{
  "schema": "ferrofinder.endpoint_parent_recovery.v4_variable_cell",
  "status": "complete",
  "input_atom_count": 48,
  "input_formula": "Ba6O30Ti12",
  "input_spacegroup": "C2",
  "input_pointgroup": "2",
  "input_is_polar_point_group": true,
  "input_energy_eV": -386.12474233416395,
  "input_cartesian_polarization_e_A2": [
    -6.884036787701688e-18,
    -0.009641219869919795,
    1.4109881702422954e-19
  ],
  "input_reduced_polarization": [
    -2.6228516944516336e-16,
    -1.5376904008698353,
    -9.427140653555809e-17
  ],
  "input_formal_targets": [
    {
      "orbit_id": 0,
      "representative_formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        -1.5,
        0.0
      ]
    },
    {
      "orbit_id": 1,
      "representative_formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        -2.0,
        0.0
      ]
    },
    {
      "orbit_id": 2,
      "representative_formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        -0.5,
        -1.5,
        0.0
      ]
    },
    {
      "orbit_id": 3,
      "representative_formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        -1.5,
        -0.5
      ]
    },
    {
      "orbit_id": 4,
      "representative_formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        -0.5,
        -2.0,
        0.0
      ]
    },
    {
      "orbit_id": 5,
      "representative_formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        -2.0,
        -0.5
      ]
    },
    {
      "orbit_id": 6,
      "representative_formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "target_reduced_polarization": [
        -0.5,
        -1.5,
        -0.5
      ]
    },
    {
      "orbit_id": 7,
      "representative_formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        -0.5,
        -2.0,
        -0.5
      ]
    }
  ],
  "parent_candidates": [
    {
      "candidate_id": "inversion_parent_endpoint_00",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "C2/m",
      "spacegroup_number": 12,
      "pointgroup": "2/m",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 3.139531961188814e-15,
      "parent_symmetrization_rmsd_A": 0.05158377966427228,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -385.89991351556506,
      "reduced_polarization": [
        2.9969978850182787e-15,
        9.033838790403982e-16,
        -2.4199623883847575e-16
      ],
      "cartesian_polarization_e_A2": [
        7.86575717993945e-17,
        5.664158792851033e-18,
        -2.161683180431325e-17
      ],
      "ranking_score": 0.05158377966427856
    },
    {
      "candidate_id": "symmetry_projection_00",
      "source": "spglib_refine_cell_from_polar_endpoint",
      "spacegroup": "C2/m",
      "spacegroup_number": 12,
      "pointgroup": "2/m",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        -1.5,
        0.0
      ],
      "formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_residual": 0.5,
      "parent_symmetrization_rmsd_A": 0.05158377966427228,
      "parent_cell_rmsd_A": 1.6730769652349071e-15,
      "energy_eV": -385.8999135160661,
      "reduced_polarization": [
        6.600692493465895e-16,
        2.840608493382751e-18,
        -9.286046427445235e-16
      ],
      "cartesian_polarization_e_A2": [
        2.0899697264742025e-17,
        1.7810432472994965e-20,
        -1.3729260777045127e-17
      ],
      "ranking_score": 1.0515837796642726
    },
    {
      "candidate_id": "bec_projection_00",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "C2",
      "spacegroup_number": 5,
      "pointgroup": "2",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        -1.5,
        0.0
      ],
      "formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_residual": 2.1575134440787735e-05,
      "parent_symmetrization_rmsd_A": 0.0010091758514359716,
      "parent_cell_rmsd_A": 0.0004899201408638872,
      "energy_eV": -386.12480054009245,
      "reduced_polarization": [
        -2.7946079435574225e-15,
        -1.4999784248655592,
        -4.397190447223972e-15
      ],
      "cartesian_polarization_e_A2": [
        -7.107978303038883e-17,
        -0.009405110806749361,
        -5.111107945105932e-17
      ],
      "ranking_score": 0.5011748061555336
    },
    {
      "candidate_id": "inversion_parent_bec_00_00",
      "source": "same_species_inversion_center_projection_after_BEC",
      "spacegroup": "C2/m",
      "spacegroup_number": 12,
      "pointgroup": "2/m",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        -1.5,
        0.0
      ],
      "formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_residual": 0.4999999999999998,
      "parent_symmetrization_rmsd_A": 0.05158378249085774,
      "parent_cell_rmsd_A": 0.0004899201408638872,
      "energy_eV": -385.8991014426446,
      "reduced_polarization": [
        -2.5505547706212334e-15,
        2.8169458081703784e-16,
        4.533205638528139e-17
      ],
      "cartesian_polarization_e_A2": [
        -6.693665120266295e-17,
        1.7662712358563023e-18,
        1.5959148080047804e-17
      ],
      "ranking_score": 1.0517062625260734
    },
    {
      "candidate_id": "symmetry_parent_00_00",
      "source": "spglib_refine_cell_after_MACEField_BEC_backprojection",
      "spacegroup": "C2/m",
      "spacegroup_number": 12,
      "pointgroup": "2/m",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        -1.5,
        0.0
      ],
      "formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_residual": 0.5,
      "parent_symmetrization_rmsd_A": 0.051583782490857766,
      "parent_cell_rmsd_A": 0.0004899201408651657,
      "energy_eV": -385.8991014431457,
      "reduced_polarization": [
        -7.280990510602195e-16,
        -5.349015576117063e-17,
        2.715019861888459e-16
      ],
      "cartesian_polarization_e_A2": [
        -2.0514375656644422e-17,
        -3.3539205208847134e-19,
        4.013896246977166e-18
      ],
      "ranking_score": 1.051706262526074
    },
    {
      "candidate_id": "bec_projection_01",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "C2",
      "spacegroup_number": 5,
      "pointgroup": "2",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        -2.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 6.845014090206547e-06,
      "parent_symmetrization_rmsd_A": 0.012483182075376673,
      "parent_cell_rmsd_A": 0.006056741486642852,
      "energy_eV": -386.09553710346404,
      "reduced_polarization": [
        1.350980878132834e-16,
        -2.00000684501409,
        4.289597685255966e-15
      ],
      "cartesian_polarization_e_A2": [
        -3.365058836680276e-17,
        -0.012534270496547916,
        8.344299707427712e-17
      ],
      "ranking_score": 0.5140110574752178
    },
    {
      "candidate_id": "symmetry_parent_01_00",
      "source": "spglib_refine_cell_after_MACEField_BEC_backprojection",
      "spacegroup": "C2/m",
      "spacegroup_number": 12,
      "pointgroup": "2/m",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        -2.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 1.3249907136276945e-15,
      "parent_symmetrization_rmsd_A": 0.0515842111147191,
      "parent_cell_rmsd_A": 0.006056741486643054,
      "energy_eV": -385.9094917102775,
      "reduced_polarization": [
        1.3237849501620925e-15,
        5.4964748904613815e-17,
        -5.651368793463701e-17
      ],
      "cartesian_polarization_e_A2": [
        3.5856068890253673e-17,
        3.444703363204802e-19,
        -8.360962854395329e-19
      ],
      "ranking_score": 0.05309839648638252
    },
    {
      "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": [
        -0.5,
        -1.5,
        0.0
      ],
      "formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_residual": 4.705610727442495e-05,
      "parent_symmetrization_rmsd_A": 0.05660153205092474,
      "parent_cell_rmsd_A": 0.013670217990896232,
      "energy_eV": -385.5521069355469,
      "reduced_polarization": [
        -0.4999632973177336,
        -1.5000272994088206,
        -1.1042310642142435e-05
      ],
      "cartesian_polarization_e_A2": [
        -0.013144048526961915,
        -0.009438134670047178,
        0.0029992103698329702
      ],
      "ranking_score": 0.5601131987631977
    },
    {
      "candidate_id": "symmetry_parent_02_00",
      "source": "spglib_refine_cell_after_MACEField_BEC_backprojection",
      "spacegroup": "C2/m",
      "spacegroup_number": 12,
      "pointgroup": "2/m",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        -0.5,
        -1.5,
        0.0
      ],
      "formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_residual": 0.7071067811865467,
      "parent_symmetrization_rmsd_A": 0.0758371899167431,
      "parent_cell_rmsd_A": 5.361820615877397e-05,
      "energy_eV": -384.0469089143872,
      "reduced_polarization": [
        -1.1548099903659008e-15,
        4.0314039473616545e-17,
        -1.6203135059612862e-15
      ],
      "cartesian_polarization_e_A2": [
        -2.562475971693363e-17,
        2.5276720627348477e-19,
        -2.39554532083462e-17
      ],
      "ranking_score": 1.4900641568413762
    },
    {
      "candidate_id": "bec_projection_03",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        -1.5,
        -0.5
      ],
      "formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_residual": 4.513456943983877e-06,
      "parent_symmetrization_rmsd_A": 0.04078482677265549,
      "parent_cell_rmsd_A": 0.001347373159223977,
      "energy_eV": -385.7979778620385,
      "reduced_polarization": [
        -1.4043387863430445e-06,
        -1.4999979165125883,
        -0.49999625057252856
      ],
      "cartesian_polarization_e_A2": [
        -9.533368166021042e-07,
        -0.009407963292228061,
        -0.007585247932095827
      ],
      "ranking_score": 0.5411306969763494
    },
    {
      "candidate_id": "symmetry_parent_03_00",
      "source": "spglib_refine_cell_after_MACEField_BEC_backprojection",
