{
  "schema": "ferrofinder.endpoint_parent_recovery.v4_variable_cell",
  "status": "complete",
  "input_atom_count": 84,
  "input_formula": "Cl48Rb24Zn12",
  "input_spacegroup": "Pna2_1",
  "input_pointgroup": "mm2",
  "input_is_polar_point_group": true,
  "input_energy_eV": -261.41035421167356,
  "input_cartesian_polarization_e_A2": [
    -8.088332425766968e-18,
    -6.422355088070507e-18,
    0.00029889335723400166
  ],
  "input_reduced_polarization": [
    -7.994351906310773e-16,
    -1.3783925634411432e-15,
    0.10939763593528573
  ],
  "input_formal_targets": [
    {
      "orbit_id": 0,
      "representative_formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ]
    },
    {
      "orbit_id": 1,
      "representative_formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.5
      ]
    },
    {
      "orbit_id": 2,
      "representative_formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        -0.5,
        0.0
      ]
    },
    {
      "orbit_id": 3,
      "representative_formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        -0.5,
        0.0,
        0.0
      ]
    },
    {
      "orbit_id": 4,
      "representative_formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        -0.5,
        0.5
      ]
    },
    {
      "orbit_id": 5,
      "representative_formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        -0.5,
        0.0,
        0.5
      ]
    },
    {
      "orbit_id": 6,
      "representative_formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        -0.5,
        -0.5,
        0.0
      ]
    },
    {
      "orbit_id": 7,
      "representative_formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "target_reduced_polarization": [
        -0.5,
        -0.5,
        0.5
      ]
    }
  ],
  "parent_candidates": [
    {
      "candidate_id": "inversion_parent_endpoint_00",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "P2_1/c",
      "spacegroup_number": 14,
      "pointgroup": "2/m",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 3.780142228595455e-15,
      "parent_symmetrization_rmsd_A": 0.2321058704340006,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -261.17469399275535,
      "reduced_polarization": [
        -8.255251321972392e-16,
        2.2538508879531994e-15,
        2.9202978785380634e-15
      ],
      "cartesian_polarization_e_A2": [
        -8.352298939662071e-18,
        1.0501384802789194e-17,
        7.978761419999188e-18
      ],
      "ranking_score": 0.23210587043400815
    },
    {
      "candidate_id": "inversion_parent_endpoint_01",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "P2_1/c",
      "spacegroup_number": 14,
      "pointgroup": "2/m",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 3.2759532360285765e-15,
      "parent_symmetrization_rmsd_A": 0.2321058704340009,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -261.17469399275535,
      "reduced_polarization": [
        -1.3020357630660092e-15,
        2.77923277622875e-16,
        -2.9932141801245324e-15
      ],
      "cartesian_polarization_e_A2": [
        -1.3173423193444352e-17,
        1.2949300681646622e-18,
        -8.177981430486059e-18
      ],
      "ranking_score": 0.23210587043400746
    },
    {
      "candidate_id": "bec_projection_00",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Pna2_1",
      "spacegroup_number": 33,
      "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": 5.788793035573749e-05,
      "parent_symmetrization_rmsd_A": 0.00906874803390061,
      "parent_cell_rmsd_A": 0.026251001541353056,
      "energy_eV": -261.3834640133204,
      "reduced_polarization": [
        1.5068445785482244e-15,
        -1.0696574234181699e-14,
        -5.788793035573749e-05
      ],
      "cartesian_polarization_e_A2": [
        1.5220528486388214e-17,
        -4.967693900232099e-17,
        -1.5863191171692692e-07
      ],
      "ranking_score": 0.5157472742799504
    },
    {
      "candidate_id": "inversion_parent_bec_00_00",
      "source": "same_species_inversion_center_projection_after_BEC",
      "spacegroup": "P2_1/c",
      "spacegroup_number": 14,
      "pointgroup": "2/m",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 3.7822942900585826e-15,
      "parent_symmetrization_rmsd_A": 0.23210673892187383,
      "parent_cell_rmsd_A": 0.026251001541353056,
      "energy_eV": -261.1671730675789,
      "reduced_polarization": [
        1.023663930620316e-15,
        3.867571624027826e-16,
        -3.620536030905765e-15
      ],
      "cartesian_polarization_e_A2": [
        1.0339410982253908e-17,
        1.7962114362818387e-18,
        -9.921455966609381e-18
      ],
      "ranking_score": 0.23866948930721968
    },
    {
      "candidate_id": "inversion_parent_bec_00_01",
      "source": "same_species_inversion_center_projection_after_BEC",
      "spacegroup": "P2_1/c",
      "spacegroup_number": 14,
      "pointgroup": "2/m",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 1.6390504105043624e-15,
      "parent_symmetrization_rmsd_A": 0.23210673892187408,
      "parent_cell_rmsd_A": 0.026251001541353056,
      "energy_eV": -261.1671730675789,
      "reduced_polarization": [
        -4.3990947547831184e-16,
        9.465372658804657e-16,
