{
  "schema": "ferrofinder.endpoint_parent_recovery.v4_variable_cell",
  "status": "complete",
  "input_atom_count": 30,
  "input_formula": "K4O18Si6Ti2",
  "input_spacegroup": "R3",
  "input_pointgroup": "3",
  "input_is_polar_point_group": true,
  "input_energy_eV": -214.7910567514282,
  "input_cartesian_polarization_e_A2": [
    0.0003860425237908582,
    0.00033823014592750236,
    0.00030097241932141677
  ],
  "input_reduced_polarization": [
    0.017720008230151966,
    0.017719965326165356,
    0.017719977207604584
  ],
  "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": "P-1",
      "spacegroup_number": 2,
      "pointgroup": "-1",
      "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": 2.6116649866500314e-15,
      "parent_symmetrization_rmsd_A": 0.9799626406908042,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -128.0921508945488,
      "reduced_polarization": [
        1.4441530309312746e-15,
        1.2804845438516505e-15,
        -1.759424723795466e-15
      ],
      "cartesian_polarization_e_A2": [
        2.3826185722710792e-17,
        1.840161247391239e-17,
        -2.988369056746777e-17
      ],
      "ranking_score": 0.9799626406908094
    },
    {
      "candidate_id": "inversion_parent_endpoint_01",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "P-1",
      "spacegroup_number": 2,
      "pointgroup": "-1",
      "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": 5.429308554533304e-15,
      "parent_symmetrization_rmsd_A": 1.01160974071781,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -142.34763060418828,
      "reduced_polarization": [
        -9.995215238695785e-16,
        1.6936202285808107e-15,
        5.0606322356986025e-15
      ],
      "cartesian_polarization_e_A2": [
        -1.9259758993586296e-18,
        3.9016544025716757e-17,
        8.59544405407311e-17
      ],
      "ranking_score": 1.0116097407178208
    },
    {
      "candidate_id": "inversion_parent_endpoint_02",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "P-1",
      "spacegroup_number": 2,
      "pointgroup": "-1",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 1.4162231811577244e-14,
      "parent_symmetrization_rmsd_A": 1.0116097424542565,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": 56.34100242813933,
      "reduced_polarization": [
        3.1402379087993635e-15,
        5.849072075409986e-15,
        1.2509838992475042e-14
      ],
      "cartesian_polarization_e_A2": [
        9.580176892938733e-17,
        1.2487779218422083e-16,
        2.124786314776295e-16
      ],
      "ranking_score": 1.011609742454285
    },
    {
      "candidate_id": "bec_projection_00",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "R3",
      "spacegroup_number": 146,
      "pointgroup": "3",
      "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": 2.7506929869515738e-05,
      "parent_symmetrization_rmsd_A": 0.0029988485641980703,
      "parent_cell_rmsd_A": 0.003475629105702774,
      "energy_eV": -214.78918858629663,
      "reduced_polarization": [
        -1.5262150331427476e-05,
        -1.6042232568185372e-05,
        -1.6320071456204404e-05
      ],
      "cartesian_polarization_e_A2": [
        -3.3650868055735357e-07,
        -3.066142546203942e-07,
        -2.7706123909195894e-07
      ],
      "ranking_score": 0.5039227697003628
    },
    {
      "candidate_id": "inversion_parent_bec_00_00",
      "source": "same_species_inversion_center_projection_after_BEC",
      "spacegroup": "P-1",
      "spacegroup_number": 2,
      "pointgroup": "-1",
      "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": 4.167455593743442e-15,
      "parent_symmetrization_rmsd_A": 0.9799627240917537,
      "parent_cell_rmsd_A": 0.003475629105702774,
      "energy_eV": -128.17059719145436,
      "reduced_polarization": [
        -1.603383802261508e-15,
        2.5882335656321304e-15,
        2.8456797989591384e-15
      ],
      "cartesian_polarization_e_A2": [
        -1.5361420065742277e-17,
        4.990908293857065e-17,
        4.832867394798493e-17
      ],
      "ranking_score": 0.9808316313681877
    },
    {
      "candidate_id": "inversion_parent_bec_00_01",
      "source": "same_species_inversion_center_projection_after_BEC",
      "spacegroup": "P-1",
      "spacegroup_number": 2,
      "pointgroup": "-1",
      "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": 2.207135249549108e-14,
      "parent_symmetrization_rmsd_A": 1.0116098146480066,
      "parent_cell_rmsd_A": 0.003475629105702774,
      "energy_eV": 56.5465696406206,
      "reduced_polarization": [
        -2.1285376982098507e-15,
        8.48532652186149e-15,
        -2.0263592032631178e-14
      ],
      "cartesian_polarization_e_A2": [
        -6.33716823743463e-17,
        1.0493605051987343e-16,
        -3.4419521603321424e-16
      ],
      "ranking_score": 1.0124787219244764
    },
    {
      "candidate_id": "bec_projection_01",
      "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,
        0.0,
        0.0
      ],
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_residual": 1.0765799737751765e-05,
      "parent_symmetrization_rmsd_A": 0.03900651472734016,
      "parent_cell_rmsd_A": 0.03855741890443683,
      "energy_eV": -213.96925415536714,
      "reduced_polarization": [
        0.49999931759892563,
        8.51497461990387e-06,
        6.5522499944269194e-06
      ],
      "cartesian_polarization_e_A2": [
        0.008614708575069631,
        6.095646069211909e-06,
        4.005837515293107e-05
      ],
      "ranking_score": 0.5486674010529249
    },
    {
      "candidate_id": "bec_projection_02",
      "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,
        0.0,
        0.5
      ],
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_residual": 1.0439210490363095e-05,
      "parent_symmetrization_rmsd_A": 0.0390195220439896,
      "parent_cell_rmsd_A": 0.036786530851264945,
      "energy_eV": -213.97157148343965,
      "reduced_polarization": [
        8.944155727338835e-06,
        5.380697445529517e-06,
        0.5000001651937859
      ],
      "cartesian_polarization_e_A2": [
        0.0011348137800424706,
        0.0010311836733829722,
        0.008481253228005064
      ],
      "ranking_score": 0.5482370331777866
    },
    {
      "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": 1.0731619280651778e-05,
      "parent_symmetrization_rmsd_A": 0.03900005868764806,
      "parent_cell_rmsd_A": 0.03839879557546897,
      "energy_eV": -213.97078364703162,
      "reduced_polarization": [
        7.1230054681498835e-06,
        0.4999993636923628,
        8.001597220331403e-06
      ],
      "cartesian_polarization_e_A2": [
        0.001171499569522565,
        0.008539720690341104,
        1.4286834399704579e-06
      ],
      "ranking_score": 0.5486212208200766
    },
    {
      "candidate_id": "bec_projection_04",
      "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,
        0.0,
        0.5
      ],
      "formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_residual": 8.174330741214224e-05,
      "parent_symmetrization_rmsd_A": 0.06279420046460286,
      "parent_cell_rmsd_A": 0.06705121998336651,
      "energy_eV": -212.83600746932999,
      "reduced_polarization": [
        0.49998455123162805,
        7.28383344786742e-05,
        0.4999662675098334
      ],
      "cartesian_polarization_e_A2": [
        0.009809334799008378,
        0.0010722470876457233,
        0.008518339910576215
      ],
      "ranking_score": 0.5797204920752688
    },
    {
      "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": 8.512499426425885e-05,
      "parent_symmetrization_rmsd_A": 0.0626642808803889,
      "parent_cell_rmsd_A": 0.07202211666150093,
      "energy_eV": -212.80745128024546,
      "reduced_polarization": [
        0.49996049207722404,
        0.4999879544238215,
        7.443314302746139e-05
      ],
      "cartesian_polarization_e_A2": [
        0.00979172575907975,
        0.00860570309529679,
        7.964077378314538e-05
      ],
      "ranking_score": 0.5808400600342927
    },
    {
      "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": 9.827980852651904e-05,
      "parent_symmetrization_rmsd_A": 0.06278019415761352,
      "parent_cell_rmsd_A": 0.06806883085908198,
      "energy_eV": -212.82822078108188,
      "reduced_polarization": [
        8.351003801919191e-05,
        0.4999517231098246,
        0.4999811761802751
      ],
      "cartesian_polarization_e_A2": [
        0.0023508430102086035,
        0.009573385294884407,
        0.00853935754609132
      ],
      "ranking_score": 0.579993961489437
