{
  "schema": "ferrofinder.endpoint_parent_recovery.v4_variable_cell",
  "status": "complete",
  "input_atom_count": 18,
  "input_formula": "C2O8Rb8",
  "input_spacegroup": "C2",
  "input_pointgroup": "2",
  "input_is_polar_point_group": true,
  "input_energy_eV": -85.44155677438647,
  "input_cartesian_polarization_e_A2": [
    6.7176007350566514e-18,
    0.009073558875155992,
    4.7004699358247646e-18
  ],
  "input_reduced_polarization": [
    2.462925964832928e-16,
    0.5687382178046861,
    4.92116957903835e-16
  ],
  "input_formal_targets": [
    {
      "orbit_id": 0,
      "representative_formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.0
      ]
    },
    {
      "orbit_id": 1,
      "representative_formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        1.0,
        0.0
      ]
    },
    {
      "orbit_id": 2,
      "representative_formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.5
      ]
    },
    {
      "orbit_id": 3,
      "representative_formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        0.5,
        0.5,
        0.0
      ]
    },
    {
      "orbit_id": 4,
      "representative_formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        1.0,
        0.5
      ]
    },
    {
      "orbit_id": 5,
      "representative_formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        0.5,
        1.0,
        0.0
      ]
    },
    {
      "orbit_id": 6,
      "representative_formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "target_reduced_polarization": [
        0.5,
        0.5,
        0.5
      ]
    },
    {
      "orbit_id": 7,
      "representative_formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        0.5,
        1.0,
        0.5
      ]
    }
  ],
  "parent_candidates": [
    {
      "candidate_id": "inversion_parent_endpoint_00",
      "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": 2.50512270446389e-15,
      "parent_symmetrization_rmsd_A": 0.661660315765908,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -75.9083982573983,
      "reduced_polarization": [
        2.9360829727797427e-16,
        1.3463266204316646e-15,
        2.092089520863545e-15
      ],
      "cartesian_polarization_e_A2": [
        7.994500048331882e-18,
        2.14790803101466e-17,
        3.020144462703156e-17
      ],
      "ranking_score": 0.661660315765913
    },
    {
      "candidate_id": "bec_projection_00",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "C2",
      "spacegroup_number": 5,
      "pointgroup": "2",
      "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": 0.00042505726923225406,
      "parent_symmetrization_rmsd_A": 0.017729192576264288,
      "parent_cell_rmsd_A": 0.05070439085021173,
      "energy_eV": -85.39948775093241,
      "reduced_polarization": [
        -5.96524764791139e-15,
        0.49957494273076775,
        5.459601481328834e-15
      ],
      "cartesian_polarization_e_A2": [
        -1.4302312606958464e-16,
        0.007976257639912379,
        2.2857070574347893e-16
      ],
      "ranking_score": 0.5312554048272817
    },
    {
      "candidate_id": "inversion_parent_bec_00_00",
      "source": "same_species_inversion_center_projection_after_BEC",
      "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,
        0.5,
        0.0
      ],
      "formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_residual": 0.4999999999999989,
      "parent_symmetrization_rmsd_A": 0.6616835235121503,
      "parent_cell_rmsd_A": 0.05070439085021173,
      "energy_eV": -75.84930117521728,
      "reduced_polarization": [
        1.0575550990261582e-15,
        -1.134482169844011e-15,
        -9.316190692496879e-16
      ],
      "cartesian_polarization_e_A2": [
        2.870078764675399e-17,
        -1.8113242479896378e-17,
        -2.944049866857755e-17
      ],
      "ranking_score": 1.674359621224701
    },
    {
      "candidate_id": "bec_projection_01",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "C2",
      "spacegroup_number": 5,
      "pointgroup": "2",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        1.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 1.5213305232242291e-06,
      "parent_symmetrization_rmsd_A": 0.11736302980686317,
      "parent_cell_rmsd_A": 0.35344288185848105,
      "energy_eV": -84.89705824429619,
      "reduced_polarization": [
        -6.925454792771557e-16,
        0.9999984786694768,
        -1.6610220493697095e-15
      ],
      "cartesian_polarization_e_A2": [
        -3.2987233936609627e-16,
        0.015871455490664897,
        -7.122535275214297e-16
      ],
      "ranking_score": 0.7057267929325299
    },
    {
      "candidate_id": "bec_projection_02",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.5
      ],
      "formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_residual": 0.00018818512463983288,
      "parent_symmetrization_rmsd_A": 0.12693224594406716,
      "parent_cell_rmsd_A": 0.2955354687230023,
      "energy_eV": -84.66538229133074,
      "reduced_polarization": [
        0.00016943780066044854,
        0.49995698762541985,
        0.5000696735852102
      ],
      "cartesian_polarization_e_A2": [
        -0.0002824584215616174,
        0.008051355174302064,
        0.008231248100161813
      ],
      "ranking_score": 0.7011924833740975
    },
    {
      "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": [
        0.5,
        0.5,
        0.0
      ],
      "formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_residual": 0.0007628628170199787,
      "parent_symmetrization_rmsd_A": 0.17270169554479992,
      "parent_cell_rmsd_A": 0.682462629422843,
      "energy_eV": -82.31339117739263,
      "reduced_polarization": [
        0.49938122113818295,
        0.49957210048464845,
        0.00012638988298896854
      ],
      "cartesian_polarization_e_A2": [
        0.014307712686063843,
        0.009223611436895278,
        -0.007498199340319199
      ],
      "ranking_score": 0.8448430785345507
    },
    {
      "candidate_id": "bec_projection_04",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        1.0,
        0.5
      ],
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_residual": 0.0006789068380030381,
      "parent_symmetrization_rmsd_A": 0.17152586585428148,
      "parent_cell_rmsd_A": 0.5303814903280799,
      "energy_eV": -83.8577365714812,
      "reduced_polarization": [
        -0.00032194699918101466,
        0.9995907827947554,
        0.49956433280667756
      ],
      "cartesian_polarization_e_A2": [
        -0.000904592029562756,
        0.01599119821833995,
        0.008425071524467576
      ],
      "ranking_score": 0.8054790521123075
    },
    {
      "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,
        1.0,
        0.0
      ],
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_residual": 0.06363126278310152,
      "parent_symmetrization_rmsd_A": 0.2389417768729702,
      "parent_cell_rmsd_A": 0.8282976013967653,
      "energy_eV": -81.56479725629285,
      "reduced_polarization": [
        0.48070572981009624,
        0.9438168514148455,
        0.022806195567642653
      ],
      "cartesian_polarization_e_A2": [
        0.015095136435161824,
        0.016719989256791835,
        -0.007802606793695256
      ],
      "ranking_score": 1.0732787027883646
    },
    {
      "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,
        0.5
      ],
      "formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "target_residual": 4.201162297889245e-05,
      "parent_symmetrization_rmsd_A": 0.18573099415140232,
      "parent_cell_rmsd_A": 0.4615821866265416,
      "energy_eV": -82.49677757001454,
      "reduced_polarization": [
        0.5000347830845738,
        0.49997732053876087,
        0.5000063840058547
      ],
      "cartesian_polarization_e_A2": [
        0.013803039183036358,
        0.008159998563801485,
        0.0008360676059852858
      ],
      "ranking_score": 0.8012105640539955
    },
    {
      "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,
        1.0,
        0.5
      ],
      "formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_residual": 0.0008991987813058828,
      "parent_symmetrization_rmsd_A": 0.2273738805921654,
      "parent_cell_rmsd_A": 0.6734619142670615,
      "energy_eV": -81.25065681169755,
      "reduced_polarization": [
        0.4995577617498375,
        0.9992175501270506,
        0.5000274949943931
      ],
      "cartesian_polarization_e_A2": [
        0.014304706729834775,
        0.016205264770186103,
        -9.469942226680451e-05
      ],
      "ranking_score": 0.8975377567215426
    }
  ],
  "formal_branches": [
    {
      "orbit_id": 0,
      "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": [
              2.462925964832928e-16,
              0.5687382178046861,
              4.92116957903835e-16
            ],
            "branch_aligned_reduced_polarization": [
              2.462925964832928e-16,
              0.5687382178046861,
              4.92116957903835e-16
            ],
            "target_residual": 0.06873821780468614,
            "energy_eV": -85.44155677438647,
            "max_atomic_step_A": 0.01639760534940119,
            "max_log_strain_component": 0.0040132019507524985,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.577357747347821,
            "cell_principal_stretches": [
              1.0037070105599213,
              1.0014718392540318,
              0.9955424082567256
            ],
            "cell_volume_ratio": 1.0007036046749935,
            "cell_rmsd_from_input_A": 0.05070439085021173
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -5.96524764791139e-15,
              0.49957494273076775,
              5.459601481328834e-15
            ],
            "branch_aligned_reduced_polarization": [
              -5.96524764791139e-15,
              0.49957494273076775,
              5.459601481328834e-15
            ],
            "target_residual": 0.00042505726923225406,
            "energy_eV": -85.39948775093241
          }
        ],
        "iterations": 1
      },
