{
  "schema": "ferrofinder.endpoint_parent_recovery.v4_variable_cell",
  "status": "complete",
  "input_atom_count": 44,
  "input_formula": "Bi16Br8O20",
  "input_spacegroup": "P2_1",
  "input_pointgroup": "2",
  "input_is_polar_point_group": true,
  "input_energy_eV": -223.01320244029378,
  "input_cartesian_polarization_e_A2": [
    2.4035342926429535e-12,
    -0.008059835220876011,
    -2.4445392366353963e-11
  ],
  "input_reduced_polarization": [
    -1.0612878752379118e-10,
    -1.3104532051733997,
    -1.5584175347689945e-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,
        -1.0,
        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,
        -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,
        -1.5,
        -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": "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": 1.00442621929409e-15,
      "parent_symmetrization_rmsd_A": 0.2537906886457398,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -221.59138239106127,
      "reduced_polarization": [
        -5.205413489557387e-16,
        -7.841829824552487e-16,
        -3.5066477447891787e-16
      ],
      "cartesian_polarization_e_A2": [
        -5.366743090157773e-18,
        -4.823053273976382e-18,
        -5.50054000930298e-18
      ],
      "ranking_score": 0.2537906886457418
    },
    {
      "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": 0.0008405755904268286,
      "parent_symmetrization_rmsd_A": 0.010676565727758413,
      "parent_cell_rmsd_A": 0.016438247436683755,
      "energy_eV": -223.05650761630562,
      "reduced_polarization": [
        -3.210705808165404e-12,
        -1.5008405755904268,
        3.373673337617462e-12
      ],
      "cartesian_polarization_e_A2": [
        1.7741738980860608e-13,
        -0.009242008895328144,
        -3.20553530418778e-13
      ],
      "ranking_score": 0.516467278767783
    },
    {
      "candidate_id": "inversion_parent_bec_00_00",
      "source": "same_species_inversion_center_projection_after_BEC",
      "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,
        -1.5,
        0.0
      ],
      "formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_residual": 0.49999999999999845,
      "parent_symmetrization_rmsd_A": 0.2537929194036099,
      "parent_cell_rmsd_A": 0.016438247436683755,
      "energy_eV": -221.67020877801704,
      "reduced_polarization": [
        1.9748667343396334e-15,
        -1.5441861014301004e-15,
        1.5494424551423347e-15
      ],
      "cartesian_polarization_e_A2": [
        1.9945065092596456e-17,
        -9.508925809185226e-18,
        2.4427102192056335e-17
      ],
      "ranking_score": 1.2579024812627777
    },
    {
      "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,
        -1.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 8.999824977484751e-06,
      "parent_symmetrization_rmsd_A": 0.01745034649105971,
      "parent_cell_rmsd_A": 0.027256854449665496,
      "energy_eV": -222.8641874857229,
      "reduced_polarization": [
        9.768290566530998e-14,
        -1.0000089998249775,
        -8.914827093051018e-14
      ],
      "cartesian_polarization_e_A2": [
        7.565609577319753e-14,
        -0.00613816453665248,
        -4.445856644978058e-13
      ],
      "ranking_score": 0.5242825597534311
    },
    {
      "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": 0.00022502786498707403,
      "parent_symmetrization_rmsd_A": 0.0922182745085198,
      "parent_cell_rmsd_A": 0.13538495000258985,
      "energy_eV": -222.11561474538638,
      "reduced_polarization": [
        3.020091561873655e-06,
        -1.5002174479452888,
        -0.4999421656662761
      ],
      "cartesian_polarization_e_A2": [
        0.0011086315640923556,
        -0.0090945454358832,
        -0.007714525420014988
      ],
      "ranking_score": 0.6265145677391414
    },
    {
      "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": 5.4913072005059915e-05,
      "parent_symmetrization_rmsd_A": 0.07240618440932392,
      "parent_cell_rmsd_A": 0.09472387789618304,
      "energy_eV": -222.38227573980424,
      "reduced_polarization": [
        -0.5000113562133898,
        -1.5000537239312715,
        4.702161407184355e-07
      ],
      "cartesian_polarization_e_A2": [
        -0.005831996974194064,
        -0.009147629193195112,
        -4.516923708277417e-05
      ],
      "ranking_score": 0.5961969800273798
    },
    {
      "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": 0.0009573796031105543,
      "parent_symmetrization_rmsd_A": 0.09376834991268726,
      "parent_cell_rmsd_A": 0.14314275485569436,
      "energy_eV": -222.01038366499338,
      "reduced_polarization": [
        -6.648770616144307e-05,
        -1.0009175678369273,
        -0.4997350012188367
      ],
      "cartesian_polarization_e_A2": [
        0.0011294366117658918,
        -0.005998544698104799,
        -0.007670622819806021
      ],
      "ranking_score": 0.6314687978328319
    },
    {
      "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": 0.00036483258768888225,
      "parent_symmetrization_rmsd_A": 0.07383851701964565,
      "parent_cell_rmsd_A": 0.10129564827584517,
      "energy_eV": -222.23801979210785,
      "reduced_polarization": [
        -0.4999123830145508,
        -1.0003531684880815,
        -2.6421580701526995e-05
      ],
      "cartesian_polarization_e_A2": [
        -0.00580995485079431,
        -0.006049961464442675,
        -2.1889583506749612e-05
      ],
      "ranking_score": 0.5998920942639847
    },
    {
      "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": 5.479160576881826e-05,
      "parent_symmetrization_rmsd_A": 0.09989917170896842,
      "parent_cell_rmsd_A": 0.09202973294625798,
      "energy_eV": -222.16159672510793,
      "reduced_polarization": [
        -0.5000157625012905,
        -1.500049176133267,
        -0.4999816868480951
      ],
      "cartesian_polarization_e_A2": [
        -0.004723379445658525,
        -0.009101119957788695,
        -0.007763310575279819
      ],
      "ranking_score": 0.6230161881570706
    },
    {
      "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": 0.0003234721965263414,
      "parent_symmetrization_rmsd_A": 0.1008077757253786,
      "parent_cell_rmsd_A": 0.09695528273057831,
      "energy_eV": -222.0908759115504,
      "reduced_polarization": [
        -0.49999857866350783,
        -1.0003139910886687,
        -0.4999222707393268
      ],
      "cartesian_polarization_e_A2": [
        -0.004680043409374092,
        -0.006003943168491551,
        -0.007697977355464611
      ],
      "ranking_score": 0.6256935408010759
    }
  ],
  "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": [
              -1.0612878752379118e-10,
              -1.3104532051733997,
              -1.5584175347689945e-09
            ],
            "branch_aligned_reduced_polarization": [
              -1.0612878752379118e-10,
              -1.3104532051733997,
              -1.5584175347689945e-09
            ],
            "target_residual": 0.1895467948266003,
            "energy_eV": -223.01320244029378,
            "max_atomic_step_A": 0.01049978900392966,
            "max_log_strain_component": 0.0037380494925197873,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 8.30004886281693,
            "cell_principal_stretches": [
              1.0000679152669478,
              0.9987190448237541,
              0.9962689283173106
            ],
            "cell_volume_ratio": 0.9950603276750452,
            "cell_rmsd_from_input_A": 0.016438247436683755
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -3.210705808165404e-12,
              -1.5008405755904268,
              3.373673337617462e-12
            ],
            "branch_aligned_reduced_polarization": [
              -3.210705808165404e-12,