    },
    {
      "candidate_id": "bec_projection_07",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.5,
        0.5,
        0.5
      ],
      "formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "target_residual": 6.388324956425123e-06,
      "parent_symmetrization_rmsd_A": 0.08528797005357552,
      "parent_cell_rmsd_A": 0.10279666231200088,
      "energy_eV": -211.57444144675475,
      "reduced_polarization": [
        0.5000039855793469,
        0.5000031393504079,
        0.5000038820525544
      ],
      "cartesian_polarization_e_A2": [
        0.011035180497533154,
        0.009678455554956517,
        0.008618308902187502
      ],
      "ranking_score": 0.6109999122814886
    }
  ],
  "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": [
              0.017720008230151966,
              0.017719965326165356,
              0.017719977207604584
            ],
            "branch_aligned_reduced_polarization": [
              0.017720008230151966,
              0.017719965326165356,
              0.017719977207604584
            ],
            "target_residual": 0.030691911883673553,
            "energy_eV": -214.7910567514282,
            "max_atomic_step_A": 0.005099353887869349,
            "max_log_strain_component": 0.00026769620486295185,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.765045034949946,
            "cell_principal_stretches": [
              1.0002520022889725,
              1.0002188309139428,
              0.9995157301400314
            ],
            "cell_volume_ratio": 0.9999863904518032,
            "cell_rmsd_from_input_A": 0.003475629105702774
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -1.5262150331427476e-05,
              -1.6042232568185372e-05,
              -1.6320071456204404e-05
            ],
            "branch_aligned_reduced_polarization": [
              -1.5262150331427476e-05,
              -1.6042232568185372e-05,
              -1.6320071456204404e-05
            ],
            "target_residual": 2.7506929869515738e-05,
            "energy_eV": -214.78918858629663
          }
        ],
        "iterations": 1
      },
      "parent": {
        "candidate_id": "bec_projection_00",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "R3",
        "spacegroup_number": 146,
        "pointgroup": "3",
        "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": 2.7506929869515738e-05,
        "parent_symmetrization_rmsd_A": 0.0029988485641980703,
        "parent_cell_rmsd_A": 0.003475629105702774,
        "energy_eV": -214.78918858629663,
        "reduced_polarization": [
          -1.5262150331427476e-05,
          -1.6042232568185372e-05,
          -1.6320071456204404e-05
        ],
        "cartesian_polarization_e_A2": [
          -3.3650868055735357e-07,
          -3.066142546203942e-07,
          -2.7706123909195894e-07
        ],
        "ranking_score": 0.5039227697003628
      },
      "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": [
          -214.7910567514282,
          -214.79128286654247,
          -214.79137813139224,
          -214.7913423115478,
          -214.79117517042874,
          -214.79087646931214,
          -214.7904459673143,
          -214.7898834213837,
          -214.78918858629658
        ],
        "cartesian_polarizations_e_A2": [
          [
            0.0003860425237908582,
            0.00033823014592749325,
            0.0003009724193214056
          ],
          [
            0.0003377473926523586,
            0.0002959137215238643,
            0.0002633157690957312
          ],
          [
            0.0002894512903694416,
            0.0002535968166077006,
            0.00022565899391664625
          ],
          [
            0.00024115438139487235,
            0.00021127957565569304,
            0.00018800222273422258
          ],
          [
            0.00019285683017323594,
            0.0001689621431261252,
            0.00015034558448121047
          ],
          [
            0.00014455880113874297,
            0.00012664466345885922,
            0.00011268920807208661
          ],
          [
            9.626045871405683e-05,
            8.432728107553829e-05,
            7.503322240214157e-05
          ],
          [
            4.796196730891569e-05,
            4.2010140377419046e-05,
            3.7377756346940785e-05
          ],
          [
            -3.365086805240679e-07,
            -3.0661425459184584e-07,
            -2.770612390569492e-07
          ]
        ],
        "raw_reduced_polarization": [
          [
            0.01772000823015211,
            0.017719965326164898,
            0.017719977207603925
          ],
          [
            0.015504063670365352,
            0.015503930172983245,
            0.015503888301247945
          ],
          [
            0.01328782857593829,
            0.013287603998260443,
            0.01328751333834386
          ],
          [
            0.011071310464264416,
            0.011070994341481424,
            0.011070859881332561
          ],
          [
            0.008854516854154488,
            0.008854108742971883,
            0.008853935493532883
          ],
          [
            0.006637455265715715,
            0.006636954743903832,
            0.006636747739085426
          ],
          [
            0.004420133220288572,
            0.004419539886313844,
            0.004419304182899041
          ],
          [
            0.0022025582403871254,
            0.0022018717129799596,
            0.0022016123906190366
          ],
          [
            -1.526215032995608e-05,
            -1.6042232566754584e-05,
            -1.632007145414244e-05
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            0.01772000823015211,
            0.017719965326164898,
            0.017719977207603925
          ],
          [
            0.015504063670365352,
            0.015503930172983245,
            0.015503888301247945
          ],
          [
            0.01328782857593829,
            0.013287603998260443,
            0.01328751333834386
          ],
          [
            0.011071310464264416,
            0.011070994341481424,
            0.011070859881332561
          ],
          [
            0.008854516854154488,
            0.008854108742971883,
            0.008853935493532883
          ],
          [
            0.006637455265715715,
            0.006636954743903832,
            0.006636747739085426
          ],
          [
            0.004420133220288572,
            0.004419539886313844,
            0.004419304182899041
          ],
          [
            0.0022025582403871254,
            0.0022018717129799596,
            0.0022016123906190366
          ],
          [
            -1.526215032995621e-05,
            -1.604223256675445e-05,
            -1.6320071454142306e-05
          ]
        ],
        "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": [
          [
            0.017720008230152073,
            0.017719965326164933,
            0.017719977207603876
          ],
          [
            0.015504063670365387,
            0.015503930172983238,
            0.015503888301247937
          ],
          [
            0.013287828575938243,
            0.013287603998260455,
            0.013287513338343881
          ],
          [
            0.011071310464264461,
            0.0110709943414814,
            0.011070859881332606
          ],
          [
            0.008854516854154504,
            0.008854108742971878,
            0.00885393549353286
          ],
          [
            0.006637455265715686,
            0.0066369547439038,
            0.006636747739085402
          ],
          [
            0.004420133220288558,
            0.004419539886313828,
            0.004419304182899042
          ],
          [
            0.0022025582403871757,
            0.0022018717129799192,
            0.002201612390619001
          ],
          [
            -1.5262150329931057e-05,
            -1.6042232566737535e-05,
            -1.63200714541345e-05
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -214.7891885862966,
          -214.78856687716507,
          -214.78784118684385,
          -214.78701135625087,
          -214.78607722488803,
          -214.7850386308395,
          -214.78389541079213,
          -214.78264740001674,
          -214.7812944323503
        ],
        "cartesian_polarizations_e_A2": [
          [
            -3.3650868050215185e-07,
            -3.066142544958719e-07,
            -2.7706123904017436e-07
          ],
          [
            -4.691156897302491e-05,
            -4.1070905505635254e-05,
