{
  "schema": "ferrofinder.endpoint_parent_recovery.v4_variable_cell",
  "status": "complete",
  "input_atom_count": 48,
  "input_formula": "B12Ge4O28Rb4",
  "input_spacegroup": "Pna2_1",
  "input_pointgroup": "mm2",
  "input_is_polar_point_group": true,
  "input_energy_eV": -334.54992185041044,
  "input_cartesian_polarization_e_A2": [
    0.0014839307800336426,
    3.2376724300526665e-08,
    -2.430975292794956e-08
  ],
  "input_reduced_polarization": [
    0.13546227625806903,
    2.1940701545652147e-06,
    -1.6262818256791284e-06
  ],
  "input_formal_targets": [
    {
      "orbit_id": 0,
      "representative_formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ]
    },
    {
      "orbit_id": 1,
      "representative_formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.0
      ]
    },
    {
      "orbit_id": 2,
      "representative_formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.0
      ]
    },
    {
      "orbit_id": 3,
      "representative_formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        -0.5
      ]
    },
    {
      "orbit_id": 4,
      "representative_formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        0.5,
        0.5,
        0.0
      ]
    },
    {
      "orbit_id": 5,
      "representative_formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        0.5,
        0.0,
        -0.5
      ]
    },
    {
      "orbit_id": 6,
      "representative_formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        -0.5
      ]
    },
    {
      "orbit_id": 7,
      "representative_formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "target_reduced_polarization": [
        0.5,
        0.5,
        -0.5
      ]
    }
  ],
  "parent_candidates": [
    {
      "candidate_id": "inversion_parent_endpoint_00",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "Pnma",
      "spacegroup_number": 62,
      "pointgroup": "mmm",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 1.0297109248924743e-15,
      "parent_symmetrization_rmsd_A": 0.4626960473186446,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -327.14031682815556,
      "reduced_polarization": [
        -6.316446726058668e-16,
        7.985654185494127e-16,
        -1.536973282413959e-16
      ],
      "cartesian_polarization_e_A2": [
        -6.919394813198304e-18,
        1.178400441686539e-17,
        -2.2974763760112843e-18
      ],
      "ranking_score": 0.46269604731864666
    },
    {
      "candidate_id": "inversion_parent_endpoint_01",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "Pnma",
      "spacegroup_number": 62,
      "pointgroup": "mmm",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 1.5465105160244726e-15,
      "parent_symmetrization_rmsd_A": 0.5373127072978343,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -291.1784732231192,
      "reduced_polarization": [
        5.021648994995979e-16,
        2.7757914663079127e-16,
        -1.4361319602461889e-15
      ],
      "cartesian_polarization_e_A2": [
        5.500999773548145e-18,
        4.096087576480212e-18,
        -2.1467381959419993e-17
      ],
      "ranking_score": 0.5373127072978374
    },
    {
      "candidate_id": "bec_projection_00",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Pna2_1",
      "spacegroup_number": 33,
      "pointgroup": "mm2",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 0.0007772946543809111,
      "parent_symmetrization_rmsd_A": 0.009335191423146911,
      "parent_cell_rmsd_A": 0.014933268227744139,
      "energy_eV": -334.4505464608157,
      "reduced_polarization": [
        -0.0007772946541592607,
        1.04277280835252e-08,
        -1.5357015446898128e-08
      ],
      "cartesian_polarization_e_A2": [
        -8.495845997405936e-06,
        1.5353496572759316e-10,
        -2.294838356782259e-10
      ],
      "ranking_score": 0.5146230977888447
    },
    {
      "candidate_id": "inversion_parent_bec_00_00",
      "source": "same_species_inversion_center_projection_after_BEC",
      "spacegroup": "Pnma",
      "spacegroup_number": 62,
      "pointgroup": "mmm",
      "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": 3.971091069679407e-15,
      "parent_symmetrization_rmsd_A": 0.4626970720702079,
      "parent_cell_rmsd_A": 0.014933268227744139,
      "energy_eV": -327.02841130032533,
      "reduced_polarization": [
        2.0897817939102347e-15,
        -1.225183173051811e-15,
        -3.146633523307021e-15
      ],
      "cartesian_polarization_e_A2": [
        2.2841358006876973e-17,
        -1.809937555811815e-17,
        -4.711771866605184e-17
      ],
      "ranking_score": 0.46643038912715185
    },
    {
      "candidate_id": "inversion_parent_bec_00_01",
      "source": "same_species_inversion_center_projection_after_BEC",
      "spacegroup": "Pnma",
      "spacegroup_number": 62,
      "pointgroup": "mmm",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 2.118582621476689e-15,
      "parent_symmetrization_rmsd_A": 0.5373146034091983,
      "parent_cell_rmsd_A": 0.014933268227744139,
      "energy_eV": -292.28418899634903,
      "reduced_polarization": [
        3.218084229239341e-16,
        1.1556160319232306e-15,
        -1.7462483356385074e-15
      ],
      "cartesian_polarization_e_A2": [
        3.5173749221737804e-18,
        1.7071676290213078e-17,
        -2.6148337803337902e-17
      ],
      "ranking_score": 0.5410479204661386
    },
    {
      "candidate_id": "bec_projection_01",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Pna2_1",
      "spacegroup_number": 33,
      "pointgroup": "mm2",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.0
      ],
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_residual": 1.4643386556290992e-05,
      "parent_symmetrization_rmsd_A": 0.025340081292502103,
      "parent_cell_rmsd_A": 0.040963594704561034,
      "energy_eV": -333.9640419142738,
      "reduced_polarization": [
        0.4999853566134445,
        -1.523516841485428e-10,
        1.5074712163265874e-11
      ],
      "cartesian_polarization_e_A2": [
        0.005510897827534485,
        3.042629228543637e-10,
        -2.4858808134202656e-10
      ],
      "ranking_score": 0.5356102667417549
    },
    {
      "candidate_id": "bec_projection_02",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Pc",
      "spacegroup_number": 7,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.0
      ],
      "formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_residual": 6.885581815871e-05,
      "parent_symmetrization_rmsd_A": 0.0551603370719698,
      "parent_cell_rmsd_A": 0.0994988469561032,
      "energy_eV": -331.55919048391877,
      "reduced_polarization": [
        -2.9269422237233998e-05,
        0.4999376748476445,
        2.620074865460304e-10
      ],
      "cartesian_polarization_e_A2": [
        -0.00010137708357999582,
        0.0073870729756531,
        -2.0559706488210205e-10
      ],
      "ranking_score": 0.580172760447313
    },
    {
      "candidate_id": "bec_projection_03",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Pc",
      "spacegroup_number": 7,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        -0.5
      ],
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_residual": 0.00015452431253808332,
      "parent_symmetrization_rmsd_A": 0.05504686176845809,
      "parent_cell_rmsd_A": 0.12260871610612492,
      "energy_eV": -331.3561915788283,
      "reduced_polarization": [
        1.1174172973003039e-05,
        2.979332978853831e-10,
        -0.4998458802380496
      ],
      "cartesian_polarization_e_A2": [
        -0.0001245902262563966,
        1.8914251740045735e-10,
        -0.007488535666132451
      ],
      "ranking_score": 0.5860080894200654
    },
    {
      "candidate_id": "bec_projection_04",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Pc",
      "spacegroup_number": 7,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.5,
        0.5,
        0.0
      ],
      "formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_residual": 1.6157274213613833e-05,
      "parent_symmetrization_rmsd_A": 0.05932729660297025,
      "parent_cell_rmsd_A": 0.1044435876563764,
      "energy_eV": -330.85520165447844,
      "reduced_polarization": [
        0.5000145109738542,
        0.49999289442839623,
        -2.616015358937456e-11
      ],
      "cartesian_polarization_e_A2": [
        0.0054114134486861,
        0.007283606347088763,
        -3.012552974972097e-10
      ],
      "ranking_score": 0.5854705080654916
    },
    {
      "candidate_id": "bec_projection_05",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Pc",
      "spacegroup_number": 7,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.5,
        0.0,
        -0.5
      ],
      "formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_residual": 2.6827647166917646e-05,
      "parent_symmetrization_rmsd_A": 0.058307550508052024,
      "parent_cell_rmsd_A": 0.12310010924964974,
      "energy_eV": -330.4999160421731,
      "reduced_polarization": [
        0.5000222706553931,
        -1.550673627145247e-10,
        -0.4999850420402176
      ],
      "cartesian_polarization_e_A2": [
        0.005389754305039227,
        4.722928103559158e-10,
        -0.007353317007650626
      ],
      "ranking_score": 0.5891362331147982
    },
    {
