{
  "schema": "ferrofinder.endpoint_parent_recovery.v4_variable_cell",
  "status": "complete",
  "input_atom_count": 56,
  "input_formula": "Bi8Nb8O36Sr4",
  "input_spacegroup": "Cmc2_1",
  "input_pointgroup": "mm2",
  "input_is_polar_point_group": true,
  "input_energy_eV": -409.8422883785645,
  "input_cartesian_polarization_e_A2": [
    -5.581900787024605e-17,
    -1.8767977351650853e-17,
    -0.02841331011833826
  ],
  "input_reduced_polarization": [
    -1.7942320764521064e-15,
    -2.7079946898768884e-15,
    -4.075224695702881
  ],
  "input_formal_targets": [
    {
      "orbit_id": 0,
      "representative_formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        -4.0
      ]
    },
    {
      "orbit_id": 1,
      "representative_formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        -4.5
      ]
    },
    {
      "orbit_id": 2,
      "representative_formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        -0.5,
        -4.0
      ]
    },
    {
      "orbit_id": 3,
      "representative_formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        -0.5,
        0.0,
        -4.0
      ]
    },
    {
      "orbit_id": 4,
      "representative_formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        -0.5,
        -4.5
      ]
    },
    {
      "orbit_id": 5,
      "representative_formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        -0.5,
        0.0,
        -4.5
      ]
    },
    {
      "orbit_id": 6,
      "representative_formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        -0.5,
        -0.5,
        -4.0
      ]
    },
    {
      "orbit_id": 7,
      "representative_formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "target_reduced_polarization": [
        -0.5,
        -0.5,
        -4.5
      ]
    }
  ],
  "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": 1.3957328883844298e-15,
      "parent_symmetrization_rmsd_A": 0.2897972081750887,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -407.98796702637924,
      "reduced_polarization": [
        -4.1507466768972894e-16,
        8.838423285182954e-17,
        1.329650910330752e-15
      ],
      "cartesian_polarization_e_A2": [
        -1.2913076544884298e-17,
        6.125541112052862e-19,
        9.270601374249454e-18
      ],
      "ranking_score": 0.28979720817509147
    },
    {
      "candidate_id": "inversion_parent_endpoint_01",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "Cmce",
      "spacegroup_number": 64,
      "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": 2.764712905328545e-15,
      "parent_symmetrization_rmsd_A": 0.36582506725860287,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -407.98041376349306,
      "reduced_polarization": [
        9.357178224584205e-16,
        -2.6014710910399994e-15,
        2.0439376385569377e-17
      ],
      "cartesian_polarization_e_A2": [
        2.9110415080426347e-17,
        -1.802970688979926e-17,
        1.4250756295253964e-19
      ],
      "ranking_score": 0.3658250672586084
    },
    {
      "candidate_id": "bec_projection_00",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cmc2_1",
      "spacegroup_number": 36,
      "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,
        -4.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 0.00029600720475242426,
      "parent_symmetrization_rmsd_A": 0.002034247493376229,
      "parent_cell_rmsd_A": 0.0025194586023515636,
      "energy_eV": -409.8114214546391,
      "reduced_polarization": [
        8.583619272633285e-16,
        -1.5280893351434805e-15,
        -3.9997039927952476
      ],
      "cartesian_polarization_e_A2": [
        3.72692489787534e-17,
        -1.6781171478939653e-17,
        -0.027877678760308937
      ],
      "ranking_score": 0.503256126553469
    },
    {
      "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,
        -4.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 7.951574315417595e-15,
      "parent_symmetrization_rmsd_A": 0.28979734067699703,
      "parent_cell_rmsd_A": 0.0025194586023515636,
      "energy_eV": -407.9725797664468,
      "reduced_polarization": [
        1.6076805060022807e-16,
        7.74895116171414e-15,
        -1.4690943675113487e-15
      ],
      "cartesian_polarization_e_A2": [
        4.998088787385328e-18,
        5.367594565249492e-17,
        -1.0239492952436879e-17
      ],
      "ranking_score": 0.2904272053276008
    },
    {
      "candidate_id": "bec_projection_01",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cmc2_1",
      "spacegroup_number": 36,
      "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,
        -4.5
      ],
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_residual": 1.191415925916317e-06,
      "parent_symmetrization_rmsd_A": 0.011788689582190147,
      "parent_cell_rmsd_A": 0.014558661583980708,
      "energy_eV": -409.93514523312336,
      "reduced_polarization": [
        2.5757895059753544e-15,
        1.225513194978853e-15,
        -4.500001191415926
      ],
      "cartesian_polarization_e_A2": [
        4.188262106696485e-18,
        4.990828978484668e-17,
        -0.03143411663178275
      ],
      "ranking_score": 0.5154307378100371
    },
    {
      "candidate_id": "bec_projection_02",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cm",
      "spacegroup_number": 8,
      "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,
        -4.0
      ],
      "formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_residual": 3.5344418126286006e-06,
      "parent_symmetrization_rmsd_A": 0.01147567015452459,
      "parent_cell_rmsd_A": 0.00875995693101927,
      "energy_eV": -409.73362852843087,
      "reduced_polarization": [
        4.561830346333622e-15,
        -0.49999650921633193,
        -4.000000553812522
      ],
      "cartesian_polarization_e_A2": [
        1.2392030989568818e-16,
        -0.0033445136713200594,
        -0.02786571649582665
      ],
      "ranking_score": 0.5136727282709047
    },
    {
      "candidate_id": "bec_projection_03",
      "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,
        -4.0
      ],
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_residual": 0.0004050118685988961,
      "parent_symmetrization_rmsd_A": 0.058257689337996146,
      "parent_cell_rmsd_A": 0.10199928411396457,
      "energy_eV": -408.74292311642654,
      "reduced_polarization": [
        -0.4999662585416032,
        -1.0890135349615423e-14,
        -4.000403603924276
      ],
      "cartesian_polarization_e_A2": [
        -0.015221354844918461,
        3.8642929320718987e-16,
        -0.027703387186588317
      ],
      "ranking_score": 0.5845675341036851
    },
    {
      "candidate_id": "bec_projection_04",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cm",
      "spacegroup_number": 8,
      "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,
        -4.5
      ],
      "formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_residual": 1.7564627106887428e-05,
      "parent_symmetrization_rmsd_A": 0.016646054069030625,
      "parent_cell_rmsd_A": 0.016993602382683406,
      "energy_eV": -409.8254811945078,
      "reduced_polarization": [
        1.88452575662211e-15,
        -0.49999992794013814,
        -4.4999824355207085
      ],
      "cartesian_polarization_e_A2": [
        -5.577450015254764e-17,
        -0.0033396186875211545,
        -0.03141980266268554
      ],
      "ranking_score": 0.5209295839189152
    },
    {
      "candidate_id": "bec_projection_05",
      "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,
        -4.5
      ],
      "formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_residual": 0.0005778693305006546,
      "parent_symmetrization_rmsd_A": 0.059929628944137794,
      "parent_cell_rmsd_A": 0.10256772016631038,
      "energy_eV": -408.8316018441513,
      "reduced_polarization": [
        -0.49997149063394225,
        -3.7373249831719e-15,
        -4.500577165642758
      ],
      "cartesian_polarization_e_A2": [
        -0.015251355294263937,
        4.510803518052047e-16,
        -0.03125770866537866
      ],
      "ranking_score": 0.5867272976467167
    },
    {
      "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,
        -4.0
      ],
      "formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_residual": 0.00042315595470775825,
      "parent_symmetrization_rmsd_A": 0.059426977058204454,
      "parent_cell_rmsd_A": 0.10245678488219105,
      "energy_eV": -408.6583029930206,
      "reduced_polarization": [
        -0.49996540786504323,
        -0.5000081471055267,
        -4.000421660966744
      ],
      "cartesian_polarization_e_A2": [
        -0.015221581695737781,