              -1.5008405755904268,
              3.373673337617462e-12
            ],
            "target_residual": 0.0008405755904268286,
            "energy_eV": -223.05650761630562
          }
        ],
        "iterations": 1
      },
      "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": 0.0008405755904268286,
        "parent_symmetrization_rmsd_A": 0.010676565727758413,
        "parent_cell_rmsd_A": 0.016438247436683755,
        "energy_eV": -223.05650761630562,
        "reduced_polarization": [
          -3.210705808165404e-12,
          -1.5008405755904268,
          3.373673337617462e-12
        ],
        "cartesian_polarization_e_A2": [
          1.7741738980860608e-13,
          -0.009242008895328144,
          -3.20553530418778e-13
        ],
        "ranking_score": 0.516467278767783
      },
      "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,
        -1.0,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -1.0612878752379118e-10,
              -1.3104532051733997,
              -1.5584175347689945e-09
            ],
            "branch_aligned_reduced_polarization": [
              -1.0612878752379118e-10,
              -1.3104532051733997,
              -1.5584175347689945e-09
            ],
            "target_residual": 0.3104532051733997,
            "energy_eV": -223.01320244029378,
            "max_atomic_step_A": 0.01719730027662026,
            "max_log_strain_component": 0.00612244299414927,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 8.30004886281693,
            "cell_principal_stretches": [
              1.006141223456131,
              1.0021015895272694,
              0.999888773514658
            ],
            "cell_volume_ratio": 1.008143574574315,
            "cell_rmsd_from_input_A": 0.027049950267229627
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              1.005271691047467e-11,
              -1.0023368407065771,
              -1.5857124649953917e-11
            ],
            "branch_aligned_reduced_polarization": [
              1.005271691047467e-11,
              -1.0023368407065771,
              -1.5857124649953917e-11
            ],
            "target_residual": 0.002336840706577137,
            "energy_eV": -222.86565679299017,
            "max_atomic_step_A": 0.00012988861715001465,
            "max_log_strain_component": 4.669339281748527e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 8.30004886281693,
            "cell_principal_stretches": [
              1.0061882047003559,
              1.0021176344581157,
              0.9998879252828436
            ],
            "cell_volume_ratio": 1.008205936453581,
            "cell_rmsd_from_input_A": 0.027256854449665496
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              9.768290566530998e-14,
              -1.0000089998249775,
              -8.914827093051018e-14
            ],
            "branch_aligned_reduced_polarization": [
              9.768290566530998e-14,
              -1.0000089998249775,
              -8.914827093051018e-14
            ],
            "target_residual": 8.999824977484751e-06,
            "energy_eV": -222.8641874857229
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "inversion_parent_endpoint_00",
        "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": 1.00442621929409e-15,
        "parent_symmetrization_rmsd_A": 0.2537906886457398,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -221.59138239106127,
        "reduced_polarization": [
          -5.205413489557387e-16,
          -7.841829824552487e-16,
          -3.5066477447891787e-16
        ],
        "cartesian_polarization_e_A2": [
          -5.366743090157773e-18,
          -4.823053273976382e-18,
          -5.50054000930298e-18
        ],
        "ranking_score": 0.2537906886457418
      },
      "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": [
          -223.0132024402938,
          -222.82793964835824,
          -222.55598448812503,
          -222.25794220747042,
          -221.99713714586866,
          -221.80683353991571,
          -221.68394339352568,
          -221.61435053982296,
          -221.59138239106127
        ],
        "cartesian_polarizations_e_A2": [
          [
            2.4035694515000396e-12,
            -0.008059835220876003,
            -2.4445363808144888e-11
          ],
          [
            2.0273784369396313e-12,
            -0.006656142541743605,
            -2.0880967603248855e-11
          ],
          [
            1.537141693636177e-12,
            -0.005426305269828204,
            -1.734483152275862e-11
          ],
          [
            1.1278536325133057e-12,
            -0.004417293666438456,
            -1.4042998079800333e-11
          ],
          [
            8.983774958446556e-13,
            -0.003563491242948019,
            -1.1109647150034444e-11
          ],
          [
            7.946744176147776e-13,
            -0.0027366860578136747,
            -8.39828942230855e-12
          ],
          [
            6.379278704157556e-13,
            -0.0018659616466863667,
            -5.660423373239227e-12
          ],
          [
            3.5266427579534767e-13,
            -0.0009472255999209693,
            -2.8419797203114084e-12
          ],
          [
            -7.522360120830563e-18,
            -1.0508647124627638e-17,
            -1.9519483870850848e-17
          ]
        ],
        "raw_reduced_polarization": [
          [
            -1.0612547159869975e-10,
            -1.3104532051733984,
            -1.5584157141553952e-09
          ],
          [
            -9.281397473753433e-11,
            -1.0822260119321503,
            -1.3311819899702373e-09
          ],
          [
            -8.944681778666104e-11,
            -0.8822660685019321,
            -1.1057498761969202e-09
          ],
          [
            -8.22281497043903e-11,
            -0.7182102964565661,
            -8.952547834089968e-10
          ],
          [
            -6.45380361073631e-11,
            -0.5793900734885026,
            -7.082508091602529e-10
          ],
          [
            -3.907274587856769e-11,
            -0.44495934690157307,
            -5.35399117414236e-10
          ],
          [
            -1.773271615391183e-11,
            -0.3033877683128382,
            -3.608574944051091e-10
          ],
          [
            -6.181471879504776e-12,
            -0.1540099505041514,
            -1.8117897079398635e-10
          ],
          [
            -8.785140062756076e-16,
            -1.708606929188282e-15,
            -1.2443860780832952e-15
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -1.0612547159869975e-10,
            -1.3104532051733984,
            -1.5584157141553952e-09
          ],
          [
            -9.281397473753433e-11,
            -1.0822260119321503,
            -1.3311819899702373e-09
          ],
          [
            -8.944681778666104e-11,
            -0.8822660685019321,
            -1.1057498761969202e-09
          ],
          [
            -8.22281497043903e-11,
            -0.7182102964565661,
            -8.952547834089968e-10
          ],
          [
            -6.45380361073631e-11,
            -0.5793900734885026,
            -7.082508091602529e-10
          ],
          [
            -3.907274587856769e-11,
            -0.44495934690157307,
            -5.35399117414236e-10
          ],
          [
            -1.773271615391183e-11,
            -0.3033877683128382,
            -3.608574944051091e-10
          ],
          [
            -6.181471879504776e-12,
            -0.1540099505041514,
            -1.8117897079398635e-10
          ],
          [
            -8.785140062759449e-16,
            -1.7208456881689926e-15,
            -1.2443860780924921e-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": [
          [
            -1.0612549727895271e-10,