        1.26373775201125e-15
      ],
      "cartesian_polarization_e_A2": [
        -4.44325986869718e-18,
        4.395991146689763e-18,
        3.4630558439118e-18
      ],
      "ranking_score": 0.23866948930721563
    },
    {
      "candidate_id": "bec_projection_01",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Pna2_1",
      "spacegroup_number": 33,
      "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": 1.892960798099974e-05,
      "parent_symmetrization_rmsd_A": 0.03309870387977816,
      "parent_cell_rmsd_A": 0.09443769430172891,
      "energy_eV": -261.22183753947456,
      "reduced_polarization": [
        -2.306152106463156e-15,
        -8.392543162758007e-17,
        0.499981070392019
      ],
      "cartesian_polarization_e_A2": [
        1.2594746345888649e-18,
        2.8398154260848927e-17,
        0.001351514262845381
      ],
      "ranking_score": 0.5567459866711724
    },
    {
      "candidate_id": "bec_projection_02",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Pc",
      "spacegroup_number": 7,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        -0.5,
        0.0
      ],
      "formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_residual": 0.0002702592398251687,
      "parent_symmetrization_rmsd_A": 0.07847919727607292,
      "parent_cell_rmsd_A": 0.17166176957867949,
      "energy_eV": -260.062585878627,
      "reduced_polarization": [
        -1.294077298417779e-15,
        -0.49990628808944804,
        0.00025349188257531806
      ],
      "cartesian_polarization_e_A2": [
        1.4898073813877235e-16,
        -0.0023217278788764707,
        7.856059930560107e-05
      ],
      "ranking_score": 0.6219351581503931
    },
    {
      "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,
        0.0
      ],
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_residual": 0.00019119399891603998,
      "parent_symmetrization_rmsd_A": 0.1794420617776863,
      "parent_cell_rmsd_A": 0.27826340928634724,
      "energy_eV": -258.134430266338,
      "reduced_polarization": [
        -0.4999550613104637,
        -1.3538438800903356e-15,
        0.0001858377233079057
      ],
      "cartesian_polarization_e_A2": [
        -0.005052186977403373,
        -6.14565351393215e-16,
        0.00012828681220228825
      ],
      "ranking_score": 0.7493903020971051
    },
    {
      "candidate_id": "bec_projection_04",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Pc",
      "spacegroup_number": 7,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        -0.5,
        0.5
      ],
      "formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_residual": 0.00022464016807427297,
      "parent_symmetrization_rmsd_A": 0.08160538927224345,
      "parent_cell_rmsd_A": 0.1942390157958263,
      "energy_eV": -260.0824289827576,
      "reduced_polarization": [
        -4.507657100150469e-16,
        -0.49997687394045043,
        0.5002234466166272
      ],
      "cartesian_polarization_e_A2": [
        1.27387404417896e-16,
        -0.0024035734708526438,
        0.0014312863760575338
      ],
      "ranking_score": 0.6306144235573485
    },
    {
      "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,
        0.5
      ],
      "formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_residual": 0.00019823188221643106,
      "parent_symmetrization_rmsd_A": 0.1825211508467364,
      "parent_cell_rmsd_A": 0.3027981957585437,
      "energy_eV": -258.1173650853939,
      "reduced_polarization": [
        -0.4999102683248172,
        5.743095572142653e-15,
        0.5001767600226181
      ],
      "cartesian_polarization_e_A2": [
        -0.005129081946528705,
        -7.712348979550196e-16,
        0.0014800762338428594
      ],
      "ranking_score": 0.7586171635508052
    },
    {
      "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,
        0.0
      ],
      "formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_residual": 6.213954999080574e-05,
      "parent_symmetrization_rmsd_A": 0.20268831778638263,
      "parent_cell_rmsd_A": 0.343327006438142,
      "energy_eV": -256.5576053641264,
      "reduced_polarization": [
        -0.4999771243977137,
        -0.4999701425207914,
        4.946272766849215e-05
      ],
      "cartesian_polarization_e_A2": [
        -0.005053397360509836,
        -0.0023265619856463276,
        0.00021784618906070448
      ],
      "ranking_score": 0.7886443484958998
    },
    {
      "candidate_id": "bec_projection_07",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        -0.5,
        -0.5,
        0.5
      ],
      "formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "target_residual": 8.666139814899797e-05,
      "parent_symmetrization_rmsd_A": 0.20594845043136215,
      "parent_cell_rmsd_A": 0.3707598404023569,
      "energy_eV": -256.59642428063546,
      "reduced_polarization": [
        -0.4999503316539696,
        -0.49994564941650194,
        0.5000457085047356
      ],
      "cartesian_polarization_e_A2": [
        -0.005133993240228124,
        -0.0024171093657227405,
        0.0015736370571121387
      ],
      "ranking_score": 0.7988117333282494
    }
  ],
  "formal_branches": [
    {
      "orbit_id": 0,