      "spacegroup": "C2/m",
      "spacegroup_number": 12,
      "pointgroup": "2/m",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        -1.5,
        -0.5
      ],
      "formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_residual": 0.7071067811865467,
      "parent_symmetrization_rmsd_A": 2.694336001472264,
      "parent_cell_rmsd_A": 0.0003648324494808796,
      "energy_eV": -385.42699066677545,
      "reduced_polarization": [
        -1.4364672304548374e-15,
        3.0361754526407168e-18,
        -1.233920279230209e-15
      ],
      "cartesian_polarization_e_A2": [
        -3.4508728254372874e-17,
        1.9037139273344576e-20,
        -1.8242571564625654e-17
      ],
      "ranking_score": 4.108640771957727
    },
    {
      "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": [
        -0.5,
        -2.0,
        0.0
      ],
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_residual": 0.0001286261271711844,
      "parent_symmetrization_rmsd_A": 0.058503577201955925,
      "parent_cell_rmsd_A": 0.015270374291987557,
      "energy_eV": -385.50778475567915,
      "reduced_polarization": [
        -0.49995112591654955,
        -2.0001180570130495,
        -1.4783309094292329e-05
      ],
      "cartesian_polarization_e_A2": [
        -0.01316242736498415,
        -0.012567799659000478,
        0.0030060170072222004
      ],
      "ranking_score": 0.5625784230292952
    },
    {
      "candidate_id": "symmetry_parent_04_00",
      "source": "spglib_refine_cell_after_MACEField_BEC_backprojection",
      "spacegroup": "C2/m",
      "spacegroup_number": 12,
      "pointgroup": "2/m",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        -0.5,
        -2.0,
        0.0
      ],
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_residual": 0.4999999999999989,
      "parent_symmetrization_rmsd_A": 0.07617579296445755,
      "parent_cell_rmsd_A": 0.0066024506894637475,
      "energy_eV": -384.0455165070758,
      "reduced_polarization": [
        1.1110756678571014e-15,
        1.2111068940605152e-17,
        1.0290080161111975e-15
      ],
      "cartesian_polarization_e_A2": [
        2.6458474327752834e-17,
        7.589843807572216e-20,
        1.522430447939265e-17
      ],
      "ranking_score": 1.0778264056368212
    },
    {
      "candidate_id": "bec_projection_05",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        -2.0,
        -0.5
      ],
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_residual": 2.9325924745233525e-05,
      "parent_symmetrization_rmsd_A": 0.042947756329286116,
      "parent_cell_rmsd_A": 0.006338976360486576,
      "energy_eV": -385.7625316693003,
      "reduced_polarization": [
        -2.04108659156514e-06,
        -2.0000285852570867,
        -0.4999937769055145
      ],
      "cartesian_polarization_e_A2": [
        5.980044155174084e-07,
        -0.01253710484552225,
        -0.007592478622548487
      ],
      "ranking_score": 0.5445911522688982
    },
    {
      "candidate_id": "symmetry_parent_05_00",
      "source": "spglib_refine_cell_after_MACEField_BEC_backprojection",
      "spacegroup": "C2/m",
      "spacegroup_number": 12,
      "pointgroup": "2/m",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        -2.0,
        -0.5
      ],
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_residual": 0.49999999999999933,
      "parent_symmetrization_rmsd_A": 2.3397621247931766,
      "parent_cell_rmsd_A": 0.006203665316595054,
      "energy_eV": -385.43220509964806,
      "reduced_polarization": [
        3.3832719230793054e-16,
        -2.0294655725232247e-17,
        7.12408387464371e-16
      ],
      "cartesian_polarization_e_A2": [
        6.708019697035583e-18,
        -1.2718751603005987e-19,
        1.0539949250353864e-17
      ],
      "ranking_score": 3.341313041122324
    },
    {
      "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,
        -1.5,
        -0.5
      ],
      "formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "target_residual": 4.97218813391403e-05,
      "parent_symmetrization_rmsd_A": 0.0625288327750536,
      "parent_cell_rmsd_A": 0.012968657959253851,
      "energy_eV": -385.4151394149588,
      "reduced_polarization": [
        -0.4999623535717144,
        -1.5000323452630773,
        -0.4999970342154993
      ],
      "cartesian_polarization_e_A2": [
        -0.013144961259470284,
        -0.009435087974949366,
        -0.004586175651714814
      ],
      "ranking_score": 0.5658704410275454
    },
    {
      "candidate_id": "symmetry_parent_06_00",
      "source": "spglib_refine_cell_after_MACEField_BEC_backprojection",
      "spacegroup": "C2/m",
      "spacegroup_number": 12,
      "pointgroup": "2/m",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        -0.5,
        -1.5,
        -0.5
      ],
      "formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "target_residual": 0.8660254037844367,
      "parent_symmetrization_rmsd_A": 2.3376639989819443,
      "parent_cell_rmsd_A": 5.331391412313114e-05,
      "energy_eV": -383.9831492425452,
      "reduced_polarization": [
        -1.867058162488047e-15,
        -3.523582118531901e-17,
        1.5322089466643187e-15
      ],
      "cartesian_polarization_e_A2": [
        -5.542605126350911e-17,
        -2.2092603170272745e-19,
        2.2653056594582255e-17
      ],
      "ranking_score": 4.069728135029348
    },
    {
      "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,
        -2.0,
        -0.5
      ],
      "formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_residual": 0.00014898612848187516,
      "parent_symmetrization_rmsd_A": 0.0643552591225508,
      "parent_cell_rmsd_A": 0.014662200824133604,
      "energy_eV": -385.3665430892972,
      "reduced_polarization": [
        -0.49995137863805456,
        -2.0001407056806007,
        -0.49999410584278325
      ],
      "cartesian_polarization_e_A2": [
        -0.013161784381418726,
        -0.012564826776404556,
        -0.004586601700421334
      ],
      "ranking_score": 0.5683187815855479
    },
    {
      "candidate_id": "symmetry_parent_07_00",
      "source": "spglib_refine_cell_after_MACEField_BEC_backprojection",
      "spacegroup": "C2/m",
      "spacegroup_number": 12,
      "pointgroup": "2/m",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        -0.5,
        -2.0,
        -0.5
      ],
      "formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_residual": 0.7071067811865458,
      "parent_symmetrization_rmsd_A": 2.1065225809126713,
      "parent_cell_rmsd_A": 0.006651418601162136,
      "energy_eV": -383.9805562515613,
      "reduced_polarization": [
        5.482891692907976e-16,
        2.157075209265971e-17,
        1.908433682832606e-15
      ],
      "cartesian_polarization_e_A2": [
        8.323234659056331e-18,
        1.3518042327053956e-19,
        2.823573882228372e-17
      ],
      "ranking_score": 3.5223989979360537
    }
  ],
  "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,
        -1.5,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -2.6228516944516336e-16,
              -1.5376904008698353,
              -9.427140653555809e-17
            ],
            "branch_aligned_reduced_polarization": [
              -2.6228516944516336e-16,
              -1.5376904008698353,
              -9.427140653555809e-17
            ],
            "target_residual": 0.03769040086983533,
            "energy_eV": -386.12474233416395,
            "max_atomic_step_A": 0.0011550647531567157,
            "max_log_strain_component": 7.740876872993137e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.700071647404039,
            "cell_principal_stretches": [
              1.0000774117648659,
              0.999996534205816,
              0.999967038700447
            ],
            "cell_volume_ratio": 1.0000409819654894,
            "cell_rmsd_from_input_A": 0.0004899201408638872
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -2.7946079435574225e-15,
              -1.4999784248655592,
              -4.397190447223972e-15
            ],
            "branch_aligned_reduced_polarization": [
              -2.7946079435574225e-15,
              -1.4999784248655592,
              -4.397190447223972e-15
            ],
            "target_residual": 2.1575134440787735e-05,
            "energy_eV": -386.12480054009245
          }
        ],
        "iterations": 1
      },
      "parent": {
        "candidate_id": "bec_projection_00",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "C2",
        "spacegroup_number": 5,
        "pointgroup": "2",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          -1.5,
          0.0
        ],
        "formal_class": [
          0.0,
          0.5,
          0.0
        ],
        "target_residual": 2.1575134440787735e-05,
        "parent_symmetrization_rmsd_A": 0.0010091758514359716,
        "parent_cell_rmsd_A": 0.0004899201408638872,
        "energy_eV": -386.12480054009245,
        "reduced_polarization": [
          -2.7946079435574225e-15,
          -1.4999784248655592,
          -4.397190447223972e-15
        ],
        "cartesian_polarization_e_A2": [
          -7.107978303038883e-17,
          -0.009405110806749361,
          -5.111107945105932e-17
        ],
        "ranking_score": 0.5011748061555336
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "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,
        -2.0,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -2.6228516944516336e-16,
              -1.5376904008698353,
              -9.427140653555809e-17
            ],
            "branch_aligned_reduced_polarization": [
              -2.6228516944516336e-16,
              -1.5376904008698353,
              -9.427140653555809e-17
            ],
            "target_residual": 0.4623095991301647,
            "energy_eV": -386.12474233416395,
