{
  "schema": "ferrofinder.endpoint_parent_recovery.v4_variable_cell",
  "status": "complete",
  "input_atom_count": 24,
  "input_formula": "Cl4F20",
  "input_spacegroup": "Cmc2_1",
  "input_pointgroup": "mm2",
  "input_is_polar_point_group": true,
  "input_energy_eV": -63.00013525762529,
  "input_cartesian_polarization_e_A2": [
    -3.480701989532519e-18,
    1.0166824775991413e-17,
    0.0033448831077741562
  ],
  "input_reduced_polarization": [
    -2.003402227076123e-16,
    4.988177198294171e-16,
    0.15615510331587876
  ],
  "input_formal_targets": [
    {
      "orbit_id": 0,
      "representative_formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ]
    },
    {
      "orbit_id": 1,
      "representative_formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.5
      ]
    },
    {
      "orbit_id": 2,
      "representative_formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.0
      ]
    },
    {
      "orbit_id": 3,
      "representative_formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        -0.5,
        0.0,
        0.0
      ]
    },
    {
      "orbit_id": 4,
      "representative_formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.5
      ]
    },
    {
      "orbit_id": 5,
      "representative_formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        -0.5,
        0.0,
        0.5
      ]
    },
    {
      "orbit_id": 6,
      "representative_formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        -0.5,
        0.5,
        0.0
      ]
    },
    {
      "orbit_id": 7,
      "representative_formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "target_reduced_polarization": [
        -0.5,
        0.5,
        0.5
      ]
    }
  ],
  "parent_candidates": [
    {
      "candidate_id": "inversion_parent_endpoint_00",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "Cmcm",
      "spacegroup_number": 63,
      "pointgroup": "mmm",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 3.2248869032134036e-15,
      "parent_symmetrization_rmsd_A": 0.26151910790254485,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -60.89044965382565,
      "reduced_polarization": [
        -6.845121922873501e-16,
        -2.6253564201548273e-16,
        3.140447998900606e-15
      ],
      "cartesian_polarization_e_A2": [
        -1.1892683942111418e-17,
        -5.350960408416533e-18,
        6.72692165629507e-17
      ],
      "ranking_score": 0.2615191079025513
    },
    {
      "candidate_id": "inversion_parent_endpoint_01",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "C2/m",
      "spacegroup_number": 12,
      "pointgroup": "2/m",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 3.4726373619911958e-15,
      "parent_symmetrization_rmsd_A": 0.8324825586692937,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -27.474525127082337,
      "reduced_polarization": [
        -1.054664386773009e-15,
        3.2788826433147967e-15,
        -4.4251767257235813e-16
      ],
      "cartesian_polarization_e_A2": [
        -1.832369146702771e-17,
        6.682967338654506e-17,
        -9.478844152052144e-18
      ],
      "ranking_score": 0.8324825586693007
    },
    {
      "candidate_id": "bec_projection_00",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cmc2_1",
      "spacegroup_number": 36,
      "pointgroup": "mm2",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 9.2901877422773e-06,
      "parent_symmetrization_rmsd_A": 0.09490428923735396,
      "parent_cell_rmsd_A": 0.026623196346894813,
      "energy_eV": -62.40991471825407,
      "reduced_polarization": [
        -1.4504433348383547e-15,
        -3.851880821238703e-15,
        9.2901877422773e-06
      ],
      "cartesian_polarization_e_A2": [
        -2.5316998016989102e-17,
        -7.915032599026287e-17,
        2.0010932944348568e-07
      ],
      "ranking_score": 0.6015786686995622
    },
    {
      "candidate_id": "inversion_parent_bec_00_00",
      "source": "same_species_inversion_center_projection_after_BEC",
      "spacegroup": "Cmcm",
      "spacegroup_number": 63,
      "pointgroup": "mmm",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 7.943717239343655e-16,
      "parent_symmetrization_rmsd_A": 0.2615977698459828,
      "parent_cell_rmsd_A": 0.026623196346894813,
      "energy_eV": -60.8431570925133,
      "reduced_polarization": [
        -6.108622039949965e-16,
        2.027253061699995e-16,
        4.65592368660732e-16
      ],
      "cartesian_polarization_e_A2": [
        -1.066152879052735e-17,
        4.1658066310664666e-18,
        1.0028793741456308e-17
      ],
      "ranking_score": 0.26825356893270813
    },
    {
      "candidate_id": "bec_projection_01",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cmc2_1",
      "spacegroup_number": 36,
      "pointgroup": "mm2",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.5
      ],
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_residual": 0.0006121559225979456,
      "parent_symmetrization_rmsd_A": 0.2752109522951726,
      "parent_cell_rmsd_A": 0.11144726042819314,
      "energy_eV": -56.13890420294168,
      "reduced_polarization": [
        -3.564784918132953e-15,
        4.326227563501211e-15,
        0.49938784407740205
      ],
      "cartesian_polarization_e_A2": [
        3.953449133113143e-16,
        -3.702324858893041e-16,
        0.01045538785626018
      ],
      "ranking_score": 0.8042970792474168
    },
    {
      "candidate_id": "bec_projection_02",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cm",
      "spacegroup_number": 8,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.0
      ],
      "formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_residual": 0.0006364288478529248,
      "parent_symmetrization_rmsd_A": 0.37616455419655465,
      "parent_cell_rmsd_A": 0.06469346238500125,
      "energy_eV": -51.083660291978184,
      "reduced_polarization": [
        5.035284718929077e-16,
        0.4995880511299936,
        -0.0004851183431698445
      ],
      "cartesian_polarization_e_A2": [
        8.825809791837175e-17,
        0.010349295062866977,
        4.149144182179182e-05
      ],
      "ranking_score": 0.8936107774885108
    },
    {
      "candidate_id": "bec_projection_03",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cc",
      "spacegroup_number": 9,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        -0.5,
        0.0,
        0.0
      ],
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_residual": 3.803426553453004e-05,
      "parent_symmetrization_rmsd_A": 0.2631635531205746,
      "parent_cell_rmsd_A": 0.07060145084774946,
      "energy_eV": -57.20230401989944,
      "reduced_polarization": [
        -0.4999625739204623,
        -4.061936290142829e-15,
        6.774505530858645e-06
      ],
      "cartesian_polarization_e_A2": [
        -0.008734209892328986,
        -1.3029954514289455e-15,
        8.701226572446694e-05
      ],
      "ranking_score": 0.780889984363581
    },
    {
      "candidate_id": "bec_projection_04",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cm",
      "spacegroup_number": 8,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.5
      ],
      "formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_residual": 1.4963829943154587e-05,
      "parent_symmetrization_rmsd_A": 0.38170393122436364,
      "parent_cell_rmsd_A": 0.09584135701572997,
      "energy_eV": -48.98771706324193,
      "reduced_polarization": [
        2.8393169272063677e-15,
        0.49998555038815934,
        0.4999961109224459
      ],
      "cartesian_polarization_e_A2": [
        6.967690350329494e-16,
        0.009952935437632062,
        0.010551199471451948
      ],
      "ranking_score": 0.9056941981381824
    },
    {
      "candidate_id": "bec_projection_05",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cc",
      "spacegroup_number": 9,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        -0.5,
        0.0,
        0.5
      ],
      "formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_residual": 0.039498620827129585,
      "parent_symmetrization_rmsd_A": 0.34983349661852015,
      "parent_cell_rmsd_A": 0.26515037461443014,
      "energy_eV": -45.599155416050735,
      "reduced_polarization": [
        -0.46235139375512396,
        9.481217796174636e-14,
        0.48805330610320846
      ],
      "cartesian_polarization_e_A2": [
        -0.008071674200900082,
        -2.279044390522846e-15,
        0.010325613792650755
      ],
      "ranking_score": 0.9951183319263869
    },
    {
      "candidate_id": "bec_projection_06",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        -0.5,
        0.5,
        0.0
      ],
      "formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_residual": 0.029498658952080807,
      "parent_symmetrization_rmsd_A": 0.4425473793648896,
      "parent_cell_rmsd_A": 0.14382825002784932,
      "energy_eV": -49.330076785974164,
      "reduced_polarization": [
        -0.4797627473224958,
        0.4830132369291564,
        -0.013117711858897091
      ],
      "cartesian_polarization_e_A2": [
        -0.008425213009103148,
        0.01005130826251549,
        -0.00019204305839591606
      ],
      "ranking_score": 1.0375017597760134
    },
    {
      "candidate_id": "bec_projection_07",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        -0.5,
        0.5,
        0.5
      ],
      "formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "target_residual": 0.03785153391874008,
      "parent_symmetrization_rmsd_A": 0.46444661857511305,
      "parent_cell_rmsd_A": 0.16775586457642977,
      "energy_eV": -40.07259805129385,
      "reduced_polarization": [
        -0.4988452368976205,
        0.4636237444952283,
        0.48959936647936864
      ],
      "cartesian_polarization_e_A2": [
        -0.008759970516871147,
        0.009095920993171032,
        0.010521587114067865
      ],
      "ranking_score": 1.0820886525567006
    }
  ],
  "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": [
              -2.003402227076123e-16,
              4.988177198294171e-16,
              0.15615510331587876
            ],
            "branch_aligned_reduced_polarization": [
              -2.003402227076123e-16,
              4.988177198294171e-16,
              0.15615510331587876
            ],
            "target_residual": 0.15615510331587876,
            "energy_eV": -63.00013525762529,
            "max_atomic_step_A": 0.08580480482565711,
            "max_log_strain_component": 0.0045351425154864945,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.8069241064699163,
            "cell_principal_stretches": [
              0.9990362350849717,
              0.9964730051469375,
              0.9954751257148374
            ],
            "cell_volume_ratio": 0.9910080698831121,
            "cell_rmsd_from_input_A": 0.02629706109756014
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -2.7078942265923637e-16,
              -5.7925192782402515e-15,
              0.0017631193134790971
            ],
            "branch_aligned_reduced_polarization": [
              -2.7078942265923637e-16,
              -5.7925192782402515e-15,
              0.0017631193134790971
            ],
            "target_residual": 0.0017631193134790971,
            "energy_eV": -62.424415375059766,