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.0,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -7.994351906310773e-16,
              -1.3783925634411432e-15,
              0.10939763593528573
            ],
            "branch_aligned_reduced_polarization": [
              -7.994351906310773e-16,
              -1.3783925634411432e-15,
              0.10939763593528573
            ],
            "target_residual": 0.10939763593528573,
            "energy_eV": -261.41035421167356,
            "max_atomic_step_A": 0.010744103148374434,
            "max_log_strain_component": 0.003953357457107828,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.1390938929902044,
            "cell_principal_stretches": [
              1.003961182282746,
              0.9992758209161945,
              0.9977469563205263
            ],
            "cell_volume_ratio": 1.0009738042676055,
            "cell_rmsd_from_input_A": 0.026251001541353056
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              1.5068445785482244e-15,
              -1.0696574234181699e-14,
              -5.788793035573749e-05
            ],
            "branch_aligned_reduced_polarization": [
              1.5068445785482244e-15,
              -1.0696574234181699e-14,
              -5.788793035573749e-05
            ],
            "target_residual": 5.788793035573749e-05,
            "energy_eV": -261.3834640133204
          }
        ],
        "iterations": 1
      },
      "parent": {
        "candidate_id": "inversion_parent_endpoint_01",
        "source": "same_species_inversion_center_projection_from_endpoint",
        "spacegroup": "P2_1/c",
        "spacegroup_number": 14,
        "pointgroup": "2/m",
        "has_inversion": true,
        "is_polar_point_group": false,
        "nonpolar_parent_hypothesis": true,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.0
        ],
        "formal_class": [
          0.0,
          0.0,
          0.0
        ],
        "target_residual": 3.2759532360285765e-15,
        "parent_symmetrization_rmsd_A": 0.2321058704340009,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -261.17469399275535,
        "reduced_polarization": [
          -1.3020357630660092e-15,
          2.77923277622875e-16,
          -2.9932141801245324e-15
        ],
        "cartesian_polarization_e_A2": [
          -1.3173423193444352e-17,
          1.2949300681646622e-18,
          -8.177981430486059e-18
        ],
        "ranking_score": 0.23210587043400746
      },
      "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": [
          -261.4103542116735,
          -261.3815360153594,
          -261.3429603201879,
          -261.3010688475945,
          -261.26087485335955,
          -261.2260739932791,
          -261.19878273337685,
          -261.1809537948966,
          -261.1746939927553
        ],
        "cartesian_polarizations_e_A2": [
          [
            -8.925056469811825e-18,
            -5.376450033014434e-18,
            0.00029889335723400713
          ],
          [
            -1.5418136432461237e-06,
            1.8452753471346437e-18,
            0.0002505330514522355
          ],
          [
            -3.387579072556929e-06,
            1.6858993387451468e-18,
            0.00020429736781036467
          ],
          [
            -5.19700601115136e-06,
            1.09944543287442e-17,
            0.0001607593573947349
          ],
          [
            -6.320350135368222e-06,
            2.154066363389294e-18,
            0.0001210945239590707
          ],
          [
            -6.3878696227923015e-06,
            7.039937120579808e-18,
            8.587953190910275e-05
          ],
          [
            -5.2567603855410524e-06,
            -8.108254426815654e-18,
            5.4783775489087e-05
          ],
          [
            -2.9896812481751424e-06,
            -7.981251670130273e-18,
            2.663876736729289e-05
          ],
          [
            -6.509513842658513e-18,
            1.02000645369278e-17,
            1.7830190938574965e-18
          ]
        ],
        "raw_reduced_polarization": [
          [
            -8.821353827653266e-16,
            -1.1539160699765134e-15,
            0.10939763593528774
          ],
          [
            -0.0001523898894016071,
            3.960406706125968e-16,
            0.09169733247390485
          ],
          [
            -0.0003348217876184285,
            3.6183472875131985e-16,
            0.07477465967488212
          ],
          [
            -0.0005136620594376325,
            2.359675520586525e-15,
            0.05883935934946586
          ],
          [
            -0.0006246912279751079,
            4.623146829688209e-16,
            0.04432167636117723
          ],
          [
            -0.0006313647240010903,
            1.5109405881535913e-15,
            0.03143267502840312
          ],
          [
            -0.0005195680666547796,
            -1.7402272921924631e-15,
            0.020051350694366622
          ],
          [
            -0.0002954943334113048,
            -1.712969432271758e-15,
            0.00975002656860773
          ],
          [
            -6.433878042825234e-16,
            2.1891802791217227e-15,
            6.52600899198893e-16