            "max_atomic_step_A": 0.014167997969706837,
            "max_log_strain_component": 0.0009494941952006506,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.700071647404039,
            "cell_principal_stretches": [
              1.0004043909573261,
              1.0000425123298609,
              0.999050956431779
            ],
            "cell_volume_ratio": 0.9994974527635616,
            "cell_rmsd_from_input_A": 0.00601176002611364
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -7.104266572524755e-16,
              -1.996658322001984,
              4.51794927855777e-15
            ],
            "branch_aligned_reduced_polarization": [
              -7.104266572524755e-16,
              -1.996658322001984,
              4.51794927855777e-15
            ],
            "target_residual": 0.0033416779980159905,
            "energy_eV": -386.09594658865717,
            "max_atomic_step_A": 0.00010392639277097444,
            "max_log_strain_component": 7.101694175749745e-06,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.700071647404039,
            "cell_principal_stretches": [
              1.0004074161952508,
              1.0000428303055073,
              0.9990438615026134
            ],
            "cell_volume_ratio": 0.9994936949384345,
            "cell_rmsd_from_input_A": 0.006056741486642852
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              1.350980878132834e-16,
              -2.00000684501409,
              4.289597685255966e-15
            ],
            "branch_aligned_reduced_polarization": [
              1.350980878132834e-16,
              -2.00000684501409,
              4.289597685255966e-15
            ],
            "target_residual": 6.845014090206547e-06,
            "energy_eV": -386.09553710346404
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "inversion_parent_endpoint_00",
        "source": "same_species_inversion_center_projection_from_endpoint",
        "spacegroup": "C2/m",
        "spacegroup_number": 12,
        "pointgroup": "2/m",
        "has_inversion": true,
        "is_polar_point_group": false,
        "nonpolar_parent_hypothesis": true,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.0
        ],
        "formal_class": [
          0.0,
          0.0,
          0.0
        ],
        "target_residual": 3.139531961188814e-15,
        "parent_symmetrization_rmsd_A": 0.05158377966427228,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -385.89991351556506,
        "reduced_polarization": [
          2.9969978850182787e-15,
          9.033838790403982e-16,
          -2.4199623883847575e-16
        ],
        "cartesian_polarization_e_A2": [
          7.86575717993945e-17,
          5.664158792851033e-18,
          -2.161683180431325e-17
        ],
        "ranking_score": 0.05158377966427856
      },
      "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": [
          -386.12474233416395,
          -386.1148352889438,
          -386.0858842908146,
          -386.0460056803393,
          -386.00249814164056,
          -385.9616719020203,
          -385.92866966581175,
          -385.9073009003769,
          -385.899913515565
        ],
        "cartesian_polarizations_e_A2": [
          [
            -5.097021904798562e-18,
            -0.009641219869919802,
            -1.5138453700721643e-17
          ],
          [
            4.7644142241337865e-18,
            -0.008621607179933318,
            -2.3235688703182263e-17
          ],
          [
            2.7590460962675016e-17,
            -0.007541129585642594,
            7.91701648607018e-18
          ],
          [
            7.395168604000833e-18,
            -0.0064001109718267975,
            -2.401990075101927e-17
          ],
          [
            3.760519862330697e-17,
            -0.00520156857229292,
            -2.4274630948439263e-17
          ],
          [
            4.881331381568235e-17,
            -0.003951612374669106,
            2.1754166551021138e-18
          ],
          [
            2.8662764981091166e-17,
            -0.0026595399903024367,
            3.808308712291803e-18
          ],
          [
            2.0214109225977626e-17,
            -0.0013375451248455556,
            -1.7066187575285355e-17
          ],
          [
            3.739663668547523e-17,
            3.246818731777027e-17,
            -4.209970099000362e-17
          ]
        ],
        "raw_reduced_polarization": [
          [
            -1.9411832157373e-16,
            -1.5376904008698364,
            -1.0749517491738651e-15
          ],
          [
            1.8164902155643655e-16,
            -1.3750710780921338,
            -1.460528184806564e-15
          ],
          [
            1.0511651482326502e-15,
            -1.2027443344318836,
            9.371858181359841e-16
          ],
          [
            2.818859171206979e-16,
            -1.0207618266838312,
            -1.4726590782490214e-15
          ],
          [
            1.4329009105598358e-15,
            -0.8296047772995737,
            -1.0349227734914263e-15
          ],
          [
            1.859794321490534e-15,
            -0.6302476759652705,
            8.778866545627298e-16
          ],
          [
            1.092042093900951e-15,
            -0.42417341052212026,
            6.823822266887517e-16
          ],
          [
            7.702556172352793e-16,
            -0.21332677056999494,
            -8.2124480212918e-16
          ],
          [
            1.4250489995729966e-15,
            5.178392428114432e-15,
            -2.2134851863921897e-15
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -1.9411832157373e-16,
            -1.5376904008698364,
            -1.0749517491738651e-15
          ],
          [
            1.8164902155643653e-16,
            -1.3750710780921338,
            -1.460528184806564e-15
          ],
          [
            1.0511651482326502e-15,
            -1.2027443344318836,
            9.371858181359843e-16
          ],
          [
            2.818859171206979e-16,
            -1.0207618266838312,
            -1.4726590782490216e-15
          ],
          [
            1.4329009105598356e-15,
            -0.8296047772995737,
            -1.0349227734914263e-15
          ],
          [
            1.859794321490534e-15,
            -0.6302476759652705,
            8.778866545627296e-16
          ],
          [
            1.092042093900951e-15,
            -0.42417341052212026,
            6.823822266887517e-16
          ],
          [
            7.702556172352793e-16,
            -0.21332677056999494,
            -8.2124480212918e-16
          ],
          [
            1.4250489995729966e-15,
            5.190292640122607e-15,
            -2.2134851863921897e-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": [
          [
            -1.6653345369377348e-16,
            0.46230959913016356,
            -1.0547118733938987e-15
          ],
          [
            2.220446049250313e-16,
            -0.3750710780921338,
            -1.4432899320127035e-15
          ],
          [
            9.992007221626409e-16,
            -0.20274433443188355,
            8.881784197001252e-16
          ],
          [
            3.3306690738754696e-16,
            -0.020761826683831197,
            -1.4988010832439613e-15
          ],
          [
            1.4432899320127035e-15,
            0.17039522270042629,
            -1.0547118733938987e-15
          ],
          [
            1.887379141862766e-15,
            0.36975232403472946,
            8.881784197001252e-16
          ],
          [
            1.1102230246251565e-15,
            -0.42417341052212026,
            6.661338147750939e-16
          ],
          [
            7.771561172376096e-16,
            -0.21332677056999494,
            -8.326672684688674e-16
          ],
          [
            1.4432899320127035e-15,
            5.218048215738236e-15,
            -2.220446049250313e-15
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -385.899913515565,
          -385.9073009003769,
          -385.9286696658118,
          -385.9616719020204,
          -386.0024981416407,
          -386.0460056803393,
          -386.0858842908146,
          -386.1148352889439,
          -386.12474233416395
        ],
        "cartesian_polarizations_e_A2": [
          [
            4.859269754039493e-17,
            -1.5057937050799856e-18,
            1.3186746993677372e-17
          ],
          [
            1.0722117705343004e-17,
            0.0013375451248455886,
            1.8304108890054516e-17
          ],
          [
            4.261250328330006e-17,
            0.0026595399903024176,
            1.309839064084388e-17
          ],
          [
            2.58352881550478e-17,
            0.003951612374669113,
            2.485603485121533e-17
          ],
          [
            3.873996990858822e-17,
            0.005201568572292945,
            -5.393474709688976e-18
          ],
          [
            4.208411966651991e-17,
            0.0064001109718268175,
            2.849507749284788e-17
          ],
          [
            6.422922393763343e-17,
            0.007541129585642573,
            -1.6518840432538048e-18
          ],
          [
            6.242459347506803e-17,
            0.008621607179933342,
            -1.998101002639046e-18
          ],
          [
            4.373474059941056e-17,
            0.009641219869919795,
            -3.591178611914419e-18
          ]
        ],
        "raw_reduced_polarization": [
          [
            1.8513304558177056e-15,
            -2.401609502979813e-16,
            1.600678717599507e-15
          ],
          [
            4.08419851886374e-16,
            0.21332677057000018,
            1.3683360462453542e-15
          ],
          [
            1.6234832457766368e-15,
            0.42417341052211716,
            1.5048755562298293e-15
          ],
