{
  "schema": "ferrofinder.endpoint_parent_recovery.v4_variable_cell",
  "status": "complete",
  "input_atom_count": 44,
  "input_formula": "Ca8Nb8O28",
  "input_spacegroup": "P2_1",
  "input_pointgroup": "2",
  "input_is_polar_point_group": true,
  "input_energy_eV": -348.69151907135927,
  "input_cartesian_polarization_e_A2": [
    -4.5104859529881575e-13,
    0.01636666108205479,
    1.7791560787878042e-10
  ],
  "input_reduced_polarization": [
    1.9073574831729944e-09,
    1.719327643611746,
    7.67110927809704e-09
  ],
  "input_formal_targets": [
    {
      "orbit_id": 0,
      "representative_formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        1.5,
        0.0
      ]
    },
    {
      "orbit_id": 1,
      "representative_formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        2.0,
        0.0
      ]
    },
    {
      "orbit_id": 2,
      "representative_formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        1.5,
        0.5
      ]
    },
    {
      "orbit_id": 3,
      "representative_formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        0.5,
        1.5,
        0.0
      ]
    },
    {
      "orbit_id": 4,
      "representative_formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        2.0,
        0.5
      ]
    },
    {
      "orbit_id": 5,
      "representative_formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        0.5,
        2.0,
        0.0
      ]
    },
    {
      "orbit_id": 6,
      "representative_formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "target_reduced_polarization": [
        0.5,
        1.5,
        0.5
      ]
    },
    {
      "orbit_id": 7,
      "representative_formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        0.5,
        2.0,
        0.5
      ]
    }
  ],
  "parent_candidates": [
    {
      "candidate_id": "inversion_parent_endpoint_00",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "P2_1/c",
      "spacegroup_number": 14,
      "pointgroup": "2/m",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 1.7314993190474163e-15,
      "parent_symmetrization_rmsd_A": 0.33861973249465,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -347.6393893019792,
      "reduced_polarization": [
        -1.0433075208458126e-15,
        1.3256739574030537e-15,
        3.9011263433982416e-16
      ],
      "cartesian_polarization_e_A2": [
        -1.5226596782506237e-17,
        1.2619384354539961e-17,
        9.047860480613558e-18
      ],
      "ranking_score": 0.33861973249465344
    },
    {
      "candidate_id": "inversion_parent_endpoint_01",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "P2_1/m",
      "spacegroup_number": 11,
      "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": 5.4985691491897135e-15,
      "parent_symmetrization_rmsd_A": 0.44002643172572686,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -344.5958297534011,
      "reduced_polarization": [
        3.939632870757262e-15,
        4.0020345883865775e-16,
        3.814890918965227e-15
      ],
      "cartesian_polarization_e_A2": [
        3.965582008016284e-17,
        3.8096254655214975e-18,
        8.847855143673679e-17
      ],
      "ranking_score": 0.44002643172573785
    },
    {
      "candidate_id": "bec_projection_00",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P2_1",
      "spacegroup_number": 4,
      "pointgroup": "2",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        1.5,
        0.0
      ],
      "formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_residual": 2.3474498167530698e-07,
      "parent_symmetrization_rmsd_A": 0.007585333627534663,
      "parent_cell_rmsd_A": 0.005647099565474381,
      "energy_eV": -348.6546042168767,
      "reduced_polarization": [
        -4.110739320233386e-15,
        1.4999997652550183,
        -2.5641796774635976e-14
      ],
      "cartesian_polarization_e_A2": [
        8.960384338619929e-14,
        0.014272849665333466,
        7.703302070952688e-13
      ],
      "ranking_score": 0.5089975780088666
    },
    {
      "candidate_id": "inversion_parent_bec_00_00",
      "source": "same_species_inversion_center_projection_after_BEC",
      "spacegroup": "P2_1/c",
      "spacegroup_number": 14,
      "pointgroup": "2/m",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        1.5,
        0.0
      ],
      "formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_residual": 0.49999999999999645,
      "parent_symmetrization_rmsd_A": 0.33862031660001624,
      "parent_cell_rmsd_A": 0.005647099565474381,
      "energy_eV": -347.63650425309686,
      "reduced_polarization": [
        -2.5459526653429523e-15,
        -3.478016000933699e-15,
        -4.843097386233265e-16
      ],
      "cartesian_polarization_e_A2": [
        -3.230845001704468e-17,
        -3.3094138189898384e-17,
        -1.123772174505902e-17
      ],
      "ranking_score": 1.3400320914913777
    },
    {
      "candidate_id": "bec_projection_01",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P2_1",
      "spacegroup_number": 4,
      "pointgroup": "2",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        2.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 5.433905139184976e-07,
      "parent_symmetrization_rmsd_A": 0.009911269107601175,
      "parent_cell_rmsd_A": 0.007377406427490854,
      "energy_eV": -348.6851813542523,
      "reduced_polarization": [
        -9.048710957724782e-15,
        1.999999456609486,
        -4.3442423559541156e-14
      ],
      "cartesian_polarization_e_A2": [
        1.2169805657541418e-13,
        0.01904887147682808,
        7.645682125066849e-13
      ],
      "ranking_score": 0.5117567074955017
    },
    {
      "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,
        1.5,
        0.5
      ],
      "formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_residual": 3.4280043440973675e-05,
      "parent_symmetrization_rmsd_A": 0.046199421389051615,
      "parent_cell_rmsd_A": 0.023222446286418254,
      "energy_eV": -347.8106382738967,
      "reduced_polarization": [
        3.710694701113095e-06,
        1.4999695179646064,
        0.5000152380327278
      ],
      "cartesian_polarization_e_A2": [
        -0.001692602498559881,
        0.014237812093013754,
        0.011555871602220937
      ],
      "ranking_score": 0.5520735930475381
    },
    {
      "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,
        1.5,
        0.0
      ],
      "formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_residual": 3.2710779403919255e-06,
      "parent_symmetrization_rmsd_A": 0.02131976572136339,
      "parent_cell_rmsd_A": 0.005494939050472401,
      "energy_eV": -348.60639914211305,
      "reduced_polarization": [
        0.5000000777068829,
        1.4999967317985095,
        1.1301128107146006e-07
      ],
      "cartesian_polarization_e_A2": [
        0.006666378377944225,
        0.014273206640972836,
        3.8955055064557016e-07
      ],
      "ranking_score": 0.5227000426398623
    },
    {
      "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,
        2.0,
        0.5
      ],
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_residual": 2.5099918730295072e-05,
      "parent_symmetrization_rmsd_A": 0.04770671574702425,
      "parent_cell_rmsd_A": 0.024389483225176922,
      "energy_eV": -347.71997646124703,
      "reduced_polarization": [
        7.305153842705658e-06,
        1.9999855659463959,
        0.5000191911110714
      ],
      "cartesian_polarization_e_A2": [
        -0.0016956776259245544,
        0.01901425232208949,
        0.011529894854867054
      ],
      "ranking_score": 0.553854286390779
    },
    {
      "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,
        2.0,
        0.0
      ],
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_residual": 7.989558980683002e-06,
      "parent_symmetrization_rmsd_A": 0.022587977610684394,
      "parent_cell_rmsd_A": 0.0075938737688744555,
      "energy_eV": -348.62979902436797,
      "reduced_polarization": [
        0.49999766353084374,
        1.9999923610461159,
        1.42646920821638e-07
      ],
      "cartesian_polarization_e_A2": [
        0.006667897502845106,
        0.01904933225241768,
        1.0143811270336422e-07
      ],
      "ranking_score": 0.5245024251708643
    },
    {
      "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,
        1.5,
        0.5
      ],
      "formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "target_residual": 3.5918142570682484e-05,
      "parent_symmetrization_rmsd_A": 0.04844907271821975,
      "parent_cell_rmsd_A": 0.023146974834502444,
      "energy_eV": -347.77525057147994,
      "reduced_polarization": [
        0.5000000566498299,
        1.4999680552904118,
        0.5000164208795699
      ],
      "cartesian_polarization_e_A2": [
        0.004973789280622833,
        0.014235364463963575,
        0.011556152106734567
      ],
      "ranking_score": 0.5543076527119868
    },
    {
      "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,
