{
  "schema": "ferrofinder.endpoint_parent_recovery.v4_variable_cell",
  "status": "complete",
  "input_atom_count": 76,
  "input_formula": "K4O52Sb20",
  "input_spacegroup": "Ama2",
  "input_pointgroup": "mm2",
  "input_is_polar_point_group": true,
  "input_energy_eV": -439.35964208395785,
  "input_cartesian_polarization_e_A2": [
    -3.0919582797781384e-17,
    9.567003580034544e-19,
    0.0006285995506181112
  ],
  "input_reduced_polarization": [
    -1.8801473658138675e-15,
    1.0916841212201434e-16,
    0.09745305098921749
  ],
  "input_formal_targets": [
    {
      "orbit_id": 0,
      "representative_formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ]
    },
    {
      "orbit_id": 1,
      "representative_formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.5
      ]
    },
    {
      "orbit_id": 2,
      "representative_formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        -0.5,
        0.0,
        0.0
      ]
    },
    {
      "orbit_id": 3,
      "representative_formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.0
      ]
    },
    {
      "orbit_id": 4,
      "representative_formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        -0.5,
        0.0,
        0.5
      ]
    },
    {
      "orbit_id": 5,
      "representative_formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.5
      ]
    },
    {
      "orbit_id": 6,
      "representative_formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        -0.5,
        0.5,
        0.0
      ]
    },
    {
      "orbit_id": 7,
      "representative_formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "target_reduced_polarization": [
        -0.5,
        0.5,
        0.5
      ]
    }
  ],
  "parent_candidates": [
    {
      "candidate_id": "inversion_parent_endpoint_00",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "Cmcm",
      "spacegroup_number": 63,
      "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": 6.873943447046812e-15,
      "parent_symmetrization_rmsd_A": 0.1731984138126521,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -439.44481774841194,
      "reduced_polarization": [
        4.2263852613278285e-15,
        4.9912103388372696e-15,
        2.1157942928159767e-15
      ],
      "cartesian_polarization_e_A2": [
        6.95041630241476e-17,
        4.374060797640968e-17,
        1.3647467453960383e-17
      ],
      "ranking_score": 0.17319841381266585
    },
    {
      "candidate_id": "bec_projection_00",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Ama2",
      "spacegroup_number": 40,
      "pointgroup": "mm2",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 3.554426788893025e-06,
      "parent_symmetrization_rmsd_A": 0.002879376469451642,
      "parent_cell_rmsd_A": 0.00024344789318370749,
      "energy_eV": -439.3502971597178,
      "reduced_polarization": [
        9.287011273020624e-17,
        -3.5559444427789195e-15,
        3.554426788893025e-06
      ],
      "cartesian_polarization_e_A2": [
        1.527153429125816e-18,
        -3.116000961053839e-17,
        2.2926877430131147e-08
      ],
      "ranking_score": 0.5029473472963254
    },
    {
      "candidate_id": "inversion_parent_bec_00_00",
      "source": "same_species_inversion_center_projection_after_BEC",
      "spacegroup": "Cmcm",
      "spacegroup_number": 63,
      "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": 6.490683724685402e-15,
      "parent_symmetrization_rmsd_A": 0.17319841645949882,
      "parent_cell_rmsd_A": 0.00024344789318370749,
      "energy_eV": -439.44427113288504,
      "reduced_polarization": [
        -2.070076790967559e-15,
        -4.88923465008146e-15,
        -3.7335160144073634e-15
      ],
      "cartesian_polarization_e_A2": [
        -3.403959434234847e-17,
        -4.284334082239011e-17,
        -2.4082044484142456e-17
      ],
      "ranking_score": 0.17325927843280775
    },
    {
      "candidate_id": "bec_projection_01",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Ama2",
      "spacegroup_number": 40,
      "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": 0.00012441176924332664,
      "parent_symmetrization_rmsd_A": 0.011899172580938722,
      "parent_cell_rmsd_A": 0.0010052156889110433,
      "energy_eV": -439.2388076370719,
      "reduced_polarization": [
        5.151663245796005e-15,
        -1.0015377089993409e-14,
        0.4998755882307567
      ],
      "cartesian_polarization_e_A2": [
        6.681801150150041e-17,
        -8.079133914241349e-17,
        0.0032244388480912505
      ],
      "ranking_score": 0.5123993000416531
    },
    {
      "candidate_id": "bec_projection_02",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cc",
      "spacegroup_number": 9,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        -0.5,
        0.0,
        0.0
      ],
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_residual": 3.1542660955596062e-06,
      "parent_symmetrization_rmsd_A": 0.0520157788502952,
      "parent_cell_rmsd_A": 0.0002627157491047833,
      "energy_eV": -437.2577509511092,
      "reduced_polarization": [
        -0.49999684615666046,
        -9.333003463533385e-15,
        -5.164098390025286e-08
      ],
      "cartesian_polarization_e_A2": [
        -0.008221776033138976,
        -3.393353877404086e-16,
        9.424094740737538e-08
      ],
      "ranking_score": 0.5520877663197625
    },
    {
      "candidate_id": "bec_projection_03",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Pm",
      "spacegroup_number": 6,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.0
      ],
      "formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_residual": 0.0003586774643207226,
      "parent_symmetrization_rmsd_A": 0.021185315531912396,
      "parent_cell_rmsd_A": 0.000286463366319196,
      "energy_eV": -438.91440294197025,
      "reduced_polarization": [
        -1.338798557773194e-15,
        0.4996434981749407,
        3.9445812717270854e-05
      ],
      "cartesian_polarization_e_A2": [
        2.5602724794393166e-17,
        0.0043782714853569295,
        1.1829810340959781e-07
      ],
      "ranking_score": 0.5219742863021336
    },
    {
      "candidate_id": "bec_projection_04",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cc",
      "spacegroup_number": 9,
      "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": 5.000297182667762e-06,
      "parent_symmetrization_rmsd_A": 0.05336960018255732,
      "parent_cell_rmsd_A": 0.001020771701870521,
      "energy_eV": -437.1400150007665,
      "reduced_polarization": [
        -0.49999564233148075,
        -5.75453096254542e-15,
        0.4999975477159644
      ],
      "cartesian_polarization_e_A2": [
        -0.00822607623097987,
        -2.3549636338535954e-16,
        0.0032253212881870105
      ],
      "ranking_score": 0.5536347937023903
    },
    {
      "candidate_id": "bec_projection_05",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Pm",
      "spacegroup_number": 6,
      "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": 0.0009552668786610525,
      "parent_symmetrization_rmsd_A": 0.024128987678249423,
      "parent_cell_rmsd_A": 0.0010164748561228714,
      "energy_eV": -438.8030573544458,
      "reduced_polarization": [
        4.229768388065715e-15,
        0.49932567574432113,
        0.4993233748396121
      ],
      "cartesian_polarization_e_A2": [
        1.1241028935587935e-16,
        0.004377273210723945,
        0.0032207407247851635
      ],
      "ranking_score": 0.5262936401496022
    },
    {
      "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,
        0.0
      ],
      "formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_residual": 3.8156876913441445e-06,
      "parent_symmetrization_rmsd_A": 0.05616893088974203,
      "parent_cell_rmsd_A": 0.0003033291285322654,
      "energy_eV": -436.8067249815862,
      "reduced_polarization": [
        -0.4999962580366112,
        0.4999992647862627,
        -1.2900897317966953e-07
      ],
      "cartesian_polarization_e_A2": [
        -0.00822176617553847,
        0.004381392762341022,
        -4.280447559138248e-08
      ],
      "ranking_score": 0.5562523945472578
    },
    {
      "candidate_id": "bec_projection_07",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        -0.5,
        0.5,
        0.5
      ],
      "formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "target_residual": 6.148223286000349e-06,
      "parent_symmetrization_rmsd_A": 0.05743438924422918,
      "parent_cell_rmsd_A": 0.0010334659198042919,
      "energy_eV": -436.6881749117264,