          [
            9.842027091920581e-16,
            0.6302476759652716,
            2.0277740880756794e-15
          ],
          [
            1.4760361586427793e-15,
            0.8296047772995778,
            2.272158441585487e-16
          ],
          [
            1.6032701081164052e-15,
            1.0207618266838343,
            2.5122170972831064e-15
          ],
          [
            2.4471666303637447e-15,
            1.2027443344318802,
            8.574505555358666e-16
          ],
          [
            2.3784113558274935e-15,
            1.3750710780921378,
            8.07468154153781e-16
          ],
          [
            1.6663292808752677e-15,
            1.5376904008698353,
            4.2121349628712765e-16
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            1.8513304558177056e-15,
            -2.401609502979813e-16,
            1.600678717599507e-15
          ],
          [
            4.0841985188637396e-16,
            0.21332677057000018,
            1.3683360462453542e-15
          ],
          [
            1.6234832457766368e-15,
            0.42417341052211716,
            1.5048755562298293e-15
          ],
          [
            9.842027091920581e-16,
            0.6302476759652716,
            2.0277740880756794e-15
          ],
          [
            1.4760361586427793e-15,
            0.8296047772995778,
            2.2721584415854863e-16
          ],
          [
            1.6032701081164052e-15,
            1.0207618266838343,
            2.5122170972831064e-15
          ],
          [
            2.4471666303637447e-15,
            1.2027443344318802,
            8.574505555358666e-16
          ],
          [
            2.3784113558274935e-15,
            1.3750710780921378,
            8.07468154153781e-16
          ],
          [
            1.6663292808752677e-15,
            1.5376904008698353,
            4.2121349628712765e-16
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          3.044216320719723e-15,
          1.5376904008698467,
          -3.352018623610515e-15
        ],
        "actual_opposite_endpoint_branch_residual": 1.2015617097352483e-14
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            -1.9411832157373e-16,
            -1.5376904008698364,
            -1.0749517491738651e-15
          ],
          [
            1.8164902155643655e-16,
            -1.3750710780921338,
            -1.460528184806564e-15
          ],
          [
            1.0511651482326502e-15,
            -1.2027443344318836,
            9.371858181359841e-16
          ],
          [
            2.818859171206979e-16,
            -1.0207618266838312,
            -1.4726590782490214e-15
          ],
          [
            1.4329009105598358e-15,
            -0.8296047772995737,
            -1.0349227734914263e-15
          ],
          [
            1.859794321490534e-15,
            -0.6302476759652705,
            8.778866545627298e-16
          ],
          [
            1.092042093900951e-15,
            -0.42417341052212026,
            6.823822266887517e-16
          ],
          [
            7.702556172352793e-16,
            -0.21332677056999494,
            -8.2124480212918e-16
          ],
          [
            1.4250489995729966e-15,
            5.178392428114432e-15,
            -2.2134851863921897e-15
          ],
          [
            4.08419851886374e-16,
            0.21332677057000018,
            1.3683360462453542e-15
          ],
          [
            1.6234832457766368e-15,
            0.42417341052211716,
            1.5048755562298293e-15
          ],
          [
            9.842027091920581e-16,
            0.6302476759652716,
            2.0277740880756794e-15
          ],
          [
            1.4760361586427793e-15,
            0.8296047772995778,
            2.272158441585487e-16
          ],
          [
            1.6032701081164052e-15,
            1.0207618266838343,
            2.5122170972831064e-15
          ],
          [
            2.4471666303637447e-15,
            1.2027443344318802,
            8.574505555358666e-16
          ],
          [
            2.3784113558274935e-15,
            1.3750710780921378,
            8.07468154153781e-16
          ],
          [
            1.6663292808752677e-15,
            1.5376904008698353,
            4.2121349628712765e-16
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -1.9411832157373e-16,
            -1.5376904008698364,
            -1.0749517491738651e-15
          ],
          [
            1.8164902155643653e-16,
            -1.3750710780921338,
            -1.460528184806564e-15
          ],
          [
            1.0511651482326502e-15,
            -1.2027443344318836,
            9.371858181359843e-16
          ],
          [
            2.818859171206979e-16,
            -1.0207618266838312,
            -1.4726590782490216e-15
          ],
          [
            1.4329009105598356e-15,
            -0.8296047772995737,
            -1.0349227734914263e-15
          ],
          [
            1.859794321490534e-15,
            -0.6302476759652705,
            8.778866545627296e-16
          ],
          [
            1.092042093900951e-15,
            -0.42417341052212026,
            6.823822266887517e-16
          ],
          [
            7.702556172352793e-16,
            -0.21332677056999494,
            -8.2124480212918e-16
          ],
          [
            1.4250489995729966e-15,
            5.190292640122607e-15,
            -2.2134851863921897e-15
          ],
          [
            4.0841985188637396e-16,
            0.21332677057000018,
            1.3683360462453542e-15
          ],
          [
            1.6234832457766368e-15,
            0.42417341052211716,
            1.5048755562298293e-15
          ],
          [
            9.842027091920581e-16,
            0.6302476759652716,
            2.0277740880756794e-15
          ],
          [
            1.4760361586427793e-15,
            0.8296047772995778,
            2.2721584415854863e-16
          ],
          [
            1.6032701081164052e-15,
            1.0207618266838343,
            2.5122170972831064e-15
          ],
          [
            2.4471666303637447e-15,
            1.2027443344318802,
            8.574505555358666e-16
          ],
          [
            2.3784113558274935e-15,
            1.3750710780921378,
            8.07468154153781e-16
          ],
          [
            1.6663292808752677e-15,
            1.5376904008698353,
            4.2121349628712765e-16
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            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": [
          [
            -1.6653345369377348e-16,
            0.46230959913016356,
            -1.0547118733938987e-15
          ],
          [
            2.220446049250313e-16,
            -0.3750710780921338,
            -1.4432899320127035e-15
          ],
          [
            9.992007221626409e-16,
            -0.20274433443188355,
            8.881784197001252e-16
          ],
          [
            3.3306690738754696e-16,
            -0.020761826683831197,
            -1.4988010832439613e-15
          ],
          [
            1.4432899320127035e-15,
            0.17039522270042629,
            -1.0547118733938987e-15
          ],
          [
            1.887379141862766e-15,
            0.36975232403472946,
            8.881784197001252e-16
          ],
          [
            1.1102230246251565e-15,
            -0.42417341052212026,
            6.661338147750939e-16
          ],
          [
            7.771561172376096e-16,
            -0.21332677056999494,
            -8.326672684688674e-16
          ],
          [
            1.4432899320127035e-15,
            5.218048215738236e-15,
            -2.220446049250313e-15
          ],
          [
            4.440892098500626e-16,
            0.21332677057000016,
            1.3322676295501878e-15
          ],
          [
            1.6653345369377348e-15,
            0.4241734105221171,
            1.5543122344752192e-15
          ],
          [
            9.992007221626409e-16,
            -0.36975232403472846,
            1.9984014443252818e-15
          ],
          [
            1.4432899320127035e-15,
            -0.17039522270042218,
            2.220446049250313e-16
          ],
          [
            1.5543122344752192e-15,
            0.020761826683834306,
            2.55351295663786e-15
          ],
          [
            2.4424906541753444e-15,
            0.20274433443188022,
            8.881784197001252e-16
          ],
          [
            2.3314683517128287e-15,
            0.3750710780921378,
            7.771561172376096e-16
          ],
          [
            1.6653345369377348e-15,
            -0.46230959913016445,
            4.440892098500626e-16
          ]
        ]
      },
      "incoming_structure_ids": [
        "incoming_01_000",
        "incoming_01_001",
        "incoming_01_002",
        "incoming_01_003",
        "incoming_01_004",
        "incoming_01_005",
        "incoming_01_006",
        "incoming_01_007",
        "incoming_01_008"
      ],
      "reflected_structure_ids": [
        "reflected_01_001",
        "reflected_01_002",
        "reflected_01_003",
        "reflected_01_004",
        "reflected_01_005",
        "reflected_01_006",
        "reflected_01_007",
        "reflected_01_008"
      ]
    },
    {
      "orbit_id": 2,
      "formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.5,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        -0.5,
        -1.5,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -2.6228516944516336e-16,
              -1.5376904008698353,
              -9.427140653555809e-17
            ],
            "branch_aligned_reduced_polarization": [
              -2.7755575615628914e-16,
              -1.5376904008698353,
