{
  "schema": "ferrofinder.endpoint_parent_recovery.v4_variable_cell",
  "status": "complete",
  "input_atom_count": 48,
  "input_formula": "B4Li4O32S8",
  "input_spacegroup": "Pc",
  "input_pointgroup": "m",
  "input_is_polar_point_group": true,
  "input_energy_eV": -296.8004539334859,
  "input_cartesian_polarization_e_A2": [
    0.00021138887601962816,
    1.9144567654170686e-11,
    2.8222512350924526e-05
  ],
  "input_reduced_polarization": [
    0.01740923106281114,
    1.2792684433131697e-09,
    0.002101893465685687
  ],
  "input_formal_targets": [
    {
      "orbit_id": 0,
      "representative_formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ]
    },
    {
      "orbit_id": 1,
      "representative_formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.0
      ]
    },
    {
      "orbit_id": 2,
      "representative_formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.5
      ]
    },
    {
      "orbit_id": 3,
      "representative_formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.0
      ]
    },
    {
      "orbit_id": 4,
      "representative_formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.5
      ]
    },
    {
      "orbit_id": 5,
      "representative_formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        0.5,
        0.5,
        0.0
      ]
    },
    {
      "orbit_id": 6,
      "representative_formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.5
      ]
    },
    {
      "orbit_id": 7,
      "representative_formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "target_reduced_polarization": [
        0.5,
        0.5,
        0.5
      ]
    }
  ],
  "parent_candidates": [
    {
      "candidate_id": "inversion_parent_endpoint_00",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "P2_1/c",
      "spacegroup_number": 14,
      "pointgroup": "2/m",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 2.2399592020125218e-15,
      "parent_symmetrization_rmsd_A": 0.7408236895571569,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -247.62020840061584,
      "reduced_polarization": [
        1.3298582778326595e-15,
        -1.6121896211045652e-16,
        1.7952444495991497e-15
      ],
      "cartesian_polarization_e_A2": [
        1.5258580398857445e-17,
        -2.412681516058656e-18,
        2.4105079291072515e-17
      ],
      "ranking_score": 0.7408236895571614
    },
    {
      "candidate_id": "inversion_parent_endpoint_01",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "P2_1/c",
      "spacegroup_number": 14,
      "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": 3.761996981185872e-15,
      "parent_symmetrization_rmsd_A": 0.8658963951429081,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -248.50866228222458,
      "reduced_polarization": [
        -3.580187795505389e-15,
        9.83290426565577e-16,
        6.066436947585944e-16
      ],
      "cartesian_polarization_e_A2": [
        -4.403687163544898e-17,
        1.4715183661006398e-17,
        8.145517100387218e-18
      ],
      "ranking_score": 0.8658963951429156
    },
    {
      "candidate_id": "inversion_parent_endpoint_02",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "P-1",
      "spacegroup_number": 2,
      "pointgroup": "-1",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 4.3258423093067905e-15,
      "parent_symmetrization_rmsd_A": 0.8844585343688816,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -252.90991129020225,
      "reduced_polarization": [
        8.494000287477975e-16,
        -3.5275725605925337e-15,
        -2.3553477675083524e-15
      ],
      "cartesian_polarization_e_A2": [
        1.1650426059526483e-17,
        -5.2790993082229376e-17,
        -3.162569014293103e-17
      ],
      "ranking_score": 0.8844585343688902
    },
    {
      "candidate_id": "bec_projection_00",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Pc",
      "spacegroup_number": 7,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 1.0614069225092776e-05,
      "parent_symmetrization_rmsd_A": 0.0016445674257320963,
      "parent_cell_rmsd_A": 0.0024240795999934325,
      "energy_eV": -296.7964803550017,
      "reduced_polarization": [
        1.0413756341260064e-05,
        -1.0654899020166246e-12,
        -2.052350939758167e-06
      ],
      "cartesian_polarization_e_A2": [
        1.2824969610588397e-07,
        -1.5945677017105262e-14,
        -2.7600468644281793e-08
      ],
      "ranking_score": 0.5022718154641806
    },
    {
      "candidate_id": "inversion_parent_bec_00_00",
      "source": "same_species_inversion_center_projection_after_BEC",
      "spacegroup": "P2_1/c",
      "spacegroup_number": 14,
      "pointgroup": "2/m",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 2.219135186074992e-15,
      "parent_symmetrization_rmsd_A": 0.7408237455693079,
      "parent_cell_rmsd_A": 0.0024240795999934325,
      "energy_eV": -247.64041289582477,
      "reduced_polarization": [
        -1.782860313037651e-15,
        6.39047447702932e-17,
        -1.3198053878762658e-15
      ],
      "cartesian_polarization_e_A2": [
        -2.1040430996972863e-17,
        9.563832271351302e-19,
        -1.7714825684434795e-17
      ],
      "ranking_score": 0.7414297654693106
    },
    {
      "candidate_id": "inversion_parent_bec_00_01",
      "source": "same_species_inversion_center_projection_after_BEC",
      "spacegroup": "P2_1/c",
      "spacegroup_number": 14,
      "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": 3.28928954008312e-15,
      "parent_symmetrization_rmsd_A": 0.865896443080112,
      "parent_cell_rmsd_A": 0.0024240795999934325,
      "energy_eV": -248.4858259815903,
      "reduced_polarization": [
        1.1609599601234112e-15,
        -1.999201844365546e-15,
        2.339826838673296e-15
      ],
      "cartesian_polarization_e_A2": [
        1.2889437583889368e-17,
        -2.991957982162515e-17,
        3.141392861402379e-17
      ],
      "ranking_score": 0.8665024629801169
    },
    {
      "candidate_id": "bec_projection_01",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Pc",
      "spacegroup_number": 7,
      "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": 5.019059953305373e-05,
      "parent_symmetrization_rmsd_A": 0.04475321636727826,
      "parent_cell_rmsd_A": 0.06778862058084775,
      "energy_eV": -294.8950560447083,
      "reduced_polarization": [
        0.5000014742694793,
        -2.0955938880646123e-14,
        -5.016894269356148e-05
      ],
      "cartesian_polarization_e_A2": [
        0.006109528987822923,
        -8.636289895667533e-14,
        5.6042595090028676e-05
      ],
      "ranking_score": 0.5618007527115563
    },
    {
      "candidate_id": "bec_projection_02",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Pc",
      "spacegroup_number": 7,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.5
      ],
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_residual": 4.052994979556039e-05,
      "parent_symmetrization_rmsd_A": 0.05283523198001016,
      "parent_cell_rmsd_A": 0.03665471801210037,
      "energy_eV": -294.06136719909637,
      "reduced_polarization": [
        3.910392443654637e-05,
        -1.4003040520183627e-13,
        0.5000106564498822
      ],
      "cartesian_polarization_e_A2": [
        -0.0002890422003017108,
        -2.754656137810933e-13,
        0.006689618324254571
      ],
      "ranking_score": 0.5620799713826263
    },
    {
      "candidate_id": "bec_projection_03",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.0
      ],
      "formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_residual": 8.545164857719519e-06,
      "parent_symmetrization_rmsd_A": 0.06302375116994802,
      "parent_cell_rmsd_A": 0.03218467043037982,
      "energy_eV": -292.8750794082587,
      "reduced_polarization": [
        -3.8082778866163276e-07,
        0.4999916180117988,
        1.6177411523822954e-06
      ],
      "cartesian_polarization_e_A2": [
        -9.36282688671304e-06,
        0.007482780186501419,
        -2.597895076677001e-05
      ],
      "ranking_score": 0.5710870091072584
    },
    {
      "candidate_id": "bec_projection_04",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Pc",
      "spacegroup_number": 7,
      "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": 6.2105469197293976e-06,
      "parent_symmetrization_rmsd_A": 0.06822644935439084,
      "parent_cell_rmsd_A": 0.06481397092917529,
      "energy_eV": -292.11061345539645,
      "reduced_polarization": [
        0.5000041869700688,
        5.527918702492149e-14,
        0.49999541304298195
      ],
      "cartesian_polarization_e_A2": [
        0.005915513989315022,
        -7.59415609092395e-13,
        0.006728487301649973
      ],
      "ranking_score": 0.5844423631805241
    },
    {
      "candidate_id": "bec_projection_05",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.5,
        0.5,
        0.0
      ],
      "formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_residual": 0.00024025948905985388,
      "parent_symmetrization_rmsd_A": 0.07832159106924991,
