{
  "schema": "ferrofinder.endpoint_parent_recovery.v4_variable_cell",
  "status": "complete",
  "input_atom_count": 64,
  "input_formula": "K16Li8S32V8",
  "input_spacegroup": "Cc",
  "input_pointgroup": "m",
  "input_is_polar_point_group": true,
  "input_energy_eV": -302.09815967004187,
  "input_cartesian_polarization_e_A2": [
    7.422609707979383e-05,
    2.1972930686346174e-11,
    -9.93695418092807e-05
  ],
  "input_reduced_polarization": [
    0.010185847536349903,
    4.26838468258884e-09,
    -0.009062543580376529
  ],
  "input_formal_targets": [
    {
      "orbit_id": 0,
      "representative_formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ]
    },
    {
      "orbit_id": 1,
      "representative_formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.0
      ]
    },
    {
      "orbit_id": 2,
      "representative_formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        -0.5
      ]
    },
    {
      "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": [
        0.5,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        0.5,
        0.5,
        0.0
      ]
    },
    {
      "orbit_id": 6,
      "representative_formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        -0.5
      ]
    },
    {
      "orbit_id": 7,
      "representative_formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "target_reduced_polarization": [
        0.5,
        0.5,
        -0.5
      ]
    }
  ],
  "parent_candidates": [
    {
      "candidate_id": "inversion_parent_endpoint_00",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "C2/c",
      "spacegroup_number": 15,
      "pointgroup": "2/m",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 2.8262209310740537e-15,
      "parent_symmetrization_rmsd_A": 0.06637752295002297,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -302.0867511115564,
      "reduced_polarization": [
        -2.607511881465904e-15,
        2.865550164478332e-16,
        -1.0518045264229544e-15
      ],
      "cartesian_polarization_e_A2": [
        -1.5874489045590146e-17,
        1.4751373136345649e-18,
        -1.1532891724779325e-17
      ],
      "ranking_score": 0.06637752295002862
    },
    {
      "candidate_id": "bec_projection_00",
      "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": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 1.0750358657259806e-06,
      "parent_symmetrization_rmsd_A": 0.0028153591954339,
      "parent_cell_rmsd_A": 0.0009191373455926066,
      "energy_eV": -302.0940875961343,
      "reduced_polarization": [
        -8.595785462559383e-07,
        4.196930510285767e-13,
        -6.456212786251394e-07
      ],
      "cartesian_polarization_e_A2": [
        -4.955705533913861e-09,
        2.1599991946853113e-15,
        -7.078602413992929e-09
      ],
      "ranking_score": 0.5030472936035635
    },
    {
      "candidate_id": "inversion_parent_bec_00_00",
      "source": "same_species_inversion_center_projection_after_BEC",
      "spacegroup": "C2/c",
      "spacegroup_number": 15,
      "pointgroup": "2/m",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 3.542865994910839e-15,
      "parent_symmetrization_rmsd_A": 0.06637753670864625,
      "parent_cell_rmsd_A": 0.0009191373455926066,
      "energy_eV": -302.0860413077307,
      "reduced_polarization": [
        4.50129809107309e-16,
        -3.461485212318005e-15,
        6.061375567908355e-16
      ],
      "cartesian_polarization_e_A2": [
        2.346531704230925e-18,
        -1.7816880011410525e-17,
        6.645713005196871e-18
      ],
      "ranking_score": 0.0666073210450515
    },
    {
      "candidate_id": "bec_projection_01",
      "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": 4.8755408603743265e-05,
      "parent_symmetrization_rmsd_A": 0.0561500271939689,
      "parent_cell_rmsd_A": 0.030485800783089448,
      "energy_eV": -300.46858996067954,
      "reduced_polarization": [
        0.4999513452124659,
        2.50118546836943e-12,
        3.130737633848343e-06
      ],
      "cartesian_polarization_e_A2": [
        0.0032345190814516162,
        2.8183904017144506e-13,
        5.013785030785853e-06
      ],
      "ranking_score": 0.5638689882069488
    },
    {
      "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": [
        0.0,
        0.0,
        -0.5
      ],
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_residual": 7.74349020555833e-06,
      "parent_symmetrization_rmsd_A": 0.12168148239603996,
      "parent_cell_rmsd_A": 0.051151604867673554,
      "energy_eV": -296.7735251322383,
      "reduced_polarization": [
        6.697694289456355e-06,
        1.4680084671774728e-12,
        -0.4999961138024023
      ],
      "cartesian_polarization_e_A2": [
        0.0004721390081730459,
        2.897470316076639e-12,
        -0.0054776568943134644
      ],
      "ranking_score": 0.6344848705933694
    },
    {
      "candidate_id": "bec_projection_03",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.0
      ],
      "formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_residual": 1.2361670622453747e-05,
      "parent_symmetrization_rmsd_A": 0.04331764395057387,
      "parent_cell_rmsd_A": 0.019739471426074563,
      "energy_eV": -301.1672313887279,
      "reduced_polarization": [
        -1.0761029665062272e-05,
        0.4999970151394802,
        -5.301108261768556e-06
      ],
      "cartesian_polarization_e_A2": [
        -6.228402797740156e-06,
        0.0025735810840375657,
        -3.3600888708896695e-06
      ],
      "ranking_score": 0.5482772351483374
    },
    {
      "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": 0.00012401739341893225,
      "parent_symmetrization_rmsd_A": 0.15727462980107967,
      "parent_cell_rmsd_A": 0.05230085790086272,
      "energy_eV": -293.9349321403944,
      "reduced_polarization": [
        0.49987647728742435,
        8.616200001041209e-12,
        -0.4999889341358955
      ],
      "cartesian_polarization_e_A2": [
        0.003700589259827941,
        3.2325065864190054e-12,
        -0.0055026103070020625
      ],
      "ranking_score": 0.6705978790631332
    },
    {
      "candidate_id": "bec_projection_05",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.5,
        0.5,
        0.0
      ],
      "formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_residual": 0.00022305581633424786,
      "parent_symmetrization_rmsd_A": 0.07217259981503939,
      "parent_cell_rmsd_A": 0.037056643825856744,
      "energy_eV": -299.3877734318735,
      "reduced_polarization": [
        0.49985340139585727,
        0.49983375837581046,
        -2.5029359775310987e-05
      ],
      "cartesian_polarization_e_A2": [
        0.0032276330378410464,
        0.00257128915709633,
        1.4027200112394242e-06
      ],
      "ranking_score": 0.581882872404172
    },
    {
      "candidate_id": "bec_projection_06",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.5,
        -0.5
      ],
      "formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_residual": 1.7473683677748454e-05,
      "parent_symmetrization_rmsd_A": 0.130946883599374,
      "parent_cell_rmsd_A": 0.05613669074607094,
      "energy_eV": -295.7898952165473,
      "reduced_polarization": [
        7.429340687484618e-06,
        0.5000147540381942,
        -0.4999943032574936
      ],
      "cartesian_polarization_e_A2": [
        0.0004657353025650199,
        0.0025917441765267056,
        -0.00548081532646699
      ],
      "ranking_score": 0.6450160036532473
    },
    {
      "candidate_id": "bec_projection_07",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.5,
        0.5,
        -0.5
      ],
      "formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "target_residual": 0.0001853317864342959,
      "parent_symmetrization_rmsd_A": 0.1648431480887118,
      "parent_cell_rmsd_A": 0.05681503271364465,
      "energy_eV": -292.89495606681083,
      "reduced_polarization": [
        0.4998184977336624,
        0.4999642223058515,
        -0.49998883062317523
      ],
      "cartesian_polarization_e_A2": [
        0.0036936523605621274,
        0.002590356557904754,
        -0.005506286241947452
      ],
      "ranking_score": 0.6794175698399916
    }
  ],
  "formal_branches": [
    {
      "orbit_id": 0,
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.0,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              0.010185847536349903,
              4.26838468258884e-09,
              -0.009062543580376529
            ],
            "branch_aligned_reduced_polarization": [
              0.010185847536349903,
              4.26838468258884e-09,
              -0.009062543580376529
            ],
            "target_residual": 0.013633825075158014,
            "energy_eV": -302.09815967004187,
            "max_atomic_step_A": 0.003659711763770093,