              -9.427140653555809e-17
            ],
            "target_residual": 0.5014185540222147,
            "energy_eV": -386.12474233416395,
            "max_atomic_step_A": 0.06830563219484577,
            "max_log_strain_component": 0.002342344379618949,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.700071647404039,
            "cell_principal_stretches": [
              1.0024420979378348,
              0.9999880784971457,
              0.997616626592466
            ],
            "cell_volume_ratio": 1.0000409819654663,
            "cell_rmsd_from_input_A": 0.013474176086717058
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.4933004322593051,
              -1.4732251489074468,
              0.00013123931422486453
            ],
            "branch_aligned_reduced_polarization": [
              -0.4933004322593051,
              -1.4732251489074468,
              0.00013123931422486453
            ],
            "target_residual": 0.027600617433277724,
            "energy_eV": -385.56919218031743,
            "max_atomic_step_A": 0.0012485448422943593,
            "max_log_strain_component": 5.817370625740123e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.700071647404039,
            "cell_principal_stretches": [
              1.002457989929514,
              0.9999970367013749,
              0.9975611513967729
            ],
            "cell_volume_ratio": 1.000010183323398,
            "cell_rmsd_from_input_A": 0.013670217990896232
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.4999632973177336,
              -1.5000272994088206,
              -1.1042310642142435e-05
            ],
            "branch_aligned_reduced_polarization": [
              -0.4999632973177336,
              -1.5000272994088206,
              -1.1042310642142435e-05
            ],
            "target_residual": 4.705610727442495e-05,
            "energy_eV": -385.5521069355469
          }
        ],
        "iterations": 2
      },
      "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": [
          -0.5,
          -1.5,
          0.0
        ],
        "formal_class": [
          0.5,
          0.5,
          0.0
        ],
        "target_residual": 4.705610727442495e-05,
        "parent_symmetrization_rmsd_A": 0.05660153205092474,
        "parent_cell_rmsd_A": 0.013670217990896232,
        "energy_eV": -385.5521069355469,
        "reduced_polarization": [
          -0.4999632973177336,
          -1.5000272994088206,
          -1.1042310642142435e-05
        ],
        "cartesian_polarization_e_A2": [
          -0.013144048526961915,
          -0.009438134670047178,
          0.0029992103698329702
        ],
        "ranking_score": 0.5601131987631977
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 3,
      "formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.5,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        -1.5,
        -0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -2.6228516944516336e-16,
              -1.5376904008698353,
              -9.427140653555809e-17
            ],
            "branch_aligned_reduced_polarization": [
              -2.6228516944516336e-16,
              -1.5376904008698353,
              -1.1102230246251565e-16
            ],
            "target_residual": 0.5014185540222149,
            "energy_eV": -386.12474233416395,
            "max_atomic_step_A": 0.04947636633169403,
            "max_log_strain_component": 0.0003698120104009577,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.700071647404039,
            "cell_principal_stretches": [
              1.0004024496599548,
              0.9999843969277933,
              0.9996542753974176
            ],
            "cell_volume_ratio": 1.000040981965503,
            "cell_rmsd_from_input_A": 0.0013810060861452944
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              1.0975720189205416e-05,
              -1.4905753911509672,
              -0.4978218977495096
            ],
            "branch_aligned_reduced_polarization": [
              1.0975720189205416e-05,
              -1.4905753911509672,
              -0.4978218977495096
            ],
            "target_residual": 0.00967302961007012,
            "energy_eV": -385.801014838007,
            "max_atomic_step_A": 0.0003507531286784812,
            "max_log_strain_component": 1.9677458859321255e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.700071647404039,
            "cell_principal_stretches": [
              1.000395402610062,
              0.999988309545049,
              0.9996469920304831
            ],
            "cell_volume_ratio": 1.0000305641113407,
            "cell_rmsd_from_input_A": 0.001347373159223977
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -1.4043387863430445e-06,
              -1.4999979165125883,
              -0.49999625057252856
            ],
            "branch_aligned_reduced_polarization": [
              -1.4043387863430445e-06,
              -1.4999979165125883,
              -0.49999625057252856
            ],
            "target_residual": 4.513456943983877e-06,
            "energy_eV": -385.7979778620385
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_03",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          -1.5,
          -0.5
        ],
        "formal_class": [
          0.0,
          0.5,
          0.5
        ],
        "target_residual": 4.513456943983877e-06,
        "parent_symmetrization_rmsd_A": 0.04078482677265549,
        "parent_cell_rmsd_A": 0.001347373159223977,
        "energy_eV": -385.7979778620385,
        "reduced_polarization": [
          -1.4043387863430445e-06,
          -1.4999979165125883,
          -0.49999625057252856
        ],
        "cartesian_polarization_e_A2": [
          -9.533368166021042e-07,
          -0.009407963292228061,
          -0.007585247932095827
        ],
        "ranking_score": 0.5411306969763494
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 4,
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.0,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        -0.5,
        -2.0,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -2.6228516944516336e-16,
              -1.5376904008698353,
              -9.427140653555809e-17
            ],
            "branch_aligned_reduced_polarization": [
              -2.7755575615628914e-16,
              -1.5376904008698353,
              -9.427140653555809e-17
            ],
            "target_residual": 0.6809773604517945,
            "energy_eV": -386.12474233416395,
            "max_atomic_step_A": 0.06989493186216346,
            "max_log_strain_component": 0.0023423443796221377,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.700071647404039,
            "cell_principal_stretches": [
              1.002177917038604,
              1.000141398966111,
              0.9971843600295446
            ],
            "cell_volume_ratio": 0.9994974527635387,
            "cell_rmsd_from_input_A": 0.014777321896557035
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.4898240664299147,
              -1.9657076441366175,
              5.9065876237553176e-05
            ],
            "branch_aligned_reduced_polarization": [
              -0.4898240664299147,
              -1.9657076441366175,
              5.9065876237553176e-05
            ],
            "target_residual": 0.0357703618022154,
            "energy_eV": -385.5382704528954,
            "max_atomic_step_A": 0.001775133923709445,
            "max_log_strain_component": 7.842164718599554e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.700071647404039,
            "cell_principal_stretches": [
              1.0022197715049599,
              1.000152481774915,
              0.9970902689829246
            ],
            "cell_volume_ratio": 0.9994559571336796,
            "cell_rmsd_from_input_A": 0.015270374291987557
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.49995112591654955,
              -2.0001180570130495,
              -1.4783309094292329e-05
            ],
            "branch_aligned_reduced_polarization": [
              -0.49995112591654955,
              -2.0001180570130495,
              -1.4783309094292329e-05
            ],
            "target_residual": 0.0001286261271711844,
            "energy_eV": -385.50778475567915
          }
        ],
        "iterations": 2
      },
      "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": [
          -0.5,
          -2.0,
          0.0
        ],
        "formal_class": [
          0.5,
          0.0,
          0.0
        ],
        "target_residual": 0.0001286261271711844,
        "parent_symmetrization_rmsd_A": 0.058503577201955925,
        "parent_cell_rmsd_A": 0.015270374291987557,
        "energy_eV": -385.50778475567915,
        "reduced_polarization": [
          -0.49995112591654955,
          -2.0001180570130495,
          -1.4783309094292329e-05
        ],
        "cartesian_polarization_e_A2": [
          -0.01316242736498415,
          -0.012567799659000478,
          0.0030060170072222004
        ],
        "ranking_score": 0.5625784230292952
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 5,
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.0,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        -2.0,
        -0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -2.6228516944516336e-16,
              -1.5376904008698353,
              -9.427140653555809e-17
            ],
            "branch_aligned_reduced_polarization": [
              -2.6228516944516336e-16,
              -1.5376904008698353,
              -1.1102230246251565e-16
            ],
            "target_residual": 0.6809773604517947,
            "energy_eV": -386.12474233416395,
            "max_atomic_step_A": 0.04964440071333297,
            "max_log_strain_component": 0.0009494941952026238,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.700071647404039,