      "parent_cell_rmsd_A": 0.07543694759968386,
      "energy_eV": -290.0983262460618,
      "reduced_polarization": [
        0.49998179627458333,
        0.4998792027876393,
        0.00020688470206891316
      ],
      "cartesian_polarization_e_A2": [
        0.006099615865057262,
        0.0074649066251932265,
        3.299675279013199e-05
      ],
      "ranking_score": 0.5976613469472906
    },
    {
      "candidate_id": "bec_projection_06",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.5
      ],
      "formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_residual": 0.0003393500130060346,
      "parent_symmetrization_rmsd_A": 0.08253782461528451,
      "parent_cell_rmsd_A": 0.0484611997604711,
      "energy_eV": -289.63214600819276,
      "reduced_polarization": [
        -0.0002679971811546988,
        0.4999480773896667,
        0.4997984063871138
      ],
      "cartesian_polarization_e_A2": [
        -0.0003014386413495759,
        0.007467793870721045,
        0.006660736217006672
      ],
      "ranking_score": 0.5953318245814143
    },
    {
      "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": 0.0004908966878220985,
      "parent_symmetrization_rmsd_A": 0.09370411618301706,
      "parent_cell_rmsd_A": 0.07285393325399958,
      "energy_eV": -286.88632825334923,
      "reduced_polarization": [
        0.5002691248359848,
        0.4996004906325595,
        0.500094570852265
      ],
      "cartesian_polarization_e_A2": [
        0.005909414401169282,
        0.007445893507687996,
        0.006703541447532922
      ],
      "ranking_score": 0.6128993928721611
    }
  ],
  "formal_branches": [
    {
      "orbit_id": 0,
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.0,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              0.01740923106281114,
              1.2792684433131697e-09,
              0.002101893465685687
            ],
            "branch_aligned_reduced_polarization": [
              0.01740923106281114,
              1.2792684433131697e-09,
              0.002101893465685687
            ],
            "target_residual": 0.017535657453869303,
            "energy_eV": -296.8004539334859,
            "max_atomic_step_A": 0.002744272256799064,
            "max_log_strain_component": 0.0003304599669314126,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.8441607878563389,
            "cell_principal_stretches": [
              1.0003157783359602,
              1.000029275752667,
              0.9996498623751087
            ],
            "cell_volume_ratio": 0.9999948048887274,
            "cell_rmsd_from_input_A": 0.0024240795999934325
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              1.0413756341260064e-05,
              -1.0654899020166246e-12,
              -2.052350939758167e-06
            ],
            "branch_aligned_reduced_polarization": [
              1.0413756341260064e-05,
              -1.0654899020166246e-12,
              -2.052350939758167e-06
            ],
            "target_residual": 1.0614069225092776e-05,
            "energy_eV": -296.7964803550017
          }
        ],
        "iterations": 1
      },
      "parent": {
        "candidate_id": "bec_projection_00",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Pc",
        "spacegroup_number": 7,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.0
        ],
        "formal_class": [
          0.0,
          0.0,
          0.0
        ],
        "target_residual": 1.0614069225092776e-05,
        "parent_symmetrization_rmsd_A": 0.0016445674257320963,
        "parent_cell_rmsd_A": 0.0024240795999934325,
        "energy_eV": -296.7964803550017,
        "reduced_polarization": [
          1.0413756341260064e-05,
          -1.0654899020166246e-12,
          -2.052350939758167e-06
        ],
        "cartesian_polarization_e_A2": [
          1.2824969610588397e-07,
          -1.5945677017105262e-14,
          -2.7600468644281793e-08
        ],
        "ranking_score": 0.5022718154641806
      },
      "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": [
          -296.800453933486,
          -296.8002761564542,
          -296.8000076107144,
          -296.7996481213895,
          -296.7991975129552,
          -296.798655609241,
          -296.7980222334285,
          -296.79729720805295,
          -296.7964803550017
        ],
        "cartesian_polarizations_e_A2": [
          [
            0.00021138887601964202,
            1.914455694925495e-11,
            2.8222512350922947e-05
          ],
          [
            0.00018496296776636766,
            1.6751585498810118e-11,
            2.4680447835762185e-05
          ],
          [
            0.0001585422855562849,
            1.4358016227228693e-11,
            2.11414748841879e-05
          ],
          [
            0.00013212683501101464,
            1.1963865569773897e-11,
            1.7605590691620513e-05
          ],
          [
            0.00010571662169013961,
            9.569091439129459e-12,
            1.4072792404348094e-05
          ],
          [
            7.931165109182206e-05,
            7.17376177248151e-12,
            1.0543077120440797e-05
          ],
          [
            5.2911928652825376e-05,
            4.777734300138043e-12,
            7.016441888696929e-06
          ],
          [
            2.6517459749191053e-05,
            2.3811667871932042e-12,
            3.492883708765354e-06
          ],
          [
            1.2824969611280688e-07,
            -1.5989606796105076e-14,
            -2.7600468598820986e-08
          ]
        ],
        "raw_reduced_polarization": [
          [
            0.017409231062812267,
            1.2792677279948016e-09,
            0.0021018934656855696
          ],
          [
            0.015233050168573178,
            1.1193527699459016e-09,
            0.001838657893731113
          ],
          [
            0.013057247961825063,
            9.594015956124857e-10,
            0.0015754919024048829
          ],
          [
            0.01088182492406941,
            7.994153026725431e-10,
            0.0013123953265496307
          ],
          [
            0.008706781531544146,
            6.393910782870672e-10,
            0.0010493679974225114
          ],
          [
            0.006532118255276176,
            4.793334615080158e-10,
            0.0007864097427622889
          ],
          [
            0.004357835561078608,
            3.192329453367181e-10,
            0.0005235203867099646
          ],
          [
            0.0021839339096056216,
            1.5910007110396111e-10,
            0.00026069974981702876
          ],
          [
            1.0413756341979234e-05,
            -1.0684252539073423e-12,
            -2.0523509363723645e-06
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            0.017409231062812267,
            1.2792677279948016e-09,
            0.0021018934656855696
          ],
          [
            0.015233050168573178,
            1.1193527699459016e-09,
            0.001838657893731113
          ],
          [
            0.013057247961825063,
            9.594015956124857e-10,
            0.0015754919024048829
          ],
          [
            0.01088182492406941,
            7.994153026725431e-10,
            0.0013123953265496307
          ],
          [
            0.008706781531544146,
            6.393910782870672e-10,
            0.0010493679974225114
          ],
          [
            0.006532118255276176,
            4.793334615080158e-10,
            0.0007864097427622889
          ],
          [
            0.004357835561078608,
            3.192329453367181e-10,
            0.0005235203867099646
          ],
          [
            0.0021839339096056216,
            1.5910007110396111e-10,
            0.00026069974981702876
          ],
          [
            1.0413756341979413e-05,
            -1.0684252539073458e-12,
            -2.0523509363723556e-06
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            0.017409231062812225,
            1.2792676917783297e-09,
            0.002101893465685567
          ],
          [
            0.015233050168573126,
            1.1193527216235566e-09,
            0.001838657893731166
          ],
          [
            0.013057247961825058,
            9.594015581981807e-10,
            0.001575491902404913
          ],
          [
            0.010881824924069416,
            7.994153117252267e-10,
            0.001312395326549587
          ],
          [
            0.008706781531544139,
            6.393910956248305e-10,
            0.0010493679974225012
          ],
          [
            0.00653211825527622,
            4.793334618113931e-10,
            0.0007864097427623395
          ],
          [
            0.004357835561078605,
            3.192329733892052e-10,
            0.0005235203867099969
          ],
          [
            0.0021839339096055843,
            1.591000664546982e-10,
            0.00026069974981701716
          ],
          [
            1.0413756342031455e-05,