      "candidate_id": "bec_projection_06",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.5,
        -0.5
      ],
      "formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_residual": 1.219715744217489e-05,
      "parent_symmetrization_rmsd_A": 0.07841971270631937,
      "parent_cell_rmsd_A": 0.16042759081439947,
      "energy_eV": -328.00431975880383,
      "reduced_polarization": [
        5.2994498321361e-06,
        0.49999371103034757,
        -0.4999909924841462
      ],
      "cartesian_polarization_e_A2": [
        -0.00023010277271347707,
        0.007391088662090537,
        -0.007493914550343838
      ],
      "ranking_score": 0.6185510047248036
    },
    {
      "candidate_id": "bec_projection_07",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.5,
        0.5,
        -0.5
      ],
      "formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "target_residual": 0.00048563969123748614,
      "parent_symmetrization_rmsd_A": 0.0797898104017401,
      "parent_cell_rmsd_A": 0.15766673871274922,
      "energy_eV": -326.96215477473834,
      "reduced_polarization": [
        0.5003149860727905,
        0.4997285129587455,
        -0.49974915249635654
      ],
      "cartesian_polarization_e_A2": [
        0.0052905302449068915,
        0.007281506383606852,
        -0.007351171399594692
      ],
      "ranking_score": 0.6201777744624024
    }
  ],
  "formal_branches": [
    {
      "orbit_id": 0,
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.0,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              0.13546227625806903,
              2.1940701545652147e-06,
              -1.6262818256791284e-06
            ],
            "branch_aligned_reduced_polarization": [
              0.13546227625806903,
              2.1940701545652147e-06,
              -1.6262818256791284e-06
            ],
            "target_residual": 0.1354622762855997,
            "energy_eV": -334.54992185041044,
            "max_atomic_step_A": 0.011672023043632443,
            "max_log_strain_component": 0.0025419050948939635,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.714187706743173,
            "cell_principal_stretches": [
              1.0014372230358368,
              1.000807597538878,
              0.9974613228084247
            ],
            "cell_volume_ratio": 0.999701602259497,
            "cell_rmsd_from_input_A": 0.014933268227744139
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.0007772946541592607,
              1.04277280835252e-08,
              -1.5357015446898128e-08
            ],
            "branch_aligned_reduced_polarization": [
              -0.0007772946541592607,
              1.04277280835252e-08,
              -1.5357015446898128e-08
            ],
            "target_residual": 0.0007772946543809111,
            "energy_eV": -334.4505464608157
          }
        ],
        "iterations": 1
      },
      "parent": {
        "candidate_id": "inversion_parent_endpoint_00",
        "source": "same_species_inversion_center_projection_from_endpoint",
        "spacegroup": "Pnma",
        "spacegroup_number": 62,
        "pointgroup": "mmm",
        "has_inversion": true,
        "is_polar_point_group": false,
        "nonpolar_parent_hypothesis": true,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.0
        ],
        "formal_class": [
          0.0,
          0.0,
          0.0
        ],
        "target_residual": 1.0297109248924743e-15,
        "parent_symmetrization_rmsd_A": 0.4626960473186446,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -327.14031682815556,
        "reduced_polarization": [
          -6.316446726058668e-16,
          7.985654185494127e-16,
          -1.536973282413959e-16
        ],
        "cartesian_polarization_e_A2": [
          -6.919394813198304e-18,
          1.178400441686539e-17,
          -2.2974763760112843e-18
        ],
        "ranking_score": 0.46269604731864666
      },
      "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": [
          -334.54992185041044,
          -334.2386518748061,
          -333.3914995847132,
          -332.1649070152864,
          -330.75128158520755,
          -329.35788364462894,
          -328.18755818001233,
          -327.41146218376895,
          -327.14031682815556
        ],
        "cartesian_polarizations_e_A2": [
          [
            0.0014839307800336428,
            3.2376724293488615e-08,
            -2.430975291399212e-08
          ],
          [
            0.0014015001645029585,
            2.8904033854556713e-08,
            -2.1445571883813362e-08
          ],
          [
            0.0012901107111764156,
            2.5117780624832187e-08,
            -1.858271942166246e-08
          ],
          [
            0.0011441833130418418,
            2.1112627052070264e-08,
            -1.5647534403468272e-08
          ],
          [
            0.0009631818115848473,
            1.6934084794229643e-08,
            -1.2598398992641836e-08
          ],
          [
            0.000748762601224471,
            1.2664950674351942e-08,
            -9.477405275753404e-09
          ],
          [
            0.0005120600355619471,
            8.401308705916619e-09,
            -6.310832606388645e-09
          ],
          [
            0.0002604815767124793,
            4.184419550343299e-09,
            -3.148639439495589e-09
          ],
          [
            -2.0245836421470332e-17,
            -5.792229173324224e-18,
            1.7392866931071342e-17
          ]
        ],
        "raw_reduced_polarization": [
          [
            0.13546227625806903,
            2.1940701540882674e-06,
            -1.6262818247453989e-06
          ],
          [
            0.12793750558589048,
            1.958736697331479e-06,
            -1.434672902653918e-06
          ],
          [
            0.11776919510821889,
            1.7021540630953898e-06,
            -1.2431528595421735e-06
          ],
          [
            0.10444804981916525,
            1.4307372317668348e-06,
            -1.0467938893690656e-06
          ],
          [
            0.087925125890775,
            1.14757038720225e-06,
            -8.428118284506066e-07
          ],
          [
            0.06835162913493859,
            8.582644132156434e-07,
            -6.340225670016003e-07
          ],
          [
            0.046743971438099385,
            5.69330625292464e-07,
            -4.2218414983861217e-07
          ],
          [
            0.023778351240859967,
            2.8356513044273857e-07,
            -2.1063871406858005e-07
          ],
          [
            -1.848163757570089e-15,
            -3.925214002389333e-16,
            1.1635537173204267e-15
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            0.13546227625806903,
            2.1940701540882674e-06,
            -1.6262818247453989e-06
          ],
          [
            0.12793750558589048,
            1.958736697331479e-06,
            -1.434672902653918e-06
          ],
          [
            0.11776919510821889,
            1.7021540630953898e-06,
            -1.2431528595421735e-06
          ],
          [
            0.10444804981916525,
            1.4307372317668348e-06,
            -1.0467938893690656e-06
          ],
          [
            0.087925125890775,
            1.14757038720225e-06,
            -8.428118284506066e-07
          ],
          [
            0.06835162913493859,
            8.582644132156434e-07,
            -6.340225670016003e-07
          ],
          [
            0.046743971438099385,
            5.69330625292464e-07,
            -4.2218414983861217e-07
          ],
          [
            0.023778351240859967,
            2.8356513044273857e-07,
            -2.1063871406858005e-07
          ],
          [
            -1.8492152253912764e-15,
            -3.925214205047472e-16,
            1.1635537277617246e-15
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            0.13546227625806906,
            2.194070154115657e-06,
            -1.6262818247625432e-06
          ],
          [
            0.12793750558589045,
            1.958736697282859e-06,
            -1.4346729026448735e-06
          ],
          [
            0.11776919510821893,
            1.7021540631434462e-06,
            -1.2431528595424624e-06
          ],
          [
            0.10444804981916522,
            1.4307372318000944e-06,
            -1.046793889347697e-06
          ],
          [
            0.08792512589077495,
            1.1475703871610676e-06,
            -8.428118284387054e-07
          ],
          [
            0.06835162913493864,
            8.582644132060224e-07,
            -6.340225670031785e-07
          ],
          [
            0.046743971438099385,
            5.693306253107266e-07,
            -4.221841498619483e-07
          ],
          [
            0.02377835124085992,
            2.835651304877729e-07,
            -2.10638714082112e-07
          ],
          [
            -1.8318679906315083e-15,
            -3.885780586188048e-16,
            1.1102230246251565e-15
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -327.14031682815556,
          -327.41146218376895,
          -328.18755818001245,
          -329.3578836446288,
          -330.7512815852075,
          -332.16490701528625,
          -333.39149958471313,
