{
  "schema": "ferrofinder.endpoint_parent_recovery.v4_variable_cell",
  "status": "complete",
  "input_atom_count": 28,
  "input_formula": "Cr4Li4O16P4",
  "input_spacegroup": "Pna2_1",
  "input_pointgroup": "mm2",
  "input_is_polar_point_group": true,
  "input_energy_eV": -192.20180839398287,
  "input_cartesian_polarization_e_A2": [
    1.417696428032886e-17,
    -9.094656330777004e-18,
    -0.010058703249223259
  ],
  "input_reduced_polarization": [
    6.485044775086261e-16,
    -3.597086466900808e-16,
    -0.7332794119948397
  ],
  "input_formal_targets": [
    {
      "orbit_id": 0,
      "representative_formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        -0.5
      ]
    },
    {
      "orbit_id": 1,
      "representative_formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        -1.0
      ]
    },
    {
      "orbit_id": 2,
      "representative_formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        0.5,
        0.0,
        -0.5
      ]
    },
    {
      "orbit_id": 3,
      "representative_formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        -0.5,
        -0.5
      ]
    },
    {
      "orbit_id": 4,
      "representative_formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        0.5,
        0.0,
        -1.0
      ]
    },
    {
      "orbit_id": 5,
      "representative_formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        -0.5,
        -1.0
      ]
    },
    {
      "orbit_id": 6,
      "representative_formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "target_reduced_polarization": [
        0.5,
        -0.5,
        -0.5
      ]
    },
    {
      "orbit_id": 7,
      "representative_formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        0.5,
        -0.5,
        -1.0
      ]
    }
  ],
  "parent_candidates": [
    {
      "candidate_id": "inversion_parent_endpoint_00",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "P2_1/c",
      "spacegroup_number": 14,
      "pointgroup": "2/m",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 1.635915787752667e-15,
      "parent_symmetrization_rmsd_A": 0.6963870699391469,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -159.04579292908258,
      "reduced_polarization": [
        1.5207517397102551e-15,
        -3.083216971629264e-16,
        5.181431673246638e-16
      ],
      "cartesian_polarization_e_A2": [
        3.3245172301579805e-17,
        -7.795419712094574e-18,
        7.107588561027407e-18
      ],
      "ranking_score": 0.6963870699391501
    },
    {
      "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": 2.6844238856193793e-15,
      "parent_symmetrization_rmsd_A": 0.7017397041823188,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -169.2071449185736,
      "reduced_polarization": [
        1.8581139072551737e-15,
        7.315083403277274e-16,
        1.7940010739628145e-15
      ],
      "cartesian_polarization_e_A2": [
        4.0620250754688886e-17,
        1.8495015395361638e-17,
        2.4609070071514246e-17
      ],
      "ranking_score": 0.7017397041823241
    },
    {
      "candidate_id": "inversion_parent_endpoint_02",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "P2_1/c",
      "spacegroup_number": 14,
      "pointgroup": "2/m",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 2.728669622471898e-15,
      "parent_symmetrization_rmsd_A": 0.7275365470973189,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -166.9477345746464,
      "reduced_polarization": [
        1.095116051641925e-15,
        2.4907556711985427e-15,
        2.0614298054852214e-16
      ],
      "cartesian_polarization_e_A2": [
        2.3940345341310054e-17,
        6.297476316437186e-17,
        2.827750287720581e-18
      ],
      "ranking_score": 0.7275365470973243
    },
    {
      "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,
        -0.5
      ],
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_residual": 0.0006577786388526352,
      "parent_symmetrization_rmsd_A": 0.021008861579935777,
      "parent_cell_rmsd_A": 0.0179254068602417,
      "energy_eV": -191.73419172899665,
      "reduced_polarization": [
        3.3461278016330204e-15,
        -3.734632241587725e-15,
        -0.5006577786388526
      ],
      "cartesian_polarization_e_A2": [
        9.790759194983816e-17,
        -9.737548547184991e-17,
        -0.006870817361387456
      ],
      "ranking_score": 0.5268057705727015
    },
    {
      "candidate_id": "inversion_parent_bec_00_00",
      "source": "same_species_inversion_center_projection_after_BEC",
      "spacegroup": "P2_1/m",
      "spacegroup_number": 11,
      "pointgroup": "2/m",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        -0.5
      ],
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_residual": 0.49999999999999867,
      "parent_symmetrization_rmsd_A": 0.6963977074255778,
      "parent_cell_rmsd_A": 0.0179254068602417,
      "energy_eV": -160.23057477962118,
      "reduced_polarization": [
        -1.0878564622845815e-15,
        6.417859853277621e-16,
        -1.3182871746884833e-15
      ],
      "cartesian_polarization_e_A2": [
        -2.3678738270477164e-17,
        1.6115224761929884e-17,
        -1.809162025160053e-17
      ],
      "ranking_score": 1.7008790591406355
    },
    {
      "candidate_id": "inversion_parent_bec_00_01",
      "source": "same_species_inversion_center_projection_after_BEC",
      "spacegroup": "P2_1/c",
      "spacegroup_number": 14,
      "pointgroup": "2/m",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        -0.5
      ],
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_residual": 0.4999999999999927,
      "parent_symmetrization_rmsd_A": 0.7275501599788673,
      "parent_cell_rmsd_A": 0.0179254068602417,
      "energy_eV": -167.91632667572912,
      "reduced_polarization": [
        3.110780557881176e-15,
        3.605505228893196e-15,
        7.308739189081714e-15
      ],
      "cartesian_polarization_e_A2": [
        6.771054932400492e-17,
        9.053411646914382e-17,
        1.0030207110078529e-16
      ],
      "ranking_score": 1.7320315116939131
    },
    {
      "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": [
        0.0,
        0.0,
        -1.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 5.260031812337473e-07,
      "parent_symmetrization_rmsd_A": 0.02442180441081978,
      "parent_cell_rmsd_A": 0.020482481370503382,
      "energy_eV": -191.8697482712637,
      "reduced_polarization": [
        -5.770059581354816e-16,
        -1.522980079004932e-16,
        -0.9999994739968188
      ],
      "cartesian_polarization_e_A2": [
        -7.059416872412293e-17,
        2.2300990119820968e-18,
        -0.013710343631643166
      ],
      "ranking_score": 0.5295434767598081
    },
    {
      "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": [
        0.5,
        0.0,
        -0.5
      ],
      "formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_residual": 9.423874328261425e-05,
      "parent_symmetrization_rmsd_A": 0.08236371452044303,
      "parent_cell_rmsd_A": 0.018647885469990463,
      "energy_eV": -188.2052732278506,
      "reduced_polarization": [
        0.5000770199812111,
        -3.0878897542661324e-16,
        -0.49994569656337096
      ],
      "cartesian_polarization_e_A2": [
        0.010876705629654333,
        2.0758965727920984e-16,
        -0.006843222166917529
      ],
      "ranking_score": 0.5872141633745058
    },
    {
      "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,
        -0.5,
        -0.5
      ],
      "formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_residual": 9.576127677242656e-05,
      "parent_symmetrization_rmsd_A": 0.0806120559346421,
      "parent_cell_rmsd_A": 0.11200604743791363,
      "energy_eV": -186.54241405311316,
      "reduced_polarization": [
        5.539753071841744e-17,
        -0.5000082725898115,
        -0.4999045967171063
      ],
      "cartesian_polarization_e_A2": [
        -2.860696203127991e-16,
        -0.012712636601357512,
        -0.007106493574593461
      ],
      "ranking_score": 0.6088050903476654
    },
    {
      "candidate_id": "bec_projection_04",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Pc",
      "spacegroup_number": 7,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.5,
        0.0,
        -1.0
      ],
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_residual": 0.00021199963720031586,
      "parent_symmetrization_rmsd_A": 0.08561874793995616,
      "parent_cell_rmsd_A": 0.02419448440920955,
      "energy_eV": -188.67447203588586,
      "reduced_polarization": [
        0.5001228834305129,
        9.965145773631207e-16,
        -0.9998272472614445
      ],
      "cartesian_polarization_e_A2": [
        0.010971579832662027,
        2.664180693394197e-16,
        -0.013689213832550071
      ],
      "ranking_score": 0.5920913683166592
    },
    {
      "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": [
        0.0,
        -0.5,
        -1.0
      ],
      "formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_residual": 0.00033290353360384504,
      "parent_symmetrization_rmsd_A": 0.08676439995395768,
      "parent_cell_rmsd_A": 0.12193550056401901,
      "energy_eV": -187.25408542007145,
      "reduced_polarization": [
        -3.3726193857056543e-16,
        -0.49994712054514395,
        -0.9996713230675267
      ],
      "cartesian_polarization_e_A2": [
        -3.869419765994207e-16,
        -0.013059702265082566,
        -0.013973499772765224