            "max_atomic_step_A": 0.001017060637310431,
            "max_log_strain_component": 5.6464273946795614e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.8069241064699163,
            "cell_principal_stretches": [
              0.9990242416960402,
              0.9964291711951517,
              0.995418918521496
            ],
            "cell_volume_ratio": 0.9908966280028347,
            "cell_rmsd_from_input_A": 0.026623196346894813
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -1.4504433348383547e-15,
              -3.851880821238703e-15,
              9.2901877422773e-06
            ],
            "branch_aligned_reduced_polarization": [
              -1.4504433348383547e-15,
              -3.851880821238703e-15,
              9.2901877422773e-06
            ],
            "target_residual": 9.2901877422773e-06,
            "energy_eV": -62.40991471825407
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "inversion_parent_endpoint_00",
        "source": "same_species_inversion_center_projection_from_endpoint",
        "spacegroup": "Cmcm",
        "spacegroup_number": 63,
        "pointgroup": "mmm",
        "has_inversion": true,
        "is_polar_point_group": false,
        "nonpolar_parent_hypothesis": true,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.0
        ],
        "formal_class": [
          0.0,
          0.0,
          0.0
        ],
        "target_residual": 3.2248869032134036e-15,
        "parent_symmetrization_rmsd_A": 0.26151910790254485,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -60.89044965382565,
        "reduced_polarization": [
          -6.845121922873501e-16,
          -2.6253564201548273e-16,
          3.140447998900606e-15
        ],
        "cartesian_polarization_e_A2": [
          -1.1892683942111418e-17,
          -5.350960408416533e-18,
          6.72692165629507e-17
        ],
        "ranking_score": 0.2615191079025513
      },
      "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": [
          -63.000135257625296,
          -62.79334846589728,
          -62.43039373442653,
          -61.98532124580405,
          -61.5404734233741,
          -61.18328402809568,
          -60.97418690521653,
          -60.90058618867045,
          -60.89044965382561
        ],
        "cartesian_polarizations_e_A2": [
          [
            -1.1865399497519138e-17,
            1.1389901440772334e-17,
            0.0033448831077741367
          ],
          [
            1.4758509205656587e-17,
            -6.681056281365786e-17,
            0.00396050936136324
          ],
          [
            -1.586190544377678e-17,
            -3.0882685785718274e-17,
            0.00415256045175511
          ],
          [
            -8.289366143524193e-18,
            -3.806826119130619e-17,
            0.0038953323686440155
          ],
          [
            -4.9546990744240336e-17,
            -5.626152657992241e-17,
            0.0033342429693086002
          ],
          [
            7.32936572393762e-17,
            6.81865240615364e-17,
            0.002661936864383952
          ],
          [
            -7.428458957960865e-18,
            -1.8422592263262637e-17,
            0.0019223212251995307
          ],
          [
            -5.3569277611087425e-17,
            4.739422076026072e-18,
            0.001032145038568552
          ],
          [
            -2.4350198547530053e-17,
            -6.711633197985309e-17,
            -4.433652909830842e-17
          ]
        ],
        "raw_reduced_polarization": [
          [
            -6.829417700786953e-16,
            5.588258665758132e-16,
            0.15615510331587787
          ],
          [
            8.494616976648132e-16,
            -3.277945016021884e-15,
            0.18489547424535566
          ],
          [
            -9.129703372279002e-16,
            -1.5152057053465e-15,
            0.193861335501424
          ],
          [
            -4.771145200861104e-16,
            -1.8677535674815767e-15,
            0.18185270123836067
          ],
          [
            -2.851796904775026e-15,
            -2.7603747503342185e-15,
            0.15565837088372814
          ],
          [
            4.218593737283478e-15,
            3.34545418111158e-15,
            0.12427191405048299
          ],
          [
            -4.275629245157281e-16,
            -9.038727103675906e-16,
            0.08974312699587686
          ],
          [
            -3.0833093551719292e-15,
            2.325315686422847e-16,
            0.048185455198731054
          ],
          [
            -1.4015345797075658e-15,
            -3.2929470527084834e-15,
            -2.069840726548127e-15
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -6.829417700786953e-16,
            5.588258665758132e-16,
            0.15615510331587787
          ],
          [
            8.494616976648131e-16,
            -3.2779450160218838e-15,
            0.18489547424535566
          ],
          [
            -9.129703372279002e-16,
            -1.5152057053465e-15,
            0.193861335501424
          ],
          [
            -4.771145200861104e-16,
            -1.8677535674815767e-15,
            0.18185270123836067
          ],
          [
            -2.851796904775026e-15,
            -2.7603747503342185e-15,
            0.15565837088372814
          ],
          [
            4.218593737283478e-15,
            3.34545418111158e-15,
            0.12427191405048299
          ],
          [
            -4.275629245157282e-16,
            -9.038727103675908e-16,
            0.08974312699587686
          ],
          [
            -3.0833093551719292e-15,
            2.3253156864228476e-16,
            0.048185455198731054
          ],
          [
            -1.4015345797075658e-15,
            -3.2929470527084834e-15,
            -2.067790383364354e-15
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            -6.661338147750939e-16,
            5.551115123125783e-16,
            0.1561551033158779
          ],
          [
            8.881784197001252e-16,
            -3.2751579226442118e-15,
            0.18489547424535568
          ],
          [
            -8.881784197001252e-16,
            -1.4988010832439613e-15,
            0.19386133550142404
          ],
          [
            -4.996003610813204e-16,
            -1.887379141862766e-15,
            0.18185270123836061
          ],
          [
            -2.831068712794149e-15,
            -2.7755575615628914e-15,
            0.15565837088372814
          ],
          [
            4.218847493575595e-15,
            3.3306690738754696e-15,
            0.12427191405048299
          ],
          [
            -4.440892098500626e-16,
            -8.881784197001252e-16,
            0.08974312699587683
          ],
          [
            -3.1086244689504383e-15,
            2.220446049250313e-16,
            0.048185455198731075
          ],
          [
            -1.3877787807814457e-15,
            -3.2751579226442118e-15,
            -2.0539125955565396e-15
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -60.890449653825605,
          -60.90058618867046,
          -60.9741869052165,
          -61.18328402809565,
          -61.54047342337411,
          -61.985321245804094,
          -62.430393734426545,
          -62.793348465897296,
          -63.00013525762528
        ],
        "cartesian_polarizations_e_A2": [
          [
            -2.949334264690355e-17,
            -5.694950720386167e-17,
            -4.433652909830842e-17
          ],
          [
            3.0535545321304076e-17,
            -6.42115249009984e-18,
            -0.0010321450385684329
          ],
          [
            -1.9983855561179053e-17,
            1.8957688304104288e-17,
            -0.0019223212251995516
          ],
          [
            2.307106731059406e-17,
            -4.11259528532585e-17,
            -0.0026619368643839565
          ],
          [
            2.760486544264964e-19,
            -5.1522104503896335e-17,
            -0.003334242969308523
          ],
          [
            9.539059778630626e-18,
            -5.82490261601914e-17,
            -0.003895332368644086
          ],
          [
            -4.252665758462579e-18,
            -4.1202395144807304e-17,
            -0.004152560451754913
          ],
          [
            -4.327756574818044e-17,
            6.520527469113289e-17,
            -0.003960509361363232
          ],
          [
            4.819752800007992e-18,
            -1.60528812252496e-18,
            -0.0033448831077741666
          ]
        ],
        "raw_reduced_polarization": [
          [
            -1.6975606794381595e-15,
            -2.7941293328790662e-15,
            -2.069840726548127e-15
          ],
          [
            1.7575471754162056e-15,
            -3.1504277041857924e-16,
            -0.04818545519872549
          ],
          [
            -1.1502191470925304e-15,
            9.301262745691388e-16,
            -0.08974312699587783
          ],
          [
            1.3279110871906331e-15,
            -2.017773934347567e-15,
            -0.12427191405048318
          ],
          [
            1.5888648057850142e-17,
            -2.5278431816919338e-15,
            -0.15565837088372456
          ],
          [
            5.490436602211825e-16,
            -2.857887988797112e-15,
            -0.18185270123836392
          ],
          [
            -2.4477246478255856e-16,
            -2.0215244435192167e-15,
            -0.19386133550141474
          ],
          [
            -2.490944983600354e-15,
            3.1991843234172394e-15,
            -0.18489547424535532
          ],
          [
            2.774125312230261e-16,
            -7.876069260464481e-17,
            -0.15615510331587926
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -1.6975606794381595e-15,
            -2.7941293328790662e-15,
            -2.069840726548127e-15
          ],
          [
            1.7575471754162056e-15,
            -3.1504277041857944e-16,
            -0.04818545519872549
          ],
          [
            -1.1502191470925304e-15,
            9.301262745691388e-16,
            -0.08974312699587783
          ],
          [
            1.3279110871906331e-15,
            -2.0177739343475668e-15,
            -0.12427191405048318
          ],
          [
            1.5888648057850084e-17,
            -2.5278431816919338e-15,
            -0.15565837088372456
          ],
          [
            5.490436602211825e-16,
            -2.857887988797112e-15,
            -0.18185270123836392
          ],
          [
            -2.4477246478255856e-16,
            -2.0215244435192167e-15,
            -0.19386133550141474
          ],
          [
            -2.490944983600354e-15,
            3.1991843234172394e-15,
            -0.18489547424535532
          ],
          [
            2.7741253122302613e-16,
            -7.876069260464476e-17,
            -0.15615510331587926
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          -2.1201273893364363e-15,
          -7.14471997199278e-15,
          -0.15615510331588198
        ],
        "actual_opposite_endpoint_branch_residual": 7.941953832842746e-15
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            -6.829417700786953e-16,
            5.588258665758132e-16,