        2.0,
        0.5
      ],
      "formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_residual": 3.158117360141337e-05,
      "parent_symmetrization_rmsd_A": 0.04996294210925592,
      "parent_cell_rmsd_A": 0.02436517669781974,
      "energy_eV": -347.6798975320825,
      "reduced_polarization": [
        0.4999948690008742,
        1.9999773682482553,
        0.5000214207186383
      ],
      "cartesian_polarization_e_A2": [
        0.004972161058058469,
        0.0190117783947627,
        0.011529853726474151
      ],
      "ranking_score": 0.5561173986309137
    }
  ],
  "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,
        1.5,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              1.9073574831729944e-09,
              1.719327643611746,
              7.67110927809704e-09
            ],
            "branch_aligned_reduced_polarization": [
              1.9073574831729944e-09,
              1.719327643611746,
              7.67110927809704e-09
            ],
            "target_residual": 0.2193276436117461,
            "energy_eV": -348.69151907135927,
            "max_atomic_step_A": 0.011956671339853332,
            "max_log_strain_component": 0.00045267979141684666,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.7983339089273653,
            "cell_principal_stretches": [
              1.000454024414506,
              0.9999687297739552,
              0.9996378652069383
            ],
            "cell_volume_ratio": 1.0000604521090943,
            "cell_rmsd_from_input_A": 0.005697150172136954
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -7.358134323951406e-12,
              1.4980048390929055,
              -2.9586408315993746e-11
            ],
            "branch_aligned_reduced_polarization": [
              -7.358134323951406e-12,
              1.4980048390929055,
              -2.9586408315993746e-11
            ],
            "target_residual": 0.001995160907094507,
            "energy_eV": -348.6541096784102,
            "max_atomic_step_A": 0.00010739810852848326,
            "max_log_strain_component": 3.975150019486692e-06,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.7983339089273653,
            "cell_principal_stretches": [
              1.0004500365598468,
              0.9999690043652126,
              0.9996410446767546
            ],
            "cell_volume_ratio": 1.0000599212406818,
            "cell_rmsd_from_input_A": 0.005647099565474381
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -4.110739320233386e-15,
              1.4999997652550183,
              -2.5641796774635976e-14
            ],
            "branch_aligned_reduced_polarization": [
              -4.110739320233386e-15,
              1.4999997652550183,
              -2.5641796774635976e-14
            ],
            "target_residual": 2.3474498167530698e-07,
            "energy_eV": -348.6546042168767
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_00",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P2_1",
        "spacegroup_number": 4,
        "pointgroup": "2",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          1.5,
          0.0
        ],
        "formal_class": [
          0.0,
          0.5,
          0.0
        ],
        "target_residual": 2.3474498167530698e-07,
        "parent_symmetrization_rmsd_A": 0.007585333627534663,
        "parent_cell_rmsd_A": 0.005647099565474381,
        "energy_eV": -348.6546042168767,
        "reduced_polarization": [
          -4.110739320233386e-15,
          1.4999997652550183,
          -2.5641796774635976e-14
        ],
        "cartesian_polarization_e_A2": [
          8.960384338619929e-14,
          0.014272849665333466,
          7.703302070952688e-13
        ],
        "ranking_score": 0.5089975780088666
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "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,
        2.0,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              1.9073574831729944e-09,
              1.719327643611746,
              7.67110927809704e-09
            ],
            "branch_aligned_reduced_polarization": [
              1.9073574831729944e-09,
              1.719327643611746,
              7.67110927809704e-09
            ],
            "target_residual": 0.28067235638825416,
            "energy_eV": -348.69151907135927,
            "max_atomic_step_A": 0.015300885216838237,
            "max_log_strain_component": 0.0005792917921975325,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.7983339089273653,
            "cell_principal_stretches": [
              1.0004636132314928,
              1.0000400177593889,
              0.9994192880366887
            ],
            "cell_volume_ratio": 0.999922645105018,
            "cell_rmsd_from_input_A": 0.007283307735674676
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              5.708371590842554e-12,
              1.9965466936411562,
              4.575335965484107e-11
            ],
            "branch_aligned_reduced_polarization": [
              5.708371590842554e-12,
              1.9965466936411562,
              4.575335965484107e-11
            ],
            "target_residual": 0.0034533063588437778,
            "energy_eV": -348.68566024413417,
            "max_atomic_step_A": 0.00019153859848293383,
            "max_log_strain_component": 7.488585776444852e-06,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.7983339089273653,
            "cell_principal_stretches": [
              1.0004696078313906,
              1.0000405350850294,
              0.9994117833004477
            ],
            "cell_volume_ratio": 0.9999216451666814,
            "cell_rmsd_from_input_A": 0.007377406427490854
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -9.048710957724782e-15,
              1.999999456609486,
              -4.3442423559541156e-14
            ],
            "branch_aligned_reduced_polarization": [
              -9.048710957724782e-15,
              1.999999456609486,
              -4.3442423559541156e-14
            ],
            "target_residual": 5.433905139184976e-07,
            "energy_eV": -348.6851813542523
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "inversion_parent_endpoint_00",
        "source": "same_species_inversion_center_projection_from_endpoint",
        "spacegroup": "P2_1/c",
        "spacegroup_number": 14,
        "pointgroup": "2/m",
        "has_inversion": true,
        "is_polar_point_group": false,
        "nonpolar_parent_hypothesis": true,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.0
        ],
        "formal_class": [
          0.0,
          0.0,
          0.0
        ],
        "target_residual": 1.7314993190474163e-15,
        "parent_symmetrization_rmsd_A": 0.33861973249465,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -347.6393893019792,
        "reduced_polarization": [
          -1.0433075208458126e-15,
          1.3256739574030537e-15,
          3.9011263433982416e-16
        ],
        "cartesian_polarization_e_A2": [
          -1.5226596782506237e-17,
          1.2619384354539961e-17,
          9.047860480613558e-18
        ],
        "ranking_score": 0.33861973249465344
      },
      "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": [
          -348.69151907135927,
          -348.6784375106544,
          -348.5644568778209,
          -348.3852055754329,
          -348.1755568773508,
          -347.96893948765614,
          -347.79515009287815,
          -347.6798539867693,
          -347.6393893019791
        ],
        "cartesian_polarizations_e_A2": [
          [
            -4.5106213137429794e-13,
            0.016366661082054795,
            1.7791559321172238e-10
          ],
          [
            -2.7924486803318975e-13,
            0.01455544783824978,
            1.5648681445408036e-10
          ],
          [
            -3.377549174098446e-13,
            0.01266312638604353,
            1.3450783301483698e-10
          ],
          [
            -5.499407103252372e-13,
            0.010693875843453687,
            1.1201096318483774e-10
          ],
          [
            -7.697524567314762e-13,
            0.008653646108242267,
            8.928361510952183e-11
          ],
          [
            -8.428278709606186e-13,
            0.006550844257510603,
            6.653714938121356e-11
          ],
          [
            -7.013759893175426e-13,
            0.0043980324790073065,
            4.399741859798939e-11
          ],
          [
            -3.9539778888483055e-13,
            0.002208988513204482,
            2.1846298755883214e-11
          ],
          [
            -8.500226819944841e-18,
            1.0285988756908044e-17,
            -8.476416660785332e-17
          ]
        ],
        "raw_reduced_polarization": [
          [
            1.9073563079112666e-09,
            1.7193276436117462,
            7.671108645703929e-09
          ],
          [
            1.6864395910839191e-09,
            1.5290585971069535,