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -8.821353827653266e-16,
            -1.1539160699765134e-15,
            0.10939763593528774
          ],
          [
            -0.0001523898894016071,
            3.9604067061259674e-16,
            0.09169733247390485
          ],
          [
            -0.0003348217876184285,
            3.6183472875131985e-16,
            0.07477465967488212
          ],
          [
            -0.0005136620594376325,
            2.359675520586525e-15,
            0.05883935934946586
          ],
          [
            -0.0006246912279751079,
            4.62314682968821e-16,
            0.04432167636117723
          ],
          [
            -0.0006313647240010903,
            1.5109405881535913e-15,
            0.03143267502840312
          ],
          [
            -0.0005195680666547796,
            -1.740227292192463e-15,
            0.020051350694366622
          ],
          [
            -0.0002954943334113048,
            -1.712969432271758e-15,
            0.00975002656860773
          ],
          [
            -6.433655691528983e-16,
            2.1891802791217227e-15,
            6.522560269672795e-16
          ]
        ],
        "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": [
          [
            -8.881784197001252e-16,
            -1.1657341758564144e-15,
            0.10939763593528773
          ],
          [
            -0.00015238988940158293,
            4.440892098500626e-16,
            0.09169733247390488
          ],
          [
            -0.0003348217876184556,
            3.3306690738754696e-16,
            0.07477465967488217
          ],
          [
            -0.0005136620594376473,
            2.3314683517128287e-15,
            0.058839359349465825
          ],
          [
            -0.0006246912279750938,
            4.440892098500626e-16,
            0.04432167636117723
          ],
          [
            -0.0006313647240011044,
            1.5543122344752192e-15,
            0.03143267502840308
          ],
          [
            -0.0005195680666547631,
            -1.7208456881689926e-15,
            0.020051350694366588
          ],
          [
            -0.0002954943334113058,
            -1.7208456881689926e-15,
            0.009750026568607684
          ],
          [
            -6.661338147750939e-16,
            2.220446049250313e-15,
            6.661338147750939e-16
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -261.1746939927553,
          -261.1809537948966,
          -261.1987827333769,
          -261.2260739932789,
          -261.2608748533595,
          -261.30106884759454,
          -261.34296032018784,
          -261.38153601535936,
          -261.4103542116736
        ],
        "cartesian_polarizations_e_A2": [
          [
            -4.905792758239201e-18,
            7.777051159381232e-18,
            2.6994311420971034e-18
          ],
          [
            2.9896812481585075e-06,
            7.119625124774557e-18,
            -2.663876736729532e-05
          ],
          [
            5.256760385524612e-06,
            8.43198694385682e-18,
            -5.478377548908013e-05
          ],
          [
            6.387869622778829e-06,
            1.8353143466103002e-17,
            -8.587953190912228e-05
          ],
          [
            6.3203501353734015e-06,
            1.0175162035616942e-17,
            -0.00012109452395907441
          ],
          [
            5.1970060111420214e-06,
            4.472489235430256e-18,
            -0.00016075935739477467
          ],
          [
            3.387579072549887e-06,
            -7.445847891946807e-18,
            -0.00020429736781037858
          ],
          [
            1.5418136432377565e-06,
            -1.1604565610860242e-17,
            -0.00025053305145224074
          ],
          [
            -1.7770424935428904e-17,
            -2.9036316528461466e-18,
            -0.00029889335723399586
          ]
        ],
        "raw_reduced_polarization": [
          [
            -4.848791026918787e-16,
            1.6691430692619973e-15,
            9.880158864966482e-16
          ],
          [
            0.00029549433340966065,
            1.52804355908423e-15,
            -0.009750026568608619
          ],
          [
            0.0005195680666531547,
            1.8097081115981816e-15,
            -0.020051350694364107
          ],
          [
            0.0006313647239997588,
            3.93902799246267e-15,
            -0.03143267502841027
          ],
          [
            0.0006246912279756197,
            2.183835600705898e-15,
            -0.04432167636117859
          ],
          [
            0.0005136620594367095,
            9.599042434820834e-16,
            -0.05883935934948042
          ],
          [
            0.0003348217876177325,
            -1.5980588463315307e-15,
            -0.0747746596748872
          ],
          [
            0.0001523898894007801,
            -2.4906201417742253e-15,
            -0.09169733247390678
          ],
          [
            -1.7563945567559629e-15,
            -6.231895032851388e-16,
            -0.10939763593528361
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -4.848791026918787e-16,