            -3.676736015891746e-05
          ],
          [
            -9.350026197997154e-05,
            -8.184755882855376e-05,
            -7.326892316288089e-05
          ],
          [
            -0.0001401024242664537,
            -0.0001226364315035728,
            -0.00010978162208353052
          ],
          [
            -0.00018671789210257924,
            -0.00016343738054787763,
            -0.00014630532851670928
          ],
          [
            -0.0002333465014666431,
            -0.00020425026271612184,
            -0.0001828399138236426
          ],
          [
            -0.00027998808804920313,
            -0.0002450749345054318,
            -0.0002193852491340223
          ],
          [
            -0.0003266424872530485,
            -0.00028591125216025103,
            -0.00025594120534857303
          ],
          [
            -0.00037330953419835504,
            -0.00032675907167151267,
            -0.0002925076531409691
          ]
        ],
        "raw_reduced_polarization": [
          [
            -1.5262150329536604e-05,
            -1.604223256125675e-05,
            -1.6320071453153354e-05
          ],
          [
            -0.0021530461374208577,
            -0.0021511055390899276,
            -0.002165653029694968
          ],
          [
            -0.004291217750075524,
            -0.004286559839608994,
            -0.004315380736029623
          ],
          [
            -0.006429769400861393,
            -0.006422397570659905,
            -0.006465495545690735
          ],
          [
            -0.008568693490513313,
            -0.008558611156815657,
            -0.008615989801864527
          ],
          [
            -0.010707982408102355,
            -0.010695193010705366,
            -0.010766855835819862
          ],
          [
            -0.012847628531216064,
            -0.012832135533289667,
            -0.012918085967093864
          ],
          [
            -0.014987624225905119,
            -0.014969431114130018,
            -0.015069672503646818
          ],
          [
            -0.017127961846978953,
            -0.017107072131331075,
            -0.01722160774197906
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -1.5262150329536604e-05,
            -1.604223256125675e-05,
            -1.6320071453153354e-05
          ],
          [
            -0.0021530461374208577,
            -0.0021511055390899276,
            -0.002165653029694968
          ],
          [
            -0.004291217750075524,
            -0.004286559839608994,
            -0.004315380736029623
          ],
          [
            -0.006429769400861393,
            -0.006422397570659905,
            -0.006465495545690735
          ],
          [
            -0.008568693490513313,
            -0.008558611156815657,
            -0.008615989801864527
          ],
          [
            -0.010707982408102355,
            -0.010695193010705366,
            -0.010766855835819862
          ],
          [
            -0.012847628531216064,
            -0.012832135533289667,
            -0.012918085967093864
          ],
          [
            -0.014987624225905119,
            -0.014969431114130018,
            -0.015069672503646818
          ],
          [
            -0.017127961846978953,
            -0.017107072131331075,
            -0.01722160774197906
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          -0.017750518515790684,
          -0.017752034767124593,
          -0.017752601584630028
        ],
        "actual_opposite_endpoint_branch_residual": 0.0010418771848854937
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            0.01772000823015211,
            0.017719965326164898,
            0.017719977207603925
          ],
          [
            0.015504063670365352,
            0.015503930172983245,
            0.015503888301247945
          ],
          [
            0.01328782857593829,
            0.013287603998260443,
            0.01328751333834386
          ],
          [
            0.011071310464264416,
            0.011070994341481424,
            0.011070859881332561
          ],
          [
            0.008854516854154488,
            0.008854108742971883,
            0.008853935493532883
          ],
          [
            0.006637455265715715,
            0.006636954743903832,
            0.006636747739085426
          ],
          [
            0.004420133220288572,
            0.004419539886313844,
            0.004419304182899041
          ],
          [
            0.0022025582403871254,
            0.0022018717129799596,
            0.0022016123906190366
          ],
          [
            -1.526215032995608e-05,
            -1.6042232566754584e-05,
            -1.632007145414244e-05
          ],
          [
            -0.0021530461374208577,
            -0.0021511055390899276,
            -0.002165653029694968
          ],
          [
            -0.004291217750075524,
            -0.004286559839608994,
            -0.004315380736029623
          ],
          [
            -0.006429769400861393,
            -0.006422397570659905,
            -0.006465495545690735
          ],
          [
            -0.008568693490513313,
            -0.008558611156815657,
            -0.008615989801864527
          ],
          [
            -0.010707982408102355,
            -0.010695193010705366,
            -0.010766855835819862
          ],
          [
            -0.012847628531216064,
            -0.012832135533289667,
            -0.012918085967093864
          ],
          [
            -0.014987624225905119,
            -0.014969431114130018,
            -0.015069672503646818
          ],
          [
            -0.017127961846978953,
            -0.017107072131331075,
            -0.01722160774197906
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            0.01772000823015211,
            0.017719965326164898,
            0.017719977207603925
          ],
          [
            0.015504063670365352,
            0.015503930172983245,
            0.015503888301247945
          ],
          [
            0.01328782857593829,
            0.013287603998260443,
            0.01328751333834386
          ],
          [
            0.011071310464264416,
            0.011070994341481424,
            0.011070859881332561
          ],
          [
            0.008854516854154488,
            0.008854108742971883,
            0.008853935493532883
          ],
          [
            0.006637455265715715,
            0.006636954743903832,
            0.006636747739085426
          ],
          [
            0.004420133220288572,
            0.004419539886313844,
            0.004419304182899041
          ],
          [
            0.0022025582403871254,
            0.0022018717129799596,
            0.0022016123906190366
          ],
          [
            -1.526215032995621e-05,
            -1.604223256675445e-05,
            -1.6320071454142306e-05
          ],
          [
            -0.0021530461374208577,
            -0.0021511055390899276,
            -0.002165653029694968
          ],
          [
            -0.004291217750075524,
            -0.004286559839608994,
            -0.004315380736029623
          ],
          [
            -0.006429769400861393,
            -0.006422397570659905,
            -0.006465495545690735
          ],
          [
            -0.008568693490513313,
            -0.008558611156815657,
            -0.008615989801864527
          ],
          [
            -0.010707982408102355,
            -0.010695193010705366,
            -0.010766855835819862
          ],
          [
            -0.012847628531216064,
            -0.012832135533289667,
            -0.012918085967093864
          ],
          [
            -0.014987624225905119,
            -0.014969431114130018,
            -0.015069672503646818
          ],
          [
            -0.017127961846978953,
            -0.017107072131331075,
            -0.01722160774197906
          ]
        ],
        "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": [
          [
            0.017720008230152073,
            0.017719965326164933,
            0.017719977207603876
          ],
          [
            0.015504063670365387,
            0.015503930172983238,
            0.015503888301247937
          ],
          [
            0.013287828575938243,
            0.013287603998260455,
            0.013287513338343881
          ],
          [
            0.011071310464264461,
            0.0110709943414814,
            0.011070859881332606
          ],
          [
            0.008854516854154504,