      "reduced_polarization": [
        -0.49999484790888077,
        0.49999853033892705,
        0.4999969839258954
      ],
      "cartesian_polarization_e_A2": [
        -0.008226068433502345,
        0.004383189010939544,
        0.003225181136173026
      ],
      "ranking_score": 0.5577050521707523
    }
  ],
  "formal_branches": [
    {
      "orbit_id": 0,
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.0,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -1.8801473658138675e-15,
              1.0916841212201434e-16,
              0.09745305098921749
            ],
            "branch_aligned_reduced_polarization": [
              -1.8801473658138675e-15,
              1.0916841212201434e-16,
              0.09745305098921749
            ],
            "target_residual": 0.09745305098921749,
            "energy_eV": -439.35964208395785,
            "max_atomic_step_A": 0.004694681112400867,
            "max_log_strain_component": 8.867270769584556e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.3595614770723492,
            "cell_principal_stretches": [
              1.0000886766392365,
              1.000012215325553,
              0.9999953607170186
            ],
            "cell_volume_ratio": 1.000096253296951,
            "cell_rmsd_from_input_A": 0.00024344789318370749
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              9.287011273020624e-17,
              -3.5559444427789195e-15,
              3.554426788893025e-06
            ],
            "branch_aligned_reduced_polarization": [
              9.287011273020624e-17,
              -3.5559444427789195e-15,
              3.554426788893025e-06
            ],
            "target_residual": 3.554426788893025e-06,
            "energy_eV": -439.3502971597178
          }
        ],
        "iterations": 1
      },
      "parent": {
        "candidate_id": "inversion_parent_endpoint_00",
        "source": "same_species_inversion_center_projection_from_endpoint",
        "spacegroup": "Cmcm",
        "spacegroup_number": 63,
        "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": 6.873943447046812e-15,
        "parent_symmetrization_rmsd_A": 0.1731984138126521,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -439.44481774841194,
        "reduced_polarization": [
          4.2263852613278285e-15,
          4.9912103388372696e-15,
          2.1157942928159767e-15
        ],
        "cartesian_polarization_e_A2": [
          6.95041630241476e-17,
          4.374060797640968e-17,
          1.3647467453960383e-17
        ],
        "ranking_score": 0.17319841381266585
      },
      "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": [
          -439.35964208395774,
          -439.3788955308028,
          -439.3959263331579,
          -439.4105893899087,
          -439.4227618611312,
          -439.43234231395127,
          -439.4392495017424,
          -439.4434219516615,
          -439.444817748412
        ],
        "cartesian_polarizations_e_A2": [
          [
            -1.6260287110411568e-17,
            -1.6994811779148774e-17,
            0.0006285995506181033
          ],
          [
            -6.505390797826501e-18,
            -6.643380807674337e-18,
            0.0005538886785298912
          ],
          [
            -3.091489282348183e-17,
            -4.233733594779972e-17,
            0.0004776092012734867
          ],
          [
            -1.697937414887236e-17,
            -1.8031794684676994e-17,
            0.00039998719546560185
          ],
          [
            -3.46269789236036e-17,
            -1.99502130599042e-17,
            0.0003212625385611583
          ],
          [
            -4.950422759036026e-17,
            2.5998164973436527e-17,
            0.00024167501846124925
          ],
          [
            -2.296635795020715e-17,
            1.6675354142123144e-17,
            0.00016145669066852886
          ],
          [
            -3.199664729850944e-17,
            4.388110243457802e-17,
            8.082921689773509e-05
          ],
          [
            6.361465134561315e-17,
            6.324926702492768e-17,
            -2.2501082441304254e-17
          ]
        ],
        "raw_reduced_polarization": [
          [
            -9.88749951057268e-16,
            -1.9392661461045236e-15,
            0.09745305098921626
          ],
          [
            -3.9557756817472013e-16,
            -7.580715610990226e-16,
            0.0858704744189624
          ],
          [
            -1.879862179468285e-15,
            -4.8310839441338265e-15,
            0.07404471383865399
          ],
          [
            -1.0324759485907784e-15,
            -2.0575955438591546e-15,
            0.062010818360296024
          ],
          [
            -2.105585435453453e-15,
            -2.2765049297052217e-15,
            0.04980597666756264
          ],
          [
            -3.0102360600850208e-15,
            2.9666325140290047e-15,
            0.03746736356041808
          ],
          [
            -1.3965304022639888e-15,
            1.9028130574414035e-15,
            0.02503095506956463
          ],
          [
            -1.9456411338604656e-15,
            5.007242063694349e-15,
            0.012531115855886111
          ],
          [
            3.868257859003335e-15,
            7.217329847563102e-15,
            -3.4883880084050296e-15
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -9.88749951057268e-16,
            -1.9392661461045236e-15,
            0.09745305098921626
          ],
          [
            -3.955775681747201e-16,
            -7.580715610990227e-16,
            0.0858704744189624
          ],
          [
            -1.879862179468285e-15,
            -4.8310839441338265e-15,
            0.07404471383865399
          ],
          [
            -1.0324759485907784e-15,
            -2.0575955438591546e-15,
            0.062010818360296024
          ],
          [
            -2.105585435453453e-15,
            -2.2765049297052217e-15,
            0.04980597666756264
          ],
          [
            -3.0102360600850208e-15,
            2.9666325140290043e-15,
            0.03746736356041808
          ],
          [
            -1.3965304022639888e-15,
            1.9028130574414035e-15,
            0.02503095506956463
          ],
          [
            -1.9456411338604656e-15,
            5.007242063694349e-15,
            0.012531115855886111
          ],
          [
            3.868257859003335e-15,
            7.217329847563102e-15,
            -3.488528910189359e-15
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            -9.992007221626409e-16,
            -1.942890293094024e-15,
            0.0974530509892163
          ],
          [
            -3.885780586188048e-16,
            -7.771561172376096e-16,
            0.08587047441896245
          ],
          [
            -1.887379141862766e-15,
            -4.829470157119431e-15,
            0.07404471383865396
          ],
          [
            -1.0547118733938987e-15,
            -2.0539125955565396e-15,
            0.06201081836029598
          ],
          [
            -2.1094237467877974e-15,
            -2.275957200481571e-15,
            0.04980597666756259
          ],
          [
            -2.9976021664879227e-15,
            2.9976021664879227e-15,
            0.03746736356041813
          ],
          [
            -1.3877787807814457e-15,
            1.887379141862766e-15,
            0.025030955069564653
          ],
          [
            -1.942890293094024e-15,
            4.9960036108132044e-15,
            0.012531115855886066
          ],
          [
            3.885780586188048e-15,
            7.216449660063518e-15,
            -3.497202527569243e-15
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -439.444817748412,
          -439.4434219516615,
          -439.4392495017422,
          -439.4323423139513,
          -439.422761861131,
          -439.4105893899087,
          -439.39592633315795,
          -439.3788955308028,
          -439.35964208395785
        ],
        "cartesian_polarizations_e_A2": [
          [
            6.579540237488654e-17,
            6.768153266952409e-17,
            -2.2262039421873788e-18
          ],
          [
            -4.6591612117857297e-17,
            1.456459216345119e-17,
            -8.082921689769128e-05
          ],
          [
            -2.3361949348100523e-17,
            2.88481954105657e-17,
            -0.000161456690668562
          ],
          [
            -4.038989432683264e-17,
            -6.904299087129824e-18,