            6.747173385015413e-09
          ],
          [
            1.4422447441488046e-09,
            1.3302690842633689,
            5.799515276477925e-09
          ],
          [
            1.1808733650754354e-09,
            1.1233981239558637,
            4.829527601205331e-09
          ],
          [
            9.164153405724064e-10,
            0.9090707565422489,
            3.849602496456326e-09
          ],
          [
            6.627542564293151e-10,
            0.6881701505557903,
            2.868853104243205e-09
          ],
          [
            4.2743878885014353e-10,
            0.4620159714158516,
            1.89701741203791e-09
          ],
          [
            2.08703159120923e-10,
            0.2320555790904451,
            9.419372874386421e-10
          ],
          [
            -1.5623724847292171e-15,
            1.080549338864376e-15,
            -3.654739416446773e-15
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            1.9073563079112666e-09,
            1.7193276436117462,
            7.671108645703929e-09
          ],
          [
            1.6864395910839191e-09,
            1.5290585971069535,
            6.747173385015413e-09
          ],
          [
            1.4422447441488046e-09,
            1.3302690842633689,
            5.799515276477925e-09
          ],
          [
            1.1808733650754354e-09,
            1.1233981239558637,
            4.829527601205331e-09
          ],
          [
            9.164153405724064e-10,
            0.9090707565422489,
            3.849602496456326e-09
          ],
          [
            6.627542564293151e-10,
            0.6881701505557903,
            2.868853104243205e-09
          ],
          [
            4.2743878885014353e-10,
            0.4620159714158516,
            1.89701741203791e-09
          ],
          [
            2.08703159120923e-10,
            0.2320555790904451,
            9.419372874386421e-10
          ],
          [
            -1.5623724847388426e-15,
            1.0824674490095276e-15,
            -3.65473941644197e-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": [
          [
            1.9073562729232663e-09,
            -0.28067235638825405,
            7.671108637197221e-09
          ],
          [
            1.6864395435689516e-09,
            -0.47094140289304676,
            6.747173375565296e-09
          ],
          [
            1.4422447680573214e-09,
            0.3302690842633689,
            5.799515312432391e-09
          ],
          [
            1.180873399064808e-09,
            0.12339812395586369,
            4.829527555649804e-09
          ],
          [
            9.164153880192316e-10,
            -0.09092924345775111,
            3.849602525640705e-09
          ],
          [
            6.627542958881349e-10,
            -0.31182984944420955,
            2.868853155035822e-09
          ],
          [
            4.274387510605493e-10,
            0.4620159714158516,
            1.897017432028747e-09
          ],
          [
            2.0870316586041326e-10,
            0.23205557909044505,
            9.419373059316172e-10
          ],
          [
            -1.5543122344752192e-15,
            1.1102230246251565e-15,
            -3.6637359812630166e-15
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -347.6393893019791,
          -347.6798539867692,
          -347.7951500928781,
          -347.96893948765626,
          -348.17555687735086,
          -348.38520557543285,
          -348.5644568778209,
          -348.6784375106545,
          -348.6915190713592
        ],
        "cartesian_polarizations_e_A2": [
          [
            -1.6333769183423423e-17,
            4.24773239405647e-17,
            -2.4667324889251697e-17
          ],
          [
            3.954438615428042e-13,
            -0.0022089885132044423,
            -2.1846360852778305e-11
          ],
          [
            7.013552387638351e-13,
            -0.004398032479007286,
            -4.399751598154035e-11
          ],
          [
            8.428371331125317e-13,
            -0.00655084425751055,
            -6.653726890821254e-11
          ],
          [
            7.697233250017446e-13,
            -0.008653646108242232,
            -8.92837161598373e-11
          ],
          [
            5.499357935273708e-13,
            -0.010693875843453757,
            -1.1201106371132971e-10
          ],
          [
            3.377252261413727e-13,
            -0.012663126386043512,
            -1.345079656850438e-10
          ],
          [
            2.7929327408676104e-13,
            -0.014555447838249786,
            -1.5648693588589207e-10
          ],
          [
            4.5105022629471816e-13,
            -0.01636666108205477,
            -1.7791566483268113e-10
          ]
        ],
        "raw_reduced_polarization": [
          [
            -1.4942046215845286e-15,
            4.462268566051034e-15,
            -1.0635702346738362e-15
          ],
          [
            -2.0870038109823273e-10,
            -0.23205557909044097,
            -9.419399648432486e-10
          ],
          [
            -4.274414077089681e-10,
            -0.4620159714158494,
            -1.8970216108817903e-09
          ],
          [
            -6.627548658742119e-10,
            -0.6881701505557848,
            -2.8688582578364273e-09
          ],
          [
            -9.164186280437607e-10,
            -0.9090707565422452,
            -3.849606853398485e-09
          ],
          [
            -1.1808748306616447e-09,
            -1.123398123955871,
            -4.829531935562021e-09
          ],
          [
            -1.4422484185824422e-09,
            -1.3302690842633669,
            -5.7995209967610785e-09
          ],
          [
            -1.686437285438298e-09,
            -1.5290585971069544,
            -6.7471786207376105e-09
          ],
          [
            -1.9073579822528967e-09,
            -1.7193276436117435,
            -7.671111733753411e-09
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -1.4942046215845286e-15,
            4.462268566051034e-15,
            -1.0635702346738362e-15
          ],
          [
            -2.0870038109823273e-10,
            -0.23205557909044097,
            -9.419399648432486e-10
          ],
          [
            -4.274414077089681e-10,
            -0.4620159714158494,
            -1.8970216108817903e-09
          ],
          [
            -6.627548658742119e-10,
            -0.6881701505557848,
            -2.8688582578364273e-09
          ],
          [
            -9.164186280437607e-10,
            -0.9090707565422452,
            -3.849606853398485e-09
          ],
          [
            -1.1808748306616447e-09,
            -1.123398123955871,
            -4.829531935562021e-09
          ],
          [
            -1.4422484185824422e-09,
            -1.3302690842633669,
            -5.7995209967610785e-09
          ],
          [
            -1.686437285438298e-09,
            -1.5290585971069544,
            -6.7471786207376105e-09
          ],
          [
            -1.9073579822528967e-09,
            -1.7193276436117435,
            -7.671111733753411e-09
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          -1.9073594326562362e-09,
          -1.719327643611744,
          -7.67111595518276e-09
        ],
        "actual_opposite_endpoint_branch_residual": 4.4856828715805935e-15
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            1.9073563079112666e-09,
            1.7193276436117462,
            7.671108645703929e-09
          ],
          [
            1.6864395910839191e-09,
            1.5290585971069535,
            6.747173385015413e-09
          ],
          [
            1.4422447441488046e-09,
            1.3302690842633689,
            5.799515276477925e-09
          ],
          [
            1.1808733650754354e-09,
            1.1233981239558637,
            4.829527601205331e-09
          ],
          [
            9.164153405724064e-10,
            0.9090707565422489,
            3.849602496456326e-09
          ],
          [
            6.627542564293151e-10,
            0.6881701505557903,
            2.868853104243205e-09
          ],
          [
            4.2743878885014353e-10,
            0.4620159714158516,
            1.89701741203791e-09
          ],
          [
            2.08703159120923e-10,
            0.2320555790904451,
            9.419372874386421e-10
          ],
          [
            -1.5623724847292171e-15,
            1.080549338864376e-15,
            -3.654739416446773e-15
          ],
          [
            -2.0870038109823273e-10,
            -0.23205557909044097,
            -9.419399648432486e-10
          ],
          [
            -4.274414077089681e-10,
            -0.4620159714158494,
            -1.8970216108817903e-09
          ],
          [
            -6.627548658742119e-10,
            -0.6881701505557848,
            -2.8688582578364273e-09
          ],
          [