            0.15615510331587787
          ],
          [
            8.494616976648132e-16,
            -3.277945016021884e-15,
            0.18489547424535566
          ],
          [
            -9.129703372279002e-16,
            -1.5152057053465e-15,
            0.193861335501424
          ],
          [
            -4.771145200861104e-16,
            -1.8677535674815767e-15,
            0.18185270123836067
          ],
          [
            -2.851796904775026e-15,
            -2.7603747503342185e-15,
            0.15565837088372814
          ],
          [
            4.218593737283478e-15,
            3.34545418111158e-15,
            0.12427191405048299
          ],
          [
            -4.275629245157281e-16,
            -9.038727103675906e-16,
            0.08974312699587686
          ],
          [
            -3.0833093551719292e-15,
            2.325315686422847e-16,
            0.048185455198731054
          ],
          [
            -1.4015345797075658e-15,
            -3.2929470527084834e-15,
            -2.069840726548127e-15
          ],
          [
            1.7575471754162056e-15,
            -3.1504277041857924e-16,
            -0.04818545519872549
          ],
          [
            -1.1502191470925304e-15,
            9.301262745691388e-16,
            -0.08974312699587783
          ],
          [
            1.3279110871906331e-15,
            -2.017773934347567e-15,
            -0.12427191405048318
          ],
          [
            1.5888648057850142e-17,
            -2.5278431816919338e-15,
            -0.15565837088372456
          ],
          [
            5.490436602211825e-16,
            -2.857887988797112e-15,
            -0.18185270123836392
          ],
          [
            -2.4477246478255856e-16,
            -2.0215244435192167e-15,
            -0.19386133550141474
          ],
          [
            -2.490944983600354e-15,
            3.1991843234172394e-15,
            -0.18489547424535532
          ],
          [
            2.774125312230261e-16,
            -7.876069260464481e-17,
            -0.15615510331587926
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -6.829417700786953e-16,
            5.588258665758132e-16,
            0.15615510331587787
          ],
          [
            8.494616976648131e-16,
            -3.2779450160218838e-15,
            0.18489547424535566
          ],
          [
            -9.129703372279002e-16,
            -1.5152057053465e-15,
            0.193861335501424
          ],
          [
            -4.771145200861104e-16,
            -1.8677535674815767e-15,
            0.18185270123836067
          ],
          [
            -2.851796904775026e-15,
            -2.7603747503342185e-15,
            0.15565837088372814
          ],
          [
            4.218593737283478e-15,
            3.34545418111158e-15,
            0.12427191405048299
          ],
          [
            -4.275629245157282e-16,
            -9.038727103675908e-16,
            0.08974312699587686
          ],
          [
            -3.0833093551719292e-15,
            2.3253156864228476e-16,
            0.048185455198731054
          ],
          [
            -1.4015345797075658e-15,
            -3.2929470527084834e-15,
            -2.067790383364354e-15
          ],
          [
            1.7575471754162054e-15,
            -3.1504277041857904e-16,
            -0.04818545519872549
          ],
          [
            -1.1502191470925302e-15,
            9.301262745691388e-16,
            -0.08974312699587783
          ],
          [
            1.3279110871906333e-15,
            -2.0177739343475668e-15,
            -0.12427191405048318
          ],
          [
            1.5888648057850084e-17,
            -2.5278431816919338e-15,
            -0.15565837088372456
          ],
          [
            5.490436602211825e-16,
            -2.857887988797112e-15,
            -0.18185270123836392
          ],
          [
            -2.4477246478255856e-16,
            -2.0215244435192167e-15,
            -0.19386133550141474
          ],
          [
            -2.490944983600354e-15,
            3.1991843234172394e-15,
            -0.18489547424535532
          ],
          [
            2.7741253122302613e-16,
            -7.876069260464476e-17,
            -0.15615510331587926
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            -6.661338147750939e-16,
            5.551115123125783e-16,
            0.1561551033158779
          ],
          [
            8.881784197001252e-16,
            -3.2751579226442118e-15,
            0.18489547424535568
          ],
          [
            -8.881784197001252e-16,
            -1.4988010832439613e-15,
            0.19386133550142404
          ],
          [
            -4.996003610813204e-16,
            -1.887379141862766e-15,
            0.18185270123836061
          ],
          [
            -2.831068712794149e-15,
            -2.7755575615628914e-15,
            0.15565837088372814
          ],
          [
            4.218847493575595e-15,
            3.3306690738754696e-15,
            0.12427191405048299
          ],
          [
            -4.440892098500626e-16,
            -8.881784197001252e-16,
            0.08974312699587683
          ],
          [
            -3.1086244689504383e-15,
            2.220446049250313e-16,
            0.048185455198731075
          ],
          [
            -1.3877787807814457e-15,
            -3.2751579226442118e-15,
            -2.0539125955565396e-15
          ],
          [
            1.7763568394002505e-15,
            -3.3306690738754696e-16,
            -0.04818545519872547
          ],
          [
            -1.1657341758564144e-15,
            8.881784197001252e-16,
            -0.08974312699587783
          ],
          [
            1.3322676295501878e-15,
            -1.9984014443252818e-15,
            -0.12427191405048321
          ],
          [
            0.0,
            -2.55351295663786e-15,
            -0.15565837088372458
          ],
          [
            5.551115123125783e-16,
            -2.831068712794149e-15,
            -0.18185270123836395
          ],
          [
            -2.220446049250313e-16,
            -1.9984014443252818e-15,
            -0.1938613355014147
          ],
          [
            -2.4980018054066022e-15,
            3.219646771412954e-15,
            -0.18489547424535535
          ],
          [
            2.220446049250313e-16,
            -5.551115123125783e-17,
            -0.15615510331587923
          ]
        ]
      },
      "incoming_structure_ids": [
        "incoming_00_000",
        "incoming_00_001",
        "incoming_00_002",
        "incoming_00_003",
        "incoming_00_004",
        "incoming_00_005",
        "incoming_00_006",
        "incoming_00_007",
        "incoming_00_008"
      ],
      "reflected_structure_ids": [
        "reflected_00_001",
        "reflected_00_002",
        "reflected_00_003",
        "reflected_00_004",
        "reflected_00_005",
        "reflected_00_006",
        "reflected_00_007",
        "reflected_00_008"
      ]
    },
    {
      "orbit_id": 1,
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.0,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -2.003402227076123e-16,
              4.988177198294171e-16,
              0.15615510331587876
            ],
            "branch_aligned_reduced_polarization": [
              -2.003402227076123e-16,
              4.988177198294171e-16,
              0.15615510331587878
            ],
            "target_residual": 0.3438448966841212,
            "energy_eV": -63.00013525762529,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.006342501483036411,
            "step_scale": 0.6351308927139528,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.8069241064699163,
            "cell_principal_stretches": [
              1.0063626577367246,
              1.0049535311842128,
              1.001349407031341
            ],
            "cell_volume_ratio": 1.0127124262507923,
            "cell_rmsd_from_input_A": 0.03711811976584538
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -6.799131860634719e-15,
              4.6496333950883477e-14,
              0.3450072645005441
            ],
            "branch_aligned_reduced_polarization": [
              -6.799131860634719e-15,
              4.6496333950883477e-14,
              0.3450072645005441
            ],
            "target_residual": 0.1549927354994559,
            "energy_eV": -61.48138232671357,
            "max_atomic_step_A": 0.1105905095392173,
            "max_log_strain_component": 0.008551315455734945,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.8069241064699163,
            "cell_principal_stretches": [
              1.0150052825254423,
              1.0116710248996692,
              1.0031716360908896
            ],
            "cell_volume_ratio": 1.0301082335205798,
            "cell_rmsd_from_input_A": 0.08779988681181645
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -1.0544616195131935e-14,
              8.920466929174723e-14,
              0.46252470130252316
            ],
            "branch_aligned_reduced_polarization": [
              -1.0544616195131935e-14,
              8.920466929174723e-14,
              0.46252470130252316
            ],
            "target_residual": 0.037475298697476844,
            "energy_eV": -57.48992997232978,
            "max_atomic_step_A": 0.02233430333841887,
            "max_log_strain_component": 0.003525398020456365,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.8069241064699163,
            "cell_principal_stretches": [
              1.0185898950195138,
              1.0144534591083456,
              1.0039238402118473
            ],
            "cell_volume_ratio": 1.0373665937587682,
            "cell_rmsd_from_input_A": 0.10890947082616706
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -7.541901297021058e-15,
              3.686754135811784e-14,
              0.495416195390888
            ],
            "branch_aligned_reduced_polarization": [
              -7.541901297021058e-15,
              3.686754135811784e-14,
              0.495416195390888
            ],
            "target_residual": 0.004583804609112008,
            "energy_eV": -56.2968827463037,
            "max_atomic_step_A": 0.0026851513322658682,
            "max_log_strain_component": 0.0004224034933642476,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.8069241064699163,
            "cell_principal_stretches": [
              1.0190202418330754,
              1.0147873556972655,
              1.0040140050705744
            ],
            "cell_volume_ratio": 1.038239694525639,
            "cell_rmsd_from_input_A": 0.11144726042819314
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              -3.564784918132953e-15,
              4.326227563501211e-15,
              0.49938784407740205
            ],
            "branch_aligned_reduced_polarization": [
              -3.564784918132953e-15,
              4.326227563501211e-15,
              0.49938784407740205
            ],
            "target_residual": 0.0006121559225979456,
            "energy_eV": -56.13890420294168
          }
        ],
        "iterations": 4
      },
      "parent": {