      "parent": {
        "candidate_id": "bec_projection_00",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "C2",
        "spacegroup_number": 5,
        "pointgroup": "2",
        "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": 0.00042505726923225406,
        "parent_symmetrization_rmsd_A": 0.017729192576264288,
        "parent_cell_rmsd_A": 0.05070439085021173,
        "energy_eV": -85.39948775093241,
        "reduced_polarization": [
          -5.96524764791139e-15,
          0.49957494273076775,
          5.459601481328834e-15
        ],
        "cartesian_polarization_e_A2": [
          -1.4302312606958464e-16,
          0.007976257639912379,
          2.2857070574347893e-16
        ],
        "ranking_score": 0.5312554048272817
      },
      "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": [
          -85.44155677438647,
          -85.43784373965381,
          -85.43368399515413,
          -85.42908018283948,
          -85.42403487578049,
          -85.41855057818464,
          -85.41262972538485,
          -85.40627468380816,
          -85.39948775093242
        ],
        "cartesian_polarizations_e_A2": [
          [
            7.272774349524144e-18,
            0.009073558875156026,
            4.77449308442043e-18
          ],
          [
            -8.69695529304453e-19,
            0.008937384477140042,
            3.10869891325847e-18
          ],
          [
            -1.7022330718848264e-17,
            0.008800921586244435,
            6.905145461167578e-17
          ],
          [
            -7.148750358601803e-17,
            0.008664173132938206,
            5.905489426671054e-17
          ],
          [
            -6.576494112264959e-17,
            0.008527142155012869,
            1.0618586836680975e-16
          ],
          [
            -1.0057174384321352e-16,
            0.008389831799971261,
            1.8434761801388008e-16
          ],
          [
            -1.0126575104697895e-16,
            0.008252245327315761,
            1.1719083080066824e-16
          ],
          [
            -1.62898688372888e-16,
            0.008114386110700592,
            2.205272434330514e-16
          ],
          [
            -1.6072071226671322e-16,
            0.007976257639912374,
            2.7694780657073955e-16
          ]
        ],
        "raw_reduced_polarization": [
          [
            2.666409704629409e-16,
            0.5687382178046884,
            5.135379586144961e-16
          ],
          [
            -1.2882547426061775e-16,
            0.560148958406346,
            -4.0170963385552887e-16
          ],
          [
            -8.160947665457127e-16,
            0.5515432620405861,
            2.594813216843572e-15
          ],
          [
            -2.9054306734359837e-15,
            0.5429213173052932,
            -2.008416756037406e-16
          ],
          [
            -2.7873775031943013e-15,
            0.5342833194514103,
            2.343578176009409e-15
          ],
          [
            -4.157185604360034e-15,
            0.525629470529393,
            5.573650574693849e-15
          ],
          [
            -4.262317742753365e-15,
            0.516959979529276,
            9.688879162284791e-16
          ],
          [
            -6.617383673397199e-15,
            0.5082750625121437,
            4.961949943440096e-15
          ],
          [
            -6.621197351543133e-15,
            0.4995749427307674,
            7.881218076274104e-15
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            2.666409704629409e-16,
            0.5687382178046884,
            5.135379586144961e-16
          ],
          [
            -1.2882547426061772e-16,
            0.560148958406346,
            -4.017096338555288e-16
          ],
          [
            -8.160947665457127e-16,
            0.5515432620405861,
            2.594813216843572e-15
          ],
          [
            -2.9054306734359837e-15,
            0.5429213173052932,
            -2.0084167560374051e-16
          ],
          [
            -2.7873775031943013e-15,
            0.5342833194514103,
            2.343578176009409e-15
          ],
          [
            -4.157185604360034e-15,
            0.525629470529393,
            5.573650574693849e-15
          ],
          [
            -4.262317742753365e-15,
            0.516959979529276,
            9.688879162284791e-16
          ],
          [
            -6.617383673397199e-15,
            0.5082750625121437,
            4.961949943440096e-15
          ],
          [
            -6.621197351543133e-15,
            0.4995749427307674,
            7.881218076274104e-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": [
          [
            2.220446049250313e-16,
            -0.43126178219531175,
            5.551115123125783e-16
          ],
          [
            -1.1102230246251565e-16,
            -0.43985104159365385,
            -3.885780586188048e-16
          ],
          [
            -8.326672684688674e-16,
            -0.44845673795941376,
            2.55351295663786e-15
          ],
          [
            -2.886579864025407e-15,
            -0.45707868269470664,
            -2.220446049250313e-16
          ],
          [
            -2.7755575615628914e-15,
            -0.4657166805485897,
            2.3314683517128287e-15
          ],
          [
            -4.163336342344337e-15,
            -0.47437052947060687,
            5.551115123125783e-15
          ],
          [
            -4.274358644806853e-15,
            -0.48304002047072414,
            9.992007221626409e-16
          ],
          [
            -6.6058269965196814e-15,
            -0.4917249374878563,
            4.9960036108132044e-15
          ],
          [
            -6.6058269965196814e-15,
            0.4995749427307674,
            7.882583474838611e-15
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -85.39948775093244,
          -85.40418029049852,
          -85.40855462991098,
          -85.41261094197814,
          -85.41634938650284,
          -85.41977011073419,
          -85.42287324696701,
          -85.42565891624758,
          -85.4281272312007
        ],
        "cartesian_polarizations_e_A2": [
          [
            -1.3832596108100505e-16,
            0.00797625763991233,
            2.780203875523837e-16
          ],
          [
            -1.1969576647926105e-16,
            0.007874679968492093,
            2.1542278862027698e-16
          ],
          [
            -1.3139577998862802e-16,
            0.007772720604923211,
            3.0118931325095983e-16
          ],
          [
            4.820488586636278e-17,
            0.007670385835045862,
            3.123143871710166e-16
          ],
          [
            3.710955608777358e-17,
            0.00756768208415649,
            2.6109884078905103e-16
          ],
          [
            1.0284654048516413e-16,
            0.007464615911997793,
            3.0892814049672073e-16
          ],
          [
            9.728632056489585e-17,
            0.007361194007255163,
            3.7537939741738433e-16
          ],
          [
            1.3826308499921004e-16,
            0.00725742318160803,
            3.1494080656939977e-16
          ],
          [
            2.5863688119325553e-16,
            0.00715331036338775,
            3.409136108573378e-16
          ]
        ],
        "raw_reduced_polarization": [
          [
            -5.799056441683183e-15,
            0.49957494273076464,
            8.623815964228479e-15
          ],
          [
            -5.01277178903573e-15,
            0.493260167638593,
            6.0631199506424166e-15
          ],
          [
            -5.353573422535484e-15,
            0.48692026538611094,
            1.1488507040296055e-14
          ],
          [
            1.331451051872704e-15,
            0.4805556227295431,
            1.813532255819672e-14
          ],
          [
            1.0197023194574204e-15,
            0.4741666353127654,
            1.5181811964169543e-14
          ],
          [
            3.5185278031640805e-15,
            0.4677537073575927,
            2.0605254616026624e-14
          ],
          [
            3.401367254621785e-15,
            0.46131725132295304,
            2.4994141772690852e-14
          ],
          [
            4.990327637781313e-15,
            0.45485768753597144,
            2.3019849760790115e-14
          ],
          [
            9.48585240645858e-15,
            0.4483754437981754,
            2.8738380607803684e-14
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -5.799056441683183e-15,
            0.49957494273076464,
            8.623815964228479e-15
          ],
          [
            -5.01277178903573e-15,
            0.493260167638593,
            6.0631199506424166e-15
          ],
          [
            -5.353573422535484e-15,
            0.48692026538611094,
            1.1488507040296055e-14
          ],
          [
            1.3314510518727043e-15,
            0.4805556227295431,
            1.813532255819672e-14
          ],
          [
            1.0197023194574204e-15,
            0.4741666353127654,
            1.5181811964169543e-14
          ],
          [
            3.5185278031640805e-15,
            0.4677537073575927,
            2.0605254616026624e-14
          ],
          [
            3.401367254621785e-15,
            0.46131725132295304,
            2.4994141772690852e-14
          ],
          [
            4.990327637781313e-15,
            0.45485768753597144,
            2.3019849760790115e-14
          ],
          [
            9.48585240645858e-15,
            0.4483754437981754,
            2.8738380607803684e-14
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          -1.203607983132663e-14,
          0.4311787094543055,
          2.3616168021489007e-14
        ],
        "actual_opposite_endpoint_branch_residual": 0.017196734343869924
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            2.666409704629409e-16,
            0.5687382178046884,
            5.135379586144961e-16