            "max_log_strain_component": 8.27715086384147e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.5588282006843359,
            "cell_principal_stretches": [
              1.0000833364829527,
              1.0000439050711898,
              0.9999910830547997
            ],
            "cell_volume_ratio": 1.0001183271331977,
            "cell_rmsd_from_input_A": 0.0009191373455926066
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -8.595785462559383e-07,
              4.196930510285767e-13,
              -6.456212786251394e-07
            ],
            "branch_aligned_reduced_polarization": [
              -8.595785462559383e-07,
              4.196930510285767e-13,
              -6.456212786251394e-07
            ],
            "target_residual": 1.0750358657259806e-06,
            "energy_eV": -302.0940875961343
          }
        ],
        "iterations": 1
      },
      "parent": {
        "candidate_id": "inversion_parent_endpoint_00",
        "source": "same_species_inversion_center_projection_from_endpoint",
        "spacegroup": "C2/c",
        "spacegroup_number": 15,
        "pointgroup": "2/m",
        "has_inversion": true,
        "is_polar_point_group": false,
        "nonpolar_parent_hypothesis": true,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.0
        ],
        "formal_class": [
          0.0,
          0.0,
          0.0
        ],
        "target_residual": 2.8262209310740537e-15,
        "parent_symmetrization_rmsd_A": 0.06637752295002297,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -302.0867511115564,
        "reduced_polarization": [
          -2.607511881465904e-15,
          2.865550164478332e-16,
          -1.0518045264229544e-15
        ],
        "cartesian_polarization_e_A2": [
          -1.5874489045590146e-17,
          1.4751373136345649e-18,
          -1.1532891724779325e-17
        ],
        "ranking_score": 0.06637752295002862
      },
      "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": [
          -302.0981596700418,
          -302.09641241738893,
          -302.0945135995662,
          -302.0925720415782,
          -302.0907280855179,
          -302.08911443934454,
          -302.0878428421256,
          -302.0870301397726,
          -302.08675111155645
        ],
        "cartesian_polarizations_e_A2": [
          [
            7.422609707977867e-05,
            2.1972926436944935e-11,
            -9.936954180927896e-05
          ],
          [
            6.34507988044497e-05,
            1.920145704217105e-11,
            -8.853359217336538e-05
          ],
          [
            5.32523393513672e-05,
            1.6439886522814465e-11,
            -7.715259774809772e-05
          ],
          [
            4.355795325965622e-05,
            1.3686472171768356e-11,
            -6.526460640936129e-05
          ],
          [
            3.4294872866845196e-05,
            1.0940028389324199e-11,
            -5.290462467043397e-05
          ],
          [
            2.5389581565253942e-05,
            8.199463959417161e-12,
            -4.0115542992833386e-05
          ],
          [
            1.6764483464307326e-05,
            5.46349498455227e-12,
            -2.6962652867730347e-05
          ],
          [
            8.332794514046348e-06,
            2.730894644990842e-12,
            -1.3549133599503437e-05
          ],
          [
            1.6092407057831615e-17,
            1.04935904356277e-17,
            -1.3301380208738946e-17
          ]
        ],
        "raw_reduced_polarization": [
          [
            0.010185847536347579,
            4.268383857115014e-09,
            -0.00906254358037637
          ],
          [
            0.008660203142340669,
            3.730007903457293e-09,
            -0.00807430046259377
          ],
          [
            0.00723095786541865,
            3.193554870724833e-09,
            -0.0070363490331208645
          ],
          [
            0.0058863533210121504,
            2.658686226728768e-09,
            -0.00595215927407766
          ],
          [
            0.004614670590321653,
            2.1251716610153964e-09,
            -0.0048249237940482526
          ],
          [
            0.003403971667847025,
            1.5927991977676083e-09,
            -0.0036585542209782726
          ],
          [
            0.002241394089281268,
            1.0613194315474235e-09,
            -0.002459005166043235
          ],
          [
            0.0011121576400530205,
            5.304940446422139e-10,
            -0.001235686624755834
          ],
          [
            2.3161945024513098e-15,
            2.0384481851857225e-15,
            -1.2130914123788001e-15
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            0.010185847536347579,
            4.268383857115014e-09,
            -0.00906254358037637
          ],
          [
            0.008660203142340669,
            3.730007903457293e-09,
            -0.00807430046259377
          ],
          [
            0.00723095786541865,
            3.193554870724833e-09,
            -0.0070363490331208645
          ],
          [
            0.0058863533210121504,
            2.658686226728768e-09,
            -0.00595215927407766
          ],
          [
            0.004614670590321653,
            2.1251716610153964e-09,
            -0.0048249237940482526
          ],
          [
            0.003403971667847025,
            1.5927991977676083e-09,
            -0.0036585542209782726
          ],
          [
            0.002241394089281268,
            1.0613194315474235e-09,
            -0.002459005166043235
          ],
          [
            0.0011121576400530205,
            5.304940446422139e-10,
            -0.001235686624755834
          ],
          [
            2.3162895212980317e-15,
            2.0384481851711617e-15,
            -1.2130053905767824e-15
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            0.010185847536347548,
            4.26838386857753e-09,
            -0.009062543580376392
          ],
          [
            0.008660203142340617,
            3.730007858138151e-09,
            -0.008074300462593775
          ],
          [
            0.007230957865418608,
            3.193554864999726e-09,
            -0.007036349033120892
          ],
          [
            0.005886353321012172,
            2.658686271139743e-09,
            -0.005952159274077662
          ],
          [
            0.004614670590321612,
            2.125171705280593e-09,
            -0.0048249237940482526
          ],
          [
            0.0034039716678470056,
            1.5927992258468748e-09,
            -0.0036585542209782718
          ],
          [
            0.0022413940892812567,
            1.0613194767472578e-09,
            -0.002459005166043249
          ],
          [
            0.001112157640053013,
            5.304940930983548e-10,
            -0.0012356866247558163
          ],
          [
            2.3314683517128287e-15,
            1.9984014443252818e-15,
            -1.2212453270876722e-15
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -302.08675111155634,
          -302.0870301397724,
          -302.0878428421255,
          -302.0891144393446,
          -302.09072808551787,
          -302.0925720415781,
          -302.0945135995661,
          -302.09641241738893,
          -302.09815967004187
        ],
        "cartesian_polarizations_e_A2": [
          [
            1.555599348923723e-17,
            1.610916998185019e-17,
            -1.1013241080203512e-17
          ],
          [
            -8.332794514001708e-06,
            -2.7309069070697616e-12,
            1.3549133599569743e-05
          ],
          [
            -1.676448346429291e-05,
            -5.46354332882514e-12,
            2.6962652867742876e-05
          ],
          [
            -2.5389581565240867e-05,
            -8.199462107114056e-12,
            4.0115542992858994e-05
          ],
          [
            -3.429487286678413e-05,
            -1.0940021080689327e-11,
            5.2904624670491495e-05
          ],
          [
            -4.3557953259653136e-05,
            -1.368649434073537e-11,
            6.526460640937981e-05
          ],
          [
            -5.3252339351346236e-05,
            -1.64398938398308e-11,
            7.715259774811335e-05
          ],
          [
            -6.345079880441112e-05,
            -1.92014745929525e-11,
            8.853359217339065e-05
          ],
          [
            -7.422609707973636e-05,
            -2.197292586700552e-11,
            9.936954180932567e-05
          ]
        ],
        "raw_reduced_polarization": [
          [
            2.263132909307004e-15,
            3.129311031890542e-15,
            -1.0044121713079668e-15
          ],
          [
            -0.0011121576400452446,