        "candidate_id": "bec_projection_01",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cmc2_1",
        "spacegroup_number": 36,
        "pointgroup": "mm2",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.5
        ],
        "formal_class": [
          0.0,
          0.0,
          0.5
        ],
        "target_residual": 0.0006121559225979456,
        "parent_symmetrization_rmsd_A": 0.2752109522951726,
        "parent_cell_rmsd_A": 0.11144726042819314,
        "energy_eV": -56.13890420294168,
        "reduced_polarization": [
          -3.564784918132953e-15,
          4.326227563501211e-15,
          0.49938784407740205
        ],
        "cartesian_polarization_e_A2": [
          3.953449133113143e-16,
          -3.702324858893041e-16,
          0.01045538785626018
        ],
        "ranking_score": 0.8042970792474168
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 2,
      "formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.5,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -2.003402227076123e-16,
              4.988177198294171e-16,
              0.15615510331587876
            ],
            "branch_aligned_reduced_polarization": [
              -2.003402227076123e-16,
              4.996003610813204e-16,
              0.15615510331587876
            ],
            "target_residual": 0.5238171592183596,
            "energy_eV": -63.00013525762529,
            "max_atomic_step_A": 0.12000000000000001,
            "max_log_strain_component": 0.0017893509678550505,
            "step_scale": 0.39455231268796565,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.8069241064699163,
            "cell_principal_stretches": [
              1.000446531578079,
              0.9982122489661646,
              0.9977815496449338
            ],
            "cell_volume_ratio": 0.9964425091016256,
            "cell_rmsd_from_input_A": 0.013942498451395753
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -1.1923815521283181e-15,
              0.18513027016132821,
              0.10612254111434644
            ],
            "branch_aligned_reduced_polarization": [
              -1.1923815521283181e-15,
              0.18513027016132821,
              0.10612254111434644
            ],
            "target_residual": 0.33227238901426087,
            "energy_eV": -61.827312669931096,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.0034171170444430485,
            "step_scale": 0.5252106780496687,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.8069241064699163,
            "cell_principal_stretches": [
              1.0005295971754915,
              0.9948070621506455,
              0.9943235092157107
            ],
            "cell_volume_ratio": 0.9896839053982768,
            "cell_rmsd_from_input_A": 0.03648610277684732
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -8.378545375163918e-16,
              0.32670941860024133,
              0.06479152161104125
            ],
            "branch_aligned_reduced_polarization": [
              -8.378545375163918e-16,
              0.32670941860024133,
              0.06479152161104125
            ],
            "target_residual": 0.18500693736868465,
            "energy_eV": -57.7787077471732,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.004217518540025746,
            "step_scale": 0.8448858078572228,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.8069241064699163,
            "cell_principal_stretches": [
              1.0007790878206595,
              0.9906202800438731,
              0.9899266148434519
            ],
            "cell_volume_ratio": 0.981405386175023,
            "cell_rmsd_from_input_A": 0.06490430442998155
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -3.076420213307317e-15,
              0.47548896170845506,
              -0.009688451524963589
            ],
            "branch_aligned_reduced_polarization": [
              -3.076420213307317e-15,
              0.47548896170845506,
              -0.009688451524963589
            ],
            "target_residual": 0.0263563482121699,
            "energy_eV": -51.944859054795465,
            "max_atomic_step_A": 0.01955194407956655,
            "max_log_strain_component": 0.00029689684647896174,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.8069241064699163,
            "cell_principal_stretches": [
              1.0011366067611112,
              0.9909144357458656,
              0.9898645019069796
            ],
            "cell_volume_ratio": 0.9819858890100962,
            "cell_rmsd_from_input_A": 0.06469346238500125
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              5.035284718929077e-16,
              0.4995880511299936,
              -0.0004851183431698445
            ],
            "branch_aligned_reduced_polarization": [
              5.035284718929077e-16,
              0.4995880511299936,
              -0.0004851183431698445
            ],
            "target_residual": 0.0006364288478529248,
            "energy_eV": -51.083660291978184
          }
        ],
        "iterations": 4
      },
      "parent": {
        "candidate_id": "bec_projection_02",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cm",
        "spacegroup_number": 8,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.5,
          0.0
        ],
        "formal_class": [
          0.0,
          0.5,
          0.0
        ],
        "target_residual": 0.0006364288478529248,
        "parent_symmetrization_rmsd_A": 0.37616455419655465,
        "parent_cell_rmsd_A": 0.06469346238500125,
        "energy_eV": -51.083660291978184,
        "reduced_polarization": [
          5.035284718929077e-16,
          0.4995880511299936,
          -0.0004851183431698445
        ],
        "cartesian_polarization_e_A2": [
          8.825809791837175e-17,
          0.010349295062866977,
          4.149144182179182e-05
        ],
        "ranking_score": 0.8936107774885108
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 3,
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.0,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        -0.5,
        0.0,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -2.003402227076123e-16,
              4.988177198294171e-16,
              0.15615510331587876
            ],
            "branch_aligned_reduced_polarization": [
              -2.220446049250313e-16,
              4.988177198294171e-16,
              0.15615510331587876
            ],
            "target_residual": 0.5238171592183598,
            "energy_eV": -63.00013525762529,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.004206065569001922,
            "step_scale": 0.5936956475674714,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.8069241064699163,
            "cell_principal_stretches": [
              1.0018231490474832,
              0.9994277048857788,
              0.9934101624476862
            ],
            "cell_volume_ratio": 0.994651736953134,
            "cell_rmsd_from_input_A": 0.03108640551040212
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.2755288004046522,
              9.783322827776884e-15,
              0.0647308959842444
            ],
            "branch_aligned_reduced_polarization": [
              -0.2755288004046522,
              9.783322827776884e-15,
              0.0647308959842444
            ],
            "target_residual": 0.23361808222545088,
            "energy_eV": -61.66594165723139,
            "max_atomic_step_A": 0.10706071810347424,
            "max_log_strain_component": 0.004973311022452009,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.8069241064699163,
            "cell_principal_stretches": [
              1.004764255883504,
              0.9989386216045025,
              0.9864536473660708
            ],
            "cell_volume_ratio": 0.9901013761911466,
            "cell_rmsd_from_input_A": 0.06507030212860324
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.4742051273981653,
              2.6254580039632515e-14,
              0.007366727239133162
            ],
            "branch_aligned_reduced_polarization": [
              -0.4742051273981653,
              2.6254580039632515e-14,
              0.007366727239133162
            ],
            "target_residual": 0.02682618352954199,
            "energy_eV": -57.805214584178955,
            "max_atomic_step_A": 0.01181396867180258,
            "max_log_strain_component": 0.0008157197999029439,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.8069241064699163,
            "cell_principal_stretches": [
              1.0051331076545396,
              0.9988310478597164,
              0.9852034357472511
            ],
            "cell_volume_ratio": 0.9891030238072237,
            "cell_rmsd_from_input_A": 0.07093204167233018
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -0.5019783877316564,
              6.304423815506803e-15,
              0.00016278280035459305
            ],
            "branch_aligned_reduced_polarization": [
              -0.5019783877316564,
              6.304423815506803e-15,
              0.00016278280035459305
            ],
            "target_residual": 0.001985073363092591,
            "energy_eV": -57.1611632567294,
            "max_atomic_step_A": 0.0006939101103946182,
            "max_log_strain_component": 5.496899879054045e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.8069241064699163,
            "cell_principal_stretches": [
              1.005084975497688,
              0.9988327268588643,
              0.9852644742100553
            ],
            "cell_volume_ratio": 0.9891185990707027,
            "cell_rmsd_from_input_A": 0.07060145084774946
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              -0.4999625739204623,
              -4.061936290142829e-15,
              6.774505530858645e-06
            ],
            "branch_aligned_reduced_polarization": [
              -0.4999625739204623,
              -4.061936290142829e-15,
              6.774505530858645e-06
            ],
            "target_residual": 3.803426553453004e-05,
            "energy_eV": -57.20230401989944
          }
        ],
        "iterations": 4
      },
      "parent": {
        "candidate_id": "bec_projection_03",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cc",
        "spacegroup_number": 9,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          -0.5,
          0.0,
          0.0
        ],
        "formal_class": [
          0.5,
          0.0,
          0.0
        ],
        "target_residual": 3.803426553453004e-05,
        "parent_symmetrization_rmsd_A": 0.2631635531205746,
        "parent_cell_rmsd_A": 0.07060145084774946,
        "energy_eV": -57.20230401989944,
        "reduced_polarization": [
          -0.4999625739204623,
          -4.061936290142829e-15,
          6.774505530858645e-06
        ],
        "cartesian_polarization_e_A2": [
          -0.008734209892328986,
          -1.3029954514289455e-15,
          8.701226572446694e-05
        ],
        "ranking_score": 0.780889984363581
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 4,
      "formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.5,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -2.003402227076123e-16,
              4.988177198294171e-16,
              0.15615510331587876
            ],
            "branch_aligned_reduced_polarization": [