            -9.164186280437607e-10,
            -0.9090707565422452,
            -3.849606853398485e-09
          ],
          [
            -1.1808748306616447e-09,
            -1.123398123955871,
            -4.829531935562021e-09
          ],
          [
            -1.4422484185824422e-09,
            -1.3302690842633669,
            -5.7995209967610785e-09
          ],
          [
            -1.686437285438298e-09,
            -1.5290585971069544,
            -6.7471786207376105e-09
          ],
          [
            -1.9073579822528967e-09,
            -1.7193276436117435,
            -7.671111733753411e-09
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            1.9073563079112666e-09,
            1.7193276436117462,
            7.671108645703929e-09
          ],
          [
            1.6864395910839191e-09,
            1.5290585971069535,
            6.747173385015413e-09
          ],
          [
            1.4422447441488046e-09,
            1.3302690842633689,
            5.799515276477925e-09
          ],
          [
            1.1808733650754354e-09,
            1.1233981239558637,
            4.829527601205331e-09
          ],
          [
            9.164153405724064e-10,
            0.9090707565422489,
            3.849602496456326e-09
          ],
          [
            6.627542564293151e-10,
            0.6881701505557903,
            2.868853104243205e-09
          ],
          [
            4.2743878885014353e-10,
            0.4620159714158516,
            1.89701741203791e-09
          ],
          [
            2.08703159120923e-10,
            0.2320555790904451,
            9.419372874386421e-10
          ],
          [
            -1.5623724847388426e-15,
            1.0824674490095276e-15,
            -3.65473941644197e-15
          ],
          [
            -2.0870038109823273e-10,
            -0.23205557909044097,
            -9.419399648432486e-10
          ],
          [
            -4.274414077089681e-10,
            -0.4620159714158494,
            -1.8970216108817903e-09
          ],
          [
            -6.627548658742119e-10,
            -0.6881701505557848,
            -2.8688582578364273e-09
          ],
          [
            -9.164186280437607e-10,
            -0.9090707565422452,
            -3.849606853398485e-09
          ],
          [
            -1.1808748306616447e-09,
            -1.123398123955871,
            -4.829531935562021e-09
          ],
          [
            -1.4422484185824422e-09,
            -1.3302690842633669,
            -5.7995209967610785e-09
          ],
          [
            -1.686437285438298e-09,
            -1.5290585971069544,
            -6.7471786207376105e-09
          ],
          [
            -1.9073579822528967e-09,
            -1.7193276436117435,
            -7.671111733753411e-09
          ]
        ],
        "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": [
          [
            1.9073562729232663e-09,
            -0.28067235638825405,
            7.671108637197221e-09
          ],
          [
            1.6864395435689516e-09,
            -0.47094140289304676,
            6.747173375565296e-09
          ],
          [
            1.4422447680573214e-09,
            0.3302690842633689,
            5.799515312432391e-09
          ],
          [
            1.180873399064808e-09,
            0.12339812395586369,
            4.829527555649804e-09
          ],
          [
            9.164153880192316e-10,
            -0.09092924345775111,
            3.849602525640705e-09
          ],
          [
            6.627542958881349e-10,
            -0.31182984944420955,
            2.868853155035822e-09
          ],
          [
            4.274387510605493e-10,
            0.4620159714158516,
            1.897017432028747e-09
          ],
          [
            2.0870316586041326e-10,
            0.23205557909044505,
            9.419373059316172e-10
          ],
          [
            -1.5543122344752192e-15,
            1.1102230246251565e-15,
            -3.6637359812630166e-15
          ],
          [
            -2.087003903028517e-10,
            -0.23205557909044094,
            -9.419399704668763e-10
          ],
          [
            -4.274414155958084e-10,
            -0.4620159714158494,
            -1.8970215953650893e-09
          ],
          [
            -6.627548509996473e-10,
            0.3118298494442152,
            -2.8688582620617353e-09
          ],
          [
            -9.16418607666003e-10,
            0.09092924345775477,
            -3.849606855510501e-09
          ],
          [
            -1.18087484235474e-09,
            -0.12339812395587102,
            -4.829531941030751e-09
          ],
          [
            -1.4422484317933026e-09,
            -0.3302690842633669,
            -5.799520974569816e-09
          ],
          [
            -1.6864372676117512e-09,
            0.47094140289304565,
            -6.747178593613512e-09
          ],
          [
            -1.9073579937689544e-09,
            0.2806723563882565,
            -7.67111174582169e-09
          ]
        ]
      },
      "incoming_structure_ids": [
        "incoming_01_000",
        "incoming_01_001",
        "incoming_01_002",
        "incoming_01_003",
        "incoming_01_004",
        "incoming_01_005",
        "incoming_01_006",
        "incoming_01_007",
        "incoming_01_008"
      ],
      "reflected_structure_ids": [
        "reflected_01_001",
        "reflected_01_002",
        "reflected_01_003",
        "reflected_01_004",
        "reflected_01_005",
        "reflected_01_006",
        "reflected_01_007",
        "reflected_01_008"
      ]
    },
    {
      "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,
        1.5,
        0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              1.9073574831729944e-09,
              1.719327643611746,
              7.67110927809704e-09
            ],
            "branch_aligned_reduced_polarization": [
              1.9073574831729944e-09,
              1.719327643611746,
              7.671109303331036e-09
            ],
            "target_residual": 0.5459895672823537,
            "energy_eV": -348.69151907135927,
            "max_atomic_step_A": 0.07584301767230572,
            "max_log_strain_component": 0.003131967136734896,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.7983339089273653,
            "cell_principal_stretches": [
              1.0032357573143955,
              0.9999719925024675,
              0.9968628558621868
            ],
            "cell_volume_ratio": 1.0000604521643566,
            "cell_rmsd_from_input_A": 0.02337308965190956
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              5.463790038898411e-06,
              1.4656099943222851,
              0.4998023213939878
            ],
            "branch_aligned_reduced_polarization": [
              5.463790038898411e-06,
              1.4656099943222851,
              0.4998023213939878
            ],
            "target_residual": 0.03439057424931341,
            "energy_eV": -347.80811598281804,
            "max_atomic_step_A": 0.001951648958318441,
            "max_log_strain_component": 6.9800459284316e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.7983339089273653,
            "cell_principal_stretches": [
              1.0032289080966512,
              0.9999763237124062,
              0.9968560520612297
            ],
            "cell_volume_ratio": 1.0000511305801407,
            "cell_rmsd_from_input_A": 0.023222446286418254
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              3.710694701113095e-06,
              1.4999695179646064,
              0.5000152380327278
            ],
            "branch_aligned_reduced_polarization": [
              3.710694701113095e-06,
              1.4999695179646064,
              0.5000152380327278
            ],
            "target_residual": 3.4280043440973675e-05,
            "energy_eV": -347.8106382738967
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_02",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          1.5,
          0.5
        ],
        "formal_class": [
          0.0,
          0.5,
          0.5
        ],
        "target_residual": 3.4280043440973675e-05,
        "parent_symmetrization_rmsd_A": 0.046199421389051615,
        "parent_cell_rmsd_A": 0.023222446286418254,
        "energy_eV": -347.8106382738967,
        "reduced_polarization": [
          3.710694701113095e-06,
          1.4999695179646064,
          0.5000152380327278
        ],
        "cartesian_polarization_e_A2": [
          -0.001692602498559881,
          0.014237812093013754,
          0.011555871602220937
        ],
        "ranking_score": 0.5520735930475381
      },
      "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,
        1.5,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              1.9073574831729944e-09,
              1.719327643611746,
              7.67110927809704e-09
            ],
            "branch_aligned_reduced_polarization": [