            1.6691430692619973e-15,
            9.880158864966482e-16
          ],
          [
            0.00029549433340966065,
            1.52804355908423e-15,
            -0.009750026568608619
          ],
          [
            0.0005195680666531547,
            1.8097081115981816e-15,
            -0.020051350694364107
          ],
          [
            0.0006313647239997588,
            3.93902799246267e-15,
            -0.03143267502841027
          ],
          [
            0.0006246912279756197,
            2.183835600705898e-15,
            -0.04432167636117859
          ],
          [
            0.0005136620594367095,
            9.599042434820834e-16,
            -0.05883935934948042
          ],
          [
            0.0003348217876177325,
            -1.5980588463315305e-15,
            -0.0747746596748872
          ],
          [
            0.0001523898894007801,
            -2.4906201417742253e-15,
            -0.09169733247390678
          ],
          [
            -1.7564075194265172e-15,
            -6.231895032851389e-16,
            -0.10939763593528361
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          -4.0464022579972003e-16,
          5.532276628219959e-15,
          -0.10939763593528642
        ],
        "actual_opposite_endpoint_branch_residual": 6.90315890155013e-15
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            -8.821353827653266e-16,
            -1.1539160699765134e-15,
            0.10939763593528774
          ],
          [
            -0.0001523898894016071,
            3.960406706125968e-16,
            0.09169733247390485
          ],
          [
            -0.0003348217876184285,
            3.6183472875131985e-16,
            0.07477465967488212
          ],
          [
            -0.0005136620594376325,
            2.359675520586525e-15,
            0.05883935934946586
          ],
          [
            -0.0006246912279751079,
            4.623146829688209e-16,
            0.04432167636117723
          ],
          [
            -0.0006313647240010903,
            1.5109405881535913e-15,
            0.03143267502840312
          ],
          [
            -0.0005195680666547796,
            -1.7402272921924631e-15,
            0.020051350694366622
          ],
          [
            -0.0002954943334113048,
            -1.712969432271758e-15,
            0.00975002656860773
          ],
          [
            -6.433878042825234e-16,
            2.1891802791217227e-15,
            6.52600899198893e-16
          ],
          [
            0.00029549433340966065,
            1.52804355908423e-15,
            -0.009750026568608619
          ],
          [
            0.0005195680666531547,
            1.8097081115981816e-15,
            -0.020051350694364107
          ],
          [
            0.0006313647239997588,
            3.93902799246267e-15,
            -0.03143267502841027
          ],
          [
            0.0006246912279756197,
            2.183835600705898e-15,
            -0.04432167636117859
          ],
          [
            0.0005136620594367095,
            9.599042434820834e-16,
            -0.05883935934948042
          ],
          [
            0.0003348217876177325,
            -1.5980588463315307e-15,
            -0.0747746596748872
          ],
          [
            0.0001523898894007801,
            -2.4906201417742253e-15,
            -0.09169733247390678
          ],
          [
            -1.7563945567559629e-15,
            -6.231895032851388e-16,
            -0.10939763593528361
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -8.821353827653266e-16,
            -1.1539160699765134e-15,
            0.10939763593528774
          ],
          [
            -0.0001523898894016071,
            3.9604067061259674e-16,
            0.09169733247390485
          ],
          [
            -0.0003348217876184285,
            3.6183472875131985e-16,
            0.07477465967488212
          ],
          [
            -0.0005136620594376325,
            2.359675520586525e-15,
            0.05883935934946586
          ],
          [
            -0.0006246912279751079,
            4.62314682968821e-16,
            0.04432167636117723
          ],
          [
            -0.0006313647240010903,
            1.5109405881535913e-15,
            0.03143267502840312
          ],
          [
            -0.0005195680666547796,
            -1.740227292192463e-15,
            0.020051350694366622
          ],
          [
            -0.0002954943334113048,
            -1.712969432271758e-15,
            0.00975002656860773
          ],
          [
            -6.433655691528983e-16,
            2.1891802791217227e-15,
            6.522560269672795e-16
          ],
          [
            0.00029549433340966065,
            1.52804355908423e-15,
            -0.009750026568608619
          ],
          [
            0.0005195680666531547,
            1.8097081115981816e-15,
            -0.020051350694364107
          ],
          [
            0.0006313647239997588,
            3.93902799246267e-15,
            -0.03143267502841027
          ],
          [
            0.0006246912279756197,
            2.183835600705898e-15,
            -0.04432167636117859