          ],
          [
            -1.2882547426061775e-16,
            0.560148958406346,
            -4.0170963385552887e-16
          ],
          [
            -8.160947665457127e-16,
            0.5515432620405861,
            2.594813216843572e-15
          ],
          [
            -2.9054306734359837e-15,
            0.5429213173052932,
            -2.008416756037406e-16
          ],
          [
            -2.7873775031943013e-15,
            0.5342833194514103,
            2.343578176009409e-15
          ],
          [
            -4.157185604360034e-15,
            0.525629470529393,
            5.573650574693849e-15
          ],
          [
            -4.262317742753365e-15,
            0.516959979529276,
            9.688879162284791e-16
          ],
          [
            -6.617383673397199e-15,
            0.5082750625121437,
            4.961949943440096e-15
          ],
          [
            -6.621197351543133e-15,
            0.4995749427307674,
            7.881218076274104e-15
          ],
          [
            -5.01277178903573e-15,
            0.493260167638593,
            6.0631199506424166e-15
          ],
          [
            -5.353573422535484e-15,
            0.48692026538611094,
            1.1488507040296055e-14
          ],
          [
            1.331451051872704e-15,
            0.4805556227295431,
            1.813532255819672e-14
          ],
          [
            1.0197023194574204e-15,
            0.4741666353127654,
            1.5181811964169543e-14
          ],
          [
            3.5185278031640805e-15,
            0.4677537073575927,
            2.0605254616026624e-14
          ],
          [
            3.401367254621785e-15,
            0.46131725132295304,
            2.4994141772690852e-14
          ],
          [
            4.990327637781313e-15,
            0.45485768753597144,
            2.3019849760790115e-14
          ],
          [
            9.48585240645858e-15,
            0.4483754437981754,
            2.8738380607803684e-14
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            2.666409704629409e-16,
            0.5687382178046884,
            5.135379586144961e-16
          ],
          [
            -1.2882547426061772e-16,
            0.560148958406346,
            -4.017096338555288e-16
          ],
          [
            -8.160947665457127e-16,
            0.5515432620405861,
            2.594813216843572e-15
          ],
          [
            -2.9054306734359837e-15,
            0.5429213173052932,
            -2.0084167560374051e-16
          ],
          [
            -2.7873775031943013e-15,
            0.5342833194514103,
            2.343578176009409e-15
          ],
          [
            -4.157185604360034e-15,
            0.525629470529393,
            5.573650574693849e-15
          ],
          [
            -4.262317742753365e-15,
            0.516959979529276,
            9.688879162284791e-16
          ],
          [
            -6.617383673397199e-15,
            0.5082750625121437,
            4.961949943440096e-15
          ],
          [
            -6.621197351543133e-15,
            0.4995749427307674,
            7.881218076274104e-15
          ],
          [
            -5.01277178903573e-15,
            0.493260167638593,
            6.0631199506424166e-15
          ],
          [
            -5.353573422535484e-15,
            0.48692026538611094,
            1.1488507040296055e-14
          ],
          [
            1.3314510518727043e-15,
            0.4805556227295431,
            1.813532255819672e-14
          ],
          [
            1.0197023194574204e-15,
            0.4741666353127654,
            1.5181811964169543e-14
          ],
          [
            3.5185278031640805e-15,
            0.4677537073575927,
            2.0605254616026624e-14
          ],
          [
            3.401367254621785e-15,
            0.46131725132295304,
            2.4994141772690852e-14
          ],
          [
            4.990327637781313e-15,
            0.45485768753597144,
            2.3019849760790115e-14
          ],
          [
            9.48585240645858e-15,
            0.4483754437981754,
            2.8738380607803684e-14
          ]
        ],
        "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": [
          [
            2.220446049250313e-16,
            -0.43126178219531175,
            5.551115123125783e-16
          ],
          [
            -1.1102230246251565e-16,
            -0.43985104159365385,
            -3.885780586188048e-16
          ],
          [
            -8.326672684688674e-16,
            -0.44845673795941376,
            2.55351295663786e-15
          ],
          [
            -2.886579864025407e-15,
            -0.45707868269470664,
            -2.220446049250313e-16
          ],
          [
            -2.7755575615628914e-15,
            -0.4657166805485897,
            2.3314683517128287e-15
          ],
          [
            -4.163336342344337e-15,
            -0.47437052947060687,
            5.551115123125783e-15
          ],
          [
            -4.274358644806853e-15,
            -0.48304002047072414,
            9.992007221626409e-16
          ],
          [
            -6.6058269965196814e-15,
            -0.4917249374878563,
            4.9960036108132044e-15
          ],
          [
            -6.6058269965196814e-15,
            0.4995749427307674,
            7.882583474838611e-15
          ],
          [
            -4.9960036108132044e-15,
            0.49326016763859304,
            6.106226635438361e-15
          ],
          [
            -5.329070518200751e-15,
            0.4869202653861109,
            1.1435297153639112e-14
          ],
          [
            1.3322676295501878e-15,
            0.4805556227295431,
            1.8096635301390052e-14
          ],
          [
            9.992007221626409e-16,
            0.47416663531276537,
            1.5210055437364645e-14
          ],
          [
            3.552713678800501e-15,
            0.4677537073575927,
            2.0650148258027912e-14
          ],
          [
            3.4416913763379853e-15,
            0.4613172513229531,
            2.4980018054066022e-14
          ],
          [
            4.9960036108132044e-15,
            0.45485768753597144,
            2.298161660974074e-14
          ],
          [
            9.43689570931383e-15,
            0.4483754437981754,
            2.8754776337791554e-14
          ]
        ]
      },
      "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,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.0,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        1.0,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              2.462925964832928e-16,
              0.5687382178046861,
              4.92116957903835e-16
            ],
            "branch_aligned_reduced_polarization": [
              2.462925964832928e-16,
              0.5687382178046861,
              4.92116957903835e-16
            ],
            "target_residual": 0.43126178219531386,
            "energy_eV": -85.44155677438647,
            "max_atomic_step_A": 0.08171831644966979,
            "max_log_strain_component": 0.02,
            "step_scale": 0.7943214227285466,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.577357747347821,
            "cell_principal_stretches": [
              1.0225139982881664,
              0.9926972014055999,
              0.9817290532233567
            ],
            "cell_volume_ratio": 0.996500918723334,
            "cell_rmsd_from_input_A": 0.25919188457849823
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              2.89020525988831e-14,
              0.8986979892520888,
              4.592796871834303e-16
            ],
            "branch_aligned_reduced_polarization": [
              2.89020525988831e-14,
              0.8986979892520888,
              4.592796871834303e-16
            ],
            "target_residual": 0.10130201074791123,
            "energy_eV": -85.18322455754625,
            "max_atomic_step_A": 0.027579110809860825,
            "max_log_strain_component": 0.006974372212198911,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.577357747347821,
            "cell_principal_stretches": [
              1.0304836699998619,
              0.9901631409435888,
              0.9754364512265491
            ],
            "cell_volume_ratio": 0.995283605370375,
            "cell_rmsd_from_input_A": 0.35219107135211364
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              9.243330908948062e-15,
              0.9987194896921439,
              -4.956031790226677e-15
            ],
            "branch_aligned_reduced_polarization": [
              9.243330908948062e-15,
              0.9987194896921439,
              -4.956031790226677e-15
            ],
            "target_residual": 0.001280510307856142,
            "energy_eV": -84.90155618388015,
            "max_atomic_step_A": 0.0003618294224246608,
            "max_log_strain_component": 9.31764710297051e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.577357747347821,
            "cell_principal_stretches": [
              1.030590562916635,
              0.9901293301351413,
              0.9753526566971895
            ],
            "cell_volume_ratio": 0.9952673523334192,
            "cell_rmsd_from_input_A": 0.35344288185848105
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -6.925454792771557e-16,
              0.9999984786694768,
              -1.6610220493697095e-15
            ],
            "branch_aligned_reduced_polarization": [
              -6.925454792771557e-16,
              0.9999984786694768,
              -1.6610220493697095e-15
            ],
            "target_residual": 1.5213305232242291e-06,
            "energy_eV": -84.89705824429619
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "inversion_parent_endpoint_00",
        "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,
          1.0,
          0.0
        ],
        "formal_class": [
          0.0,
          0.0,