      ],
      "ranking_score": 0.6179140821621701
    },
    {
      "candidate_id": "bec_projection_06",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.5,
        -0.5,
        -0.5
      ],
      "formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "target_residual": 0.0008535560600866976,
      "parent_symmetrization_rmsd_A": 0.11434255969468413,
      "parent_cell_rmsd_A": 0.11482331839039701,
      "energy_eV": -182.6519978129149,
      "reduced_polarization": [
        0.5000096157963726,
        -0.49997096148454256,
        -0.49914699223403836
      ],
      "cartesian_polarization_e_A2": [
        0.010892572461607096,
        -0.012731244849373841,
        -0.007084138151945846
      ],
      "ranking_score": 0.6447555014124567
    },
    {
      "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,
        -1.0
      ],
      "formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_residual": 4.842893467883458e-05,
      "parent_symmetrization_rmsd_A": 0.1212351260662929,
      "parent_cell_rmsd_A": 0.12719384025944744,
      "energy_eV": -183.4735818427058,
      "reduced_polarization": [
        0.5000009515933936,
        -0.5000028542374904,
        -0.9999516646142822
      ],
      "cartesian_polarization_e_A2": [
        0.010988621682696209,
        -0.013094583819720423,
        -0.01396680609902916
      ],
      "ranking_score": 0.6531304440005125
    }
  ],
  "formal_branches": [
    {
      "orbit_id": 0,
      "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": [
              6.485044775086261e-16,
              -3.597086466900808e-16,
              -0.7332794119948397
            ],
            "branch_aligned_reduced_polarization": [
              6.485044775086261e-16,
              -3.597086466900808e-16,
              -0.7332794119948397
            ],
            "target_residual": 0.2332794119948397,
            "energy_eV": -192.20180839398287,
            "max_atomic_step_A": 0.033290176346051054,
            "max_log_strain_component": 0.0058341913449556845,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.4934303970362643,
            "cell_principal_stretches": [
              1.0058512433847726,
              1.001049423915728,
              0.9985033996866061
            ],
            "cell_volume_ratio": 1.0053998706912297,
            "cell_rmsd_from_input_A": 0.0179254068602417
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              3.3461278016330204e-15,
              -3.734632241587725e-15,
              -0.5006577786388526
            ],
            "branch_aligned_reduced_polarization": [
              3.3461278016330204e-15,
              -3.734632241587725e-15,
              -0.5006577786388526
            ],
            "target_residual": 0.0006577786388526352,
            "energy_eV": -191.73419172899665
          }
        ],
        "iterations": 1
      },
      "parent": {
        "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,
          -0.5
        ],
        "formal_class": [
          0.0,
          0.0,
          0.5
        ],
        "target_residual": 0.0006577786388526352,
        "parent_symmetrization_rmsd_A": 0.021008861579935777,
        "parent_cell_rmsd_A": 0.0179254068602417,
        "energy_eV": -191.73419172899665,
        "reduced_polarization": [
          3.3461278016330204e-15,
          -3.734632241587725e-15,
          -0.5006577786388526
        ],
        "cartesian_polarization_e_A2": [
          9.790759194983816e-17,
          -9.737548547184991e-17,
          -0.006870817361387456
        ],
        "ranking_score": 0.5268057705727015
      },
      "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": [
          -192.20180839398284,
          -192.1761383227889,
          -192.1403091963229,
          -192.09473796080877,
          -192.03982497249416,
          -191.97595413892898,
          -191.9034931272455,
          -191.82279363640856,
          -191.73419172899662
        ],
        "cartesian_polarizations_e_A2": [
          [
            1.509407248175175e-17,
            -7.031162877575499e-18,
            -0.010058703249223262
          ],
          [
            3.358557795161071e-17,
            2.306502453982134e-17,
            -0.009661023762417354
          ],
          [
            2.976591463704697e-17,
            -4.808340056753741e-17,
            -0.009262904510801135
          ],
          [
            4.4714165251320206e-17,
            -3.8135748615198466e-19,
            -0.008864455291622674
          ],
          [
            3.012602257980664e-17,
            -2.5762417791207194e-17,
            -0.008465781771826438
          ],
          [
            7.578803487262453e-17,
            -1.139486433863782e-16,
            -0.008066985478775107
          ],
          [
            7.845823895313953e-17,
            -1.2178819531896506e-18,
            -0.00766816395615952
          ],
          [
            7.743559456153772e-17,
            2.2819919811848053e-18,
            -0.007269411059309278
          ],
          [
            8.618224563131135e-17,
            -1.1007002573242675e-16,
            -0.006870817361387411
          ]
        ],
        "raw_reduced_polarization": [
          [
            6.904562496385641e-16,
            -2.7809407979401205e-16,
            -0.73327941199484
          ],
          [
            1.3345422058737374e-15,
            9.164368226739903e-16,
            -0.7042490658975216
          ],
          [
            9.744518548495955e-16,
            -1.8985462859115575e-15,
            -0.67518991969648
          ],
          [
            1.490717668845926e-15,
            -5.778204147818626e-18,
            -0.6461099813848071
          ],
          [
            6.703563177660254e-16,
            -1.0105556036631366e-15,
            -0.6170169561274764
          ],
          [
            2.6294824573750226e-15,
            -4.512102652271733e-15,
            -0.5879182456698583
          ],
          [
            2.634561129490812e-15,
            -3.223286531348485e-17,
            -0.5588209597845991
          ],
          [
            2.4868922895897667e-15,
            1.0871032039384143e-16,
            -0.5297319378729828
          ],
          [
            2.807438044626944e-15,
            -4.240190069652515e-15,
            -0.5006577786388493
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            6.904562496385641e-16,
            -2.7809407979401205e-16,
            -0.73327941199484
          ],
          [
            1.3345422058737374e-15,
            9.164368226739903e-16,
            -0.7042490658975216
          ],
          [
            9.744518548495955e-16,
            -1.898546285911558e-15,
            -0.67518991969648
          ],
          [
            1.490717668845926e-15,
            -5.7782041478186055e-18,
            -0.6461099813848071
          ],
          [
            6.703563177660254e-16,
            -1.0105556036631366e-15,
            -0.6170169561274764
          ],
          [
            2.6294824573750226e-15,
            -4.512102652271733e-15,
            -0.5879182456698583
          ],
          [
            2.634561129490812e-15,
            -3.223286531348505e-17,
            -0.5588209597845991
          ],
          [
            2.4868922895897667e-15,
            1.0871032039384143e-16,
            -0.5297319378729828
          ],
          [
            2.807438044626944e-15,
            -4.240190069652515e-15,
            -0.5006577786388493
          ]
        ],
        "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": [
          [
            6.661338147750939e-16,
            -2.7755575615628914e-16,
            0.26672058800515996
          ],
          [
            1.3322676295501878e-15,
            8.881784197001252e-16,
            0.29575093410247844
          ],
          [
            9.992007221626409e-16,
            -1.887379141862766e-15,
            0.32481008030352
          ],
          [
            1.4432899320127035e-15,
            0.0,
            0.35389001861519287
          ],
          [
            6.661338147750939e-16,
            -9.992007221626409e-16,
            0.3829830438725236
          ],
          [
            2.6645352591003757e-15,
            -4.496403249731884e-15,
            0.4120817543301417
          ],
          [
            2.6645352591003757e-15,
            -5.551115123125783e-17,
            0.4411790402154009
          ],
          [
            2.4424906541753444e-15,
            1.1102230246251565e-16,
            0.4702680621270172
          ],
          [
            2.7755575615628914e-15,
            -4.218847493575595e-15,
            0.4993422213611507
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -191.73419172899662,
          -191.67101317830375,
          -191.60236590512744,
          -191.52839853039134,
          -191.44925547669618,
          -191.36507692850148,
          -191.27599873788475,
          -191.18215230189784,
          -191.08366444418738
        ],
        "cartesian_polarizations_e_A2": [
          [
            1.0729547052577373e-16,
            -8.74174928123555e-17,
            -0.00687081736138743
          ],
          [
            8.829407307200876e-17,
            -3.7272535692685154e-18,
            -0.006535807924134241
          ],
          [
            1.0782061166832126e-16,
            -3.942892823451494e-17,
            -0.006200658334994597
          ],
          [