            0.008854108742971878,
            0.00885393549353286
          ],
          [
            0.006637455265715686,
            0.0066369547439038,
            0.006636747739085402
          ],
          [
            0.004420133220288558,
            0.004419539886313828,
            0.004419304182899042
          ],
          [
            0.0022025582403871757,
            0.0022018717129799192,
            0.002201612390619001
          ],
          [
            -1.5262150329931057e-05,
            -1.6042232566737535e-05,
            -1.63200714541345e-05
          ],
          [
            -0.0021530461374208443,
            -0.002151105539089926,
            -0.0021656530296949583
          ],
          [
            -0.0042912177500755155,
            -0.0042865598396090165,
            -0.004315380736029606
          ],
          [
            -0.006429769400861374,
            -0.006422397570659877,
            -0.006465495545690758
          ],
          [
            -0.008568693490513313,
            -0.008558611156815665,
            -0.00861598980186451
          ],
          [
            -0.010707982408102334,
            -0.010695193010705373,
            -0.010766855835819877
          ],
          [
            -0.012847628531216071,
            -0.012832135533289657,
            -0.012918085967093873
          ],
          [
            -0.014987624225905105,
            -0.014969431114130016,
            -0.015069672503646825
          ],
          [
            -0.017127961846978956,
            -0.017107072131331058,
            -0.01722160774197906
          ]
        ]
      },
      "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": [
              0.017720008230151966,
              0.017719965326165356,
              0.017719977207604584
            ],
            "branch_aligned_reduced_polarization": [
              0.017720008230151962,
              0.017719965326165356,
              0.017719977207604584
            ],
            "target_residual": 0.4829306215440508,
            "energy_eV": -214.7910567514282,
            "max_atomic_step_A": 0.06967127898123261,
            "max_log_strain_component": 0.004609461109589697,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.765045034949946,
            "cell_principal_stretches": [
              1.0043544203009451,
              1.001400098078791,
              0.9943860816137001
            ],
            "cell_volume_ratio": 1.0001143569864954,
            "cell_rmsd_from_input_A": 0.03821182249076871
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.49728056425842876,
              8.757709150835536e-05,
              -0.003391389658663661
            ],
            "branch_aligned_reduced_polarization": [
              0.49728056425842876,
              8.757709150835536e-05,
              -0.003391389658663661
            ],
            "target_residual": 0.004347933338539473,
            "energy_eV": -213.97961394836634,
            "max_atomic_step_A": 0.0007026361294304362,
            "max_log_strain_component": 3.9724771125813114e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.765045034949946,
            "cell_principal_stretches": [
              1.0044096990459734,
              1.0013786927506687,
              0.9943542417972395
            ],
            "cell_volume_ratio": 1.000115999029457,
            "cell_rmsd_from_input_A": 0.03855741890443683
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.49999931759892563,
              8.51497461990387e-06,
              6.5522499944269194e-06
            ],
            "branch_aligned_reduced_polarization": [
              0.49999931759892563,
              8.51497461990387e-06,
              6.5522499944269194e-06
            ],
            "target_residual": 1.0765799737751765e-05,
            "energy_eV": -213.96925415536714
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_01",
        "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,
          0.0,
          0.0
        ],
        "formal_class": [
          0.5,
          0.0,
          0.0
        ],
        "target_residual": 1.0765799737751765e-05,
        "parent_symmetrization_rmsd_A": 0.03900651472734016,
        "parent_cell_rmsd_A": 0.03855741890443683,
        "energy_eV": -213.96925415536714,
        "reduced_polarization": [
          0.49999931759892563,
          8.51497461990387e-06,
          6.5522499944269194e-06
        ],
        "cartesian_polarization_e_A2": [
          0.008614708575069631,
          6.095646069211909e-06,
          4.005837515293107e-05
        ],
        "ranking_score": 0.5486674010529249
      },
      "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": [
              0.017720008230151966,
              0.017719965326165356,
              0.017719977207604584
            ],
            "branch_aligned_reduced_polarization": [
              0.017720008230151966,
              0.017719965326165356,
              0.017719977207604598
            ],
            "target_residual": 0.48293065366310156,
            "energy_eV": -214.7910567514282,
            "max_atomic_step_A": 0.06970805213931366,
            "max_log_strain_component": 0.004243015354325082,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.765045034949946,
            "cell_principal_stretches": [
              1.0039498162115328,
              1.0017453066111974,
              0.9944442043876187
            ],
            "cell_volume_ratio": 1.0001145416126482,
            "cell_rmsd_from_input_A": 0.03643276458037144
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.00024247235207889054,
              -0.0034375936664374617,
              0.49720901912014787
            ],
            "branch_aligned_reduced_polarization": [
              0.00024247235207889054,
              -0.0034375936664374617,
              0.49720901912014787
            ],
            "target_residual": 0.004434570703997605,
            "energy_eV": -213.98213030498715,
            "max_atomic_step_A": 0.0007104419857967994,
            "max_log_strain_component": 4.5100878182085304e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.765045034949946,
            "cell_principal_stretches": [
              1.0040049113053693,
              1.001729634438127,
              0.9944068138768863
            ],
            "cell_volume_ratio": 1.0001161735270414,
            "cell_rmsd_from_input_A": 0.036786530851264945
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              8.944155727338835e-06,
              5.380697445529517e-06,
              0.5000001651937859
            ],
            "branch_aligned_reduced_polarization": [
              8.944155727338835e-06,
              5.380697445529517e-06,
              0.5000001651937859
            ],
            "target_residual": 1.0439210490363095e-05,
            "energy_eV": -213.97157148343965
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_02",
        "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,
          0.0,
          0.5
        ],
        "formal_class": [
          0.0,
          0.0,
          0.5
        ],
        "target_residual": 1.0439210490363095e-05,
        "parent_symmetrization_rmsd_A": 0.0390195220439896,
        "parent_cell_rmsd_A": 0.036786530851264945,
        "energy_eV": -213.97157148343965,
        "reduced_polarization": [
          8.944155727338835e-06,
          5.380697445529517e-06,
          0.5000001651937859
        ],
        "cartesian_polarization_e_A2": [
          0.0011348137800424706,
          0.0010311836733829722,
          0.008481253228005064
        ],
        "ranking_score": 0.5482370331777866
      },
      "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": [
              0.017720008230151966,
              0.017719965326165356,
              0.017719977207604584
            ],
            "branch_aligned_reduced_polarization": [
              0.017720008230151966,
              0.017719965326165377,
              0.017719977207604584
            ],
            "target_residual": 0.48293066596449413,
            "energy_eV": -214.7910567514282,
            "max_atomic_step_A": 0.06968424416055401,
            "max_log_strain_component": 0.004389985950760246,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.765045034949946,
            "cell_principal_stretches": [
              1.0043276403010182,
              1.0013854965611375,
              0.994427051315667
            ],
            "cell_volume_ratio": 1.000114311675004,
            "cell_rmsd_from_input_A": 0.03800134043937697