          0.0
        ],
        "target_residual": 2.4975951297768027e-15,
        "parent_symmetrization_rmsd_A": 0.661660315765908,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -75.9083982573983,
        "reduced_polarization": [
          2.9360829727797427e-16,
          1.3463266204316646e-15,
          2.092089520863545e-15
        ],
        "cartesian_polarization_e_A2": [
          7.994500048331882e-18,
          2.14790803101466e-17,
          3.020144462703156e-17
        ],
        "ranking_score": 0.661660315765913
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 2,
      "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": [
              2.462925964832928e-16,
              0.5687382178046861,
              4.92116957903835e-16
            ],
            "branch_aligned_reduced_polarization": [
              2.462925964832928e-16,
              0.5687382178046861,
              4.996003610813204e-16
            ],
            "target_residual": 0.5047028260144418,
            "energy_eV": -85.44155677438647,
            "max_atomic_step_A": 0.06955260374077517,
            "max_log_strain_component": 0.020000000000000004,
            "step_scale": 0.5323849341070606,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.577357747347821,
            "cell_principal_stretches": [
              1.0205374095768491,
              1.001155212157397,
              0.9791117956178174
            ],
            "cell_volume_ratio": 1.0003745269269064,
            "cell_rmsd_from_input_A": 0.1603584082475412
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.0031042782841171532,
              0.5241726556423356,
              0.2621539191043677
            ],
            "branch_aligned_reduced_polarization": [
              -0.0031042782841171532,
              0.5241726556423356,
              0.2621539191043677
            ],
            "target_residual": 0.23909143025604213,
            "energy_eV": -85.22460733156159,
            "max_atomic_step_A": 0.057219489799866276,
            "max_log_strain_component": 0.017418493957181695,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.577357747347821,
            "cell_principal_stretches": [
              1.0386525009709928,
              1.0015753962982152,
              0.9618102562908717
            ],
            "cell_volume_ratio": 1.0005604279920295,
            "cell_rmsd_from_input_A": 0.293581249154172
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.0030440792743916412,
              0.4876472930466785,
              0.49158430277149606
            ],
            "branch_aligned_reduced_polarization": [
              -0.0030440792743916412,
              0.4876472930466785,
              0.49158430277149606
            ],
            "target_residual": 0.015253843697418284,
            "energy_eV": -84.67341471012877,
            "max_atomic_step_A": 0.004726595344866344,
            "max_log_strain_component": 0.0006569790713568236,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.577357747347821,
            "cell_principal_stretches": [
              1.0391330847527769,
              1.0012287830579323,
              0.9615875200339363
            ],
            "cell_volume_ratio": 1.0004452273722622,
            "cell_rmsd_from_input_A": 0.2955354687230023
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.00016943780066044854,
              0.49995698762541985,
              0.5000696735852102
            ],
            "branch_aligned_reduced_polarization": [
              0.00016943780066044854,
              0.49995698762541985,
              0.5000696735852102
            ],
            "target_residual": 0.00018818512463983288,
            "energy_eV": -84.66538229133074
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_02",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.5,
          0.5
        ],
        "formal_class": [
          0.0,
          0.5,
          0.5
        ],
        "target_residual": 0.00018818512463983288,
        "parent_symmetrization_rmsd_A": 0.12693224594406716,
        "parent_cell_rmsd_A": 0.2955354687230023,
        "energy_eV": -84.66538229133074,
        "reduced_polarization": [
          0.00016943780066044854,
          0.49995698762541985,
          0.5000696735852102
        ],
        "cartesian_polarization_e_A2": [
          -0.0002824584215616174,
          0.008051355174302064,
          0.008231248100161813
        ],
        "ranking_score": 0.7011924833740975
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 3,
      "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": [
              2.462925964832928e-16,
              0.5687382178046861,
              4.92116957903835e-16
            ],
            "branch_aligned_reduced_polarization": [
              2.220446049250313e-16,
              0.5687382178046861,
              4.92116957903835e-16
            ],
            "target_residual": 0.5047028260144422,
            "energy_eV": -85.44155677438647,
            "max_atomic_step_A": 0.051221461326405406,
            "max_log_strain_component": 0.02,
            "step_scale": 0.24274596257948072,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.577357747347821,
            "cell_principal_stretches": [
              1.0247718632588532,
              1.0007788430563993,
              0.9752340181515643
            ],
            "cell_volume_ratio": 1.0001707517118539,
            "cell_rmsd_from_input_A": 0.19120974049633618
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.12278689705855382,
              0.5308589948372873,
              -0.0006670274991918903
            ],
            "branch_aligned_reduced_polarization": [
              0.12278689705855383,
              0.5308589948372873,
              -0.0006670274991918903
            ],
            "target_residual": 0.3784738399397856,
            "energy_eV": -85.17837971502736,
            "max_atomic_step_A": 0.04962070528086665,
            "max_log_strain_component": 0.02,
            "step_scale": 0.34012758156460177,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.577357747347821,
            "cell_principal_stretches": [
              1.0508297581447503,
              0.9998397045815668,
              0.9517480393076089
            ],
            "cell_volume_ratio": 0.9999648464790333,
            "cell_rmsd_from_input_A": 0.3840034371049885
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.25548670167688264,
              0.4806780327921032,
              0.0015423008198477708
            ],
            "branch_aligned_reduced_polarization": [
              0.25548670167688264,
              0.4806780327921032,
              0.0015423008198477708
            ],
            "target_residual": 0.24528039091099746,
            "energy_eV": -84.34268745032853,
            "max_atomic_step_A": 0.06602731835285007,
            "max_log_strain_component": 0.02,
            "step_scale": 0.6256845515364408,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.577357747347821,
            "cell_principal_stretches": [
              1.078507522260372,
              0.9971297533800306,
              0.9292916736138677
            ],
            "cell_volume_ratio": 0.9993713612588487,
            "cell_rmsd_from_input_A": 0.5874557535027483
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.4197856198056373,
              0.44127498667940795,
              0.003172334061438923
            ],
            "branch_aligned_reduced_polarization": [
              0.4197856198056373,
              0.44127498667940795,
              0.003172334061438923
            ],
            "target_residual": 0.09946375059722437,
            "energy_eV": -82.71726773371883,
            "max_atomic_step_A": 0.04637920514176536,
            "max_log_strain_component": 0.009093770494744705,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.577357747347821,
            "cell_principal_stretches": [
              1.093010202935393,
              0.9935166511542897,
              0.9195755704801171
            ],
            "cell_volume_ratio": 0.9985890314454604,
            "cell_rmsd_from_input_A": 0.6976138056470284
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              0.48474514449590356,
              0.4537910054079794,
              0.016407607031709705
            ],
            "branch_aligned_reduced_polarization": [
              0.48474514449590356,
              0.4537910054079794,
              0.016407607031709705
            ],
            "target_residual": 0.05135359156050588,
            "energy_eV": -82.06997456121691,
            "max_atomic_step_A": 0.03258474442940038,
            "max_log_strain_component": 0.004483050100524143,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": true,
            "strain_jacobian_frobenius_norm": 4.402412218932721,
            "cell_principal_stretches": [
              1.0876217659862604,
              0.9904987825856969,
              0.917324705334846
            ],
            "cell_volume_ratio": 0.9882229293800499,
            "cell_rmsd_from_input_A": 0.682462629422843
          },
          {
            "iteration": 5,
            "reduced_polarization": [
              0.49938122113818295,
              0.49957210048464845,
              0.00012638988298896854
            ],
            "branch_aligned_reduced_polarization": [
              0.49938122113818295,
              0.49957210048464845,
              0.00012638988298896854
            ],
            "target_residual": 0.0007628628170199787,
            "energy_eV": -82.31339117739263
          }
        ],
        "iterations": 5
      },
      "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": [
          0.5,
          0.5,
          0.0
        ],
        "formal_class": [
          0.5,
          0.5,
          0.0
        ],
        "target_residual": 0.0007628628170199787,
        "parent_symmetrization_rmsd_A": 0.17270169554479992,
        "parent_cell_rmsd_A": 0.682462629422843,
        "energy_eV": -82.31339117739263,
        "reduced_polarization": [