            -5.304964266307881e-10,
            0.0012356866247618813
          ],
          [
            -0.0022413940892788728,
            -1.0613288227368263e-09,
            0.0024590051660443773
          ],
          [
            -0.0034039716678446667,
            -1.5927988379456845e-09,
            0.003658554220980608
          ],
          [
            -0.004614670590311451,
            -2.1251702412655423e-09,
            0.004824923794053498
          ],
          [
            -0.005886353321011431,
            -2.658690533194782e-09,
            0.005952159274079351
          ],
          [
            -0.007230957865415203,
            -3.1935562921028405e-09,
            0.0070363490331222895
          ],
          [
            -0.008660203142334368,
            -3.7300113128107286e-09,
            0.008074300462596074
          ],
          [
            -0.010185847536340421,
            -4.268383746400576e-09,
            0.00906254358038063
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            2.263132909307004e-15,
            3.129311031890542e-15,
            -1.0044121713079668e-15
          ],
          [
            -0.0011121576400452446,
            -5.304964266307881e-10,
            0.0012356866247618813
          ],
          [
            -0.0022413940892788728,
            -1.0613288227368263e-09,
            0.0024590051660443773
          ],
          [
            -0.0034039716678446667,
            -1.5927988379456845e-09,
            0.003658554220980608
          ],
          [
            -0.004614670590311451,
            -2.1251702412655423e-09,
            0.004824923794053498
          ],
          [
            -0.005886353321011431,
            -2.658690533194782e-09,
            0.005952159274079351
          ],
          [
            -0.007230957865415203,
            -3.1935562921028405e-09,
            0.0070363490331222895
          ],
          [
            -0.008660203142334368,
            -3.7300113128107286e-09,
            0.008074300462596074
          ],
          [
            -0.010185847536340421,
            -4.268383746400576e-09,
            0.00906254358038063
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          -0.010185847536342947,
          -4.268379780218644e-09,
          0.009062543580373944
        ],
        "actual_opposite_endpoint_branch_residual": 8.173592932833039e-15
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            0.010185847536347579,
            4.268383857115014e-09,
            -0.00906254358037637
          ],
          [
            0.008660203142340669,
            3.730007903457293e-09,
            -0.00807430046259377
          ],
          [
            0.00723095786541865,
            3.193554870724833e-09,
            -0.0070363490331208645
          ],
          [
            0.0058863533210121504,
            2.658686226728768e-09,
            -0.00595215927407766
          ],
          [
            0.004614670590321653,
            2.1251716610153964e-09,
            -0.0048249237940482526
          ],
          [
            0.003403971667847025,
            1.5927991977676083e-09,
            -0.0036585542209782726
          ],
          [
            0.002241394089281268,
            1.0613194315474235e-09,
            -0.002459005166043235
          ],
          [
            0.0011121576400530205,
            5.304940446422139e-10,
            -0.001235686624755834
          ],
          [
            2.3161945024513098e-15,
            2.0384481851857225e-15,
            -1.2130914123788001e-15
          ],
          [
            -0.0011121576400452446,
            -5.304964266307881e-10,
            0.0012356866247618813
          ],
          [
            -0.0022413940892788728,
            -1.0613288227368263e-09,
            0.0024590051660443773
          ],
          [
            -0.0034039716678446667,
            -1.5927988379456845e-09,
            0.003658554220980608
          ],
          [
            -0.004614670590311451,
            -2.1251702412655423e-09,
            0.004824923794053498
          ],
          [
            -0.005886353321011431,
            -2.658690533194782e-09,
            0.005952159274079351
          ],
          [
            -0.007230957865415203,
            -3.1935562921028405e-09,
            0.0070363490331222895
          ],
          [
            -0.008660203142334368,
            -3.7300113128107286e-09,
            0.008074300462596074
          ],
          [
            -0.010185847536340421,
            -4.268383746400576e-09,
            0.00906254358038063
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            0.010185847536347579,
            4.268383857115014e-09,
            -0.00906254358037637
          ],
          [
            0.008660203142340669,
            3.730007903457293e-09,
            -0.00807430046259377
          ],
          [
            0.00723095786541865,
            3.193554870724833e-09,
            -0.0070363490331208645
          ],
          [
            0.0058863533210121504,
            2.658686226728768e-09,
            -0.00595215927407766
          ],
          [
            0.004614670590321653,
            2.1251716610153964e-09,
            -0.0048249237940482526
          ],
          [
            0.003403971667847025,
            1.5927991977676083e-09,
            -0.0036585542209782726
          ],
          [
            0.002241394089281268,
            1.0613194315474235e-09,
            -0.002459005166043235
          ],
          [
            0.0011121576400530205,
            5.304940446422139e-10,
            -0.001235686624755834
          ],
          [
            2.3162895212980317e-15,
            2.0384481851711617e-15,
            -1.2130053905767824e-15
          ],
          [
            -0.0011121576400452446,
            -5.304964266307881e-10,
            0.0012356866247618813
          ],
          [
            -0.0022413940892788728,
            -1.0613288227368263e-09,
            0.0024590051660443773
          ],
          [
            -0.0034039716678446667,
            -1.5927988379456845e-09,
            0.003658554220980608
          ],
          [
            -0.004614670590311451,
            -2.1251702412655423e-09,
            0.004824923794053498
          ],
          [
            -0.005886353321011431,
            -2.658690533194782e-09,
            0.005952159274079351
          ],
          [
            -0.007230957865415203,
            -3.1935562921028405e-09,
            0.0070363490331222895
          ],
          [
            -0.008660203142334368,
            -3.7300113128107286e-09,
            0.008074300462596074
          ],
          [
            -0.010185847536340421,
            -4.268383746400576e-09,
            0.00906254358038063
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            0.010185847536347548,
            4.26838386857753e-09,
            -0.009062543580376392
          ],
          [
            0.008660203142340617,
            3.730007858138151e-09,
            -0.008074300462593775
          ],
          [
            0.007230957865418608,
            3.193554864999726e-09,
            -0.007036349033120892
          ],
          [
            0.005886353321012172,
            2.658686271139743e-09,
            -0.005952159274077662
          ],
          [
            0.004614670590321612,
            2.125171705280593e-09,
            -0.0048249237940482526
          ],
          [
            0.0034039716678470056,
            1.5927992258468748e-09,
            -0.0036585542209782718
          ],
          [
            0.0022413940892812567,
            1.0613194767472578e-09,
            -0.002459005166043249
          ],
          [
            0.001112157640053013,
            5.304940930983548e-10,
            -0.0012356866247558163
          ],
          [
            2.3314683517128287e-15,
            1.9984014443252818e-15,
            -1.2212453270876722e-15
          ],
          [
            -0.0011121576400452415,
            -5.304964245667065e-10,
            0.0012356866247619225
          ],
          [
            -0.0022413940892788697,
            -1.0613288026206646e-09,
            0.002459005166044359
          ],
          [
            -0.003403971667844674,
            -1.5927988372688162e-09,
            0.0036585542209806032
          ],
          [
            -0.004614670590311454,
            -2.125170261990661e-09,
            0.004824923794053526
          ],
          [
            -0.0058863533210114505,
            -2.6586905454983878e-09,
            0.005952159274079327
          ],
          [
            -0.007230957865415222,
            -3.193556308289658e-09,
            0.0070363490331223355
          ],
          [