              1.9073574941685933e-09,
              1.719327643611746,
              7.67110927809704e-09
            ],
            "target_residual": 0.5459895725606155,
            "energy_eV": -348.69151907135927,
            "max_atomic_step_A": 0.03468424666664195,
            "max_log_strain_component": 0.0004526797868941835,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.7983339089273653,
            "cell_principal_stretches": [
              1.0004544110532263,
              0.9999718626985986,
              0.9996343470074744
            ],
            "cell_volume_ratio": 1.000060452109801,
            "cell_rmsd_from_input_A": 0.005699479740606576
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.4985446015937374,
              1.491945462272159,
              -1.283942363600458e-05
            ],
            "branch_aligned_reduced_polarization": [
              0.4985446015937374,
              1.491945462272159,
              -1.283942363600458e-05
            ],
            "target_residual": 0.008184981819220115,
            "energy_eV": -348.60478288821133,
            "max_atomic_step_A": 0.00045073189547080087,
            "max_log_strain_component": 1.6252839389126866e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.7983339089273653,
            "cell_principal_stretches": [
              1.00043812032268,
              0.9999731197567999,
              0.9996471983768301
            ],
            "cell_volume_ratio": 1.0000582815975165,
            "cell_rmsd_from_input_A": 0.005494939050472401
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.5000000777068829,
              1.4999967317985095,
              1.1301128107146006e-07
            ],
            "branch_aligned_reduced_polarization": [
              0.5000000777068829,
              1.4999967317985095,
              1.1301128107146006e-07
            ],
            "target_residual": 3.2710779403919255e-06,
            "energy_eV": -348.60639914211305
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_03",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.5,
          1.5,
          0.0
        ],
        "formal_class": [
          0.5,
          0.5,
          0.0
        ],
        "target_residual": 3.2710779403919255e-06,
        "parent_symmetrization_rmsd_A": 0.02131976572136339,
        "parent_cell_rmsd_A": 0.005494939050472401,
        "energy_eV": -348.60639914211305,
        "reduced_polarization": [
          0.5000000777068829,
          1.4999967317985095,
          1.1301128107146006e-07
        ],
        "cartesian_polarization_e_A2": [
          0.006666378377944225,
          0.014273206640972836,
          3.8955055064557016e-07
        ],
        "ranking_score": 0.5227000426398623
      },
      "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,
        2.0,
        0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              1.9073574831729944e-09,
              1.719327643611746,
              7.67110927809704e-09
            ],
            "branch_aligned_reduced_polarization": [
              1.9073574831729944e-09,
              1.719327643611746,
              7.671109303331036e-09
            ],
            "target_residual": 0.5733907602755959,
            "energy_eV": -348.69151907135927,
            "max_atomic_step_A": 0.0767031708092458,
            "max_log_strain_component": 0.003131967150946398,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.7983339089273653,
            "cell_principal_stretches": [
              1.0031512796784545,
              1.000035884054315,
              0.9967457405724314
            ],
            "cell_volume_ratio": 0.9999226451602733,
            "cell_rmsd_from_input_A": 0.02374139219704914
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              6.168848360303699e-05,
              1.9596379882446409,
              0.4950151728782108
            ],
            "branch_aligned_reduced_polarization": [
              6.168848360303699e-05,
              1.9596379882446409,
              0.4950151728782108
            ],
            "target_residual": 0.04066871401756987,
            "energy_eV": -347.7543087771556,
            "max_atomic_step_A": 0.002555348362706853,
            "max_log_strain_component": 9.157715293236779e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.7983339089273653,
            "cell_principal_stretches": [
              1.003197444356123,
              1.0000415941285223,
              0.9966819931989238
            ],
            "cell_volume_ratio": 0.9999104170854819,
            "cell_rmsd_from_input_A": 0.024389483225176922
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              7.305153842705658e-06,
              1.9999855659463959,
              0.5000191911110714
            ],
            "branch_aligned_reduced_polarization": [
              7.305153842705658e-06,
              1.9999855659463959,
              0.5000191911110714
            ],
            "target_residual": 2.5099918730295072e-05,
            "energy_eV": -347.71997646124703
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_04",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          2.0,
          0.5
        ],
        "formal_class": [
          0.0,
          0.0,
          0.5
        ],
        "target_residual": 2.5099918730295072e-05,
        "parent_symmetrization_rmsd_A": 0.04770671574702425,
        "parent_cell_rmsd_A": 0.024389483225176922,
        "energy_eV": -347.71997646124703,
        "reduced_polarization": [
          7.305153842705658e-06,
          1.9999855659463959,
          0.5000191911110714
        ],
        "cartesian_polarization_e_A2": [
          -0.0016956776259245544,
          0.01901425232208949,
          0.011529894854867054
        ],
        "ranking_score": 0.553854286390779
      },
      "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,
        2.0,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              1.9073574831729944e-09,
              1.719327643611746,
              7.67110927809704e-09
            ],
            "branch_aligned_reduced_polarization": [
              1.9073574941685933e-09,
              1.719327643611746,
              7.67110927809704e-09
            ],
            "target_residual": 0.5733907653016201,
            "energy_eV": -348.69151907135927,
            "max_atomic_step_A": 0.03592569705619736,
            "max_log_strain_component": 0.0005792917967201957,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.7983339089273653,
            "cell_principal_stretches": [
              1.0004663752859577,
              1.0000375586418813,
              0.9994189864640741
            ],
            "cell_volume_ratio": 0.999922645105725,
            "cell_rmsd_from_input_A": 0.007285129503667098
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.49480110837791397,
              1.9889655309149008,
              4.886975978020272e-05
            ],
            "branch_aligned_reduced_polarization": [
              0.49480110837791397,
              1.9889655309149008,
              4.886975978020272e-05
            ],
            "target_residual": 0.012197965828023426,
            "energy_eV": -348.63271350413953,
            "max_atomic_step_A": 0.0007170727318303218,
            "max_log_strain_component": 2.457120293851609e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.7983339089273653,
            "cell_principal_stretches": [
              1.0004860101112683,
              1.0000392963300788,
              0.9993943567779272
            ],
            "cell_volume_ratio": 0.9999193641578357,
            "cell_rmsd_from_input_A": 0.0075938737688744555
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.49999766353084374,
              1.9999923610461159,
              1.42646920821638e-07
            ],
            "branch_aligned_reduced_polarization": [
              0.49999766353084374,
              1.9999923610461159,
              1.42646920821638e-07
            ],
            "target_residual": 7.989558980683002e-06,
            "energy_eV": -348.62979902436797
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_05",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.5,
          2.0,
          0.0
        ],
        "formal_class": [
          0.5,
          0.0,
          0.0
        ],
        "target_residual": 7.989558980683002e-06,
        "parent_symmetrization_rmsd_A": 0.022587977610684394,
        "parent_cell_rmsd_A": 0.0075938737688744555,
        "energy_eV": -348.62979902436797,
        "reduced_polarization": [
          0.49999766353084374,
          1.9999923610461159,
          1.42646920821638e-07
        ],
        "cartesian_polarization_e_A2": [
          0.006667897502845106,
          0.01904933225241768,
          1.0143811270336422e-07
        ],
        "ranking_score": 0.5245024251708643
      },
      "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,
        1.5,