        -0.003343076790688972,
        -0.027689064147000213
      ],
      "ranking_score": 0.5858874851881677
    },
    {
      "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,
        -4.5
      ],
      "formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "target_residual": 0.0005821060409359802,
      "parent_symmetrization_rmsd_A": 0.06114703755187477,
      "parent_cell_rmsd_A": 0.10304595513841511,
      "energy_eV": -408.715782596475,
      "reduced_polarization": [
        -0.4999670475891654,
        -0.5000421096940303,
        -4.500579645025152
      ],
      "cartesian_polarization_e_A2": [
        -0.015251510865975836,
        -0.0033383822687407224,
        -0.0312431598029823
      ],
      "ranking_score": 0.5880727384183505
    }
  ],
  "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,
        -4.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -1.7942320764521064e-15,
              -2.7079946898768884e-15,
              -4.075224695702881
            ],
            "branch_aligned_reduced_polarization": [
              -1.7942320764521064e-15,
              -2.7079946898768884e-15,
              -4.075224695702881
            ],
            "target_residual": 0.0752246957028806,
            "energy_eV": -409.8422883785645,
            "max_atomic_step_A": 0.0031973160321362034,
            "max_log_strain_component": 0.00044974404701870525,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 10.620403921922358,
            "cell_principal_stretches": [
              1.0004498451970358,
              1.0002393918656536,
              1.0000864892105161
            ],
            "cell_volume_ratio": 1.0007758935833704,
            "cell_rmsd_from_input_A": 0.0025194586023515636
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              8.583619272633285e-16,
              -1.5280893351434805e-15,
              -3.9997039927952476
            ],
            "branch_aligned_reduced_polarization": [
              8.583619272633285e-16,
              -1.5280893351434805e-15,
              -3.9997039927952476
            ],
            "target_residual": 0.00029600720475242426,
            "energy_eV": -409.8114214546391
          }
        ],
        "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": 1.3957328883844298e-15,
        "parent_symmetrization_rmsd_A": 0.2897972081750887,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -407.98796702637924,
        "reduced_polarization": [
          -4.1507466768972894e-16,
          8.838423285182954e-17,
          1.329650910330752e-15
        ],
        "cartesian_polarization_e_A2": [
          -1.2913076544884298e-17,
          6.125541112052862e-19,
          9.270601374249454e-18
        ],
        "ranking_score": 0.28979720817509147
      },
      "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": [
          -409.8422883785645,
          -409.57478759311397,
          -409.2283762277681,
          -408.8827173118087,
          -408.58145258370996,
          -408.3355201293934,
          -408.1487327068328,
          -408.02934600236534,
          -407.9879670263793
        ],
        "cartesian_polarizations_e_A2": [
          [
            -3.433499596094418e-17,
            8.269480501271363e-18,
            -0.028413310118338267
          ],
          [
            -2.8424802714154165e-17,
            1.4020682989809885e-17,
            -0.025637136593770538
          ],
          [
            -2.4807495738161327e-17,
            -1.6164622379028386e-18,
            -0.02294526409888747
          ],
          [
            -2.4404602876974153e-17,
            1.842766951209236e-17,
            -0.020057681219080054
          ],
          [
            2.5565090932270638e-18,
            -3.265253720563734e-17,
            -0.016729299292652336
          ],
          [
            -4.474902586358463e-18,
            3.489856894672339e-17,
            -0.012930916606961817
          ],
          [
            3.6451834747034795e-18,
            -2.2970779170198233e-18,
            -0.008789250696122523
          ],
          [
            2.8989911972085875e-18,
            -1.5484006699911403e-18,
            -0.004443503830067045
          ],
          [
            1.5541743492131585e-17,
            3.309493739706338e-17,
            4.241028302440376e-18
          ]
        ],
        "raw_reduced_polarization": [
          [
            -1.1036554293688489e-15,
            1.1931871434996987e-15,
            -4.0752246957028815
          ],
          [
            -9.13679671898e-16,
            2.0230168852752096e-15,
            -3.677047543524718
          ],
          [
            -7.974058710130523e-16,
            -2.3323617002566127e-16,
            -3.2909614020951548
          ],
          [
            -7.844553847450776e-16,
            2.6588923382925386e-15,
            -2.876805183982252
          ],
          [
            8.21757819392297e-17,
            -4.7113706345183576e-15,
            -2.3994266537505684
          ],
          [
            -1.4384013736157173e-16,
            5.0354461549750666e-15,
            -1.8546375088045257
          ],
          [
            1.1716985601158263e-16,
            -3.3144087319436075e-16,
            -1.2606124152512874
          ],
          [
            9.318444010103137e-17,
            -2.2341569970879133e-16,
            -0.6373166825097326
          ],
          [
            4.995698734451609e-16,
            4.775203691578013e-15,
            6.082763043551605e-16
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -1.1036554293688489e-15,
            1.1931871434996987e-15,
            -4.0752246957028815
          ],
          [
            -9.13679671898e-16,
            2.0230168852752096e-15,
            -3.677047543524718
          ],
          [
            -7.974058710130523e-16,
            -2.3323617002566137e-16,
            -3.2909614020951548
          ],
          [
            -7.844553847450776e-16,
            2.6588923382925386e-15,
            -2.876805183982252
          ],
          [
            8.21757819392297e-17,
            -4.711370634518358e-15,
            -2.3994266537505684
          ],
          [
            -1.4384013736157173e-16,
            5.0354461549750666e-15,
            -2.854637508804526
          ],
          [
            1.1716985601158263e-16,
            -3.3144087319436085e-16,
            -3.2606124152512876
          ],
          [
            9.318444010103137e-17,
            -2.2341569970879133e-16,
            -3.6373166825097325
          ],
          [
            4.995698734451609e-16,
            4.775203691578013e-15,
            -3.9999999999999996
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            -1
          ],
          [
            0,
            0,
            -2
          ],
          [
            0,
            0,
            -3
          ],
          [
            0,
            0,
            -4
          ]
        ],
        "folded_reduced_polarization": [
          [
            -1.1102230246251565e-15,
            1.2212453270876722e-15,
            -0.07522469570288148
          ],
          [
            -8.881784197001252e-16,
            1.9984014443252818e-15,
            0.3229524564752819
          ],
          [
            -7.771561172376096e-16,
            -2.220446049250313e-16,
            -0.29096140209515475
          ],
          [
            -7.771561172376096e-16,
            2.6645352591003757e-15,
            0.12319481601774784
          ],
          [
            1.1102230246251565e-16,
            -4.718447854656915e-15,
            -0.3994266537505684
          ],
          [
            -1.6653345369377348e-16,
            4.9960036108132044e-15,
            0.14536249119547406
          ],
          [
            1.1102230246251565e-16,
            -3.3306690738754696e-16,
            -0.26061241525128764
          ],
          [
            1.1102230246251565e-16,
            -2.220446049250313e-16,
            0.3626833174902675
          ],
          [
            4.440892098500626e-16,
            4.773959005888173e-15,
            4.440892098500626e-16
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -407.9879670263793,
          -408.02934600236534,
          -408.1487327068328,
          -408.33552012939333,
          -408.58145258371013,
          -408.8827173118088,
          -409.22837622776814,
          -409.574787593114,
          -409.8422883785644
        ],
        "cartesian_polarizations_e_A2": [
          [
            2.3534774179683196e-17,
            5.210113023640518e-17,
            -2.4866093783606543e-18