          ],
          [
            0.0005136620594367095,
            9.599042434820834e-16,
            -0.05883935934948042
          ],
          [
            0.0003348217876177325,
            -1.5980588463315305e-15,
            -0.0747746596748872
          ],
          [
            0.0001523898894007801,
            -2.4906201417742253e-15,
            -0.09169733247390678
          ],
          [
            -1.7564075194265172e-15,
            -6.231895032851389e-16,
            -0.10939763593528361
          ]
        ],
        "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": [
          [
            -8.881784197001252e-16,
            -1.1657341758564144e-15,
            0.10939763593528773
          ],
          [
            -0.00015238988940158293,
            4.440892098500626e-16,
            0.09169733247390488
          ],
          [
            -0.0003348217876184556,
            3.3306690738754696e-16,
            0.07477465967488217
          ],
          [
            -0.0005136620594376473,
            2.3314683517128287e-15,
            0.058839359349465825
          ],
          [
            -0.0006246912279750938,
            4.440892098500626e-16,
            0.04432167636117723
          ],
          [
            -0.0006313647240011044,
            1.5543122344752192e-15,
            0.03143267502840308
          ],
          [
            -0.0005195680666547631,
            -1.7208456881689926e-15,
            0.020051350694366588
          ],
          [
            -0.0002954943334113058,
            -1.7208456881689926e-15,
            0.009750026568607684
          ],
          [
            -6.661338147750939e-16,
            2.220446049250313e-15,
            6.661338147750939e-16
          ],
          [
            0.000295494333409696,
            1.5543122344752192e-15,
            -0.009750026568608627
          ],
          [
            0.0005195680666532088,
            1.7763568394002505e-15,
            -0.02005135069436409
          ],
          [
            0.0006313647239997167,
            3.885780586188048e-15,
            -0.031432675028410295
          ],
          [
            0.0006246912279755934,
            2.220446049250313e-15,
            -0.044321676361178564
          ],
          [
            0.0005136620594367036,
            9.992007221626409e-16,
            -0.058839359349480425
          ],
          [
            0.00033482178761767845,
            -1.609823385706477e-15,
            -0.07477465967488717
          ],
          [
            0.00015238988940080578,
            -2.4980018054066022e-15,
            -0.09169733247390677
          ],
          [
            -1.7763568394002505e-15,
            -6.106226635438361e-16,
            -0.10939763593528362
          ]
        ]
      },
      "incoming_structure_ids": [
        "incoming_00_000",
        "incoming_00_001",
        "incoming_00_002",
        "incoming_00_003",
        "incoming_00_004",
        "incoming_00_005",
        "incoming_00_006",
        "incoming_00_007",
        "incoming_00_008"
      ],
      "reflected_structure_ids": [
        "reflected_00_001",
        "reflected_00_002",
        "reflected_00_003",
        "reflected_00_004",
        "reflected_00_005",
        "reflected_00_006",
        "reflected_00_007",
        "reflected_00_008"
      ]
    },
    {
      "orbit_id": 1,
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "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": [
              -7.994351906310773e-16,
              -1.3783925634411432e-15,
              0.10939763593528573
            ],
            "branch_aligned_reduced_polarization": [
              -7.994351906310773e-16,
              -1.3783925634411432e-15,
              0.10939763593528573
            ],
            "target_residual": 0.39060236406471427,
            "energy_eV": -261.41035421167356,
            "max_atomic_step_A": 0.03836163417637951,
            "max_log_strain_component": 0.014115394318508421,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.1390938929902044,
            "cell_principal_stretches": [
              1.0080860462170116,
              1.0025899537203802,
              0.9859837607738691
            ],
            "cell_volume_ratio": 0.9965307722927569,
            "cell_rmsd_from_input_A": 0.09402354572845059
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              4.048237685699659e-15,
              4.035812637910289e-14,
              0.4983160775361011
            ],
            "branch_aligned_reduced_polarization": [
              4.048237685699659e-15,
              4.035812637910289e-14,
              0.4983160775361011
            ],
            "target_residual": 0.0016839224638989236,
            "energy_eV": -261.22356782459974,
            "max_atomic_step_A": 0.00016985820220715762,
            "max_log_strain_component": 6.201834450708166e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.1390938929902044,
            "cell_principal_stretches": [
              1.0081217174963393,
              1.0026013479030873,
              0.9859226135894583
            ],
            "cell_volume_ratio": 0.9965155562477767,