            -0.008660203142334344,
            -3.730011299829528e-09,
            0.008074300462596051
          ],
          [
            -0.010185847536340442,
            -4.2683837575552275e-09,
            0.009062543580380611
          ]
        ]
      },
      "incoming_structure_ids": [
        "incoming_00_000",
        "incoming_00_001",
        "incoming_00_002",
        "incoming_00_003",
        "incoming_00_004",
        "incoming_00_005",
        "incoming_00_006",
        "incoming_00_007",
        "incoming_00_008"
      ],
      "reflected_structure_ids": [
        "reflected_00_001",
        "reflected_00_002",
        "reflected_00_003",
        "reflected_00_004",
        "reflected_00_005",
        "reflected_00_006",
        "reflected_00_007",
        "reflected_00_008"
      ]
    },
    {
      "orbit_id": 1,
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.0,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              0.010185847536349903,
              4.26838468258884e-09,
              -0.009062543580376529
            ],
            "branch_aligned_reduced_polarization": [
              0.010185847536349879,
              4.26838468258884e-09,
              -0.009062543580376529
            ],
            "target_residual": 0.48989798290034847,
            "energy_eV": -302.09815967004187,
            "max_atomic_step_A": 0.07859463891083378,
            "max_log_strain_component": 0.002782610961474213,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.5588282006843359,
            "cell_principal_stretches": [
              1.0010345384843828,
              0.9984033544655061,
              0.9966403712899604
            ],
            "cell_volume_ratio": 0.9960785064689862,
            "cell_rmsd_from_input_A": 0.029624064937197058
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.48836047370375685,
              1.6421721956056145e-11,
              -0.0018725012657883821
            ],
            "branch_aligned_reduced_polarization": [
              0.48836047370375685,
              1.6421721956056145e-11,
              -0.0018725012657883821
            ],
            "target_residual": 0.011789182897525804,
            "energy_eV": -300.54417497600207,
            "max_atomic_step_A": 0.0020925274941390117,
            "max_log_strain_component": 7.013254784898669e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.5588282006843359,
            "cell_principal_stretches": [
              1.0010762521103265,
              0.9983517415623008,
              0.9965519611188838
            ],
            "cell_volume_ratio": 0.9959801592665654,
            "cell_rmsd_from_input_A": 0.030485800783089448
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.4999513452124659,
              2.50118546836943e-12,
              3.130737633848343e-06
            ],
            "branch_aligned_reduced_polarization": [
              0.4999513452124659,
              2.50118546836943e-12,
              3.130737633848343e-06
            ],
            "target_residual": 4.8755408603743265e-05,
            "energy_eV": -300.46858996067954
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_01",
        "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": 4.8755408603743265e-05,
        "parent_symmetrization_rmsd_A": 0.0561500271939689,
        "parent_cell_rmsd_A": 0.030485800783089448,
        "energy_eV": -300.46858996067954,
        "reduced_polarization": [
          0.4999513452124659,
          2.50118546836943e-12,
          3.130737633848343e-06
        ],
        "cartesian_polarization_e_A2": [
          0.0032345190814516162,
          2.8183904017144506e-13,
          5.013785030785853e-06
        ],
        "ranking_score": 0.5638689882069488
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 2,
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.0,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        -0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              0.010185847536349903,
              4.26838468258884e-09,
              -0.009062543580376529
            ],
            "branch_aligned_reduced_polarization": [
              0.010185847536349903,
              4.26838468258884e-09,
              -0.009062543580376503
            ],
            "target_residual": 0.49104311175883886,
            "energy_eV": -302.09815967004187,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.002346921904510414,
            "step_scale": 0.8188576640956499,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.5588282006843359,
            "cell_principal_stretches": [
              1.001859726808172,
              0.9996504093856143,
              0.9969728063310274
            ],
            "cell_volume_ratio": 0.9984777228751595,
            "cell_rmsd_from_input_A": 0.03998136356024904
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.0025985162248205376,
              1.2053802806774436e-09,
              -0.3994715481435339
            ],
            "branch_aligned_reduced_polarization": [
              -0.0025985162248205376,
              1.2053802806774436e-09,
              -0.3994715481435339
            ],
            "target_residual": 0.10056203020637798,
            "energy_eV": -298.5583145230039,
            "max_atomic_step_A": 0.04019994667409575,
            "max_log_strain_component": 0.000650797952145483,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.5588282006843359,
            "cell_principal_stretches": [
              1.0023562671795432,
              0.9995006912970598,
              0.9961403928850991
            ],
            "cell_volume_ratio": 0.9979890122676905,
            "cell_rmsd_from_input_A": 0.05098981872931166
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.00026066126472398685,
              1.0280876582744304e-10,
              -0.49863265103467613
            ],
            "branch_aligned_reduced_polarization": [
              0.00026066126472398685,
              1.0280876582744304e-10,
              -0.49863265103467613
            ],
            "target_residual": 0.0013919725169340696,
            "energy_eV": -296.7981698285182,
            "max_atomic_step_A": 0.0005322723796445859,
            "max_log_strain_component": 9.484727277578426e-06,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.5588282006843359,
            "cell_principal_stretches": [
              1.0023642893779767,
              0.9995006015689871,
              0.9961280533761528
            ],
            "cell_volume_ratio": 0.9979845474141993,
            "cell_rmsd_from_input_A": 0.051151604867673554
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              6.697694289456355e-06,
              1.4680084671774728e-12,
              -0.4999961138024023
            ],
            "branch_aligned_reduced_polarization": [
              6.697694289456355e-06,
              1.4680084671774728e-12,
              -0.4999961138024023
            ],
            "target_residual": 7.74349020555833e-06,
            "energy_eV": -296.7735251322383
          }
        ],
        "iterations": 3
      },
      "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": [
          0.0,
          0.0,
          -0.5
        ],
        "formal_class": [
          0.0,
          0.0,
          0.5
        ],
        "target_residual": 7.74349020555833e-06,
        "parent_symmetrization_rmsd_A": 0.12168148239603996,
        "parent_cell_rmsd_A": 0.051151604867673554,
        "energy_eV": -296.7735251322383,
        "reduced_polarization": [
          6.697694289456355e-06,
          1.4680084671774728e-12,
          -0.4999961138024023
        ],
        "cartesian_polarization_e_A2": [
          0.0004721390081730459,
          2.897470316076639e-12,
          -0.0054776568943134644
        ],
        "ranking_score": 0.6344848705933694
      },
      "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": [
              0.010185847536349903,
              4.26838468258884e-09,
              -0.009062543580376529
            ],
            "branch_aligned_reduced_polarization": [
              0.010185847536349903,
              4.268384701244798e-09,
              -0.009062543580376529
            ],
            "target_residual": 0.500185842380405,
            "energy_eV": -302.09815967004187,
            "max_atomic_step_A": 0.05710381766852742,
            "max_log_strain_component": 0.002372720083632311,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.5588282006843359,
            "cell_principal_stretches": [
              1.0027265231203752,
              1.0000568952038074,
              0.9973421520769855
            ],
            "cell_volume_ratio": 1.000118327212343,
            "cell_rmsd_from_input_A": 0.01955598420330303
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.0004278822430343902,