            -0.31045320517339836,
            -1.5584157297965362e-09
          ],
          [
            -9.281397872484831e-11,
            -0.08222601193215029,
            -1.3311819979655581e-09
          ],
          [
            -8.94468388246139e-11,
            0.11773393149806788,
            -1.1057498805477906e-09
          ],
          [
            -8.222816871850114e-11,
            0.2817897035434339,
            -8.952547592144811e-10
          ],
          [
            -6.453804157757759e-11,
            0.4206099265114974,
            -7.08250791348064e-10
          ],
          [
            -3.907274503944791e-11,
            -0.44495934690157307,
            -5.353991139323e-10
          ],
          [
            -1.7732704193917925e-11,
            -0.3033877683128382,
            -3.608575105396028e-10
          ],
          [
            -6.181444245356715e-12,
            -0.1540099505041514,
            -1.8117896072311623e-10
          ],
          [
            -8.881784197001252e-16,
            -1.7208456881689926e-15,
            -1.2212453270876722e-15
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -221.5913823910613,
          -221.61435053982296,
          -221.6839433935257,
          -221.80683353991566,
          -221.99713714586863,
          -222.25794220747048,
          -222.55598448812503,
          -222.82793964835824,
          -223.0132024402938
        ],
        "cartesian_polarizations_e_A2": [
          [
            -3.97674176348256e-18,
            7.044602608242352e-18,
            -1.525284878255367e-17
          ],
          [
            -3.5272524259150486e-13,
            0.0009472255999209667,
            2.8419790067278398e-12
          ],
          [
            -6.380336220140155e-13,
            0.0018659616466863737,
            5.660387411600625e-12
          ],
          [
            -7.947535510592898e-13,
            0.002736686057813685,
            8.398197251097583e-12
          ],
          [
            -8.983562667334845e-13,
            0.0035634912429479988,
            1.1109626024987543e-11
          ],
          [
            -1.1278912591802343e-12,
            0.004417293666438479,
            1.4042957405536913e-11
          ],
          [
            -1.5370453449880682e-12,
            0.005426305269828221,
            1.734478923549901e-11
          ],
          [
            -2.027353907504455e-12,
            0.006656142541743604,
            2.088095182264556e-11
          ],
          [
            -2.4036501459086086e-12,
            0.008059835220876022,
            2.4445373887512796e-11
          ]
        ],
        "raw_reduced_polarization": [
          [
            -5.266347844432885e-16,
            1.1453859556871574e-15,
            -9.72383942203702e-16
          ],
          [
            6.176337285594822e-12,
            0.15400995050415098,
            1.8117892530233992e-10
          ],
          [
            1.7723372019823157e-11,
            0.3033877683128393,
            3.608552018156781e-10
          ],
          [
            3.906493091471179e-11,
            0.4449593469015748,
            5.353932414099068e-10
          ],
          [
            6.453955454319902e-11,
            0.5793900734884992,
            7.082494624179704e-10
          ],
          [
            8.222447355092116e-11,
            0.7182102964565699,
            8.952521903851508e-10
          ],
          [
            8.945438486282568e-11,
            0.8822660685019348,
            1.1057471803429986e-09
          ],
          [
            9.281583801883507e-11,
            1.08222601193215,
            1.3311809839414318e-09
          ],
          [
            1.0611881453958593e-10,
            1.3104532051734015,
            1.5584163567249008e-09
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -5.266347844432885e-16,
            1.1453859556871574e-15,
            -9.72383942203702e-16
          ],
          [
            6.176337285594822e-12,
            0.15400995050415098,
            1.8117892530233992e-10
          ],
          [
            1.7723372019823157e-11,
            0.3033877683128393,
            3.608552018156781e-10
          ],
          [
            3.906493091471179e-11,
            0.4449593469015748,
            5.353932414099068e-10
          ],
          [
            6.453955454319902e-11,
            0.5793900734884992,
            7.082494624179704e-10
          ],
          [
            8.222447355092116e-11,
            0.7182102964565699,
            8.952521903851508e-10
          ],
          [
            8.945438486282568e-11,
            0.8822660685019348,
            1.1057471803429986e-09
          ],
          [
            9.281583801883507e-11,
            1.08222601193215,
            1.3311809839414318e-09
          ],
          [
            1.0611881453958593e-10,
            1.3104532051734015,
            1.5584163567249008e-09
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          1.061237145706872e-10,
          1.310453205173395,
          1.558413225383239e-09
        ],
        "actual_opposite_endpoint_branch_residual": 8.676410935810333e-15
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            -1.0612547159869975e-10,
            -1.3104532051733984,
            -1.5584157141553952e-09
          ],
          [
            -9.281397473753433e-11,
            -1.0822260119321503,
            -1.3311819899702373e-09
          ],
          [
            -8.944681778666104e-11,
            -0.8822660685019321,
            -1.1057498761969202e-09
          ],
          [
            -8.22281497043903e-11,
            -0.7182102964565661,
            -8.952547834089968e-10
          ],
          [
            -6.45380361073631e-11,
            -0.5793900734885026,
            -7.082508091602529e-10
          ],
          [
            -3.907274587856769e-11,
            -0.44495934690157307,
            -5.35399117414236e-10
          ],
          [
            -1.773271615391183e-11,
            -0.3033877683128382,
            -3.608574944051091e-10
          ],
          [
            -6.181471879504776e-12,
            -0.1540099505041514,
            -1.8117897079398635e-10
          ],
          [
            -8.785140062756076e-16,
            -1.708606929188282e-15,
            -1.2443860780832952e-15
          ],
          [
            6.176337285594822e-12,
            0.15400995050415098,
            1.8117892530233992e-10
          ],
          [
            1.7723372019823157e-11,
            0.3033877683128393,
            3.608552018156781e-10
          ],
          [
            3.906493091471179e-11,
            0.4449593469015748,
            5.353932414099068e-10
          ],
          [
            6.453955454319902e-11,
            0.5793900734884992,
            7.082494624179704e-10
          ],
          [
            8.222447355092116e-11,
            0.7182102964565699,
            8.952521903851508e-10
          ],
          [
            8.945438486282568e-11,
            0.8822660685019348,
            1.1057471803429986e-09
          ],
          [
            9.281583801883507e-11,
            1.08222601193215,
            1.3311809839414318e-09
          ],
          [
            1.0611881453958593e-10,
            1.3104532051734015,
            1.5584163567249008e-09
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -1.0612547159869975e-10,
            -1.3104532051733984,
            -1.5584157141553952e-09
          ],
          [
            -9.281397473753433e-11,
            -1.0822260119321503,
            -1.3311819899702373e-09
          ],
          [
            -8.944681778666104e-11,
            -0.8822660685019321,
            -1.1057498761969202e-09
          ],
          [