          -334.2386518748061,
          -334.5499218504105
        ],
        "cartesian_polarizations_e_A2": [
          [
            -2.2359946138363343e-17,
            -7.895552616151455e-18,
            1.5089997418027167e-17
          ],
          [
            -0.00026048157671250573,
            -4.1844195747849965e-09,
            3.1486394532049434e-09
          ],
          [
            -0.0005120600355619471,
            -8.401308699444854e-09,
            6.310832582874568e-09
          ],
          [
            -0.0007487626012244558,
            -1.2664950700271359e-08,
            9.47740527734438e-09
          ],
          [
            -0.0009631818115848797,
            -1.693408482613005e-08,
            1.259839900452022e-08
          ],
          [
            -0.0011441833130418904,
            -2.1112627086656452e-08,
            1.5647534408769725e-08
          ],
          [
            -0.0012901107111764083,
            -2.5117780628240647e-08,
            1.858271943106674e-08
          ],
          [
            -0.001401500164502948,
            -2.8904033840324224e-08,
            2.1445571892767318e-08
          ],
          [
            -0.0014839307800336742,
            -3.23767242981375e-08,
            2.430975292183644e-08
          ]
        ],
        "raw_reduced_polarization": [
          [
            -2.041152620907189e-15,
            -5.350571042363112e-16,
            1.009495597228699e-15
          ],
          [
            -0.023778351240862382,
            -2.8356513209907656e-07,
            2.1063871498571295e-07
          ],
          [
            -0.046743971438099385,
            -5.693306248538924e-07,
            4.221841482655597e-07
          ],
          [
            -0.0683516291349372,
            -8.582644149721219e-07,
            6.34022567108034e-07
          ],
          [
            -0.08792512589077797,
            -1.1475703893640415e-06,
            8.428118292452507e-07
          ],
          [
            -0.10444804981916969,
            -1.4307372341106336e-06,
            1.046793889723724e-06
          ],
          [
            -0.11776919510821823,
            -1.7021540633263706e-06,
            1.2431528601713045e-06
          ],
          [
            -0.1279375055858895,
            -1.9587366963669873e-06,
            1.4346729032529226e-06
          ],
          [
            -0.13546227625807192,
            -2.1940701544033086e-06,
            1.6262818252701707e-06
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -2.041152620907189e-15,
            -5.350571042363112e-16,
            1.009495597228699e-15
          ],
          [
            -0.023778351240862382,
            -2.8356513209907656e-07,
            2.1063871498571295e-07
          ],
          [
            -0.046743971438099385,
            -5.693306248538924e-07,
            4.221841482655597e-07
          ],
          [
            -0.0683516291349372,
            -8.582644149721219e-07,
            6.34022567108034e-07
          ],
          [
            -0.08792512589077797,
            -1.1475703893640415e-06,
            8.428118292452507e-07
          ],
          [
            -0.10444804981916969,
            -1.4307372341106336e-06,
            1.046793889723724e-06
          ],
          [
            -0.11776919510821823,
            -1.7021540633263706e-06,
            1.2431528601713045e-06
          ],
          [
            -0.1279375055858895,
            -1.9587366963669873e-06,
            1.4346729032529226e-06
          ],
          [
            -0.13546227625807192,
            -2.1940701544033086e-06,
            1.6262818252701707e-06
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          -0.13546227625807275,
          -2.1940701548733107e-06,
          1.6262818270725065e-06
        ],
        "actual_opposite_endpoint_branch_residual": 2.04025756349987e-15
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            0.13546227625806903,
            2.1940701540882674e-06,
            -1.6262818247453989e-06
          ],
          [
            0.12793750558589048,
            1.958736697331479e-06,
            -1.434672902653918e-06
          ],
          [
            0.11776919510821889,
            1.7021540630953898e-06,
            -1.2431528595421735e-06
          ],
          [
            0.10444804981916525,
            1.4307372317668348e-06,
            -1.0467938893690656e-06
          ],
          [
            0.087925125890775,
            1.14757038720225e-06,
            -8.428118284506066e-07
          ],
          [
            0.06835162913493859,
            8.582644132156434e-07,
            -6.340225670016003e-07
          ],
          [
            0.046743971438099385,
            5.69330625292464e-07,
            -4.2218414983861217e-07
          ],
          [
            0.023778351240859967,
            2.8356513044273857e-07,
            -2.1063871406858005e-07
          ],
          [
            -1.848163757570089e-15,
            -3.925214002389333e-16,
            1.1635537173204267e-15
          ],
          [
            -0.023778351240862382,
            -2.8356513209907656e-07,
            2.1063871498571295e-07
          ],
          [
            -0.046743971438099385,
            -5.693306248538924e-07,
            4.221841482655597e-07
          ],
          [
            -0.0683516291349372,
            -8.582644149721219e-07,
            6.34022567108034e-07
          ],
          [
            -0.08792512589077797,
            -1.1475703893640415e-06,
            8.428118292452507e-07
          ],
          [
            -0.10444804981916969,
            -1.4307372341106336e-06,
            1.046793889723724e-06
          ],
          [
            -0.11776919510821823,
            -1.7021540633263706e-06,
            1.2431528601713045e-06
          ],
          [
            -0.1279375055858895,
            -1.9587366963669873e-06,
            1.4346729032529226e-06
          ],
          [
            -0.13546227625807192,
            -2.1940701544033086e-06,
            1.6262818252701707e-06
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            0.13546227625806903,
            2.1940701540882674e-06,
            -1.6262818247453989e-06
          ],
          [
            0.12793750558589048,
            1.958736697331479e-06,
            -1.434672902653918e-06
          ],
          [
            0.11776919510821889,
            1.7021540630953898e-06,
            -1.2431528595421735e-06
          ],
          [
            0.10444804981916525,
            1.4307372317668348e-06,
            -1.0467938893690656e-06
          ],
          [
            0.087925125890775,
            1.14757038720225e-06,
            -8.428118284506066e-07
          ],
          [
            0.06835162913493859,
            8.582644132156434e-07,
            -6.340225670016003e-07
          ],
          [
            0.046743971438099385,
            5.69330625292464e-07,
            -4.2218414983861217e-07
          ],
          [
            0.023778351240859967,
            2.8356513044273857e-07,
            -2.1063871406858005e-07
          ],
          [
            -1.8492152253912764e-15,
            -3.925214205047472e-16,
            1.1635537277617246e-15
          ],
          [
            -0.023778351240862382,
            -2.8356513209907656e-07,
            2.1063871498571295e-07
          ],
          [
            -0.046743971438099385,
            -5.693306248538924e-07,
            4.221841482655597e-07
          ],
          [
            -0.0683516291349372,
            -8.582644149721219e-07,
            6.34022567108034e-07
          ],
          [
            -0.08792512589077797,
            -1.1475703893640415e-06,
            8.428118292452507e-07
          ],
          [
            -0.10444804981916969,
            -1.4307372341106336e-06,
            1.046793889723724e-06
          ],
          [
            -0.11776919510821823,
            -1.7021540633263706e-06,
            1.2431528601713045e-06
          ],
          [
            -0.1279375055858895,
            -1.9587366963669873e-06,
            1.4346729032529226e-06
          ],
          [
            -0.13546227625807192,
            -2.1940701544033086e-06,
            1.6262818252701707e-06
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            0.13546227625806906,
            2.194070154115657e-06,
            -1.6262818247625432e-06
          ],
          [
            0.12793750558589045,
            1.958736697282859e-06,
            -1.4346729026448735e-06
          ],
          [
            0.11776919510821893,
            1.7021540631434462e-06,
            -1.2431528595424624e-06
          ],
          [
            0.10444804981916522,
            1.4307372318000944e-06,
            -1.046793889347697e-06
          ],
          [
            0.08792512589077495,
            1.1475703871610676e-06,
            -8.428118284387054e-07
          ],
          [
            0.06835162913493864,
            8.582644132060224e-07,
            -6.340225670031785e-07
          ],
          [
            0.046743971438099385,
            5.693306253107266e-07,
            -4.221841498619483e-07