            "cell_principal_stretches": [
              1.000466951537657,
              1.0000868705696242,
              0.9989441748740732
            ],
            "cell_volume_ratio": 0.9994974527635749,
            "cell_rmsd_from_input_A": 0.006149263787938828
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              9.372130847372654e-05,
              -1.986199660763093,
              -0.49494268532288077
            ],
            "branch_aligned_reduced_polarization": [
              9.372130847372654e-05,
              -1.986199660763093,
              -0.49494268532288077
            ],
            "target_residual": 0.014698114793427888,
            "energy_eV": -385.7712474103743,
            "max_atomic_step_A": 0.0006250577681449423,
            "max_log_strain_component": 3.0209877488945036e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.700071647404039,
            "cell_principal_stretches": [
              1.0004789362382271,
              1.000088345878723,
              0.9989147587141953
            ],
            "cell_volume_ratio": 0.9994814674592948,
            "cell_rmsd_from_input_A": 0.006338976360486576
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -2.04108659156514e-06,
              -2.0000285852570867,
              -0.4999937769055145
            ],
            "branch_aligned_reduced_polarization": [
              -2.04108659156514e-06,
              -2.0000285852570867,
              -0.4999937769055145
            ],
            "target_residual": 2.9325924745233525e-05,
            "energy_eV": -385.7625316693003
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_05",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          -2.0,
          -0.5
        ],
        "formal_class": [
          0.0,
          0.0,
          0.5
        ],
        "target_residual": 2.9325924745233525e-05,
        "parent_symmetrization_rmsd_A": 0.042947756329286116,
        "parent_cell_rmsd_A": 0.006338976360486576,
        "energy_eV": -385.7625316693003,
        "reduced_polarization": [
          -2.04108659156514e-06,
          -2.0000285852570867,
          -0.4999937769055145
        ],
        "cartesian_polarization_e_A2": [
          5.980044155174084e-07,
          -0.01253710484552225,
          -0.007592478622548487
        ],
        "ranking_score": 0.5445911522688982
      },
      "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,
        -1.5,
        -0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -2.6228516944516336e-16,
              -1.5376904008698353,
              -9.427140653555809e-17
            ],
            "branch_aligned_reduced_polarization": [
              -2.7755575615628914e-16,
              -1.5376904008698353,
              -1.1102230246251565e-16
            ],
            "target_residual": 0.7081105608008741,
            "energy_eV": -386.12474233416395,
            "max_atomic_step_A": 0.07844122474959393,
            "max_log_strain_component": 0.0023189092790016513,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.700071647404039,
            "cell_principal_stretches": [
              1.002359982083626,
              0.9999837850709822,
              0.9977026374727345
            ],
            "cell_volume_ratio": 1.0000409819654799,
            "cell_rmsd_from_input_A": 0.012789249579258683
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.49355031170352714,
              -1.4684989640252575,
              -0.49328046855384605
            ],
            "branch_aligned_reduced_polarization": [
              -0.49355031170352714,
              -1.4684989640252575,
              -0.49328046855384605
            ],
            "target_residual": 0.0328491377277933,
            "energy_eV": -385.4353607532644,
            "max_atomic_step_A": 0.0014792581162647296,
            "max_log_strain_component": 6.843714026322827e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.700071647404039,
            "cell_principal_stretches": [
              1.0023681916335807,
              0.9999981200931871,
              0.9976440174023951
            ],
            "cell_volume_ratio": 1.0000047496984235,
            "cell_rmsd_from_input_A": 0.012968657959253851
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.4999623535717144,
              -1.5000323452630773,
              -0.4999970342154993
            ],
            "branch_aligned_reduced_polarization": [
              -0.4999623535717144,
              -1.5000323452630773,
              -0.4999970342154993
            ],
            "target_residual": 4.97218813391403e-05,
            "energy_eV": -385.4151394149588
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_06",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          -0.5,
          -1.5,
          -0.5
        ],
        "formal_class": [
          0.5,
          0.5,
          0.5
        ],
        "target_residual": 4.97218813391403e-05,
        "parent_symmetrization_rmsd_A": 0.0625288327750536,
        "parent_cell_rmsd_A": 0.012968657959253851,
        "energy_eV": -385.4151394149588,
        "reduced_polarization": [
          -0.4999623535717144,
          -1.5000323452630773,
          -0.4999970342154993
        ],
        "cartesian_polarization_e_A2": [
          -0.013144961259470284,
          -0.009435087974949366,
          -0.004586175651714814
        ],
        "ranking_score": 0.5658704410275454
      },
      "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,
        -2.0,
        -0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -2.6228516944516336e-16,
              -1.5376904008698353,
              -9.427140653555809e-17
            ],
            "branch_aligned_reduced_polarization": [
              -2.7755575615628914e-16,
              -1.5376904008698353,
              -1.1102230246251565e-16
            ],
            "target_residual": 0.8448255236721326,
            "energy_eV": -386.12474233416395,
            "max_atomic_step_A": 0.07977158625125091,
            "max_log_strain_component": 0.00231890927900484,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.700071647404039,
            "cell_principal_stretches": [
              1.0020658922718255,
              1.0001922680562714,
              0.9972451172914577
            ],
            "cell_volume_ratio": 0.9994974527635518,
            "cell_rmsd_from_input_A": 0.014149940342490456
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.48993920283251363,
              -1.9613711466512669,
              -0.49064941624055186
            ],
            "branch_aligned_reduced_polarization": [
              -0.48993920283251363,
              -1.9613711466512669,
              -0.49064941624055186
            ],
            "target_residual": 0.04099806540954935,
            "energy_eV": -385.4017530847812,
            "max_atomic_step_A": 0.002036729132488863,
            "max_log_strain_component": 8.83516482579095e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.700071647404039,
            "cell_principal_stretches": [
              1.0021015904264874,
              1.0002090323006048,
              0.9971462361444333
            ],
            "cell_volume_ratio": 0.9994507029465258,
            "cell_rmsd_from_input_A": 0.014662200824133604
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.49995137863805456,
              -2.0001407056806007,
              -0.49999410584278325
            ],
            "branch_aligned_reduced_polarization": [
              -0.49995137863805456,
              -2.0001407056806007,
              -0.49999410584278325
            ],
            "target_residual": 0.00014898612848187516,
            "energy_eV": -385.3665430892972
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_07",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          -0.5,
          -2.0,
          -0.5
        ],
        "formal_class": [
          0.5,
          0.0,
          0.5
        ],
        "target_residual": 0.00014898612848187516,
        "parent_symmetrization_rmsd_A": 0.0643552591225508,
        "parent_cell_rmsd_A": 0.014662200824133604,
        "energy_eV": -385.3665430892972,
        "reduced_polarization": [
          -0.49995137863805456,
          -2.0001407056806007,
          -0.49999410584278325
        ],
        "cartesian_polarization_e_A2": [
          -0.013161784381418726,
          -0.012564826776404556,
          -0.004586601700421334
        ],
        "ranking_score": 0.5683187815855479
      },
      "branch_status": "awaiting_branch_sampling"
    }
  ],
  "sampled_polarization_branches": [
    {
      "orbit_id": 1,
      "candidate_id": "inversion_parent_endpoint_00",
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "construction": "MACEField-BEC-parent plus variable-cell P-N-P path and symmetric log-strain continuation beyond both polar endpoints",
      "geometry_diagnostics": {
        "collision_aware": false,
        "permutations_tested": 1,
        "selected_order": [
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          10,
          11,
          12,
          13,
          14,
          15,
          16,
          17,
          18,
          19,
          20,
          21,
          22,
          23,
          24,
          25,
          26,
          27,
          28,
          29,
          30,
          31,
          32,
          33,
          34,
          35,
          36,
          37,
          38,
          39,
          40,
          41,
          42,
          43,
          44,
          45,
          46,
          47
        ],
        "endpoint_rmsd_A": 0.05158377966427228,
        "minimum_distance_A_by_image": [
          1.7361615853037693,
          1.7361565644129568,
          1.736152212962508,
          1.7361485309574558,
          1.7361455184020596,
          1.7361431752998033,
          1.736141501653399,
