{
  "schema": "ferrofinder.endpoint_parent_recovery.v4_variable_cell",
  "status": "complete",
  "input_atom_count": 24,
  "input_formula": "B8O14Pb2",
  "input_spacegroup": "Pmn2_1",
  "input_pointgroup": "mm2",
  "input_is_polar_point_group": true,
  "input_energy_eV": -177.6943690365187,
  "input_cartesian_polarization_e_A2": [
    1.8442058661770995e-17,
    1.111445347416437e-16,
    0.00828510919404557
  ],
  "input_reduced_polarization": [
    3.5643543314248743e-16,
    5.234107845330422e-15,
    0.4094186050256718
  ],
  "input_formal_targets": [
    {
      "orbit_id": 0,
      "representative_formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.5
      ]
    },
    {
      "orbit_id": 1,
      "representative_formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ]
    },
    {
      "orbit_id": 2,
      "representative_formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.5
      ]
    },
    {
      "orbit_id": 3,
      "representative_formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.5
      ]
    },
    {
      "orbit_id": 4,
      "representative_formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.0
      ]
    },
    {
      "orbit_id": 5,
      "representative_formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.0
      ]
    },
    {
      "orbit_id": 6,
      "representative_formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "target_reduced_polarization": [
        0.5,
        0.5,
        0.5
      ]
    },
    {
      "orbit_id": 7,
      "representative_formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        0.5,
        0.5,
        0.0
      ]
    }
  ],
  "parent_candidates": [
    {
      "candidate_id": "inversion_parent_endpoint_00",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "Pmmn",
      "spacegroup_number": 59,
      "pointgroup": "mmm",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 2.908068172176977e-15,
      "parent_symmetrization_rmsd_A": 0.42051236853255375,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -168.44387386070588,
      "reduced_polarization": [
        -2.430645175367164e-15,
        -1.4391100169380674e-15,
        -6.912212993257562e-16
      ],
      "cartesian_polarization_e_A2": [
        -1.2576219068588603e-16,
        -3.0559021327257945e-17,
        -1.398774719044548e-17
      ],
      "ranking_score": 0.4205123685325596
    },
    {
      "candidate_id": "inversion_parent_endpoint_01",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "Pmmn",
      "spacegroup_number": 59,
      "pointgroup": "mmm",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 1.580536390202192e-15,
      "parent_symmetrization_rmsd_A": 0.4227569822847435,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -170.8322482340248,
      "reduced_polarization": [
        -9.215686635658652e-16,
        2.1648282374710755e-16,
        -1.265678342277089e-15
      ],
      "cartesian_polarization_e_A2": [
        -4.7682193671069374e-17,
        4.596940574389444e-18,
        -2.5612620290293706e-17
      ],
      "ranking_score": 0.4227569822847467
    },
    {
      "candidate_id": "inversion_parent_endpoint_02",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "Pnnm",
      "spacegroup_number": 58,
      "pointgroup": "mmm",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 1.0188162973088077e-15,
      "parent_symmetrization_rmsd_A": 0.49836909745483776,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -162.211355229965,
      "reduced_polarization": [
        9.927892062897569e-16,
        2.1760306665243331e-16,
        7.074704884332548e-17
      ],
      "cartesian_polarization_e_A2": [
        5.1367162405118093e-17,
        4.620728558930331e-18,
        1.431657031772344e-18
      ],
      "ranking_score": 0.4983690974548398
    },
    {
      "candidate_id": "bec_projection_00",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Pmn2_1",
      "spacegroup_number": 31,
      "pointgroup": "mm2",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.5
      ],
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_residual": 0.0006728488723972692,
      "parent_symmetrization_rmsd_A": 0.010076714328416133,
      "parent_cell_rmsd_A": 0.003660610739751307,
      "energy_eV": -177.68741813304322,
      "reduced_polarization": [
        -9.30151964940517e-16,
        -3.6932241811484116e-15,
        0.5006728488723973
      ],
      "cartesian_polarization_e_A2": [
        -6.656353534791332e-17,
        -9.948168551770542e-17,
        0.010128511361445986
      ],
      "ranking_score": 0.5123375647581485
    },
    {
      "candidate_id": "inversion_parent_bec_00_00",
      "source": "same_species_inversion_center_projection_after_BEC",
      "spacegroup": "Pmmn",
      "spacegroup_number": 59,
      "pointgroup": "mmm",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.5
      ],
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_residual": 0.4999999999999965,
      "parent_symmetrization_rmsd_A": 0.42051349931038506,
      "parent_cell_rmsd_A": 0.003660610739751307,
      "energy_eV": -168.36002626340297,
      "reduced_polarization": [
        1.232002096565574e-15,
        -3.993343701592424e-15,
        3.503653494835044e-15
      ],
      "cartesian_polarization_e_A2": [
        6.3842651645395e-17,
        -8.491899517928288e-17,
        7.087820781360356e-17
      ],
      "ranking_score": 1.4214286519953159
    },
    {
      "candidate_id": "inversion_parent_bec_00_01",
      "source": "same_species_inversion_center_projection_after_BEC",
      "spacegroup": "Pmmn",
      "spacegroup_number": 59,
      "pointgroup": "mmm",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.5
      ],
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_residual": 0.4999999999999971,
      "parent_symmetrization_rmsd_A": 0.4227583553506714,
      "parent_cell_rmsd_A": 0.003660610739751307,
      "energy_eV": -170.82425720911357,
      "reduced_polarization": [
        1.8181196858047183e-15,
        -2.896406697142669e-15,
        -2.8520270671967962e-15
      ],
      "cartesian_polarization_e_A2": [
        9.421540927084618e-17,
        -6.159248107139345e-17,
        -5.769593581579737e-17
      ],
      "ranking_score": 1.4236735080356033
    },
    {
      "candidate_id": "bec_projection_01",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Pmn2_1",
      "spacegroup_number": 31,
      "pointgroup": "mm2",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 0.00013214184069602097,
      "parent_symmetrization_rmsd_A": 0.04697004354061369,
      "parent_cell_rmsd_A": 0.01737423194247487,
      "energy_eV": -177.3770001881602,
      "reduced_polarization": [
        4.939902168237584e-16,
        3.940562707165103e-15,
        0.00013214184069602097
      ],
      "cartesian_polarization_e_A2": [
        2.539576317819759e-17,
        8.313748025286085e-17,
        2.6781067648167136e-06
      ],
      "ranking_score": 0.5515778852076244
    },
    {
      "candidate_id": "bec_projection_02",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Pm",
      "spacegroup_number": 6,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.5
      ],
      "formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_residual": 1.0278833347956536e-05,
      "parent_symmetrization_rmsd_A": 0.06156623359477819,
      "parent_cell_rmsd_A": 0.005408641685047636,
      "energy_eV": -177.23674400153627,
      "reduced_polarization": [
        3.9279792325979956e-15,
        0.49998998931792493,
        0.5000023325221086
      ],
      "cartesian_polarization_e_A2": [
        1.3553495530948268e-16,
        0.010648564213824591,
        0.010130649463291818
      ],
      "ranking_score": 0.562938951682736
    },
    {
      "candidate_id": "bec_projection_03",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Pc",
      "spacegroup_number": 7,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.5
      ],
      "formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_residual": 3.584202767686111e-05,
      "parent_symmetrization_rmsd_A": 0.1448342099817048,
      "parent_cell_rmsd_A": 0.059697705116983336,
      "energy_eV": -174.33698078444047,
      "reduced_polarization": [
        0.4999859843065679,
        2.341251441574771e-15,
        0.49996701195238263
      ],
      "cartesian_polarization_e_A2": [
        0.02605374243257061,
        6.533860317251936e-16,
        0.010362809066940743
      ],
      "ranking_score": 0.6598303203163043
    },
    {
      "candidate_id": "bec_projection_04",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Pm",
      "spacegroup_number": 6,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.0
      ],
      "formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_residual": 8.632766855601747e-05,
      "parent_symmetrization_rmsd_A": 0.07492832234294407,
      "parent_cell_rmsd_A": 0.017515481825301805,
      "energy_eV": -176.91434618901525,
      "reduced_polarization": [
        8.639617856280244e-16,
        0.49999299087153587,
        8.604265498281027e-05
      ],
      "cartesian_polarization_e_A2": [
        -1.260401857317689e-16,
        0.01054655207305638,
        1.7097582733831356e-05
      ],