          ],
          [
            1.42843786861904e-17,
            8.933080788410424e-18,
            0.004443503830067105
          ],
          [
            1.1049770833964365e-17,
            1.1570466544988739e-18,
            0.008789250696122634
          ],
          [
            -8.581794742667103e-18,
            3.273761416552696e-17,
            0.012930916606961869
          ],
          [
            -2.8070283915082006e-18,
            1.11280663535627e-17,
            0.016729299292652357
          ],
          [
            9.941297320877807e-18,
            3.050859781641884e-17,
            0.020057681219080067
          ],
          [
            4.1158358354442246e-17,
            3.275462955750489e-17,
            0.02294526409888752
          ],
          [
            2.2030723816101903e-17,
            1.4173821517611208e-17,
            0.025637136593770548
          ],
          [
            3.7022876526965614e-17,
            6.062584161734541e-17,
            0.02841331011833831
          ]
        ],
        "raw_reduced_polarization": [
          [
            7.564958310151753e-16,
            7.517570027563947e-15,
            -3.566459488548453e-16
          ],
          [
            4.591534570182362e-16,
            1.2889367290891806e-15,
            0.6373166825097412
          ],
          [
            3.551810400111365e-16,
            1.669479953867891e-16,
            1.2606124152513034
          ],
          [
            -2.7585104050244188e-16,
            4.723646222414445e-15,
            1.854637508804533
          ],
          [
            -9.022841092524016e-17,
            1.6056468968082364e-15,
            2.399426653750571
          ],
          [
            3.1955054765805394e-16,
            4.402025819536955e-15,
            2.8768051839822544
          ],
          [
            1.3229838650180453e-15,
            4.726101339993663e-15,
            3.290961402095162
          ],
          [
            7.081500163921338e-16,
            2.045112943488167e-15,
            3.6770475435247203
          ],
          [
            1.19005398271538e-15,
            8.747583934751907e-15,
            4.075224695702888
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            7.564958310151753e-16,
            7.517570027563947e-15,
            -4.0
          ],
          [
            4.591534570182362e-16,
            1.2889367290891802e-15,
            -4.362683317490259
          ],
          [
            3.551810400111365e-16,
            1.669479953867892e-16,
            -4.739387584748696
          ],
          [
            -2.7585104050244188e-16,
            4.723646222414445e-15,
            -5.145362491195467
          ],
          [
            -9.022841092524014e-17,
            1.6056468968082366e-15,
            -5.600573346249429
          ],
          [
            3.1955054765805394e-16,
            4.402025819536955e-15,
            -5.123194816017746
          ],
          [
            1.3229838650180453e-15,
            4.726101339993663e-15,
            -4.709038597904838
          ],
          [
            7.081500163921338e-16,
            2.045112943488167e-15,
            -4.32295245647528
          ],
          [
            1.19005398271538e-15,
            8.747583934751907e-15,
            -3.9247753042971123
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          -4
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          2.1027951762591706e-15,
          8.357220239656327e-15,
          4.075224695702882
        ],
        "actual_opposite_endpoint_branch_residual": 5.420744680281192e-15
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            -1.1036554293688489e-15,
            1.1931871434996987e-15,
            -4.0752246957028815
          ],
          [
            -9.13679671898e-16,
            2.0230168852752096e-15,
            -3.677047543524718
          ],
          [
            -7.974058710130523e-16,
            -2.3323617002566127e-16,
            -3.2909614020951548
          ],
          [
            -7.844553847450776e-16,
            2.6588923382925386e-15,
            -2.876805183982252
          ],
          [
            8.21757819392297e-17,
            -4.7113706345183576e-15,
            -2.3994266537505684
          ],
          [
            -1.4384013736157173e-16,
            5.0354461549750666e-15,
            -1.8546375088045257
          ],
          [
            1.1716985601158263e-16,
            -3.3144087319436075e-16,
            -1.2606124152512874
          ],
          [
            9.318444010103137e-17,
            -2.2341569970879133e-16,
            -0.6373166825097326
          ],
          [
            4.995698734451609e-16,
            4.775203691578013e-15,
            6.082763043551605e-16
          ],
          [
            4.591534570182362e-16,
            1.2889367290891806e-15,
            0.6373166825097412
          ],
          [
            3.551810400111365e-16,
            1.669479953867891e-16,
            1.2606124152513034
          ],
          [
            -2.7585104050244188e-16,
            4.723646222414445e-15,
            1.854637508804533
          ],
          [
            -9.022841092524016e-17,
            1.6056468968082364e-15,
            2.399426653750571
          ],
          [
            3.1955054765805394e-16,
            4.402025819536955e-15,
            2.8768051839822544
          ],
          [
            1.3229838650180453e-15,
            4.726101339993663e-15,
            3.290961402095162
          ],
          [
            7.081500163921338e-16,
            2.045112943488167e-15,
            3.6770475435247203
          ],
          [
            1.19005398271538e-15,
            8.747583934751907e-15,
            4.075224695702888
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -1.1036554293688489e-15,
            1.1931871434996987e-15,
            -4.0752246957028815
          ],
          [
            -9.13679671898e-16,
            2.0230168852752096e-15,
            -3.677047543524718
          ],
          [
            -7.974058710130523e-16,
            -2.3323617002566137e-16,
            -3.2909614020951548
          ],
          [
            -7.844553847450776e-16,
            2.6588923382925386e-15,
            -2.876805183982252
          ],
          [
            8.21757819392297e-17,
            -4.711370634518358e-15,
            -2.3994266537505684
          ],
          [
            -1.4384013736157173e-16,
            5.0354461549750666e-15,
            -2.854637508804526
          ],
          [
            1.1716985601158263e-16,
            -3.3144087319436085e-16,
            -3.2606124152512876
          ],
          [
            9.318444010103137e-17,
            -2.2341569970879133e-16,
            -3.6373166825097325
          ],
          [
            4.995698734451609e-16,
            4.775203691578013e-15,
            -3.9999999999999996
          ],
          [
            4.591534570182362e-16,
            1.2889367290891806e-15,
            -4.362683317490259
          ],
          [
            3.551810400111365e-16,
            1.669479953867892e-16,
            -4.739387584748696
          ],
          [
            -2.7585104050244188e-16,
            4.723646222414445e-15,
            -5.145362491195467
          ],
          [
            -9.022841092524014e-17,
            1.6056468968082366e-15,
            -5.600573346249429
          ],
          [
            3.1955054765805394e-16,
            4.402025819536955e-15,
            -5.1231948160177465
          ],
          [
            1.3229838650180453e-15,
            4.726101339993663e-15,
            -4.709038597904839
          ],
          [
            7.081500163921338e-16,
            2.045112943488167e-15,
            -4.322952456475281
          ],
          [
            1.19005398271538e-15,
            8.747583934751907e-15,
            -3.924775304297113
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            -1
          ],
          [
            0,
            0,
            -2
          ],
          [
            0,
            0,
            -3
          ],
          [
            0,
            0,
            -4
          ],
          [
            0,
            0,
            -5
          ],
          [
            0,
            0,
            -6
          ],
          [
            0,
            0,
            -7
          ],
          [
            0,
            0,
            -8
          ],
          [
            0,
            0,
            -8
          ],
          [