          1.7361404974647818,
          1.7361401627351138
        ],
        "minimum_distance_A": 1.7361401627351138,
        "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": [
          633.0262731137962,
          633.0262731137962,
          633.0262731137962,
          633.0262731137962,
          633.0262731137962,
          633.0262731137962,
          633.0262731137962,
          633.0262731137962,
          633.0262731137962
        ],
        "cell_deformation_log_strain_norm": 0.0
      },
      "parent_reduced_polarization": [
        1.4250489995729966e-15,
        5.178392428114432e-15,
        -2.2134851863921897e-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": [
          -386.12474233416395,
          -386.1148352889438,
          -386.0858842908146,
          -386.0460056803393,
          -386.00249814164056,
          -385.9616719020203,
          -385.92866966581175,
          -385.9073009003769,
          -385.899913515565
        ],
        "cartesian_polarizations_e_A2": [
          [
            -5.097021904798562e-18,
            -0.009641219869919802,
            -1.5138453700721643e-17
          ],
          [
            4.7644142241337865e-18,
            -0.008621607179933318,
            -2.3235688703182263e-17
          ],
          [
            2.7590460962675016e-17,
            -0.007541129585642594,
            7.91701648607018e-18
          ],
          [
            7.395168604000833e-18,
            -0.0064001109718267975,
            -2.401990075101927e-17
          ],
          [
            3.760519862330697e-17,
            -0.00520156857229292,
            -2.4274630948439263e-17
          ],
          [
            4.881331381568235e-17,
            -0.003951612374669106,
            2.1754166551021138e-18
          ],
          [
            2.8662764981091166e-17,
            -0.0026595399903024367,
            3.808308712291803e-18
          ],
          [
            2.0214109225977626e-17,
            -0.0013375451248455556,
            -1.7066187575285355e-17
          ],
          [
            3.739663668547523e-17,
            3.246818731777027e-17,
            -4.209970099000362e-17
          ]
        ],
        "raw_reduced_polarization": [
          [
            -1.9411832157373e-16,
            -1.5376904008698364,
            -1.0749517491738651e-15
          ],
          [
            1.8164902155643655e-16,
            -1.3750710780921338,
            -1.460528184806564e-15
          ],
          [
            1.0511651482326502e-15,
            -1.2027443344318836,
            9.371858181359841e-16
          ],
          [
            2.818859171206979e-16,
            -1.0207618266838312,
            -1.4726590782490214e-15
          ],
          [
            1.4329009105598358e-15,
            -0.8296047772995737,
            -1.0349227734914263e-15
          ],
          [
            1.859794321490534e-15,
            -0.6302476759652705,
            8.778866545627298e-16
          ],
          [
            1.092042093900951e-15,
            -0.42417341052212026,
            6.823822266887517e-16
          ],
          [
            7.702556172352793e-16,
            -0.21332677056999494,
            -8.2124480212918e-16
          ],
          [
            1.4250489995729966e-15,
            5.178392428114432e-15,
            -2.2134851863921897e-15
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -1.9411832157373e-16,
            -1.5376904008698364,
            -1.0749517491738651e-15
          ],
          [
            1.8164902155643653e-16,
            -1.3750710780921338,
            -1.460528184806564e-15
          ],
          [
            1.0511651482326502e-15,
            -1.2027443344318836,
            9.371858181359843e-16
          ],
          [
            2.818859171206979e-16,
            -1.0207618266838312,
            -1.4726590782490216e-15
          ],
          [
            1.4329009105598356e-15,
            -0.8296047772995737,
            -1.0349227734914263e-15
          ],
          [
            1.859794321490534e-15,
            -0.6302476759652705,
            8.778866545627296e-16
          ],
          [
            1.092042093900951e-15,
            -0.42417341052212026,
            6.823822266887517e-16
          ],
          [
            7.702556172352793e-16,
            -0.21332677056999494,
            -8.2124480212918e-16
          ],
          [
            1.4250489995729966e-15,
            5.190292640122607e-15,
            -2.2134851863921897e-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": [
          [
            -1.6653345369377348e-16,
            0.46230959913016356,
            -1.0547118733938987e-15
          ],
          [
            2.220446049250313e-16,
            -0.3750710780921338,
            -1.4432899320127035e-15
          ],
          [
            9.992007221626409e-16,
            -0.20274433443188355,
            8.881784197001252e-16
          ],
          [
            3.3306690738754696e-16,
            -0.020761826683831197,
            -1.4988010832439613e-15
          ],
          [
            1.4432899320127035e-15,
            0.17039522270042629,
            -1.0547118733938987e-15
          ],
          [
            1.887379141862766e-15,
            0.36975232403472946,
            8.881784197001252e-16
          ],
          [
            1.1102230246251565e-15,
            -0.42417341052212026,
            6.661338147750939e-16
          ],
          [
            7.771561172376096e-16,
            -0.21332677056999494,
            -8.326672684688674e-16
          ],
          [
            1.4432899320127035e-15,
            5.218048215738236e-15,
            -2.220446049250313e-15
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -385.899913515565,
          -385.9073009003769,
          -385.9286696658118,
          -385.9616719020204,
          -386.0024981416407,
          -386.0460056803393,
          -386.0858842908146,
          -386.1148352889439,
          -386.12474233416395
        ],
        "cartesian_polarizations_e_A2": [
          [
            4.859269754039493e-17,
            -1.5057937050799856e-18,
            1.3186746993677372e-17
          ],
          [
            1.0722117705343004e-17,
            0.0013375451248455886,
            1.8304108890054516e-17
          ],
          [
            4.261250328330006e-17,
            0.0026595399903024176,
            1.309839064084388e-17
          ],
          [
            2.58352881550478e-17,
            0.003951612374669113,
            2.485603485121533e-17
          ],
          [
            3.873996990858822e-17,
            0.005201568572292945,
            -5.393474709688976e-18
          ],
          [
            4.208411966651991e-17,
            0.0064001109718268175,
            2.849507749284788e-17
          ],
          [
            6.422922393763343e-17,
            0.007541129585642573,
            -1.6518840432538048e-18
          ],
          [
            6.242459347506803e-17,
            0.008621607179933342,
            -1.998101002639046e-18
          ],
          [
            4.373474059941056e-17,
            0.009641219869919795,
            -3.591178611914419e-18
          ]
        ],
        "raw_reduced_polarization": [
          [
            1.8513304558177056e-15,
            -2.401609502979813e-16,
            1.600678717599507e-15
          ],
          [
            4.08419851886374e-16,
            0.21332677057000018,
            1.3683360462453542e-15
          ],
          [
            1.6234832457766368e-15,
            0.42417341052211716,
            1.5048755562298293e-15
          ],
          [
            9.842027091920581e-16,
            0.6302476759652716,
            2.0277740880756794e-15
          ],
          [
            1.4760361586427793e-15,
            0.8296047772995778,
            2.272158441585487e-16
          ],
          [
            1.6032701081164052e-15,
            1.0207618266838343,
            2.5122170972831064e-15
          ],
          [
            2.4471666303637447e-15,
            1.2027443344318802,
            8.574505555358666e-16
          ],
          [
            2.3784113558274935e-15,
            1.3750710780921378,
            8.07468154153781e-16
          ],
          [
            1.6663292808752677e-15,
            1.5376904008698353,
            4.2121349628712765e-16
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            1.8513304558177056e-15,
            -2.401609502979813e-16,
            1.600678717599507e-15
          ],
          [
            4.0841985188637396e-16,
            0.21332677057000018,
            1.3683360462453542e-15
          ],
          [
            1.6234832457766368e-15,
            0.42417341052211716,
            1.5048755562298293e-15
          ],
          [
            9.842027091920581e-16,
            0.6302476759652716,
            2.0277740880756794e-15
          ],
          [
            1.4760361586427793e-15,
            0.8296047772995778,
            2.2721584415854863e-16
          ],
          [
            1.6032701081164052e-15,
            1.0207618266838343,
            2.5122170972831064e-15
          ],
          [
            2.4471666303637447e-15,
            1.2027443344318802,
            8.574505555358666e-16
          ],
          [
            2.3784113558274935e-15,
            1.3750710780921378,
            8.07468154153781e-16
          ],
          [
            1.6663292808752677e-15,
            1.5376904008698353,
            4.2121349628712765e-16
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          3.044216320719723e-15,
          1.5376904008698467,
          -3.352018623610515e-15
        ],
        "actual_opposite_endpoint_branch_residual": 1.2015617097352483e-14