            -0.0002416750184612632
          ],
          [
            -8.194425361651919e-18,
            -1.3748386263616074e-17,
            -0.0003212625385611822
          ],
          [
            -3.964210818535295e-17,
            -1.5155003398372902e-17,
            -0.00039998719546562196
          ],
          [
            -1.2383329342282102e-17,
            -2.7961742281646417e-17,
            -0.00047760920127355987
          ],
          [
            -3.056006451738272e-17,
            -1.4087914537522893e-17,
            -0.0005538886785299124
          ],
          [
            -2.5573415473718542e-17,
            -2.344752153645179e-17,
            -0.0006285995506181251
          ]
        ],
        "raw_reduced_polarization": [
          [
            4.000864218215867e-15,
            7.723092596030475e-15,
            -3.4513286889412043e-16
          ],
          [
            -2.833126739300521e-15,
            1.6619554768505258e-15,
            -0.01253111585587932
          ],
          [
            -1.4205853880492826e-15,
            3.2918475039868936e-15,
            -0.025030955069569767
          ],
          [
            -2.4560148149716887e-15,
            -7.878447644050264e-16,
            -0.03746736356042024
          ],
          [
            -4.982838015257341e-16,
            -1.5688187895855906e-15,
            -0.049805976667566344
          ],
          [
            -2.410543692243731e-15,
            -1.7293268920237272e-15,
            -0.06201081836029913
          ],
          [
            -7.530012353390449e-16,
            -3.190694954293419e-15,
            -0.07404471383866533
          ],
          [
            -1.858285901761319e-15,
            -1.6075621246568647e-15,
            -0.08587047441896567
          ],
          [
            -1.555059460285654e-15,
            -2.675580366326082e-15,
            -0.09745305098921964
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            4.000864218215867e-15,
            7.723092596030475e-15,
            -3.4513286889412043e-16
          ],
          [
            -2.833126739300521e-15,
            1.6619554768505256e-15,
            -0.01253111585587932
          ],
          [
            -1.4205853880492826e-15,
            3.2918475039868936e-15,
            -0.025030955069569767
          ],
          [
            -2.4560148149716887e-15,
            -7.878447644050262e-16,
            -0.03746736356042024
          ],
          [
            -4.982838015257343e-16,
            -1.5688187895855906e-15,
            -0.049805976667566344
          ],
          [
            -2.410543692243731e-15,
            -1.7293268920237272e-15,
            -0.06201081836029913
          ],
          [
            -7.530012353390449e-16,
            -3.190694954293419e-15,
            -0.07404471383866533
          ],
          [
            -1.858285901761319e-15,
            -1.6075621246568647e-15,
            -0.08587047441896567
          ],
          [
            -1.555059460285654e-15,
            -2.675580366326082e-15,
            -0.09745305098921964
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          8.725265669063938e-15,
          1.6373925841230725e-14,
          -0.09745305098922323
        ],
        "actual_opposite_endpoint_branch_residual": 2.1942837149667452e-14
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            -9.88749951057268e-16,
            -1.9392661461045236e-15,
            0.09745305098921626
          ],
          [
            -3.9557756817472013e-16,
            -7.580715610990226e-16,
            0.0858704744189624
          ],
          [
            -1.879862179468285e-15,
            -4.8310839441338265e-15,
            0.07404471383865399
          ],
          [
            -1.0324759485907784e-15,
            -2.0575955438591546e-15,
            0.062010818360296024
          ],
          [
            -2.105585435453453e-15,
            -2.2765049297052217e-15,
            0.04980597666756264
          ],
          [
            -3.0102360600850208e-15,
            2.9666325140290047e-15,
            0.03746736356041808
          ],
          [
            -1.3965304022639888e-15,
            1.9028130574414035e-15,
            0.02503095506956463
          ],
          [
            -1.9456411338604656e-15,
            5.007242063694349e-15,
            0.012531115855886111
          ],
          [
            3.868257859003335e-15,
            7.217329847563102e-15,
            -3.4883880084050296e-15
          ],
          [
            -2.833126739300521e-15,
            1.6619554768505258e-15,
            -0.01253111585587932
          ],
          [
            -1.4205853880492826e-15,
            3.2918475039868936e-15,
            -0.025030955069569767
          ],
          [
            -2.4560148149716887e-15,
            -7.878447644050264e-16,
            -0.03746736356042024
          ],
          [
            -4.982838015257341e-16,
            -1.5688187895855906e-15,
            -0.049805976667566344
          ],
          [
            -2.410543692243731e-15,
            -1.7293268920237272e-15,
            -0.06201081836029913
          ],
          [
            -7.530012353390449e-16,
            -3.190694954293419e-15,
            -0.07404471383866533
          ],
          [
            -1.858285901761319e-15,
            -1.6075621246568647e-15,
            -0.08587047441896567
          ],
          [
            -1.555059460285654e-15,
            -2.675580366326082e-15,
            -0.09745305098921964
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -9.88749951057268e-16,
            -1.9392661461045236e-15,
            0.09745305098921626
          ],
          [
            -3.955775681747201e-16,
            -7.580715610990227e-16,
            0.0858704744189624
          ],
          [
            -1.879862179468285e-15,
            -4.8310839441338265e-15,
            0.07404471383865399
          ],
          [
            -1.0324759485907784e-15,
            -2.0575955438591546e-15,
            0.062010818360296024
          ],
          [
            -2.105585435453453e-15,
            -2.2765049297052217e-15,
            0.04980597666756264
          ],
          [
            -3.0102360600850208e-15,
            2.9666325140290043e-15,
            0.03746736356041808
          ],
          [
            -1.3965304022639888e-15,
            1.9028130574414035e-15,
            0.02503095506956463
          ],
          [
            -1.9456411338604656e-15,
            5.007242063694349e-15,
            0.012531115855886111
          ],
          [
            3.868257859003335e-15,
            7.217329847563102e-15,
            -3.488528910189359e-15
          ],
          [
            -2.833126739300521e-15,
            1.6619554768505256e-15,
            -0.01253111585587932
          ],
          [
            -1.4205853880492826e-15,
            3.2918475039868936e-15,
            -0.025030955069569767
          ],
          [
            -2.4560148149716887e-15,
            -7.878447644050262e-16,
            -0.03746736356042024
          ],
          [
            -4.982838015257343e-16,
            -1.5688187895855906e-15,
            -0.049805976667566344
          ],
          [
            -2.410543692243731e-15,
            -1.7293268920237272e-15,
            -0.06201081836029913
          ],
          [
            -7.530012353390449e-16,
            -3.190694954293419e-15,
            -0.07404471383866533
          ],
          [
            -1.858285901761319e-15,
            -1.6075621246568647e-15,
            -0.08587047441896567
          ],
          [
            -1.555059460285654e-15,
            -2.675580366326082e-15,
            -0.09745305098921964
          ]
        ],
        "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": [
          [
            -9.992007221626409e-16,
            -1.942890293094024e-15,
            0.0974530509892163
          ],
          [
            -3.885780586188048e-16,
            -7.771561172376096e-16,
            0.08587047441896245
          ],
          [
            -1.887379141862766e-15,
            -4.829470157119431e-15,
            0.07404471383865396
          ],
          [
            -1.0547118733938987e-15,
            -2.0539125955565396e-15,
            0.06201081836029598
          ],
          [
            -2.1094237467877974e-15,
            -2.275957200481571e-15,
            0.04980597666756259
          ],
          [
            -2.9976021664879227e-15,