              -2.003402227076123e-16,
              4.996003610813204e-16,
              0.15615510331587878
            ],
            "target_residual": 0.6068190117124821,
            "energy_eV": -63.00013525762529,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.00327726695767352,
            "step_scale": 0.32818178979641416,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.8069241064699163,
            "cell_principal_stretches": [
              1.0032826430684085,
              1.0030132063152433,
              1.0002413888324069
            ],
            "cell_volume_ratio": 1.0065486516322588,
            "cell_rmsd_from_input_A": 0.020652641683882044
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -3.807623654742662e-15,
              0.1560401165650574,
              0.25678461225301247
            ],
            "branch_aligned_reduced_polarization": [
              -3.807623654742662e-15,
              0.1560401165650574,
              0.25678461225301247
            ],
            "target_residual": 0.42126253838846955,
            "energy_eV": -61.82022253801615,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.004690126791750757,
            "step_scale": 0.46789249748478157,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.8069241064699163,
            "cell_principal_stretches": [
              1.007999217893353,
              1.0071443288401158,
              1.0007825679050855
            ],
            "cell_volume_ratio": 1.0159951592582979,
            "cell_rmsd_from_input_A": 0.04968734170494672
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -3.278051916369961e-15,
              0.2929944157096405,
              0.35907118720599485
            ],
            "branch_aligned_reduced_polarization": [
              -3.278051916369961e-15,
              0.2929944157096405,
              0.35907118720599485
            ],
            "target_residual": 0.25042412464241715,
            "energy_eV": -57.90669885132991,
            "max_atomic_step_A": 0.11796425871783232,
            "max_log_strain_component": 0.007127351526303052,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.8069241064699163,
            "cell_principal_stretches": [
              1.0152092463392306,
              1.0136446159911863,
              1.0014179575895843
            ],
            "cell_volume_ratio": 1.0305205520595881,
            "cell_rmsd_from_input_A": 0.09500852354864735
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -4.771460119625619e-15,
              0.4574919265944703,
              0.4915483505854865
            ],
            "branch_aligned_reduced_polarization": [
              -4.771460119625619e-15,
              0.4574919265944703,
              0.4915483505854865
            ],
            "target_residual": 0.04334012785486156,
            "energy_eV": -48.89226784210117,
            "max_atomic_step_A": 0.03070052657840339,
            "max_log_strain_component": 0.0006241097188798683,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.8069241064699163,
            "cell_principal_stretches": [
              1.0157659391310419,
              1.0144886185219881,
              1.0011289423407321
            ],
            "cell_volume_ratio": 1.0316463402031555,
            "cell_rmsd_from_input_A": 0.09983263123183593
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              -6.1783287003783824e-15,
              0.4959998889470215,
              0.49487812306835943
            ],
            "branch_aligned_reduced_polarization": [
              -6.1783287003783824e-15,
              0.4959998889470215,
              0.49487812306835943
            ],
            "target_residual": 0.006498808486102081,
            "energy_eV": -49.13690814026608,
            "max_atomic_step_A": 0.0018318152578349373,
            "max_log_strain_component": 0.0010691633143202644,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": true,
            "strain_jacobian_frobenius_norm": 3.2951103826531165,
            "cell_principal_stretches": [
              1.015835593889131,
              1.0134716544862798,
              1.0014721071111183
            ],
            "cell_volume_ratio": 1.0310361445917675,
            "cell_rmsd_from_input_A": 0.09584135701572997
          },
          {
            "iteration": 5,
            "reduced_polarization": [
              2.8393169272063677e-15,
              0.49998555038815934,
              0.4999961109224459
            ],
            "branch_aligned_reduced_polarization": [
              2.8393169272063677e-15,
              0.49998555038815934,
              0.4999961109224459
            ],
            "target_residual": 1.4963829943154587e-05,
            "energy_eV": -48.98771706324193
          }
        ],
        "iterations": 5
      },
      "parent": {
        "candidate_id": "bec_projection_04",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cm",
        "spacegroup_number": 8,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.5,
          0.5
        ],
        "formal_class": [
          0.0,
          0.5,
          0.5
        ],
        "target_residual": 1.4963829943154587e-05,
        "parent_symmetrization_rmsd_A": 0.38170393122436364,
        "parent_cell_rmsd_A": 0.09584135701572997,
        "energy_eV": -48.98771706324193,
        "reduced_polarization": [
          2.8393169272063677e-15,
          0.49998555038815934,
          0.4999961109224459
        ],
        "cartesian_polarization_e_A2": [
          6.967690350329494e-16,
          0.009952935437632062,
          0.010551199471451948
        ],
        "ranking_score": 0.9056941981381824
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 5,
      "formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.0,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        -0.5,
        0.0,
        0.5
      ],
      "bec_backprojection": {
        "converged_to_target": false,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -2.003402227076123e-16,
              4.988177198294171e-16,
              0.15615510331587876
            ],
            "branch_aligned_reduced_polarization": [
              -2.220446049250313e-16,
              4.988177198294171e-16,
              0.15615510331587878
            ],
            "target_residual": 0.6068190117124823,
            "energy_eV": -63.00013525762529,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.004555754953646716,
            "step_scale": 0.4562081252068079,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.8069241064699163,
            "cell_principal_stretches": [
              1.0073503750492974,
              1.0009690813607448,
              1.0007818558095785
            ],
            "cell_volume_ratio": 1.0091149455156483,
            "cell_rmsd_from_input_A": 0.03393970315344637
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.19356528760782749,
              3.671083704352354e-14,
              0.292172980134451
            ],
            "branch_aligned_reduced_polarization": [
              -0.19356528760782749,
              3.671083704352354e-14,
              0.292172980134451
            ],
            "target_residual": 0.3702624787162059,
            "energy_eV": -61.534411246011985,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.006575072501382827,
            "step_scale": 0.5091912891136992,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.8069241064699163,
            "cell_principal_stretches": [
              1.0184221813728418,
              1.0023693596011072,
              1.0015492595022264
            ],
            "cell_volume_ratio": 1.0224167283641798,
            "cell_rmsd_from_input_A": 0.085314523157553
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.2751368461266379,
              1.0254057203047152e-13,
              0.34622394992769745
            ],
            "branch_aligned_reduced_polarization": [
              -0.2751368461266379,
              1.0254057203047152e-13,
              0.34622394992769745
            ],
            "target_residual": 0.2724160633033864,
            "energy_eV": -57.70305383216212,
            "max_atomic_step_A": 0.10463378987660865,
            "max_log_strain_component": 0.02,
            "step_scale": 0.4752612546033462,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.8069241064699163,
            "cell_principal_stretches": [
              1.0499180544224185,
              1.0066943575107763,
              1.006640767116477
            ],
            "cell_volume_ratio": 1.063965517336284,
            "cell_rmsd_from_input_A": 0.23589093989622467
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -0.30200757095854647,
              2.509952712883586e-13,
              0.3892661902888265
            ],
            "branch_aligned_reduced_polarization": [
              -0.30200757095854647,
              2.509952712883586e-13,
              0.3892661902888265
            ],
            "target_residual": 0.22685453173980324,
            "energy_eV": -55.50664925834557,
            "max_atomic_step_A": 0.11727653308446825,
            "max_log_strain_component": 0.02,
            "step_scale": 0.7751940357555168,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.8069241064699163,
            "cell_principal_stretches": [
              1.0864796424794716,
              1.0109303764274162,
              1.0080552120561157
            ],
            "cell_volume_ratio": 1.1072027585971371,
            "cell_rmsd_from_input_A": 0.41368289131960484
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              -0.34943562278797013,
              2.3068318822041757e-13,
              0.43924306169202204
            ],
            "branch_aligned_reduced_polarization": [
              -0.34943562278797013,
              2.3068318822041757e-13,
              0.43924306169202204
            ],
            "target_residual": 0.16236082420893858,
            "energy_eV": -50.30669043208409,
            "max_atomic_step_A": 0.03781920882423065,
            "max_log_strain_component": 0.02,
            "step_scale": 0.7813744019316091,
            "strain_jacobian_refreshed": true,
            "strain_jacobian_frobenius_norm": 3.766070101542175,
            "cell_principal_stretches": [
              1.0561586055770087,
              1.0034241812169609,
              1.001090328403128
            ],
            "cell_volume_ratio": 1.0609305869114096,
            "cell_rmsd_from_input_A": 0.26515037461443014
          },
          {
            "iteration": 5,
            "reduced_polarization": [
              -0.46235139375512396,
              9.481217796174636e-14,
              0.48805330610320846
            ],
            "branch_aligned_reduced_polarization": [
              -0.46235139375512396,
              9.481217796174636e-14,
              0.48805330610320846
            ],
            "target_residual": 0.039498620827129585,
            "energy_eV": -45.599155416050735
          }
        ],
        "iterations": 5
      },
      "parent": {
        "candidate_id": "bec_projection_05",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cc",
        "spacegroup_number": 9,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          -0.5,
          0.0,