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            -1.9411832157373e-16,
            -1.5376904008698364,
            -1.0749517491738651e-15
          ],
          [
            1.8164902155643655e-16,
            -1.3750710780921338,
            -1.460528184806564e-15
          ],
          [
            1.0511651482326502e-15,
            -1.2027443344318836,
            9.371858181359841e-16
          ],
          [
            2.818859171206979e-16,
            -1.0207618266838312,
            -1.4726590782490214e-15
          ],
          [
            1.4329009105598358e-15,
            -0.8296047772995737,
            -1.0349227734914263e-15
          ],
          [
            1.859794321490534e-15,
            -0.6302476759652705,
            8.778866545627298e-16
          ],
          [
            1.092042093900951e-15,
            -0.42417341052212026,
            6.823822266887517e-16
          ],
          [
            7.702556172352793e-16,
            -0.21332677056999494,
            -8.2124480212918e-16
          ],
          [
            1.4250489995729966e-15,
            5.178392428114432e-15,
            -2.2134851863921897e-15
          ],
          [
            4.08419851886374e-16,
            0.21332677057000018,
            1.3683360462453542e-15
          ],
          [
            1.6234832457766368e-15,
            0.42417341052211716,
            1.5048755562298293e-15
          ],
          [
            9.842027091920581e-16,
            0.6302476759652716,
            2.0277740880756794e-15
          ],
          [
            1.4760361586427793e-15,
            0.8296047772995778,
            2.272158441585487e-16
          ],
          [
            1.6032701081164052e-15,
            1.0207618266838343,
            2.5122170972831064e-15
          ],
          [
            2.4471666303637447e-15,
            1.2027443344318802,
            8.574505555358666e-16
          ],
          [
            2.3784113558274935e-15,
            1.3750710780921378,
            8.07468154153781e-16
          ],
          [
            1.6663292808752677e-15,
            1.5376904008698353,
            4.2121349628712765e-16
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -1.9411832157373e-16,
            -1.5376904008698364,
            -1.0749517491738651e-15
          ],
          [
            1.8164902155643653e-16,
            -1.3750710780921338,
            -1.460528184806564e-15
          ],
          [
            1.0511651482326502e-15,
            -1.2027443344318836,
            9.371858181359843e-16
          ],
          [
            2.818859171206979e-16,
            -1.0207618266838312,
            -1.4726590782490216e-15
          ],
          [
            1.4329009105598356e-15,
            -0.8296047772995737,
            -1.0349227734914263e-15
          ],
          [
            1.859794321490534e-15,
            -0.6302476759652705,
            8.778866545627296e-16
          ],
          [
            1.092042093900951e-15,
            -0.42417341052212026,
            6.823822266887517e-16
          ],
          [
            7.702556172352793e-16,
            -0.21332677056999494,
            -8.2124480212918e-16
          ],
          [
            1.4250489995729966e-15,
            5.190292640122607e-15,
            -2.2134851863921897e-15
          ],
          [
            4.0841985188637396e-16,
            0.21332677057000018,
            1.3683360462453542e-15
          ],
          [
            1.6234832457766368e-15,
            0.42417341052211716,
            1.5048755562298293e-15
          ],
          [
            9.842027091920581e-16,
            0.6302476759652716,
            2.0277740880756794e-15
          ],
          [
            1.4760361586427793e-15,
            0.8296047772995778,
            2.2721584415854863e-16
          ],
          [
            1.6032701081164052e-15,
            1.0207618266838343,
            2.5122170972831064e-15
          ],
          [
            2.4471666303637447e-15,
            1.2027443344318802,
            8.574505555358666e-16
          ],
          [
            2.3784113558274935e-15,
            1.3750710780921378,
            8.07468154153781e-16
          ],
          [
            1.6663292808752677e-15,
            1.5376904008698353,
            4.2121349628712765e-16
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            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": [
          [
            -1.6653345369377348e-16,
            0.46230959913016356,
            -1.0547118733938987e-15
          ],
          [
            2.220446049250313e-16,
            -0.3750710780921338,
            -1.4432899320127035e-15
          ],
          [
            9.992007221626409e-16,
            -0.20274433443188355,
            8.881784197001252e-16
          ],
          [
            3.3306690738754696e-16,
            -0.020761826683831197,
            -1.4988010832439613e-15
          ],
          [
            1.4432899320127035e-15,
            0.17039522270042629,
            -1.0547118733938987e-15
          ],
          [
            1.887379141862766e-15,
            0.36975232403472946,
            8.881784197001252e-16
          ],
          [
            1.1102230246251565e-15,
            -0.42417341052212026,
            6.661338147750939e-16
          ],
          [
            7.771561172376096e-16,
            -0.21332677056999494,
            -8.326672684688674e-16
          ],
          [
            1.4432899320127035e-15,
            5.218048215738236e-15,
            -2.220446049250313e-15
          ],
          [
            4.440892098500626e-16,
            0.21332677057000016,
            1.3322676295501878e-15
          ],
          [
            1.6653345369377348e-15,
            0.4241734105221171,
            1.5543122344752192e-15
          ],
          [
            9.992007221626409e-16,
            -0.36975232403472846,
            1.9984014443252818e-15
          ],
          [
            1.4432899320127035e-15,
            -0.17039522270042218,
            2.220446049250313e-16
          ],
          [
            1.5543122344752192e-15,
            0.020761826683834306,
            2.55351295663786e-15
          ],
          [
            2.4424906541753444e-15,
            0.20274433443188022,
            8.881784197001252e-16
          ],
          [
            2.3314683517128287e-15,
            0.3750710780921378,
            7.771561172376096e-16
          ],
          [
            1.6653345369377348e-15,
            -0.46230959913016445,
            4.440892098500626e-16
          ]
        ]
      },
      "incoming_structure_ids": [
        "incoming_01_000",
        "incoming_01_001",
        "incoming_01_002",
        "incoming_01_003",
        "incoming_01_004",
        "incoming_01_005",
        "incoming_01_006",
        "incoming_01_007",
        "incoming_01_008"
      ],
      "reflected_structure_ids": [
        "reflected_01_001",
        "reflected_01_002",
        "reflected_01_003",
        "reflected_01_004",
        "reflected_01_005",
        "reflected_01_006",
        "reflected_01_007",
        "reflected_01_008"
      ],
      "positive_extension_structure_ids": [
        "extension_plus_01_000",
        "extension_plus_01_001",
        "extension_plus_01_002",
        "extension_plus_01_003"
      ],
      "negative_extension_structure_ids": [
        "extension_minus_01_000",
        "extension_minus_01_001",
        "extension_minus_01_002",
        "extension_minus_01_003"
      ],
      "extension": {
        "enabled": true,
        "fraction_beyond_polar_endpoint": 0.35,
        "images_per_side": 4,
        "construction": "continue fractional atomic displacements and symmetric log strain beyond +P; reflect these structures about N for the -P side",
        "positive_path_coordinates": [
          1.35,
          1.2625,
          1.175,
          1.0875
        ],
        "negative_path_coordinates": [
          -1.0875,
          -1.175,
          -1.2625,
          -1.35
        ]
      },
      "branch_coordinates": [
        1.35,
        1.2625,
        1.175,
        1.0875,
        1.0,
        0.875,
        0.75,
        0.625,
        0.5,
        0.375,
        0.25,
        0.125,
        0.0,
        -0.125,
        -0.25,
        -0.375,
        -0.5,
        -0.625,
        -0.75,
        -0.875,
        -1.0,
        -1.0875,
        -1.175,
        -1.2625,
        -1.35
      ],
      "parent": {
        "candidate_id": "inversion_parent_endpoint_00",
        "source": "same_species_inversion_center_projection_from_endpoint",
        "spacegroup": "C2/m",
        "spacegroup_number": 12,
        "pointgroup": "2/m",
        "has_inversion": true,
        "is_polar_point_group": false,
        "nonpolar_parent_hypothesis": true,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.0
        ],
        "formal_class": [
          0.0,
          0.0,
          0.0
        ],
        "target_residual": 3.139531961188814e-15,
        "parent_symmetrization_rmsd_A": 0.05158377966427228,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -385.89991351556506,
        "reduced_polarization": [
          2.9969978850182787e-15,
          9.033838790403982e-16,
          -2.4199623883847575e-16
        ],
        "cartesian_polarization_e_A2": [
          7.86575717993945e-17,
          5.664158792851033e-18,
          -2.161683180431325e-17
        ],
        "ranking_score": 0.05158377966427856
      }
    }
  ],
  "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": 57,
      "full_response": 16,
      "energy_polarization": 41
    },
    "model_evaluations_for_recovery_and_path_properties": {
      "total": 82,
      "full_response": 41,
      "energy_polarization": 41
    },
    "elapsed_seconds": 1132.5695048809866
  }
}