          ],
          [
            0.02377835124085992,
            2.835651304877729e-07,
            -2.10638714082112e-07
          ],
          [
            -1.8318679906315083e-15,
            -3.885780586188048e-16,
            1.1102230246251565e-15
          ],
          [
            -0.02377835124086236,
            -2.8356513209759626e-07,
            2.1063871502580156e-07
          ],
          [
            -0.046743971438099385,
            -5.693306248666374e-07,
            4.2218414830763606e-07
          ],
          [
            -0.0683516291349372,
            -8.582644149823793e-07,
            6.340225671142008e-07
          ],
          [
            -0.08792512589077794,
            -1.1475703893815137e-06,
            8.428118292158615e-07
          ],
          [
            -0.10444804981916966,
            -1.4307372341315627e-06,
            1.0467938896807638e-06
          ],
          [
            -0.11776919510821826,
            -1.7021540633099796e-06,
            1.2431528602085962e-06
          ],
          [
            -0.1279375055858895,
            -1.9587366963946806e-06,
            1.4346729032554961e-06
          ],
          [
            -0.13546227625807195,
            -2.194070154393213e-06,
            1.6262818253176548e-06
          ]
        ]
      },
      "incoming_structure_ids": [
        "incoming_00_000",
        "incoming_00_001",
        "incoming_00_002",
        "incoming_00_003",
        "incoming_00_004",
        "incoming_00_005",
        "incoming_00_006",
        "incoming_00_007",
        "incoming_00_008"
      ],
      "reflected_structure_ids": [
        "reflected_00_001",
        "reflected_00_002",
        "reflected_00_003",
        "reflected_00_004",
        "reflected_00_005",
        "reflected_00_006",
        "reflected_00_007",
        "reflected_00_008"
      ]
    },
    {
      "orbit_id": 1,
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.0,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              0.13546227625806903,
              2.1940701545652147e-06,
              -1.6262818256791284e-06
            ],
            "branch_aligned_reduced_polarization": [
              0.13546227625806906,
              2.1940701545652147e-06,
              -1.6262818256791284e-06
            ],
            "target_residual": 0.36453772375216137,
            "energy_eV": -334.54992185041044,
            "max_atomic_step_A": 0.03141017275683453,
            "max_log_strain_component": 0.006840430582548837,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.714187706743173,
            "cell_principal_stretches": [
              1.0068638797654026,
              0.997829938028003,
              0.9961425758342863
            ],
            "cell_volume_ratio": 1.0008034499935514,
            "cell_rmsd_from_input_A": 0.04022908418462048
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.4937129196472642,
              -3.832474470481617e-08,
              3.5345217230588695e-08
            ],
            "branch_aligned_reduced_polarization": [
              0.4937129196472642,
              -3.832474470481617e-08,
              3.5345217230588695e-08
            ],
            "target_residual": 0.0062870803529519485,
            "energy_eV": -333.98420374221513,
            "max_atomic_step_A": 0.000569996975460676,
            "max_log_strain_component": 0.00012479015186718008,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.714187706743173,
            "cell_principal_stretches": [
              1.006989534301895,
              0.9977903933008683,
              0.9960723431219818
            ],
            "cell_volume_ratio": 1.0008181133466139,
            "cell_rmsd_from_input_A": 0.040963594704561034
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.4999853566134445,
              -1.523516841485428e-10,
              1.5074712163265874e-11
            ],
            "branch_aligned_reduced_polarization": [
              0.4999853566134445,
              -1.523516841485428e-10,
              1.5074712163265874e-11
            ],
            "target_residual": 1.4643386556290992e-05,
            "energy_eV": -333.9640419142738
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_01",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Pna2_1",
        "spacegroup_number": 33,
        "pointgroup": "mm2",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.5,
          0.0,
          0.0
        ],
        "formal_class": [
          0.5,
          0.0,
          0.0
        ],
        "target_residual": 1.4643386556290992e-05,
        "parent_symmetrization_rmsd_A": 0.025340081292502103,
        "parent_cell_rmsd_A": 0.040963594704561034,
        "energy_eV": -333.9640419142738,
        "reduced_polarization": [
          0.4999853566134445,
          -1.523516841485428e-10,
          1.5074712163265874e-11
        ],
        "cartesian_polarization_e_A2": [
          0.005510897827534485,
          3.042629228543637e-10,
          -2.4858808134202656e-10
        ],
        "ranking_score": 0.5356102667417549
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 2,
      "formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.5,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              0.13546227625806903,
              2.1940701545652147e-06,
              -1.6262818256791284e-06
            ],
            "branch_aligned_reduced_polarization": [
              0.13546227625806903,
              2.1940701545597463e-06,
              -1.6262818256791284e-06
            ],
            "target_residual": 0.518023005499101,
            "energy_eV": -334.54992185041044,
            "max_atomic_step_A": 0.08733761875874883,
            "max_log_strain_component": 0.01350687968906623,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.714187706743173,
            "cell_principal_stretches": [
              1.0128245131840852,
              1.001437233429406,
              0.985626686716752
            ],
            "cell_volume_ratio": 0.9997016116709557,
            "cell_rmsd_from_input_A": 0.09782720281956495
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.014403679266136577,
              0.4934162912717367,
              3.862407301045007e-08
            ],
            "branch_aligned_reduced_polarization": [
              0.014403679266136577,
              0.4934162912717367,
              3.862407301045007e-08
            ],
            "target_residual": 0.01583701982766439,
            "energy_eV": -331.6516941471607,
            "max_atomic_step_A": 0.0018137661060580361,
            "max_log_strain_component": 0.00028003498770065544,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.714187706743173,
            "cell_principal_stretches": [
              1.0129545560086575,
              1.001595694862493,
              0.9853118412089067
            ],
            "cell_volume_ratio": 0.9996687435767346,
            "cell_rmsd_from_input_A": 0.0994988469561032
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -2.9269422237233998e-05,
              0.4999376748476445,
              2.620074865460304e-10
            ],
            "branch_aligned_reduced_polarization": [
              -2.9269422237233998e-05,
              0.4999376748476445,
              2.620074865460304e-10
            ],
            "target_residual": 6.885581815871e-05,
            "energy_eV": -331.55919048391877
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_02",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Pc",
        "spacegroup_number": 7,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.5,
          0.0
        ],
        "formal_class": [
          0.0,
          0.5,
          0.0
        ],
        "target_residual": 6.885581815871e-05,
        "parent_symmetrization_rmsd_A": 0.0551603370719698,
        "parent_cell_rmsd_A": 0.0994988469561032,
        "energy_eV": -331.55919048391877,
        "reduced_polarization": [
          -2.9269422237233998e-05,
          0.4999376748476445,
          2.620074865460304e-10
        ],
        "cartesian_polarization_e_A2": [
          -0.00010137708357999582,
          0.0073870729756531,
          -2.0559706488210205e-10
        ],
        "ranking_score": 0.580172760447313
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 3,
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.0,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        -0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              0.13546227625806903,
              2.1940701545652147e-06,
              -1.6262818256791284e-06
            ],
            "branch_aligned_reduced_polarization": [
              0.13546227625806903,
              2.1940701545652147e-06,
              -1.6262818257062328e-06
            ],
            "target_residual": 0.5180235535327041,
            "energy_eV": -334.54992185041044,
            "max_atomic_step_A": 0.07802835053771061,
            "max_log_strain_component": 0.01632299538795439,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.714187706743173,
            "cell_principal_stretches": [
              1.0160177924990295,
              1.0008076095439906,
              0.9831470158954347
            ],
            "cell_volume_ratio": 0.9997015778151069,