        0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              1.9073574831729944e-09,
              1.719327643611746,
              7.67110927809704e-09
            ],
            "branch_aligned_reduced_polarization": [
              1.9073574941685933e-09,
              1.719327643611746,
              7.671109303331036e-09
            ],
            "target_residual": 0.7403408712706697,
            "energy_eV": -348.69151907135927,
            "max_atomic_step_A": 0.07890037687420637,
            "max_log_strain_component": 0.0031158877156121046,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.7983339089273653,
            "cell_principal_stretches": [
              1.0032160113150195,
              0.9999712655319504,
              0.9968832015400121
            ],
            "cell_volume_ratio": 1.0000604521650638,
            "cell_rmsd_from_input_A": 0.023282786861289873
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.4973867302361107,
              1.4631576134559587,
              0.49918193499107866
            ],
            "branch_aligned_reduced_polarization": [
              0.4973867302361107,
              1.4631576134559587,
              0.49918193499107866
            ],
            "target_residual": 0.03694400973741524,
            "energy_eV": -347.7752430252834,
            "max_atomic_step_A": 0.0021010661953418746,
            "max_log_strain_component": 7.537884631756581e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.7983339089273653,
            "cell_principal_stretches": [
              1.0032122481308718,
              0.9999760589778945,
              0.9968721277848347
            ],
            "cell_volume_ratio": 1.000050385612426,
            "cell_rmsd_from_input_A": 0.023146974834502444
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.5000000566498299,
              1.4999680552904118,
              0.5000164208795699
            ],
            "branch_aligned_reduced_polarization": [
              0.5000000566498299,
              1.4999680552904118,
              0.5000164208795699
            ],
            "target_residual": 3.5918142570682484e-05,
            "energy_eV": -347.77525057147994
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_06",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.5,
          1.5,
          0.5
        ],
        "formal_class": [
          0.5,
          0.5,
          0.5
        ],
        "target_residual": 3.5918142570682484e-05,
        "parent_symmetrization_rmsd_A": 0.04844907271821975,
        "parent_cell_rmsd_A": 0.023146974834502444,
        "energy_eV": -347.77525057147994,
        "reduced_polarization": [
          0.5000000566498299,
          1.4999680552904118,
          0.5000164208795699
        ],
        "cartesian_polarization_e_A2": [
          0.004973789280622833,
          0.014235364463963575,
          0.011556152106734567
        ],
        "ranking_score": 0.5543076527119868
      },
      "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,
        2.0,
        0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              1.9073574831729944e-09,
              1.719327643611746,
              7.67110927809704e-09
            ],
            "branch_aligned_reduced_polarization": [
              1.9073574941685933e-09,
              1.719327643611746,
              7.671109303331036e-09
            ],
            "target_residual": 0.7607739230954675,
            "energy_eV": -348.69151907135927,
            "max_atomic_step_A": 0.07962202711996974,
            "max_log_strain_component": 0.003115887729823607,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.7983339089273653,
            "cell_principal_stretches": [
              1.0031308085040977,
              1.0000368054895885,
              0.99676516302398
            ],
            "cell_volume_ratio": 0.9999226451609797,
            "cell_rmsd_from_input_A": 0.02365304899953466
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.4936934963508847,
              1.9564350935534507,
              0.49445955908621686
            ],
            "branch_aligned_reduced_polarization": [
              0.4936934963508847,
              1.9564350935534507,
              0.49445955908621686
            ],
            "target_residual": 0.04436631095202778,
            "energy_eV": -347.71895458460796,
            "max_atomic_step_A": 0.0028040684257123276,
            "max_log_strain_component": 9.949169216905573e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.7983339089273653,
            "cell_principal_stretches": [
              1.0031816327730882,
              1.0000431608520282,
              0.996695087451701
            ],
            "cell_volume_ratio": 0.9999093602840443,
            "cell_rmsd_from_input_A": 0.02436517669781974
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.4999948690008742,
              1.9999773682482553,
              0.5000214207186383
            ],
            "branch_aligned_reduced_polarization": [
              0.4999948690008742,
              1.9999773682482553,
              0.5000214207186383
            ],
            "target_residual": 3.158117360141337e-05,
            "energy_eV": -347.6798975320825
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_07",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.5,
          2.0,
          0.5
        ],
        "formal_class": [
          0.5,
          0.0,
          0.5
        ],
        "target_residual": 3.158117360141337e-05,
        "parent_symmetrization_rmsd_A": 0.04996294210925592,
        "parent_cell_rmsd_A": 0.02436517669781974,
        "energy_eV": -347.6798975320825,
        "reduced_polarization": [
          0.4999948690008742,
          1.9999773682482553,
          0.5000214207186383
        ],
        "cartesian_polarization_e_A2": [
          0.004972161058058469,
          0.0190117783947627,
          0.011529853726474151
        ],
        "ranking_score": 0.5561173986309137
      },
      "branch_status": "awaiting_branch_sampling"
    }
  ],
  "sampled_polarization_branches": [
    {
      "orbit_id": 1,
      "candidate_id": "inversion_parent_endpoint_00",
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "construction": "MACEField-BEC-parent plus variable-cell P-N-P path and symmetric log-strain continuation beyond both polar endpoints",
      "geometry_diagnostics": {
        "collision_aware": false,
        "permutations_tested": 1,
        "selected_order": [
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          10,
          11,
          12,
          13,
          14,
          15,
          16,
          17,
          18,
          19,
          20,
          21,
          22,
          23,
          24,
          25,
          26,
          27,
          28,
          29,
          30,
          31,
          32,
          33,
          34,
          35,
          36,
          37,
          38,
          39,
          40,
          41,
          42,
          43
        ],
        "endpoint_rmsd_A": 0.33861973249465,
        "minimum_distance_A_by_image": [
          1.8295940258957475,
          1.825186441775335,
          1.8218325669803261,
          1.8195382282882226,
          1.8183074364685614,
          1.8181423514274146,
          1.8190432633155427,
          1.821008589984081,
          1.8240348908396664
        ],
        "minimum_distance_A": 1.8181423514274146,
        "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": [
          582.8515347102126,
          582.8515347102126,
          582.8515347102126,
          582.8515347102126,
          582.8515347102126,
          582.8515347102126,
          582.8515347102126,
          582.8515347102126,
          582.8515347102126
        ],
        "cell_deformation_log_strain_norm": 0.0
      },
      "parent_reduced_polarization": [
        -1.5623724847292171e-15,
        1.080549338864376e-15,
        -3.654739416446773e-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": [
          -348.69151907135927,
          -348.6784375106544,
          -348.5644568778209,
          -348.3852055754329,
          -348.1755568773508,
          -347.96893948765614,
          -347.79515009287815,
          -347.6798539867693,
          -347.6393893019791
        ],
        "cartesian_polarizations_e_A2": [
          [
            -4.5106213137429794e-13,
            0.016366661082054795,
            1.7791559321172238e-10
          ],
          [
            -2.7924486803318975e-13,
            0.01455544783824978,
            1.5648681445408036e-10
          ],
          [
            -3.377549174098446e-13,
            0.01266312638604353,
            1.3450783301483698e-10
          ],
          [
            -5.499407103252372e-13,
            0.010693875843453687,
            1.1201096318483774e-10
          ],
          [
            -7.697524567314762e-13,
            0.008653646108242267,
            8.928361510952183e-11
          ],
          [
            -8.428278709606186e-13,