            -1.0684231277480194e-12,
            -2.0523509363656878e-06
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -296.7964803550017,
          -296.79578611979815,
          -296.7950163205041,
          -296.7941708338343,
          -296.79324953613695,
          -296.79225230330655,
          -296.79117901077495,
          -296.7900295335113,
          -296.7888037460217
        ],
        "cartesian_polarizations_e_A2": [
          [
            1.2824969614595697e-07,
            -1.5971219513464062e-14,
            -2.7600468637826205e-08
          ],
          [
            -2.4634839255591375e-05,
            -2.3975744980509093e-12,
            -3.6508836525662877e-06
          ],
          [
            -4.9396014819250894e-05,
            -4.779546884453618e-12,
            -7.278963639350594e-06
          ],
          [
            -7.415528180588659e-05,
            -7.1618232326700566e-12,
            -1.0911839952038493e-05
          ],
          [
            -9.891264496523403e-05,
            -9.544344898576756e-12,
            -1.454951165269772e-05
          ],
          [
            -0.00012366810906996734,
            -1.192723430242386e-11,
            -1.8191977754474793e-05
          ],
          [
            -0.00014842167892720897,
            -1.431042213994048e-11,
            -2.183923725837019e-05
          ],
          [
            -0.00017317335937774739,
            -1.6693853640190923e-11,
            -2.549128915435533e-05
          ],
          [
            -0.0001979231552959943,
            -1.907761315960706e-11,
            -2.9148132420311972e-05
          ]
        ],
        "raw_reduced_polarization": [
          [
            1.0413756344564392e-05,
            -1.0671966307251967e-12,
            -2.0523509392764093e-06
          ],
          [
            -0.0020302409415862825,
            -1.601967490325899e-10,
            -0.0002724260804468649
          ],
          [
            -0.004070696869935383,
            -3.193545973494797e-10,
            -0.0005430065780459693
          ],
          [
            -0.006110954387444003,
            -4.785363896887299e-10,
            -0.0008137938318681216
          ],
          [
            -0.008151013846286744,
            -6.377382085444324e-10,
            -0.0010847877956560858
          ],
          [
            -0.010190875600352771,
            -7.969682351774138e-10,
            -0.0013559884194530307
          ],
          [
            -0.012230540006311607,
            -9.562218397829438e-10,
            -0.0016273956523410213
          ],
          [
            -0.01427000742355288,
            -1.115495363611621e-09,
            -0.0018990094425236535
          ],
          [
            -0.01630927821417944,
            -1.274794444548587e-09,
            -0.0021708297372465455
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            1.0413756344564392e-05,
            -1.0671966307251967e-12,
            -2.0523509392764093e-06
          ],
          [
            -0.0020302409415862825,
            -1.601967490325899e-10,
            -0.0002724260804468649
          ],
          [
            -0.004070696869935383,
            -3.193545973494797e-10,
            -0.0005430065780459693
          ],
          [
            -0.006110954387444003,
            -4.785363896887299e-10,
            -0.0008137938318681216
          ],
          [
            -0.008151013846286744,
            -6.377382085444324e-10,
            -0.0010847877956560858
          ],
          [
            -0.010190875600352771,
            -7.969682351774138e-10,
            -0.0013559884194530307
          ],
          [
            -0.012230540006311607,
            -9.562218397829438e-10,
            -0.0016273956523410213
          ],
          [
            -0.01427000742355288,
            -1.115495363611621e-09,
            -0.0018990094425236535
          ],
          [
            -0.01630927821417944,
            -1.274794444548587e-09,
            -0.0021708297372465455
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          -0.01738840345280578,
          -1.2814046265411408e-09,
          -0.0021060045982365188
        ],
        "actual_opposite_endpoint_branch_residual": 0.00108107057091016
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            0.017409231062812267,
            1.2792677279948016e-09,
            0.0021018934656855696
          ],
          [
            0.015233050168573178,
            1.1193527699459016e-09,
            0.001838657893731113
          ],
          [
            0.013057247961825063,
            9.594015956124857e-10,
            0.0015754919024048829
          ],
          [
            0.01088182492406941,
            7.994153026725431e-10,
            0.0013123953265496307
          ],
          [
            0.008706781531544146,
            6.393910782870672e-10,
            0.0010493679974225114
          ],
          [
            0.006532118255276176,
            4.793334615080158e-10,
            0.0007864097427622889
          ],
          [
            0.004357835561078608,
            3.192329453367181e-10,
            0.0005235203867099646
          ],
          [
            0.0021839339096056216,
            1.5910007110396111e-10,
            0.00026069974981702876
          ],
          [
            1.0413756341979234e-05,
            -1.0684252539073423e-12,
            -2.0523509363723645e-06
          ],
          [
            -0.0020302409415862825,
            -1.601967490325899e-10,
            -0.0002724260804468649
          ],
          [
            -0.004070696869935383,
            -3.193545973494797e-10,
            -0.0005430065780459693
          ],
          [
            -0.006110954387444003,
            -4.785363896887299e-10,
            -0.0008137938318681216
          ],
          [
            -0.008151013846286744,
            -6.377382085444324e-10,
            -0.0010847877956560858
          ],
          [
            -0.010190875600352771,
            -7.969682351774138e-10,
            -0.0013559884194530307
          ],
          [
            -0.012230540006311607,
            -9.562218397829438e-10,
            -0.0016273956523410213
          ],
          [
            -0.01427000742355288,
            -1.115495363611621e-09,
            -0.0018990094425236535
          ],
          [
            -0.01630927821417944,
            -1.274794444548587e-09,
            -0.0021708297372465455
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            0.017409231062812267,
            1.2792677279948016e-09,
            0.0021018934656855696
          ],
          [
            0.015233050168573178,
            1.1193527699459016e-09,
            0.001838657893731113
          ],
          [
            0.013057247961825063,
            9.594015956124857e-10,
            0.0015754919024048829
          ],
          [
            0.01088182492406941,
            7.994153026725431e-10,
            0.0013123953265496307
          ],
          [
            0.008706781531544146,
            6.393910782870672e-10,
            0.0010493679974225114
          ],
          [
            0.006532118255276176,
            4.793334615080158e-10,
            0.0007864097427622889
          ],
          [
            0.004357835561078608,
            3.192329453367181e-10,
            0.0005235203867099646
          ],
          [
            0.0021839339096056216,
            1.5910007110396111e-10,
            0.00026069974981702876
          ],
          [
            1.0413756341979413e-05,
            -1.0684252539073458e-12,
            -2.0523509363723556e-06
          ],
          [
            -0.0020302409415862825,
            -1.601967490325899e-10,
            -0.0002724260804468649
          ],
          [
            -0.004070696869935383,
            -3.193545973494797e-10,
            -0.0005430065780459693
          ],
          [
            -0.006110954387444003,
            -4.785363896887299e-10,
            -0.0008137938318681216
          ],
          [
            -0.008151013846286744,
            -6.377382085444324e-10,
            -0.0010847877956560858
          ],
          [
            -0.010190875600352771,
            -7.969682351774138e-10,
            -0.0013559884194530307
          ],
          [
            -0.012230540006311607,
            -9.562218397829438e-10,
            -0.0016273956523410213
          ],
          [
            -0.01427000742355288,
            -1.115495363611621e-09,
            -0.0018990094425236535
          ],
          [
            -0.01630927821417944,
            -1.274794444548587e-09,
            -0.0021708297372465455
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            0.017409231062812225,
            1.2792676917783297e-09,
            0.002101893465685567
          ],
          [
            0.015233050168573126,
            1.1193527216235566e-09,
            0.001838657893731166
          ],
          [
            0.013057247961825058,