            0,
            0,
            -8
          ],
          [
            0,
            0,
            -8
          ],
          [
            0,
            0,
            -8
          ]
        ],
        "folded_reduced_polarization": [
          [
            -1.1102230246251565e-15,
            1.2212453270876722e-15,
            -0.07522469570288148
          ],
          [
            -8.881784197001252e-16,
            1.9984014443252818e-15,
            0.3229524564752819
          ],
          [
            -7.771561172376096e-16,
            -2.220446049250313e-16,
            -0.29096140209515475
          ],
          [
            -7.771561172376096e-16,
            2.6645352591003757e-15,
            0.12319481601774784
          ],
          [
            1.1102230246251565e-16,
            -4.718447854656915e-15,
            -0.3994266537505684
          ],
          [
            -1.6653345369377348e-16,
            4.9960036108132044e-15,
            0.14536249119547406
          ],
          [
            1.1102230246251565e-16,
            -3.3306690738754696e-16,
            -0.26061241525128764
          ],
          [
            1.1102230246251565e-16,
            -2.220446049250313e-16,
            0.3626833174902675
          ],
          [
            4.440892098500626e-16,
            4.773959005888173e-15,
            4.440892098500626e-16
          ],
          [
            4.440892098500626e-16,
            1.3322676295501878e-15,
            -0.3626833174902586
          ],
          [
            3.3306690738754696e-16,
            2.220446049250313e-16,
            0.26061241525130363
          ],
          [
            -2.7755575615628914e-16,
            4.773959005888173e-15,
            -0.14536249119546696
          ],
          [
            -1.1102230246251565e-16,
            1.5543122344752192e-15,
            0.39942665375057107
          ],
          [
            3.3306690738754696e-16,
            4.440892098500626e-15,
            -0.12319481601774651
          ],
          [
            1.3322676295501878e-15,
            4.773959005888173e-15,
            0.29096140209516097
          ],
          [
            6.661338147750939e-16,
            1.9984014443252818e-15,
            -0.3229524564752806
          ],
          [
            1.2212453270876722e-15,
            8.770761894538737e-15,
            0.07522469570288681
          ]
        ]
      },
      "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,
        -4.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -1.7942320764521064e-15,
              -2.7079946898768884e-15,
              -4.075224695702881
            ],
            "branch_aligned_reduced_polarization": [
              -1.7942320764521064e-15,
              -2.7079946898768884e-15,
              -4.075224695702881
            ],
            "target_residual": 0.4247753042971194,
            "energy_eV": -409.8422883785645,
            "max_atomic_step_A": 0.01805445509343149,
            "max_log_strain_component": 0.002539593715111206,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 10.620403921922358,
            "cell_principal_stretches": [
              0.9995117571067648,
              0.998649287986114,
              0.9974636283248732
            ],
            "cell_volume_ratio": 0.9956299954937569,
            "cell_rmsd_from_input_A": 0.014216185561599492
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              2.0223759826648115e-15,
              2.1212344413619752e-14,
              -4.490678617967493
            ],
            "branch_aligned_reduced_polarization": [
              2.0223759826648115e-15,
              2.1212344413619752e-14,
              -4.490678617967493
            ],
            "target_residual": 0.009321382032506875,
            "energy_eV": -409.93481143142145,
            "max_atomic_step_A": 0.0004097093655666229,
            "max_log_strain_component": 6.12198431300116e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 10.620403921922358,
            "cell_principal_stretches": [
              0.999499990390206,
              0.9986167500410464,
              0.9974025656271626
            ],
            "cell_volume_ratio": 0.9955248875433393,
            "cell_rmsd_from_input_A": 0.014558661583980708
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              2.5757895059753544e-15,
              1.225513194978853e-15,
              -4.500001191415926
            ],
            "branch_aligned_reduced_polarization": [
              2.5757895059753544e-15,
              1.225513194978853e-15,
              -4.500001191415926
            ],
            "target_residual": 1.191415925916317e-06,
            "energy_eV": -409.93514523312336
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_01",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cmc2_1",
        "spacegroup_number": 36,
        "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,
          -4.5
        ],
        "formal_class": [
          0.0,
          0.0,
          0.5
        ],
        "target_residual": 1.191415925916317e-06,
        "parent_symmetrization_rmsd_A": 0.011788689582190147,
        "parent_cell_rmsd_A": 0.014558661583980708,
        "energy_eV": -409.93514523312336,
        "reduced_polarization": [
          2.5757895059753544e-15,
          1.225513194978853e-15,
          -4.500001191415926
        ],
        "cartesian_polarization_e_A2": [
          4.188262106696485e-18,
          4.990828978484668e-17,
          -0.03143411663178275
        ],
        "ranking_score": 0.5154307378100371
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 2,
      "formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.5,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        -0.5,
        -4.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -1.7942320764521064e-15,
              -2.7079946898768884e-15,
              -4.075224695702881
            ],
            "branch_aligned_reduced_polarization": [
              -1.7942320764521064e-15,
              -2.7200464103316335e-15,
              -4.075224695702881
            ],
            "target_residual": 0.5056270906939108,
            "energy_eV": -409.8422883785645,
            "max_atomic_step_A": 0.018675738985851436,
            "max_log_strain_component": 0.004274846306387734,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 10.620403921922358,
            "cell_principal_stretches": [
              1.0046313858112343,
              1.0000864892105163,
              0.9960761318878323
            ],
            "cell_volume_ratio": 1.0007758935833664,
            "cell_rmsd_from_input_A": 0.008809289941199262
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              3.154151156266176e-16,
              -0.5007667820852925,
              -3.9957178995855345
            ],
            "branch_aligned_reduced_polarization": [
              3.154151156266176e-16,
              -0.5007667820852925,
              -3.9957178995855345
            ],
            "target_residual": 0.004350211342669607,
            "energy_eV": -409.7317768218692,
            "max_atomic_step_A": 0.00018318131499005144,
            "max_log_strain_component": 2.5063485099959538e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 10.620403921922358,
            "cell_principal_stretches": [
              1.0046068093487797,
              1.0000816691143553,
              0.9960622473464232
            ],
            "cell_volume_ratio": 1.0007326384935717,
            "cell_rmsd_from_input_A": 0.00875995693101927
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              4.561830346333622e-15,
              -0.49999650921633193,
              -4.000000553812522
            ],
            "branch_aligned_reduced_polarization": [
              4.561830346333622e-15,
              -0.49999650921633193,
              -4.000000553812522
            ],
            "target_residual": 3.5344418126286006e-06,
            "energy_eV": -409.73362852843087
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_02",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cm",
        "spacegroup_number": 8,
        "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,
          -4.0
        ],
        "formal_class": [
          0.0,
          0.5,
          0.0
        ],
        "target_residual": 3.5344418126286006e-06,
        "parent_symmetrization_rmsd_A": 0.01147567015452459,
        "parent_cell_rmsd_A": 0.00875995693101927,
        "energy_eV": -409.73362852843087,
        "reduced_polarization": [
          4.561830346333622e-15,