          0.5
        ],
        "formal_class": [
          0.5,
          0.0,
          0.5
        ],
        "target_residual": 0.039498620827129585,
        "parent_symmetrization_rmsd_A": 0.34983349661852015,
        "parent_cell_rmsd_A": 0.26515037461443014,
        "energy_eV": -45.599155416050735,
        "reduced_polarization": [
          -0.46235139375512396,
          9.481217796174636e-14,
          0.48805330610320846
        ],
        "cartesian_polarization_e_A2": [
          -0.008071674200900082,
          -2.279044390522846e-15,
          0.010325613792650755
        ],
        "ranking_score": 0.9951183319263869
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 6,
      "formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.5,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        -0.5,
        0.5,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": false,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -2.003402227076123e-16,
              4.988177198294171e-16,
              0.15615510331587876
            ],
            "branch_aligned_reduced_polarization": [
              -2.220446049250313e-16,
              4.996003610813204e-16,
              0.15615510331587876
            ],
            "target_residual": 0.7241439195985782,
            "energy_eV": -63.00013525762529,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.0023950713643509495,
            "step_scale": 0.3380697284202633,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.8069241064699163,
            "cell_principal_stretches": [
              1.0014051727298334,
              0.999456930794759,
              0.9960930333134813
            ],
            "cell_volume_ratio": 0.9969510085037154,
            "cell_rmsd_from_input_A": 0.019450857999915205
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.1641855804845848,
              0.1583697611268448,
              0.11017898430022921
            ],
            "branch_aligned_reduced_polarization": [
              -0.16418558048458476,
              0.1583697611268448,
              0.11017898430022921
            ],
            "target_residual": 0.4915505600123293,
            "energy_eV": -61.78254499770834,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.002665977537312251,
            "step_scale": 0.41908347957551895,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.8069241064699163,
            "cell_principal_stretches": [
              1.002471719425596,
              0.9985005592603247,
              0.9910616569662004
            ],
            "cell_volume_ratio": 0.9920215720221565,
            "cell_rmsd_from_input_A": 0.043494686093024586
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.293095839128216,
              0.27003249157456166,
              0.0745133187301372
            ],
            "branch_aligned_reduced_polarization": [
              -0.293095839128216,
              0.27003249157456166,
              0.0745133187301372
            ],
            "target_residual": 0.31819274250937923,
            "energy_eV": -58.12136835750121,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.0034528326706230942,
            "step_scale": 0.3973044084817825,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.8069241064699163,
            "cell_principal_stretches": [
              1.0042537794305835,
              0.9973940073065707,
              0.9849307282584538
            ],
            "cell_volume_ratio": 0.9865427657790492,
            "cell_rmsd_from_input_A": 0.07341984091885155
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -0.3706672495179686,
              0.3443527608358652,
              0.033900067380188234
            ],
            "branch_aligned_reduced_polarization": [
              -0.3706672495179686,
              0.3443527608358652,
              0.033900067380188234
            ],
            "target_residual": 0.20518829882584944,
            "energy_eV": -53.77352336512018,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.007483265431670583,
            "step_scale": 0.6452024883307999,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.8069241064699163,
            "cell_principal_stretches": [
              1.0123243904589125,
              0.9976845128072721,
              0.9771871308813991
            ],
            "cell_volume_ratio": 0.986939816389208,
            "cell_rmsd_from_input_A": 0.12083166371953405
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              -0.4419853068225299,
              0.4357268316665603,
              -0.008787273863345654
            ],
            "branch_aligned_reduced_polarization": [
              -0.4419853068225299,
              0.4357268316665603,
              -0.008787273863345654
            ],
            "target_residual": 0.08702850667479083,
            "energy_eV": -48.853642969162394,
            "max_atomic_step_A": 0.0354753366092781,
            "max_log_strain_component": 0.011290332441363094,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": true,
            "strain_jacobian_frobenius_norm": 3.9715366844014146,
            "cell_principal_stretches": [
              1.005208954968536,
              0.9871737320795017,
              0.9704587400792453
            ],
            "cell_volume_ratio": 0.9630016143915512,
            "cell_rmsd_from_input_A": 0.14382825002784932
          },
          {
            "iteration": 5,
            "reduced_polarization": [
              -0.4797627473224958,
              0.4830132369291564,
              -0.013117711858897091
            ],
            "branch_aligned_reduced_polarization": [
              -0.4797627473224958,
              0.4830132369291564,
              -0.013117711858897091
            ],
            "target_residual": 0.029498658952080807,
            "energy_eV": -49.330076785974164
          }
        ],
        "iterations": 5
      },
      "parent": {
        "candidate_id": "bec_projection_06",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          -0.5,
          0.5,
          0.0
        ],
        "formal_class": [
          0.5,
          0.5,
          0.0
        ],
        "target_residual": 0.029498658952080807,
        "parent_symmetrization_rmsd_A": 0.4425473793648896,
        "parent_cell_rmsd_A": 0.14382825002784932,
        "energy_eV": -49.330076785974164,
        "reduced_polarization": [
          -0.4797627473224958,
          0.4830132369291564,
          -0.013117711858897091
        ],
        "cartesian_polarization_e_A2": [
          -0.008425213009103148,
          0.01005130826251549,
          -0.00019204305839591606
        ],
        "ranking_score": 1.0375017597760134
      },
      "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": false,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -2.003402227076123e-16,
              4.988177198294171e-16,
              0.15615510331587876
            ],
            "branch_aligned_reduced_polarization": [
              -2.220446049250313e-16,
              4.996003610813204e-16,
              0.15615510331587878
            ],
            "target_residual": 0.786275596070305,
            "energy_eV": -63.00013525762529,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.002930694647318855,
            "step_scale": 0.2934764323829249,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.8069241064699163,
            "cell_principal_stretches": [
              1.004810381745274,
              1.0012098361608637,
              0.9998290983719684
            ],
            "cell_volume_ratio": 1.0058541061922395,
            "cell_rmsd_from_input_A": 0.022862344479513453
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.13423208952290688,
              0.1391172220682632,
              0.245199648480408
            ],
            "branch_aligned_reduced_polarization": [
              -0.13423208952290688,
              0.1391172220682632,
              0.24519964848040798
            ],
            "target_residual": 0.5735379349938535,
            "energy_eV": -61.77622657144118,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.004140431025206428,
            "step_scale": 0.35734542981635337,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.8069241064699163,
            "cell_principal_stretches": [
              1.0116183349781291,
              1.0027216072378162,
              0.9998142422777866
            ],
            "cell_volume_ratio": 1.0141831354095368,
            "cell_rmsd_from_input_A": 0.054985634330660345
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.22783376617933468,
              0.24130037590757814,
              0.3142779327649496
            ],
            "branch_aligned_reduced_polarization": [
              -0.2278337661793347,
              0.24130037590757814,
              0.3142779327649496
            ],
            "target_residual": 0.418918417589566,
            "energy_eV": -58.25633753648336,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.009005639760602943,
            "step_scale": 0.5074803655413772,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.8069241064699163,
            "cell_principal_stretches": [
              1.028603101239562,
              1.0046592686628424,
              0.9980293097031782
            ],
            "cell_volume_ratio": 1.031359136676256,
            "cell_rmsd_from_input_A": 0.13457353474151718
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -0.3230606499644614,
              0.3239780853100635,
              0.3773380868062528
            ],
            "branch_aligned_reduced_polarization": [
              -0.3230606499644614,
              0.3239780853100635,
              0.3773380868062528
            ],
            "target_residual": 0.27809565438974504,
            "energy_eV": -50.97814711484359,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.009260326071849267,
            "step_scale": 0.7000432802604767,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.8069241064699163,
            "cell_principal_stretches": [
              1.0423035758783445,
              1.0055020480100128,
              0.9924649432504284
            ],
            "cell_volume_ratio": 1.0401413515233455,
            "cell_rmsd_from_input_A": 0.20223832745439096
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              -0.38809772628714756,
              0.38718995463209,
              0.39100109358177376
            ],
            "branch_aligned_reduced_polarization": [
              -0.38809772628714756,
              0.38718995463209,
              0.39100109358177376
            ],
            "target_residual": 0.19268883413001725,
            "energy_eV": -50.72208071222427,
            "max_atomic_step_A": 0.10695795836150464,
            "max_log_strain_component": 0.01515854903662223,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": true,
            "strain_jacobian_frobenius_norm": 2.5171391193646113,
            "cell_principal_stretches": [
              1.0327788443570691,
              0.9941330183918056,
              0.9894927414563028
            ],
            "cell_volume_ratio": 1.015931542109522,
            "cell_rmsd_from_input_A": 0.16775586457642977
          },
          {
            "iteration": 5,
