            0.5161088385276894,
            8.755162684916912e-15
          ],
          [
            2.0518019944521464e-14,
            0.5319290401432661,
            1.7573853779224438e-14
          ],
          [
            1.585849026346612e-14,
            0.5473211219695887,
            1.7729666353147333e-14
          ],
          [
            2.8449704791520816e-14,
            0.5622819719853928,
            3.024927688320574e-14
          ],
          [
            7.589277364630211e-15,
            0.5768072794736706,
            2.2613550514364276e-14
          ],
          [
            3.301663768725205e-14,
            0.590892271191665,
            3.682841202959658e-14
          ],
          [
            2.768422146766719e-14,
            0.6045325026717089,
            4.0842004829842537e-14
          ],
          [
            2.6494796250518678e-14,
            0.6177246366848727,
            4.1279339357043943e-14
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            1.076890036953066e-14,
            0.49986182250256056,
            4.3693208863732826e-15
          ],
          [
            1.448188569368907e-14,
            0.5161088385276894,
            8.755162684916912e-15
          ],
          [
            2.0518019944521464e-14,
            0.5319290401432661,
            1.7573853779224438e-14
          ],
          [
            1.585849026346612e-14,
            0.5473211219695887,
            1.7729666353147333e-14
          ],
          [
            2.8449704791520816e-14,
            0.5622819719853928,
            3.024927688320574e-14
          ],
          [
            7.58927736463021e-15,
            0.5768072794736706,
            2.2613550514364276e-14
          ],
          [
            3.301663768725205e-14,
            0.590892271191665,
            3.682841202959658e-14
          ],
          [
            2.768422146766719e-14,
            0.6045325026717089,
            4.0842004829842537e-14
          ],
          [
            2.6494796250518678e-14,
            0.6177246366848727,
            4.1279339357043943e-14
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          -5.487234539449312e-14,
          0.6579752418232278,
          -2.741838036496855e-14
        ],
        "actual_opposite_endpoint_branch_residual": 0.0402506051383551
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            4.5065421745336637e-17,
            0.33903949892054164,
            -1.0684432868637226e-15
          ],
          [
            -1.951183378042906e-15,
            0.36074312647237466,
            5.851810447345043e-16
          ],
          [
            -3.5686673904633376e-15,
            0.3819776838786677,
            -1.2264547777696263e-15
          ],
          [
            -3.4164422864446472e-15,
            0.4027488135385636,
            -3.3621662525814347e-15
          ],
          [
            -1.3061604525205535e-14,
            0.4230630034412823,
            -7.49455015416476e-15
          ],
          [
            1.4798964681545155e-14,
            0.4429266623898155,
            6.227605083946798e-15
          ],
          [
            6.69142430465738e-15,
            0.4623453207207253,
            5.0578533078719516e-15
          ],
          [
            1.0949664077311018e-14,
            0.4813230019830602,
            6.079507963774625e-15
          ],
          [
            9.63597605024451e-15,
            0.49986182250256284,
            3.127526365610454e-15
          ],
          [
            1.448188569368907e-14,
            0.5161088385276894,
            8.755162684916912e-15
          ],
          [
            2.0518019944521464e-14,
            0.5319290401432661,
            1.7573853779224438e-14
          ],
          [
            1.585849026346612e-14,
            0.5473211219695887,
            1.7729666353147333e-14
          ],
          [
            2.8449704791520816e-14,
            0.5622819719853928,
            3.024927688320574e-14
          ],
          [
            7.589277364630211e-15,
            0.5768072794736706,
            2.2613550514364276e-14
          ],
          [
            3.301663768725205e-14,
            0.590892271191665,
            3.682841202959658e-14
          ],
          [
            2.768422146766719e-14,
            0.6045325026717089,
            4.0842004829842537e-14
          ],
          [
            2.6494796250518678e-14,
            0.6177246366848727,
            4.1279339357043943e-14
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            4.5065421745336637e-17,
            0.33903949892054164,
            -1.0684432868637226e-15
          ],
          [
            -1.951183378042906e-15,
            0.36074312647237466,
            5.851810447345043e-16
          ],
          [
            -3.5686673904633376e-15,
            0.3819776838786677,
            -1.2264547777696261e-15
          ],
          [
            -3.4164422864446472e-15,
            0.4027488135385636,
            -3.3621662525814344e-15
          ],
          [
            -1.3061604525205535e-14,
            0.4230630034412823,
            -7.49455015416476e-15
          ],
          [
            1.479896468154516e-14,
            0.4429266623898155,
            6.2276050839467984e-15
          ],
          [
            6.69142430465738e-15,
            0.4623453207207253,
            5.0578533078719516e-15
          ],
          [
            1.0949664077311018e-14,
            0.4813230019830602,
            6.079507963774625e-15
          ],
          [
            9.63597605024451e-15,
            0.49986182250256284,
            3.127526365610454e-15
          ],
          [
            1.448188569368907e-14,
            0.5161088385276894,
            8.755162684916912e-15
          ],
          [
            2.0518019944521464e-14,
            0.5319290401432661,
            1.7573853779224438e-14
          ],
          [
            1.585849026346612e-14,