            0.006550844257510603,
            6.653714938121356e-11
          ],
          [
            -7.013759893175426e-13,
            0.0043980324790073065,
            4.399741859798939e-11
          ],
          [
            -3.9539778888483055e-13,
            0.002208988513204482,
            2.1846298755883214e-11
          ],
          [
            -8.500226819944841e-18,
            1.0285988756908044e-17,
            -8.476416660785332e-17
          ]
        ],
        "raw_reduced_polarization": [
          [
            1.9073563079112666e-09,
            1.7193276436117462,
            7.671108645703929e-09
          ],
          [
            1.6864395910839191e-09,
            1.5290585971069535,
            6.747173385015413e-09
          ],
          [
            1.4422447441488046e-09,
            1.3302690842633689,
            5.799515276477925e-09
          ],
          [
            1.1808733650754354e-09,
            1.1233981239558637,
            4.829527601205331e-09
          ],
          [
            9.164153405724064e-10,
            0.9090707565422489,
            3.849602496456326e-09
          ],
          [
            6.627542564293151e-10,
            0.6881701505557903,
            2.868853104243205e-09
          ],
          [
            4.2743878885014353e-10,
            0.4620159714158516,
            1.89701741203791e-09
          ],
          [
            2.08703159120923e-10,
            0.2320555790904451,
            9.419372874386421e-10
          ],
          [
            -1.5623724847292171e-15,
            1.080549338864376e-15,
            -3.654739416446773e-15
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            1.9073563079112666e-09,
            1.7193276436117462,
            7.671108645703929e-09
          ],
          [
            1.6864395910839191e-09,
            1.5290585971069535,
            6.747173385015413e-09
          ],
          [
            1.4422447441488046e-09,
            1.3302690842633689,
            5.799515276477925e-09
          ],
          [
            1.1808733650754354e-09,
            1.1233981239558637,
            4.829527601205331e-09
          ],
          [
            9.164153405724064e-10,
            0.9090707565422489,
            3.849602496456326e-09
          ],
          [
            6.627542564293151e-10,
            0.6881701505557903,
            2.868853104243205e-09
          ],
          [
            4.2743878885014353e-10,
            0.4620159714158516,
            1.89701741203791e-09
          ],
          [
            2.08703159120923e-10,
            0.2320555790904451,
            9.419372874386421e-10
          ],
          [
            -1.5623724847388426e-15,
            1.0824674490095276e-15,
            -3.65473941644197e-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": [
          [
            1.9073562729232663e-09,
            -0.28067235638825405,
            7.671108637197221e-09
          ],
          [
            1.6864395435689516e-09,
            -0.47094140289304676,
            6.747173375565296e-09
          ],
          [
            1.4422447680573214e-09,
            0.3302690842633689,
            5.799515312432391e-09
          ],
          [
            1.180873399064808e-09,
            0.12339812395586369,
            4.829527555649804e-09
          ],
          [
            9.164153880192316e-10,
            -0.09092924345775111,
            3.849602525640705e-09
          ],
          [
            6.627542958881349e-10,
            -0.31182984944420955,
            2.868853155035822e-09
          ],
          [
            4.274387510605493e-10,
            0.4620159714158516,
            1.897017432028747e-09
          ],
          [
            2.0870316586041326e-10,
            0.23205557909044505,
            9.419373059316172e-10
          ],
          [
            -1.5543122344752192e-15,
            1.1102230246251565e-15,
            -3.6637359812630166e-15
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -347.6393893019791,
          -347.6798539867692,
          -347.7951500928781,
          -347.96893948765626,
          -348.17555687735086,
          -348.38520557543285,
          -348.5644568778209,
          -348.6784375106545,
          -348.6915190713592
        ],
        "cartesian_polarizations_e_A2": [
          [
            -1.6333769183423423e-17,
            4.24773239405647e-17,
            -2.4667324889251697e-17
          ],
          [
            3.954438615428042e-13,
            -0.0022089885132044423,
            -2.1846360852778305e-11
          ],
          [
            7.013552387638351e-13,
            -0.004398032479007286,
            -4.399751598154035e-11
          ],
          [
            8.428371331125317e-13,
            -0.00655084425751055,
            -6.653726890821254e-11
          ],
          [
            7.697233250017446e-13,
            -0.008653646108242232,
            -8.92837161598373e-11
          ],
          [
            5.499357935273708e-13,
            -0.010693875843453757,
            -1.1201106371132971e-10
          ],
          [
            3.377252261413727e-13,
            -0.012663126386043512,
            -1.345079656850438e-10
          ],
          [
            2.7929327408676104e-13,
            -0.014555447838249786,
            -1.5648693588589207e-10
          ],
          [
            4.5105022629471816e-13,
            -0.01636666108205477,
            -1.7791566483268113e-10
          ]
        ],
        "raw_reduced_polarization": [
          [
            -1.4942046215845286e-15,
            4.462268566051034e-15,
            -1.0635702346738362e-15
          ],
          [
            -2.0870038109823273e-10,
            -0.23205557909044097,
            -9.419399648432486e-10
          ],
          [
            -4.274414077089681e-10,
            -0.4620159714158494,
            -1.8970216108817903e-09
          ],
          [
            -6.627548658742119e-10,
            -0.6881701505557848,
            -2.8688582578364273e-09
          ],
          [
            -9.164186280437607e-10,
            -0.9090707565422452,
            -3.849606853398485e-09
          ],
          [
            -1.1808748306616447e-09,
            -1.123398123955871,
            -4.829531935562021e-09
          ],
          [
            -1.4422484185824422e-09,
            -1.3302690842633669,
            -5.7995209967610785e-09
          ],
          [
            -1.686437285438298e-09,
            -1.5290585971069544,
            -6.7471786207376105e-09
          ],
          [
            -1.9073579822528967e-09,
            -1.7193276436117435,
            -7.671111733753411e-09
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -1.4942046215845286e-15,
            4.462268566051034e-15,
            -1.0635702346738362e-15
          ],
          [
            -2.0870038109823273e-10,
            -0.23205557909044097,
            -9.419399648432486e-10
          ],
          [
            -4.274414077089681e-10,
            -0.4620159714158494,
            -1.8970216108817903e-09
          ],
          [
            -6.627548658742119e-10,
            -0.6881701505557848,
            -2.8688582578364273e-09
          ],
          [
            -9.164186280437607e-10,
            -0.9090707565422452,
            -3.849606853398485e-09
          ],
          [
            -1.1808748306616447e-09,
            -1.123398123955871,
            -4.829531935562021e-09
          ],
          [
            -1.4422484185824422e-09,
            -1.3302690842633669,
            -5.7995209967610785e-09
          ],
          [
            -1.686437285438298e-09,
            -1.5290585971069544,
            -6.7471786207376105e-09
          ],
          [
            -1.9073579822528967e-09,
            -1.7193276436117435,
            -7.671111733753411e-09
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          -1.9073594326562362e-09,
          -1.719327643611744,
          -7.67111595518276e-09
        ],
        "actual_opposite_endpoint_branch_residual": 4.4856828715805935e-15
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            1.9073563079112666e-09,
            1.7193276436117462,
            7.671108645703929e-09
          ],
          [
            1.6864395910839191e-09,
            1.5290585971069535,
            6.747173385015413e-09
          ],
          [
            1.4422447441488046e-09,
            1.3302690842633689,
            5.799515276477925e-09
          ],
          [
            1.1808733650754354e-09,
            1.1233981239558637,
            4.829527601205331e-09
          ],
          [
            9.164153405724064e-10,
            0.9090707565422489,
            3.849602496456326e-09
          ],
          [
            6.627542564293151e-10,
            0.6881701505557903,
            2.868853104243205e-09
          ],
          [
            4.2743878885014353e-10,
            0.4620159714158516,