            1.1286323685679537e-16,
            -5.446074867731311e-17,
            -0.005865410930414561
          ],
          [
            1.522688465751011e-16,
            -1.188272465576687e-16,
            -0.005530105307931807
          ],
          [
            1.520281618544887e-16,
            -1.0304279275826627e-16,
            -0.005194778143080736
          ],
          [
            1.3135163869322522e-16,
            -6.655353221411528e-17,
            -0.004859463002412744
          ],
          [
            8.744852019236899e-17,
            -1.1738722754207087e-16,
            -0.004524190163305563
          ],
          [
            1.6255742870220747e-16,
            -1.6561445604028377e-16,
            -0.0041889864560634826
          ]
        ],
        "raw_reduced_polarization": [
          [
            3.7774288388469715e-15,
            -3.33805693933331e-15,
            -0.5006577786388507
          ],
          [
            3.0933403953850543e-15,
            -1.3220827568383674e-16,
            -0.4762732728923712
          ],
          [
            4.166961748067801e-15,
            -1.5544622835367522e-15,
            -0.4518758156279009
          ],
          [
            4.561121040887558e-15,
            -2.152985778987501e-15,
            -0.42746849035678974
          ],
          [
            6.5161797933812126e-15,
            -4.708240296893897e-15,
            -0.40305418166104356
          ],
          [
            6.638625585241522e-15,
            -4.080569512663496e-15,
            -0.37863556179205404
          ],
          [
            5.8111280885960246e-15,
            -2.6334218011107656e-15,
            -0.35421507698164784
          ],
          [
            3.907490798599828e-15,
            -4.645266286235898e-15,
            -0.3297949342434354
          ],
          [
            7.435951610031522e-15,
            -6.550324683843741e-15,
            -0.3053770897947285
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            3.7774288388469715e-15,
            -3.33805693933331e-15,
            -0.5006577786388507
          ],
          [
            3.0933403953850543e-15,
            -1.3220827568383684e-16,
            -0.4762732728923712
          ],
          [
            4.166961748067801e-15,
            -1.5544622835367522e-15,
            -0.4518758156279009
          ],
          [
            4.561121040887558e-15,
            -2.152985778987501e-15,
            -0.42746849035678974
          ],
          [
            6.5161797933812126e-15,
            -4.708240296893897e-15,
            -0.40305418166104356
          ],
          [
            6.638625585241522e-15,
            -4.080569512663496e-15,
            -0.37863556179205404
          ],
          [
            5.8111280885960246e-15,
            -2.6334218011107656e-15,
            -0.35421507698164784
          ],
          [
            3.907490798599828e-15,
            -4.645266286235898e-15,
            -0.3297949342434354
          ],
          [
            7.435951610031522e-15,
            -6.550324683843741e-15,
            -0.3053770897947285
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          7.194105080773023e-15,
          -8.428807766154232e-15,
          -0.26848568433030573
        ],
        "actual_opposite_endpoint_branch_residual": 0.036891405464422766
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            6.904562496385641e-16,
            -2.7809407979401205e-16,
            -0.73327941199484
          ],
          [
            1.3345422058737374e-15,
            9.164368226739903e-16,
            -0.7042490658975216
          ],
          [
            9.744518548495955e-16,
            -1.8985462859115575e-15,
            -0.67518991969648
          ],
          [
            1.490717668845926e-15,
            -5.778204147818626e-18,
            -0.6461099813848071
          ],
          [
            6.703563177660254e-16,
            -1.0105556036631366e-15,
            -0.6170169561274764
          ],
          [
            2.6294824573750226e-15,
            -4.512102652271733e-15,
            -0.5879182456698583
          ],
          [
            2.634561129490812e-15,
            -3.223286531348485e-17,
            -0.5588209597845991
          ],
          [
            2.4868922895897667e-15,
            1.0871032039384143e-16,
            -0.5297319378729828
          ],
          [
            2.807438044626944e-15,
            -4.240190069652515e-15,
            -0.5006577786388493
          ],
          [
            3.0933403953850543e-15,
            -1.3220827568383674e-16,
            -0.4762732728923712
          ],
          [
            4.166961748067801e-15,
            -1.5544622835367522e-15,
            -0.4518758156279009
          ],
          [
            4.561121040887558e-15,
            -2.152985778987501e-15,
            -0.42746849035678974
          ],
          [
            6.5161797933812126e-15,
            -4.708240296893897e-15,
            -0.40305418166104356
          ],
          [
            6.638625585241522e-15,
            -4.080569512663496e-15,
            -0.37863556179205404
          ],
          [
            5.8111280885960246e-15,
            -2.6334218011107656e-15,
            -0.35421507698164784
          ],
          [
            3.907490798599828e-15,
            -4.645266286235898e-15,
            -0.3297949342434354
          ],
          [
            7.435951610031522e-15,
            -6.550324683843741e-15,
            -0.3053770897947285
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            6.904562496385641e-16,
            -2.7809407979401205e-16,
            -0.73327941199484
          ],
          [
            1.3345422058737374e-15,
            9.164368226739903e-16,
            -0.7042490658975216
          ],
          [
            9.744518548495955e-16,
            -1.898546285911558e-15,
            -0.67518991969648
          ],
          [
            1.490717668845926e-15,
            -5.7782041478186055e-18,
            -0.6461099813848071
          ],
          [
            6.703563177660254e-16,
            -1.0105556036631366e-15,
            -0.6170169561274764
          ],
          [
            2.6294824573750226e-15,
            -4.512102652271733e-15,
            -0.5879182456698583
          ],
          [
            2.634561129490812e-15,
            -3.223286531348505e-17,
            -0.5588209597845991
          ],
          [
            2.4868922895897667e-15,
            1.0871032039384143e-16,
            -0.5297319378729828
          ],
          [
            2.807438044626944e-15,
            -4.240190069652515e-15,
            -0.5006577786388493
          ],
          [
            3.0933403953850543e-15,
            -1.3220827568383684e-16,
            -0.4762732728923712
          ],
          [
            4.166961748067801e-15,
            -1.5544622835367522e-15,
            -0.4518758156279009
          ],
          [
            4.561121040887558e-15,
            -2.152985778987501e-15,
            -0.42746849035678974
          ],
          [
            6.5161797933812126e-15,
            -4.708240296893897e-15,
            -0.40305418166104356
          ],
          [
            6.638625585241522e-15,
            -4.080569512663496e-15,
            -0.37863556179205404
          ],
          [
            5.8111280885960246e-15,
            -2.6334218011107656e-15,
            -0.35421507698164784
          ],
          [
            3.907490798599828e-15,
            -4.645266286235898e-15,
            -0.3297949342434354
          ],
          [
            7.435951610031522e-15,
            -6.550324683843741e-15,
            -0.3053770897947285
          ]
        ],
        "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": [
          [
            6.661338147750939e-16,
            -2.7755575615628914e-16,
            0.26672058800515996
          ],
          [
            1.3322676295501878e-15,
            8.881784197001252e-16,
            0.29575093410247844
          ],
          [
            9.992007221626409e-16,
            -1.887379141862766e-15,
            0.32481008030352
          ],
          [
            1.4432899320127035e-15,
            0.0,
            0.35389001861519287
          ],
          [
            6.661338147750939e-16,
            -9.992007221626409e-16,
            0.3829830438725236
          ],
          [
            2.6645352591003757e-15,
            -4.496403249731884e-15,
            0.4120817543301417
          ],
          [
            2.6645352591003757e-15,
            -5.551115123125783e-17,
            0.4411790402154009
          ],
          [
            2.4424906541753444e-15,
            1.1102230246251565e-16,
            0.4702680621270172
          ],
          [
            2.7755575615628914e-15,
            -4.218847493575595e-15,
            0.4993422213611507
          ],
          [
            3.1086244689504383e-15,
            -1.1102230246251565e-16,
            -0.4762732728923712
          ],
          [
            4.218847493575595e-15,
            -1.5543122344752192e-15,
            -0.4518758156279009
          ],
          [
            4.551914400963142e-15,
            -2.1649348980190553e-15,
            -0.42746849035678974
          ],
          [
            6.5503158452884236e-15,
            -4.718447854656915e-15,
            -0.40305418166104356
          ],
          [