      "ranking_score": 0.5794798481363815
    },
    {
      "candidate_id": "bec_projection_05",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Pc",
      "spacegroup_number": 7,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.0
      ],
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_residual": 2.826077749291033e-05,
      "parent_symmetrization_rmsd_A": 0.14327372740572236,
      "parent_cell_rmsd_A": 0.05721024593114961,
      "energy_eV": -173.8248004655673,
      "reduced_polarization": [
        0.49999929345240685,
        -1.13976807745557e-15,
        -2.8251943915461724e-05
      ],
      "cartesian_polarization_e_A2": [
        0.02572161293970202,
        1.8573814687845117e-16,
        0.000233567242340614
      ],
      "ranking_score": 0.6576328104434956
    },
    {
      "candidate_id": "bec_projection_06",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.5,
        0.5,
        0.5
      ],
      "formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "target_residual": 8.984233562022214e-05,
      "parent_symmetrization_rmsd_A": 0.15781463662818296,
      "parent_cell_rmsd_A": 0.0603892597911791,
      "energy_eV": -173.69597383751,
      "reduced_polarization": [
        0.499963671779159,
        0.4999708215773377,
        0.4999231851232432
      ],
      "cartesian_polarization_e_A2": [
        0.02606354113123065,
        0.010668759404462285,
        0.010379643880522677
      ],
      "ranking_score": 0.6730916362472181
    },
    {
      "candidate_id": "bec_projection_07",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.5,
        0.5,
        0.0
      ],
      "formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_residual": 6.745639415094524e-05,
      "parent_symmetrization_rmsd_A": 0.1554546723262151,
      "parent_cell_rmsd_A": 0.05729845336377266,
      "energy_eV": -173.18435914155083,
      "reduced_polarization": [
        0.4999972810266224,
        0.4999926781491675,
        -6.700270737817864e-05
      ],
      "cartesian_polarization_e_A2": [
        0.025729879928085737,
        0.010563559750029282,
        0.00024919820930929733
      ],
      "ranking_score": 0.6699141984554602
    }
  ],
  "formal_branches": [
    {
      "orbit_id": 0,
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.0,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              3.5643543314248743e-16,
              5.234107845330422e-15,
              0.4094186050256718
            ],
            "branch_aligned_reduced_polarization": [
              3.5643543314248743e-16,
              5.234107845330422e-15,
              0.4094186050256718
            ],
            "target_residual": 0.09058139497432821,
            "energy_eV": -177.6943690365187,
            "max_atomic_step_A": 0.010973671678408245,
            "max_log_strain_component": 0.0016494970461419245,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.1530218493539404,
            "cell_principal_stretches": [
              1.0002156769274608,
              1.0001046030330283,
              0.9983518626264161
            ],
            "cell_volume_ratio": 0.9986716372448103,
            "cell_rmsd_from_input_A": 0.003660610739751307
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -9.30151964940517e-16,
              -3.6932241811484116e-15,
              0.5006728488723973
            ],
            "branch_aligned_reduced_polarization": [
              -9.30151964940517e-16,
              -3.6932241811484116e-15,
              0.5006728488723973
            ],
            "target_residual": 0.0006728488723972692,
            "energy_eV": -177.68741813304322
          }
        ],
        "iterations": 1
      },
      "parent": {
        "candidate_id": "bec_projection_00",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Pmn2_1",
        "spacegroup_number": 31,
        "pointgroup": "mm2",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.5
        ],
        "formal_class": [
          0.0,
          0.0,
          0.5
        ],
        "target_residual": 0.0006728488723972692,
        "parent_symmetrization_rmsd_A": 0.010076714328416133,
        "parent_cell_rmsd_A": 0.003660610739751307,
        "energy_eV": -177.68741813304322,
        "reduced_polarization": [
          -9.30151964940517e-16,
          -3.6932241811484116e-15,
          0.5006728488723973
        ],
        "cartesian_polarization_e_A2": [
          -6.656353534791332e-17,
          -9.948168551770542e-17,
          0.010128511361445986
        ],
        "ranking_score": 0.5123375647581485
      },
      "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,
        0.0,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              3.5643543314248743e-16,
              5.234107845330422e-15,
              0.4094186050256718
            ],
            "branch_aligned_reduced_polarization": [
              3.5643543314248743e-16,
              5.234107845330422e-15,
              0.4094186050256718
            ],
            "target_residual": 0.4094186050256718,
            "energy_eV": -177.6943690365187,
            "max_atomic_step_A": 0.04959986928725153,
            "max_log_strain_component": 0.007455557289847329,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.1530218493539404,
            "cell_principal_stretches": [
              1.0074834191559705,
              0.9995273414950252,
              0.9990257424393049
            ],
            "cell_volume_ratio": 1.0060261391480676,
            "cell_rmsd_from_input_A": 0.01662462558116591
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              6.51766139952129e-15,
              1.4303817057494237e-14,
              0.015938973661448527
            ],
            "branch_aligned_reduced_polarization": [
              6.51766139952129e-15,
              1.4303817057494237e-14,
              0.015938973661448527
            ],
            "target_residual": 0.015938973661448527,
            "energy_eV": -177.39870060618213,
            "max_atomic_step_A": 0.002246289696607101,
            "max_log_strain_component": 0.00033479657733183354,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.1530218493539404,
            "cell_principal_stretches": [
              1.0078207776265018,
              0.9995061217041341,
              0.9989820150549208
            ],
            "cell_volume_ratio": 1.006297597131997,
            "cell_rmsd_from_input_A": 0.01737423194247487
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              4.939902168237584e-16,
              3.940562707165103e-15,
              0.00013214184069602097
            ],
            "branch_aligned_reduced_polarization": [
              4.939902168237584e-16,
              3.940562707165103e-15,
              0.00013214184069602097
            ],
            "target_residual": 0.00013214184069602097,
            "energy_eV": -177.3770001881602
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "inversion_parent_endpoint_00",
        "source": "same_species_inversion_center_projection_from_endpoint",
        "spacegroup": "Pmmn",
        "spacegroup_number": 59,
        "pointgroup": "mmm",
        "has_inversion": true,
        "is_polar_point_group": false,
        "nonpolar_parent_hypothesis": true,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.0
        ],
        "formal_class": [
          0.0,
          0.0,
          0.0
        ],
        "target_residual": 2.908068172176977e-15,
        "parent_symmetrization_rmsd_A": 0.42051236853255375,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -168.44387386070588,
        "reduced_polarization": [
          -2.430645175367164e-15,
          -1.4391100169380674e-15,
          -6.912212993257562e-16
        ],
        "cartesian_polarization_e_A2": [
          -1.2576219068588603e-16,
          -3.0559021327257945e-17,
          -1.398774719044548e-17
        ],
        "ranking_score": 0.4205123685325596
      },
      "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": [
          -177.69436903651874,
          -177.28670036401735,
          -176.2323361624608,
          -174.71005638615404,
          -172.94590922359217,
          -171.20294894740152,
          -169.74143907075657,
          -168.77780464767727,
          -168.44387386070585
        ],
        "cartesian_polarizations_e_A2": [
          [
            -1.0524735565479173e-17,
            6.628755589831327e-17,
            0.008285109194045561
          ],
          [
            5.590339885037647e-17,
            1.0469900240602293e-17,
            0.008980609117434434
          ],
          [
            2.573981033771206e-18,
            9.422910216542063e-18,
            0.009221192172792098
          ],
          [
            -5.1262645656744464e-17,
            -2.0808926728197058e-17,
            0.008909151214894597
          ],
          [
            -3.660736417284655e-17,
            -1.832232542105401e-17,
            0.00804418301336772
          ],
          [
            -3.2733696269436754e-17,
            -1.4134365324813094e-17,
            0.006666050813996713
          ],
          [
            1.5096961368414554e-18,
            2.5913003095490674e-17,
            0.004807533663414433