            2.9976021664879227e-15,
            0.03746736356041813
          ],
          [
            -1.3877787807814457e-15,
            1.887379141862766e-15,
            0.025030955069564653
          ],
          [
            -1.942890293094024e-15,
            4.9960036108132044e-15,
            0.012531115855886066
          ],
          [
            3.885780586188048e-15,
            7.216449660063518e-15,
            -3.497202527569243e-15
          ],
          [
            -2.831068712794149e-15,
            1.6653345369377348e-15,
            -0.012531115855879293
          ],
          [
            -1.4432899320127035e-15,
            3.3306690738754696e-15,
            -0.02503095506956976
          ],
          [
            -2.4424906541753444e-15,
            -7.771561172376096e-16,
            -0.03746736356042024
          ],
          [
            -4.996003610813204e-16,
            -1.5543122344752192e-15,
            -0.049805976667566365
          ],
          [
            -2.3869795029440866e-15,
            -1.7208456881689926e-15,
            -0.06201081836029915
          ],
          [
            -7.771561172376096e-16,
            -3.164135620181696e-15,
            -0.07404471383866534
          ],
          [
            -1.8318679906315083e-15,
            -1.609823385706477e-15,
            -0.08587047441896567
          ],
          [
            -1.5543122344752192e-15,
            -2.6645352591003757e-15,
            -0.09745305098921964
          ]
        ]
      },
      "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,
        0.5
      ],
      "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": [
              -1.8801473658138675e-15,
              1.0916841212201434e-16,
              0.09745305098921749
            ],
            "branch_aligned_reduced_polarization": [
              -1.8801473658138675e-15,
              1.0916841212201434e-16,
              0.09745305098921747
            ],
            "target_residual": 0.40254694901078253,
            "energy_eV": -439.35964208395785,
            "max_atomic_step_A": 0.019392205161279284,
            "max_log_strain_component": 0.00036627819838536374,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.3595614770723492,
            "cell_principal_stretches": [
              1.0000191636015197,
              0.9999495440327653,
              0.9996337888732848
            ],
            "cell_volume_ratio": 0.999602507000618,
            "cell_rmsd_from_input_A": 0.0010052156889110433
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              5.151663245796005e-15,
              -1.0015377089993409e-14,
              0.4998755882307567
            ],
            "branch_aligned_reduced_polarization": [
              5.151663245796005e-15,
              -1.0015377089993409e-14,
              0.4998755882307567
            ],
            "target_residual": 0.00012441176924332664,
            "energy_eV": -439.2388076370719
          }
        ],
        "iterations": 1
      },
      "parent": {
        "candidate_id": "bec_projection_01",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Ama2",
        "spacegroup_number": 40,
        "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": 0.00012441176924332664,
        "parent_symmetrization_rmsd_A": 0.011899172580938722,
        "parent_cell_rmsd_A": 0.0010052156889110433,
        "energy_eV": -439.2388076370719,
        "reduced_polarization": [
          5.151663245796005e-15,
          -1.0015377089993409e-14,
          0.4998755882307567
        ],
        "cartesian_polarization_e_A2": [
          6.681801150150041e-17,
          -8.079133914241349e-17,
          0.0032244388480912505
        ],
        "ranking_score": 0.5123993000416531
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 2,
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.0,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        -0.5,
        0.0,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -1.8801473658138675e-15,
              1.0916841212201434e-16,
              0.09745305098921749
            ],
            "branch_aligned_reduced_polarization": [
              -1.887379141862766e-15,
              1.0916841212201434e-16,
              0.09745305098921749
            ],
            "target_residual": 0.5094085758476246,
            "energy_eV": -439.35964208395785,
            "max_atomic_step_A": 0.08734130523141555,
            "max_log_strain_component": 8.867270770091704e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.3595614770723492,
            "cell_principal_stretches": [
              1.000090036925059,
              1.0000122153255468,
              0.9999940005599142
            ],
            "cell_volume_ratio": 1.0000962532968876,
            "cell_rmsd_from_input_A": 0.00026449483821021705
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.49367256709817253,
              1.0297504172508414e-14,
              -0.0009607586095693221
            ],
            "branch_aligned_reduced_polarization": [
              -0.49367256709817253,
              1.0297504172508414e-14,
              -0.0009607586095693221
            ],
            "target_residual": 0.006399958143065495,
            "energy_eV": -437.31326566803455,
            "max_atomic_step_A": 0.0011486761595579022,
            "max_log_strain_component": 9.259314008401851e-07,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.3595614770723492,
            "cell_principal_stretches": [
              1.0000891620121026,
              1.0000120877708327,
              0.9999939979071798
            ],
            "cell_volume_ratio": 1.0000952481601681,
            "cell_rmsd_from_input_A": 0.0002627157491047833
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.49999684615666046,
              -9.333003463533385e-15,
              -5.164098390025286e-08
            ],
            "branch_aligned_reduced_polarization": [
              -0.49999684615666046,
              -9.333003463533385e-15,
              -5.164098390025286e-08
            ],
            "target_residual": 3.1542660955596062e-06,
            "energy_eV": -437.2577509511092
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_02",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cc",
        "spacegroup_number": 9,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          -0.5,
          0.0,
          0.0
        ],
        "formal_class": [
          0.5,
          0.0,
          0.0
        ],
        "target_residual": 3.1542660955596062e-06,
        "parent_symmetrization_rmsd_A": 0.0520157788502952,
        "parent_cell_rmsd_A": 0.0002627157491047833,
        "energy_eV": -437.2577509511092,
        "reduced_polarization": [
          -0.49999684615666046,
          -9.333003463533385e-15,
          -5.164098390025286e-08
        ],
        "cartesian_polarization_e_A2": [
          -0.008221776033138976,
          -3.393353877404086e-16,
          9.424094740737538e-08
        ],
        "ranking_score": 0.5520877663197625
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 3,
      "formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.5,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -1.8801473658138675e-15,
              1.0916841212201434e-16,
              0.09745305098921749
            ],
            "branch_aligned_reduced_polarization": [
              -1.8801473658138675e-15,
              1.1102230246251565e-16,
              0.09745305098921749
            ],
            "target_residual": 0.5094085758476263,
            "energy_eV": -439.35964208395785,
            "max_atomic_step_A": 0.03512182024433436,
            "max_log_strain_component": 8.867270769246577e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.3595614770723492,
            "cell_principal_stretches": [
              1.0000997255000652,
              1.000001167431514,
              0.9999953607170116
            ],
            "cell_volume_ratio": 1.0000962532969424,
            "cell_rmsd_from_input_A": 0.000286463366319196
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -1.338798557773194e-15,
              0.4996434981749407,
              3.9445812717270854e-05
            ],
            "branch_aligned_reduced_polarization": [
              -1.338798557773194e-15,
              0.4996434981749407,
              3.9445812717270854e-05
            ],
            "target_residual": 0.0003586774643207226,
            "energy_eV": -438.91440294197025
          }
        ],
        "iterations": 1
      },