          0.49938122113818295,
          0.49957210048464845,
          0.00012638988298896854
        ],
        "cartesian_polarization_e_A2": [
          0.014307712686063843,
          0.009223611436895278,
          -0.007498199340319199
        ],
        "ranking_score": 0.8448430785345507
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 4,
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.0,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        1.0,
        0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              2.462925964832928e-16,
              0.5687382178046861,
              4.92116957903835e-16
            ],
            "branch_aligned_reduced_polarization": [
              2.462925964832928e-16,
              0.5687382178046861,
              4.996003610813204e-16
            ],
            "target_residual": 0.6602929083234786,
            "energy_eV": -85.44155677438647,
            "max_atomic_step_A": 0.10739774427473862,
            "max_log_strain_component": 0.019999999999999997,
            "step_scale": 0.5323849341068188,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.577357747347821,
            "cell_principal_stretches": [
              1.0269915354779464,
              0.9932858936017447,
              0.9779993498240485
            ],
            "cell_volume_ratio": 0.997653425285769,
            "cell_rmsd_from_input_A": 0.2383352430102852
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.011478543811980798,
              0.7848922391917658,
              0.2742981261600571
            ],
            "branch_aligned_reduced_polarization": [
              0.011478543811980798,
              0.7848922391917658,
              0.2742981261600571
            ],
            "target_residual": 0.3120007076640013,
            "energy_eV": -85.15749208791311,
            "max_atomic_step_A": 0.09890411470000245,
            "max_log_strain_component": 0.019785221899517594,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.577357747347821,
            "cell_principal_stretches": [
              1.057258217598641,
              0.9829120002430214,
              0.9576160101787127
            ],
            "cell_volume_ratio": 0.9951466952075473,
            "cell_rmsd_from_input_A": 0.5101459162122901
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.0008934275526410212,
              0.9742024694610287,
              0.49555689600366876
            ],
            "branch_aligned_reduced_polarization": [
              -0.0008934275526410212,
              0.9742024694610287,
              0.49555689600366876
            ],
            "target_residual": 0.02619259375898439,
            "energy_eV": -83.98479713898124,
            "max_atomic_step_A": 0.008038879660141404,
            "max_log_strain_component": 0.0018149222724494524,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.577357747347821,
            "cell_principal_stretches": [
              1.0588046895725503,
              0.9820856464745082,
              0.9567175543467092
            ],
            "cell_volume_ratio": 0.9948302044538269,
            "cell_rmsd_from_input_A": 0.5303814903280799
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -0.00032194699918101466,
              0.9995907827947554,
              0.49956433280667756
            ],
            "branch_aligned_reduced_polarization": [
              -0.00032194699918101466,
              0.9995907827947554,
              0.49956433280667756
            ],
            "target_residual": 0.0006789068380030381,
            "energy_eV": -83.8577365714812
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_04",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          1.0,
          0.5
        ],
        "formal_class": [
          0.0,
          0.0,
          0.5
        ],
        "target_residual": 0.0006789068380030381,
        "parent_symmetrization_rmsd_A": 0.17152586585428148,
        "parent_cell_rmsd_A": 0.5303814903280799,
        "energy_eV": -83.8577365714812,
        "reduced_polarization": [
          -0.00032194699918101466,
          0.9995907827947554,
          0.49956433280667756
        ],
        "cartesian_polarization_e_A2": [
          -0.000904592029562756,
          0.01599119821833995,
          0.008425071524467576
        ],
        "ranking_score": 0.8054790521123075
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 5,
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.0,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.5,
        1.0,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": false,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              2.462925964832928e-16,
              0.5687382178046861,
              4.92116957903835e-16
            ],
            "branch_aligned_reduced_polarization": [
              2.220446049250313e-16,
              0.5687382178046861,
              4.92116957903835e-16
            ],
            "target_residual": 0.6602929083234789,
            "energy_eV": -85.44155677438647,
            "max_atomic_step_A": 0.06657834605120491,
            "max_log_strain_component": 0.02,
            "step_scale": 0.24274596257932243,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.577357747347821,
            "cell_principal_stretches": [
              1.0275448112003969,
              0.9951652963854063,
              0.9768745386904496
            ],
            "cell_volume_ratio": 0.9989293732044358,
            "cell_rmsd_from_input_A": 0.2097359914010516
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.11904004169406732,
              0.6520877687525731,
              0.006806030104608082
            ],
            "branch_aligned_reduced_polarization": [
              0.11904004169406734,
              0.6520877687525731,
              0.006806030104608082
            ],
            "target_residual": 0.5159648559057155,
            "energy_eV": -85.22775443149375,
            "max_atomic_step_A": 0.059552086578192345,
            "max_log_strain_component": 0.02,
            "step_scale": 0.3148149342142606,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.577357747347821,
            "cell_principal_stretches": [
              1.0576656542615714,
              0.9885526770760287,
              0.9540427288252022
            ],
            "cell_volume_ratio": 0.9975072116031142,
            "cell_rmsd_from_input_A": 0.44633604677290795
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.24390717707503418,
              0.7262522824289203,
              0.012255773927685714
            ],
            "branch_aligned_reduced_polarization": [
              0.24390717707503418,
              0.7262522824289203,
              0.012255773927685714
            ],
            "target_residual": 0.3750620626291335,
            "energy_eV": -84.55263214353484,
            "max_atomic_step_A": 0.09961886918789001,
            "max_log_strain_component": 0.02,
            "step_scale": 0.6411831611876422,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.577357747347821,
            "cell_principal_stretches": [
              1.0908658675115024,
              0.9793094257629477,
              0.9318701407813796
            ],
            "cell_volume_ratio": 0.9955124229255445,
            "cell_rmsd_from_input_A": 0.7218776659012618
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.390449166764336,
              0.8095908235254876,
              0.03911082524936254
            ],
            "branch_aligned_reduced_polarization": [
              0.390449166764336,
              0.8095908235254876,
              0.03911082524936254
            ],
            "target_residual": 0.22312932617658407,
            "energy_eV": -83.29805567200624,
            "max_atomic_step_A": 0.0728455616393716,
            "max_log_strain_component": 0.02,
            "step_scale": 0.7030255131590185,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.577357747347821,
            "cell_principal_stretches": [
              1.127606977672583,
              0.9694789123838008,
              0.9088587414535961
            ],
            "cell_volume_ratio": 0.9935563657582338,
            "cell_rmsd_from_input_A": 1.0357165654192975
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              0.4287095828947655,
              0.8350921181855631,
              0.05726793534989937
            ],
            "branch_aligned_reduced_polarization": [
              0.4287095828947655,
              0.8350921181855631,
              0.05726793534989937
            ],
            "target_residual": 0.18856444382439352,
            "energy_eV": -82.48464016019282,
            "max_atomic_step_A": 0.07101111630338393,
            "max_log_strain_component": 0.02,
            "step_scale": 0.7036909208575053,
            "strain_jacobian_refreshed": true,
            "strain_jacobian_frobenius_norm": 4.883628458720264,
            "cell_principal_stretches": [
              1.0956330045695026,
              0.9629403413997103,
              0.9016769642569216
            ],
            "cell_volume_ratio": 0.9512955438131094,
            "cell_rmsd_from_input_A": 0.8282976013967653
          },
          {
            "iteration": 5,
            "reduced_polarization": [
              0.48070572981009624,
              0.9438168514148455,
              0.022806195567642653
            ],
            "branch_aligned_reduced_polarization": [
              0.48070572981009624,
              0.9438168514148455,
              0.022806195567642653
            ],
            "target_residual": 0.06363126278310152,
            "energy_eV": -81.56479725629285
          }
        ],
        "iterations": 5
      },
      "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,
          1.0,
          0.0
        ],
        "formal_class": [
          0.5,
          0.0,
          0.0
        ],
        "target_residual": 0.06363126278310152,
        "parent_symmetrization_rmsd_A": 0.2389417768729702,
        "parent_cell_rmsd_A": 0.8282976013967653,