          ],
          [
            8.168916928864716e-17,
            3.520503955902521e-17,
            0.0025329355110766828
          ],
          [
            -4.249824106880794e-17,
            1.4396112830828152e-17,
            -3.9454771166595286e-17
          ]
        ],
        "raw_reduced_polarization": [
          [
            -2.034148545340038e-16,
            3.121666910403131e-15,
            0.40941860502567134
          ],
          [
            1.0804624661928973e-15,
            4.930569651179674e-16,
            0.44378756767422417
          ],
          [
            4.974813612184246e-17,
            4.4375126860617067e-16,
            0.4556762678241436
          ],
          [
            -9.907691784197437e-16,
            -9.799507181719603e-16,
            0.44025638973912273
          ],
          [
            -7.075219716224631e-16,
            -8.628496889564429e-16,
            0.3975129489266333
          ],
          [
            -6.326543810608878e-16,
            -6.65626902909256e-16,
            0.3294108938549937
          ],
          [
            2.9178369200401913e-17,
            1.2203159886669692e-15,
            0.23757004041705193
          ],
          [
            1.57883211264294e-15,
            1.6579040452091655e-15,
            0.1251680453783647
          ],
          [
            -8.213767910062461e-16,
            6.779533270372052e-16,
            -1.9497048251631877e-15
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -2.034148545340038e-16,
            3.121666910403131e-15,
            0.40941860502567134
          ],
          [
            1.080462466192897e-15,
            4.930569651179674e-16,
            0.44378756767422417
          ],
          [
            4.9748136121842456e-17,
            4.4375126860617067e-16,
            0.4556762678241436
          ],
          [
            -9.907691784197437e-16,
            -9.799507181719603e-16,
            0.44025638973912273
          ],
          [
            -7.075219716224631e-16,
            -8.628496889564429e-16,
            0.3975129489266333
          ],
          [
            -6.326543810608878e-16,
            -6.65626902909256e-16,
            0.3294108938549937
          ],
          [
            2.917836920040192e-17,
            1.2203159886669692e-15,
            0.23757004041705193
          ],
          [
            1.57883211264294e-15,
            1.6579040452091655e-15,
            0.1251680453783647
          ],
          [
            -8.213767910062459e-16,
            6.779533270372052e-16,
            -1.942890293094024e-15
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            -2.220446049250313e-16,
            3.1086244689504383e-15,
            0.4094186050256714
          ],
          [
            1.1102230246251565e-15,
            4.440892098500626e-16,
            0.4437875676742242
          ],
          [
            0.0,
            4.440892098500626e-16,
            0.4556762678241436
          ],
          [
            -9.992007221626409e-16,
            -9.992007221626409e-16,
            0.44025638973912273
          ],
          [
            -7.216449660063518e-16,
            -8.881784197001252e-16,
            0.39751294892663336
          ],
          [
            -6.106226635438361e-16,
            -6.661338147750939e-16,
            0.3294108938549938
          ],
          [
            0.0,
            1.2212453270876722e-15,
            0.237570040417052
          ],
          [
            1.5543122344752192e-15,
            1.6653345369377348e-15,
            0.12516804537836468
          ],
          [
            -8.326672684688674e-16,
            6.661338147750939e-16,
            -1.942890293094024e-15
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -168.44387386070585,
          -168.77780464767727,
          -169.7414390707566,
          -171.20294894740152,
          -172.94590922359214,
          -174.710056386154,
          -176.2323361624608,
          -177.28670036401738,
          -177.69436903651874
        ],
        "cartesian_polarizations_e_A2": [
          [
            -4.249824106880794e-17,
            1.4396112830828152e-17,
            -3.9454771166595286e-17
          ],
          [
            1.4686020313872763e-17,
            6.563318713327562e-17,
            -0.0025329355110766715
          ],
          [
            -8.585504333921408e-17,
            -8.245046439474305e-18,
            -0.004807533663414456
          ],
          [
            -7.714683143285164e-17,
            -2.4800576194926682e-17,
            -0.006666050813996699
          ],
          [
            3.9011244392109304e-17,
            -3.3307370140416044e-17,
            -0.008044183013367697
          ],
          [
            -7.634385450381684e-17,
            6.478250773872668e-17,
            -0.008909151214894603
          ],
          [
            -3.4167573597145185e-17,
            -8.114172686466777e-17,
            -0.00922119217279218
          ],
          [
            -3.858908910832682e-17,
            4.0276397488066944e-17,
            -0.008980609117434509
          ],
          [
            -5.424563903725023e-17,
            -4.637838622204297e-17,
            -0.008285109194045563
          ]
        ],
        "raw_reduced_polarization": [
          [
            -8.213767910062461e-16,
            6.779533270372052e-16,
            -1.9497048251631877e-15
          ],
          [
            2.838413057738276e-16,
            3.0908508500832583e-15,
            -0.12516804537836412
          ],
          [
            -1.659347262760583e-15,
            -3.8828236003039934e-16,
            -0.23757004041705307
          ],
          [
            -1.4910409288709157e-15,
            -1.1679286861231854e-15,
            -0.32941089385499306
          ],
          [
            7.539825161251068e-16,
            -1.5685374702815337e-15,
            -0.39751294892663214
          ],
          [
            -1.4755215427355035e-15,
            3.050789971667423e-15,
            -0.4402563897391229
          ],
          [
            -6.60367376434576e-16,
            -3.821191479664248e-15,
            -0.45567626782414766
          ],
          [
            -7.458233889805697e-16,
            1.896728512688181e-15,
            -0.44378756767422783
          ],
          [
            -1.0484224240330314e-15,
            -2.184088275170996e-15,
            -0.40941860502567146
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -8.213767910062461e-16,
            6.779533270372052e-16,
            -1.9497048251631877e-15
          ],
          [
            2.8384130577382764e-16,
            3.090850850083258e-15,
            -0.12516804537836412
          ],
          [
            -1.659347262760583e-15,
            -3.882823600303992e-16,
            -0.23757004041705307
          ],
          [
            -1.4910409288709157e-15,
            -1.1679286861231854e-15,
            -0.32941089385499306
          ],
          [
            7.539825161251066e-16,
            -1.5685374702815337e-15,
            -0.39751294892663214
          ],
          [
            -1.4755215427355035e-15,
            3.0507899716674224e-15,
            -0.4402563897391229
          ],
          [
            -6.60367376434576e-16,
            -3.821191479664248e-15,
            -0.45567626782414766
          ],
          [
            -7.458233889805697e-16,
            1.8967285126881814e-15,
            -0.44378756767422783
          ],
          [
            -1.0484224240330314e-15,
            -2.1840882751709965e-15,
            -0.40941860502567146
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          -1.4393387274784886e-15,
          -1.7657602563287209e-15,
          -0.40941860502567523
        ],
        "actual_opposite_endpoint_branch_residual": 3.8179332089760936e-15
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            -2.034148545340038e-16,
            3.121666910403131e-15,
            0.40941860502567134
          ],
          [
            1.0804624661928973e-15,
            4.930569651179674e-16,
            0.44378756767422417
          ],
          [
            4.974813612184246e-17,
            4.4375126860617067e-16,
            0.4556762678241436
          ],
          [
            -9.907691784197437e-16,
            -9.799507181719603e-16,
            0.44025638973912273
          ],
          [
            -7.075219716224631e-16,
            -8.628496889564429e-16,
            0.3975129489266333
          ],
          [
            -6.326543810608878e-16,
            -6.65626902909256e-16,
            0.3294108938549937
          ],
          [
            2.9178369200401913e-17,
            1.2203159886669692e-15,
            0.23757004041705193
          ],
          [
            1.57883211264294e-15,
            1.6579040452091655e-15,
            0.1251680453783647
          ],
          [
            -8.213767910062461e-16,
            6.779533270372052e-16,
            -1.9497048251631877e-15
          ],
          [
            2.838413057738276e-16,
            3.0908508500832583e-15,