      "parent": {
        "candidate_id": "bec_projection_03",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Pm",
        "spacegroup_number": 6,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.5,
          0.0
        ],
        "formal_class": [
          0.0,
          0.5,
          0.0
        ],
        "target_residual": 0.0003586774643207226,
        "parent_symmetrization_rmsd_A": 0.021185315531912396,
        "parent_cell_rmsd_A": 0.000286463366319196,
        "energy_eV": -438.91440294197025,
        "reduced_polarization": [
          -1.338798557773194e-15,
          0.4996434981749407,
          3.9445812717270854e-05
        ],
        "cartesian_polarization_e_A2": [
          2.5602724794393166e-17,
          0.0043782714853569295,
          1.1829810340959781e-07
        ],
        "ranking_score": 0.5219742863021336
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 4,
      "formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.0,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        -0.5,
        0.0,
        0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -1.8801473658138675e-15,
              1.0916841212201434e-16,
              0.09745305098921749
            ],
            "branch_aligned_reduced_polarization": [
              -1.887379141862766e-15,
              1.0916841212201434e-16,
              0.09745305098921747
            ],
            "target_residual": 0.641906571206346,
            "energy_eV": -439.35964208395785,
            "max_atomic_step_A": 0.08943073570682004,
            "max_log_strain_component": 0.0003662781983802923,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.3595614770723492,
            "cell_principal_stretches": [
              1.0000194974023782,
              0.9999495440327587,
              0.9996334552011167
            ],
            "cell_volume_ratio": 0.9996025070005543,
            "cell_rmsd_from_input_A": 0.001010515173030412
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.4930907947913535,
              6.133997142753692e-15,
              0.4961863077549214
            ],
            "branch_aligned_reduced_polarization": [
              -0.4930907947913535,
              6.133997142753692e-15,
              0.4961863077549214
            ],
            "target_residual": 0.007891854354672346,
            "energy_eV": -437.2033861894255,
            "max_atomic_step_A": 0.0012706665338373922,
            "max_log_strain_component": 3.7002307818619957e-06,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.3595614770723492,
            "cell_principal_stretches": [
              1.0000196976068496,
              0.9999490343273861,
              0.9996297497288492
            ],
            "cell_volume_ratio": 0.9995984922365649,
            "cell_rmsd_from_input_A": 0.001020771701870521
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.49999564233148075,
              -5.75453096254542e-15,
              0.4999975477159644
            ],
            "branch_aligned_reduced_polarization": [
              -0.49999564233148075,
              -5.75453096254542e-15,
              0.4999975477159644
            ],
            "target_residual": 5.000297182667762e-06,
            "energy_eV": -437.1400150007665
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_04",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cc",
        "spacegroup_number": 9,
        "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": 5.000297182667762e-06,
        "parent_symmetrization_rmsd_A": 0.05336960018255732,
        "parent_cell_rmsd_A": 0.001020771701870521,
        "energy_eV": -437.1400150007665,
        "reduced_polarization": [
          -0.49999564233148075,
          -5.75453096254542e-15,
          0.4999975477159644
        ],
        "cartesian_polarization_e_A2": [
          -0.00822607623097987,
          -2.3549636338535954e-16,
          0.0032253212881870105
        ],
        "ranking_score": 0.5536347937023903
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 5,
      "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": [
              -1.8801473658138675e-15,
              1.0916841212201434e-16,
              0.09745305098921749
            ],
            "branch_aligned_reduced_polarization": [
              -1.8801473658138675e-15,
              1.1102230246251565e-16,
              0.09745305098921747
            ],
            "target_residual": 0.6419065712063473,
            "energy_eV": -439.35964208395785,
            "max_atomic_step_A": 0.039351774292400075,
            "max_log_strain_component": 0.0003662781983887435,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.3595614770723492,
            "cell_principal_stretches": [
              1.000019163601513,
              0.9999525758234563,
              0.9996307580491332
            ],
            "cell_volume_ratio": 0.9996025070006098,
            "cell_rmsd_from_input_A": 0.0010164748561228714
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              4.229768388065715e-15,
              0.49932567574432113,
              0.4993233748396121
            ],
            "branch_aligned_reduced_polarization": [
              4.229768388065715e-15,
              0.49932567574432113,
              0.4993233748396121
            ],
            "target_residual": 0.0009552668786610525,
            "energy_eV": -438.8030573544458
          }
        ],
        "iterations": 1
      },
      "parent": {
        "candidate_id": "bec_projection_05",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Pm",
        "spacegroup_number": 6,
        "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": 0.0009552668786610525,
        "parent_symmetrization_rmsd_A": 0.024128987678249423,
        "parent_cell_rmsd_A": 0.0010164748561228714,
        "energy_eV": -438.8030573544458,
        "reduced_polarization": [
          4.229768388065715e-15,
          0.49932567574432113,
          0.4993233748396121
        ],
        "cartesian_polarization_e_A2": [
          1.1241028935587935e-16,
          0.004377273210723945,
          0.0032207407247851635
        ],
        "ranking_score": 0.5262936401496022
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 6,
      "formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.5,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        -0.5,
        0.5,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -1.8801473658138675e-15,
              1.0916841212201434e-16,
              0.09745305098921749
            ],
            "branch_aligned_reduced_polarization": [
              -1.887379141862766e-15,
              1.1102230246251565e-16,
              0.09745305098921749
            ],
            "target_residual": 0.7137906535862634,
            "energy_eV": -439.35964208395785,
            "max_atomic_step_A": 0.09484205301068496,
            "max_log_strain_component": 8.867270769753724e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.3595614770723492,
            "cell_principal_stretches": [
              1.000100811399902,
              1.0000028353237076,
              0.9999926070536932
            ],
            "cell_volume_ratio": 1.000096253296879,
            "cell_rmsd_from_input_A": 0.00030455197091067577
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.493134626278643,
              0.4985625205383364,
              -0.0009328913063544776
            ],
            "branch_aligned_reduced_polarization": [
              -0.493134626278643,
              0.4985625205383364,
              -0.0009328913063544776
            ],
            "target_residual": 0.007076015102165589,
            "energy_eV": -436.8699456607422,
            "max_atomic_step_A": 0.0012642660522014478,
            "max_log_strain_component": 9.060523144062155e-07,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.3595614770723492,
            "cell_principal_stretches": [
              1.0001000931557882,
              1.0000026766354757,
              0.9999925004512699
            ],
            "cell_volume_ratio": 1.0000952697397176,
            "cell_rmsd_from_input_A": 0.0003033291285322654
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.4999962580366112,
              0.4999992647862627,
              -1.2900897317966953e-07
            ],
            "branch_aligned_reduced_polarization": [
              -0.4999962580366112,
              0.4999992647862627,
              -1.2900897317966953e-07
            ],
            "target_residual": 3.8156876913441445e-06,
            "energy_eV": -436.8067249815862