            6.661338147750939e-15,
            -4.107825191113079e-15,
            -0.37863556179205404
          ],
          [
            5.773159728050814e-15,
            -2.609024107869118e-15,
            -0.35421507698164784
          ],
          [
            3.885780586188048e-15,
            -4.6629367034256575e-15,
            -0.3297949342434354
          ],
          [
            7.438494264988549e-15,
            -6.5503158452884236e-15,
            -0.3053770897947285
          ]
        ]
      },
      "incoming_structure_ids": [
        "incoming_00_000",
        "incoming_00_001",
        "incoming_00_002",
        "incoming_00_003",
        "incoming_00_004",
        "incoming_00_005",
        "incoming_00_006",
        "incoming_00_007",
        "incoming_00_008"
      ],
      "reflected_structure_ids": [
        "reflected_00_001",
        "reflected_00_002",
        "reflected_00_003",
        "reflected_00_004",
        "reflected_00_005",
        "reflected_00_006",
        "reflected_00_007",
        "reflected_00_008"
      ]
    },
    {
      "orbit_id": 1,
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.0,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        -1.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              6.485044775086261e-16,
              -3.597086466900808e-16,
              -0.7332794119948397
            ],
            "branch_aligned_reduced_polarization": [
              6.485044775086261e-16,
              -3.597086466900808e-16,
              -0.7332794119948397
            ],
            "target_residual": 0.2667205880051603,
            "energy_eV": -192.20180839398287,
            "max_atomic_step_A": 0.03806240479554469,
            "max_log_strain_component": 0.006670536987188646,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.4934303970362643,
            "cell_principal_stretches": [
              1.0017138904006124,
              0.99880148652458,
              0.9933516616582727
            ],
            "cell_volume_ratio": 0.9938615717190429,
            "cell_rmsd_from_input_A": 0.02038582447754672
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -4.504139180295381e-15,
              4.835141917857965e-15,
              -0.9987746565513962
            ],
            "branch_aligned_reduced_polarization": [
              -4.504139180295381e-15,
              4.835141917857965e-15,
              -0.9987746565513962
            ],
            "target_residual": 0.0012253434486038106,
            "energy_eV": -191.8738176130459,
            "max_atomic_step_A": 0.00017356074098477127,
            "max_log_strain_component": 3.171720117531827e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.4934303970362643,
            "cell_principal_stretches": [
              1.0017220466532528,
              0.9987957912416033,
              0.9933201558234234
            ],
            "cell_volume_ratio": 0.9938324747901881,
            "cell_rmsd_from_input_A": 0.020482481370503382
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -5.770059581354816e-16,
              -1.522980079004932e-16,
              -0.9999994739968188
            ],
            "branch_aligned_reduced_polarization": [
              -5.770059581354816e-16,
              -1.522980079004932e-16,
              -0.9999994739968188
            ],
            "target_residual": 5.260031812337473e-07,
            "energy_eV": -191.8697482712637
          }
        ],
        "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": [
          0.0,
          0.0,
          -1.0
        ],
        "formal_class": [
          0.0,
          0.0,
          0.0
        ],
        "target_residual": 5.260031812337473e-07,
        "parent_symmetrization_rmsd_A": 0.02442180441081978,
        "parent_cell_rmsd_A": 0.020482481370503382,
        "energy_eV": -191.8697482712637,
        "reduced_polarization": [
          -5.770059581354816e-16,
          -1.522980079004932e-16,
          -0.9999994739968188
        ],
        "cartesian_polarization_e_A2": [
          -7.059416872412293e-17,
          2.2300990119820968e-18,
          -0.013710343631643166
        ],
        "ranking_score": 0.5295434767598081
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 2,
      "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": [
              6.485044775086261e-16,
              -3.597086466900808e-16,
              -0.7332794119948397
            ],
            "branch_aligned_reduced_polarization": [
              6.661338147750939e-16,
              -3.597086466900808e-16,
              -0.7332794119948397
            ],
            "target_residual": 0.5517420448548919,
            "energy_eV": -192.20180839398287,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.00578445976827746,
            "step_scale": 0.9914758406560628,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.4934303970362643,
            "cell_principal_stretches": [
              1.0062992747596415,
              1.0005450238721447,
              0.9985161474765049
            ],
            "cell_volume_ratio": 1.0053537183391719,
            "cell_rmsd_from_input_A": 0.01949050330497206
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.49826616346937685,
              -2.093752316060426e-15,
              -0.4882094196077576
            ],
            "branch_aligned_reduced_polarization": [
              0.49826616346937685,
              -2.093752316060426e-15,
              -0.4882094196077576
            ],
            "target_residual": 0.01191738121823978,
            "energy_eV": -188.17421434336356,
            "max_atomic_step_A": 0.001888678815744143,
            "max_log_strain_component": 0.0003058806681125063,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.4934303970362643,
            "cell_principal_stretches": [
              1.0060180610408955,
              1.0004636032128902,
              0.9985945580305529
            ],
            "cell_volume_ratio": 1.0050698987526259,
            "cell_rmsd_from_input_A": 0.018647885469990463
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.5000770199812111,
              -3.0878897542661324e-16,
              -0.49994569656337096
            ],
            "branch_aligned_reduced_polarization": [
              0.5000770199812111,
              -3.0878897542661324e-16,
              -0.49994569656337096
            ],
            "target_residual": 9.423874328261425e-05,
            "energy_eV": -188.2052732278506
          }
        ],
        "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": [
          0.5,
          0.0,
          -0.5
        ],
        "formal_class": [
          0.5,
          0.0,
          0.5
        ],
        "target_residual": 9.423874328261425e-05,
        "parent_symmetrization_rmsd_A": 0.08236371452044303,
        "parent_cell_rmsd_A": 0.018647885469990463,
        "energy_eV": -188.2052732278506,
        "reduced_polarization": [
          0.5000770199812111,
          -3.0878897542661324e-16,
          -0.49994569656337096
        ],
        "cartesian_polarization_e_A2": [
          0.010876705629654333,
          2.0758965727920984e-16,
          -0.006843222166917529
        ],
        "ranking_score": 0.5872141633745058
      },
      "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,
        -0.5,
        -0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              6.485044775086261e-16,
              -3.597086466900808e-16,
              -0.7332794119948397
            ],
            "branch_aligned_reduced_polarization": [
              6.485044775086261e-16,
              -3.3306690738754696e-16,
              -0.7332794119948397
            ],
            "target_residual": 0.5517420448548922,
            "energy_eV": -192.20180839398287,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.01654120985313604,
            "step_scale": 0.8787163418763103,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.4934303970362643,
            "cell_principal_stretches": [
              1.0189342474911722,
              1.000922087282879,
              0.985164448855395
            ],
            "cell_volume_ratio": 1.0047434039738687,
            "cell_rmsd_from_input_A": 0.0957365939735219
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              3.4046251162096783e-14,
              -0.4326059212128861,
              -0.49303249829524215
            ],
            "branch_aligned_reduced_polarization": [
              3.4046251162096783e-14,
              -0.4326059212128861,
              -0.49303249829524215
            ],
            "target_residual": 0.0677532872676265,
            "energy_eV": -187.7719187502874,
            "max_atomic_step_A": 0.018439383096692574,
            "max_log_strain_component": 0.0028594256126079987,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.4934303970362643,
            "cell_principal_stretches": [
              1.0215012270849442,
              1.0008075188828776,
              0.9822238214401543
            ],
            "cell_volume_ratio": 1.004153057161571,
            "cell_rmsd_from_input_A": 0.11159736918709948
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              3.8849600338437815e-15,
              -0.4985707290967838,
              -0.4958690801923666
            ],
            "branch_aligned_reduced_polarization": [
              3.8849600338437815e-15,
              -0.4985707290967838,
              -0.4958690801923666
            ],