          -0.49999650921633193,
          -4.000000553812522
        ],
        "cartesian_polarization_e_A2": [
          1.2392030989568818e-16,
          -0.0033445136713200594,
          -0.02786571649582665
        ],
        "ranking_score": 0.5136727282709047
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 3,
      "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,
        -4.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -1.7942320764521064e-15,
              -2.7079946898768884e-15,
              -4.075224695702881
            ],
            "branch_aligned_reduced_polarization": [
              -1.7763568394002505e-15,
              -2.7079946898768884e-15,
              -4.075224695702881
            ],
            "target_residual": 0.5056270906939117,
            "energy_eV": -409.8422883785645,
            "max_atomic_step_A": 0.09537709520125608,
            "max_log_strain_component": 0.01127657777130441,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 10.620403921922358,
            "cell_principal_stretches": [
              1.0116130693014016,
              1.0002393918656651,
              0.9890504617593094
            ],
            "cell_volume_ratio": 1.0007758935833768,
            "cell_rmsd_from_input_A": 0.10009280750465357
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.49138410931216586,
              -8.936759420911815e-14,
              -4.021728838199829
            ],
            "branch_aligned_reduced_polarization": [
              -0.49138410931216586,
              -8.936759420911815e-14,
              -4.021728838199829
            ],
            "target_residual": 0.023374686775635263,
            "energy_eV": -408.79228018631767,
            "max_atomic_step_A": 0.0019701682899660434,
            "max_log_strain_component": 0.00020804136352248632,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 10.620403921922358,
            "cell_principal_stretches": [
              1.0118983871419542,
              1.000304668933759,
              0.9889161513147324
            ],
            "cell_volume_ratio": 1.0009875354526134,
            "cell_rmsd_from_input_A": 0.10199928411396457
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.4999662585416032,
              -1.0890135349615423e-14,
              -4.000403603924276
            ],
            "branch_aligned_reduced_polarization": [
              -0.4999662585416032,
              -1.0890135349615423e-14,
              -4.000403603924276
            ],
            "target_residual": 0.0004050118685988961,
            "energy_eV": -408.74292311642654
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_03",
        "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,
          -4.0
        ],
        "formal_class": [
          0.5,
          0.0,
          0.0
        ],
        "target_residual": 0.0004050118685988961,
        "parent_symmetrization_rmsd_A": 0.058257689337996146,
        "parent_cell_rmsd_A": 0.10199928411396457,
        "energy_eV": -408.74292311642654,
        "reduced_polarization": [
          -0.4999662585416032,
          -1.0890135349615423e-14,
          -4.000403603924276
        ],
        "cartesian_polarization_e_A2": [
          -0.015221354844918461,
          3.8642929320718987e-16,
          -0.027703387186588317
        ],
        "ranking_score": 0.5845675341036851
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 4,
      "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,
        -4.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -1.7942320764521064e-15,
              -2.7079946898768884e-15,
              -4.075224695702881
            ],
            "branch_aligned_reduced_polarization": [
              -1.7942320764521064e-15,
              -2.7200464103316335e-15,
              -4.075224695702881
            ],
            "target_residual": 0.656074735941499,
            "energy_eV": -409.8422883785645,
            "max_atomic_step_A": 0.026013064429799657,
            "max_log_strain_component": 0.004274846306389058,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 10.620403921922358,
            "cell_principal_stretches": [
              1.0023731177157968,
              0.9995117571067653,
              0.9937580374148715
            ],
            "cell_volume_ratio": 0.995629995493753,
            "cell_rmsd_from_input_A": 0.016503978504240537
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              5.505996428957798e-15,
              -0.4929766630367247,
              -4.486821985453645
            ],
            "branch_aligned_reduced_polarization": [
              5.505996428957798e-15,
              -0.4929766630367247,
              -4.486821985453645
            ],
            "target_residual": 0.014932760276775913,
            "energy_eV": -409.8290052890219,
            "max_atomic_step_A": 0.0006444955289653322,
            "max_log_strain_component": 8.778044717029354e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 10.620403921922358,
            "cell_principal_stretches": [
              1.0023752851851495,
              0.9994948853712189,
              0.9936222383514991
            ],
            "cell_volume_ratio": 0.9954792892665055,
            "cell_rmsd_from_input_A": 0.016993602382683406
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              1.88452575662211e-15,
              -0.49999992794013814,
              -4.4999824355207085
            ],
            "branch_aligned_reduced_polarization": [
              1.88452575662211e-15,
              -0.49999992794013814,
              -4.4999824355207085
            ],
            "target_residual": 1.7564627106887428e-05,
            "energy_eV": -409.8254811945078
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_04",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cm",
        "spacegroup_number": 8,
        "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,
          -4.5
        ],
        "formal_class": [
          0.0,
          0.5,
          0.5
        ],
        "target_residual": 1.7564627106887428e-05,
        "parent_symmetrization_rmsd_A": 0.016646054069030625,
        "parent_cell_rmsd_A": 0.016993602382683406,
        "energy_eV": -409.8254811945078,
        "reduced_polarization": [
          1.88452575662211e-15,
          -0.49999992794013814,
          -4.4999824355207085
        ],
        "cartesian_polarization_e_A2": [
          -5.577450015254764e-17,
          -0.0033396186875211545,
          -0.03141980266268554
        ],
        "ranking_score": 0.5209295839189152
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 5,
      "formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.0,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        -0.5,
        0.0,
        -4.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -1.7942320764521064e-15,
              -2.7079946898768884e-15,
              -4.075224695702881
            ],
            "branch_aligned_reduced_polarization": [
              -1.7763568394002505e-15,
              -2.7079946898768884e-15,
              -4.075224695702881
            ],
            "target_residual": 0.6560747359414998,
            "energy_eV": -409.8422883785645,
            "max_atomic_step_A": 0.09850716710650556,
            "max_log_strain_component": 0.011276577771301617,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 10.620403921922358,
            "cell_principal_stretches": [
              1.0098574115229255,
              0.9986492879861254,
              0.9872449441090679
            ],
            "cell_volume_ratio": 0.9956299954937636,
            "cell_rmsd_from_input_A": 0.1001400474814817
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.48856911443441664,
              -5.2547408992654784e-14,
              -4.5075324421087615
            ],
            "branch_aligned_reduced_polarization": [
              -0.48856911443441664,
              -5.2547408992654784e-14,
              -4.5075324421087615
            ],
            "target_residual": 0.013689515292197346,
            "energy_eV": -408.88741555777324,
            "max_atomic_step_A": 0.002365643327293058,
            "max_log_strain_component": 0.0002804621949744914,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 10.620403921922358,
            "cell_principal_stretches": [
              1.0101608647348888,
              0.9986692973365131,
              0.9869926758190842
            ],
            "cell_volume_ratio": 0.995694635893285,
            "cell_rmsd_from_input_A": 0.10256772016631038
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.49997149063394225,
              -3.7373249831719e-15,