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_06",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          -0.5,
          0.5,
          0.0
        ],
        "formal_class": [
          0.5,
          0.5,
          0.0
        ],
        "target_residual": 3.8156876913441445e-06,
        "parent_symmetrization_rmsd_A": 0.05616893088974203,
        "parent_cell_rmsd_A": 0.0003033291285322654,
        "energy_eV": -436.8067249815862,
        "reduced_polarization": [
          -0.4999962580366112,
          0.4999992647862627,
          -1.2900897317966953e-07
        ],
        "cartesian_polarization_e_A2": [
          -0.00822176617553847,
          0.004381392762341022,
          -4.280447559138248e-08
        ],
        "ranking_score": 0.5562523945472578
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 7,
      "formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.5,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        -0.5,
        0.5,
        0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -1.8801473658138675e-15,
              1.0916841212201434e-16,
              0.09745305098921749
            ],
            "branch_aligned_reduced_polarization": [
              -1.887379141862766e-15,
              1.1102230246251565e-16,
              0.09745305098921747
            ],
            "target_residual": 0.8136608913779054,
            "energy_eV": -439.35964208395785,
            "max_atomic_step_A": 0.0967672665574879,
            "max_log_strain_component": 0.00036627819838367206,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.3595614770723492,
            "cell_principal_stretches": [
              1.0000195097905653,
              0.9999525577218018,
              0.9996304300904186
            ],
            "cell_volume_ratio": 0.9996025070005459,
            "cell_rmsd_from_input_A": 0.0010217159423334978
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.49255549461634385,
              0.49824578281673104,
              0.49561435107598784
            ],
            "branch_aligned_reduced_polarization": [
              -0.49255549461634385,
              0.49824578281673104,
              0.49561435107598784
            ],
            "target_residual": 0.008816567065363398,
            "energy_eV": -436.76022226278525,
            "max_atomic_step_A": 0.0013915255970708745,
            "max_log_strain_component": 4.258956067673436e-06,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.3595614770723492,
            "cell_principal_stretches": [
              1.0000197395759614,
              0.999951959376884,
              0.9996261774345023
            ],
            "cell_volume_ratio": 0.9995978860189706,
            "cell_rmsd_from_input_A": 0.0010334659198042919
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.49999484790888077,
              0.49999853033892705,
              0.4999969839258954
            ],
            "branch_aligned_reduced_polarization": [
              -0.49999484790888077,
              0.49999853033892705,
              0.4999969839258954
            ],
            "target_residual": 6.148223286000349e-06,
            "energy_eV": -436.6881749117264
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_07",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          -0.5,
          0.5,
          0.5
        ],
        "formal_class": [
          0.5,
          0.5,
          0.5
        ],
        "target_residual": 6.148223286000349e-06,
        "parent_symmetrization_rmsd_A": 0.05743438924422918,
        "parent_cell_rmsd_A": 0.0010334659198042919,
        "energy_eV": -436.6881749117264,
        "reduced_polarization": [
          -0.49999484790888077,
          0.49999853033892705,
          0.4999969839258954
        ],
        "cartesian_polarization_e_A2": [
          -0.008226068433502345,
          0.004383189010939544,
          0.003225181136173026
        ],
        "ranking_score": 0.5577050521707523
      },
      "branch_status": "awaiting_branch_sampling"
    }
  ],
  "sampled_polarization_branches": [
    {
      "orbit_id": 0,
      "candidate_id": "inversion_parent_endpoint_00",
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "construction": "MACEField-BEC-parent plus variable-cell P-N-P path and symmetric log-strain continuation beyond both polar endpoints",
      "geometry_diagnostics": {
        "collision_aware": false,
        "permutations_tested": 1,
        "selected_order": [
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          10,
          11,
          12,
          13,
          14,
          15,
          16,
          17,
          18,
          19,
          20,
          21,
          22,
          23,
          24,
          25,
          26,
          27,
          28,
          29,
          30,
          31,
          32,
          33,
          34,
          35,
          36,
          37,
          38,
          39,
          40,
          41,
          42,
          43,
          44,
          45,
          46,
          47,
          48,
          49,
          50,
          51,
          52,
          53,
          54,
          55,
          56,
          57,
          58,
          59,
          60,
          61,
          62,
          63,
          64,
          65,
          66,
          67,
          68,
          69,
          70,
          71,
          72,
          73,
          74,
          75
        ],
        "endpoint_rmsd_A": 0.1731984138126521,
        "minimum_distance_A_by_image": [
          1.9332303211238615,
          1.9332271036723627,
          1.9332243152100654,
          1.9332219557388246,
          1.9332200252602143,
          1.933218523775518,
          1.9332174512857352,
          1.93321680779158,
          1.9332165932934806
        ],
        "minimum_distance_A": 1.9332165932934806,
        "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": [
          1037.1709594940396,
          1037.1709594940396,
          1037.1709594940396,
          1037.1709594940396,
          1037.1709594940396,
          1037.1709594940396,
          1037.1709594940396,
          1037.1709594940396,
          1037.1709594940396
        ],
        "cell_deformation_log_strain_norm": 0.0
      },
      "parent_reduced_polarization": [
        3.868257859003335e-15,
        7.217329847563102e-15,
        -3.4883880084050296e-15
      ],
      "incoming": {
        "reached": true,
        "construction": "variable_cell_linear_interpolation",
        "continuation_fractions": [
          0.0,
          0.125,
          0.25,
          0.375,
          0.5,
          0.625,
          0.75,
          0.875,
          1.0
        ],
        "energies_eV": [
          -439.35964208395774,
          -439.3788955308028,
          -439.3959263331579,
          -439.4105893899087,
          -439.4227618611312,
          -439.43234231395127,
          -439.4392495017424,
          -439.4434219516615,
          -439.444817748412
        ],
        "cartesian_polarizations_e_A2": [
          [
            -1.6260287110411568e-17,
            -1.6994811779148774e-17,
            0.0006285995506181033
          ],
          [
            -6.505390797826501e-18,
            -6.643380807674337e-18,
            0.0005538886785298912
          ],
          [
            -3.091489282348183e-17,
            -4.233733594779972e-17,
            0.0004776092012734867
          ],
          [
            -1.697937414887236e-17,
            -1.8031794684676994e-17,
            0.00039998719546560185
          ],
          [
            -3.46269789236036e-17,
            -1.99502130599042e-17,
            0.0003212625385611583
          ],
          [
            -4.950422759036026e-17,
            2.5998164973436527e-17,
            0.00024167501846124925
          ],
          [
            -2.296635795020715e-17,
            1.6675354142123144e-17,
            0.00016145669066852886
          ],
          [
            -3.199664729850944e-17,
            4.388110243457802e-17,
            8.082921689773509e-05
          ],
          [
            6.361465134561315e-17,
            6.324926702492768e-17,
            -2.2501082441304254e-17
          ]
        ],
        "raw_reduced_polarization": [
          [
            -9.88749951057268e-16,
            -1.9392661461045236e-15,
            0.09745305098921626
          ],
          [
            -3.9557756817472013e-16,
            -7.580715610990226e-16,
            0.0858704744189624
          ],
          [