            -0.12516804537836412
          ],
          [
            -1.659347262760583e-15,
            -3.8828236003039934e-16,
            -0.23757004041705307
          ],
          [
            -1.4910409288709157e-15,
            -1.1679286861231854e-15,
            -0.32941089385499306
          ],
          [
            7.539825161251068e-16,
            -1.5685374702815337e-15,
            -0.39751294892663214
          ],
          [
            -1.4755215427355035e-15,
            3.050789971667423e-15,
            -0.4402563897391229
          ],
          [
            -6.60367376434576e-16,
            -3.821191479664248e-15,
            -0.45567626782414766
          ],
          [
            -7.458233889805697e-16,
            1.896728512688181e-15,
            -0.44378756767422783
          ],
          [
            -1.0484224240330314e-15,
            -2.184088275170996e-15,
            -0.40941860502567146
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -2.034148545340038e-16,
            3.121666910403131e-15,
            0.40941860502567134
          ],
          [
            1.080462466192897e-15,
            4.930569651179674e-16,
            0.44378756767422417
          ],
          [
            4.9748136121842456e-17,
            4.4375126860617067e-16,
            0.4556762678241436
          ],
          [
            -9.907691784197437e-16,
            -9.799507181719603e-16,
            0.44025638973912273
          ],
          [
            -7.075219716224631e-16,
            -8.628496889564429e-16,
            0.3975129489266333
          ],
          [
            -6.326543810608878e-16,
            -6.65626902909256e-16,
            0.3294108938549937
          ],
          [
            2.917836920040192e-17,
            1.2203159886669692e-15,
            0.23757004041705193
          ],
          [
            1.57883211264294e-15,
            1.6579040452091655e-15,
            0.1251680453783647
          ],
          [
            -8.213767910062459e-16,
            6.779533270372052e-16,
            -1.942890293094024e-15
          ],
          [
            2.8384130577382764e-16,
            3.090850850083258e-15,
            -0.12516804537836412
          ],
          [
            -1.659347262760583e-15,
            -3.882823600303992e-16,
            -0.23757004041705307
          ],
          [
            -1.4910409288709157e-15,
            -1.1679286861231854e-15,
            -0.32941089385499306
          ],
          [
            7.539825161251066e-16,
            -1.5685374702815337e-15,
            -0.39751294892663214
          ],
          [
            -1.4755215427355035e-15,
            3.0507899716674224e-15,
            -0.4402563897391229
          ],
          [
            -6.60367376434576e-16,
            -3.821191479664248e-15,
            -0.45567626782414766
          ],
          [
            -7.458233889805697e-16,
            1.8967285126881814e-15,
            -0.44378756767422783
          ],
          [
            -1.0484224240330314e-15,
            -2.1840882751709965e-15,
            -0.40941860502567146
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            -2.220446049250313e-16,
            3.1086244689504383e-15,
            0.4094186050256714
          ],
          [
            1.1102230246251565e-15,
            4.440892098500626e-16,
            0.4437875676742242
          ],
          [
            0.0,
            4.440892098500626e-16,
            0.4556762678241436
          ],
          [
            -9.992007221626409e-16,
            -9.992007221626409e-16,
            0.44025638973912273
          ],
          [
            -7.216449660063518e-16,
            -8.881784197001252e-16,
            0.39751294892663336
          ],
          [
            -6.106226635438361e-16,
            -6.661338147750939e-16,
            0.3294108938549938
          ],
          [
            0.0,
            1.2212453270876722e-15,
            0.237570040417052
          ],
          [
            1.5543122344752192e-15,
            1.6653345369377348e-15,
            0.12516804537836468
          ],
          [
            -8.326672684688674e-16,
            6.661338147750939e-16,
            -1.942890293094024e-15
          ],
          [
            3.3306690738754696e-16,
            3.1086244689504383e-15,
            -0.12516804537836412
          ],
          [
            -1.6653345369377348e-15,
            -3.885780586188048e-16,
            -0.2375700404170531
          ],
          [
            -1.4988010832439613e-15,
            -1.1657341758564144e-15,
            -0.32941089385499306
          ],
          [
            7.771561172376096e-16,
            -1.5543122344752192e-15,
            -0.39751294892663214
          ],
          [
            -1.4988010832439613e-15,
            2.9976021664879227e-15,
            -0.4402563897391229
          ],
          [
            -6.661338147750939e-16,
            -3.83026943495679e-15,
            -0.45567626782414766
          ],
          [
            -7.216449660063518e-16,
            1.887379141862766e-15,
            -0.44378756767422783
          ],
          [
            -1.0547118733938987e-15,
            -2.1649348980190553e-15,
            -0.40941860502567146
          ]
        ]
      },
      "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,
        0.5,
        0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              3.5643543314248743e-16,
              5.234107845330422e-15,
              0.4094186050256718
            ],
            "branch_aligned_reduced_polarization": [
              3.5643543314248743e-16,
              5.218048215738236e-15,
              0.4094186050256718
            ],
            "target_residual": 0.508138749866107,
            "energy_eV": -177.6943690365187,
            "max_atomic_step_A": 0.06974783226793366,
            "max_log_strain_component": 0.0016494970461455238,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.1530218493539404,
            "cell_principal_stretches": [
              1.0009508055928806,
              1.0002156769274737,
              0.9975078572097035
            ],
            "cell_volume_ratio": 0.9986716372448274,
            "cell_rmsd_from_input_A": 0.005206248126352526
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              4.4625461603976125e-15,
              0.4954219606999878,
              0.4940088810932417
            ],
            "branch_aligned_reduced_polarization": [
              4.4625461603976125e-15,
              0.4954219606999878,
              0.4940088810932417
            ],
            "target_residual": 0.007540023182150905,
            "energy_eV": -177.2464661602699,
            "max_atomic_step_A": 0.0010448002161782919,
            "max_log_strain_component": 0.00011175630974720506,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.1530218493539404,
            "cell_principal_stretches": [
              1.0009420893343735,
              1.0002302910989533,
              0.9974121393273456
            ],
            "cell_volume_ratio": 0.9985817021967949,
            "cell_rmsd_from_input_A": 0.005408641685047636
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              3.9279792325979956e-15,
              0.49998998931792493,
              0.5000023325221086
            ],
            "branch_aligned_reduced_polarization": [
              3.9279792325979956e-15,
              0.49998998931792493,
              0.5000023325221086
            ],
            "target_residual": 1.0278833347956536e-05,
            "energy_eV": -177.23674400153627
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_02",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Pm",
        "spacegroup_number": 6,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.5,
          0.5
        ],
        "formal_class": [
          0.0,
          0.5,
          0.5
        ],
        "target_residual": 1.0278833347956536e-05,
        "parent_symmetrization_rmsd_A": 0.06156623359477819,
        "parent_cell_rmsd_A": 0.005408641685047636,
        "energy_eV": -177.23674400153627,
        "reduced_polarization": [
          3.9279792325979956e-15,
          0.49998998931792493,
          0.5000023325221086
        ],
        "cartesian_polarization_e_A2": [
          1.3553495530948268e-16,
          0.010648564213824591,
          0.010130649463291818
        ],
        "ranking_score": 0.562938951682736
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 3,
      "formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.0,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              3.5643543314248743e-16,
              5.234107845330422e-15,
              0.4094186050256718
            ],
            "branch_aligned_reduced_polarization": [
              3.3306690738754696e-16,
              5.234107845330422e-15,
              0.4094186050256718
            ],
            "target_residual": 0.5081387498661118,
            "energy_eV": -177.6943690365187,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.008067902064724589,