              0.4955210728844183,
              -0.0003459125021191891
            ],
            "branch_aligned_reduced_polarization": [
              -0.0004278822430343902,
              0.4955210728844183,
              -0.0003459125021191891
            ],
            "target_residual": 0.004512596456555727,
            "energy_eV": -301.18345820679605,
            "max_atomic_step_A": 0.0006246288202621311,
            "max_log_strain_component": 2.2195492150814588e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.5588282006843359,
            "cell_principal_stretches": [
              1.0027508985851925,
              1.0000564902864744,
              0.9973161505620186
            ],
            "cell_volume_ratio": 1.0001161598066213,
            "cell_rmsd_from_input_A": 0.019739471426074563
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -1.0761029665062272e-05,
              0.4999970151394802,
              -5.301108261768556e-06
            ],
            "branch_aligned_reduced_polarization": [
              -1.0761029665062272e-05,
              0.4999970151394802,
              -5.301108261768556e-06
            ],
            "target_residual": 1.2361670622453747e-05,
            "energy_eV": -301.1672313887279
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_03",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.5,
          0.0
        ],
        "formal_class": [
          0.0,
          0.5,
          0.0
        ],
        "target_residual": 1.2361670622453747e-05,
        "parent_symmetrization_rmsd_A": 0.04331764395057387,
        "parent_cell_rmsd_A": 0.019739471426074563,
        "energy_eV": -301.1672313887279,
        "reduced_polarization": [
          -1.0761029665062272e-05,
          0.4999970151394802,
          -5.301108261768556e-06
        ],
        "cartesian_polarization_e_A2": [
          -6.228402797740156e-06,
          0.0025735810840375657,
          -3.3600888708896695e-06
        ],
        "ranking_score": 0.5482772351483374
      },
      "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": [
              0.010185847536349903,
              4.26838468258884e-09,
              -0.009062543580376529
            ],
            "branch_aligned_reduced_polarization": [
              0.010185847536349879,
              4.26838468258884e-09,
              -0.009062543580376503
            ],
            "target_residual": 0.6934965681742439,
            "energy_eV": -302.09815967004187,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.0025733823523273096,
            "step_scale": 0.6232842846706682,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.5588282006843359,
            "cell_principal_stretches": [
              1.0004239291552288,
              0.9984700789177534,
              0.9974282244856165
            ],
            "cell_volume_ratio": 0.9963244300114011,
            "cell_rmsd_from_input_A": 0.030212619686359212
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.30691583497387864,
              2.0242790188501484e-09,
              -0.30597959256813745
            ],
            "branch_aligned_reduced_polarization": [
              0.30691583497387864,
              2.0242790188501484e-09,
              -0.30597959256813745
            ],
            "target_residual": 0.2737250687895802,
            "energy_eV": -298.8960720966894,
            "max_atomic_step_A": 0.09891586658250599,
            "max_log_strain_component": 0.0018138031634187604,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.5588282006843359,
            "cell_principal_stretches": [
              1.0007235268538222,
              0.997392403673025,
              0.9956195664197519
            ],
            "cell_volume_ratio": 0.993741871586235,
            "cell_rmsd_from_input_A": 0.05144985382018164
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.4907251620823606,
              1.6714638597414617e-10,
              -0.4939056833492743
            ],
            "branch_aligned_reduced_polarization": [
              0.4907251620823606,
              1.6714638597414617e-10,
              -0.4939056833492743
            ],
            "target_residual": 0.0110978968204698,
            "energy_eV": -294.1252202265148,
            "max_atomic_step_A": 0.003817707171191757,
            "max_log_strain_component": 8.790073599616749e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.5588282006843359,
            "cell_principal_stretches": [
              1.0007232710618323,
              0.997356168605794,
              0.9955311416716855
            ],
            "cell_volume_ratio": 0.9936172603899897,
            "cell_rmsd_from_input_A": 0.05230085790086272
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.49987647728742435,
              8.616200001041209e-12,
              -0.4999889341358955
            ],
            "branch_aligned_reduced_polarization": [
              0.49987647728742435,
              8.616200001041209e-12,
              -0.4999889341358955
            ],
            "target_residual": 0.00012401739341893225,
            "energy_eV": -293.9349321403944
          }
        ],
        "iterations": 3
      },
      "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": 0.00012401739341893225,
        "parent_symmetrization_rmsd_A": 0.15727462980107967,
        "parent_cell_rmsd_A": 0.05230085790086272,
        "energy_eV": -293.9349321403944,
        "reduced_polarization": [
          0.49987647728742435,
          8.616200001041209e-12,
          -0.4999889341358955
        ],
        "cartesian_polarization_e_A2": [
          0.003700589259827941,
          3.2325065864190054e-12,
          -0.0055026103070020625
        ],
        "ranking_score": 0.6705978790631332
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 5,
      "formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.5,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.5,
        0.5,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              0.010185847536349903,
              4.26838468258884e-09,
              -0.009062543580376529
            ],
            "branch_aligned_reduced_polarization": [
              0.010185847536349879,
              4.268384701244798e-09,
              -0.009062543580376529
            ],
            "target_residual": 0.7000000209867464,
            "energy_eV": -302.09815967004187,
            "max_atomic_step_A": 0.10371007687202034,
            "max_log_strain_component": 0.002782610948960878,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.5588282006843359,
            "cell_principal_stretches": [
              1.0022898549186459,
              0.9984558418799071,
              0.9953398042623909
            ],
            "cell_volume_ratio": 0.9960785065478123,
            "cell_rmsd_from_input_A": 0.03547625451699027
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.4823112236358454,
              0.4847385834537832,
              -0.00375956746455371
            ],
            "branch_aligned_reduced_polarization": [
              0.4823112236358454,
              0.4847385834537832,
              -0.00375956746455371
            ],
            "target_residual": 0.023663008933327696,
            "energy_eV": -299.5628657081087,
            "max_atomic_step_A": 0.004631265340228842,
            "max_log_strain_component": 0.00011002544163788725,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.5588282006843359,
            "cell_principal_stretches": [
              1.0023923186033918,
              0.9983875468714696,
              0.9951521585490876
            ],
            "cell_volume_ratio": 0.9959244045587132,
            "cell_rmsd_from_input_A": 0.037056643825856744
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.49985340139585727,
              0.49983375837581046,
              -2.5029359775310987e-05
            ],
            "branch_aligned_reduced_polarization": [
              0.49985340139585727,
              0.49983375837581046,
              -2.5029359775310987e-05
            ],
            "target_residual": 0.00022305581633424786,
            "energy_eV": -299.3877734318735
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_05",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.5,
          0.5,
          0.0
        ],
        "formal_class": [
          0.5,
          0.5,
          0.0
        ],
        "target_residual": 0.00022305581633424786,
        "parent_symmetrization_rmsd_A": 0.07217259981503939,
        "parent_cell_rmsd_A": 0.037056643825856744,
        "energy_eV": -299.3877734318735,
        "reduced_polarization": [
          0.49985340139585727,
          0.49983375837581046,
          -2.5029359775310987e-05
        ],
        "cartesian_polarization_e_A2": [
          0.0032276330378410464,