            "cell_rmsd_from_input_A": 0.09443769430172891
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -2.306152106463156e-15,
              -8.392543162758007e-17,
              0.499981070392019
            ],
            "branch_aligned_reduced_polarization": [
              -2.306152106463156e-15,
              -8.392543162758007e-17,
              0.499981070392019
            ],
            "target_residual": 1.892960798099974e-05,
            "energy_eV": -261.22183753947456
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_01",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Pna2_1",
        "spacegroup_number": 33,
        "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": 1.892960798099974e-05,
        "parent_symmetrization_rmsd_A": 0.03309870387977816,
        "parent_cell_rmsd_A": 0.09443769430172891,
        "energy_eV": -261.22183753947456,
        "reduced_polarization": [
          -2.306152106463156e-15,
          -8.392543162758007e-17,
          0.499981070392019
        ],
        "cartesian_polarization_e_A2": [
          1.2594746345888649e-18,
          2.8398154260848927e-17,
          0.001351514262845381
        ],
        "ranking_score": 0.5567459866711724
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 2,
      "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": [
              -7.994351906310773e-16,
              -1.3783925634411432e-15,
              0.10939763593528573
            ],
            "branch_aligned_reduced_polarization": [
              -7.994351906310773e-16,
              -1.3877787807814457e-15,
              0.10939763593528573
            ],
            "target_residual": 0.5118279425238798,
            "energy_eV": -261.41035421167356,
            "max_atomic_step_A": 0.05164669239865149,
            "max_log_strain_component": 0.02,
            "step_scale": 0.6140920871551765,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.1390938929902044,
            "cell_principal_stretches": [
              1.0208258439970084,
              0.9995552251930863,
              0.9806208745920181
            ],
            "cell_volume_ratio": 1.0005978931807578,
            "cell_rmsd_from_input_A": 0.10229359018178856
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -1.3008479450093047e-14,
              -0.3047553399681003,
              0.047003206830044116
            ],
            "branch_aligned_reduced_polarization": [
              -1.3008479450093047e-14,
              -0.3047553399681003,
              0.047003206830044116
            ],
            "target_residual": 0.20082275449579912,
            "energy_eV": -260.9196455239842,
            "max_atomic_step_A": 0.03351189062158266,
            "max_log_strain_component": 0.013113922748651722,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.1390938929902044,
            "cell_principal_stretches": [
              1.0348022296729809,
              0.999211497944509,
              0.9681563411197059
            ],
            "cell_volume_ratio": 1.0010603794099575,
            "cell_rmsd_from_input_A": 0.16977706116458258
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -6.539425074928744e-15,
              -0.49573141797373416,
              0.008953940902218797
            ],
            "branch_aligned_reduced_polarization": [
              -6.539425074928744e-15,
              -0.49573141797373416,
              0.008953940902218797
            ],
            "target_residual": 0.009919367429195601,
            "energy_eV": -260.09054234587694,
            "max_atomic_step_A": 0.0012762038203770097,
            "max_log_strain_component": 0.00033570556989435854,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.1390938929902044,
            "cell_principal_stretches": [
              1.035216599775894,
              0.999150031257573,
              0.9679083457725806
            ],
            "cell_volume_ratio": 1.0011431223567118,
            "cell_rmsd_from_input_A": 0.17166176957867949
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -1.294077298417779e-15,
              -0.49990628808944804,
              0.00025349188257531806
            ],
            "branch_aligned_reduced_polarization": [
              -1.294077298417779e-15,
              -0.49990628808944804,
              0.00025349188257531806
            ],
            "target_residual": 0.0002702592398251687,
            "energy_eV": -260.062585878627
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_02",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Pc",
        "spacegroup_number": 7,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          -0.5,
          0.0
        ],
        "formal_class": [
          0.0,
          0.5,
          0.0
        ],
        "target_residual": 0.0002702592398251687,
        "parent_symmetrization_rmsd_A": 0.07847919727607292,
        "parent_cell_rmsd_A": 0.17166176957867949,
        "energy_eV": -260.062585878627,
        "reduced_polarization": [
          -1.294077298417779e-15,
          -0.49990628808944804,
          0.00025349188257531806
        ],
        "cartesian_polarization_e_A2": [
          1.4898073813877235e-16,
          -0.0023217278788764707,