            "step_scale": 0.8638102449962,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.1530218493539404,
            "cell_principal_stretches": [
              1.007516846127968,
              1.000090356528005,
              0.9913106683546534
            ],
            "cell_volume_ratio": 0.9988524427982126,
            "cell_rmsd_from_input_A": 0.049260422133569945
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.4251387365048189,
              -3.7215769265339786e-14,
              0.43220491140234624
            ],
            "branch_aligned_reduced_polarization": [
              0.4251387365048189,
              -3.7215769265339786e-14,
              0.43220491140234624
            ],
            "target_residual": 0.10099694455803429,
            "energy_eV": -175.34864884500968,
            "max_atomic_step_A": 0.026058739606101396,
            "max_log_strain_component": 0.0019776815858698134,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.1530218493539404,
            "cell_principal_stretches": [
              1.0084336256599022,
              1.0002157840561983,
              0.9887082841256952
            ],
            "cell_volume_ratio": 0.9972618264576161,
            "cell_rmsd_from_input_A": 0.059454510435005804
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.49858886918989914,
              -1.660447773221412e-14,
              0.4965822454034789
            ],
            "branch_aligned_reduced_polarization": [
              0.49858886918989914,
              -1.660447773221412e-14,
              0.4965822454034789
            ],
            "target_residual": 0.0036976122897428073,
            "energy_eV": -174.35801553385213,
            "max_atomic_step_A": 0.0007089208938279941,
            "max_log_strain_component": 7.992815595689545e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.1530218493539404,
            "cell_principal_stretches": [
              1.0084440492204967,
              1.0002208535502704,
              0.9886293737614854
            ],
            "cell_volume_ratio": 0.9971975948546415,
            "cell_rmsd_from_input_A": 0.059697705116983336
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.4999859843065679,
              2.341251441574771e-15,
              0.49996701195238263
            ],
            "branch_aligned_reduced_polarization": [
              0.4999859843065679,
              2.341251441574771e-15,
              0.49996701195238263
            ],
            "target_residual": 3.584202767686111e-05,
            "energy_eV": -174.33698078444047
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_03",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Pc",
        "spacegroup_number": 7,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.5,
          0.0,
          0.5
        ],
        "formal_class": [
          0.5,
          0.0,
          0.5
        ],
        "target_residual": 3.584202767686111e-05,
        "parent_symmetrization_rmsd_A": 0.1448342099817048,
        "parent_cell_rmsd_A": 0.059697705116983336,
        "energy_eV": -174.33698078444047,
        "reduced_polarization": [
          0.4999859843065679,
          2.341251441574771e-15,
          0.49996701195238263
        ],
        "cartesian_polarization_e_A2": [
          0.02605374243257061,
          6.533860317251936e-16,
          0.010362809066940743
        ],
        "ranking_score": 0.6598303203163043
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 4,
      "formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.5,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              3.5643543314248743e-16,
              5.234107845330422e-15,
              0.4094186050256718
            ],
            "branch_aligned_reduced_polarization": [
              3.5643543314248743e-16,
              5.218048215738236e-15,
              0.4094186050256718
            ],
            "target_residual": 0.6462380321067167,
            "energy_eV": -177.6943690365187,
            "max_atomic_step_A": 0.08864868034812082,
            "max_log_strain_component": 0.0074555572898437296,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.1530218493539404,
            "cell_principal_stretches": [
              1.0077537257357643,
              0.9992592414521422,
              0.9990257424393176
            ],
            "cell_volume_ratio": 1.006026139148085,
            "cell_rmsd_from_input_A": 0.01704189135998158
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              1.6603949801114003e-14,
              0.5111135072956593,
              0.010085507639273933
            ],
            "branch_aligned_reduced_polarization": [
              1.6603949801114003e-14,
              0.5111135072956593,
              0.010085507639273933
            ],
            "target_residual": 0.015007581709007128,
            "energy_eV": -176.9068855605211,
            "max_atomic_step_A": 0.002200197202794788,
            "max_log_strain_component": 0.0002247194846197884,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.1530218493539404,
            "cell_principal_stretches": [
              1.0079614468682352,
              0.9992636061740946,
              0.998996391882426
            ],
            "cell_volume_ratio": 1.0062083369264667,
            "cell_rmsd_from_input_A": 0.017515481825301805
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              8.639617856280244e-16,
              0.49999299087153587,
              8.604265498281027e-05
            ],
            "branch_aligned_reduced_polarization": [
              8.639617856280244e-16,
              0.49999299087153587,
              8.604265498281027e-05
            ],
            "target_residual": 8.632766855601747e-05,
            "energy_eV": -176.91434618901525
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_04",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Pm",
        "spacegroup_number": 6,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.5,
          0.0
        ],
        "formal_class": [
          0.0,
          0.5,
          0.0
        ],
        "target_residual": 8.632766855601747e-05,
        "parent_symmetrization_rmsd_A": 0.07492832234294407,
        "parent_cell_rmsd_A": 0.017515481825301805,
        "energy_eV": -176.91434618901525,
        "reduced_polarization": [
          8.639617856280244e-16,
          0.49999299087153587,
          8.604265498281027e-05
        ],
        "cartesian_polarization_e_A2": [
          -1.260401857317689e-16,
          0.01054655207305638,
          1.7097582733831356e-05
        ],
        "ranking_score": 0.5794798481363815
      },
      "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,
        0.0,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              3.5643543314248743e-16,
              5.234107845330422e-15,
              0.4094186050256718
            ],
            "branch_aligned_reduced_polarization": [
              3.3306690738754696e-16,
              5.234107845330422e-15,
              0.4094186050256718
            ],
            "target_residual": 0.6462380321067205,
            "energy_eV": -177.6943690365187,
            "max_atomic_step_A": 0.12000000000000001,
            "max_log_strain_component": 0.00761924070535279,
            "step_scale": 0.81577318707741,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.1530218493539404,
            "cell_principal_stretches": [
              1.0110634288595048,
              0.999614401074318,
              0.9943005103944661
            ],
            "cell_volume_ratio": 1.0049132404155752,
            "cell_rmsd_from_input_A": 0.048536832271316895
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.4186456105007596,
              3.723221944286619e-15,
              0.04098235759306699
            ],
            "branch_aligned_reduced_polarization": [
              0.4186456105007596,
              3.723221944286619e-15,
              0.04098235759306699
            ],
            "target_residual": 0.09109385448360462,
            "energy_eV": -175.06150494424335,
            "max_atomic_step_A": 0.02188884120760681,
            "max_log_strain_component": 0.0014467351958986883,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.1530218493539404,
            "cell_principal_stretches": [
              1.0125291239900807,
              0.999603301034414,
              0.9930123480858816
            ],
            "cell_volume_ratio": 1.0050550603875648,
            "cell_rmsd_from_input_A": 0.05719017447507895
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.4997700900549178,
              -3.721455431983349e-15,
              -0.0029681846399548604
            ],
            "branch_aligned_reduced_polarization": [
              0.4997700900549178,
              -3.721455431983349e-15,
              -0.0029681846399548604
            ],
            "target_residual": 0.0029770755179725737,
            "energy_eV": -173.82272443654475,
            "max_atomic_step_A": 0.0004608311997736998,
            "max_log_strain_component": 6.77699132318919e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.1530218493539404,
            "cell_principal_stretches": [
              1.0124946085842168,