        "energy_eV": -81.56479725629285,
        "reduced_polarization": [
          0.48070572981009624,
          0.9438168514148455,
          0.022806195567642653
        ],
        "cartesian_polarization_e_A2": [
          0.015095136435161824,
          0.016719989256791835,
          -0.007802606793695256
        ],
        "ranking_score": 1.0732787027883646
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 6,
      "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": [
              2.462925964832928e-16,
              0.5687382178046861,
              4.92116957903835e-16
            ],
            "branch_aligned_reduced_polarization": [
              2.220446049250313e-16,
              0.5687382178046861,
              4.996003610813204e-16
            ],
            "target_residual": 0.710439964097575,
            "energy_eV": -85.44155677438647,
            "max_atomic_step_A": 0.05388860244178213,
            "max_log_strain_component": 0.020000000000000004,
            "step_scale": 0.2740025938755217,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.577357747347821,
            "cell_principal_stretches": [
              1.021108448019622,
              1.0003446317146447,
              0.9791792074966403
            ],
            "cell_volume_ratio": 1.000192740286053,
            "cell_rmsd_from_input_A": 0.1409823394469601
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.13757159501921934,
              0.5407095128881152,
              0.13529463645201834
            ],
            "branch_aligned_reduced_polarization": [
              0.13757159501921934,
              0.5407095128881152,
              0.13529463645201834
            ],
            "target_residual": 0.5157728331127628,
            "energy_eV": -85.21358175898649,
            "max_atomic_step_A": 0.05316321139340751,
            "max_log_strain_component": 0.02,
            "step_scale": 0.3950280610955592,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.577357747347821,
            "cell_principal_stretches": [
              1.0425273304312486,
              1.0005117046167236,
              0.9590136058837088
            ],
            "cell_volume_ratio": 1.0003094955875387,
            "cell_rmsd_from_input_A": 0.27845846375115263
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.2827471781807085,
              0.5028444006367006,
              0.2788918009537953
            ],
            "branch_aligned_reduced_polarization": [
              0.2827471781807085,
              0.5028444006367006,
              0.2788918009537953
            ],
            "target_residual": 0.30999308845340884,
            "energy_eV": -84.5096761962899,
            "max_atomic_step_A": 0.06125563716510656,
            "max_log_strain_component": 0.02,
            "step_scale": 0.7367707396582064,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.577357747347821,
            "cell_principal_stretches": [
              1.0642832823852002,
              1.000310824422317,
              0.939499482687892
            ],
            "cell_volume_ratio": 1.0002043845827622,
            "cell_rmsd_from_input_A": 0.41407096225164497
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.44461083011013136,
              0.46822959366534456,
              0.4434249434791128
            ],
            "branch_aligned_reduced_polarization": [
              0.44461083011013136,
              0.46822959366534456,
              0.4434249434791128
            ],
            "target_residual": 0.08531152255175982,
            "energy_eV": -83.10590630957898,
            "max_atomic_step_A": 0.022581882521831288,
            "max_log_strain_component": 0.0062482061460495345,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.577357747347821,
            "cell_principal_stretches": [
              1.0713330248144453,
              0.9997880527967797,
              0.9334855181969066
            ],
            "cell_volume_ratio": 0.9998619009719187,
            "cell_rmsd_from_input_A": 0.460350078856411
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              0.49822909155160505,
              0.48976921364004644,
              0.49986103535183896
            ],
            "branch_aligned_reduced_polarization": [
              0.49822909155160505,
              0.48976921364004644,
              0.49986103535183896
            ],
            "target_residual": 0.010383853689697622,
            "energy_eV": -82.5073007319774,
            "max_atomic_step_A": 0.002868668182814091,
            "max_log_strain_component": 0.0005094828766041967,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": true,
            "strain_jacobian_frobenius_norm": 3.8989533425422853,
            "cell_principal_stretches": [
              1.0713501987947398,
              0.9995161926857826,
              0.9335501414781148
            ],
            "cell_volume_ratio": 0.9996752453551264,
            "cell_rmsd_from_input_A": 0.4615821866265416
          },
          {
            "iteration": 5,
            "reduced_polarization": [
              0.5000347830845738,
              0.49997732053876087,
              0.5000063840058547
            ],
            "branch_aligned_reduced_polarization": [
              0.5000347830845738,
              0.49997732053876087,
              0.5000063840058547
            ],
            "target_residual": 4.201162297889245e-05,
            "energy_eV": -82.49677757001454
          }
        ],
        "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,
          0.5
        ],
        "formal_class": [
          0.5,
          0.5,
          0.5
        ],
        "target_residual": 4.201162297889245e-05,
        "parent_symmetrization_rmsd_A": 0.18573099415140232,
        "parent_cell_rmsd_A": 0.4615821866265416,
        "energy_eV": -82.49677757001454,
        "reduced_polarization": [
          0.5000347830845738,
          0.49997732053876087,
          0.5000063840058547
        ],
        "cartesian_polarization_e_A2": [
          0.013803039183036358,
          0.008159998563801485,
          0.0008360676059852858
        ],
        "ranking_score": 0.8012105640539955
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 7,
      "formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.0,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.5,
        1.0,
        0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              2.462925964832928e-16,
              0.5687382178046861,
              4.92116957903835e-16
            ],
            "branch_aligned_reduced_polarization": [
              2.220446049250313e-16,
              0.5687382178046861,
              4.996003610813204e-16
            ],
            "target_residual": 0.8282431555903601,
            "energy_eV": -85.44155677438647,
            "max_atomic_step_A": 0.07304979604409387,
            "max_log_strain_component": 0.02,
            "step_scale": 0.27400259387532006,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.577357747347821,
            "cell_principal_stretches": [
              1.022851165989611,
              0.9978099031672888,
              0.978621215434415
            ],
            "cell_volume_ratio": 0.9987915997070019,
            "cell_rmsd_from_input_A": 0.16816404201271093
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.13681457703730016,
              0.6764097069044335,
              0.14836825269414347
            ],
            "branch_aligned_reduced_polarization": [
              0.13681457703730016,
              0.6764097069044335,
              0.14836825269414344
            ],
            "target_residual": 0.600215973589207,
            "energy_eV": -85.22438799944895,
            "max_atomic_step_A": 0.07203858422228061,
            "max_log_strain_component": 0.02,
            "step_scale": 0.37890740928720623,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.577357747347821,
            "cell_principal_stretches": [
              1.047610900231473,
              0.9943525913906277,
              0.9575103374115055
            ],
            "cell_volume_ratio": 0.9974333607700108,
            "cell_rmsd_from_input_A": 0.3576495770969899
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.27582522142628674,
              0.7748063471071838,
              0.2923849529613855
            ],
            "branch_aligned_reduced_polarization": [
              0.27582522142628674,
              0.7748063471071838,
              0.2923849529613855
            ],
            "target_residual": 0.37956622664382256,
            "energy_eV": -84.41130639608879,
            "max_atomic_step_A": 0.07803989673065796,
            "max_log_strain_component": 0.02,
            "step_scale": 0.7278373714919518,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.577357747347821,
            "cell_principal_stretches": [
              1.0740319047962503,
              0.990106277706,
              0.9362766584970298
            ],
            "cell_volume_ratio": 0.9956419648173818,
            "cell_rmsd_from_input_A": 0.5734568707226027
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.4423664672011968,
              0.9022050406893122,
              0.44677176284838194
            ],
            "branch_aligned_reduced_polarization": [
              0.4423664672011968,
              0.9022050406893122,
              0.44677176284838194
            ],
            "target_residual": 0.12537433309780238,
            "energy_eV": -82.57478572004138,
            "max_atomic_step_A": 0.03735690492580034,
            "max_log_strain_component": 0.007017989720389902,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.577357747347821,
            "cell_principal_stretches": [
              1.085280957380067,
              0.9873292282251067,
              0.9280651472315004
            ],
            "cell_volume_ratio": 0.9944492853208946,
            "cell_rmsd_from_input_A": 0.6814807274091282
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              0.48574444227040753,