            9.594015581981807e-10,
            0.001575491902404913
          ],
          [
            0.010881824924069416,
            7.994153117252267e-10,
            0.001312395326549587
          ],
          [
            0.008706781531544139,
            6.393910956248305e-10,
            0.0010493679974225012
          ],
          [
            0.00653211825527622,
            4.793334618113931e-10,
            0.0007864097427623395
          ],
          [
            0.004357835561078605,
            3.192329733892052e-10,
            0.0005235203867099969
          ],
          [
            0.0021839339096055843,
            1.591000664546982e-10,
            0.00026069974981701716
          ],
          [
            1.0413756342031455e-05,
            -1.0684231277480194e-12,
            -2.0523509363656878e-06
          ],
          [
            -0.00203024094158627,
            -1.6019674475842294e-10,
            -0.00027242608044686367
          ],
          [
            -0.004070696869935386,
            -3.193545983215529e-10,
            -0.000543006578045957
          ],
          [
            -0.006110954387444023,
            -4.785363771908635e-10,
            -0.000813793831868137
          ],
          [
            -0.008151013846286748,
            -6.377381955857686e-10,
            -0.0010847877956560725
          ],
          [
            -0.010190875600352756,
            -7.969682136454992e-10,
            -0.001355988419453058
          ],
          [
            -0.01223054000631163,
            -9.56221823944503e-10,
            -0.001627395652341046
          ],
          [
            -0.014270007423552888,
            -1.115495362746799e-09,
            -0.001899009442523636
          ],
          [
            -0.016309278214179435,
            -1.2747944366786612e-09,
            -0.002170829737246527
          ]
        ]
      },
      "incoming_structure_ids": [
        "incoming_00_000",
        "incoming_00_001",
        "incoming_00_002",
        "incoming_00_003",
        "incoming_00_004",
        "incoming_00_005",
        "incoming_00_006",
        "incoming_00_007",
        "incoming_00_008"
      ],
      "reflected_structure_ids": [
        "reflected_00_001",
        "reflected_00_002",
        "reflected_00_003",
        "reflected_00_004",
        "reflected_00_005",
        "reflected_00_006",
        "reflected_00_007",
        "reflected_00_008"
      ]
    },
    {
      "orbit_id": 1,
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.0,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              0.01740923106281114,
              1.2792684433131697e-09,
              0.002101893465685687
            ],
            "branch_aligned_reduced_polarization": [
              0.017409231062811115,
              1.2792684433131697e-09,
              0.002101893465685687
            ],
            "target_residual": 0.4825953462472761,
            "energy_eV": -296.8004539334859,
            "max_atomic_step_A": 0.07656963451768649,
            "max_log_strain_component": 0.009421852595741043,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.8441607878563389,
            "cell_principal_stretches": [
              1.010039277709797,
              0.9991927424303577,
              0.9911467287237813
            ],
            "cell_volume_ratio": 1.0002889827516983,
            "cell_rmsd_from_input_A": 0.06875499599938018
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.5070574124607208,
              -1.563458379586752e-11,
              -0.000832192789408707
            ],
            "branch_aligned_reduced_polarization": [
              0.5070574124607208,
              -1.563458379586752e-11,
              -0.000832192789408707
            ],
            "target_residual": 0.007106308146955125,
            "energy_eV": -294.84076545438916,
            "max_atomic_step_A": 0.001054247169108968,
            "max_log_strain_component": 0.00013276371305878738,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.8441607878563389,
            "cell_principal_stretches": [
              1.009896855963629,
              0.9992037799550516,
              0.9912698029773973
            ],
            "cell_volume_ratio": 1.0002831772709855,
            "cell_rmsd_from_input_A": 0.06778862058084775
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.5000014742694793,
              -2.0955938880646123e-14,
              -5.016894269356148e-05
            ],
            "branch_aligned_reduced_polarization": [
              0.5000014742694793,
              -2.0955938880646123e-14,
              -5.016894269356148e-05
            ],
            "target_residual": 5.019059953305373e-05,
            "energy_eV": -294.8950560447083
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_01",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Pc",
        "spacegroup_number": 7,
        "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": 5.019059953305373e-05,
        "parent_symmetrization_rmsd_A": 0.04475321636727826,
        "parent_cell_rmsd_A": 0.06778862058084775,
        "energy_eV": -294.8950560447083,
        "reduced_polarization": [
          0.5000014742694793,
          -2.0955938880646123e-14,
          -5.016894269356148e-05
        ],
        "cartesian_polarization_e_A2": [
          0.006109528987822923,
          -8.636289895667533e-14,
          5.6042595090028676e-05
        ],
        "ranking_score": 0.5618007527115563
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 2,
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.0,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              0.01740923106281114,
              1.2792684433131697e-09,
              0.002101893465685687
            ],
            "branch_aligned_reduced_polarization": [
              0.01740923106281114,
              1.2792684433131697e-09,
              0.002101893465685678
            ],
            "target_residual": 0.4982023743587075,
            "energy_eV": -296.8004539334859,
            "max_atomic_step_A": 0.08464973980651351,
            "max_log_strain_component": 0.004945805289994793,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.8441607878563389,
            "cell_principal_stretches": [
              1.0044188881820617,
              0.9999966418563385,
              0.9944043198695214
            ],
            "cell_volume_ratio": 0.998795127257995,
            "cell_rmsd_from_input_A": 0.03721780995625243
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.002673605262379999,
              1.3245026378964362e-10,
              0.5059122228651923
            ],
            "branch_aligned_reduced_polarization": [
              -0.002673605262379999,
              1.3245026378964362e-10,
              0.5059122228651923
            ],
            "target_residual": 0.006488647340295898,
            "energy_eV": -293.99557366240253,
            "max_atomic_step_A": 0.0010143389401786424,
            "max_log_strain_component": 7.548764271041038e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.8441607878563389,
            "cell_principal_stretches": [
              1.0043509643556596,
              0.9999926137764048,
              0.994490502195415
            ],
            "cell_volume_ratio": 0.9988101174331614,
            "cell_rmsd_from_input_A": 0.03665471801210037
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              3.910392443654637e-05,
              -1.4003040520183627e-13,
              0.5000106564498822
            ],
            "branch_aligned_reduced_polarization": [
              3.910392443654637e-05,
              -1.4003040520183627e-13,
              0.5000106564498822
            ],
            "target_residual": 4.052994979556039e-05,
            "energy_eV": -294.06136719909637
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_02",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Pc",
        "spacegroup_number": 7,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.5
        ],
        "formal_class": [
          0.0,
          0.0,
          0.5
        ],
        "target_residual": 4.052994979556039e-05,
        "parent_symmetrization_rmsd_A": 0.05283523198001016,
        "parent_cell_rmsd_A": 0.03665471801210037,
        "energy_eV": -294.06136719909637,
        "reduced_polarization": [
          3.910392443654637e-05,
          -1.4003040520183627e-13,
          0.5000106564498822
        ],
        "cartesian_polarization_e_A2": [
          -0.0002890422003017108,
          -2.754656137810933e-13,
          0.006689618324254571
        ],
        "ranking_score": 0.5620799713826263
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 3,
      "formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.5,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              0.01740923106281114,
              1.2792684433131697e-09,
              0.002101893465685687
            ],
            "branch_aligned_reduced_polarization": [
              0.01740923106281114,