              0.9996075967504626,
              0.9929877009821166
            ],
            "cell_volume_ratio": 1.0050001734899796,
            "cell_rmsd_from_input_A": 0.05721024593114961
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.49999929345240685,
              -1.13976807745557e-15,
              -2.8251943915461724e-05
            ],
            "branch_aligned_reduced_polarization": [
              0.49999929345240685,
              -1.13976807745557e-15,
              -2.8251943915461724e-05
            ],
            "target_residual": 2.826077749291033e-05,
            "energy_eV": -173.8248004655673
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_05",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Pc",
        "spacegroup_number": 7,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.5,
          0.0,
          0.0
        ],
        "formal_class": [
          0.5,
          0.0,
          0.0
        ],
        "target_residual": 2.826077749291033e-05,
        "parent_symmetrization_rmsd_A": 0.14327372740572236,
        "parent_cell_rmsd_A": 0.05721024593114961,
        "energy_eV": -173.8248004655673,
        "reduced_polarization": [
          0.49999929345240685,
          -1.13976807745557e-15,
          -2.8251943915461724e-05
        ],
        "cartesian_polarization_e_A2": [
          0.02572161293970202,
          1.8573814687845117e-16,
          0.000233567242340614
        ],
        "ranking_score": 0.6576328104434956
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 6,
      "formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.5,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.5,
        0.5,
        0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              3.5643543314248743e-16,
              5.234107845330422e-15,
              0.4094186050256718
            ],
            "branch_aligned_reduced_polarization": [
              3.3306690738754696e-16,
              5.218048215738236e-15,
              0.4094186050256718
            ],
            "target_residual": 0.7128849760764283,
            "energy_eV": -177.6943690365187,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.007228193075764108,
            "step_scale": 0.7739046881784997,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.1530218493539404,
            "cell_principal_stretches": [
              1.0068214097080832,
              1.0000830606437947,
              0.9921211859349998
            ],
            "cell_volume_ratio": 0.9989718193753773,
            "cell_rmsd_from_input_A": 0.04422851400178593
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.3809553661795967,
              0.3792952850344487,
              0.4307144188255687
            ],
            "branch_aligned_reduced_polarization": [
              0.3809553661795967,
              0.3792952850344487,
              0.4307144188255687
            ],
            "target_residual": 0.18314405481758778,
            "energy_eV": -175.53327979989444,
            "max_atomic_step_A": 0.044238279404161786,
            "max_log_strain_component": 0.0024937115135395464,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.1530218493539404,
            "cell_principal_stretches": [
              1.0084901357973506,
              1.0002403885900284,
              0.9883960953736265
            ],
            "cell_volume_ratio": 0.9970273288376716,
            "cell_rmsd_from_input_A": 0.05986034865746705
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.49727131669485514,
              0.49747583848611343,
              0.4910897521631372
            ],
            "branch_aligned_reduced_polarization": [
              0.49727131669485514,
              0.49747583848611343,
              0.4910897521631372
            ],
            "target_residual": 0.009654512957279635,
            "energy_eV": -173.7456305714199,
            "max_atomic_step_A": 0.0017535630466862877,
            "max_log_strain_component": 0.00020262500105928003,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.1530218493539404,
            "cell_principal_stretches": [
              1.008503432336765,
              1.0002535560350616,
              0.98820867974355
            ],
            "cell_volume_ratio": 0.9968645423343643,
            "cell_rmsd_from_input_A": 0.0603892597911791
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.499963671779159,
              0.4999708215773377,
              0.4999231851232432
            ],
            "branch_aligned_reduced_polarization": [
              0.499963671779159,
              0.4999708215773377,
              0.4999231851232432
            ],
            "target_residual": 8.984233562022214e-05,
            "energy_eV": -173.69597383751
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_06",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.5,
          0.5,
          0.5
        ],
        "formal_class": [
          0.5,
          0.5,
          0.5
        ],
        "target_residual": 8.984233562022214e-05,
        "parent_symmetrization_rmsd_A": 0.15781463662818296,
        "parent_cell_rmsd_A": 0.0603892597911791,
        "energy_eV": -173.69597383751,
        "reduced_polarization": [
          0.499963671779159,
          0.4999708215773377,
          0.4999231851232432
        ],
        "cartesian_polarization_e_A2": [
          0.02606354113123065,
          0.010668759404462285,
          0.010379643880522677
        ],
        "ranking_score": 0.6730916362472181
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 7,
      "formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.5,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.5,
        0.5,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              3.5643543314248743e-16,
              5.234107845330422e-15,
              0.4094186050256718
            ],
            "branch_aligned_reduced_polarization": [
              3.3306690738754696e-16,
              5.218048215738236e-15,
              0.4094186050256718
            ],
            "target_residual": 0.8170823668034707,
            "energy_eV": -177.6943690365187,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.006816259852605318,
            "step_scale": 0.729800020624224,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.1530218493539404,
            "cell_principal_stretches": [
              1.0099731843894453,
              0.999646403547408,
              0.9948279781554646
            ],
            "cell_volume_ratio": 1.0043943051297968,
            "cell_rmsd_from_input_A": 0.0434915619252336
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.3730827350955227,
              0.3663131570773747,
              0.07908712126401894
            ],
            "branch_aligned_reduced_polarization": [
              0.3730827350955227,
              0.3663131570773747,
              0.07908712126401894
            ],
            "target_residual": 0.20058648222470424,
            "energy_eV": -175.34786033839353,
            "max_atomic_step_A": 0.03985822989086335,
            "max_log_strain_component": 0.0022627650315095007,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.1530218493539404,
            "cell_principal_stretches": [
              1.0124968064537776,
              0.9996090784221966,
              0.992836843148614
            ],
            "cell_volume_ratio": 1.0048511613950644,
            "cell_rmsd_from_input_A": 0.05724834620849582
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.49951432591285466,
              0.4989205909245753,
              -0.006954009200826056
            ],
            "branch_aligned_reduced_polarization": [
              0.49951432591285466,
              0.4989205909245753,
              -0.006954009200826056
            ],
            "target_residual": 0.007054023478569312,
            "energy_eV": -173.181735866928,
            "max_atomic_step_A": 0.00112211343145017,
            "max_log_strain_component": 0.00016053639118900767,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.1530218493539404,
            "cell_principal_stretches": [
              1.01241702537956,
              0.999619498251241,
              0.9927762894040496
            ],
            "cell_volume_ratio": 1.0047211741015527,
            "cell_rmsd_from_input_A": 0.05729845336377266
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.4999972810266224,
              0.4999926781491675,
              -6.700270737817864e-05
            ],
            "branch_aligned_reduced_polarization": [
              0.4999972810266224,
              0.4999926781491675,
              -6.700270737817864e-05
            ],
            "target_residual": 6.745639415094524e-05,
            "energy_eV": -173.18435914155083
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_07",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.5,
          0.5,
          0.0
        ],
        "formal_class": [
          0.5,
          0.5,
          0.0
        ],
        "target_residual": 6.745639415094524e-05,
        "parent_symmetrization_rmsd_A": 0.1554546723262151,
        "parent_cell_rmsd_A": 0.05729845336377266,
        "energy_eV": -173.18435914155083,