            "reduced_polarization": [
              -0.4988452368976205,
              0.4636237444952283,
              0.48959936647936864
            ],
            "branch_aligned_reduced_polarization": [
              -0.4988452368976205,
              0.4636237444952283,
              0.48959936647936864
            ],
            "target_residual": 0.03785153391874008,
            "energy_eV": -40.07259805129385
          }
        ],
        "iterations": 5
      },
      "parent": {
        "candidate_id": "bec_projection_07",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          -0.5,
          0.5,
          0.5
        ],
        "formal_class": [
          0.5,
          0.5,
          0.5
        ],
        "target_residual": 0.03785153391874008,
        "parent_symmetrization_rmsd_A": 0.46444661857511305,
        "parent_cell_rmsd_A": 0.16775586457642977,
        "energy_eV": -40.07259805129385,
        "reduced_polarization": [
          -0.4988452368976205,
          0.4636237444952283,
          0.48959936647936864
        ],
        "cartesian_polarization_e_A2": [
          -0.008759970516871147,
          0.009095920993171032,
          0.010521587114067865
        ],
        "ranking_score": 1.0820886525567006
      },
      "branch_status": "awaiting_branch_sampling"
    }
  ],
  "sampled_polarization_branches": [
    {
      "orbit_id": 0,
      "candidate_id": "inversion_parent_endpoint_00",
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "construction": "MACEField-BEC-parent plus variable-cell P-N-P path and symmetric log-strain continuation beyond both polar endpoints",
      "geometry_diagnostics": {
        "collision_aware": false,
        "permutations_tested": 1,
        "selected_order": [
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          10,
          11,
          12,
          13,
          14,
          15,
          16,
          17,
          18,
          19,
          20,
          21,
          22,
          23
        ],
        "endpoint_rmsd_A": 0.26151910790254485,
        "minimum_distance_A_by_image": [
          1.63130635102341,
          1.6360369064698843,
          1.6407971864297002,
          1.6455869329456665,
          1.6504058894675757,
          1.655253800877324,
          1.6601304135128148,
          1.6650354751906828,
          1.6699687352278567
        ],
        "minimum_distance_A": 1.63130635102341,
        "minimum_distance_floor_A": 0.0,
        "geometry_valid": true,
        "parameters": [
          0.0,
          0.125,
          0.25,
          0.375,
          0.5,
          0.625,
          0.75,
          0.875,
          1.0
        ],
        "cell_mode": "variable_cell",
        "cell_volume_A3_by_image": [
          363.09188347535684,
          363.09188347535684,
          363.09188347535684,
          363.09188347535684,
          363.09188347535684,
          363.09188347535684,
          363.09188347535684,
          363.09188347535684,
          363.09188347535684
        ],
        "cell_deformation_log_strain_norm": 0.0
      },
      "parent_reduced_polarization": [
        -1.4015345797075658e-15,
        -3.2929470527084834e-15,
        -2.069840726548127e-15
      ],
      "incoming": {
        "reached": true,
        "construction": "variable_cell_linear_interpolation",
        "continuation_fractions": [
          0.0,
          0.125,
          0.25,
          0.375,
          0.5,
          0.625,
          0.75,
          0.875,
          1.0
        ],
        "energies_eV": [
          -63.000135257625296,
          -62.79334846589728,
          -62.43039373442653,
          -61.98532124580405,
          -61.5404734233741,
          -61.18328402809568,
          -60.97418690521653,
          -60.90058618867045,
          -60.89044965382561
        ],
        "cartesian_polarizations_e_A2": [
          [
            -1.1865399497519138e-17,
            1.1389901440772334e-17,
            0.0033448831077741367
          ],
          [
            1.4758509205656587e-17,
            -6.681056281365786e-17,
            0.00396050936136324
          ],
          [
            -1.586190544377678e-17,
            -3.0882685785718274e-17,
            0.00415256045175511
          ],
          [
            -8.289366143524193e-18,
            -3.806826119130619e-17,
            0.0038953323686440155
          ],
          [
            -4.9546990744240336e-17,
            -5.626152657992241e-17,
            0.0033342429693086002
          ],
          [
            7.32936572393762e-17,
            6.81865240615364e-17,
            0.002661936864383952
          ],
          [
            -7.428458957960865e-18,
            -1.8422592263262637e-17,
            0.0019223212251995307
          ],
          [
            -5.3569277611087425e-17,
            4.739422076026072e-18,
            0.001032145038568552
          ],
          [
            -2.4350198547530053e-17,
            -6.711633197985309e-17,
            -4.433652909830842e-17
          ]
        ],
        "raw_reduced_polarization": [
          [
            -6.829417700786953e-16,
            5.588258665758132e-16,
            0.15615510331587787
          ],
          [
            8.494616976648132e-16,
            -3.277945016021884e-15,
            0.18489547424535566
          ],
          [
            -9.129703372279002e-16,
            -1.5152057053465e-15,
            0.193861335501424
          ],
          [
            -4.771145200861104e-16,
            -1.8677535674815767e-15,
            0.18185270123836067
          ],
          [
            -2.851796904775026e-15,
            -2.7603747503342185e-15,
            0.15565837088372814
          ],
          [
            4.218593737283478e-15,
            3.34545418111158e-15,
            0.12427191405048299
          ],
          [
            -4.275629245157281e-16,
            -9.038727103675906e-16,
            0.08974312699587686
          ],
          [
            -3.0833093551719292e-15,
            2.325315686422847e-16,
            0.048185455198731054
          ],
          [
            -1.4015345797075658e-15,
            -3.2929470527084834e-15,
            -2.069840726548127e-15
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -6.829417700786953e-16,
            5.588258665758132e-16,
            0.15615510331587787
          ],
          [
            8.494616976648131e-16,
            -3.2779450160218838e-15,
            0.18489547424535566
          ],
          [
            -9.129703372279002e-16,
            -1.5152057053465e-15,
            0.193861335501424
          ],
          [
            -4.771145200861104e-16,
            -1.8677535674815767e-15,
            0.18185270123836067
          ],
          [
            -2.851796904775026e-15,
            -2.7603747503342185e-15,
            0.15565837088372814
          ],
          [
            4.218593737283478e-15,
            3.34545418111158e-15,
            0.12427191405048299
          ],
          [
            -4.275629245157282e-16,
            -9.038727103675908e-16,
            0.08974312699587686
          ],
          [
            -3.0833093551719292e-15,
            2.3253156864228476e-16,
            0.048185455198731054
          ],
          [
            -1.4015345797075658e-15,
            -3.2929470527084834e-15,
            -2.067790383364354e-15
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            -6.661338147750939e-16,
            5.551115123125783e-16,
            0.1561551033158779
          ],
          [
            8.881784197001252e-16,
            -3.2751579226442118e-15,
            0.18489547424535568
          ],
          [
            -8.881784197001252e-16,
            -1.4988010832439613e-15,
            0.19386133550142404
          ],
          [
            -4.996003610813204e-16,
            -1.887379141862766e-15,
            0.18185270123836061
          ],
          [
            -2.831068712794149e-15,
            -2.7755575615628914e-15,
            0.15565837088372814
          ],
          [
            4.218847493575595e-15,
            3.3306690738754696e-15,
            0.12427191405048299
          ],
          [
            -4.440892098500626e-16,
            -8.881784197001252e-16,
            0.08974312699587683
          ],
          [
            -3.1086244689504383e-15,
            2.220446049250313e-16,
            0.048185455198731075
          ],
          [
            -1.3877787807814457e-15,
            -3.2751579226442118e-15,
            -2.0539125955565396e-15
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -60.890449653825605,
          -60.90058618867046,
          -60.9741869052165,
          -61.18328402809565,
          -61.54047342337411,
          -61.985321245804094,
          -62.430393734426545,
          -62.793348465897296,
          -63.00013525762528
        ],
        "cartesian_polarizations_e_A2": [
          [
            -2.949334264690355e-17,
            -5.694950720386167e-17,
            -4.433652909830842e-17
          ],
          [
            3.0535545321304076e-17,
            -6.42115249009984e-18,
            -0.0010321450385684329
          ],
          [
            -1.9983855561179053e-17,
            1.8957688304104288e-17,
            -0.0019223212251995516
          ],
          [
            2.307106731059406e-17,
            -4.11259528532585e-17,
            -0.0026619368643839565
          ],
          [
            2.760486544264964e-19,
            -5.1522104503896335e-17,
            -0.003334242969308523
          ],
          [
            9.539059778630626e-18,
            -5.82490261601914e-17,
            -0.003895332368644086
          ],
          [
            -4.252665758462579e-18,
            -4.1202395144807304e-17,
            -0.004152560451754913
          ],
          [
            -4.327756574818044e-17,
            6.520527469113289e-17,
            -0.003960509361363232
          ],
          [
            4.819752800007992e-18,
            -1.60528812252496e-18,
            -0.0033448831077741666
          ]
        ],
        "raw_reduced_polarization": [
          [
            -1.6975606794381595e-15,
            -2.7941293328790662e-15,
            -2.069840726548127e-15
          ],
          [
            1.7575471754162056e-15,
            -3.1504277041857924e-16,
            -0.04818545519872549
          ],
          [
            -1.1502191470925304e-15,
            9.301262745691388e-16,
            -0.08974312699587783
          ],
          [
            1.3279110871906331e-15,
            -2.017773934347567e-15,
            -0.12427191405048318
          ],
          [
            1.5888648057850142e-17,
            -2.5278431816919338e-15,
            -0.15565837088372456
          ],
          [
            5.490436602211825e-16,
            -2.857887988797112e-15,
            -0.18185270123836392
          ],
          [
            -2.4477246478255856e-16,
            -2.0215244435192167e-15,
            -0.19386133550141474
          ],
          [
            -2.490944983600354e-15,
            3.1991843234172394e-15,
            -0.18489547424535532
          ],
          [
            2.774125312230261e-16,
            -7.876069260464481e-17,
            -0.15615510331587926