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.0032060712230552223,
              0.49718566299760397,
              -3.881534786819938e-05
            ],
            "branch_aligned_reduced_polarization": [
              -0.0032060712230552223,
              0.49718566299760397,
              -3.881534786819938e-05
            ],
            "target_residual": 0.004266250353833961,
            "energy_eV": -213.98166487820674,
            "max_atomic_step_A": 0.000692860149936714,
            "max_log_strain_component": 4.5046537254213836e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.765045034949946,
            "cell_principal_stretches": [
              1.004388045927124,
              1.0013684158967826,
              0.9943858459532451
            ],
            "cell_volume_ratio": 1.0001159610743575,
            "cell_rmsd_from_input_A": 0.03839879557546897
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              7.1230054681498835e-06,
              0.4999993636923628,
              8.001597220331403e-06
            ],
            "branch_aligned_reduced_polarization": [
              7.1230054681498835e-06,
              0.4999993636923628,
              8.001597220331403e-06
            ],
            "target_residual": 1.0731619280651778e-05,
            "energy_eV": -213.97078364703162
          }
        ],
        "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": 1.0731619280651778e-05,
        "parent_symmetrization_rmsd_A": 0.03900005868764806,
        "parent_cell_rmsd_A": 0.03839879557546897,
        "energy_eV": -213.97078364703162,
        "reduced_polarization": [
          7.1230054681498835e-06,
          0.4999993636923628,
          8.001597220331403e-06
        ],
        "cartesian_polarization_e_A2": [
          0.001171499569522565,
          0.008539720690341104,
          1.4286834399704579e-06
        ],
        "ranking_score": 0.5486212208200766
      },
      "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": [
              0.017720008230151966,
              0.017719965326165356,
              0.017719977207604584
            ],
            "branch_aligned_reduced_polarization": [
              0.017720008230151962,
              0.017719965326165356,
              0.017719977207604598
            ],
            "target_residual": 0.6822770756938259,
            "energy_eV": -214.7910567514282,
            "max_atomic_step_A": 0.10624593932137208,
            "max_log_strain_component": 0.005587345859836538,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.765045034949946,
            "cell_principal_stretches": [
              1.0086522265533253,
              0.9987704242836191,
              0.9928832616294615
            ],
            "cell_volume_ratio": 1.0002425245466238,
            "cell_rmsd_from_input_A": 0.06460228064276817
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.48508006175102886,
              -0.0016551626498511592,
              0.48540209883367785
            ],
            "branch_aligned_reduced_polarization": [
              0.48508006175102886,
              -0.0016551626498511592,
              0.48540209883367785
            ],
            "target_residual": 0.02093902670164695,
            "energy_eV": -212.9629443115731,
            "max_atomic_step_A": 0.003588171994167222,
            "max_log_strain_component": 0.0001997611313318836,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.765045034949946,
            "cell_principal_stretches": [
              1.0089847838209776,
              0.9987010917360255,
              0.9926341516296515
            ],
            "cell_volume_ratio": 1.0002518297452232,
            "cell_rmsd_from_input_A": 0.06705121998336651
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.49998455123162805,
              7.28383344786742e-05,
              0.4999662675098334
            ],
            "branch_aligned_reduced_polarization": [
              0.49998455123162805,
              7.28383344786742e-05,
              0.4999662675098334
            ],
            "target_residual": 8.174330741214224e-05,
            "energy_eV": -212.83600746932999
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_04",
        "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,
          0.0,
          0.5
        ],
        "formal_class": [
          0.5,
          0.0,
          0.5
        ],
        "target_residual": 8.174330741214224e-05,
        "parent_symmetrization_rmsd_A": 0.06279420046460286,
        "parent_cell_rmsd_A": 0.06705121998336651,
        "energy_eV": -212.83600746932999,
        "reduced_polarization": [
          0.49998455123162805,
          7.28383344786742e-05,
          0.4999662675098334
        ],
        "cartesian_polarization_e_A2": [
          0.009809334799008378,
          0.0010722470876457233,
          0.008518339910576215
        ],
        "ranking_score": 0.5797204920752688
      },
      "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": [
              0.017720008230151966,
              0.017719965326165356,
              0.017719977207604584
            ],
            "branch_aligned_reduced_polarization": [
              0.017720008230151962,
              0.017719965326165377,
              0.017719977207604584
            ],
            "target_residual": 0.682277084401021,
            "energy_eV": -214.7910567514282,
            "max_atomic_step_A": 0.10602201268493504,
            "max_log_strain_component": 0.006637101557004056,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.765045034949946,
            "cell_principal_stretches": [
              1.0090993622353852,
              0.9994411963185994,
              0.9917770079161494
            ],
            "cell_volume_ratio": 1.000242294579555,
            "cell_rmsd_from_input_A": 0.06942987720032062
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.48572546615513645,
              0.4848971509085962,
              -0.001853867664937634
            ],
            "branch_aligned_reduced_polarization": [
              0.48572546615513645,
              0.4848971509085962,
              -0.001853867664937634
            ],
            "target_residual": 0.020863729112624445,
            "energy_eV": -212.93563469034368,
            "max_atomic_step_A": 0.0035782744867786185,
            "max_log_strain_component": 0.00023356465422706463,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.765045034949946,
            "cell_principal_stretches": [
              1.0094457399699315,
              0.999394526086225,
              0.9914922225194427
            ],
            "cell_volume_ratio": 1.0002516070672247,
            "cell_rmsd_from_input_A": 0.07202211666150093
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.49996049207722404,
              0.4999879544238215,
              7.443314302746139e-05
            ],
            "branch_aligned_reduced_polarization": [
              0.49996049207722404,
              0.4999879544238215,
              7.443314302746139e-05
            ],
            "target_residual": 8.512499426425885e-05,
            "energy_eV": -212.80745128024546
          }
        ],
        "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": 8.512499426425885e-05,
        "parent_symmetrization_rmsd_A": 0.0626642808803889,
        "parent_cell_rmsd_A": 0.07202211666150093,
        "energy_eV": -212.80745128024546,
        "reduced_polarization": [
          0.49996049207722404,
          0.4999879544238215,
          7.443314302746139e-05
        ],
        "cartesian_polarization_e_A2": [
          0.00979172575907975,
          0.00860570309529679,
          7.964077378314538e-05
        ],
        "ranking_score": 0.5808400600342927
      },
      "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": [
              0.017720008230151966,
              0.017719965326165356,
              0.017719977207604584
            ],
            "branch_aligned_reduced_polarization": [
              0.017720008230151966,
              0.017719965326165377,
              0.017719977207604598
            ],
            "target_residual": 0.682277107135587,
            "energy_eV": -214.7910567514282,
            "max_atomic_step_A": 0.10619020732540192,
            "max_log_strain_component": 0.006351543860495232,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.765045034949946,
            "cell_principal_stretches": [
              1.008613487206757,
              0.9993206905678356,
              0.9923746092656609
            ],
            "cell_volume_ratio": 1.0002424792293254,
            "cell_rmsd_from_input_A": 0.06555396173023897