        "reduced_polarization": [
          0.4999972810266224,
          0.4999926781491675,
          -6.700270737817864e-05
        ],
        "cartesian_polarization_e_A2": [
          0.025729879928085737,
          0.010563559750029282,
          0.00024919820930929733
        ],
        "ranking_score": 0.6699141984554602
      },
      "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
        ],
        "endpoint_rmsd_A": 0.42051236853255375,
        "minimum_distance_A_by_image": [
          1.4261133963549844,
          1.3935989652433978,
          1.366102257820684,
          1.343931295844044,
          1.3273529761545397,
          1.316578582878575,
          1.3117511397798662,
          1.3129362462678755,
          1.320117709541524
        ],
        "minimum_distance_A": 1.3117511397798662,
        "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": [
          212.07900727071103,
          212.07900727071103,
          212.07900727071103,
          212.07900727071103,
          212.07900727071103,
          212.07900727071103,
          212.07900727071103,
          212.07900727071103,
          212.07900727071103
        ],
        "cell_deformation_log_strain_norm": 0.0
      },
      "parent_reduced_polarization": [
        -8.213767910062461e-16,
        6.779533270372052e-16,
        -1.9497048251631877e-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": [
          -177.69436903651874,
          -177.28670036401735,
          -176.2323361624608,
          -174.71005638615404,
          -172.94590922359217,
          -171.20294894740152,
          -169.74143907075657,
          -168.77780464767727,
          -168.44387386070585
        ],
        "cartesian_polarizations_e_A2": [
          [
            -1.0524735565479173e-17,
            6.628755589831327e-17,
            0.008285109194045561
          ],
          [
            5.590339885037647e-17,
            1.0469900240602293e-17,
            0.008980609117434434
          ],
          [
            2.573981033771206e-18,
            9.422910216542063e-18,
            0.009221192172792098
          ],
          [
            -5.1262645656744464e-17,
            -2.0808926728197058e-17,
            0.008909151214894597
          ],
          [
            -3.660736417284655e-17,
            -1.832232542105401e-17,
            0.00804418301336772
          ],
          [
            -3.2733696269436754e-17,
            -1.4134365324813094e-17,
            0.006666050813996713
          ],
          [
            1.5096961368414554e-18,
            2.5913003095490674e-17,
            0.004807533663414433
          ],
          [
            8.168916928864716e-17,
            3.520503955902521e-17,
            0.0025329355110766828
          ],
          [
            -4.249824106880794e-17,
            1.4396112830828152e-17,
            -3.9454771166595286e-17
          ]
        ],
        "raw_reduced_polarization": [
          [
            -2.034148545340038e-16,
            3.121666910403131e-15,
            0.40941860502567134
          ],
          [
            1.0804624661928973e-15,
            4.930569651179674e-16,
            0.44378756767422417
          ],
          [
            4.974813612184246e-17,
            4.4375126860617067e-16,
            0.4556762678241436
          ],
          [
            -9.907691784197437e-16,
            -9.799507181719603e-16,
            0.44025638973912273
          ],
          [
            -7.075219716224631e-16,
            -8.628496889564429e-16,
            0.3975129489266333
          ],
          [
            -6.326543810608878e-16,
            -6.65626902909256e-16,
            0.3294108938549937
          ],
          [
            2.9178369200401913e-17,
            1.2203159886669692e-15,
            0.23757004041705193
          ],
          [
            1.57883211264294e-15,
            1.6579040452091655e-15,
            0.1251680453783647
          ],
          [
            -8.213767910062461e-16,
            6.779533270372052e-16,
            -1.9497048251631877e-15
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -2.034148545340038e-16,
            3.121666910403131e-15,
            0.40941860502567134
          ],
          [
            1.080462466192897e-15,
            4.930569651179674e-16,
            0.44378756767422417
          ],
          [
            4.9748136121842456e-17,
            4.4375126860617067e-16,
            0.4556762678241436
          ],
          [
            -9.907691784197437e-16,
            -9.799507181719603e-16,
            0.44025638973912273
          ],
          [
            -7.075219716224631e-16,
            -8.628496889564429e-16,
            0.3975129489266333
          ],
          [
            -6.326543810608878e-16,
            -6.65626902909256e-16,
            0.3294108938549937
          ],
          [
            2.917836920040192e-17,
            1.2203159886669692e-15,
            0.23757004041705193
          ],
          [
            1.57883211264294e-15,
            1.6579040452091655e-15,
            0.1251680453783647
          ],
          [
            -8.213767910062459e-16,
            6.779533270372052e-16,
            -1.942890293094024e-15
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            -2.220446049250313e-16,
            3.1086244689504383e-15,
            0.4094186050256714
          ],
          [
            1.1102230246251565e-15,
            4.440892098500626e-16,
            0.4437875676742242
          ],
          [
            0.0,
            4.440892098500626e-16,
            0.4556762678241436
          ],
          [
            -9.992007221626409e-16,
            -9.992007221626409e-16,
            0.44025638973912273
          ],
          [
            -7.216449660063518e-16,
            -8.881784197001252e-16,
            0.39751294892663336
          ],
          [
            -6.106226635438361e-16,
            -6.661338147750939e-16,
            0.3294108938549938
          ],
          [
            0.0,
            1.2212453270876722e-15,
            0.237570040417052
          ],
          [
            1.5543122344752192e-15,
            1.6653345369377348e-15,
            0.12516804537836468
          ],
          [
            -8.326672684688674e-16,
            6.661338147750939e-16,
            -1.942890293094024e-15
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -168.44387386070585,
          -168.77780464767727,
          -169.7414390707566,
          -171.20294894740152,
          -172.94590922359214,
          -174.710056386154,
          -176.2323361624608,
          -177.28670036401738,
          -177.69436903651874
        ],
        "cartesian_polarizations_e_A2": [
          [
            -4.249824106880794e-17,
            1.4396112830828152e-17,
            -3.9454771166595286e-17
          ],
          [
            1.4686020313872763e-17,
            6.563318713327562e-17,
            -0.0025329355110766715
          ],
          [
            -8.585504333921408e-17,
            -8.245046439474305e-18,
            -0.004807533663414456
          ],
          [
            -7.714683143285164e-17,
            -2.4800576194926682e-17,
            -0.006666050813996699
          ],
          [
            3.9011244392109304e-17,
            -3.3307370140416044e-17,
            -0.008044183013367697
          ],
          [
            -7.634385450381684e-17,
            6.478250773872668e-17,
            -0.008909151214894603
          ],
          [
            -3.4167573597145185e-17,
            -8.114172686466777e-17,
            -0.00922119217279218
          ],
          [
            -3.858908910832682e-17,
            4.0276397488066944e-17,
            -0.008980609117434509
          ],
          [
            -5.424563903725023e-17,
            -4.637838622204297e-17,
            -0.008285109194045563
          ]
        ],
        "raw_reduced_polarization": [
          [
            -8.213767910062461e-16,
            6.779533270372052e-16,
            -1.9497048251631877e-15
          ],
          [
            2.838413057738276e-16,
            3.0908508500832583e-15,
            -0.12516804537836412
          ],
          [
            -1.659347262760583e-15,
            -3.8828236003039934e-16,
            -0.23757004041705307
          ],
          [
            -1.4910409288709157e-15,
            -1.1679286861231854e-15,
            -0.32941089385499306
          ],
          [
            7.539825161251068e-16,
            -1.5685374702815337e-15,
            -0.39751294892663214
          ],
          [
            -1.4755215427355035e-15,
            3.050789971667423e-15,
            -0.4402563897391229
          ],
          [
            -6.60367376434576e-16,
            -3.821191479664248e-15,
            -0.45567626782414766
          ],
          [
            -7.458233889805697e-16,
            1.896728512688181e-15,
            -0.44378756767422783
          ],
          [
            -1.0484224240330314e-15,
            -2.184088275170996e-15,
            -0.40941860502567146
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -8.213767910062461e-16,