            -1.879862179468285e-15,
            -4.8310839441338265e-15,
            0.07404471383865399
          ],
          [
            -1.0324759485907784e-15,
            -2.0575955438591546e-15,
            0.062010818360296024
          ],
          [
            -2.105585435453453e-15,
            -2.2765049297052217e-15,
            0.04980597666756264
          ],
          [
            -3.0102360600850208e-15,
            2.9666325140290047e-15,
            0.03746736356041808
          ],
          [
            -1.3965304022639888e-15,
            1.9028130574414035e-15,
            0.02503095506956463
          ],
          [
            -1.9456411338604656e-15,
            5.007242063694349e-15,
            0.012531115855886111
          ],
          [
            3.868257859003335e-15,
            7.217329847563102e-15,
            -3.4883880084050296e-15
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -9.88749951057268e-16,
            -1.9392661461045236e-15,
            0.09745305098921626
          ],
          [
            -3.955775681747201e-16,
            -7.580715610990227e-16,
            0.0858704744189624
          ],
          [
            -1.879862179468285e-15,
            -4.8310839441338265e-15,
            0.07404471383865399
          ],
          [
            -1.0324759485907784e-15,
            -2.0575955438591546e-15,
            0.062010818360296024
          ],
          [
            -2.105585435453453e-15,
            -2.2765049297052217e-15,
            0.04980597666756264
          ],
          [
            -3.0102360600850208e-15,
            2.9666325140290043e-15,
            0.03746736356041808
          ],
          [
            -1.3965304022639888e-15,
            1.9028130574414035e-15,
            0.02503095506956463
          ],
          [
            -1.9456411338604656e-15,
            5.007242063694349e-15,
            0.012531115855886111
          ],
          [
            3.868257859003335e-15,
            7.217329847563102e-15,
            -3.488528910189359e-15
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            -9.992007221626409e-16,
            -1.942890293094024e-15,
            0.0974530509892163
          ],
          [
            -3.885780586188048e-16,
            -7.771561172376096e-16,
            0.08587047441896245
          ],
          [
            -1.887379141862766e-15,
            -4.829470157119431e-15,
            0.07404471383865396
          ],
          [
            -1.0547118733938987e-15,
            -2.0539125955565396e-15,
            0.06201081836029598
          ],
          [
            -2.1094237467877974e-15,
            -2.275957200481571e-15,
            0.04980597666756259
          ],
          [
            -2.9976021664879227e-15,
            2.9976021664879227e-15,
            0.03746736356041813
          ],
          [
            -1.3877787807814457e-15,
            1.887379141862766e-15,
            0.025030955069564653
          ],
          [
            -1.942890293094024e-15,
            4.9960036108132044e-15,
            0.012531115855886066
          ],
          [
            3.885780586188048e-15,
            7.216449660063518e-15,
            -3.497202527569243e-15
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -439.444817748412,
          -439.4434219516615,
          -439.4392495017422,
          -439.4323423139513,
          -439.422761861131,
          -439.4105893899087,
          -439.39592633315795,
          -439.3788955308028,
          -439.35964208395785
        ],
        "cartesian_polarizations_e_A2": [
          [
            6.579540237488654e-17,
            6.768153266952409e-17,
            -2.2262039421873788e-18
          ],
          [
            -4.6591612117857297e-17,
            1.456459216345119e-17,
            -8.082921689769128e-05
          ],
          [
            -2.3361949348100523e-17,
            2.88481954105657e-17,
            -0.000161456690668562
          ],
          [
            -4.038989432683264e-17,
            -6.904299087129824e-18,
            -0.0002416750184612632
          ],
          [
            -8.194425361651919e-18,
            -1.3748386263616074e-17,
            -0.0003212625385611822
          ],
          [
            -3.964210818535295e-17,
            -1.5155003398372902e-17,
            -0.00039998719546562196
          ],
          [
            -1.2383329342282102e-17,
            -2.7961742281646417e-17,
            -0.00047760920127355987
          ],
          [
            -3.056006451738272e-17,
            -1.4087914537522893e-17,
            -0.0005538886785299124
          ],
          [
            -2.5573415473718542e-17,
            -2.344752153645179e-17,
            -0.0006285995506181251
          ]
        ],
        "raw_reduced_polarization": [
          [
            4.000864218215867e-15,
            7.723092596030475e-15,
            -3.4513286889412043e-16
          ],
          [
            -2.833126739300521e-15,
            1.6619554768505258e-15,
            -0.01253111585587932
          ],
          [
            -1.4205853880492826e-15,
            3.2918475039868936e-15,
            -0.025030955069569767
          ],
          [
            -2.4560148149716887e-15,
            -7.878447644050264e-16,
            -0.03746736356042024
          ],
          [
            -4.982838015257341e-16,
            -1.5688187895855906e-15,
            -0.049805976667566344
          ],
          [
            -2.410543692243731e-15,
            -1.7293268920237272e-15,
            -0.06201081836029913
          ],
          [
            -7.530012353390449e-16,
            -3.190694954293419e-15,
            -0.07404471383866533
          ],
          [
            -1.858285901761319e-15,
            -1.6075621246568647e-15,
            -0.08587047441896567
          ],
          [
            -1.555059460285654e-15,
            -2.675580366326082e-15,
            -0.09745305098921964
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            4.000864218215867e-15,
            7.723092596030475e-15,
            -3.4513286889412043e-16
          ],
          [
            -2.833126739300521e-15,
            1.6619554768505256e-15,
            -0.01253111585587932
          ],
          [
            -1.4205853880492826e-15,
            3.2918475039868936e-15,
            -0.025030955069569767
          ],
          [
            -2.4560148149716887e-15,
            -7.878447644050262e-16,
            -0.03746736356042024
          ],
          [
            -4.982838015257343e-16,
            -1.5688187895855906e-15,
            -0.049805976667566344
          ],
          [
            -2.410543692243731e-15,
            -1.7293268920237272e-15,
            -0.06201081836029913
          ],
          [
            -7.530012353390449e-16,
            -3.190694954293419e-15,
            -0.07404471383866533
          ],
          [
            -1.858285901761319e-15,
            -1.6075621246568647e-15,
            -0.08587047441896567
          ],
          [
            -1.555059460285654e-15,
            -2.675580366326082e-15,
            -0.09745305098921964
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          8.725265669063938e-15,
          1.6373925841230725e-14,
          -0.09745305098922323
        ],
        "actual_opposite_endpoint_branch_residual": 2.1942837149667452e-14
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            -9.88749951057268e-16,
            -1.9392661461045236e-15,
            0.09745305098921626
          ],
          [
            -3.9557756817472013e-16,
            -7.580715610990226e-16,
            0.0858704744189624
          ],
          [
            -1.879862179468285e-15,
            -4.8310839441338265e-15,
            0.07404471383865399
          ],
          [
            -1.0324759485907784e-15,
            -2.0575955438591546e-15,
            0.062010818360296024
          ],
          [
            -2.105585435453453e-15,
            -2.2765049297052217e-15,
            0.04980597666756264
          ],
          [
            -3.0102360600850208e-15,
            2.9666325140290047e-15,
            0.03746736356041808
          ],
          [
            -1.3965304022639888e-15,
            1.9028130574414035e-15,
            0.02503095506956463
          ],
          [
            -1.9456411338604656e-15,
            5.007242063694349e-15,
            0.012531115855886111
          ],
          [
            3.868257859003335e-15,
            7.217329847563102e-15,