            -8.22281497043903e-11,
            -0.7182102964565661,
            -8.952547834089968e-10
          ],
          [
            -6.45380361073631e-11,
            -0.5793900734885026,
            -7.082508091602529e-10
          ],
          [
            -3.907274587856769e-11,
            -0.44495934690157307,
            -5.35399117414236e-10
          ],
          [
            -1.773271615391183e-11,
            -0.3033877683128382,
            -3.608574944051091e-10
          ],
          [
            -6.181471879504776e-12,
            -0.1540099505041514,
            -1.8117897079398635e-10
          ],
          [
            -8.785140062759449e-16,
            -1.7208456881689926e-15,
            -1.2443860780924921e-15
          ],
          [
            6.176337285594822e-12,
            0.15400995050415098,
            1.8117892530233992e-10
          ],
          [
            1.7723372019823157e-11,
            0.3033877683128393,
            3.608552018156781e-10
          ],
          [
            3.906493091471179e-11,
            0.4449593469015748,
            5.353932414099068e-10
          ],
          [
            6.453955454319902e-11,
            0.5793900734884992,
            7.082494624179704e-10
          ],
          [
            8.222447355092116e-11,
            0.7182102964565699,
            8.952521903851508e-10
          ],
          [
            8.945438486282568e-11,
            0.8822660685019348,
            1.1057471803429986e-09
          ],
          [
            9.281583801883507e-11,
            1.08222601193215,
            1.3311809839414318e-09
          ],
          [
            1.0611881453958593e-10,
            1.3104532051734015,
            1.5584163567249008e-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": [
          [
            -1.0612549727895271e-10,
            -0.31045320517339836,
            -1.5584157297965362e-09
          ],
          [
            -9.281397872484831e-11,
            -0.08222601193215029,
            -1.3311819979655581e-09
          ],
          [
            -8.94468388246139e-11,
            0.11773393149806788,
            -1.1057498805477906e-09
          ],
          [
            -8.222816871850114e-11,
            0.2817897035434339,
            -8.952547592144811e-10
          ],
          [
            -6.453804157757759e-11,
            0.4206099265114974,
            -7.08250791348064e-10
          ],
          [
            -3.907274503944791e-11,
            -0.44495934690157307,
            -5.353991139323e-10
          ],
          [
            -1.7732704193917925e-11,
            -0.3033877683128382,
            -3.608575105396028e-10
          ],
          [
            -6.181444245356715e-12,
            -0.1540099505041514,
            -1.8117896072311623e-10
          ],
          [
            -8.881784197001252e-16,
            -1.7208456881689926e-15,
            -1.2212453270876722e-15
          ],
          [
            6.176392730594671e-12,
            0.154009950504151,
            1.8117896072311623e-10
          ],
          [
            1.7723378320511074e-11,
            0.3033877683128393,
            3.608552345824023e-10
          ],
          [
            3.906497347827553e-11,
            0.4449593469015748,
            5.353932852614207e-10
          ],
          [
            6.453959588981206e-11,
            -0.42060992651150064,
            7.082494590804345e-10
          ],
          [
            8.222444947136864e-11,
            -0.28178970354343,
            8.952522057015244e-10
          ],
          [
            8.945433283003013e-11,
            -0.11773393149806521,
            1.1057471605013802e-09
          ],
          [
            9.281586610399017e-11,
            0.08222601193215007,
            1.3311809432536847e-09
          ],
          [
            1.0611878042965373e-10,
            0.31045320517340147,
            1.558416395930351e-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": [
              -1.0612878752379118e-10,
              -1.3104532051733997,
              -1.5584175347689945e-09
            ],
            "branch_aligned_reduced_polarization": [
              -1.0612878752379118e-10,
              -1.3104532051733997,
              -1.5584175616645268e-09
            ],
            "target_residual": 0.5347223446524558,
            "energy_eV": -223.01320244029378,
            "max_atomic_step_A": 0.09479458935399568,
            "max_log_strain_component": 0.01705799245866972,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 8.30004886281693,
            "cell_principal_stretches": [
              1.0163691548991571,
              0.9997647170930867,
              0.9792647668288704
            ],
            "cell_volume_ratio": 0.9950603277003645,
            "cell_rmsd_from_input_A": 0.13435502668343968
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.0005401112314550154,
              -1.5229762051157962,
              -0.496527253601761
            ],
            "branch_aligned_reduced_polarization": [
              -0.0005401112314550154,
              -1.5229762051157962,
              -0.496527253601761
            ],
            "target_residual": 0.023243444004965506,
            "energy_eV": -222.1281623177856,
            "max_atomic_step_A": 0.0014180300023779856,
            "max_log_strain_component": 0.0004651044965698601,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 8.30004886281693,
            "cell_principal_stretches": [
              1.016812771093765,
              0.9997956733506175,
              0.9794104916122138
            ],
            "cell_volume_ratio": 0.9956736117842964,
            "cell_rmsd_from_input_A": 0.13538495000258985
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              3.020091561873655e-06,
              -1.5002174479452888,
              -0.4999421656662761
            ],
            "branch_aligned_reduced_polarization": [
              3.020091561873655e-06,
              -1.5002174479452888,
              -0.4999421656662761
            ],
            "target_residual": 0.00022502786498707403,
            "energy_eV": -222.11561474538638
          }
        ],
        "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": 0.00022502786498707403,
        "parent_symmetrization_rmsd_A": 0.0922182745085198,
        "parent_cell_rmsd_A": 0.13538495000258985,
        "energy_eV": -222.11561474538638,
        "reduced_polarization": [
          3.020091561873655e-06,
          -1.5002174479452888,
          -0.4999421656662761
        ],
        "cartesian_polarization_e_A2": [
          0.0011086315640923556,
          -0.0090945454358832,
          -0.007714525420014988
        ],
        "ranking_score": 0.6265145677391414
      },
      "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": [
              -1.0612878752379118e-10,
              -1.3104532051733997,
              -1.5584175347689945e-09
            ],
            "branch_aligned_reduced_polarization": [
              -1.0612877243687535e-10,
              -1.3104532051733997,
              -1.5584175347689945e-09
            ],
            "target_residual": 0.5347223460104398,
            "energy_eV": -223.01320244029378,
            "max_atomic_step_A": 0.06582588707721208,
            "max_log_strain_component": 0.0149918251117717,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 8.30004886281693,
            "cell_principal_stretches": [
              1.0133904163760519,
              0.9998725691884692,
              0.982037257477319
            ],
            "cell_volume_ratio": 0.9950603277461919,
            "cell_rmsd_from_input_A": 0.09431362052012243
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.4969820023491272,
              -1.512242822519675,