              1.279268468934447e-09,
              0.002101893465685687
            ],
            "target_residual": 0.5003074035061553,
            "energy_eV": -296.8004539334859,
            "max_atomic_step_A": 0.09028941542904653,
            "max_log_strain_component": 0.003482351010431525,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.8441607878563389,
            "cell_principal_stretches": [
              1.00363686078574,
              1.0001612346485322,
              0.996210518032725
            ],
            "cell_volume_ratio": 0.9999948048187026,
            "cell_rmsd_from_input_A": 0.03228349710775987
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.00363010603382773,
              0.5011910945364493,
              -0.0019052521025924836
            ],
            "branch_aligned_reduced_polarization": [
              -0.00363010603382773,
              0.5011910945364493,
              -0.0019052521025924836
            ],
            "target_residual": 0.004269234309103319,
            "energy_eV": -292.8613592789487,
            "max_atomic_step_A": 0.0006403453083686005,
            "max_log_strain_component": 6.0346814914020766e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.8441607878563389,
            "cell_principal_stretches": [
              1.0036333517926144,
              1.000141075968497,
              0.9962316355279686
            ],
            "cell_volume_ratio": 0.9999923505166427,
            "cell_rmsd_from_input_A": 0.03218467043037982
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -3.8082778866163276e-07,
              0.4999916180117988,
              1.6177411523822954e-06
            ],
            "branch_aligned_reduced_polarization": [
              -3.8082778866163276e-07,
              0.4999916180117988,
              1.6177411523822954e-06
            ],
            "target_residual": 8.545164857719519e-06,
            "energy_eV": -292.8750794082587
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_03",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.5,
          0.0
        ],
        "formal_class": [
          0.0,
          0.5,
          0.0
        ],
        "target_residual": 8.545164857719519e-06,
        "parent_symmetrization_rmsd_A": 0.06302375116994802,
        "parent_cell_rmsd_A": 0.03218467043037982,
        "energy_eV": -292.8750794082587,
        "reduced_polarization": [
          -3.8082778866163276e-07,
          0.4999916180117988,
          1.6177411523822954e-06
        ],
        "cartesian_polarization_e_A2": [
          -9.36282688671304e-06,
          0.007482780186501419,
          -2.597895076677001e-05
        ],
        "ranking_score": 0.5710870091072584
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 4,
      "formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.0,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              0.01740923106281114,
              1.2792684433131697e-09,
              0.002101893465685687
            ],
            "branch_aligned_reduced_polarization": [
              0.017409231062811115,
              1.2792684433131697e-09,
              0.002101893465685678
            ],
            "target_residual": 0.6933948188109301,
            "energy_eV": -296.8004539334859,
            "max_atomic_step_A": 0.09909512117153509,
            "max_log_strain_component": 0.007257004848269756,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.8441607878563389,
            "cell_principal_stretches": [
              1.0088075778949588,
              0.9991601358325722,
              0.9911986968016612
            ],
            "cell_volume_ratio": 0.999088952200531,
            "cell_rmsd_from_input_A": 0.06468734665694656
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.49917455989466725,
              5.854911697600897e-11,
              0.49813070759927836
            ],
            "branch_aligned_reduced_polarization": [
              0.49917455989466725,
              5.854911697600897e-11,
              0.49813070759927836
            ],
            "target_residual": 0.0020434298243119193,
            "energy_eV": -292.139490808784,
            "max_atomic_step_A": 0.00034075727216280154,
            "max_log_strain_component": 1.8507451264679105e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.8441607878563389,
            "cell_principal_stretches": [
              1.008823539174356,
              0.9991585799852353,
              0.9911806579995569
            ],
            "cell_volume_ratio": 0.9990850212953917,
            "cell_rmsd_from_input_A": 0.06481397092917529
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.5000041869700688,
              5.527918702492149e-14,
              0.49999541304298195
            ],
            "branch_aligned_reduced_polarization": [
              0.5000041869700688,
              5.527918702492149e-14,
              0.49999541304298195
            ],
            "target_residual": 6.2105469197293976e-06,
            "energy_eV": -292.11061345539645
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_04",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Pc",
        "spacegroup_number": 7,
        "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": 6.2105469197293976e-06,
        "parent_symmetrization_rmsd_A": 0.06822644935439084,
        "parent_cell_rmsd_A": 0.06481397092917529,
        "energy_eV": -292.11061345539645,
        "reduced_polarization": [
          0.5000041869700688,
          5.527918702492149e-14,
          0.49999541304298195
        ],
        "cartesian_polarization_e_A2": [
          0.005915513989315022,
          -7.59415609092395e-13,
          0.006728487301649973
        ],
        "ranking_score": 0.5844423631805241
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 5,
      "formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.5,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.5,
        0.5,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              0.01740923106281114,
              1.2792684433131697e-09,
              0.002101893465685687
            ],
            "branch_aligned_reduced_polarization": [
              0.017409231062811115,
              1.279268468934447e-09,
              0.002101893465685687
            ],
            "target_residual": 0.6949088191556212,
            "energy_eV": -296.8004539334859,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.0085322956144811,
            "step_scale": 0.9055857684137952,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.8441607878563389,
            "cell_principal_stretches": [
              1.0099444127520418,
              0.998745306759375,
              0.9916568482595395
            ],
            "cell_volume_ratio": 1.0002616950340966,
            "cell_rmsd_from_input_A": 0.06881545895746644
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.4592163797894105,
              0.444954454610111,
              -0.0014340848593710977
            ],
            "branch_aligned_reduced_polarization": [
              0.4592163797894105,
              0.444954454610111,
              -0.0014340848593710977
            ],
            "target_residual": 0.06852278704296703,
            "energy_eV": -291.4412005493607,
            "max_atomic_step_A": 0.013481647706884599,
            "max_log_strain_component": 0.0007638516603361119,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.8441607878563389,
            "cell_principal_stretches": [
              1.0108944414919154,
              0.9986020034259839,
              0.9908852764656197
            ],
            "cell_volume_ratio": 1.0002800723424632,
            "cell_rmsd_from_input_A": 0.07543694759968386
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.49998179627458333,
              0.4998792027876393,
              0.00020688470206891316
            ],
            "branch_aligned_reduced_polarization": [
              0.49998179627458333,
              0.4998792027876393,
              0.00020688470206891316
            ],
            "target_residual": 0.00024025948905985388,
            "energy_eV": -290.0983262460618
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_05",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.5,
          0.5,
          0.0
        ],
        "formal_class": [
          0.5,
          0.5,
          0.0
        ],
        "target_residual": 0.00024025948905985388,
        "parent_symmetrization_rmsd_A": 0.07832159106924991,
        "parent_cell_rmsd_A": 0.07543694759968386,
        "energy_eV": -290.0983262460618,
        "reduced_polarization": [
          0.49998179627458333,
          0.4998792027876393,
          0.00020688470206891316
        ],
        "cartesian_polarization_e_A2": [
          0.006099615865057262,
          0.0074649066251932265,
          3.299675279013199e-05
        ],
        "ranking_score": 0.5976613469472906
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 6,
      "formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.5,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              0.01740923106281114,