            "cell_rmsd_from_input_A": 0.11945353199785429
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.02738977974522048,
              -2.8914704335511333e-09,
              -0.4909715740041035
            ],
            "branch_aligned_reduced_polarization": [
              0.02738977974522048,
              -2.8914704335511333e-09,
              -0.4909715740041035
            ],
            "target_residual": 0.02883942631979835,
            "energy_eV": -331.48845851370453,
            "max_atomic_step_A": 0.0030262932512787845,
            "max_log_strain_component": 0.0005477571866547031,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.714187706743173,
            "cell_principal_stretches": [
              1.0163359141656814,
              1.0009817249765354,
              0.9826051275502679
            ],
            "cell_volume_ratio": 0.9996372869753346,
            "cell_rmsd_from_input_A": 0.12260871610612492
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              1.1174172973003039e-05,
              2.979332978853831e-10,
              -0.4998458802380496
            ],
            "branch_aligned_reduced_polarization": [
              1.1174172973003039e-05,
              2.979332978853831e-10,
              -0.4998458802380496
            ],
            "target_residual": 0.00015452431253808332,
            "energy_eV": -331.3561915788283
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_03",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Pc",
        "spacegroup_number": 7,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          -0.5
        ],
        "formal_class": [
          0.0,
          0.0,
          0.5
        ],
        "target_residual": 0.00015452431253808332,
        "parent_symmetrization_rmsd_A": 0.05504686176845809,
        "parent_cell_rmsd_A": 0.12260871610612492,
        "energy_eV": -331.3561915788283,
        "reduced_polarization": [
          1.1174172973003039e-05,
          2.979332978853831e-10,
          -0.4998458802380496
        ],
        "cartesian_polarization_e_A2": [
          -0.0001245902262563966,
          1.8914251740045735e-10,
          -0.007488535666132451
        ],
        "ranking_score": 0.5860080894200654
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 4,
      "formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.5,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.5,
        0.5,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              0.13546227625806903,
              2.1940701545652147e-06,
              -1.6262818256791284e-06
            ],
            "branch_aligned_reduced_polarization": [
              0.13546227625806906,
              2.1940701545597463e-06,
              -1.6262818256791284e-06
            ],
            "target_residual": 0.618777470475657,
            "energy_eV": -334.54992185041044,
            "max_atomic_step_A": 0.09215813569120875,
            "max_log_strain_component": 0.013506882856919408,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.714187706743173,
            "cell_principal_stretches": [
              1.0167109050531042,
              0.9961425861739039,
              0.9881657772978892
            ],
            "cell_volume_ratio": 1.0008034594153832,
            "cell_rmsd_from_input_A": 0.10528269834771242
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.5057271351516758,
              0.5033669186718762,
              7.660133407049187e-08
            ],
            "branch_aligned_reduced_polarization": [
              0.5057271351516758,
              0.5033669186718762,
              7.660133407049187e-08
            ],
            "target_residual": 0.00664350949381852,
            "energy_eV": -330.7882972935441,
            "max_atomic_step_A": 0.0007540740089708146,
            "max_log_strain_component": 0.00011045928093743627,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.714187706743173,
            "cell_principal_stretches": [
              1.0165645859886272,
              0.9962047574703923,
              0.988233513856405
            ],
            "cell_volume_ratio": 1.0007904801105494,
            "cell_rmsd_from_input_A": 0.1044435876563764
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.5000145109738542,
              0.49999289442839623,
              -2.616015358937456e-11
            ],
            "branch_aligned_reduced_polarization": [
              0.5000145109738542,
              0.49999289442839623,
              -2.616015358937456e-11
            ],
            "target_residual": 1.6157274213613833e-05,
            "energy_eV": -330.85520165447844
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_04",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Pc",
        "spacegroup_number": 7,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.5,
          0.5,
          0.0
        ],
        "formal_class": [
          0.5,
          0.5,
          0.0
        ],
        "target_residual": 1.6157274213613833e-05,
        "parent_symmetrization_rmsd_A": 0.05932729660297025,
        "parent_cell_rmsd_A": 0.1044435876563764,
        "energy_eV": -330.85520165447844,
        "reduced_polarization": [
          0.5000145109738542,
          0.49999289442839623,
          -2.616015358937456e-11
        ],
        "cartesian_polarization_e_A2": [
          0.0054114134486861,
          0.007283606347088763,
          -3.012552974972097e-10
        ],
        "ranking_score": 0.5854705080654916
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 5,
      "formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.0,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.5,
        0.0,
        -0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              0.13546227625806903,
              2.1940701545652147e-06,
              -1.6262818256791284e-06
            ],
            "branch_aligned_reduced_polarization": [
              0.13546227625806906,
              2.1940701545652147e-06,
              -1.6262818257062328e-06
            ],
            "target_residual": 0.6187779292739694,
            "energy_eV": -334.54992185041044,
            "max_atomic_step_A": 0.08391527835118416,
            "max_log_strain_component": 0.016323004184337,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.714187706743173,
            "cell_principal_stretches": [
              1.0188412802602216,
              0.9978299499987562,
              0.9844319832533205
            ],
            "cell_volume_ratio": 1.000803425522219,
            "cell_rmsd_from_input_A": 0.12535172146686244
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.5155122650823889,
              -4.7902690828142156e-08,
              -0.508389244413429
            ],
            "branch_aligned_reduced_polarization": [
              0.5155122650823889,
              -4.7902690828142156e-08,
              -0.508389244413429
            ],
            "target_residual": 0.017635469651156067,
            "energy_eV": -330.30825557007876,
            "max_atomic_step_A": 0.001974434709062636,
            "max_log_strain_component": 0.0002938942851695007,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.714187706743173,
            "cell_principal_stretches": [
              1.0184658118935472,
              0.9979230881755274,
              0.9846690147452649
            ],
            "cell_volume_ratio": 1.000768892937817,
            "cell_rmsd_from_input_A": 0.12310010924964974
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.5000222706553931,
              -1.550673627145247e-10,
              -0.4999850420402176
            ],
            "branch_aligned_reduced_polarization": [
              0.5000222706553931,
              -1.550673627145247e-10,
              -0.4999850420402176
            ],
            "target_residual": 2.6827647166917646e-05,
            "energy_eV": -330.4999160421731
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_05",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Pc",
        "spacegroup_number": 7,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.5,
          0.0,
          -0.5
        ],
        "formal_class": [
          0.5,
          0.0,
          0.5
        ],
        "target_residual": 2.6827647166917646e-05,
        "parent_symmetrization_rmsd_A": 0.058307550508052024,
        "parent_cell_rmsd_A": 0.12310010924964974,
        "energy_eV": -330.4999160421731,
        "reduced_polarization": [
          0.5000222706553931,
          -1.550673627145247e-10,
          -0.4999850420402176
        ],
        "cartesian_polarization_e_A2": [
          0.005389754305039227,
          4.722928103559158e-10,
          -0.007353317007650626
        ],
        "ranking_score": 0.5891362331147982
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 6,
      "formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.5,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        -0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              0.13546227625806903,
              2.1940701545652147e-06,
              -1.6262818256791284e-06
            ],
            "branch_aligned_reduced_polarization": [
              0.13546227625806903,
              2.1940701545597463e-06,
              -1.6262818257062328e-06