              0.00034743200466525104
            ],
            "branch_aligned_reduced_polarization": [
              -0.4969820023491272,
              -1.512242822519675,
              0.00034743200466525104
            ],
            "target_residual": 0.012614108056727528,
            "energy_eV": -222.39036646378884,
            "max_atomic_step_A": 0.0008320033042913685,
            "max_log_strain_component": 0.0002446598834972529,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 8.30004886281693,
            "cell_principal_stretches": [
              1.0136378206949017,
              0.9998808951791902,
              0.9821076487462117
            ],
            "cell_volume_ratio": 0.9953828877402798,
            "cell_rmsd_from_input_A": 0.09472387789618304
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.5000113562133898,
              -1.5000537239312715,
              4.702161407184355e-07
            ],
            "branch_aligned_reduced_polarization": [
              -0.5000113562133898,
              -1.5000537239312715,
              4.702161407184355e-07
            ],
            "target_residual": 5.4913072005059915e-05,
            "energy_eV": -222.38227573980424
          }
        ],
        "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": 5.4913072005059915e-05,
        "parent_symmetrization_rmsd_A": 0.07240618440932392,
        "parent_cell_rmsd_A": 0.09472387789618304,
        "energy_eV": -222.38227573980424,
        "reduced_polarization": [
          -0.5000113562133898,
          -1.5000537239312715,
          4.702161407184355e-07
        ],
        "cartesian_polarization_e_A2": [
          -0.005831996974194064,
          -0.009147629193195112,
          -4.516923708277417e-05
        ],
        "ranking_score": 0.5961969800273798
      },
      "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": [
              -1.0612878752379118e-10,
              -1.3104532051733997,
              -1.5584175347689945e-09
            ],
            "branch_aligned_reduced_polarization": [
              -1.0612878752379118e-10,
              -1.3104532051733997,
              -1.5584175616645268e-09
            ],
            "target_residual": 0.5885415797070072,
            "energy_eV": -223.01320244029378,
            "max_atomic_step_A": 0.09665216688131574,
            "max_log_strain_component": 0.017057992427440802,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 8.30004886281693,
            "cell_principal_stretches": [
              1.0228103063385194,
              1.0003945625022985,
              0.9852716086148035
            ],
            "cell_volume_ratio": 1.0081435745999674,
            "cell_rmsd_from_input_A": 0.1389008990085161
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.0041387685121413624,
              -1.0329772468088865,
              -0.4907117644068648
            ],
            "branch_aligned_reduced_polarization": [
              -0.0041387685121413624,
              -1.0329772468088865,
              -0.4907117644068648
            ],
            "target_residual": 0.03450941222804134,
            "energy_eV": -222.0642950159013,
            "max_atomic_step_A": 0.0026952182931430763,
            "max_log_strain_component": 0.0007071761966648319,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 8.30004886281693,
            "cell_principal_stretches": [
              1.0237911623904254,
              1.0004308728143054,
              0.9852144660585375
            ],
            "cell_volume_ratio": 1.0090884649387197,
            "cell_rmsd_from_input_A": 0.14314275485569436
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -6.648770616144307e-05,
              -1.0009175678369273,
              -0.4997350012188367
            ],
            "branch_aligned_reduced_polarization": [
              -6.648770616144307e-05,
              -1.0009175678369273,
              -0.4997350012188367
            ],
            "target_residual": 0.0009573796031105543,
            "energy_eV": -222.01038366499338
          }
        ],
        "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,
          -1.0,
          -0.5
        ],
        "formal_class": [
          0.0,
          0.0,
          0.5
        ],
        "target_residual": 0.0009573796031105543,
        "parent_symmetrization_rmsd_A": 0.09376834991268726,
        "parent_cell_rmsd_A": 0.14314275485569436,
        "energy_eV": -222.01038366499338,
        "reduced_polarization": [
          -6.648770616144307e-05,
          -1.0009175678369273,
          -0.4997350012188367
        ],
        "cartesian_polarization_e_A2": [
          0.0011294366117658918,
          -0.005998544698104799,
          -0.007670622819806021
        ],
        "ranking_score": 0.6314687978328319
      },
      "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": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -1.0612878752379118e-10,
              -1.3104532051733997,
              -1.5584175347689945e-09
            ],
            "branch_aligned_reduced_polarization": [
              -1.0612877243687535e-10,
              -1.3104532051733997,
              -1.5584175347689945e-09
            ],
            "target_residual": 0.5885415809408102,
            "energy_eV": -223.01320244029378,
            "max_atomic_step_A": 0.06745878729765577,
            "max_log_strain_component": 0.01499182509920356,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 8.30004886281693,
            "cell_principal_stretches": [
              1.0199635876028244,
              1.0002182472843497,
              0.9881956672856995
            ],
            "cell_volume_ratio": 1.0081435746463974,
            "cell_rmsd_from_input_A": 0.09878874675875887
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.49235628628194117,
              -1.018819657353966,
              -0.0020469693589114054
            ],
            "branch_aligned_reduced_polarization": [
              -0.49235628628194117,
              -1.018819657353966,
              -0.0020469693589114054
            ],
            "target_residual": 0.020415580958685748,
            "energy_eV": -222.27027290116177,
            "max_atomic_step_A": 0.0016077777927855947,
            "max_log_strain_component": 0.00039577939537204014,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 8.30004886281693,
            "cell_principal_stretches": [
              1.0205613538571836,
              1.0002270914495774,
              0.9881260659135798
            ],
            "cell_volume_ratio": 1.0086722844556106,
            "cell_rmsd_from_input_A": 0.10129564827584517
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.4999123830145508,
              -1.0003531684880815,
              -2.6421580701526995e-05
            ],
            "branch_aligned_reduced_polarization": [
              -0.4999123830145508,
              -1.0003531684880815,
              -2.6421580701526995e-05
            ],
            "target_residual": 0.00036483258768888225,
            "energy_eV": -222.23801979210785
          }
        ],
        "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,
          -1.0,
          0.0
        ],
        "formal_class": [
          0.5,
          0.0,
          0.0
        ],
        "target_residual": 0.00036483258768888225,
        "parent_symmetrization_rmsd_A": 0.07383851701964565,
        "parent_cell_rmsd_A": 0.10129564827584517,
        "energy_eV": -222.23801979210785,
        "reduced_polarization": [
          -0.4999123830145508,
          -1.0003531684880815,
          -2.6421580701526995e-05
        ],
        "cartesian_polarization_e_A2": [
          -0.00580995485079431,
          -0.006049961464442675,
          -2.1889583506749612e-05
        ],
        "ranking_score": 0.5998920942639847
      },