          0.00257128915709633,
          1.4027200112394242e-06
        ],
        "ranking_score": 0.581882872404172
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 6,
      "formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.5,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        -0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              0.010185847536349903,
              4.26838468258884e-09,
              -0.009062543580376529
            ],
            "branch_aligned_reduced_polarization": [
              0.010185847536349903,
              4.268384701244798e-09,
              -0.009062543580376503
            ],
            "target_residual": 0.7008019216136745,
            "energy_eV": -302.09815967004187,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.0022349679329263772,
            "step_scale": 0.779796145971325,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.5588282006843359,
            "cell_principal_stretches": [
              1.0027353404799555,
              0.9993549043597313,
              0.9964691803888477
            ],
            "cell_volume_ratio": 0.9985502866251736,
            "cell_rmsd_from_input_A": 0.0409893744262804
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.0002645257187658081,
              0.3767511021330425,
              -0.37953208312682446
            ],
            "branch_aligned_reduced_polarization": [
              -0.0002645257187658081,
              0.3767511021330425,
              -0.37953208312682446
            ],
            "target_residual": 0.17234523432644702,
            "energy_eV": -298.32843434749753,
            "max_atomic_step_A": 0.051117760732809714,
            "max_log_strain_component": 0.0008050126863330281,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.5588282006843359,
            "cell_principal_stretches": [
              1.00374499637175,
              0.9991043068694547,
              0.9951778164525301
            ],
            "cell_volume_ratio": 0.9980100416383754,
            "cell_rmsd_from_input_A": 0.055789287207151074
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.0006197013979191621,
              0.49734502093881666,
              -0.49750152940532044
            ],
            "branch_aligned_reduced_polarization": [
              0.0006197013979191621,
              0.49734502093881666,
              -0.49750152940532044
            ],
            "target_residual": 0.003698012838050099,
            "energy_eV": -295.8437147808103,
            "max_atomic_step_A": 0.001051770776115331,
            "max_log_strain_component": 1.862535894605826e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.5588282006843359,
            "cell_principal_stretches": [
              1.00377106284627,
              0.9991024371317391,
              0.9951476144754732
            ],
            "cell_volume_ratio": 0.9980038027819899,
            "cell_rmsd_from_input_A": 0.05613669074607094
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              7.429340687484618e-06,
              0.5000147540381942,
              -0.4999943032574936
            ],
            "branch_aligned_reduced_polarization": [
              7.429340687484618e-06,
              0.5000147540381942,
              -0.4999943032574936
            ],
            "target_residual": 1.7473683677748454e-05,
            "energy_eV": -295.7898952165473
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_06",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.5,
          -0.5
        ],
        "formal_class": [
          0.0,
          0.5,
          0.5
        ],
        "target_residual": 1.7473683677748454e-05,
        "parent_symmetrization_rmsd_A": 0.130946883599374,
        "parent_cell_rmsd_A": 0.05613669074607094,
        "energy_eV": -295.7898952165473,
        "reduced_polarization": [
          7.429340687484618e-06,
          0.5000147540381942,
          -0.4999943032574936
        ],
        "cartesian_polarization_e_A2": [
          0.0004657353025650199,
          0.0025917441765267056,
          -0.00548081532646699
        ],
        "ranking_score": 0.6450160036532473
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 7,
      "formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.5,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.5,
        0.5,
        -0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              0.010185847536349903,
              4.26838468258884e-09,
              -0.009062543580376529
            ],
            "branch_aligned_reduced_polarization": [
              0.010185847536349879,
              4.268384701244798e-09,
              -0.009062543580376503
            ],
            "target_residual": 0.8549488205741141,
            "energy_eV": -302.09815967004187,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.0024761885023769853,
            "step_scale": 0.5997435175910034,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.5588282006843359,
            "cell_principal_stretches": [
              1.0011886000717654,
              0.9983725472532531,
              0.996902428218531
            ],
            "cell_volume_ratio": 0.9964630065226736,
            "cell_rmsd_from_input_A": 0.03132883188730272
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.29554645750404257,
              0.29424609927626355,
              -0.2947120060083723
            ],
            "branch_aligned_reduced_polarization": [
              0.29554645750404257,
              0.29424609927626355,
              -0.2947120060083723
            ],
            "target_residual": 0.3553576778110838,
            "energy_eV": -298.8077560440459,
            "max_atomic_step_A": 0.1094866192578386,
            "max_log_strain_component": 0.0019218855324904549,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.5588282006843359,
            "cell_principal_stretches": [
              1.002106490209252,
              0.9971080961256981,
              0.9945133774050499
            ],
            "cell_volume_ratio": 0.9937262146643911,
            "cell_rmsd_from_input_A": 0.055606915440193194
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.4891496500608999,
              0.4912754151376994,
              -0.4919857647988436
            ],
            "branch_aligned_reduced_polarization": [
              0.4891496500608999,
              0.4912754151376994,
              -0.4919857647988436
            ],
            "target_residual": 0.016064757722414273,
            "energy_eV": -293.1614168709132,
            "max_atomic_step_A": 0.00510175699725588,
            "max_log_strain_component": 0.00010809798669593891,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.5588282006843359,
            "cell_principal_stretches": [
              1.002145431197533,
              0.9970444197455658,
              0.9943847235879483
            ],
            "cell_volume_ratio": 0.9935728183542865,
            "cell_rmsd_from_input_A": 0.05681503271364465
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.4998184977336624,
              0.4999642223058515,
              -0.49998883062317523
            ],
            "branch_aligned_reduced_polarization": [
              0.4998184977336624,
              0.4999642223058515,
              -0.49998883062317523
            ],
            "target_residual": 0.0001853317864342959,
            "energy_eV": -292.89495606681083
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_07",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.5,
          0.5,
          -0.5
        ],
        "formal_class": [
          0.5,
          0.5,
          0.5
        ],
        "target_residual": 0.0001853317864342959,
        "parent_symmetrization_rmsd_A": 0.1648431480887118,
        "parent_cell_rmsd_A": 0.05681503271364465,
        "energy_eV": -292.89495606681083,
        "reduced_polarization": [
          0.4998184977336624,
          0.4999642223058515,
          -0.49998883062317523
        ],
        "cartesian_polarization_e_A2": [
          0.0036936523605621274,
          0.002590356557904754,
          -0.005506286241947452
        ],
        "ranking_score": 0.6794175698399916
      },
      "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
        ],
        "endpoint_rmsd_A": 0.06637752295002297,
        "minimum_distance_A_by_image": [
          2.1439921860459195,
          2.144043834830451,
          2.144095509202167,
          2.1441472091592133,
          2.144198934699741,
          2.1442506858218953,
          2.1443024625238314,
          2.1443542648036926,
          2.1444060926596222
        ],
        "minimum_distance_A": 2.1439921860459195,
        "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": [
          1655.771724841895,