            ],
            "target_residual": 0.7199626434367938,
            "energy_eV": -334.54992185041044,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.015509807715910798,
            "step_scale": 0.950180296651708,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.714187706743173,
            "cell_principal_stretches": [
              1.0197571517185466,
              1.0010096689538648,
              0.97935874803288
            ],
            "cell_volume_ratio": 0.9997164519544777,
            "cell_rmsd_from_input_A": 0.1460582052076497
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.04721783664845314,
              0.46541985357339594,
              -0.46173736115397984
            ],
            "branch_aligned_reduced_polarization": [
              0.04721783664845314,
              0.46541985357339594,
              -0.46173736115397984
            ],
            "target_residual": 0.06992381680161884,
            "energy_eV": -329.03157978806524,
            "max_atomic_step_A": 0.011244775930875623,
            "max_log_strain_component": 0.0015167013652958993,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.714187706743173,
            "cell_principal_stretches": [
              1.0214403814389093,
              1.0014654415245907,
              0.9771733445169711
            ],
            "cell_volume_ratio": 0.9995870065714298,
            "cell_rmsd_from_input_A": 0.16014855116657326
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.0005740727097990811,
              0.4993865571981079,
              -0.4991874418429896
            ],
            "branch_aligned_reduced_polarization": [
              0.0005740727097990811,
              0.4993865571981079,
              -0.4991874418429896
            ],
            "target_residual": 0.0011688123484346973,
            "energy_eV": -328.02539712986453,
            "max_atomic_step_A": 0.0002066145661416864,
            "max_log_strain_component": 3.1977268250467726e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.714187706743173,
            "cell_principal_stretches": [
              1.0214755081671887,
              1.001471747485752,
              0.9771317981049911
            ],
            "cell_volume_ratio": 0.9995851750234753,
            "cell_rmsd_from_input_A": 0.16042759081439947
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              5.2994498321361e-06,
              0.49999371103034757,
              -0.4999909924841462
            ],
            "branch_aligned_reduced_polarization": [
              5.2994498321361e-06,
              0.49999371103034757,
              -0.4999909924841462
            ],
            "target_residual": 1.219715744217489e-05,
            "energy_eV": -328.00431975880383
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_06",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.5,
          -0.5
        ],
        "formal_class": [
          0.0,
          0.5,
          0.5
        ],
        "target_residual": 1.219715744217489e-05,
        "parent_symmetrization_rmsd_A": 0.07841971270631937,
        "parent_cell_rmsd_A": 0.16042759081439947,
        "energy_eV": -328.00431975880383,
        "reduced_polarization": [
          5.2994498321361e-06,
          0.49999371103034757,
          -0.4999909924841462
        ],
        "cartesian_polarization_e_A2": [
          -0.00023010277271347707,
          0.007391088662090537,
          -0.007493914550343838
        ],
        "ranking_score": 0.6185510047248036
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 7,
      "formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.5,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.5,
        0.5,
        -0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              0.13546227625806903,
              2.1940701545652147e-06,
              -1.6262818256791284e-06
            ],
            "branch_aligned_reduced_polarization": [
              0.13546227625806906,
              2.1940701545597463e-06,
              -1.6262818257062328e-06
            ],
            "target_residual": 0.7955400251944756,
            "energy_eV": -334.54992185041044,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.01505941510185093,
            "step_scale": 0.9225873111938204,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.714187706743173,
            "cell_principal_stretches": [
              1.0220235927270336,
              0.9973782051770241,
              0.9817501847363851
            ],
            "cell_volume_ratio": 1.0007412158403306,
            "cell_rmsd_from_input_A": 0.1463924224484301
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.49726367299717894,
              0.46181410441730736,
              -0.4643641215797262
            ],
            "branch_aligned_reduced_polarization": [
              0.49726367299717894,
              0.46181410441730736,
              -0.4643641215797262
            ],
            "target_residual": 0.05230263796122726,
            "energy_eV": -328.07255835445767,
            "max_atomic_step_A": 0.009253818837257092,
            "max_log_strain_component": 0.0012178342846180666,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.714187706743173,
            "cell_principal_stretches": [
              1.023600813764216,
              0.9974139452206121,
              0.9801907407740564
            ],
            "cell_volume_ratio": 1.0007293889718147,
            "cell_rmsd_from_input_A": 0.15766673871274922
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.5003149860727905,
              0.4997285129587455,
              -0.49974915249635654
            ],
            "branch_aligned_reduced_polarization": [
              0.5003149860727905,
              0.4997285129587455,
              -0.49974915249635654
            ],
            "target_residual": 0.00048563969123748614,
            "energy_eV": -326.96215477473834
          }
        ],
        "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,
          0.5,
          -0.5
        ],
        "formal_class": [
          0.5,
          0.5,
          0.5
        ],
        "target_residual": 0.00048563969123748614,
        "parent_symmetrization_rmsd_A": 0.0797898104017401,
        "parent_cell_rmsd_A": 0.15766673871274922,
        "energy_eV": -326.96215477473834,
        "reduced_polarization": [
          0.5003149860727905,
          0.4997285129587455,
          -0.49974915249635654
        ],
        "cartesian_polarization_e_A2": [
          0.0052905302449068915,
          0.007281506383606852,
          -0.007351171399594692
        ],
        "ranking_score": 0.6201777744624024
      },
      "branch_status": "awaiting_branch_sampling"
    }
  ],
  "sampled_polarization_branches": [
    {
      "orbit_id": 0,
      "candidate_id": "inversion_parent_endpoint_00",
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "construction": "MACEField-BEC-parent plus variable-cell P-N-P path and symmetric log-strain continuation beyond both polar endpoints",
      "geometry_diagnostics": {
        "collision_aware": false,
        "permutations_tested": 1,
        "selected_order": [
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          10,
          11,
          12,
          13,
          14,
          15,
          16,
          17,
          18,
          19,
          20,
          21,
          22,
          23,
          24,
          25,
          26,
          27,
          28,
          29,
          30,
          31,
          32,
          33,
          34,
          35,
          36,
          37,
          38,
          39,
          40,
          41,
          42,
          43,
          44,
          45,
          46,
          47
        ],
        "endpoint_rmsd_A": 0.4626960473186446,
        "minimum_distance_A_by_image": [
          1.3595126854228086,
          1.3505727643255763,
          1.3427898853830416,
          1.336184267035226,
          1.3307734402573608,
          1.3240312290153575,
          1.3189292828473658,
          1.3159727492520314,
          1.3151760970580975
        ],
        "minimum_distance_A": 1.3151760970580975,
        "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": [
          643.3077688912787,
          643.3077688912787,
          643.3077688912787,
          643.3077688912787,
          643.3077688912787,
          643.3077688912787,
          643.3077688912787,
          643.3077688912787,
          643.3077688912787
        ],
        "cell_deformation_log_strain_norm": 0.0
      },
      "parent_reduced_polarization": [
        -1.848163757570089e-15,
        -3.925214002389333e-16,
        1.1635537173204267e-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": [
          -334.54992185041044,
          -334.2386518748061,
          -333.3914995847132,
          -332.1649070152864,
          -330.75128158520755,
          -329.35788364462894,
          -328.18755818001233,
          -327.41146218376895,
          -327.14031682815556
        ],
        "cartesian_polarizations_e_A2": [
          [
            0.0014839307800336428,
            3.2376724293488615e-08,
            -2.430975291399212e-08
          ],
          [
            0.0014015001645029585,
            2.8904033854556713e-08,