            "target_residual": 0.004371191344688375,
            "energy_eV": -186.5522599957172,
            "max_atomic_step_A": 0.0008453794513841666,
            "max_log_strain_component": 0.00011638587498724433,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.4934303970362643,
            "cell_principal_stretches": [
              1.0215281298659549,
              1.0007865782983343,
              0.9821129895269325
            ],
            "cell_volume_ratio": 1.0040451849415792,
            "cell_rmsd_from_input_A": 0.11200604743791363
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              5.539753071841744e-17,
              -0.5000082725898115,
              -0.4999045967171063
            ],
            "branch_aligned_reduced_polarization": [
              5.539753071841744e-17,
              -0.5000082725898115,
              -0.4999045967171063
            ],
            "target_residual": 9.576127677242656e-05,
            "energy_eV": -186.54241405311316
          }
        ],
        "iterations": 3
      },
      "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,
          -0.5,
          -0.5
        ],
        "formal_class": [
          0.0,
          0.5,
          0.5
        ],
        "target_residual": 9.576127677242656e-05,
        "parent_symmetrization_rmsd_A": 0.0806120559346421,
        "parent_cell_rmsd_A": 0.11200604743791363,
        "energy_eV": -186.54241405311316,
        "reduced_polarization": [
          5.539753071841744e-17,
          -0.5000082725898115,
          -0.4999045967171063
        ],
        "cartesian_polarization_e_A2": [
          -2.860696203127991e-16,
          -0.012712636601357512,
          -0.007106493574593461
        ],
        "ranking_score": 0.6088050903476654
      },
      "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,
        0.0,
        -1.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              6.485044775086261e-16,
              -3.597086466900808e-16,
              -0.7332794119948397
            ],
            "branch_aligned_reduced_polarization": [
              6.661338147750939e-16,
              -3.597086466900808e-16,
              -0.7332794119948397
            ],
            "target_residual": 0.5666920434114262,
            "energy_eV": -192.20180839398287,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.00649814131552167,
            "step_scale": 0.9741556531342693,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.4934303970362643,
            "cell_principal_stretches": [
              1.0016695590674074,
              0.9992664380491845,
              0.9930914256155612
            ],
            "cell_volume_ratio": 0.9940197400625466,
            "cell_rmsd_from_input_A": 0.021303902501649295
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.4839370789802524,
              3.0152723010374477e-15,
              -0.9664518538579516
            ],
            "branch_aligned_reduced_polarization": [
              0.4839370789802524,
              3.0152723010374477e-15,
              -0.9664518538579516
            ],
            "target_residual": 0.037195369890012986,
            "energy_eV": -188.9514395946507,
            "max_atomic_step_A": 0.0066956897453731784,
            "max_log_strain_component": 0.000978568859190127,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.4934303970362643,
            "cell_principal_stretches": [
              1.0019212228771746,
              0.9990673128117687,
              0.9921432724789299
            ],
            "cell_volume_ratio": 0.9931222636908268,
            "cell_rmsd_from_input_A": 0.02419448440920955
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.5001228834305129,
              9.965145773631207e-16,
              -0.9998272472614445
            ],
            "branch_aligned_reduced_polarization": [
              0.5001228834305129,
              9.965145773631207e-16,
              -0.9998272472614445
            ],
            "target_residual": 0.00021199963720031586,
            "energy_eV": -188.67447203588586
          }
        ],
        "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,
          0.0,
          -1.0
        ],
        "formal_class": [
          0.5,
          0.0,
          0.0
        ],
        "target_residual": 0.00021199963720031586,
        "parent_symmetrization_rmsd_A": 0.08561874793995616,
        "parent_cell_rmsd_A": 0.02419448440920955,
        "energy_eV": -188.67447203588586,
        "reduced_polarization": [
          0.5001228834305129,
          9.965145773631207e-16,
          -0.9998272472614445
        ],
        "cartesian_polarization_e_A2": [
          0.010971579832662027,
          2.664180693394197e-16,
          -0.013689213832550071
        ],
        "ranking_score": 0.5920913683166592
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 5,
      "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,
        -1.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              6.485044775086261e-16,
              -3.597086466900808e-16,
              -0.7332794119948397
            ],
            "branch_aligned_reduced_polarization": [
              6.485044775086261e-16,
              -3.3306690738754696e-16,
              -0.7332794119948397
            ],
            "target_residual": 0.5666920434114265,
            "energy_eV": -192.20180839398287,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.016338327090559657,
            "step_scale": 0.8679386296930508,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.4934303970362643,
            "cell_principal_stretches": [
              1.0146936836400149,
              0.9989596814963195,
              0.9812871843046522
            ],
            "cell_volume_ratio": 0.9946700564707687,
            "cell_rmsd_from_input_A": 0.09448525974173962
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              2.441804457147019e-14,
              -0.4098657684077724,
              -0.9304870706413578
            ],
            "branch_aligned_reduced_polarization": [
              2.441804457147019e-14,
              -0.4098657684077724,
              -0.9304870706413578
            ],
            "target_residual": 0.11382542357813082,
            "energy_eV": -189.00706451674387,
            "max_atomic_step_A": 0.029596157239398402,
            "max_log_strain_component": 0.004431421821460893,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.4934303970362643,
            "cell_principal_stretches": [
              1.0185114350476312,
              0.9985189936759646,
              0.9758271538610366
            ],
            "cell_volume_ratio": 0.9924191558109731,
            "cell_rmsd_from_input_A": 0.12054746183669113
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              8.330957976469154e-15,
              -0.49640163813791566,
              -0.9922960631807406
            ],
            "branch_aligned_reduced_polarization": [
              8.330957976469154e-15,
              -0.49640163813791566,
              -0.9922960631807406
            ],
            "target_residual": 0.008502873079474008,
            "energy_eV": -187.342811125443,
            "max_atomic_step_A": 0.00182350452791155,
            "max_log_strain_component": 0.00023759215959629856,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.4934303970362643,
            "cell_principal_stretches": [
              1.0186804533135185,
              0.998476343417354,
              0.9754929596519814
            ],
            "cell_volume_ratio": 0.9922015290114498,
            "cell_rmsd_from_input_A": 0.12193550056401901
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -3.3726193857056543e-16,
              -0.49994712054514395,
              -0.9996713230675267
            ],
            "branch_aligned_reduced_polarization": [
              -3.3726193857056543e-16,
              -0.49994712054514395,
              -0.9996713230675267
            ],
            "target_residual": 0.00033290353360384504,
            "energy_eV": -187.25408542007145
          }
        ],
        "iterations": 3
      },
      "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": [
          0.0,
          -0.5,
          -1.0
        ],
        "formal_class": [
          0.0,
          0.5,
          0.0
        ],
        "target_residual": 0.00033290353360384504,
        "parent_symmetrization_rmsd_A": 0.08676439995395768,
        "parent_cell_rmsd_A": 0.12193550056401901,
        "energy_eV": -187.25408542007145,
        "reduced_polarization": [
          -3.3726193857056543e-16,
          -0.49994712054514395,
          -0.9996713230675267
        ],
        "cartesian_polarization_e_A2": [
          -3.869419765994207e-16,
          -0.013059702265082566,
          -0.013973499772765224
        ],
        "ranking_score": 0.6179140821621701
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 6,
      "formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.5,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.5,
        -0.5,
        -0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              6.485044775086261e-16,
              -3.597086466900808e-16,
              -0.7332794119948397
            ],
            "branch_aligned_reduced_polarization": [
              6.661338147750939e-16,
              -3.3306690738754696e-16,
              -0.7332794119948397
            ],
            "target_residual": 0.7445933682626089,