          1655.771724841895,
          1655.771724841895,
          1655.771724841895,
          1655.771724841895,
          1655.771724841895,
          1655.771724841895,
          1655.771724841895,
          1655.771724841895
        ],
        "cell_deformation_log_strain_norm": 0.0
      },
      "parent_reduced_polarization": [
        2.3161945024513098e-15,
        2.0384481851857225e-15,
        -1.2130914123788001e-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": [
          -302.0981596700418,
          -302.09641241738893,
          -302.0945135995662,
          -302.0925720415782,
          -302.0907280855179,
          -302.08911443934454,
          -302.0878428421256,
          -302.0870301397726,
          -302.08675111155645
        ],
        "cartesian_polarizations_e_A2": [
          [
            7.422609707977867e-05,
            2.1972926436944935e-11,
            -9.936954180927896e-05
          ],
          [
            6.34507988044497e-05,
            1.920145704217105e-11,
            -8.853359217336538e-05
          ],
          [
            5.32523393513672e-05,
            1.6439886522814465e-11,
            -7.715259774809772e-05
          ],
          [
            4.355795325965622e-05,
            1.3686472171768356e-11,
            -6.526460640936129e-05
          ],
          [
            3.4294872866845196e-05,
            1.0940028389324199e-11,
            -5.290462467043397e-05
          ],
          [
            2.5389581565253942e-05,
            8.199463959417161e-12,
            -4.0115542992833386e-05
          ],
          [
            1.6764483464307326e-05,
            5.46349498455227e-12,
            -2.6962652867730347e-05
          ],
          [
            8.332794514046348e-06,
            2.730894644990842e-12,
            -1.3549133599503437e-05
          ],
          [
            1.6092407057831615e-17,
            1.04935904356277e-17,
            -1.3301380208738946e-17
          ]
        ],
        "raw_reduced_polarization": [
          [
            0.010185847536347579,
            4.268383857115014e-09,
            -0.00906254358037637
          ],
          [
            0.008660203142340669,
            3.730007903457293e-09,
            -0.00807430046259377
          ],
          [
            0.00723095786541865,
            3.193554870724833e-09,
            -0.0070363490331208645
          ],
          [
            0.0058863533210121504,
            2.658686226728768e-09,
            -0.00595215927407766
          ],
          [
            0.004614670590321653,
            2.1251716610153964e-09,
            -0.0048249237940482526
          ],
          [
            0.003403971667847025,
            1.5927991977676083e-09,
            -0.0036585542209782726
          ],
          [
            0.002241394089281268,
            1.0613194315474235e-09,
            -0.002459005166043235
          ],
          [
            0.0011121576400530205,
            5.304940446422139e-10,
            -0.001235686624755834
          ],
          [
            2.3161945024513098e-15,
            2.0384481851857225e-15,
            -1.2130914123788001e-15
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            0.010185847536347579,
            4.268383857115014e-09,
            -0.00906254358037637
          ],
          [
            0.008660203142340669,
            3.730007903457293e-09,
            -0.00807430046259377
          ],
          [
            0.00723095786541865,
            3.193554870724833e-09,
            -0.0070363490331208645
          ],
          [
            0.0058863533210121504,
            2.658686226728768e-09,
            -0.00595215927407766
          ],
          [
            0.004614670590321653,
            2.1251716610153964e-09,
            -0.0048249237940482526
          ],
          [
            0.003403971667847025,
            1.5927991977676083e-09,
            -0.0036585542209782726
          ],
          [
            0.002241394089281268,
            1.0613194315474235e-09,
            -0.002459005166043235
          ],
          [
            0.0011121576400530205,
            5.304940446422139e-10,
            -0.001235686624755834
          ],
          [
            2.3162895212980317e-15,
            2.0384481851711617e-15,
            -1.2130053905767824e-15
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            0.010185847536347548,
            4.26838386857753e-09,
            -0.009062543580376392
          ],
          [
            0.008660203142340617,
            3.730007858138151e-09,
            -0.008074300462593775
          ],
          [
            0.007230957865418608,
            3.193554864999726e-09,
            -0.007036349033120892
          ],
          [
            0.005886353321012172,
            2.658686271139743e-09,
            -0.005952159274077662
          ],
          [
            0.004614670590321612,
            2.125171705280593e-09,
            -0.0048249237940482526
          ],
          [
            0.0034039716678470056,
            1.5927992258468748e-09,
            -0.0036585542209782718
          ],
          [
            0.0022413940892812567,
            1.0613194767472578e-09,
            -0.002459005166043249
          ],
          [
            0.001112157640053013,
            5.304940930983548e-10,
            -0.0012356866247558163
          ],
          [
            2.3314683517128287e-15,
            1.9984014443252818e-15,
            -1.2212453270876722e-15
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -302.08675111155634,
          -302.0870301397724,
          -302.0878428421255,
          -302.0891144393446,
          -302.09072808551787,
          -302.0925720415781,
          -302.0945135995661,
          -302.09641241738893,
          -302.09815967004187
        ],
        "cartesian_polarizations_e_A2": [
          [
            1.555599348923723e-17,
            1.610916998185019e-17,
            -1.1013241080203512e-17
          ],
          [
            -8.332794514001708e-06,
            -2.7309069070697616e-12,
            1.3549133599569743e-05
          ],
          [
            -1.676448346429291e-05,
            -5.46354332882514e-12,
            2.6962652867742876e-05
          ],
          [
            -2.5389581565240867e-05,
            -8.199462107114056e-12,
            4.0115542992858994e-05
          ],
          [
            -3.429487286678413e-05,
            -1.0940021080689327e-11,
            5.2904624670491495e-05
          ],
          [
            -4.3557953259653136e-05,
            -1.368649434073537e-11,
            6.526460640937981e-05
          ],
          [
            -5.3252339351346236e-05,
            -1.64398938398308e-11,
            7.715259774811335e-05
          ],
          [
            -6.345079880441112e-05,
            -1.92014745929525e-11,
            8.853359217339065e-05
          ],
          [
            -7.422609707973636e-05,
            -2.197292586700552e-11,
            9.936954180932567e-05
          ]
        ],
        "raw_reduced_polarization": [
          [
            2.263132909307004e-15,
            3.129311031890542e-15,
            -1.0044121713079668e-15
          ],
          [
            -0.0011121576400452446,
            -5.304964266307881e-10,
            0.0012356866247618813
          ],
          [
            -0.0022413940892788728,
            -1.0613288227368263e-09,
            0.0024590051660443773
          ],
          [
            -0.0034039716678446667,
            -1.5927988379456845e-09,
            0.003658554220980608
          ],
          [
            -0.004614670590311451,
            -2.1251702412655423e-09,
            0.004824923794053498
          ],
          [
            -0.005886353321011431,
            -2.658690533194782e-09,
            0.005952159274079351
          ],
          [
            -0.007230957865415203,
            -3.1935562921028405e-09,
            0.0070363490331222895
          ],
          [
            -0.008660203142334368,
            -3.7300113128107286e-09,
            0.008074300462596074
          ],
          [
            -0.010185847536340421,
            -4.268383746400576e-09,
            0.00906254358038063
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            2.263132909307004e-15,
            3.129311031890542e-15,
            -1.0044121713079668e-15
          ],
          [
            -0.0011121576400452446,
            -5.304964266307881e-10,
            0.0012356866247618813
          ],
          [
            -0.0022413940892788728,
            -1.0613288227368263e-09,
            0.0024590051660443773
          ],
          [
            -0.0034039716678446667,
            -1.5927988379456845e-09,
            0.003658554220980608