            -3.4883880084050296e-15
          ],
          [
            -2.833126739300521e-15,
            1.6619554768505258e-15,
            -0.01253111585587932
          ],
          [
            -1.4205853880492826e-15,
            3.2918475039868936e-15,
            -0.025030955069569767
          ],
          [
            -2.4560148149716887e-15,
            -7.878447644050264e-16,
            -0.03746736356042024
          ],
          [
            -4.982838015257341e-16,
            -1.5688187895855906e-15,
            -0.049805976667566344
          ],
          [
            -2.410543692243731e-15,
            -1.7293268920237272e-15,
            -0.06201081836029913
          ],
          [
            -7.530012353390449e-16,
            -3.190694954293419e-15,
            -0.07404471383866533
          ],
          [
            -1.858285901761319e-15,
            -1.6075621246568647e-15,
            -0.08587047441896567
          ],
          [
            -1.555059460285654e-15,
            -2.675580366326082e-15,
            -0.09745305098921964
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -9.88749951057268e-16,
            -1.9392661461045236e-15,
            0.09745305098921626
          ],
          [
            -3.955775681747201e-16,
            -7.580715610990227e-16,
            0.0858704744189624
          ],
          [
            -1.879862179468285e-15,
            -4.8310839441338265e-15,
            0.07404471383865399
          ],
          [
            -1.0324759485907784e-15,
            -2.0575955438591546e-15,
            0.062010818360296024
          ],
          [
            -2.105585435453453e-15,
            -2.2765049297052217e-15,
            0.04980597666756264
          ],
          [
            -3.0102360600850208e-15,
            2.9666325140290043e-15,
            0.03746736356041808
          ],
          [
            -1.3965304022639888e-15,
            1.9028130574414035e-15,
            0.02503095506956463
          ],
          [
            -1.9456411338604656e-15,
            5.007242063694349e-15,
            0.012531115855886111
          ],
          [
            3.868257859003335e-15,
            7.217329847563102e-15,
            -3.488528910189359e-15
          ],
          [
            -2.833126739300521e-15,
            1.6619554768505256e-15,
            -0.01253111585587932
          ],
          [
            -1.4205853880492826e-15,
            3.2918475039868936e-15,
            -0.025030955069569767
          ],
          [
            -2.4560148149716887e-15,
            -7.878447644050262e-16,
            -0.03746736356042024
          ],
          [
            -4.982838015257343e-16,
            -1.5688187895855906e-15,
            -0.049805976667566344
          ],
          [
            -2.410543692243731e-15,
            -1.7293268920237272e-15,
            -0.06201081836029913
          ],
          [
            -7.530012353390449e-16,
            -3.190694954293419e-15,
            -0.07404471383866533
          ],
          [
            -1.858285901761319e-15,
            -1.6075621246568647e-15,
            -0.08587047441896567
          ],
          [
            -1.555059460285654e-15,
            -2.675580366326082e-15,
            -0.09745305098921964
          ]
        ],
        "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": [
          [
            -9.992007221626409e-16,
            -1.942890293094024e-15,
            0.0974530509892163
          ],
          [
            -3.885780586188048e-16,
            -7.771561172376096e-16,
            0.08587047441896245
          ],
          [
            -1.887379141862766e-15,
            -4.829470157119431e-15,
            0.07404471383865396
          ],
          [
            -1.0547118733938987e-15,
            -2.0539125955565396e-15,
            0.06201081836029598
          ],
          [
            -2.1094237467877974e-15,
            -2.275957200481571e-15,
            0.04980597666756259
          ],
          [
            -2.9976021664879227e-15,
            2.9976021664879227e-15,
            0.03746736356041813
          ],
          [
            -1.3877787807814457e-15,
            1.887379141862766e-15,
            0.025030955069564653
          ],
          [
            -1.942890293094024e-15,
            4.9960036108132044e-15,
            0.012531115855886066
          ],
          [
            3.885780586188048e-15,
            7.216449660063518e-15,
            -3.497202527569243e-15
          ],
          [
            -2.831068712794149e-15,
            1.6653345369377348e-15,
            -0.012531115855879293
          ],
          [
            -1.4432899320127035e-15,
            3.3306690738754696e-15,
            -0.02503095506956976
          ],
          [
            -2.4424906541753444e-15,
            -7.771561172376096e-16,
            -0.03746736356042024
          ],
          [
            -4.996003610813204e-16,
            -1.5543122344752192e-15,
            -0.049805976667566365
          ],
          [
            -2.3869795029440866e-15,
            -1.7208456881689926e-15,
            -0.06201081836029915
          ],
          [
            -7.771561172376096e-16,
            -3.164135620181696e-15,
            -0.07404471383866534
          ],
          [
            -1.8318679906315083e-15,
            -1.609823385706477e-15,
            -0.08587047441896567
          ],
          [
            -1.5543122344752192e-15,
            -2.6645352591003757e-15,
            -0.09745305098921964
          ]
        ]
      },
      "incoming_structure_ids": [
        "incoming_00_000",
        "incoming_00_001",
        "incoming_00_002",
        "incoming_00_003",
        "incoming_00_004",
        "incoming_00_005",
        "incoming_00_006",
        "incoming_00_007",
        "incoming_00_008"
      ],
      "reflected_structure_ids": [
        "reflected_00_001",
        "reflected_00_002",
        "reflected_00_003",
        "reflected_00_004",
        "reflected_00_005",
        "reflected_00_006",
        "reflected_00_007",
        "reflected_00_008"
      ],
      "positive_extension_structure_ids": [
        "extension_plus_00_000",
        "extension_plus_00_001",
        "extension_plus_00_002",
        "extension_plus_00_003"
      ],
      "negative_extension_structure_ids": [
        "extension_minus_00_000",
        "extension_minus_00_001",
        "extension_minus_00_002",
        "extension_minus_00_003"
      ],
      "extension": {
        "enabled": true,
        "fraction_beyond_polar_endpoint": 0.35,
        "images_per_side": 4,
        "construction": "continue fractional atomic displacements and symmetric log strain beyond +P; reflect these structures about N for the -P side",
        "positive_path_coordinates": [
          1.35,
          1.2625,
          1.175,
          1.0875
        ],
        "negative_path_coordinates": [
          -1.0875,
          -1.175,
          -1.2625,
          -1.35
        ]
      },
      "branch_coordinates": [
        1.35,
        1.2625,
        1.175,
        1.0875,
        1.0,
        0.875,
        0.75,
        0.625,
        0.5,
        0.375,
        0.25,
        0.125,
        0.0,
        -0.125,
        -0.25,
        -0.375,
        -0.5,
        -0.625,
        -0.75,
        -0.875,
        -1.0,
        -1.0875,
        -1.175,
        -1.2625,
        -1.35
      ],
      "parent": {
        "candidate_id": "inversion_parent_endpoint_00",
        "source": "same_species_inversion_center_projection_from_endpoint",
        "spacegroup": "Cmcm",
        "spacegroup_number": 63,
        "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": 6.873943447046812e-15,
        "parent_symmetrization_rmsd_A": 0.1731984138126521,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -439.44481774841194,
        "reduced_polarization": [
          4.2263852613278285e-15,
          4.9912103388372696e-15,
          2.1157942928159767e-15
        ],
        "cartesian_polarization_e_A2": [
          6.95041630241476e-17,
          4.374060797640968e-17,
          1.3647467453960383e-17
        ],
        "ranking_score": 0.17319841381266585
      }
    }
  ],
  "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": 45,
      "full_response": 13,
      "energy_polarization": 32
    },
    "model_evaluations_for_recovery_and_path_properties": {
      "total": 70,
      "full_response": 38,
      "energy_polarization": 32
    },
    "elapsed_seconds": 1827.8590813329793
  }
}