              0.9699705816476635,
              0.5067037548680994
            ],
            "branch_aligned_reduced_polarization": [
              0.48574444227040753,
              0.9699705816476635,
              0.5067037548680994
            ],
            "target_residual": 0.0339105768469508,
            "energy_eV": -81.4458222649319,
            "max_atomic_step_A": 0.0230427087107291,
            "max_log_strain_component": 0.004249969025563248,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": true,
            "strain_jacobian_frobenius_norm": 3.7627917704838825,
            "cell_principal_stretches": [
              1.0829419864509673,
              0.9831847273468438,
              0.9279071919536874
            ],
            "cell_volume_ratio": 0.9879725004214156,
            "cell_rmsd_from_input_A": 0.6734619142670615
          },
          {
            "iteration": 5,
            "reduced_polarization": [
              0.4995577617498375,
              0.9992175501270506,
              0.5000274949943931
            ],
            "branch_aligned_reduced_polarization": [
              0.4995577617498375,
              0.9992175501270506,
              0.5000274949943931
            ],
            "target_residual": 0.0008991987813058828,
            "energy_eV": -81.25065681169755
          }
        ],
        "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,
          1.0,
          0.5
        ],
        "formal_class": [
          0.5,
          0.0,
          0.5
        ],
        "target_residual": 0.0008991987813058828,
        "parent_symmetrization_rmsd_A": 0.2273738805921654,
        "parent_cell_rmsd_A": 0.6734619142670615,
        "energy_eV": -81.25065681169755,
        "reduced_polarization": [
          0.4995577617498375,
          0.9992175501270506,
          0.5000274949943931
        ],
        "cartesian_polarization_e_A2": [
          0.014304706729834775,
          0.016205264770186103,
          -9.469942226680451e-05
        ],
        "ranking_score": 0.8975377567215426
      },
      "branch_status": "awaiting_branch_sampling"
    }
  ],
  "sampled_polarization_branches": [
    {
      "orbit_id": 0,
      "candidate_id": "bec_projection_00",
      "formal_class": [
        0.0,
        0.5,
        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
        ],
        "endpoint_rmsd_A": 0.017729192576264288,
        "minimum_distance_A_by_image": [
          1.4333488935809995,
          1.4319441789608174,
          1.4305398698220995,
          1.4291359664147578,
          1.4277324689927748,
          1.4263293778142028,
          1.4249266931411921,
          1.423524415239999,
          1.4221225443810137
        ],
        "minimum_distance_A": 1.4221225443810137,
        "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": [
          374.95805220657877,
          374.99101983939556,
          375.02399037084245,
          375.0569638011749,
          375.0899401306475,
          375.12291935951515,
          375.1559014880325,
          375.18888651645506,
          375.2218744450378
        ],
        "cell_deformation_log_strain_norm": 0.005984425236601445
      },
      "parent_reduced_polarization": [
        -6.621197351543133e-15,
        0.4995749427307674,
        7.881218076274104e-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": [
          -85.44155677438647,
          -85.43784373965381,
          -85.43368399515413,
          -85.42908018283948,
          -85.42403487578049,
          -85.41855057818464,
          -85.41262972538485,
          -85.40627468380816,
          -85.39948775093242
        ],
        "cartesian_polarizations_e_A2": [
          [
            7.272774349524144e-18,
            0.009073558875156026,
            4.77449308442043e-18
          ],
          [
            -8.69695529304453e-19,
            0.008937384477140042,
            3.10869891325847e-18
          ],
          [
            -1.7022330718848264e-17,
            0.008800921586244435,
            6.905145461167578e-17
          ],
          [
            -7.148750358601803e-17,
            0.008664173132938206,
            5.905489426671054e-17
          ],
          [
            -6.576494112264959e-17,
            0.008527142155012869,
            1.0618586836680975e-16
          ],
          [
            -1.0057174384321352e-16,
            0.008389831799971261,
            1.8434761801388008e-16
          ],
          [
            -1.0126575104697895e-16,
            0.008252245327315761,
            1.1719083080066824e-16
          ],
          [
            -1.62898688372888e-16,
            0.008114386110700592,
            2.205272434330514e-16
          ],
          [
            -1.6072071226671322e-16,
            0.007976257639912374,
            2.7694780657073955e-16
          ]
        ],
        "raw_reduced_polarization": [
          [
            2.666409704629409e-16,
            0.5687382178046884,
            5.135379586144961e-16
          ],
          [
            -1.2882547426061775e-16,
            0.560148958406346,
            -4.0170963385552887e-16
          ],
          [
            -8.160947665457127e-16,
            0.5515432620405861,
            2.594813216843572e-15
          ],
          [
            -2.9054306734359837e-15,
            0.5429213173052932,
            -2.008416756037406e-16
          ],
          [
            -2.7873775031943013e-15,
            0.5342833194514103,
            2.343578176009409e-15
          ],
          [
            -4.157185604360034e-15,
            0.525629470529393,
            5.573650574693849e-15
          ],
          [
            -4.262317742753365e-15,
            0.516959979529276,
            9.688879162284791e-16
          ],
          [
            -6.617383673397199e-15,
            0.5082750625121437,
            4.961949943440096e-15
          ],
          [
            -6.621197351543133e-15,
            0.4995749427307674,
            7.881218076274104e-15
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            2.666409704629409e-16,
            0.5687382178046884,
            5.135379586144961e-16
          ],
          [
            -1.2882547426061772e-16,
            0.560148958406346,
            -4.017096338555288e-16
          ],
          [
            -8.160947665457127e-16,
            0.5515432620405861,
            2.594813216843572e-15
          ],
          [
            -2.9054306734359837e-15,
            0.5429213173052932,
            -2.0084167560374051e-16
          ],
          [
            -2.7873775031943013e-15,
            0.5342833194514103,
            2.343578176009409e-15
          ],
          [
            -4.157185604360034e-15,
            0.525629470529393,
            5.573650574693849e-15
          ],
          [
            -4.262317742753365e-15,
            0.516959979529276,
            9.688879162284791e-16
          ],
          [
            -6.617383673397199e-15,
            0.5082750625121437,
            4.961949943440096e-15
          ],
          [
            -6.621197351543133e-15,
            0.4995749427307674,
            7.881218076274104e-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": [
          [
            2.220446049250313e-16,
            -0.43126178219531175,
            5.551115123125783e-16
          ],
          [
            -1.1102230246251565e-16,
            -0.43985104159365385,
            -3.885780586188048e-16
          ],
          [
            -8.326672684688674e-16,
            -0.44845673795941376,
            2.55351295663786e-15
          ],
          [
            -2.886579864025407e-15,
            -0.45707868269470664,
            -2.220446049250313e-16
          ],
          [
            -2.7755575615628914e-15,
            -0.4657166805485897,
            2.3314683517128287e-15
          ],
          [
            -4.163336342344337e-15,
            -0.47437052947060687,
            5.551115123125783e-15
          ],
          [
            -4.274358644806853e-15,
            -0.48304002047072414,
            9.992007221626409e-16
          ],
          [
            -6.6058269965196814e-15,
            -0.4917249374878563,
            4.9960036108132044e-15
          ],
          [
            -6.6058269965196814e-15,
            0.4995749427307674,
            7.882583474838611e-15
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -85.39948775093244,
          -85.40418029049852,
          -85.40855462991098,
          -85.41261094197814,
          -85.41634938650284,
          -85.41977011073419,
          -85.42287324696701,
          -85.42565891624758,
          -85.4281272312007
        ],
        "cartesian_polarizations_e_A2": [
          [
            -1.3832596108100505e-16,
            0.00797625763991233,
            2.780203875523837e-16
          ],
          [
            -1.1969576647926105e-16,
            0.007874679968492093,
            2.1542278862027698e-16
          ],
          [
            -1.3139577998862802e-16,
            0.007772720604923211,
            3.0118931325095983e-16
          ],
          [
            4.820488586636278e-17,
            0.007670385835045862,
            3.123143871710166e-16
          ],
          [
            3.710955608777358e-17,
            0.00756768208415649,
            2.6109884078905103e-16
          ],
          [
            1.0284654048516413e-16,
            0.007464615911997793,
            3.0892814049672073e-16
          ],
          [
            9.728632056489585e-17,
            0.007361194007255163,
            3.7537939741738433e-16
          ],
          [
            1.3826308499921004e-16,
            0.00725742318160803,
            3.1494080656939977e-16
          ],
          [
            2.5863688119325553e-16,
            0.00715331036338775,
            3.409136108573378e-16
          ]
        ],
        "raw_reduced_polarization": [
          [
            -5.799056441683183e-15,
            0.49957494273076464,
            8.623815964228479e-15
          ],