              1.2792684433131697e-09,
              0.002101893465685687
            ],
            "branch_aligned_reduced_polarization": [
              0.01740923106281114,
              1.279268468934447e-09,
              0.002101893465685678
            ],
            "target_residual": 0.7058368115488064,
            "energy_eV": -296.8004539334859,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.0042077071767951165,
            "step_scale": 0.8507628031209993,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.8441607878563389,
            "cell_principal_stretches": [
              1.0037853770796128,
              1.0015284285104922,
              0.9936888284124041
            ],
            "cell_volume_ratio": 0.9989748468274899,
            "cell_rmsd_from_input_A": 0.04175825301352966
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.0016519000649132323,
              0.42628995094121747,
              0.427127670934281
            ],
            "branch_aligned_reduced_polarization": [
              -0.0016519000649132323,
              0.42628995094121747,
              0.427127670934281
            ],
            "target_residual": 0.10366424865658856,
            "energy_eV": -291.67278703807483,
            "max_atomic_step_A": 0.02156274302451632,
            "max_log_strain_component": 0.0007050566704362708,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.8441607878563389,
            "cell_principal_stretches": [
              1.0043772366925374,
              1.0017849219491834,
              0.9926830462071461
            ],
            "cell_volume_ratio": 0.998807872477121,
            "cell_rmsd_from_input_A": 0.0484611997604711
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.0002679971811546988,
              0.4999480773896667,
              0.4997984063871138
            ],
            "branch_aligned_reduced_polarization": [
              -0.0002679971811546988,
              0.4999480773896667,
              0.4997984063871138
            ],
            "target_residual": 0.0003393500130060346,
            "energy_eV": -289.63214600819276
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_06",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.5,
          0.5
        ],
        "formal_class": [
          0.0,
          0.5,
          0.5
        ],
        "target_residual": 0.0003393500130060346,
        "parent_symmetrization_rmsd_A": 0.08253782461528451,
        "parent_cell_rmsd_A": 0.0484611997604711,
        "energy_eV": -289.63214600819276,
        "reduced_polarization": [
          -0.0002679971811546988,
          0.4999480773896667,
          0.4997984063871138
        ],
        "cartesian_polarization_e_A2": [
          -0.0003014386413495759,
          0.007467793870721045,
          0.006660736217006672
        ],
        "ranking_score": 0.5953318245814143
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 7,
      "formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.5,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.5,
        0.5,
        0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              0.01740923106281114,
              1.2792684433131697e-09,
              0.002101893465685687
            ],
            "branch_aligned_reduced_polarization": [
              0.017409231062811115,
              1.279268468934447e-09,
              0.002101893465685678
            ],
            "target_residual": 0.8548662898223173,
            "energy_eV": -296.8004539334859,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.005794880480607174,
            "step_scale": 0.7985223393257594,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.8441607878563389,
            "cell_principal_stretches": [
              1.0076259347430334,
              0.9993318360080169,
              0.9923727952347089
            ],
            "cell_volume_ratio": 0.9992724411319989,
            "cell_rmsd_from_input_A": 0.057698496111944
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.4011522246212077,
              0.3932383718582096,
              0.3969039922651393
            ],
            "branch_aligned_reduced_polarization": [
              0.4011522246212077,
              0.3932383718582096,
              0.3969039922651393
            ],
            "target_residual": 0.17831913736805866,
            "energy_eV": -290.79744491174677,
            "max_atomic_step_A": 0.034207504828403894,
            "max_log_strain_component": 0.0015070772272455716,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.8441607878563389,
            "cell_principal_stretches": [
              1.0096361508240126,
              0.9991581956307797,
              0.9903816222542111
            ],
            "cell_volume_ratio": 0.9990833476308207,
            "cell_rmsd_from_input_A": 0.07285393325399958
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.5002691248359848,
              0.4996004906325595,
              0.500094570852265
            ],
            "branch_aligned_reduced_polarization": [
              0.5002691248359848,
              0.4996004906325595,
              0.500094570852265
            ],
            "target_residual": 0.0004908966878220985,
            "energy_eV": -286.88632825334923
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_07",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.5,
          0.5,
          0.5
        ],
        "formal_class": [
          0.5,
          0.5,
          0.5
        ],
        "target_residual": 0.0004908966878220985,
        "parent_symmetrization_rmsd_A": 0.09370411618301706,
        "parent_cell_rmsd_A": 0.07285393325399958,
        "energy_eV": -286.88632825334923,
        "reduced_polarization": [
          0.5002691248359848,
          0.4996004906325595,
          0.500094570852265
        ],
        "cartesian_polarization_e_A2": [
          0.005909414401169282,
          0.007445893507687996,
          0.006703541447532922
        ],
        "ranking_score": 0.6128993928721611
      },
      "branch_status": "awaiting_branch_sampling"
    }
  ],
  "sampled_polarization_branches": [
    {
      "orbit_id": 0,
      "candidate_id": "bec_projection_00",
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "construction": "MACEField-BEC-parent plus variable-cell P-N-P path and symmetric log-strain continuation beyond both polar endpoints",
      "geometry_diagnostics": {
        "collision_aware": false,
        "permutations_tested": 1,
        "selected_order": [
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          10,
          11,
          12,
          13,
          14,
          15,
          16,
          17,
          18,
          19,
          20,
          21,
          22,
          23,
          24,
          25,
          26,
          27,
          28,
          29,
          30,
          31,
          32,
          33,
          34,
          35,
          36,
          37,
          38,
          39,
          40,
          41,
          42,
          43,
          44,
          45,
          46,
          47
        ],
        "endpoint_rmsd_A": 0.0016445674257320963,
        "minimum_distance_A_by_image": [
          1.4396771318494863,
          1.4399357095085883,
          1.4401943791746434,
          1.4404531407954961,
          1.4402827819397472,
          1.4398550506680543,
          1.4394273434032234,
          1.438999660147562,
          1.438572000903382
        ],
        "minimum_distance_A": 1.438572000903382,
        "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": [
          638.4740117642427,
          638.4735971453581,
          638.4731825267438,
          638.4727679083976,
          638.4723532903207,
          638.4719386725136,
          638.4715240549763,
          638.4711094377077,
          638.4706948207066
        ],
        "cell_deformation_log_strain_norm": 0.0004724201718614622
      },
      "parent_reduced_polarization": [
        1.0413756341979234e-05,
        -1.0684252539073423e-12,
        -2.0523509363723645e-06
      ],
      "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": [
          -296.800453933486,
          -296.8002761564542,
          -296.8000076107144,
          -296.7996481213895,
          -296.7991975129552,
          -296.798655609241,
          -296.7980222334285,
          -296.79729720805295,
          -296.7964803550017
        ],
        "cartesian_polarizations_e_A2": [
          [
            0.00021138887601964202,
            1.914455694925495e-11,
            2.8222512350922947e-05
          ],
          [
            0.00018496296776636766,
            1.6751585498810118e-11,
            2.4680447835762185e-05
          ],
          [
            0.0001585422855562849,
            1.4358016227228693e-11,
            2.11414748841879e-05
          ],
          [
            0.00013212683501101464,
            1.1963865569773897e-11,
            1.7605590691620513e-05
          ],
          [