            "energy_eV": -192.20180839398287,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.012002591686810234,
            "step_scale": 0.6376119735931722,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.4934303970362643,
            "cell_principal_stretches": [
              1.0137535410475844,
              1.0006573834861745,
              0.9891757806954886
            ],
            "cell_volume_ratio": 1.0034396617069108,
            "cell_rmsd_from_input_A": 0.06959857749493939
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.3170358648807961,
              -0.3153379825887202,
              -0.5586549956410937
            ],
            "branch_aligned_reduced_polarization": [
              0.3170358648807961,
              -0.3153379825887202,
              -0.5586549956410937
            ],
            "target_residual": 0.2664889189590795,
            "energy_eV": -188.48091839790663,
            "max_atomic_step_A": 0.06581928510225456,
            "max_log_strain_component": 0.007442522918055494,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.4934303970362643,
            "cell_principal_stretches": [
              1.0213606715228467,
              1.0006950604122997,
              0.9819623841507745
            ],
            "cell_volume_ratio": 1.0036348624194475,
            "cell_rmsd_from_input_A": 0.11191550773529287
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.4965284913166148,
              -0.4906139836353283,
              -0.47851142335152136
            ],
            "branch_aligned_reduced_polarization": [
              0.4965284913166148,
              -0.4906139836353283,
              -0.47851142335152136
            ],
            "target_residual": 0.02370459031736775,
            "energy_eV": -182.80795548643604,
            "max_atomic_step_A": 0.0049746953074593725,
            "max_log_strain_component": 0.0006449429332961679,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.4934303970362643,
            "cell_principal_stretches": [
              1.02162716010663,
              1.0005812725535348,
              0.9812335566928766
            ],
            "cell_volume_ratio": 1.003037551417054,
            "cell_rmsd_from_input_A": 0.11482331839039701
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.5000096157963726,
              -0.49997096148454256,
              -0.49914699223403836
            ],
            "branch_aligned_reduced_polarization": [
              0.5000096157963726,
              -0.49997096148454256,
              -0.49914699223403836
            ],
            "target_residual": 0.0008535560600866976,
            "energy_eV": -182.6519978129149
          }
        ],
        "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": [
          0.5,
          -0.5,
          -0.5
        ],
        "formal_class": [
          0.5,
          0.5,
          0.5
        ],
        "target_residual": 0.0008535560600866976,
        "parent_symmetrization_rmsd_A": 0.11434255969468413,
        "parent_cell_rmsd_A": 0.11482331839039701,
        "energy_eV": -182.6519978129149,
        "reduced_polarization": [
          0.5000096157963726,
          -0.49997096148454256,
          -0.49914699223403836
        ],
        "cartesian_polarization_e_A2": [
          0.010892572461607096,
          -0.012731244849373841,
          -0.007084138151945846
        ],
        "ranking_score": 0.6447555014124567
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 7,
      "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,
        -1.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              6.485044775086261e-16,
              -3.597086466900808e-16,
              -0.7332794119948397
            ],
            "branch_aligned_reduced_polarization": [
              6.661338147750939e-16,
              -3.3306690738754696e-16,
              -0.7332794119948397
            ],
            "target_residual": 0.7557379652140135,
            "energy_eV": -192.20180839398287,
            "max_atomic_step_A": 0.12000000000000001,
            "max_log_strain_component": 0.011893779902440515,
            "step_scale": 0.6318315806253811,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.4934303970362643,
            "cell_principal_stretches": [
              1.0107118768017997,
              0.9992555832341466,
              0.9862941693314082
            ],
            "cell_volume_ratio": 0.9961171522388944,
            "cell_rmsd_from_input_A": 0.06900009758881621
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.31190551436898334,
              -0.303219098575665,
              -0.8733496081646196
            ],
            "branch_aligned_reduced_polarization": [
              0.31190551436898334,
              -0.303219098575665,
              -0.8733496081646196
            ],
            "target_residual": 0.30023754002826825,
            "energy_eV": -189.20625685698127,
            "max_atomic_step_A": 0.07776993283789384,
            "max_log_strain_component": 0.0089018817063575,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.4934303970362643,
            "cell_principal_stretches": [
              1.0184150037874178,
              0.9983978436510058,
              0.9753107481816854
            ],
            "cell_volume_ratio": 0.9916797237053386,
            "cell_rmsd_from_input_A": 0.12145968929213126
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.4979833160913799,
              -0.4858898393157469,
              -0.9720151751888513
            ],
            "branch_aligned_reduced_polarization": [
              0.4979833160913799,
              -0.4858898393157469,
              -0.9720151751888513
            ],
            "target_residual": 0.03140563752311699,
            "energy_eV": -183.88429056253418,
            "max_atomic_step_A": 0.007209411019490007,
            "max_log_strain_component": 0.0009084639351476678,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.4934303970362643,
            "cell_principal_stretches": [
              1.019110372470063,
              0.9982353919716799,
              0.973986777151137
            ],
            "cell_volume_ratio": 0.9908484772664271,
            "cell_rmsd_from_input_A": 0.1270307772666968
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.4999004959273696,
              -0.4997493292192982,
              -0.9983350013900106
            ],
            "branch_aligned_reduced_polarization": [
              0.4999004959273696,
              -0.4997493292192982,
              -0.9983350013900106
            ],
            "target_residual": 0.0016867001132490015,
            "energy_eV": -183.4850222180033,
            "max_atomic_step_A": 0.0002951634517430876,
            "max_log_strain_component": 4.733430617402134e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.4934303970362643,
            "cell_principal_stretches": [
              1.0191240667293144,
              0.9982269710253269,
              0.9739393508040162
            ],
            "cell_volume_ratio": 0.990805185378222,
            "cell_rmsd_from_input_A": 0.12719384025944744
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              0.5000009515933936,
              -0.5000028542374904,
              -0.9999516646142822
            ],
            "branch_aligned_reduced_polarization": [
              0.5000009515933936,
              -0.5000028542374904,
              -0.9999516646142822
            ],
            "target_residual": 4.842893467883458e-05,
            "energy_eV": -183.4735818427058
          }
        ],
        "iterations": 4
      },
      "parent": {
        "candidate_id": "bec_projection_07",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.5,
          -0.5,
          -1.0
        ],
        "formal_class": [
          0.5,
          0.5,
          0.0
        ],
        "target_residual": 4.842893467883458e-05,
        "parent_symmetrization_rmsd_A": 0.1212351260662929,
        "parent_cell_rmsd_A": 0.12719384025944744,
        "energy_eV": -183.4735818427058,
        "reduced_polarization": [
          0.5000009515933936,
          -0.5000028542374904,
          -0.9999516646142822
        ],
        "cartesian_polarization_e_A2": [
          0.010988621682696209,
          -0.013094583819720423,
          -0.01396680609902916
        ],
        "ranking_score": 0.6531304440005125
      },
      "branch_status": "awaiting_branch_sampling"
    }
  ],
  "sampled_polarization_branches": [
    {
      "orbit_id": 0,
      "candidate_id": "bec_projection_00",
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "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
        ],
        "endpoint_rmsd_A": 0.021008861579935777,
        "minimum_distance_A_by_image": [
          1.51961847464899,
          1.527237889546001,
          1.5348677500178396,
          1.5425080644834428,
          1.5452945863239056,
          1.5427326991595633,
          1.5401797743688683,
          1.5376359247455305,
          1.5351012638840746
        ],
        "minimum_distance_A": 1.51961847464899,
        "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": [
          363.1707871228219,
          363.415344364722,
          363.66006629014413,
          363.9049530099866,
          364.15000463522017,
          364.39522127689145,
          364.6406030461213,
          364.88615005410685,
          365.1318624121175
        ],
        "cell_deformation_log_strain_norm": 0.006114007998164729
      },
      "parent_reduced_polarization": [