      "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": [
              -1.0612878752379118e-10,
              -1.3104532051733997,
              -1.5584175347689945e-09
            ],
            "branch_aligned_reduced_polarization": [
              -1.0612877243687535e-10,
              -1.3104532051733997,
              -1.5584175616645268e-09
            ],
            "target_residual": 0.7320710250819186,
            "energy_eV": -223.01320244029378,
            "max_atomic_step_A": 0.10146757770366298,
            "max_log_strain_component": 0.012565195887169776,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 8.30004886281693,
            "cell_principal_stretches": [
              1.0131198404012143,
              0.9987399439915221,
              0.9834135130679643
            ],
            "cell_volume_ratio": 0.9950603277715114,
            "cell_rmsd_from_input_A": 0.09197437672492702
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.4971907583613694,
              -1.511291026201291,
              -0.49884004623998945
            ],
            "branch_aligned_reduced_polarization": [
              -0.4971907583613694,
              -1.511291026201291,
              -0.49884004623998945
            ],
            "target_residual": 0.01169292965803781,
            "energy_eV": -222.16638868565303,
            "max_atomic_step_A": 0.000760322238328405,
            "max_log_strain_component": 0.00022556808763811852,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 8.30004886281693,
            "cell_principal_stretches": [
              1.0132689210584662,
              0.9988149237501486,
              0.983488851744867
            ],
            "cell_volume_ratio": 0.9953577133497236,
            "cell_rmsd_from_input_A": 0.09202973294625798
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.5000157625012905,
              -1.500049176133267,
              -0.4999816868480951
            ],
            "branch_aligned_reduced_polarization": [
              -0.5000157625012905,
              -1.500049176133267,
              -0.4999816868480951
            ],
            "target_residual": 5.479160576881826e-05,
            "energy_eV": -222.16159672510793
          }
        ],
        "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": 5.479160576881826e-05,
        "parent_symmetrization_rmsd_A": 0.09989917170896842,
        "parent_cell_rmsd_A": 0.09202973294625798,
        "energy_eV": -222.16159672510793,
        "reduced_polarization": [
          -0.5000157625012905,
          -1.500049176133267,
          -0.4999816868480951
        ],
        "cartesian_polarization_e_A2": [
          -0.004723379445658525,
          -0.009101119957788695,
          -0.007763310575279819
        ],
        "ranking_score": 0.6230161881570706
      },
      "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": [
              -1.0612878752379118e-10,
              -1.3104532051733997,
              -1.5584175347689945e-09
            ],
            "branch_aligned_reduced_polarization": [
              -1.0612877243687535e-10,
              -1.3104532051733997,
              -1.5584175616645268e-09
            ],
            "target_residual": 0.7722572051705899,
            "energy_eV": -223.01320244029378,
            "max_atomic_step_A": 0.10252972847883465,
            "max_log_strain_component": 0.012565195855940858,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 8.30004886281693,
            "cell_principal_stretches": [
              1.0182699871898104,
              1.0020680841117509,
              0.9880119855465594
            ],
            "cell_volume_ratio": 1.00814357467205,
            "cell_rmsd_from_input_A": 0.09551186748823033
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.49606228566551136,
              -1.0213109967496186,
              -0.4956034445374459
            ],
            "branch_aligned_reduced_polarization": [
              -0.49606228566551136,
              -1.0213109967496186,
              -0.4956034445374459
            ],
            "target_residual": 0.022113205931696203,
            "energy_eV": -222.11321090509819,
            "max_atomic_step_A": 0.001471202294917429,
            "max_log_strain_component": 0.0004427011904009935,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 8.30004886281693,
            "cell_principal_stretches": [
              1.018674407237255,
              1.0022173988264877,
              0.9880518821245022
            ],
            "cell_volume_ratio": 1.008734984280519,
            "cell_rmsd_from_input_A": 0.09695528273057831
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.49999857866350783,
              -1.0003139910886687,
              -0.4999222707393268
            ],
            "branch_aligned_reduced_polarization": [
              -0.49999857866350783,
              -1.0003139910886687,
              -0.4999222707393268
            ],
            "target_residual": 0.0003234721965263414,
            "energy_eV": -222.0908759115504
          }
        ],
        "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,
          -1.0,
          -0.5
        ],
        "formal_class": [
          0.5,
          0.0,
          0.5
        ],
        "target_residual": 0.0003234721965263414,
        "parent_symmetrization_rmsd_A": 0.1008077757253786,
        "parent_cell_rmsd_A": 0.09695528273057831,
        "energy_eV": -222.0908759115504,
        "reduced_polarization": [
          -0.49999857866350783,
          -1.0003139910886687,
          -0.4999222707393268
        ],
        "cartesian_polarization_e_A2": [
          -0.004680043409374092,
          -0.006003943168491551,
          -0.007697977355464611
        ],
        "ranking_score": 0.6256935408010759
      },
      "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": 0.2537906886457398,
        "minimum_distance_A_by_image": [
          2.123434399655828,
          2.1247536516321417,
          2.1214758421984894,
          2.117300138442374,
          2.113877518247532,
          2.111211644232889,
          2.1093053856719486,
          2.108160803162976,
          2.107779137539982
        ],
        "minimum_distance_A": 2.107779137539982,
        "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": [
          933.50497954873,
          933.50497954873,
          933.50497954873,
          933.50497954873,
          933.50497954873,
          933.50497954873,
          933.50497954873,
          933.50497954873,
          933.50497954873
        ],
        "cell_deformation_log_strain_norm": 0.0
      },
      "parent_reduced_polarization": [
        -8.785140062756076e-16,
        -1.708606929188282e-15,
        -1.2443860780832952e-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": [
          -223.0132024402938,
          -222.82793964835824,
          -222.55598448812503,
          -222.25794220747042,
          -221.99713714586866,
          -221.80683353991571,
          -221.68394339352568,
          -221.61435053982296,
          -221.59138239106127
        ],
        "cartesian_polarizations_e_A2": [
          [
            2.4035694515000396e-12,
            -0.008059835220876003,
            -2.4445363808144888e-11
          ],
          [
            2.0273784369396313e-12,
            -0.006656142541743605,
            -2.0880967603248855e-11
          ],
          [
            1.537141693636177e-12,
            -0.005426305269828204,
            -1.734483152275862e-11
          ],
          [
            1.1278536325133057e-12,
            -0.004417293666438456,
            -1.4042998079800333e-11
          ],
          [
            8.983774958446556e-13,
            -0.003563491242948019,
            -1.1109647150034444e-11
          ],
          [
            7.946744176147776e-13,