            -2.1445571883813362e-08
          ],
          [
            0.0012901107111764156,
            2.5117780624832187e-08,
            -1.858271942166246e-08
          ],
          [
            0.0011441833130418418,
            2.1112627052070264e-08,
            -1.5647534403468272e-08
          ],
          [
            0.0009631818115848473,
            1.6934084794229643e-08,
            -1.2598398992641836e-08
          ],
          [
            0.000748762601224471,
            1.2664950674351942e-08,
            -9.477405275753404e-09
          ],
          [
            0.0005120600355619471,
            8.401308705916619e-09,
            -6.310832606388645e-09
          ],
          [
            0.0002604815767124793,
            4.184419550343299e-09,
            -3.148639439495589e-09
          ],
          [
            -2.0245836421470332e-17,
            -5.792229173324224e-18,
            1.7392866931071342e-17
          ]
        ],
        "raw_reduced_polarization": [
          [
            0.13546227625806903,
            2.1940701540882674e-06,
            -1.6262818247453989e-06
          ],
          [
            0.12793750558589048,
            1.958736697331479e-06,
            -1.434672902653918e-06
          ],
          [
            0.11776919510821889,
            1.7021540630953898e-06,
            -1.2431528595421735e-06
          ],
          [
            0.10444804981916525,
            1.4307372317668348e-06,
            -1.0467938893690656e-06
          ],
          [
            0.087925125890775,
            1.14757038720225e-06,
            -8.428118284506066e-07
          ],
          [
            0.06835162913493859,
            8.582644132156434e-07,
            -6.340225670016003e-07
          ],
          [
            0.046743971438099385,
            5.69330625292464e-07,
            -4.2218414983861217e-07
          ],
          [
            0.023778351240859967,
            2.8356513044273857e-07,
            -2.1063871406858005e-07
          ],
          [
            -1.848163757570089e-15,
            -3.925214002389333e-16,
            1.1635537173204267e-15
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            0.13546227625806903,
            2.1940701540882674e-06,
            -1.6262818247453989e-06
          ],
          [
            0.12793750558589048,
            1.958736697331479e-06,
            -1.434672902653918e-06
          ],
          [
            0.11776919510821889,
            1.7021540630953898e-06,
            -1.2431528595421735e-06
          ],
          [
            0.10444804981916525,
            1.4307372317668348e-06,
            -1.0467938893690656e-06
          ],
          [
            0.087925125890775,
            1.14757038720225e-06,
            -8.428118284506066e-07
          ],
          [
            0.06835162913493859,
            8.582644132156434e-07,
            -6.340225670016003e-07
          ],
          [
            0.046743971438099385,
            5.69330625292464e-07,
            -4.2218414983861217e-07
          ],
          [
            0.023778351240859967,
            2.8356513044273857e-07,
            -2.1063871406858005e-07
          ],
          [
            -1.8492152253912764e-15,
            -3.925214205047472e-16,
            1.1635537277617246e-15
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            0.13546227625806906,
            2.194070154115657e-06,
            -1.6262818247625432e-06
          ],
          [
            0.12793750558589045,
            1.958736697282859e-06,
            -1.4346729026448735e-06
          ],
          [
            0.11776919510821893,
            1.7021540631434462e-06,
            -1.2431528595424624e-06
          ],
          [
            0.10444804981916522,
            1.4307372318000944e-06,
            -1.046793889347697e-06
          ],
          [
            0.08792512589077495,
            1.1475703871610676e-06,
            -8.428118284387054e-07
          ],
          [
            0.06835162913493864,
            8.582644132060224e-07,
            -6.340225670031785e-07
          ],
          [
            0.046743971438099385,
            5.693306253107266e-07,
            -4.221841498619483e-07
          ],
          [
            0.02377835124085992,
            2.835651304877729e-07,
            -2.10638714082112e-07
          ],
          [
            -1.8318679906315083e-15,
            -3.885780586188048e-16,
            1.1102230246251565e-15
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -327.14031682815556,
          -327.41146218376895,
          -328.18755818001245,
          -329.3578836446288,
          -330.7512815852075,
          -332.16490701528625,
          -333.39149958471313,
          -334.2386518748061,
          -334.5499218504105
        ],
        "cartesian_polarizations_e_A2": [
          [
            -2.2359946138363343e-17,
            -7.895552616151455e-18,
            1.5089997418027167e-17
          ],
          [
            -0.00026048157671250573,
            -4.1844195747849965e-09,
            3.1486394532049434e-09
          ],
          [
            -0.0005120600355619471,
            -8.401308699444854e-09,
            6.310832582874568e-09
          ],
          [
            -0.0007487626012244558,
            -1.2664950700271359e-08,
            9.47740527734438e-09
          ],
          [
            -0.0009631818115848797,
            -1.693408482613005e-08,
            1.259839900452022e-08
          ],
          [
            -0.0011441833130418904,
            -2.1112627086656452e-08,
            1.5647534408769725e-08
          ],
          [
            -0.0012901107111764083,
            -2.5117780628240647e-08,
            1.858271943106674e-08
          ],
          [
            -0.001401500164502948,
            -2.8904033840324224e-08,
            2.1445571892767318e-08
          ],
          [
            -0.0014839307800336742,
            -3.23767242981375e-08,
            2.430975292183644e-08
          ]
        ],
        "raw_reduced_polarization": [
          [
            -2.041152620907189e-15,
            -5.350571042363112e-16,
            1.009495597228699e-15
          ],
          [
            -0.023778351240862382,
            -2.8356513209907656e-07,
            2.1063871498571295e-07
          ],
          [
            -0.046743971438099385,
            -5.693306248538924e-07,
            4.221841482655597e-07
          ],
          [
            -0.0683516291349372,
            -8.582644149721219e-07,
            6.34022567108034e-07
          ],
          [
            -0.08792512589077797,
            -1.1475703893640415e-06,
            8.428118292452507e-07
          ],
          [
            -0.10444804981916969,
            -1.4307372341106336e-06,
            1.046793889723724e-06
          ],
          [
            -0.11776919510821823,
            -1.7021540633263706e-06,
            1.2431528601713045e-06
          ],
          [
            -0.1279375055858895,
            -1.9587366963669873e-06,
            1.4346729032529226e-06
          ],
          [
            -0.13546227625807192,
            -2.1940701544033086e-06,
            1.6262818252701707e-06
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -2.041152620907189e-15,
            -5.350571042363112e-16,
            1.009495597228699e-15
          ],
          [
            -0.023778351240862382,
            -2.8356513209907656e-07,
            2.1063871498571295e-07
          ],
          [
            -0.046743971438099385,
            -5.693306248538924e-07,
            4.221841482655597e-07
          ],
          [
            -0.0683516291349372,
            -8.582644149721219e-07,
            6.34022567108034e-07
          ],
          [
            -0.08792512589077797,
            -1.1475703893640415e-06,
            8.428118292452507e-07
          ],
          [
            -0.10444804981916969,
            -1.4307372341106336e-06,
            1.046793889723724e-06
          ],
          [
            -0.11776919510821823,
            -1.7021540633263706e-06,
            1.2431528601713045e-06
          ],
          [
            -0.1279375055858895,
            -1.9587366963669873e-06,
            1.4346729032529226e-06
          ],
          [
            -0.13546227625807192,
            -2.1940701544033086e-06,
            1.6262818252701707e-06
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          -0.13546227625807275,
          -2.1940701548733107e-06,
          1.6262818270725065e-06
        ],
        "actual_opposite_endpoint_branch_residual": 2.04025756349987e-15
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            0.13546227625806903,
            2.1940701540882674e-06,
            -1.6262818247453989e-06
          ],
          [
            0.12793750558589048,
            1.958736697331479e-06,
            -1.434672902653918e-06
          ],
          [
            0.11776919510821889,
            1.7021540630953898e-06,
            -1.2431528595421735e-06
          ],
          [
            0.10444804981916525,
            1.4307372317668348e-06,
            -1.0467938893690656e-06
          ],
          [
            0.087925125890775,