            1.89701741203791e-09
          ],
          [
            2.08703159120923e-10,
            0.2320555790904451,
            9.419372874386421e-10
          ],
          [
            -1.5623724847292171e-15,
            1.080549338864376e-15,
            -3.654739416446773e-15
          ],
          [
            -2.0870038109823273e-10,
            -0.23205557909044097,
            -9.419399648432486e-10
          ],
          [
            -4.274414077089681e-10,
            -0.4620159714158494,
            -1.8970216108817903e-09
          ],
          [
            -6.627548658742119e-10,
            -0.6881701505557848,
            -2.8688582578364273e-09
          ],
          [
            -9.164186280437607e-10,
            -0.9090707565422452,
            -3.849606853398485e-09
          ],
          [
            -1.1808748306616447e-09,
            -1.123398123955871,
            -4.829531935562021e-09
          ],
          [
            -1.4422484185824422e-09,
            -1.3302690842633669,
            -5.7995209967610785e-09
          ],
          [
            -1.686437285438298e-09,
            -1.5290585971069544,
            -6.7471786207376105e-09
          ],
          [
            -1.9073579822528967e-09,
            -1.7193276436117435,
            -7.671111733753411e-09
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            1.9073563079112666e-09,
            1.7193276436117462,
            7.671108645703929e-09
          ],
          [
            1.6864395910839191e-09,
            1.5290585971069535,
            6.747173385015413e-09
          ],
          [
            1.4422447441488046e-09,
            1.3302690842633689,
            5.799515276477925e-09
          ],
          [
            1.1808733650754354e-09,
            1.1233981239558637,
            4.829527601205331e-09
          ],
          [
            9.164153405724064e-10,
            0.9090707565422489,
            3.849602496456326e-09
          ],
          [
            6.627542564293151e-10,
            0.6881701505557903,
            2.868853104243205e-09
          ],
          [
            4.2743878885014353e-10,
            0.4620159714158516,
            1.89701741203791e-09
          ],
          [
            2.08703159120923e-10,
            0.2320555790904451,
            9.419372874386421e-10
          ],
          [
            -1.5623724847388426e-15,
            1.0824674490095276e-15,
            -3.65473941644197e-15
          ],
          [
            -2.0870038109823273e-10,
            -0.23205557909044097,
            -9.419399648432486e-10
          ],
          [
            -4.274414077089681e-10,
            -0.4620159714158494,
            -1.8970216108817903e-09
          ],
          [
            -6.627548658742119e-10,
            -0.6881701505557848,
            -2.8688582578364273e-09
          ],
          [
            -9.164186280437607e-10,
            -0.9090707565422452,
            -3.849606853398485e-09
          ],
          [
            -1.1808748306616447e-09,
            -1.123398123955871,
            -4.829531935562021e-09
          ],
          [
            -1.4422484185824422e-09,
            -1.3302690842633669,
            -5.7995209967610785e-09
          ],
          [
            -1.686437285438298e-09,
            -1.5290585971069544,
            -6.7471786207376105e-09
          ],
          [
            -1.9073579822528967e-09,
            -1.7193276436117435,
            -7.671111733753411e-09
          ]
        ],
        "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": [
          [
            1.9073562729232663e-09,
            -0.28067235638825405,
            7.671108637197221e-09
          ],
          [
            1.6864395435689516e-09,
            -0.47094140289304676,
            6.747173375565296e-09
          ],
          [
            1.4422447680573214e-09,
            0.3302690842633689,
            5.799515312432391e-09
          ],
          [
            1.180873399064808e-09,
            0.12339812395586369,
            4.829527555649804e-09
          ],
          [
            9.164153880192316e-10,
            -0.09092924345775111,
            3.849602525640705e-09
          ],
          [
            6.627542958881349e-10,
            -0.31182984944420955,
            2.868853155035822e-09
          ],
          [
            4.274387510605493e-10,
            0.4620159714158516,
            1.897017432028747e-09
          ],
          [
            2.0870316586041326e-10,
            0.23205557909044505,
            9.419373059316172e-10
          ],
          [
            -1.5543122344752192e-15,
            1.1102230246251565e-15,
            -3.6637359812630166e-15
          ],
          [
            -2.087003903028517e-10,
            -0.23205557909044094,
            -9.419399704668763e-10
          ],
          [
            -4.274414155958084e-10,
            -0.4620159714158494,
            -1.8970215953650893e-09
          ],
          [
            -6.627548509996473e-10,
            0.3118298494442152,
            -2.8688582620617353e-09
          ],
          [
            -9.16418607666003e-10,
            0.09092924345775477,
            -3.849606855510501e-09
          ],
          [
            -1.18087484235474e-09,
            -0.12339812395587102,
            -4.829531941030751e-09
          ],
          [
            -1.4422484317933026e-09,
            -0.3302690842633669,
            -5.799520974569816e-09
          ],
          [
            -1.6864372676117512e-09,
            0.47094140289304565,
            -6.747178593613512e-09
          ],
          [
            -1.9073579937689544e-09,
            0.2806723563882565,
            -7.67111174582169e-09
          ]
        ]
      },
      "incoming_structure_ids": [
        "incoming_01_000",
        "incoming_01_001",
        "incoming_01_002",
        "incoming_01_003",
        "incoming_01_004",
        "incoming_01_005",
        "incoming_01_006",
        "incoming_01_007",
        "incoming_01_008"
      ],
      "reflected_structure_ids": [
        "reflected_01_001",
        "reflected_01_002",
        "reflected_01_003",
        "reflected_01_004",
        "reflected_01_005",
        "reflected_01_006",
        "reflected_01_007",
        "reflected_01_008"
      ],
      "positive_extension_structure_ids": [
        "extension_plus_01_000",
        "extension_plus_01_001",
        "extension_plus_01_002",
        "extension_plus_01_003"
      ],
      "negative_extension_structure_ids": [
        "extension_minus_01_000",
        "extension_minus_01_001",
        "extension_minus_01_002",
        "extension_minus_01_003"
      ],
      "extension": {
        "enabled": true,
        "fraction_beyond_polar_endpoint": 0.35,
        "images_per_side": 4,
        "construction": "continue fractional atomic displacements and symmetric log strain beyond +P; reflect these structures about N for the -P side",
        "positive_path_coordinates": [
          1.35,
          1.2625,
          1.175,
          1.0875
        ],
        "negative_path_coordinates": [
          -1.0875,
          -1.175,
          -1.2625,
          -1.35
        ]
      },
      "branch_coordinates": [
        1.35,
        1.2625,
        1.175,
        1.0875,
        1.0,
        0.875,
        0.75,
        0.625,
        0.5,
        0.375,
        0.25,
        0.125,
        0.0,
        -0.125,
        -0.25,
        -0.375,
        -0.5,
        -0.625,
        -0.75,
        -0.875,
        -1.0,
        -1.0875,
        -1.175,
        -1.2625,
        -1.35
      ],
      "parent": {
        "candidate_id": "inversion_parent_endpoint_00",
        "source": "same_species_inversion_center_projection_from_endpoint",
        "spacegroup": "P2_1/c",
        "spacegroup_number": 14,
        "pointgroup": "2/m",
        "has_inversion": true,
        "is_polar_point_group": false,
        "nonpolar_parent_hypothesis": true,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.0
        ],
        "formal_class": [
          0.0,
          0.0,
          0.0
        ],
        "target_residual": 1.7314993190474163e-15,
        "parent_symmetrization_rmsd_A": 0.33861973249465,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -347.6393893019792,
        "reduced_polarization": [
          -1.0433075208458126e-15,
          1.3256739574030537e-15,
          3.9011263433982416e-16
        ],
        "cartesian_polarization_e_A2": [
          -1.5226596782506237e-17,
          1.2619384354539961e-17,
          9.047860480613558e-18
        ],
        "ranking_score": 0.33861973249465344
      }
    }
  ],
  "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": 50,
      "full_response": 17,
      "energy_polarization": 33
    },
    "model_evaluations_for_recovery_and_path_properties": {
      "total": 75,
      "full_response": 42,
      "energy_polarization": 33
    },
    "elapsed_seconds": 898.2470141960075
  }
}