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -1.6975606794381595e-15,
            -2.7941293328790662e-15,
            -2.069840726548127e-15
          ],
          [
            1.7575471754162056e-15,
            -3.1504277041857944e-16,
            -0.04818545519872549
          ],
          [
            -1.1502191470925304e-15,
            9.301262745691388e-16,
            -0.08974312699587783
          ],
          [
            1.3279110871906331e-15,
            -2.0177739343475668e-15,
            -0.12427191405048318
          ],
          [
            1.5888648057850084e-17,
            -2.5278431816919338e-15,
            -0.15565837088372456
          ],
          [
            5.490436602211825e-16,
            -2.857887988797112e-15,
            -0.18185270123836392
          ],
          [
            -2.4477246478255856e-16,
            -2.0215244435192167e-15,
            -0.19386133550141474
          ],
          [
            -2.490944983600354e-15,
            3.1991843234172394e-15,
            -0.18489547424535532
          ],
          [
            2.7741253122302613e-16,
            -7.876069260464476e-17,
            -0.15615510331587926
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          -2.1201273893364363e-15,
          -7.14471997199278e-15,
          -0.15615510331588198
        ],
        "actual_opposite_endpoint_branch_residual": 7.941953832842746e-15
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            -6.829417700786953e-16,
            5.588258665758132e-16,
            0.15615510331587787
          ],
          [
            8.494616976648132e-16,
            -3.277945016021884e-15,
            0.18489547424535566
          ],
          [
            -9.129703372279002e-16,
            -1.5152057053465e-15,
            0.193861335501424
          ],
          [
            -4.771145200861104e-16,
            -1.8677535674815767e-15,
            0.18185270123836067
          ],
          [
            -2.851796904775026e-15,
            -2.7603747503342185e-15,
            0.15565837088372814
          ],
          [
            4.218593737283478e-15,
            3.34545418111158e-15,
            0.12427191405048299
          ],
          [
            -4.275629245157281e-16,
            -9.038727103675906e-16,
            0.08974312699587686
          ],
          [
            -3.0833093551719292e-15,
            2.325315686422847e-16,
            0.048185455198731054
          ],
          [
            -1.4015345797075658e-15,
            -3.2929470527084834e-15,
            -2.069840726548127e-15
          ],
          [
            1.7575471754162056e-15,
            -3.1504277041857924e-16,
            -0.04818545519872549
          ],
          [
            -1.1502191470925304e-15,
            9.301262745691388e-16,
            -0.08974312699587783
          ],
          [
            1.3279110871906331e-15,
            -2.017773934347567e-15,
            -0.12427191405048318
          ],
          [
            1.5888648057850142e-17,
            -2.5278431816919338e-15,
            -0.15565837088372456
          ],
          [
            5.490436602211825e-16,
            -2.857887988797112e-15,
            -0.18185270123836392
          ],
          [
            -2.4477246478255856e-16,
            -2.0215244435192167e-15,
            -0.19386133550141474
          ],
          [
            -2.490944983600354e-15,
            3.1991843234172394e-15,
            -0.18489547424535532
          ],
          [
            2.774125312230261e-16,
            -7.876069260464481e-17,
            -0.15615510331587926
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -6.829417700786953e-16,
            5.588258665758132e-16,
            0.15615510331587787
          ],
          [
            8.494616976648131e-16,
            -3.2779450160218838e-15,
            0.18489547424535566
          ],
          [
            -9.129703372279002e-16,
            -1.5152057053465e-15,
            0.193861335501424
          ],
          [
            -4.771145200861104e-16,
            -1.8677535674815767e-15,
            0.18185270123836067
          ],
          [
            -2.851796904775026e-15,
            -2.7603747503342185e-15,
            0.15565837088372814
          ],
          [
            4.218593737283478e-15,
            3.34545418111158e-15,
            0.12427191405048299
          ],
          [
            -4.275629245157282e-16,
            -9.038727103675908e-16,
            0.08974312699587686
          ],
          [
            -3.0833093551719292e-15,
            2.3253156864228476e-16,
            0.048185455198731054
          ],
          [
            -1.4015345797075658e-15,
            -3.2929470527084834e-15,
            -2.067790383364354e-15
          ],
          [
            1.7575471754162054e-15,
            -3.1504277041857904e-16,
            -0.04818545519872549
          ],
          [
            -1.1502191470925302e-15,
            9.301262745691388e-16,
            -0.08974312699587783
          ],
          [
            1.3279110871906333e-15,
            -2.0177739343475668e-15,
            -0.12427191405048318
          ],
          [
            1.5888648057850084e-17,
            -2.5278431816919338e-15,
            -0.15565837088372456
          ],
          [
            5.490436602211825e-16,
            -2.857887988797112e-15,
            -0.18185270123836392
          ],
          [
            -2.4477246478255856e-16,
            -2.0215244435192167e-15,
            -0.19386133550141474
          ],
          [
            -2.490944983600354e-15,
            3.1991843234172394e-15,
            -0.18489547424535532
          ],
          [
            2.7741253122302613e-16,
            -7.876069260464476e-17,
            -0.15615510331587926
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            -6.661338147750939e-16,
            5.551115123125783e-16,
            0.1561551033158779
          ],
          [
            8.881784197001252e-16,
            -3.2751579226442118e-15,
            0.18489547424535568
          ],
          [
            -8.881784197001252e-16,
            -1.4988010832439613e-15,
            0.19386133550142404
          ],
          [
            -4.996003610813204e-16,
            -1.887379141862766e-15,
            0.18185270123836061
          ],
          [
            -2.831068712794149e-15,
            -2.7755575615628914e-15,
            0.15565837088372814
          ],
          [
            4.218847493575595e-15,
            3.3306690738754696e-15,
            0.12427191405048299
          ],
          [
            -4.440892098500626e-16,
            -8.881784197001252e-16,
            0.08974312699587683
          ],
          [
            -3.1086244689504383e-15,
            2.220446049250313e-16,
            0.048185455198731075
          ],
          [
            -1.3877787807814457e-15,
            -3.2751579226442118e-15,
            -2.0539125955565396e-15
          ],
          [
            1.7763568394002505e-15,
            -3.3306690738754696e-16,
            -0.04818545519872547
          ],
          [
            -1.1657341758564144e-15,
            8.881784197001252e-16,
            -0.08974312699587783
          ],
          [
            1.3322676295501878e-15,
            -1.9984014443252818e-15,
            -0.12427191405048321
          ],
          [
            0.0,
            -2.55351295663786e-15,
            -0.15565837088372458
          ],
          [
            5.551115123125783e-16,
            -2.831068712794149e-15,
            -0.18185270123836395
          ],
          [
            -2.220446049250313e-16,
            -1.9984014443252818e-15,
            -0.1938613355014147
          ],
          [
            -2.4980018054066022e-15,
            3.219646771412954e-15,
            -0.18489547424535535
          ],
          [
            2.220446049250313e-16,
            -5.551115123125783e-17,
            -0.15615510331587923
          ]
        ]
      },
      "incoming_structure_ids": [
        "incoming_00_000",
        "incoming_00_001",
        "incoming_00_002",
        "incoming_00_003",
        "incoming_00_004",
        "incoming_00_005",
        "incoming_00_006",
        "incoming_00_007",
        "incoming_00_008"
      ],
      "reflected_structure_ids": [
        "reflected_00_001",
        "reflected_00_002",
        "reflected_00_003",
        "reflected_00_004",
        "reflected_00_005",
        "reflected_00_006",
        "reflected_00_007",
        "reflected_00_008"
      ],
      "positive_extension_structure_ids": [
        "extension_plus_00_000",
        "extension_plus_00_001",
        "extension_plus_00_002",
        "extension_plus_00_003"
      ],
      "negative_extension_structure_ids": [
        "extension_minus_00_000",
        "extension_minus_00_001",
        "extension_minus_00_002",
        "extension_minus_00_003"
      ],
      "extension": {
        "enabled": true,
        "fraction_beyond_polar_endpoint": 0.35,
        "images_per_side": 4,
        "construction": "continue fractional atomic displacements and symmetric log strain beyond +P; reflect these structures about N for the -P side",
        "positive_path_coordinates": [
          1.35,
          1.2625,
          1.175,
          1.0875
        ],
        "negative_path_coordinates": [
          -1.0875,
          -1.175,
          -1.2625,
          -1.35
        ]
      },
      "branch_coordinates": [
        1.35,
        1.2625,
        1.175,
        1.0875,
        1.0,
        0.875,
        0.75,
        0.625,
        0.5,
        0.375,
        0.25,
        0.125,
        0.0,
        -0.125,
        -0.25,
        -0.375,
        -0.5,
        -0.625,
        -0.75,
        -0.875,
        -1.0,
        -1.0875,
        -1.175,
        -1.2625,
        -1.35
      ],
      "parent": {
        "candidate_id": "inversion_parent_endpoint_00",
        "source": "same_species_inversion_center_projection_from_endpoint",
        "spacegroup": "Cmcm",
        "spacegroup_number": 63,
        "pointgroup": "mmm",
        "has_inversion": true,
        "is_polar_point_group": false,
        "nonpolar_parent_hypothesis": true,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.0
        ],
        "formal_class": [
          0.0,
          0.0,
          0.0
        ],
        "target_residual": 3.2248869032134036e-15,
        "parent_symmetrization_rmsd_A": 0.26151910790254485,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -60.89044965382565,
        "reduced_polarization": [
          -6.845121922873501e-16,
          -2.6253564201548273e-16,
          3.140447998900606e-15
        ],
        "cartesian_polarization_e_A2": [
          -1.1892683942111418e-17,
          -5.350960408416533e-18,
          6.72692165629507e-17
        ],
        "ranking_score": 0.2615191079025513
      }
    }
  ],
  "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": 116,
      "full_response": 35,
      "energy_polarization": 81
    },
    "model_evaluations_for_recovery_and_path_properties": {
      "total": 141,
      "full_response": 60,
      "energy_polarization": 81
    },
    "elapsed_seconds": 784.3859340100316
  }
}