              -4.500577165642758
            ],
            "branch_aligned_reduced_polarization": [
              -0.49997149063394225,
              -3.7373249831719e-15,
              -4.500577165642758
            ],
            "target_residual": 0.0005778693305006546,
            "energy_eV": -408.8316018441513
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_05",
        "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,
          -4.5
        ],
        "formal_class": [
          0.5,
          0.0,
          0.5
        ],
        "target_residual": 0.0005778693305006546,
        "parent_symmetrization_rmsd_A": 0.059929628944137794,
        "parent_cell_rmsd_A": 0.10256772016631038,
        "energy_eV": -408.8316018441513,
        "reduced_polarization": [
          -0.49997149063394225,
          -3.7373249831719e-15,
          -4.500577165642758
        ],
        "cartesian_polarization_e_A2": [
          -0.015251355294263937,
          4.510803518052047e-16,
          -0.03125770866537866
        ],
        "ranking_score": 0.5867272976467167
      },
      "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,
        -4.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -1.7942320764521064e-15,
              -2.7079946898768884e-15,
              -4.075224695702881
            ],
            "branch_aligned_reduced_polarization": [
              -1.7763568394002505e-15,
              -2.7200464103316335e-15,
              -4.075224695702881
            ],
            "target_residual": 0.7110968674123002,
            "energy_eV": -409.8422883785645,
            "max_atomic_step_A": 0.09826901711251497,
            "max_log_strain_component": 0.011276577771303333,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 10.620403921922358,
            "cell_principal_stretches": [
              1.0124151516559605,
              1.0002201820609655,
              0.988285870233246
            ],
            "cell_volume_ratio": 1.0007758935833733,
            "cell_rmsd_from_input_A": 0.1004503409270958
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.4909286452983132,
              -0.4948071366593915,
              -4.018218706933877
            ],
            "branch_aligned_reduced_polarization": [
              -0.4909286452983132,
              -0.4948071366593915,
              -4.018218706933877
            ],
            "target_residual": 0.02100420405872459,
            "energy_eV": -408.7095317682643,
            "max_atomic_step_A": 0.0020255542795150914,
            "max_log_strain_component": 0.00022044078468482485,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 10.620403921922358,
            "cell_principal_stretches": [
              1.0127032838134038,
              1.0002698312291232,
              0.9881271336707411
            ],
            "cell_volume_ratio": 1.000949607698049,
            "cell_rmsd_from_input_A": 0.10245678488219105
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.49996540786504323,
              -0.5000081471055267,
              -4.000421660966744
            ],
            "branch_aligned_reduced_polarization": [
              -0.49996540786504323,
              -0.5000081471055267,
              -4.000421660966744
            ],
            "target_residual": 0.00042315595470775825,
            "energy_eV": -408.6583029930206
          }
        ],
        "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,
          -4.0
        ],
        "formal_class": [
          0.5,
          0.5,
          0.0
        ],
        "target_residual": 0.00042315595470775825,
        "parent_symmetrization_rmsd_A": 0.059426977058204454,
        "parent_cell_rmsd_A": 0.10245678488219105,
        "energy_eV": -408.6583029930206,
        "reduced_polarization": [
          -0.49996540786504323,
          -0.5000081471055267,
          -4.000421660966744
        ],
        "cartesian_polarization_e_A2": [
          -0.015221581695737781,
          -0.003343076790688972,
          -0.027689064147000213
        ],
        "ranking_score": 0.5858874851881677
      },
      "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,
        -4.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -1.7942320764521064e-15,
              -2.7079946898768884e-15,
              -4.075224695702881
            ],
            "branch_aligned_reduced_polarization": [
              -1.7763568394002505e-15,
              -2.7200464103316335e-15,
              -4.075224695702881
            ],
            "target_residual": 0.8248842701498834,
            "energy_eV": -409.8422883785645,
            "max_atomic_step_A": 0.10136975476950238,
            "max_log_strain_component": 0.01127657777130054,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 10.620403921922358,
            "cell_principal_stretches": [
              1.010589945655256,
              0.9987568940010485,
              0.9864230431681258
            ],
            "cell_volume_ratio": 0.9956299954937595,
            "cell_rmsd_from_input_A": 0.10049254426741126
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.48815398161593676,
              -0.48788414770237365,
              -4.504123244132878
            ],
            "branch_aligned_reduced_polarization": [
              -0.48815398161593676,
              -0.48788414770237365,
              -4.504123244132878
            ],
            "target_residual": 0.017439127576595586,
            "energy_eV": -408.7792615474457,
            "max_atomic_step_A": 0.002534604418070233,
            "max_log_strain_component": 0.00029243118291105865,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 10.620403921922358,
            "cell_principal_stretches": [
              1.0109139072936422,
              0.998763359820756,
              0.9861222451627233
            ],
            "cell_volume_ratio": 0.9956519042625175,
            "cell_rmsd_from_input_A": 0.10304595513841511
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.4999670475891654,
              -0.5000421096940303,
              -4.500579645025152
            ],
            "branch_aligned_reduced_polarization": [
              -0.4999670475891654,
              -0.5000421096940303,
              -4.500579645025152
            ],
            "target_residual": 0.0005821060409359802,
            "energy_eV": -408.715782596475
          }
        ],
        "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,
          -4.5
        ],
        "formal_class": [
          0.5,
          0.5,
          0.5
        ],
        "target_residual": 0.0005821060409359802,
        "parent_symmetrization_rmsd_A": 0.06114703755187477,
        "parent_cell_rmsd_A": 0.10304595513841511,
        "energy_eV": -408.715782596475,
        "reduced_polarization": [
          -0.4999670475891654,
          -0.5000421096940303,
          -4.500579645025152
        ],
        "cartesian_polarization_e_A2": [
          -0.015251510865975836,
          -0.0033383822687407224,
          -0.0312431598029823
        ],
        "ranking_score": 0.5880727384183505
      },
      "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
        ],
        "endpoint_rmsd_A": 0.2897972081750887,
        "minimum_distance_A_by_image": [
          1.9098988721411676,
          1.9070533557078575,
          1.9045838026366015,
          1.9024916769997695,
          1.9007782250645902,
          1.8994444716138958,
          1.898491216900434,
          1.8979190342557266,
          1.8977282683700767
        ],
        "minimum_distance_A": 1.8977282683700767,
        "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": [
          815.6020046919388,
          815.6020046919388,
          815.6020046919388,
          815.6020046919388,
          815.6020046919388,
          815.6020046919388,
          815.6020046919388,
          815.6020046919388,
          815.6020046919388
        ],
        "cell_deformation_log_strain_norm": 0.0
      },
      "parent_reduced_polarization": [
        4.995698734451609e-16,
        4.775203691578013e-15,
        6.082763043551605e-16
      ],
      "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": [
          -409.8422883785645,
          -409.57478759311397,
          -409.2283762277681,
          -408.8827173118087,
          -408.58145258370996,
          -408.3355201293934,
          -408.1487327068328,
          -408.02934600236534,
          -407.9879670263793
        ],
        "cartesian_polarizations_e_A2": [
          [
            -3.433499596094418e-17,
            8.269480501271363e-18,
            -0.028413310118338267
          ],
          [