          [
            -5.01277178903573e-15,
            0.493260167638593,
            6.0631199506424166e-15
          ],
          [
            -5.353573422535484e-15,
            0.48692026538611094,
            1.1488507040296055e-14
          ],
          [
            1.331451051872704e-15,
            0.4805556227295431,
            1.813532255819672e-14
          ],
          [
            1.0197023194574204e-15,
            0.4741666353127654,
            1.5181811964169543e-14
          ],
          [
            3.5185278031640805e-15,
            0.4677537073575927,
            2.0605254616026624e-14
          ],
          [
            3.401367254621785e-15,
            0.46131725132295304,
            2.4994141772690852e-14
          ],
          [
            4.990327637781313e-15,
            0.45485768753597144,
            2.3019849760790115e-14
          ],
          [
            9.48585240645858e-15,
            0.4483754437981754,
            2.8738380607803684e-14
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -5.799056441683183e-15,
            0.49957494273076464,
            8.623815964228479e-15
          ],
          [
            -5.01277178903573e-15,
            0.493260167638593,
            6.0631199506424166e-15
          ],
          [
            -5.353573422535484e-15,
            0.48692026538611094,
            1.1488507040296055e-14
          ],
          [
            1.3314510518727043e-15,
            0.4805556227295431,
            1.813532255819672e-14
          ],
          [
            1.0197023194574204e-15,
            0.4741666353127654,
            1.5181811964169543e-14
          ],
          [
            3.5185278031640805e-15,
            0.4677537073575927,
            2.0605254616026624e-14
          ],
          [
            3.401367254621785e-15,
            0.46131725132295304,
            2.4994141772690852e-14
          ],
          [
            4.990327637781313e-15,
            0.45485768753597144,
            2.3019849760790115e-14
          ],
          [
            9.48585240645858e-15,
            0.4483754437981754,
            2.8738380607803684e-14
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          -1.203607983132663e-14,
          0.4311787094543055,
          2.3616168021489007e-14
        ],
        "actual_opposite_endpoint_branch_residual": 0.017196734343869924
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            2.666409704629409e-16,
            0.5687382178046884,
            5.135379586144961e-16
          ],
          [
            -1.2882547426061775e-16,
            0.560148958406346,
            -4.0170963385552887e-16
          ],
          [
            -8.160947665457127e-16,
            0.5515432620405861,
            2.594813216843572e-15
          ],
          [
            -2.9054306734359837e-15,
            0.5429213173052932,
            -2.008416756037406e-16
          ],
          [
            -2.7873775031943013e-15,
            0.5342833194514103,
            2.343578176009409e-15
          ],
          [
            -4.157185604360034e-15,
            0.525629470529393,
            5.573650574693849e-15
          ],
          [
            -4.262317742753365e-15,
            0.516959979529276,
            9.688879162284791e-16
          ],
          [
            -6.617383673397199e-15,
            0.5082750625121437,
            4.961949943440096e-15
          ],
          [
            -6.621197351543133e-15,
            0.4995749427307674,
            7.881218076274104e-15
          ],
          [
            -5.01277178903573e-15,
            0.493260167638593,
            6.0631199506424166e-15
          ],
          [
            -5.353573422535484e-15,
            0.48692026538611094,
            1.1488507040296055e-14
          ],
          [
            1.331451051872704e-15,
            0.4805556227295431,
            1.813532255819672e-14
          ],
          [
            1.0197023194574204e-15,
            0.4741666353127654,
            1.5181811964169543e-14
          ],
          [
            3.5185278031640805e-15,
            0.4677537073575927,
            2.0605254616026624e-14
          ],
          [
            3.401367254621785e-15,
            0.46131725132295304,
            2.4994141772690852e-14
          ],
          [
            4.990327637781313e-15,
            0.45485768753597144,
            2.3019849760790115e-14
          ],
          [
            9.48585240645858e-15,
            0.4483754437981754,
            2.8738380607803684e-14
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            2.666409704629409e-16,
            0.5687382178046884,
            5.135379586144961e-16
          ],
          [
            -1.2882547426061772e-16,
            0.560148958406346,
            -4.017096338555288e-16
          ],
          [
            -8.160947665457127e-16,
            0.5515432620405861,
            2.594813216843572e-15
          ],
          [
            -2.9054306734359837e-15,
            0.5429213173052932,
            -2.0084167560374051e-16
          ],
          [
            -2.7873775031943013e-15,
            0.5342833194514103,
            2.343578176009409e-15
          ],
          [
            -4.157185604360034e-15,
            0.525629470529393,
            5.573650574693849e-15
          ],
          [
            -4.262317742753365e-15,
            0.516959979529276,
            9.688879162284791e-16
          ],
          [
            -6.617383673397199e-15,
            0.5082750625121437,
            4.961949943440096e-15
          ],
          [
            -6.621197351543133e-15,
            0.4995749427307674,
            7.881218076274104e-15
          ],
          [
            -5.01277178903573e-15,
            0.493260167638593,
            6.0631199506424166e-15
          ],
          [
            -5.353573422535484e-15,
            0.48692026538611094,
            1.1488507040296055e-14
          ],
          [
            1.3314510518727043e-15,
            0.4805556227295431,
            1.813532255819672e-14
          ],
          [
            1.0197023194574204e-15,
            0.4741666353127654,
            1.5181811964169543e-14
          ],
          [
            3.5185278031640805e-15,
            0.4677537073575927,
            2.0605254616026624e-14
          ],
          [
            3.401367254621785e-15,
            0.46131725132295304,
            2.4994141772690852e-14
          ],
          [
            4.990327637781313e-15,
            0.45485768753597144,
            2.3019849760790115e-14
          ],
          [
            9.48585240645858e-15,
            0.4483754437981754,
            2.8738380607803684e-14
          ]
        ],
        "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": [
          [
            2.220446049250313e-16,
            -0.43126178219531175,
            5.551115123125783e-16
          ],
          [
            -1.1102230246251565e-16,
            -0.43985104159365385,
            -3.885780586188048e-16
          ],
          [
            -8.326672684688674e-16,
            -0.44845673795941376,
            2.55351295663786e-15
          ],
          [
            -2.886579864025407e-15,
            -0.45707868269470664,
            -2.220446049250313e-16
          ],
          [
            -2.7755575615628914e-15,
            -0.4657166805485897,
            2.3314683517128287e-15
          ],
          [
            -4.163336342344337e-15,
            -0.47437052947060687,
            5.551115123125783e-15
          ],
          [
            -4.274358644806853e-15,
            -0.48304002047072414,
            9.992007221626409e-16
          ],
          [
            -6.6058269965196814e-15,
            -0.4917249374878563,
            4.9960036108132044e-15
          ],
          [
            -6.6058269965196814e-15,
            0.4995749427307674,
            7.882583474838611e-15
          ],
          [
            -4.9960036108132044e-15,
            0.49326016763859304,
            6.106226635438361e-15
          ],
          [
            -5.329070518200751e-15,
            0.4869202653861109,
            1.1435297153639112e-14
          ],
          [
            1.3322676295501878e-15,
            0.4805556227295431,
            1.8096635301390052e-14
          ],
          [
            9.992007221626409e-16,
            0.47416663531276537,
            1.5210055437364645e-14
          ],
          [
            3.552713678800501e-15,
            0.4677537073575927,
            2.0650148258027912e-14
          ],
          [
            3.4416913763379853e-15,
            0.4613172513229531,
            2.4980018054066022e-14
          ],
          [
            4.9960036108132044e-15,
            0.45485768753597144,
            2.298161660974074e-14
          ],
          [
            9.43689570931383e-15,
            0.4483754437981754,
            2.8754776337791554e-14
          ]
        ]
      },
      "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": "C2",
        "spacegroup_number": 5,
        "pointgroup": "2",
        "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": 0.00042505726923225406,
        "parent_symmetrization_rmsd_A": 0.017729192576264288,
        "parent_cell_rmsd_A": 0.05070439085021173,
        "energy_eV": -85.39948775093241,
        "reduced_polarization": [
          -5.96524764791139e-15,
          0.49957494273076775,
          5.459601481328834e-15
        ],
        "cartesian_polarization_e_A2": [
          -1.4302312606958464e-16,
          0.007976257639912379,
          2.2857070574347893e-16
        ],
        "ranking_score": 0.5312554048272817
      }
    }
  ],
  "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": 111,
      "full_response": 31,
      "energy_polarization": 80
    },
    "model_evaluations_for_recovery_and_path_properties": {
      "total": 136,
      "full_response": 56,
      "energy_polarization": 80
    },
    "elapsed_seconds": 283.04087512899423
  }
}