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.0012936379848460862,
              0.4851847640148703,
              0.4845669926053905
            ],
            "branch_aligned_reduced_polarization": [
              -0.0012936379848460862,
              0.4851847640148703,
              0.4845669926053905
            ],
            "target_residual": 0.02143227551551608,
            "energy_eV": -212.95846458414482,
            "max_atomic_step_A": 0.0036551592280773255,
            "max_log_strain_component": 0.00023549871038353715,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.765045034949946,
            "cell_principal_stretches": [
              1.008948929065735,
              0.9992750793249503,
              0.9920993084861716
            ],
            "cell_volume_ratio": 1.0002519055137244,
            "cell_rmsd_from_input_A": 0.06806883085908198
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              8.351003801919191e-05,
              0.4999517231098246,
              0.4999811761802751
            ],
            "branch_aligned_reduced_polarization": [
              8.351003801919191e-05,
              0.4999517231098246,
              0.4999811761802751
            ],
            "target_residual": 9.827980852651904e-05,
            "energy_eV": -212.82822078108188
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_06",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.5,
          0.5
        ],
        "formal_class": [
          0.0,
          0.5,
          0.5
        ],
        "target_residual": 9.827980852651904e-05,
        "parent_symmetrization_rmsd_A": 0.06278019415761352,
        "parent_cell_rmsd_A": 0.06806883085908198,
        "energy_eV": -212.82822078108188,
        "reduced_polarization": [
          8.351003801919191e-05,
          0.4999517231098246,
          0.4999811761802751
        ],
        "cartesian_polarization_e_A2": [
          0.0023508430102086035,
          0.009573385294884407,
          0.00853935754609132
        ],
        "ranking_score": 0.579993961489437
      },
      "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": [
              0.017720008230151966,
              0.017719965326165356,
              0.017719977207604584
            ],
            "branch_aligned_reduced_polarization": [
              0.017720008230151962,
              0.017719965326165377,
              0.017719977207604598
            ],
            "target_residual": 0.8353334919007817,
            "energy_eV": -214.7910567514282,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.006299535948219744,
            "step_scale": 0.864629684884357,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.765045034949946,
            "cell_principal_stretches": [
              1.0114640025346844,
              0.9948641844386247,
              0.9940880724435212
            ],
            "cell_volume_ratio": 1.000320318707841,
            "cell_rmsd_from_input_A": 0.08250406039654996
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.418034677478123,
              0.4175759537373105,
              0.41739660073949714
            ],
            "branch_aligned_reduced_polarization": [
              0.418034677478123,
              0.4175759537373105,
              0.41739660073949714
            ],
            "target_residual": 0.1426021005028304,
            "energy_eV": -212.61091937234445,
            "max_atomic_step_A": 0.026773285443475476,
            "max_log_strain_component": 0.0015110647072885857,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.765045034949946,
            "cell_principal_stretches": [
              1.0142295182096652,
              0.9936370308786621,
              0.9926780017579849
            ],
            "cell_volume_ratio": 1.000397072950992,
            "cell_rmsd_from_input_A": 0.10247326948894907
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.4987984556282563,
              0.49873785504971174,
              0.4987451768704938
            ],
            "branch_aligned_reduced_polarization": [
              0.4987984556282563,
              0.49873785504971174,
              0.4987451768704938
            ],
            "target_residual": 0.0021473937317480507,
            "energy_eV": -211.59193949044257,
            "max_atomic_step_A": 0.000412601352032901,
            "max_log_strain_component": 2.4621502457745468e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.765045034949946,
            "cell_principal_stretches": [
              1.0142742707180592,
              0.9936173221018886,
              0.9926551225470078
            ],
            "cell_volume_ratio": 1.0003983136901866,
            "cell_rmsd_from_input_A": 0.10279666231200088
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.5000039855793469,
              0.5000031393504079,
              0.5000038820525544
            ],
            "branch_aligned_reduced_polarization": [
              0.5000039855793469,
              0.5000031393504079,
              0.5000038820525544
            ],
            "target_residual": 6.388324956425123e-06,
            "energy_eV": -211.57444144675475
          }
        ],
        "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": 6.388324956425123e-06,
        "parent_symmetrization_rmsd_A": 0.08528797005357552,
        "parent_cell_rmsd_A": 0.10279666231200088,
        "energy_eV": -211.57444144675475,
        "reduced_polarization": [
          0.5000039855793469,
          0.5000031393504079,
          0.5000038820525544
        ],
        "cartesian_polarization_e_A2": [
          0.011035180497533154,
          0.009678455554956517,
          0.008618308902187502
        ],
        "ranking_score": 0.6109999122814886
      },
      "branch_status": "awaiting_branch_sampling"
    }
  ],
  "sampled_polarization_branches": [
    {
      "orbit_id": 0,
      "candidate_id": "bec_projection_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
        ],
        "endpoint_rmsd_A": 0.0029988485641980703,
        "minimum_distance_A_by_image": [
          1.6145978595898203,
          1.614972720317695,
          1.615347818056107,
          1.6157231700657138,
          1.6160987760822818,
          1.6164746358417321,
          1.6168507490801407,
          1.6172271155337268,
          1.6176037349388652
        ],
        "minimum_distance_A": 1.6145978595898203,
        "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": [
          446.74642313594217,
          446.7456631292942,
          446.74490312394,
          446.74414311987795,
          446.74338311710994,
          446.7426231156341,
          446.7418631154508,
          446.7411031165612,
          446.7403431189645
        ],
        "cell_deformation_log_strain_norm": 0.0005882147253503749
      },
      "parent_reduced_polarization": [
        -1.526215032995608e-05,
        -1.6042232566754584e-05,
        -1.632007145414244e-05
      ],
      "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": [
          -214.7910567514282,
          -214.79128286654247,
          -214.79137813139224,
          -214.7913423115478,
          -214.79117517042874,
          -214.79087646931214,
          -214.7904459673143,
          -214.7898834213837,
          -214.78918858629658
        ],
        "cartesian_polarizations_e_A2": [
          [
            0.0003860425237908582,
            0.00033823014592749325,
            0.0003009724193214056
          ],
          [
            0.0003377473926523586,
            0.0002959137215238643,
            0.0002633157690957312
          ],
          [
            0.0002894512903694416,
            0.0002535968166077006,
            0.00022565899391664625
          ],
          [
            0.00024115438139487235,
            0.00021127957565569304,
            0.00018800222273422258
          ],
          [
            0.00019285683017323594,
            0.0001689621431261252,
            0.00015034558448121047
          ],
          [
            0.00014455880113874297,
            0.00012664466345885922,
            0.00011268920807208661
          ],
          [
            9.626045871405683e-05,
            8.432728107553829e-05,
            7.503322240214157e-05
          ],
          [
            4.796196730891569e-05,
            4.2010140377419046e-05,
            3.7377756346940785e-05
          ],
          [
            -3.365086805240679e-07,
            -3.0661425459184584e-07,
            -2.770612390569492e-07
          ]
        ],
        "raw_reduced_polarization": [
          [
            0.01772000823015211,