          ],
          [
            -0.004614670590311451,
            -2.1251702412655423e-09,
            0.004824923794053498
          ],
          [
            -0.005886353321011431,
            -2.658690533194782e-09,
            0.005952159274079351
          ],
          [
            -0.007230957865415203,
            -3.1935562921028405e-09,
            0.0070363490331222895
          ],
          [
            -0.008660203142334368,
            -3.7300113128107286e-09,
            0.008074300462596074
          ],
          [
            -0.010185847536340421,
            -4.268383746400576e-09,
            0.00906254358038063
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          -0.010185847536342947,
          -4.268379780218644e-09,
          0.009062543580373944
        ],
        "actual_opposite_endpoint_branch_residual": 8.173592932833039e-15
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            0.010185847536347579,
            4.268383857115014e-09,
            -0.00906254358037637
          ],
          [
            0.008660203142340669,
            3.730007903457293e-09,
            -0.00807430046259377
          ],
          [
            0.00723095786541865,
            3.193554870724833e-09,
            -0.0070363490331208645
          ],
          [
            0.0058863533210121504,
            2.658686226728768e-09,
            -0.00595215927407766
          ],
          [
            0.004614670590321653,
            2.1251716610153964e-09,
            -0.0048249237940482526
          ],
          [
            0.003403971667847025,
            1.5927991977676083e-09,
            -0.0036585542209782726
          ],
          [
            0.002241394089281268,
            1.0613194315474235e-09,
            -0.002459005166043235
          ],
          [
            0.0011121576400530205,
            5.304940446422139e-10,
            -0.001235686624755834
          ],
          [
            2.3161945024513098e-15,
            2.0384481851857225e-15,
            -1.2130914123788001e-15
          ],
          [
            -0.0011121576400452446,
            -5.304964266307881e-10,
            0.0012356866247618813
          ],
          [
            -0.0022413940892788728,
            -1.0613288227368263e-09,
            0.0024590051660443773
          ],
          [
            -0.0034039716678446667,
            -1.5927988379456845e-09,
            0.003658554220980608
          ],
          [
            -0.004614670590311451,
            -2.1251702412655423e-09,
            0.004824923794053498
          ],
          [
            -0.005886353321011431,
            -2.658690533194782e-09,
            0.005952159274079351
          ],
          [
            -0.007230957865415203,
            -3.1935562921028405e-09,
            0.0070363490331222895
          ],
          [
            -0.008660203142334368,
            -3.7300113128107286e-09,
            0.008074300462596074
          ],
          [
            -0.010185847536340421,
            -4.268383746400576e-09,
            0.00906254358038063
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            0.010185847536347579,
            4.268383857115014e-09,
            -0.00906254358037637
          ],
          [
            0.008660203142340669,
            3.730007903457293e-09,
            -0.00807430046259377
          ],
          [
            0.00723095786541865,
            3.193554870724833e-09,
            -0.0070363490331208645
          ],
          [
            0.0058863533210121504,
            2.658686226728768e-09,
            -0.00595215927407766
          ],
          [
            0.004614670590321653,
            2.1251716610153964e-09,
            -0.0048249237940482526
          ],
          [
            0.003403971667847025,
            1.5927991977676083e-09,
            -0.0036585542209782726
          ],
          [
            0.002241394089281268,
            1.0613194315474235e-09,
            -0.002459005166043235
          ],
          [
            0.0011121576400530205,
            5.304940446422139e-10,
            -0.001235686624755834
          ],
          [
            2.3162895212980317e-15,
            2.0384481851711617e-15,
            -1.2130053905767824e-15
          ],
          [
            -0.0011121576400452446,
            -5.304964266307881e-10,
            0.0012356866247618813
          ],
          [
            -0.0022413940892788728,
            -1.0613288227368263e-09,
            0.0024590051660443773
          ],
          [
            -0.0034039716678446667,
            -1.5927988379456845e-09,
            0.003658554220980608
          ],
          [
            -0.004614670590311451,
            -2.1251702412655423e-09,
            0.004824923794053498
          ],
          [
            -0.005886353321011431,
            -2.658690533194782e-09,
            0.005952159274079351
          ],
          [
            -0.007230957865415203,
            -3.1935562921028405e-09,
            0.0070363490331222895
          ],
          [
            -0.008660203142334368,
            -3.7300113128107286e-09,
            0.008074300462596074
          ],
          [
            -0.010185847536340421,
            -4.268383746400576e-09,
            0.00906254358038063
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            0.010185847536347548,
            4.26838386857753e-09,
            -0.009062543580376392
          ],
          [
            0.008660203142340617,
            3.730007858138151e-09,
            -0.008074300462593775
          ],
          [
            0.007230957865418608,
            3.193554864999726e-09,
            -0.007036349033120892
          ],
          [
            0.005886353321012172,
            2.658686271139743e-09,
            -0.005952159274077662
          ],
          [
            0.004614670590321612,
            2.125171705280593e-09,
            -0.0048249237940482526
          ],
          [
            0.0034039716678470056,
            1.5927992258468748e-09,
            -0.0036585542209782718
          ],
          [
            0.0022413940892812567,
            1.0613194767472578e-09,
            -0.002459005166043249
          ],
          [
            0.001112157640053013,
            5.304940930983548e-10,
            -0.0012356866247558163
          ],
          [
            2.3314683517128287e-15,
            1.9984014443252818e-15,
            -1.2212453270876722e-15
          ],
          [
            -0.0011121576400452415,
            -5.304964245667065e-10,
            0.0012356866247619225
          ],
          [
            -0.0022413940892788697,
            -1.0613288026206646e-09,
            0.002459005166044359
          ],
          [
            -0.003403971667844674,
            -1.5927988372688162e-09,
            0.0036585542209806032
          ],
          [
            -0.004614670590311454,
            -2.125170261990661e-09,
            0.004824923794053526
          ],
          [
            -0.0058863533210114505,
            -2.6586905454983878e-09,
            0.005952159274079327
          ],
          [
            -0.007230957865415222,
            -3.193556308289658e-09,
            0.0070363490331223355
          ],
          [
            -0.008660203142334344,
            -3.730011299829528e-09,
            0.008074300462596051
          ],
          [
            -0.010185847536340442,
            -4.2683837575552275e-09,
            0.009062543580380611
          ]
        ]
      },
      "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": "C2/c",
        "spacegroup_number": 15,
        "pointgroup": "2/m",
        "has_inversion": true,
        "is_polar_point_group": false,
        "nonpolar_parent_hypothesis": true,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.0
        ],
        "formal_class": [
          0.0,
          0.0,
          0.0
        ],
        "target_residual": 2.8262209310740537e-15,
        "parent_symmetrization_rmsd_A": 0.06637752295002297,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -302.0867511115564,
        "reduced_polarization": [
          -2.607511881465904e-15,
          2.865550164478332e-16,
          -1.0518045264229544e-15
        ],
        "cartesian_polarization_e_A2": [
          -1.5874489045590146e-17,
          1.4751373136345649e-18,
          -1.1532891724779325e-17
        ],
        "ranking_score": 0.06637752295002862
      }
    }
  ],
  "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": 52,
      "full_response": 20,
      "energy_polarization": 32
    },
    "model_evaluations_for_recovery_and_path_properties": {
      "total": 77,
      "full_response": 45,
      "energy_polarization": 32
    },
    "elapsed_seconds": 708.2400926239789
  }
}