            -2.8424802714154165e-17,
            1.4020682989809885e-17,
            -0.025637136593770538
          ],
          [
            -2.4807495738161327e-17,
            -1.6164622379028386e-18,
            -0.02294526409888747
          ],
          [
            -2.4404602876974153e-17,
            1.842766951209236e-17,
            -0.020057681219080054
          ],
          [
            2.5565090932270638e-18,
            -3.265253720563734e-17,
            -0.016729299292652336
          ],
          [
            -4.474902586358463e-18,
            3.489856894672339e-17,
            -0.012930916606961817
          ],
          [
            3.6451834747034795e-18,
            -2.2970779170198233e-18,
            -0.008789250696122523
          ],
          [
            2.8989911972085875e-18,
            -1.5484006699911403e-18,
            -0.004443503830067045
          ],
          [
            1.5541743492131585e-17,
            3.309493739706338e-17,
            4.241028302440376e-18
          ]
        ],
        "raw_reduced_polarization": [
          [
            -1.1036554293688489e-15,
            1.1931871434996987e-15,
            -4.0752246957028815
          ],
          [
            -9.13679671898e-16,
            2.0230168852752096e-15,
            -3.677047543524718
          ],
          [
            -7.974058710130523e-16,
            -2.3323617002566127e-16,
            -3.2909614020951548
          ],
          [
            -7.844553847450776e-16,
            2.6588923382925386e-15,
            -2.876805183982252
          ],
          [
            8.21757819392297e-17,
            -4.7113706345183576e-15,
            -2.3994266537505684
          ],
          [
            -1.4384013736157173e-16,
            5.0354461549750666e-15,
            -1.8546375088045257
          ],
          [
            1.1716985601158263e-16,
            -3.3144087319436075e-16,
            -1.2606124152512874
          ],
          [
            9.318444010103137e-17,
            -2.2341569970879133e-16,
            -0.6373166825097326
          ],
          [
            4.995698734451609e-16,
            4.775203691578013e-15,
            6.082763043551605e-16
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -1.1036554293688489e-15,
            1.1931871434996987e-15,
            -4.0752246957028815
          ],
          [
            -9.13679671898e-16,
            2.0230168852752096e-15,
            -3.677047543524718
          ],
          [
            -7.974058710130523e-16,
            -2.3323617002566137e-16,
            -3.2909614020951548
          ],
          [
            -7.844553847450776e-16,
            2.6588923382925386e-15,
            -2.876805183982252
          ],
          [
            8.21757819392297e-17,
            -4.711370634518358e-15,
            -2.3994266537505684
          ],
          [
            -1.4384013736157173e-16,
            5.0354461549750666e-15,
            -2.854637508804526
          ],
          [
            1.1716985601158263e-16,
            -3.3144087319436085e-16,
            -3.2606124152512876
          ],
          [
            9.318444010103137e-17,
            -2.2341569970879133e-16,
            -3.6373166825097325
          ],
          [
            4.995698734451609e-16,
            4.775203691578013e-15,
            -3.9999999999999996
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            -1
          ],
          [
            0,
            0,
            -2
          ],
          [
            0,
            0,
            -3
          ],
          [
            0,
            0,
            -4
          ]
        ],
        "folded_reduced_polarization": [
          [
            -1.1102230246251565e-15,
            1.2212453270876722e-15,
            -0.07522469570288148
          ],
          [
            -8.881784197001252e-16,
            1.9984014443252818e-15,
            0.3229524564752819
          ],
          [
            -7.771561172376096e-16,
            -2.220446049250313e-16,
            -0.29096140209515475
          ],
          [
            -7.771561172376096e-16,
            2.6645352591003757e-15,
            0.12319481601774784
          ],
          [
            1.1102230246251565e-16,
            -4.718447854656915e-15,
            -0.3994266537505684
          ],
          [
            -1.6653345369377348e-16,
            4.9960036108132044e-15,
            0.14536249119547406
          ],
          [
            1.1102230246251565e-16,
            -3.3306690738754696e-16,
            -0.26061241525128764
          ],
          [
            1.1102230246251565e-16,
            -2.220446049250313e-16,
            0.3626833174902675
          ],
          [
            4.440892098500626e-16,
            4.773959005888173e-15,
            4.440892098500626e-16
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -407.9879670263793,
          -408.02934600236534,
          -408.1487327068328,
          -408.33552012939333,
          -408.58145258371013,
          -408.8827173118088,
          -409.22837622776814,
          -409.574787593114,
          -409.8422883785644
        ],
        "cartesian_polarizations_e_A2": [
          [
            2.3534774179683196e-17,
            5.210113023640518e-17,
            -2.4866093783606543e-18
          ],
          [
            1.42843786861904e-17,
            8.933080788410424e-18,
            0.004443503830067105
          ],
          [
            1.1049770833964365e-17,
            1.1570466544988739e-18,
            0.008789250696122634
          ],
          [
            -8.581794742667103e-18,
            3.273761416552696e-17,
            0.012930916606961869
          ],
          [
            -2.8070283915082006e-18,
            1.11280663535627e-17,
            0.016729299292652357
          ],
          [
            9.941297320877807e-18,
            3.050859781641884e-17,
            0.020057681219080067
          ],
          [
            4.1158358354442246e-17,
            3.275462955750489e-17,
            0.02294526409888752
          ],
          [
            2.2030723816101903e-17,
            1.4173821517611208e-17,
            0.025637136593770548
          ],
          [
            3.7022876526965614e-17,
            6.062584161734541e-17,
            0.02841331011833831
          ]
        ],
        "raw_reduced_polarization": [
          [
            7.564958310151753e-16,
            7.517570027563947e-15,
            -3.566459488548453e-16
          ],
          [
            4.591534570182362e-16,
            1.2889367290891806e-15,
            0.6373166825097412
          ],
          [
            3.551810400111365e-16,
            1.669479953867891e-16,
            1.2606124152513034
          ],
          [
            -2.7585104050244188e-16,
            4.723646222414445e-15,
            1.854637508804533
          ],
          [
            -9.022841092524016e-17,
            1.6056468968082364e-15,
            2.399426653750571
          ],
          [
            3.1955054765805394e-16,
            4.402025819536955e-15,
            2.8768051839822544
          ],
          [
            1.3229838650180453e-15,
            4.726101339993663e-15,
            3.290961402095162
          ],
          [
            7.081500163921338e-16,
            2.045112943488167e-15,
            3.6770475435247203
          ],
          [
            1.19005398271538e-15,
            8.747583934751907e-15,
            4.075224695702888
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            7.564958310151753e-16,
            7.517570027563947e-15,
            -4.0
          ],
          [
            4.591534570182362e-16,
            1.2889367290891802e-15,
            -4.362683317490259
          ],
          [
            3.551810400111365e-16,
            1.669479953867892e-16,
            -4.739387584748696
          ],
          [
            -2.7585104050244188e-16,
            4.723646222414445e-15,
            -5.145362491195467
          ],
          [
            -9.022841092524014e-17,
            1.6056468968082366e-15,
            -5.600573346249429
          ],
          [
            3.1955054765805394e-16,
            4.402025819536955e-15,
            -5.123194816017746
          ],
          [
            1.3229838650180453e-15,
            4.726101339993663e-15,
            -4.709038597904838
          ],
          [
            7.081500163921338e-16,
            2.045112943488167e-15,
            -4.32295245647528
          ],
          [
            1.19005398271538e-15,
            8.747583934751907e-15,