            0.017719965326164898,
            0.017719977207603925
          ],
          [
            0.015504063670365352,
            0.015503930172983245,
            0.015503888301247945
          ],
          [
            0.01328782857593829,
            0.013287603998260443,
            0.01328751333834386
          ],
          [
            0.011071310464264416,
            0.011070994341481424,
            0.011070859881332561
          ],
          [
            0.008854516854154488,
            0.008854108742971883,
            0.008853935493532883
          ],
          [
            0.006637455265715715,
            0.006636954743903832,
            0.006636747739085426
          ],
          [
            0.004420133220288572,
            0.004419539886313844,
            0.004419304182899041
          ],
          [
            0.0022025582403871254,
            0.0022018717129799596,
            0.0022016123906190366
          ],
          [
            -1.526215032995608e-05,
            -1.6042232566754584e-05,
            -1.632007145414244e-05
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            0.01772000823015211,
            0.017719965326164898,
            0.017719977207603925
          ],
          [
            0.015504063670365352,
            0.015503930172983245,
            0.015503888301247945
          ],
          [
            0.01328782857593829,
            0.013287603998260443,
            0.01328751333834386
          ],
          [
            0.011071310464264416,
            0.011070994341481424,
            0.011070859881332561
          ],
          [
            0.008854516854154488,
            0.008854108742971883,
            0.008853935493532883
          ],
          [
            0.006637455265715715,
            0.006636954743903832,
            0.006636747739085426
          ],
          [
            0.004420133220288572,
            0.004419539886313844,
            0.004419304182899041
          ],
          [
            0.0022025582403871254,
            0.0022018717129799596,
            0.0022016123906190366
          ],
          [
            -1.526215032995621e-05,
            -1.604223256675445e-05,
            -1.6320071454142306e-05
          ]
        ],
        "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": [
          [
            0.017720008230152073,
            0.017719965326164933,
            0.017719977207603876
          ],
          [
            0.015504063670365387,
            0.015503930172983238,
            0.015503888301247937
          ],
          [
            0.013287828575938243,
            0.013287603998260455,
            0.013287513338343881
          ],
          [
            0.011071310464264461,
            0.0110709943414814,
            0.011070859881332606
          ],
          [
            0.008854516854154504,
            0.008854108742971878,
            0.00885393549353286
          ],
          [
            0.006637455265715686,
            0.0066369547439038,
            0.006636747739085402
          ],
          [
            0.004420133220288558,
            0.004419539886313828,
            0.004419304182899042
          ],
          [
            0.0022025582403871757,
            0.0022018717129799192,
            0.002201612390619001
          ],
          [
            -1.5262150329931057e-05,
            -1.6042232566737535e-05,
            -1.63200714541345e-05
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -214.7891885862966,
          -214.78856687716507,
          -214.78784118684385,
          -214.78701135625087,
          -214.78607722488803,
          -214.7850386308395,
          -214.78389541079213,
          -214.78264740001674,
          -214.7812944323503
        ],
        "cartesian_polarizations_e_A2": [
          [
            -3.3650868050215185e-07,
            -3.066142544958719e-07,
            -2.7706123904017436e-07
          ],
          [
            -4.691156897302491e-05,
            -4.1070905505635254e-05,
            -3.676736015891746e-05
          ],
          [
            -9.350026197997154e-05,
            -8.184755882855376e-05,
            -7.326892316288089e-05
          ],
          [
            -0.0001401024242664537,
            -0.0001226364315035728,
            -0.00010978162208353052
          ],
          [
            -0.00018671789210257924,
            -0.00016343738054787763,
            -0.00014630532851670928
          ],
          [
            -0.0002333465014666431,
            -0.00020425026271612184,
            -0.0001828399138236426
          ],
          [
            -0.00027998808804920313,
            -0.0002450749345054318,
            -0.0002193852491340223
          ],
          [
            -0.0003266424872530485,
            -0.00028591125216025103,
            -0.00025594120534857303
          ],
          [
            -0.00037330953419835504,
            -0.00032675907167151267,
            -0.0002925076531409691
          ]
        ],
        "raw_reduced_polarization": [
          [
            -1.5262150329536604e-05,
            -1.604223256125675e-05,
            -1.6320071453153354e-05
          ],
          [
            -0.0021530461374208577,
            -0.0021511055390899276,
            -0.002165653029694968
          ],
          [
            -0.004291217750075524,
            -0.004286559839608994,
            -0.004315380736029623
          ],
          [
            -0.006429769400861393,
            -0.006422397570659905,
            -0.006465495545690735
          ],
          [
            -0.008568693490513313,
            -0.008558611156815657,
            -0.008615989801864527
          ],
          [
            -0.010707982408102355,
            -0.010695193010705366,
            -0.010766855835819862
          ],
          [
            -0.012847628531216064,
            -0.012832135533289667,
            -0.012918085967093864
          ],
          [
            -0.014987624225905119,
            -0.014969431114130018,
            -0.015069672503646818
          ],
          [
            -0.017127961846978953,
            -0.017107072131331075,
            -0.01722160774197906
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -1.5262150329536604e-05,
            -1.604223256125675e-05,
            -1.6320071453153354e-05
          ],
          [
            -0.0021530461374208577,
            -0.0021511055390899276,
            -0.002165653029694968
          ],
          [
            -0.004291217750075524,
            -0.004286559839608994,
            -0.004315380736029623
          ],
          [
            -0.006429769400861393,
            -0.006422397570659905,
            -0.006465495545690735
          ],
          [
            -0.008568693490513313,
            -0.008558611156815657,
            -0.008615989801864527
          ],
          [
            -0.010707982408102355,
            -0.010695193010705366,
            -0.010766855835819862
          ],
          [
            -0.012847628531216064,
            -0.012832135533289667,
            -0.012918085967093864
          ],
          [
            -0.014987624225905119,
            -0.014969431114130018,
            -0.015069672503646818
          ],
          [
            -0.017127961846978953,
            -0.017107072131331075,
            -0.01722160774197906
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          -0.017750518515790684,
          -0.017752034767124593,
          -0.017752601584630028
        ],
        "actual_opposite_endpoint_branch_residual": 0.0010418771848854937
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            0.01772000823015211,
            0.017719965326164898,
            0.017719977207603925
          ],
          [
            0.015504063670365352,
            0.015503930172983245,
            0.015503888301247945
          ],
          [
            0.01328782857593829,
            0.013287603998260443,
            0.01328751333834386
          ],
          [
            0.011071310464264416,
            0.011070994341481424,
            0.011070859881332561
          ],
          [
            0.008854516854154488,
            0.008854108742971883,
            0.008853935493532883
          ],
          [
            0.006637455265715715,
            0.006636954743903832,
            0.006636747739085426
          ],
          [
            0.004420133220288572,
            0.004419539886313844,
            0.004419304182899041
          ],
          [
            0.0022025582403871254,