            1.14757038720225e-06,
            -8.428118284506066e-07
          ],
          [
            0.06835162913493859,
            8.582644132156434e-07,
            -6.340225670016003e-07
          ],
          [
            0.046743971438099385,
            5.69330625292464e-07,
            -4.2218414983861217e-07
          ],
          [
            0.023778351240859967,
            2.8356513044273857e-07,
            -2.1063871406858005e-07
          ],
          [
            -1.848163757570089e-15,
            -3.925214002389333e-16,
            1.1635537173204267e-15
          ],
          [
            -0.023778351240862382,
            -2.8356513209907656e-07,
            2.1063871498571295e-07
          ],
          [
            -0.046743971438099385,
            -5.693306248538924e-07,
            4.221841482655597e-07
          ],
          [
            -0.0683516291349372,
            -8.582644149721219e-07,
            6.34022567108034e-07
          ],
          [
            -0.08792512589077797,
            -1.1475703893640415e-06,
            8.428118292452507e-07
          ],
          [
            -0.10444804981916969,
            -1.4307372341106336e-06,
            1.046793889723724e-06
          ],
          [
            -0.11776919510821823,
            -1.7021540633263706e-06,
            1.2431528601713045e-06
          ],
          [
            -0.1279375055858895,
            -1.9587366963669873e-06,
            1.4346729032529226e-06
          ],
          [
            -0.13546227625807192,
            -2.1940701544033086e-06,
            1.6262818252701707e-06
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            0.13546227625806903,
            2.1940701540882674e-06,
            -1.6262818247453989e-06
          ],
          [
            0.12793750558589048,
            1.958736697331479e-06,
            -1.434672902653918e-06
          ],
          [
            0.11776919510821889,
            1.7021540630953898e-06,
            -1.2431528595421735e-06
          ],
          [
            0.10444804981916525,
            1.4307372317668348e-06,
            -1.0467938893690656e-06
          ],
          [
            0.087925125890775,
            1.14757038720225e-06,
            -8.428118284506066e-07
          ],
          [
            0.06835162913493859,
            8.582644132156434e-07,
            -6.340225670016003e-07
          ],
          [
            0.046743971438099385,
            5.69330625292464e-07,
            -4.2218414983861217e-07
          ],
          [
            0.023778351240859967,
            2.8356513044273857e-07,
            -2.1063871406858005e-07
          ],
          [
            -1.8492152253912764e-15,
            -3.925214205047472e-16,
            1.1635537277617246e-15
          ],
          [
            -0.023778351240862382,
            -2.8356513209907656e-07,
            2.1063871498571295e-07
          ],
          [
            -0.046743971438099385,
            -5.693306248538924e-07,
            4.221841482655597e-07
          ],
          [
            -0.0683516291349372,
            -8.582644149721219e-07,
            6.34022567108034e-07
          ],
          [
            -0.08792512589077797,
            -1.1475703893640415e-06,
            8.428118292452507e-07
          ],
          [
            -0.10444804981916969,
            -1.4307372341106336e-06,
            1.046793889723724e-06
          ],
          [
            -0.11776919510821823,
            -1.7021540633263706e-06,
            1.2431528601713045e-06
          ],
          [
            -0.1279375055858895,
            -1.9587366963669873e-06,
            1.4346729032529226e-06
          ],
          [
            -0.13546227625807192,
            -2.1940701544033086e-06,
            1.6262818252701707e-06
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            0.13546227625806906,
            2.194070154115657e-06,
            -1.6262818247625432e-06
          ],
          [
            0.12793750558589045,
            1.958736697282859e-06,
            -1.4346729026448735e-06
          ],
          [
            0.11776919510821893,
            1.7021540631434462e-06,
            -1.2431528595424624e-06
          ],
          [
            0.10444804981916522,
            1.4307372318000944e-06,
            -1.046793889347697e-06
          ],
          [
            0.08792512589077495,
            1.1475703871610676e-06,
            -8.428118284387054e-07
          ],
          [
            0.06835162913493864,
            8.582644132060224e-07,
            -6.340225670031785e-07
          ],
          [
            0.046743971438099385,
            5.693306253107266e-07,
            -4.221841498619483e-07
          ],
          [
            0.02377835124085992,
            2.835651304877729e-07,
            -2.10638714082112e-07
          ],
          [
            -1.8318679906315083e-15,
            -3.885780586188048e-16,
            1.1102230246251565e-15
          ],
          [
            -0.02377835124086236,
            -2.8356513209759626e-07,
            2.1063871502580156e-07
          ],
          [
            -0.046743971438099385,
            -5.693306248666374e-07,
            4.2218414830763606e-07
          ],
          [
            -0.0683516291349372,
            -8.582644149823793e-07,
            6.340225671142008e-07
          ],
          [
            -0.08792512589077794,
            -1.1475703893815137e-06,
            8.428118292158615e-07
          ],
          [
            -0.10444804981916966,
            -1.4307372341315627e-06,
            1.0467938896807638e-06
          ],
          [
            -0.11776919510821826,
            -1.7021540633099796e-06,
            1.2431528602085962e-06
          ],
          [
            -0.1279375055858895,
            -1.9587366963946806e-06,
            1.4346729032554961e-06
          ],
          [
            -0.13546227625807195,
            -2.194070154393213e-06,
            1.6262818253176548e-06
          ]
        ]
      },
      "incoming_structure_ids": [
        "incoming_00_000",
        "incoming_00_001",
        "incoming_00_002",
        "incoming_00_003",
        "incoming_00_004",
        "incoming_00_005",
        "incoming_00_006",
        "incoming_00_007",
        "incoming_00_008"
      ],
      "reflected_structure_ids": [
        "reflected_00_001",
        "reflected_00_002",
        "reflected_00_003",
        "reflected_00_004",
        "reflected_00_005",
        "reflected_00_006",
        "reflected_00_007",
        "reflected_00_008"
      ],
      "positive_extension_structure_ids": [
        "extension_plus_00_000",
        "extension_plus_00_001",
        "extension_plus_00_002",
        "extension_plus_00_003"
      ],
      "negative_extension_structure_ids": [
        "extension_minus_00_000",
        "extension_minus_00_001",
        "extension_minus_00_002",
        "extension_minus_00_003"
      ],
      "extension": {
        "enabled": true,
        "fraction_beyond_polar_endpoint": 0.35,
        "images_per_side": 4,
        "construction": "continue fractional atomic displacements and symmetric log strain beyond +P; reflect these structures about N for the -P side",
        "positive_path_coordinates": [
          1.35,
          1.2625,
          1.175,
          1.0875
        ],
        "negative_path_coordinates": [
          -1.0875,
          -1.175,
          -1.2625,
          -1.35
        ]
      },
      "branch_coordinates": [
        1.35,
        1.2625,
        1.175,
        1.0875,
        1.0,
        0.875,
        0.75,
        0.625,
        0.5,
        0.375,
        0.25,
        0.125,
        0.0,
        -0.125,
        -0.25,
        -0.375,
        -0.5,
        -0.625,
        -0.75,
        -0.875,
        -1.0,
        -1.0875,
        -1.175,
        -1.2625,
        -1.35
      ],
      "parent": {
        "candidate_id": "inversion_parent_endpoint_00",
        "source": "same_species_inversion_center_projection_from_endpoint",
        "spacegroup": "Pnma",
        "spacegroup_number": 62,
        "pointgroup": "mmm",
        "has_inversion": true,
        "is_polar_point_group": false,
        "nonpolar_parent_hypothesis": true,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.0
        ],
        "formal_class": [
          0.0,
          0.0,
          0.0
        ],
        "target_residual": 1.0297109248924743e-15,
        "parent_symmetrization_rmsd_A": 0.4626960473186446,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -327.14031682815556,
        "reduced_polarization": [
          -6.316446726058668e-16,
          7.985654185494127e-16,
          -1.536973282413959e-16
        ],
        "cartesian_polarization_e_A2": [
          -6.919394813198304e-18,
          1.178400441686539e-17,
          -2.2974763760112843e-18
        ],
        "ranking_score": 0.46269604731864666
      }
    }
  ],
  "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": 51,
      "full_response": 17,
      "energy_polarization": 34
    },
    "model_evaluations_for_recovery_and_path_properties": {
      "total": 76,
      "full_response": 42,
      "energy_polarization": 34
    },
    "elapsed_seconds": 1169.75270525401
  }
}