            -0.0027366860578136747,
            -8.39828942230855e-12
          ],
          [
            6.379278704157556e-13,
            -0.0018659616466863667,
            -5.660423373239227e-12
          ],
          [
            3.5266427579534767e-13,
            -0.0009472255999209693,
            -2.8419797203114084e-12
          ],
          [
            -7.522360120830563e-18,
            -1.0508647124627638e-17,
            -1.9519483870850848e-17
          ]
        ],
        "raw_reduced_polarization": [
          [
            -1.0612547159869975e-10,
            -1.3104532051733984,
            -1.5584157141553952e-09
          ],
          [
            -9.281397473753433e-11,
            -1.0822260119321503,
            -1.3311819899702373e-09
          ],
          [
            -8.944681778666104e-11,
            -0.8822660685019321,
            -1.1057498761969202e-09
          ],
          [
            -8.22281497043903e-11,
            -0.7182102964565661,
            -8.952547834089968e-10
          ],
          [
            -6.45380361073631e-11,
            -0.5793900734885026,
            -7.082508091602529e-10
          ],
          [
            -3.907274587856769e-11,
            -0.44495934690157307,
            -5.35399117414236e-10
          ],
          [
            -1.773271615391183e-11,
            -0.3033877683128382,
            -3.608574944051091e-10
          ],
          [
            -6.181471879504776e-12,
            -0.1540099505041514,
            -1.8117897079398635e-10
          ],
          [
            -8.785140062756076e-16,
            -1.708606929188282e-15,
            -1.2443860780832952e-15
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -1.0612547159869975e-10,
            -1.3104532051733984,
            -1.5584157141553952e-09
          ],
          [
            -9.281397473753433e-11,
            -1.0822260119321503,
            -1.3311819899702373e-09
          ],
          [
            -8.944681778666104e-11,
            -0.8822660685019321,
            -1.1057498761969202e-09
          ],
          [
            -8.22281497043903e-11,
            -0.7182102964565661,
            -8.952547834089968e-10
          ],
          [
            -6.45380361073631e-11,
            -0.5793900734885026,
            -7.082508091602529e-10
          ],
          [
            -3.907274587856769e-11,
            -0.44495934690157307,
            -5.35399117414236e-10
          ],
          [
            -1.773271615391183e-11,
            -0.3033877683128382,
            -3.608574944051091e-10
          ],
          [
            -6.181471879504776e-12,
            -0.1540099505041514,
            -1.8117897079398635e-10
          ],
          [
            -8.785140062759449e-16,
            -1.7208456881689926e-15,
            -1.2443860780924921e-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": [
          [
            -1.0612549727895271e-10,
            -0.31045320517339836,
            -1.5584157297965362e-09
          ],
          [
            -9.281397872484831e-11,
            -0.08222601193215029,
            -1.3311819979655581e-09
          ],
          [
            -8.94468388246139e-11,
            0.11773393149806788,
            -1.1057498805477906e-09
          ],
          [
            -8.222816871850114e-11,
            0.2817897035434339,
            -8.952547592144811e-10
          ],
          [
            -6.453804157757759e-11,
            0.4206099265114974,
            -7.08250791348064e-10
          ],
          [
            -3.907274503944791e-11,
            -0.44495934690157307,
            -5.353991139323e-10
          ],
          [
            -1.7732704193917925e-11,
            -0.3033877683128382,
            -3.608575105396028e-10
          ],
          [
            -6.181444245356715e-12,
            -0.1540099505041514,
            -1.8117896072311623e-10
          ],
          [
            -8.881784197001252e-16,
            -1.7208456881689926e-15,
            -1.2212453270876722e-15
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -221.5913823910613,
          -221.61435053982296,
          -221.6839433935257,
          -221.80683353991566,
          -221.99713714586863,
          -222.25794220747048,
          -222.55598448812503,
          -222.82793964835824,
          -223.0132024402938
        ],
        "cartesian_polarizations_e_A2": [
          [
            -3.97674176348256e-18,
            7.044602608242352e-18,
            -1.525284878255367e-17
          ],
          [
            -3.5272524259150486e-13,
            0.0009472255999209667,
            2.8419790067278398e-12
          ],
          [
            -6.380336220140155e-13,
            0.0018659616466863737,
            5.660387411600625e-12
          ],
          [
            -7.947535510592898e-13,
            0.002736686057813685,
            8.398197251097583e-12
          ],
          [
            -8.983562667334845e-13,
            0.0035634912429479988,
            1.1109626024987543e-11
          ],
          [
            -1.1278912591802343e-12,
            0.004417293666438479,
            1.4042957405536913e-11
          ],
          [
            -1.5370453449880682e-12,
            0.005426305269828221,
            1.734478923549901e-11
          ],
          [
            -2.027353907504455e-12,
            0.006656142541743604,
            2.088095182264556e-11
          ],
          [
            -2.4036501459086086e-12,
            0.008059835220876022,
            2.4445373887512796e-11
          ]
        ],
        "raw_reduced_polarization": [
          [
            -5.266347844432885e-16,
            1.1453859556871574e-15,
            -9.72383942203702e-16
          ],
          [
            6.176337285594822e-12,
            0.15400995050415098,
            1.8117892530233992e-10
          ],
          [
            1.7723372019823157e-11,
            0.3033877683128393,
            3.608552018156781e-10
          ],
          [
            3.906493091471179e-11,
            0.4449593469015748,
            5.353932414099068e-10
          ],
          [
            6.453955454319902e-11,
            0.5793900734884992,
            7.082494624179704e-10
          ],
          [
            8.222447355092116e-11,
            0.7182102964565699,
            8.952521903851508e-10
          ],
          [
            8.945438486282568e-11,
            0.8822660685019348,
            1.1057471803429986e-09
          ],
          [
            9.281583801883507e-11,
            1.08222601193215,
            1.3311809839414318e-09
          ],
          [
            1.0611881453958593e-10,
            1.3104532051734015,
            1.5584163567249008e-09
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -5.266347844432885e-16,
            1.1453859556871574e-15,
            -9.72383942203702e-16
          ],
          [
            6.176337285594822e-12,
            0.15400995050415098,
            1.8117892530233992e-10
          ],
          [
            1.7723372019823157e-11,
            0.3033877683128393,
            3.608552018156781e-10
          ],
          [
            3.906493091471179e-11,
            0.4449593469015748,
            5.353932414099068e-10
          ],
          [
            6.453955454319902e-11,
            0.5793900734884992,
            7.082494624179704e-10
          ],
          [
            8.222447355092116e-11,
            0.7182102964565699,
            8.952521903851508e-10
          ],
          [
            8.945438486282568e-11,
            0.8822660685019348,
            1.1057471803429986e-09
          ],
          [
            9.281583801883507e-11,
            1.08222601193215,
            1.3311809839414318e-09
          ],
          [
            1.0611881453958593e-10,