            0.0022018717129799596,
            0.0022016123906190366
          ],
          [
            -1.526215032995608e-05,
            -1.6042232566754584e-05,
            -1.632007145414244e-05
          ],
          [
            -0.0021530461374208577,
            -0.0021511055390899276,
            -0.002165653029694968
          ],
          [
            -0.004291217750075524,
            -0.004286559839608994,
            -0.004315380736029623
          ],
          [
            -0.006429769400861393,
            -0.006422397570659905,
            -0.006465495545690735
          ],
          [
            -0.008568693490513313,
            -0.008558611156815657,
            -0.008615989801864527
          ],
          [
            -0.010707982408102355,
            -0.010695193010705366,
            -0.010766855835819862
          ],
          [
            -0.012847628531216064,
            -0.012832135533289667,
            -0.012918085967093864
          ],
          [
            -0.014987624225905119,
            -0.014969431114130018,
            -0.015069672503646818
          ],
          [
            -0.017127961846978953,
            -0.017107072131331075,
            -0.01722160774197906
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            0.01772000823015211,
            0.017719965326164898,
            0.017719977207603925
          ],
          [
            0.015504063670365352,
            0.015503930172983245,
            0.015503888301247945
          ],
          [
            0.01328782857593829,
            0.013287603998260443,
            0.01328751333834386
          ],
          [
            0.011071310464264416,
            0.011070994341481424,
            0.011070859881332561
          ],
          [
            0.008854516854154488,
            0.008854108742971883,
            0.008853935493532883
          ],
          [
            0.006637455265715715,
            0.006636954743903832,
            0.006636747739085426
          ],
          [
            0.004420133220288572,
            0.004419539886313844,
            0.004419304182899041
          ],
          [
            0.0022025582403871254,
            0.0022018717129799596,
            0.0022016123906190366
          ],
          [
            -1.526215032995621e-05,
            -1.604223256675445e-05,
            -1.6320071454142306e-05
          ],
          [
            -0.0021530461374208577,
            -0.0021511055390899276,
            -0.002165653029694968
          ],
          [
            -0.004291217750075524,
            -0.004286559839608994,
            -0.004315380736029623
          ],
          [
            -0.006429769400861393,
            -0.006422397570659905,
            -0.006465495545690735
          ],
          [
            -0.008568693490513313,
            -0.008558611156815657,
            -0.008615989801864527
          ],
          [
            -0.010707982408102355,
            -0.010695193010705366,
            -0.010766855835819862
          ],
          [
            -0.012847628531216064,
            -0.012832135533289667,
            -0.012918085967093864
          ],
          [
            -0.014987624225905119,
            -0.014969431114130018,
            -0.015069672503646818
          ],
          [
            -0.017127961846978953,
            -0.017107072131331075,
            -0.01722160774197906
          ]
        ],
        "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": [
          [
            0.017720008230152073,
            0.017719965326164933,
            0.017719977207603876
          ],
          [
            0.015504063670365387,
            0.015503930172983238,
            0.015503888301247937
          ],
          [
            0.013287828575938243,
            0.013287603998260455,
            0.013287513338343881
          ],
          [
            0.011071310464264461,
            0.0110709943414814,
            0.011070859881332606
          ],
          [
            0.008854516854154504,
            0.008854108742971878,
            0.00885393549353286
          ],
          [
            0.006637455265715686,
            0.0066369547439038,
            0.006636747739085402
          ],
          [
            0.004420133220288558,
            0.004419539886313828,
            0.004419304182899042
          ],
          [
            0.0022025582403871757,
            0.0022018717129799192,
            0.002201612390619001
          ],
          [
            -1.5262150329931057e-05,
            -1.6042232566737535e-05,
            -1.63200714541345e-05
          ],
          [
            -0.0021530461374208443,
            -0.002151105539089926,
            -0.0021656530296949583
          ],
          [
            -0.0042912177500755155,
            -0.0042865598396090165,
            -0.004315380736029606
          ],
          [
            -0.006429769400861374,
            -0.006422397570659877,
            -0.006465495545690758
          ],
          [
            -0.008568693490513313,
            -0.008558611156815665,
            -0.00861598980186451
          ],
          [
            -0.010707982408102334,
            -0.010695193010705373,
            -0.010766855835819877
          ],
          [
            -0.012847628531216071,
            -0.012832135533289657,
            -0.012918085967093873
          ],
          [
            -0.014987624225905105,
            -0.014969431114130016,
            -0.015069672503646825
          ],
          [
            -0.017127961846978956,
            -0.017107072131331058,
            -0.01722160774197906
          ]
        ]
      },
      "incoming_structure_ids": [
        "incoming_00_000",
        "incoming_00_001",
        "incoming_00_002",
        "incoming_00_003",
        "incoming_00_004",
        "incoming_00_005",
        "incoming_00_006",
        "incoming_00_007",
        "incoming_00_008"
      ],
      "reflected_structure_ids": [
        "reflected_00_001",
        "reflected_00_002",
        "reflected_00_003",
        "reflected_00_004",
        "reflected_00_005",
        "reflected_00_006",
        "reflected_00_007",
        "reflected_00_008"
      ],
      "positive_extension_structure_ids": [
        "extension_plus_00_000",
        "extension_plus_00_001",
        "extension_plus_00_002",
        "extension_plus_00_003"
      ],
      "negative_extension_structure_ids": [
        "extension_minus_00_000",
        "extension_minus_00_001",
        "extension_minus_00_002",
        "extension_minus_00_003"
      ],
      "extension": {
        "enabled": true,
        "fraction_beyond_polar_endpoint": 0.35,
        "images_per_side": 4,
        "construction": "continue fractional atomic displacements and symmetric log strain beyond +P; reflect these structures about N for the -P side",
        "positive_path_coordinates": [
          1.35,
          1.2625,
          1.175,
          1.0875
        ],
        "negative_path_coordinates": [
          -1.0875,
          -1.175,
          -1.2625,
          -1.35
        ]
      },
      "branch_coordinates": [
        1.35,
        1.2625,
        1.175,
        1.0875,
        1.0,
        0.875,
        0.75,
        0.625,
        0.5,
        0.375,
        0.25,
        0.125,
        0.0,
        -0.125,
        -0.25,
        -0.375,
        -0.5,
        -0.625,
        -0.75,
        -0.875,
        -1.0,
        -1.0875,
        -1.175,
        -1.2625,
        -1.35
      ],
      "parent": {
        "candidate_id": "bec_projection_00",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "R3",
        "spacegroup_number": 146,
        "pointgroup": "3",
        "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": 2.7506929869515738e-05,
        "parent_symmetrization_rmsd_A": 0.0029988485641980703,
        "parent_cell_rmsd_A": 0.003475629105702774,
        "energy_eV": -214.78918858629663,
        "reduced_polarization": [
          -1.5262150331427476e-05,
          -1.6042232568185372e-05,
          -1.6320071456204404e-05
        ],
        "cartesian_polarization_e_A2": [
          -3.3650868055735357e-07,
          -3.066142546203942e-07,
          -2.7706123909195894e-07
        ],
        "ranking_score": 0.5039227697003628
      }
    }
  ],
  "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": 17,
      "energy_polarization": 35
    },
    "model_evaluations_for_recovery_and_path_properties": {
      "total": 77,
      "full_response": 42,
      "energy_polarization": 35
    },
    "elapsed_seconds": 384.6369999090093
  }
}