        2.807438044626944e-15,
        -4.240190069652515e-15,
        -0.5006577786388493
      ],
      "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": [
          -192.20180839398284,
          -192.1761383227889,
          -192.1403091963229,
          -192.09473796080877,
          -192.03982497249416,
          -191.97595413892898,
          -191.9034931272455,
          -191.82279363640856,
          -191.73419172899662
        ],
        "cartesian_polarizations_e_A2": [
          [
            1.509407248175175e-17,
            -7.031162877575499e-18,
            -0.010058703249223262
          ],
          [
            3.358557795161071e-17,
            2.306502453982134e-17,
            -0.009661023762417354
          ],
          [
            2.976591463704697e-17,
            -4.808340056753741e-17,
            -0.009262904510801135
          ],
          [
            4.4714165251320206e-17,
            -3.8135748615198466e-19,
            -0.008864455291622674
          ],
          [
            3.012602257980664e-17,
            -2.5762417791207194e-17,
            -0.008465781771826438
          ],
          [
            7.578803487262453e-17,
            -1.139486433863782e-16,
            -0.008066985478775107
          ],
          [
            7.845823895313953e-17,
            -1.2178819531896506e-18,
            -0.00766816395615952
          ],
          [
            7.743559456153772e-17,
            2.2819919811848053e-18,
            -0.007269411059309278
          ],
          [
            8.618224563131135e-17,
            -1.1007002573242675e-16,
            -0.006870817361387411
          ]
        ],
        "raw_reduced_polarization": [
          [
            6.904562496385641e-16,
            -2.7809407979401205e-16,
            -0.73327941199484
          ],
          [
            1.3345422058737374e-15,
            9.164368226739903e-16,
            -0.7042490658975216
          ],
          [
            9.744518548495955e-16,
            -1.8985462859115575e-15,
            -0.67518991969648
          ],
          [
            1.490717668845926e-15,
            -5.778204147818626e-18,
            -0.6461099813848071
          ],
          [
            6.703563177660254e-16,
            -1.0105556036631366e-15,
            -0.6170169561274764
          ],
          [
            2.6294824573750226e-15,
            -4.512102652271733e-15,
            -0.5879182456698583
          ],
          [
            2.634561129490812e-15,
            -3.223286531348485e-17,
            -0.5588209597845991
          ],
          [
            2.4868922895897667e-15,
            1.0871032039384143e-16,
            -0.5297319378729828
          ],
          [
            2.807438044626944e-15,
            -4.240190069652515e-15,
            -0.5006577786388493
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            6.904562496385641e-16,
            -2.7809407979401205e-16,
            -0.73327941199484
          ],
          [
            1.3345422058737374e-15,
            9.164368226739903e-16,
            -0.7042490658975216
          ],
          [
            9.744518548495955e-16,
            -1.898546285911558e-15,
            -0.67518991969648
          ],
          [
            1.490717668845926e-15,
            -5.7782041478186055e-18,
            -0.6461099813848071
          ],
          [
            6.703563177660254e-16,
            -1.0105556036631366e-15,
            -0.6170169561274764
          ],
          [
            2.6294824573750226e-15,
            -4.512102652271733e-15,
            -0.5879182456698583
          ],
          [
            2.634561129490812e-15,
            -3.223286531348505e-17,
            -0.5588209597845991
          ],
          [
            2.4868922895897667e-15,
            1.0871032039384143e-16,
            -0.5297319378729828
          ],
          [
            2.807438044626944e-15,
            -4.240190069652515e-15,
            -0.5006577786388493
          ]
        ],
        "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": [
          [
            6.661338147750939e-16,
            -2.7755575615628914e-16,
            0.26672058800515996
          ],
          [
            1.3322676295501878e-15,
            8.881784197001252e-16,
            0.29575093410247844
          ],
          [
            9.992007221626409e-16,
            -1.887379141862766e-15,
            0.32481008030352
          ],
          [
            1.4432899320127035e-15,
            0.0,
            0.35389001861519287
          ],
          [
            6.661338147750939e-16,
            -9.992007221626409e-16,
            0.3829830438725236
          ],
          [
            2.6645352591003757e-15,
            -4.496403249731884e-15,
            0.4120817543301417
          ],
          [
            2.6645352591003757e-15,
            -5.551115123125783e-17,
            0.4411790402154009
          ],
          [
            2.4424906541753444e-15,
            1.1102230246251565e-16,
            0.4702680621270172
          ],
          [
            2.7755575615628914e-15,
            -4.218847493575595e-15,
            0.4993422213611507
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -191.73419172899662,
          -191.67101317830375,
          -191.60236590512744,
          -191.52839853039134,
          -191.44925547669618,
          -191.36507692850148,
          -191.27599873788475,
          -191.18215230189784,
          -191.08366444418738
        ],
        "cartesian_polarizations_e_A2": [
          [
            1.0729547052577373e-16,
            -8.74174928123555e-17,
            -0.00687081736138743
          ],
          [
            8.829407307200876e-17,
            -3.7272535692685154e-18,
            -0.006535807924134241
          ],
          [
            1.0782061166832126e-16,
            -3.942892823451494e-17,
            -0.006200658334994597
          ],
          [
            1.1286323685679537e-16,
            -5.446074867731311e-17,
            -0.005865410930414561
          ],
          [
            1.522688465751011e-16,
            -1.188272465576687e-16,
            -0.005530105307931807
          ],
          [
            1.520281618544887e-16,
            -1.0304279275826627e-16,
            -0.005194778143080736
          ],
          [
            1.3135163869322522e-16,
            -6.655353221411528e-17,
            -0.004859463002412744
          ],
          [
            8.744852019236899e-17,
            -1.1738722754207087e-16,
            -0.004524190163305563
          ],
          [
            1.6255742870220747e-16,
            -1.6561445604028377e-16,
            -0.0041889864560634826
          ]
        ],
        "raw_reduced_polarization": [
          [
            3.7774288388469715e-15,
            -3.33805693933331e-15,
            -0.5006577786388507
          ],
          [
            3.0933403953850543e-15,
            -1.3220827568383674e-16,
            -0.4762732728923712
          ],
          [
            4.166961748067801e-15,
            -1.5544622835367522e-15,
            -0.4518758156279009
          ],
          [
            4.561121040887558e-15,
            -2.152985778987501e-15,
            -0.42746849035678974
          ],
          [
            6.5161797933812126e-15,
            -4.708240296893897e-15,
            -0.40305418166104356
          ],
          [
            6.638625585241522e-15,
            -4.080569512663496e-15,
            -0.37863556179205404
          ],
          [
            5.8111280885960246e-15,
            -2.6334218011107656e-15,
            -0.35421507698164784
          ],
          [
            3.907490798599828e-15,
            -4.645266286235898e-15,
            -0.3297949342434354
          ],
          [
            7.435951610031522e-15,
            -6.550324683843741e-15,
            -0.3053770897947285
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            3.7774288388469715e-15,
            -3.33805693933331e-15,
            -0.5006577786388507
          ],
          [
            3.0933403953850543e-15,
            -1.3220827568383684e-16,
            -0.4762732728923712
          ],
          [
            4.166961748067801e-15,
            -1.5544622835367522e-15,
            -0.4518758156279009
          ],
          [
            4.561121040887558e-15,
            -2.152985778987501e-15,
            -0.42746849035678974
          ],
          [
            6.5161797933812126e-15,
            -4.708240296893897e-15,
            -0.40305418166104356
          ],
          [
            6.638625585241522e-15,
            -4.080569512663496e-15,
            -0.37863556179205404
          ],
          [
            5.8111280885960246e-15,
            -2.6334218011107656e-15,
            -0.35421507698164784
          ],
          [
            3.907490798599828e-15,
            -4.645266286235898e-15,
            -0.3297949342434354
          ],
          [
            7.435951610031522e-15,
            -6.550324683843741e-15,
            -0.3053770897947285
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          7.194105080773023e-15,
          -8.428807766154232e-15,
          -0.26848568433030573
        ],
        "actual_opposite_endpoint_branch_residual": 0.036891405464422766
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            6.904562496385641e-16,
            -2.7809407979401205e-16,
            -0.73327941199484