            0.00010571662169013961,
            9.569091439129459e-12,
            1.4072792404348094e-05
          ],
          [
            7.931165109182206e-05,
            7.17376177248151e-12,
            1.0543077120440797e-05
          ],
          [
            5.2911928652825376e-05,
            4.777734300138043e-12,
            7.016441888696929e-06
          ],
          [
            2.6517459749191053e-05,
            2.3811667871932042e-12,
            3.492883708765354e-06
          ],
          [
            1.2824969611280688e-07,
            -1.5989606796105076e-14,
            -2.7600468598820986e-08
          ]
        ],
        "raw_reduced_polarization": [
          [
            0.017409231062812267,
            1.2792677279948016e-09,
            0.0021018934656855696
          ],
          [
            0.015233050168573178,
            1.1193527699459016e-09,
            0.001838657893731113
          ],
          [
            0.013057247961825063,
            9.594015956124857e-10,
            0.0015754919024048829
          ],
          [
            0.01088182492406941,
            7.994153026725431e-10,
            0.0013123953265496307
          ],
          [
            0.008706781531544146,
            6.393910782870672e-10,
            0.0010493679974225114
          ],
          [
            0.006532118255276176,
            4.793334615080158e-10,
            0.0007864097427622889
          ],
          [
            0.004357835561078608,
            3.192329453367181e-10,
            0.0005235203867099646
          ],
          [
            0.0021839339096056216,
            1.5910007110396111e-10,
            0.00026069974981702876
          ],
          [
            1.0413756341979234e-05,
            -1.0684252539073423e-12,
            -2.0523509363723645e-06
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            0.017409231062812267,
            1.2792677279948016e-09,
            0.0021018934656855696
          ],
          [
            0.015233050168573178,
            1.1193527699459016e-09,
            0.001838657893731113
          ],
          [
            0.013057247961825063,
            9.594015956124857e-10,
            0.0015754919024048829
          ],
          [
            0.01088182492406941,
            7.994153026725431e-10,
            0.0013123953265496307
          ],
          [
            0.008706781531544146,
            6.393910782870672e-10,
            0.0010493679974225114
          ],
          [
            0.006532118255276176,
            4.793334615080158e-10,
            0.0007864097427622889
          ],
          [
            0.004357835561078608,
            3.192329453367181e-10,
            0.0005235203867099646
          ],
          [
            0.0021839339096056216,
            1.5910007110396111e-10,
            0.00026069974981702876
          ],
          [
            1.0413756341979413e-05,
            -1.0684252539073458e-12,
            -2.0523509363723556e-06
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            0.017409231062812225,
            1.2792676917783297e-09,
            0.002101893465685567
          ],
          [
            0.015233050168573126,
            1.1193527216235566e-09,
            0.001838657893731166
          ],
          [
            0.013057247961825058,
            9.594015581981807e-10,
            0.001575491902404913
          ],
          [
            0.010881824924069416,
            7.994153117252267e-10,
            0.001312395326549587
          ],
          [
            0.008706781531544139,
            6.393910956248305e-10,
            0.0010493679974225012
          ],
          [
            0.00653211825527622,
            4.793334618113931e-10,
            0.0007864097427623395
          ],
          [
            0.004357835561078605,
            3.192329733892052e-10,
            0.0005235203867099969
          ],
          [
            0.0021839339096055843,
            1.591000664546982e-10,
            0.00026069974981701716
          ],
          [
            1.0413756342031455e-05,
            -1.0684231277480194e-12,
            -2.0523509363656878e-06
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -296.7964803550017,
          -296.79578611979815,
          -296.7950163205041,
          -296.7941708338343,
          -296.79324953613695,
          -296.79225230330655,
          -296.79117901077495,
          -296.7900295335113,
          -296.7888037460217
        ],
        "cartesian_polarizations_e_A2": [
          [
            1.2824969614595697e-07,
            -1.5971219513464062e-14,
            -2.7600468637826205e-08
          ],
          [
            -2.4634839255591375e-05,
            -2.3975744980509093e-12,
            -3.6508836525662877e-06
          ],
          [
            -4.9396014819250894e-05,
            -4.779546884453618e-12,
            -7.278963639350594e-06
          ],
          [
            -7.415528180588659e-05,
            -7.1618232326700566e-12,
            -1.0911839952038493e-05
          ],
          [
            -9.891264496523403e-05,
            -9.544344898576756e-12,
            -1.454951165269772e-05
          ],
          [
            -0.00012366810906996734,
            -1.192723430242386e-11,
            -1.8191977754474793e-05
          ],
          [
            -0.00014842167892720897,
            -1.431042213994048e-11,
            -2.183923725837019e-05
          ],
          [
            -0.00017317335937774739,
            -1.6693853640190923e-11,
            -2.549128915435533e-05
          ],
          [
            -0.0001979231552959943,
            -1.907761315960706e-11,
            -2.9148132420311972e-05
          ]
        ],
        "raw_reduced_polarization": [
          [
            1.0413756344564392e-05,
            -1.0671966307251967e-12,
            -2.0523509392764093e-06
          ],
          [
            -0.0020302409415862825,
            -1.601967490325899e-10,
            -0.0002724260804468649
          ],
          [
            -0.004070696869935383,
            -3.193545973494797e-10,
            -0.0005430065780459693
          ],
          [
            -0.006110954387444003,
            -4.785363896887299e-10,
            -0.0008137938318681216
          ],
          [
            -0.008151013846286744,
            -6.377382085444324e-10,
            -0.0010847877956560858
          ],
          [
            -0.010190875600352771,
            -7.969682351774138e-10,
            -0.0013559884194530307
          ],
          [
            -0.012230540006311607,
            -9.562218397829438e-10,
            -0.0016273956523410213
          ],
          [
            -0.01427000742355288,
            -1.115495363611621e-09,
            -0.0018990094425236535
          ],
          [
            -0.01630927821417944,
            -1.274794444548587e-09,
            -0.0021708297372465455
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            1.0413756344564392e-05,
            -1.0671966307251967e-12,
            -2.0523509392764093e-06
          ],
          [
            -0.0020302409415862825,
            -1.601967490325899e-10,
            -0.0002724260804468649
          ],
          [
            -0.004070696869935383,
            -3.193545973494797e-10,
            -0.0005430065780459693
          ],
          [
            -0.006110954387444003,
            -4.785363896887299e-10,
            -0.0008137938318681216
          ],
          [
            -0.008151013846286744,
            -6.377382085444324e-10,
            -0.0010847877956560858
          ],
          [
            -0.010190875600352771,
            -7.969682351774138e-10,
            -0.0013559884194530307
          ],
          [
            -0.012230540006311607,
            -9.562218397829438e-10,
            -0.0016273956523410213
          ],
          [
            -0.01427000742355288,
            -1.115495363611621e-09,
            -0.0018990094425236535
          ],
          [
            -0.01630927821417944,
            -1.274794444548587e-09,
            -0.0021708297372465455
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          -0.01738840345280578,
          -1.2814046265411408e-09,
          -0.0021060045982365188
        ],
        "actual_opposite_endpoint_branch_residual": 0.00108107057091016
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            0.017409231062812267,
            1.2792677279948016e-09,
            0.0021018934656855696
          ],
          [
            0.015233050168573178,
            1.1193527699459016e-09,
            0.001838657893731113
          ],
          [
            0.013057247961825063,
            9.594015956124857e-10,
            0.0015754919024048829
          ],
          [
            0.01088182492406941,
            7.994153026725431e-10,
            0.0013123953265496307
          ],
          [
            0.008706781531544146,
            6.393910782870672e-10,
            0.0010493679974225114