            1.3104532051734015,
            1.5584163567249008e-09
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          1.061237145706872e-10,
          1.310453205173395,
          1.558413225383239e-09
        ],
        "actual_opposite_endpoint_branch_residual": 8.676410935810333e-15
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            -1.0612547159869975e-10,
            -1.3104532051733984,
            -1.5584157141553952e-09
          ],
          [
            -9.281397473753433e-11,
            -1.0822260119321503,
            -1.3311819899702373e-09
          ],
          [
            -8.944681778666104e-11,
            -0.8822660685019321,
            -1.1057498761969202e-09
          ],
          [
            -8.22281497043903e-11,
            -0.7182102964565661,
            -8.952547834089968e-10
          ],
          [
            -6.45380361073631e-11,
            -0.5793900734885026,
            -7.082508091602529e-10
          ],
          [
            -3.907274587856769e-11,
            -0.44495934690157307,
            -5.35399117414236e-10
          ],
          [
            -1.773271615391183e-11,
            -0.3033877683128382,
            -3.608574944051091e-10
          ],
          [
            -6.181471879504776e-12,
            -0.1540099505041514,
            -1.8117897079398635e-10
          ],
          [
            -8.785140062756076e-16,
            -1.708606929188282e-15,
            -1.2443860780832952e-15
          ],
          [
            6.176337285594822e-12,
            0.15400995050415098,
            1.8117892530233992e-10
          ],
          [
            1.7723372019823157e-11,
            0.3033877683128393,
            3.608552018156781e-10
          ],
          [
            3.906493091471179e-11,
            0.4449593469015748,
            5.353932414099068e-10
          ],
          [
            6.453955454319902e-11,
            0.5793900734884992,
            7.082494624179704e-10
          ],
          [
            8.222447355092116e-11,
            0.7182102964565699,
            8.952521903851508e-10
          ],
          [
            8.945438486282568e-11,
            0.8822660685019348,
            1.1057471803429986e-09
          ],
          [
            9.281583801883507e-11,
            1.08222601193215,
            1.3311809839414318e-09
          ],
          [
            1.0611881453958593e-10,
            1.3104532051734015,
            1.5584163567249008e-09
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -1.0612547159869975e-10,
            -1.3104532051733984,
            -1.5584157141553952e-09
          ],
          [
            -9.281397473753433e-11,
            -1.0822260119321503,
            -1.3311819899702373e-09
          ],
          [
            -8.944681778666104e-11,
            -0.8822660685019321,
            -1.1057498761969202e-09
          ],
          [
            -8.22281497043903e-11,
            -0.7182102964565661,
            -8.952547834089968e-10
          ],
          [
            -6.45380361073631e-11,
            -0.5793900734885026,
            -7.082508091602529e-10
          ],
          [
            -3.907274587856769e-11,
            -0.44495934690157307,
            -5.35399117414236e-10
          ],
          [
            -1.773271615391183e-11,
            -0.3033877683128382,
            -3.608574944051091e-10
          ],
          [
            -6.181471879504776e-12,
            -0.1540099505041514,
            -1.8117897079398635e-10
          ],
          [
            -8.785140062759449e-16,
            -1.7208456881689926e-15,
            -1.2443860780924921e-15
          ],
          [
            6.176337285594822e-12,
            0.15400995050415098,
            1.8117892530233992e-10
          ],
          [
            1.7723372019823157e-11,
            0.3033877683128393,
            3.608552018156781e-10
          ],
          [
            3.906493091471179e-11,
            0.4449593469015748,
            5.353932414099068e-10
          ],
          [
            6.453955454319902e-11,
            0.5793900734884992,
            7.082494624179704e-10
          ],
          [
            8.222447355092116e-11,
            0.7182102964565699,
            8.952521903851508e-10
          ],
          [
            8.945438486282568e-11,
            0.8822660685019348,
            1.1057471803429986e-09
          ],
          [
            9.281583801883507e-11,
            1.08222601193215,
            1.3311809839414318e-09
          ],
          [
            1.0611881453958593e-10,
            1.3104532051734015,
            1.5584163567249008e-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": [
          [
            -1.0612549727895271e-10,
            -0.31045320517339836,
            -1.5584157297965362e-09
          ],
          [
            -9.281397872484831e-11,
            -0.08222601193215029,
            -1.3311819979655581e-09
          ],
          [
            -8.94468388246139e-11,
            0.11773393149806788,
            -1.1057498805477906e-09
          ],
          [
            -8.222816871850114e-11,
            0.2817897035434339,
            -8.952547592144811e-10
          ],
          [
            -6.453804157757759e-11,
            0.4206099265114974,
            -7.08250791348064e-10
          ],
          [
            -3.907274503944791e-11,
            -0.44495934690157307,
            -5.353991139323e-10
          ],
          [
            -1.7732704193917925e-11,
            -0.3033877683128382,
            -3.608575105396028e-10
          ],
          [
            -6.181444245356715e-12,
            -0.1540099505041514,
            -1.8117896072311623e-10
          ],
          [
            -8.881784197001252e-16,
            -1.7208456881689926e-15,
            -1.2212453270876722e-15
          ],
          [
            6.176392730594671e-12,
            0.154009950504151,
            1.8117896072311623e-10
          ],
          [
            1.7723378320511074e-11,
            0.3033877683128393,
            3.608552345824023e-10
          ],
          [
            3.906497347827553e-11,
            0.4449593469015748,
            5.353932852614207e-10
          ],
          [
            6.453959588981206e-11,
            -0.42060992651150064,
            7.082494590804345e-10
          ],
          [
            8.222444947136864e-11,
            -0.28178970354343,
            8.952522057015244e-10
          ],
          [
            8.945433283003013e-11,
            -0.11773393149806521,
            1.1057471605013802e-09
          ],
          [
            9.281586610399017e-11,
            0.08222601193215007,
            1.3311809432536847e-09
          ],
          [
            1.0611878042965373e-10,
            0.31045320517340147,
            1.558416395930351e-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/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": 1.00442621929409e-15,
        "parent_symmetrization_rmsd_A": 0.2537906886457398,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -221.59138239106127,
        "reduced_polarization": [
          -5.205413489557387e-16,
          -7.841829824552487e-16,
          -3.5066477447891787e-16
        ],
        "cartesian_polarization_e_A2": [
          -5.366743090157773e-18,
          -4.823053273976382e-18,
          -5.50054000930298e-18
        ],
        "ranking_score": 0.2537906886457418
      }
    }
  ],
  "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": 48,
      "full_response": 16,
      "energy_polarization": 32
    },
    "model_evaluations_for_recovery_and_path_properties": {
      "total": 73,
      "full_response": 41,
      "energy_polarization": 32
    },
    "elapsed_seconds": 398.8980290759937
  }
}