            -3.9247753042971123
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          -4
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          2.1027951762591706e-15,
          8.357220239656327e-15,
          4.075224695702882
        ],
        "actual_opposite_endpoint_branch_residual": 5.420744680281192e-15
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            -1.1036554293688489e-15,
            1.1931871434996987e-15,
            -4.0752246957028815
          ],
          [
            -9.13679671898e-16,
            2.0230168852752096e-15,
            -3.677047543524718
          ],
          [
            -7.974058710130523e-16,
            -2.3323617002566127e-16,
            -3.2909614020951548
          ],
          [
            -7.844553847450776e-16,
            2.6588923382925386e-15,
            -2.876805183982252
          ],
          [
            8.21757819392297e-17,
            -4.7113706345183576e-15,
            -2.3994266537505684
          ],
          [
            -1.4384013736157173e-16,
            5.0354461549750666e-15,
            -1.8546375088045257
          ],
          [
            1.1716985601158263e-16,
            -3.3144087319436075e-16,
            -1.2606124152512874
          ],
          [
            9.318444010103137e-17,
            -2.2341569970879133e-16,
            -0.6373166825097326
          ],
          [
            4.995698734451609e-16,
            4.775203691578013e-15,
            6.082763043551605e-16
          ],
          [
            4.591534570182362e-16,
            1.2889367290891806e-15,
            0.6373166825097412
          ],
          [
            3.551810400111365e-16,
            1.669479953867891e-16,
            1.2606124152513034
          ],
          [
            -2.7585104050244188e-16,
            4.723646222414445e-15,
            1.854637508804533
          ],
          [
            -9.022841092524016e-17,
            1.6056468968082364e-15,
            2.399426653750571
          ],
          [
            3.1955054765805394e-16,
            4.402025819536955e-15,
            2.8768051839822544
          ],
          [
            1.3229838650180453e-15,
            4.726101339993663e-15,
            3.290961402095162
          ],
          [
            7.081500163921338e-16,
            2.045112943488167e-15,
            3.6770475435247203
          ],
          [
            1.19005398271538e-15,
            8.747583934751907e-15,
            4.075224695702888
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -1.1036554293688489e-15,
            1.1931871434996987e-15,
            -4.0752246957028815
          ],
          [
            -9.13679671898e-16,
            2.0230168852752096e-15,
            -3.677047543524718
          ],
          [
            -7.974058710130523e-16,
            -2.3323617002566137e-16,
            -3.2909614020951548
          ],
          [
            -7.844553847450776e-16,
            2.6588923382925386e-15,
            -2.876805183982252
          ],
          [
            8.21757819392297e-17,
            -4.711370634518358e-15,
            -2.3994266537505684
          ],
          [
            -1.4384013736157173e-16,
            5.0354461549750666e-15,
            -2.854637508804526
          ],
          [
            1.1716985601158263e-16,
            -3.3144087319436085e-16,
            -3.2606124152512876
          ],
          [
            9.318444010103137e-17,
            -2.2341569970879133e-16,
            -3.6373166825097325
          ],
          [
            4.995698734451609e-16,
            4.775203691578013e-15,
            -3.9999999999999996
          ],
          [
            4.591534570182362e-16,
            1.2889367290891806e-15,
            -4.362683317490259
          ],
          [
            3.551810400111365e-16,
            1.669479953867892e-16,
            -4.739387584748696
          ],
          [
            -2.7585104050244188e-16,
            4.723646222414445e-15,
            -5.145362491195467
          ],
          [
            -9.022841092524014e-17,
            1.6056468968082366e-15,
            -5.600573346249429
          ],
          [
            3.1955054765805394e-16,
            4.402025819536955e-15,
            -5.1231948160177465
          ],
          [
            1.3229838650180453e-15,
            4.726101339993663e-15,
            -4.709038597904839
          ],
          [
            7.081500163921338e-16,
            2.045112943488167e-15,
            -4.322952456475281
          ],
          [
            1.19005398271538e-15,
            8.747583934751907e-15,
            -3.924775304297113
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            -1
          ],
          [
            0,
            0,
            -2
          ],
          [
            0,
            0,
            -3
          ],
          [
            0,
            0,
            -4
          ],
          [
            0,
            0,
            -5
          ],
          [
            0,
            0,
            -6
          ],
          [
            0,
            0,
            -7
          ],
          [
            0,
            0,
            -8
          ],
          [
            0,
            0,
            -8
          ],
          [
            0,
            0,
            -8
          ],
          [
            0,
            0,
            -8
          ],
          [
            0,
            0,
            -8
          ]
        ],
        "folded_reduced_polarization": [
          [
            -1.1102230246251565e-15,
            1.2212453270876722e-15,
            -0.07522469570288148
          ],
          [
            -8.881784197001252e-16,
            1.9984014443252818e-15,
            0.3229524564752819
          ],
          [
            -7.771561172376096e-16,
            -2.220446049250313e-16,
            -0.29096140209515475
          ],
          [
            -7.771561172376096e-16,
            2.6645352591003757e-15,
            0.12319481601774784
          ],
          [
            1.1102230246251565e-16,
            -4.718447854656915e-15,
            -0.3994266537505684
          ],
          [
            -1.6653345369377348e-16,
            4.9960036108132044e-15,
            0.14536249119547406
          ],
          [
            1.1102230246251565e-16,
            -3.3306690738754696e-16,
            -0.26061241525128764
          ],
          [
            1.1102230246251565e-16,
            -2.220446049250313e-16,
            0.3626833174902675
          ],
          [
            4.440892098500626e-16,
            4.773959005888173e-15,
            4.440892098500626e-16
          ],
          [
            4.440892098500626e-16,
            1.3322676295501878e-15,
            -0.3626833174902586
          ],
          [
            3.3306690738754696e-16,
            2.220446049250313e-16,
            0.26061241525130363
          ],
          [
            -2.7755575615628914e-16,
            4.773959005888173e-15,
            -0.14536249119546696
          ],
          [
            -1.1102230246251565e-16,
            1.5543122344752192e-15,
            0.39942665375057107
          ],
          [
            3.3306690738754696e-16,
            4.440892098500626e-15,
            -0.12319481601774651
          ],
          [
            1.3322676295501878e-15,
            4.773959005888173e-15,
            0.29096140209516097
          ],
          [
            6.661338147750939e-16,
            1.9984014443252818e-15,
            -0.3229524564752806
          ],
          [
            1.2212453270876722e-15,
            8.770761894538737e-15,
            0.07522469570288681
          ]
        ]
      },
      "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": 1.3957328883844298e-15,
        "parent_symmetrization_rmsd_A": 0.2897972081750887,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -407.98796702637924,
        "reduced_polarization": [
          -4.1507466768972894e-16,
          8.838423285182954e-17,
          1.329650910330752e-15
        ],
        "cartesian_polarization_e_A2": [
          -1.2913076544884298e-17,
          6.125541112052862e-19,
          9.270601374249454e-18
        ],
        "ranking_score": 0.28979720817509147
      }
    }
  ],
  "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": 49,
      "full_response": 16,
      "energy_polarization": 33
    },
    "model_evaluations_for_recovery_and_path_properties": {
      "total": 74,
      "full_response": 41,
      "energy_polarization": 33
    },
    "elapsed_seconds": 751.2465310400003
  }
}