          ],
          [
            0.006532118255276176,
            4.793334615080158e-10,
            0.0007864097427622889
          ],
          [
            0.004357835561078608,
            3.192329453367181e-10,
            0.0005235203867099646
          ],
          [
            0.0021839339096056216,
            1.5910007110396111e-10,
            0.00026069974981702876
          ],
          [
            1.0413756341979234e-05,
            -1.0684252539073423e-12,
            -2.0523509363723645e-06
          ],
          [
            -0.0020302409415862825,
            -1.601967490325899e-10,
            -0.0002724260804468649
          ],
          [
            -0.004070696869935383,
            -3.193545973494797e-10,
            -0.0005430065780459693
          ],
          [
            -0.006110954387444003,
            -4.785363896887299e-10,
            -0.0008137938318681216
          ],
          [
            -0.008151013846286744,
            -6.377382085444324e-10,
            -0.0010847877956560858
          ],
          [
            -0.010190875600352771,
            -7.969682351774138e-10,
            -0.0013559884194530307
          ],
          [
            -0.012230540006311607,
            -9.562218397829438e-10,
            -0.0016273956523410213
          ],
          [
            -0.01427000742355288,
            -1.115495363611621e-09,
            -0.0018990094425236535
          ],
          [
            -0.01630927821417944,
            -1.274794444548587e-09,
            -0.0021708297372465455
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            0.017409231062812267,
            1.2792677279948016e-09,
            0.0021018934656855696
          ],
          [
            0.015233050168573178,
            1.1193527699459016e-09,
            0.001838657893731113
          ],
          [
            0.013057247961825063,
            9.594015956124857e-10,
            0.0015754919024048829
          ],
          [
            0.01088182492406941,
            7.994153026725431e-10,
            0.0013123953265496307
          ],
          [
            0.008706781531544146,
            6.393910782870672e-10,
            0.0010493679974225114
          ],
          [
            0.006532118255276176,
            4.793334615080158e-10,
            0.0007864097427622889
          ],
          [
            0.004357835561078608,
            3.192329453367181e-10,
            0.0005235203867099646
          ],
          [
            0.0021839339096056216,
            1.5910007110396111e-10,
            0.00026069974981702876
          ],
          [
            1.0413756341979413e-05,
            -1.0684252539073458e-12,
            -2.0523509363723556e-06
          ],
          [
            -0.0020302409415862825,
            -1.601967490325899e-10,
            -0.0002724260804468649
          ],
          [
            -0.004070696869935383,
            -3.193545973494797e-10,
            -0.0005430065780459693
          ],
          [
            -0.006110954387444003,
            -4.785363896887299e-10,
            -0.0008137938318681216
          ],
          [
            -0.008151013846286744,
            -6.377382085444324e-10,
            -0.0010847877956560858
          ],
          [
            -0.010190875600352771,
            -7.969682351774138e-10,
            -0.0013559884194530307
          ],
          [
            -0.012230540006311607,
            -9.562218397829438e-10,
            -0.0016273956523410213
          ],
          [
            -0.01427000742355288,
            -1.115495363611621e-09,
            -0.0018990094425236535
          ],
          [
            -0.01630927821417944,
            -1.274794444548587e-09,
            -0.0021708297372465455
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            0.017409231062812225,
            1.2792676917783297e-09,
            0.002101893465685567
          ],
          [
            0.015233050168573126,
            1.1193527216235566e-09,
            0.001838657893731166
          ],
          [
            0.013057247961825058,
            9.594015581981807e-10,
            0.001575491902404913
          ],
          [
            0.010881824924069416,
            7.994153117252267e-10,
            0.001312395326549587
          ],
          [
            0.008706781531544139,
            6.393910956248305e-10,
            0.0010493679974225012
          ],
          [
            0.00653211825527622,
            4.793334618113931e-10,
            0.0007864097427623395
          ],
          [
            0.004357835561078605,
            3.192329733892052e-10,
            0.0005235203867099969
          ],
          [
            0.0021839339096055843,
            1.591000664546982e-10,
            0.00026069974981701716
          ],
          [
            1.0413756342031455e-05,
            -1.0684231277480194e-12,
            -2.0523509363656878e-06
          ],
          [
            -0.00203024094158627,
            -1.6019674475842294e-10,
            -0.00027242608044686367
          ],
          [
            -0.004070696869935386,
            -3.193545983215529e-10,
            -0.000543006578045957
          ],
          [
            -0.006110954387444023,
            -4.785363771908635e-10,
            -0.000813793831868137
          ],
          [
            -0.008151013846286748,
            -6.377381955857686e-10,
            -0.0010847877956560725
          ],
          [
            -0.010190875600352756,
            -7.969682136454992e-10,
            -0.001355988419453058
          ],
          [
            -0.01223054000631163,
            -9.56221823944503e-10,
            -0.001627395652341046
          ],
          [
            -0.014270007423552888,
            -1.115495362746799e-09,
            -0.001899009442523636
          ],
          [
            -0.016309278214179435,
            -1.2747944366786612e-09,
            -0.002170829737246527
          ]
        ]
      },
      "incoming_structure_ids": [
        "incoming_00_000",
        "incoming_00_001",
        "incoming_00_002",
        "incoming_00_003",
        "incoming_00_004",
        "incoming_00_005",
        "incoming_00_006",
        "incoming_00_007",
        "incoming_00_008"
      ],
      "reflected_structure_ids": [
        "reflected_00_001",
        "reflected_00_002",
        "reflected_00_003",
        "reflected_00_004",
        "reflected_00_005",
        "reflected_00_006",
        "reflected_00_007",
        "reflected_00_008"
      ],
      "positive_extension_structure_ids": [
        "extension_plus_00_000",
        "extension_plus_00_001",
        "extension_plus_00_002",
        "extension_plus_00_003"
      ],
      "negative_extension_structure_ids": [
        "extension_minus_00_000",
        "extension_minus_00_001",
        "extension_minus_00_002",
        "extension_minus_00_003"
      ],
      "extension": {
        "enabled": true,
        "fraction_beyond_polar_endpoint": 0.35,
        "images_per_side": 4,
        "construction": "continue fractional atomic displacements and symmetric log strain beyond +P; reflect these structures about N for the -P side",
        "positive_path_coordinates": [
          1.35,
          1.2625,
          1.175,
          1.0875
        ],
        "negative_path_coordinates": [
          -1.0875,
          -1.175,
          -1.2625,
          -1.35
        ]
      },
      "branch_coordinates": [
        1.35,
        1.2625,
        1.175,
        1.0875,
        1.0,
        0.875,
        0.75,
        0.625,
        0.5,
        0.375,
        0.25,
        0.125,
        0.0,
        -0.125,
        -0.25,
        -0.375,
        -0.5,
        -0.625,
        -0.75,
        -0.875,
        -1.0,
        -1.0875,
        -1.175,
        -1.2625,
        -1.35
      ],
      "parent": {
        "candidate_id": "bec_projection_00",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Pc",
        "spacegroup_number": 7,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.0
        ],
        "formal_class": [
          0.0,
          0.0,
          0.0
        ],
        "target_residual": 1.0614069225092776e-05,
        "parent_symmetrization_rmsd_A": 0.0016445674257320963,
        "parent_cell_rmsd_A": 0.0024240795999934325,
        "energy_eV": -296.7964803550017,
        "reduced_polarization": [
          1.0413756341260064e-05,
          -1.0654899020166246e-12,
          -2.052350939758167e-06
        ],
        "cartesian_polarization_e_A2": [
          1.2824969610588397e-07,
          -1.5945677017105262e-14,
          -2.7600468644281793e-08
        ],
        "ranking_score": 0.5022718154641806
      }
    }
  ],
  "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": 51,
      "full_response": 16,
      "energy_polarization": 35
    },
    "model_evaluations_for_recovery_and_path_properties": {
      "total": 76,
      "full_response": 41,
      "energy_polarization": 35
    },
    "elapsed_seconds": 1219.9871016109828
  }
}