          ],
          [
            1.3345422058737374e-15,
            9.164368226739903e-16,
            -0.7042490658975216
          ],
          [
            9.744518548495955e-16,
            -1.8985462859115575e-15,
            -0.67518991969648
          ],
          [
            1.490717668845926e-15,
            -5.778204147818626e-18,
            -0.6461099813848071
          ],
          [
            6.703563177660254e-16,
            -1.0105556036631366e-15,
            -0.6170169561274764
          ],
          [
            2.6294824573750226e-15,
            -4.512102652271733e-15,
            -0.5879182456698583
          ],
          [
            2.634561129490812e-15,
            -3.223286531348485e-17,
            -0.5588209597845991
          ],
          [
            2.4868922895897667e-15,
            1.0871032039384143e-16,
            -0.5297319378729828
          ],
          [
            2.807438044626944e-15,
            -4.240190069652515e-15,
            -0.5006577786388493
          ],
          [
            3.0933403953850543e-15,
            -1.3220827568383674e-16,
            -0.4762732728923712
          ],
          [
            4.166961748067801e-15,
            -1.5544622835367522e-15,
            -0.4518758156279009
          ],
          [
            4.561121040887558e-15,
            -2.152985778987501e-15,
            -0.42746849035678974
          ],
          [
            6.5161797933812126e-15,
            -4.708240296893897e-15,
            -0.40305418166104356
          ],
          [
            6.638625585241522e-15,
            -4.080569512663496e-15,
            -0.37863556179205404
          ],
          [
            5.8111280885960246e-15,
            -2.6334218011107656e-15,
            -0.35421507698164784
          ],
          [
            3.907490798599828e-15,
            -4.645266286235898e-15,
            -0.3297949342434354
          ],
          [
            7.435951610031522e-15,
            -6.550324683843741e-15,
            -0.3053770897947285
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            6.904562496385641e-16,
            -2.7809407979401205e-16,
            -0.73327941199484
          ],
          [
            1.3345422058737374e-15,
            9.164368226739903e-16,
            -0.7042490658975216
          ],
          [
            9.744518548495955e-16,
            -1.898546285911558e-15,
            -0.67518991969648
          ],
          [
            1.490717668845926e-15,
            -5.7782041478186055e-18,
            -0.6461099813848071
          ],
          [
            6.703563177660254e-16,
            -1.0105556036631366e-15,
            -0.6170169561274764
          ],
          [
            2.6294824573750226e-15,
            -4.512102652271733e-15,
            -0.5879182456698583
          ],
          [
            2.634561129490812e-15,
            -3.223286531348505e-17,
            -0.5588209597845991
          ],
          [
            2.4868922895897667e-15,
            1.0871032039384143e-16,
            -0.5297319378729828
          ],
          [
            2.807438044626944e-15,
            -4.240190069652515e-15,
            -0.5006577786388493
          ],
          [
            3.0933403953850543e-15,
            -1.3220827568383684e-16,
            -0.4762732728923712
          ],
          [
            4.166961748067801e-15,
            -1.5544622835367522e-15,
            -0.4518758156279009
          ],
          [
            4.561121040887558e-15,
            -2.152985778987501e-15,
            -0.42746849035678974
          ],
          [
            6.5161797933812126e-15,
            -4.708240296893897e-15,
            -0.40305418166104356
          ],
          [
            6.638625585241522e-15,
            -4.080569512663496e-15,
            -0.37863556179205404
          ],
          [
            5.8111280885960246e-15,
            -2.6334218011107656e-15,
            -0.35421507698164784
          ],
          [
            3.907490798599828e-15,
            -4.645266286235898e-15,
            -0.3297949342434354
          ],
          [
            7.435951610031522e-15,
            -6.550324683843741e-15,
            -0.3053770897947285
          ]
        ],
        "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": [
          [
            6.661338147750939e-16,
            -2.7755575615628914e-16,
            0.26672058800515996
          ],
          [
            1.3322676295501878e-15,
            8.881784197001252e-16,
            0.29575093410247844
          ],
          [
            9.992007221626409e-16,
            -1.887379141862766e-15,
            0.32481008030352
          ],
          [
            1.4432899320127035e-15,
            0.0,
            0.35389001861519287
          ],
          [
            6.661338147750939e-16,
            -9.992007221626409e-16,
            0.3829830438725236
          ],
          [
            2.6645352591003757e-15,
            -4.496403249731884e-15,
            0.4120817543301417
          ],
          [
            2.6645352591003757e-15,
            -5.551115123125783e-17,
            0.4411790402154009
          ],
          [
            2.4424906541753444e-15,
            1.1102230246251565e-16,
            0.4702680621270172
          ],
          [
            2.7755575615628914e-15,
            -4.218847493575595e-15,
            0.4993422213611507
          ],
          [
            3.1086244689504383e-15,
            -1.1102230246251565e-16,
            -0.4762732728923712
          ],
          [
            4.218847493575595e-15,
            -1.5543122344752192e-15,
            -0.4518758156279009
          ],
          [
            4.551914400963142e-15,
            -2.1649348980190553e-15,
            -0.42746849035678974
          ],
          [
            6.5503158452884236e-15,
            -4.718447854656915e-15,
            -0.40305418166104356
          ],
          [
            6.661338147750939e-15,
            -4.107825191113079e-15,
            -0.37863556179205404
          ],
          [
            5.773159728050814e-15,
            -2.609024107869118e-15,
            -0.35421507698164784
          ],
          [
            3.885780586188048e-15,
            -4.6629367034256575e-15,
            -0.3297949342434354
          ],
          [
            7.438494264988549e-15,
            -6.5503158452884236e-15,
            -0.3053770897947285
          ]
        ]
      },
      "incoming_structure_ids": [
        "incoming_00_000",
        "incoming_00_001",
        "incoming_00_002",
        "incoming_00_003",
        "incoming_00_004",
        "incoming_00_005",
        "incoming_00_006",
        "incoming_00_007",
        "incoming_00_008"
      ],
      "reflected_structure_ids": [
        "reflected_00_001",
        "reflected_00_002",
        "reflected_00_003",
        "reflected_00_004",
        "reflected_00_005",
        "reflected_00_006",
        "reflected_00_007",
        "reflected_00_008"
      ],
      "positive_extension_structure_ids": [
        "extension_plus_00_000",
        "extension_plus_00_001",
        "extension_plus_00_002",
        "extension_plus_00_003"
      ],
      "negative_extension_structure_ids": [
        "extension_minus_00_000",
        "extension_minus_00_001",
        "extension_minus_00_002",
        "extension_minus_00_003"
      ],
      "extension": {
        "enabled": true,
        "fraction_beyond_polar_endpoint": 0.35,
        "images_per_side": 4,
        "construction": "continue fractional atomic displacements and symmetric log strain beyond +P; reflect these structures about N for the -P side",
        "positive_path_coordinates": [
          1.35,
          1.2625,
          1.175,
          1.0875
        ],
        "negative_path_coordinates": [
          -1.0875,
          -1.175,
          -1.2625,
          -1.35
        ]
      },
      "branch_coordinates": [
        1.35,
        1.2625,
        1.175,
        1.0875,
        1.0,
        0.875,
        0.75,
        0.625,
        0.5,
        0.375,
        0.25,
        0.125,
        0.0,
        -0.125,
        -0.25,
        -0.375,
        -0.5,
        -0.625,
        -0.75,
        -0.875,
        -1.0,
        -1.0875,
        -1.175,
        -1.2625,
        -1.35
      ],
      "parent": {
        "candidate_id": "bec_projection_00",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "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,
          -0.5
        ],
        "formal_class": [
          0.0,
          0.0,
          0.5
        ],
        "target_residual": 0.0006577786388526352,
        "parent_symmetrization_rmsd_A": 0.021008861579935777,
        "parent_cell_rmsd_A": 0.0179254068602417,
        "energy_eV": -191.73419172899665,
        "reduced_polarization": [
          3.3461278016330204e-15,
          -3.734632241587725e-15,
          -0.5006577786388526
        ],
        "cartesian_polarization_e_A2": [
          9.790759194983816e-17,
          -9.737548547184991e-17,
          -0.006870817361387456
        ],
        "ranking_score": 0.5268057705727015
      }
    }
  ],
  "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": 56,
      "full_response": 21,
      "energy_polarization": 35
    },
    "model_evaluations_for_recovery_and_path_properties": {
      "total": 81,
      "full_response": 46,
      "energy_polarization": 35
    },
    "elapsed_seconds": 459.57380848401226
  }
}