            6.779533270372052e-16,
            -1.9497048251631877e-15
          ],
          [
            2.8384130577382764e-16,
            3.090850850083258e-15,
            -0.12516804537836412
          ],
          [
            -1.659347262760583e-15,
            -3.882823600303992e-16,
            -0.23757004041705307
          ],
          [
            -1.4910409288709157e-15,
            -1.1679286861231854e-15,
            -0.32941089385499306
          ],
          [
            7.539825161251066e-16,
            -1.5685374702815337e-15,
            -0.39751294892663214
          ],
          [
            -1.4755215427355035e-15,
            3.0507899716674224e-15,
            -0.4402563897391229
          ],
          [
            -6.60367376434576e-16,
            -3.821191479664248e-15,
            -0.45567626782414766
          ],
          [
            -7.458233889805697e-16,
            1.8967285126881814e-15,
            -0.44378756767422783
          ],
          [
            -1.0484224240330314e-15,
            -2.1840882751709965e-15,
            -0.40941860502567146
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          -1.4393387274784886e-15,
          -1.7657602563287209e-15,
          -0.40941860502567523
        ],
        "actual_opposite_endpoint_branch_residual": 3.8179332089760936e-15
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            -2.034148545340038e-16,
            3.121666910403131e-15,
            0.40941860502567134
          ],
          [
            1.0804624661928973e-15,
            4.930569651179674e-16,
            0.44378756767422417
          ],
          [
            4.974813612184246e-17,
            4.4375126860617067e-16,
            0.4556762678241436
          ],
          [
            -9.907691784197437e-16,
            -9.799507181719603e-16,
            0.44025638973912273
          ],
          [
            -7.075219716224631e-16,
            -8.628496889564429e-16,
            0.3975129489266333
          ],
          [
            -6.326543810608878e-16,
            -6.65626902909256e-16,
            0.3294108938549937
          ],
          [
            2.9178369200401913e-17,
            1.2203159886669692e-15,
            0.23757004041705193
          ],
          [
            1.57883211264294e-15,
            1.6579040452091655e-15,
            0.1251680453783647
          ],
          [
            -8.213767910062461e-16,
            6.779533270372052e-16,
            -1.9497048251631877e-15
          ],
          [
            2.838413057738276e-16,
            3.0908508500832583e-15,
            -0.12516804537836412
          ],
          [
            -1.659347262760583e-15,
            -3.8828236003039934e-16,
            -0.23757004041705307
          ],
          [
            -1.4910409288709157e-15,
            -1.1679286861231854e-15,
            -0.32941089385499306
          ],
          [
            7.539825161251068e-16,
            -1.5685374702815337e-15,
            -0.39751294892663214
          ],
          [
            -1.4755215427355035e-15,
            3.050789971667423e-15,
            -0.4402563897391229
          ],
          [
            -6.60367376434576e-16,
            -3.821191479664248e-15,
            -0.45567626782414766
          ],
          [
            -7.458233889805697e-16,
            1.896728512688181e-15,
            -0.44378756767422783
          ],
          [
            -1.0484224240330314e-15,
            -2.184088275170996e-15,
            -0.40941860502567146
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -2.034148545340038e-16,
            3.121666910403131e-15,
            0.40941860502567134
          ],
          [
            1.080462466192897e-15,
            4.930569651179674e-16,
            0.44378756767422417
          ],
          [
            4.9748136121842456e-17,
            4.4375126860617067e-16,
            0.4556762678241436
          ],
          [
            -9.907691784197437e-16,
            -9.799507181719603e-16,
            0.44025638973912273
          ],
          [
            -7.075219716224631e-16,
            -8.628496889564429e-16,
            0.3975129489266333
          ],
          [
            -6.326543810608878e-16,
            -6.65626902909256e-16,
            0.3294108938549937
          ],
          [
            2.917836920040192e-17,
            1.2203159886669692e-15,
            0.23757004041705193
          ],
          [
            1.57883211264294e-15,
            1.6579040452091655e-15,
            0.1251680453783647
          ],
          [
            -8.213767910062459e-16,
            6.779533270372052e-16,
            -1.942890293094024e-15
          ],
          [
            2.8384130577382764e-16,
            3.090850850083258e-15,
            -0.12516804537836412
          ],
          [
            -1.659347262760583e-15,
            -3.882823600303992e-16,
            -0.23757004041705307
          ],
          [
            -1.4910409288709157e-15,
            -1.1679286861231854e-15,
            -0.32941089385499306
          ],
          [
            7.539825161251066e-16,
            -1.5685374702815337e-15,
            -0.39751294892663214
          ],
          [
            -1.4755215427355035e-15,
            3.0507899716674224e-15,
            -0.4402563897391229
          ],
          [
            -6.60367376434576e-16,
            -3.821191479664248e-15,
            -0.45567626782414766
          ],
          [
            -7.458233889805697e-16,
            1.8967285126881814e-15,
            -0.44378756767422783
          ],
          [
            -1.0484224240330314e-15,
            -2.1840882751709965e-15,
            -0.40941860502567146
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            -2.220446049250313e-16,
            3.1086244689504383e-15,
            0.4094186050256714
          ],
          [
            1.1102230246251565e-15,
            4.440892098500626e-16,
            0.4437875676742242
          ],
          [
            0.0,
            4.440892098500626e-16,
            0.4556762678241436
          ],
          [
            -9.992007221626409e-16,
            -9.992007221626409e-16,
            0.44025638973912273
          ],
          [
            -7.216449660063518e-16,
            -8.881784197001252e-16,
            0.39751294892663336
          ],
          [
            -6.106226635438361e-16,
            -6.661338147750939e-16,
            0.3294108938549938
          ],
          [
            0.0,
            1.2212453270876722e-15,
            0.237570040417052
          ],
          [
            1.5543122344752192e-15,
            1.6653345369377348e-15,
            0.12516804537836468
          ],
          [
            -8.326672684688674e-16,
            6.661338147750939e-16,
            -1.942890293094024e-15
          ],
          [
            3.3306690738754696e-16,
            3.1086244689504383e-15,
            -0.12516804537836412
          ],
          [
            -1.6653345369377348e-15,
            -3.885780586188048e-16,
            -0.2375700404170531
          ],
          [
            -1.4988010832439613e-15,
            -1.1657341758564144e-15,
            -0.32941089385499306
          ],
          [
            7.771561172376096e-16,
            -1.5543122344752192e-15,
            -0.39751294892663214
          ],
          [
            -1.4988010832439613e-15,
            2.9976021664879227e-15,
            -0.4402563897391229
          ],
          [
            -6.661338147750939e-16,
            -3.83026943495679e-15,
            -0.45567626782414766
          ],
          [
            -7.216449660063518e-16,
            1.887379141862766e-15,
            -0.44378756767422783
          ],
          [
            -1.0547118733938987e-15,
            -2.1649348980190553e-15,
            -0.40941860502567146
          ]
        ]
      },
      "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": "Pmmn",
        "spacegroup_number": 59,
        "pointgroup": "mmm",
        "has_inversion": true,
        "is_polar_point_group": false,
        "nonpolar_parent_hypothesis": true,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.0
        ],
        "formal_class": [
          0.0,
          0.0,
          0.0
        ],
        "target_residual": 2.908068172176977e-15,
        "parent_symmetrization_rmsd_A": 0.42051236853255375,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -168.44387386070588,
        "reduced_polarization": [
          -2.430645175367164e-15,
          -1.4391100169380674e-15,
          -6.912212993257562e-16
        ],
        "cartesian_polarization_e_A2": [
          -1.2576219068588603e-16,
          -3.0559021327257945e-17,
          -1.398774719044548e-17
        ],
        "ranking_score": 0.4205123685325596
      }
    }
  ],
  "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": 55,
      "full_response": 20,
      "energy_polarization": 35
    },
    "model_evaluations_for_recovery_and_path_properties": {
      "total": 80,
      "full_response": 45,
      "energy_polarization": 35
    },
    "elapsed_seconds": 650.5367127170321
  }
}