            0.5473211219695887,
            1.7729666353147333e-14
          ],
          [
            2.8449704791520816e-14,
            0.5622819719853928,
            3.024927688320574e-14
          ],
          [
            7.58927736463021e-15,
            0.5768072794736706,
            2.2613550514364276e-14
          ],
          [
            3.301663768725205e-14,
            0.590892271191665,
            3.682841202959658e-14
          ],
          [
            2.768422146766719e-14,
            0.6045325026717089,
            4.0842004829842537e-14
          ],
          [
            2.6494796250518678e-14,
            0.6177246366848727,
            4.1279339357043943e-14
          ]
        ],
        "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": [
          [
            0.0,
            0.33903949892054164,
            -1.0547118733938987e-15
          ],
          [
            -1.942890293094024e-15,
            0.3607431264723746,
            5.551115123125783e-16
          ],
          [
            -3.552713678800501e-15,
            0.3819776838786677,
            -1.2212453270876722e-15
          ],
          [
            -3.4416913763379853e-15,
            0.4027488135385636,
            -3.3861802251067274e-15
          ],
          [
            -1.304512053934559e-14,
            0.42306300344128234,
            -7.494005416219807e-15
          ],
          [
            1.4765966227514582e-14,
            0.4429266623898155,
            6.217248937900877e-15
          ],
          [
            6.661338147750939e-15,
            0.4623453207207253,
            5.10702591327572e-15
          ],
          [
            1.099120794378905e-14,
            0.4813230019830602,
            6.106226635438361e-15
          ],
          [
            9.658940314238862e-15,
            0.49986182250256284,
            3.1086244689504383e-15
          ],
          [
            1.4432899320127035e-14,
            -0.4838911614723105,
            8.770761894538737e-15
          ],
          [
            2.0539125955565396e-14,
            -0.46807095985673386,
            1.7541523789077473e-14
          ],
          [
            1.587618925213974e-14,
            -0.4526788780304112,
            1.7763568394002505e-14
          ],
          [
            2.842170943040401e-14,
            -0.43771802801460735,
            3.019806626980426e-14
          ],
          [
            7.549516567451064e-15,
            -0.4231927205263295,
            2.2648549702353193e-14
          ],
          [
            3.297362383136715e-14,
            -0.4091077288083351,
            3.68594044175552e-14
          ],
          [
            2.7644553313166398e-14,
            -0.395467497328291,
            4.085620730620576e-14
          ],
          [
            2.653433028854124e-14,
            -0.38227536331512724,
            4.1300296516055823e-14
          ]
        ]
      },
      "incoming_structure_ids": [
        "incoming_00_000",
        "incoming_00_001",
        "incoming_00_002",
        "incoming_00_003",
        "incoming_00_004",
        "incoming_00_005",
        "incoming_00_006",
        "incoming_00_007",
        "incoming_00_008"
      ],
      "reflected_structure_ids": [
        "reflected_00_001",
        "reflected_00_002",
        "reflected_00_003",
        "reflected_00_004",
        "reflected_00_005",
        "reflected_00_006",
        "reflected_00_007",
        "reflected_00_008"
      ],
      "positive_extension_structure_ids": [
        "extension_plus_00_000",
        "extension_plus_00_001",
        "extension_plus_00_002",
        "extension_plus_00_003"
      ],
      "negative_extension_structure_ids": [
        "extension_minus_00_000",
        "extension_minus_00_001",
        "extension_minus_00_002",
        "extension_minus_00_003"
      ],
      "extension": {
        "enabled": true,
        "fraction_beyond_polar_endpoint": 0.35,
        "images_per_side": 4,
        "construction": "continue fractional atomic displacements and symmetric log strain beyond +P; reflect these structures about N for the -P side",
        "positive_path_coordinates": [
          1.35,
          1.2625,
          1.175,
          1.0875
        ],
        "negative_path_coordinates": [
          -1.0875,
          -1.175,
          -1.2625,
          -1.35
        ]
      },
      "branch_coordinates": [
        1.35,
        1.2625,
        1.175,
        1.0875,
        1.0,
        0.875,
        0.75,
        0.625,
        0.5,
        0.375,
        0.25,
        0.125,
        0.0,
        -0.125,
        -0.25,
        -0.375,
        -0.5,
        -0.625,
        -0.75,
        -0.875,
        -1.0,
        -1.0875,
        -1.175,
        -1.2625,
        -1.35
      ],
      "parent": {
        "candidate_id": "bec_projection_00",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P2_1",
        "spacegroup_number": 4,
        "pointgroup": "2",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.5,
          0.0
        ],
        "formal_class": [
          0.0,
          0.5,
          0.0
        ],
        "target_residual": 0.00013817749743938457,
        "parent_symmetrization_rmsd_A": 0.040615766283219154,
        "parent_cell_rmsd_A": 0.024191256457124995,
        "energy_eV": -65.6547692225937,
        "reduced_polarization": [
          1.0298485397184484e-14,
          0.4998618225025606,
          4.759276524381709e-15
        ],
        "cartesian_polarization_e_A2": [
          -8.544949685401602e-16,
          0.01698266328701576,
          -6.145646439009307e-17
        ],
        "ranking_score": 0.5469399353923792
      }
    }
  ],
  "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": 103,
      "full_response": 32,
      "energy_polarization": 71
    },
    "model_evaluations_for_recovery_and_path_properties": {
      "total": 128,
      "full_response": 57,
      "energy_polarization": 71
    },
    "elapsed_seconds": 279.1801562799956
  }
}