          7.856059930560107e-05
        ],
        "ranking_score": 0.6219351581503931
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 3,
      "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": [
              -7.994351906310773e-16,
              -1.3783925634411432e-15,
              0.10939763593528573
            ],
            "branch_aligned_reduced_polarization": [
              -7.771561172376096e-16,
              -1.3783925634411432e-15,
              0.10939763593528573
            ],
            "target_residual": 0.5118279425238803,
            "energy_eV": -261.41035421167356,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.01780985437854417,
            "step_scale": 0.7482100193078196,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.1390938929902044,
            "cell_principal_stretches": [
              1.019287218896824,
              0.9983137715373371,
              0.9834507971807315
            ],
            "cell_volume_ratio": 1.000728520820963,
            "cell_rmsd_from_input_A": 0.1963300281768601
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.3656853811711308,
              -1.542556656546438e-14,
              0.023021313210515627
            ],
            "branch_aligned_reduced_polarization": [
              -0.3656853811711308,
              -1.542556656546438e-14,
              0.023021313210515627
            ],
            "target_residual": 0.1362732464318697,
            "energy_eV": -259.65039784844294,
            "max_atomic_step_A": 0.04428187961821424,
            "max_log_strain_component": 0.007183175675000023,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.1390938929902044,
            "cell_principal_stretches": [
              1.0268821658815237,
              0.9979811646554306,
              0.9766428382016278
            ],
            "cell_volume_ratio": 1.0008724288465052,
            "cell_rmsd_from_input_A": 0.2754225284284975
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.49569176815410726,
              -1.624031942966204e-14,
              0.0014740955114045076
            ],
            "branch_aligned_reduced_polarization": [
              -0.49569176815410726,
              -1.624031942966204e-14,
              0.0014740955114045076
            ],
            "target_residual": 0.00455344037126954,
            "energy_eV": -258.1896384561233,
            "max_atomic_step_A": 0.0015454391972007358,
            "max_log_strain_component": 0.00025690684271413426,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.1390938929902044,
            "cell_principal_stretches": [
              1.0271612613733012,
              0.9979615836555691,
              0.9764048938001905
            ],
            "cell_volume_ratio": 1.00088090303913,
            "cell_rmsd_from_input_A": 0.27826340928634724
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -0.4999550613104637,
              -1.3538438800903356e-15,
              0.0001858377233079057
            ],
            "branch_aligned_reduced_polarization": [
              -0.4999550613104637,
              -1.3538438800903356e-15,
              0.0001858377233079057
            ],
            "target_residual": 0.00019119399891603998,
            "energy_eV": -258.134430266338
          }
        ],
        "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,
          0.0
        ],
        "formal_class": [
          0.5,
          0.0,
          0.0
        ],
        "target_residual": 0.00019119399891603998,
        "parent_symmetrization_rmsd_A": 0.1794420617776863,
        "parent_cell_rmsd_A": 0.27826340928634724,
        "energy_eV": -258.134430266338,
        "reduced_polarization": [
          -0.4999550613104637,
          -1.3538438800903356e-15,
          0.0001858377233079057
        ],
        "cartesian_polarization_e_A2": [
          -0.005052186977403373,
          -6.14565351393215e-16,
          0.00012828681220228825
        ],
        "ranking_score": 0.7493903020971051
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 4,
      "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": [
              -7.994351906310773e-16,
              -1.3783925634411432e-15,
              0.10939763593528573
            ],
            "branch_aligned_reduced_polarization": [
              -7.994351906310773e-16,
              -1.3877787807814457e-15,
              0.10939763593528573
            ],
            "target_residual": 0.634484205329764,
            "energy_eV": -261.41035421167356,
            "max_atomic_step_A": 0.058008789794231894,
            "max_log_strain_component": 0.02,
            "step_scale": 0.6140920871557435,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.1390938929902044,
            "cell_principal_stretches": [
              1.0194521117165483,
              1.0015896762109608,
              0.9772743273503743
            ],
            "cell_volume_ratio": 0.99786814631677,
            "cell_rmsd_from_input_A": 0.11655519795738611
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -1.0740290064810404e-14,
              -0.3041571901268906,
              0.351078535759116
            ],
            "branch_aligned_reduced_polarization": [
              -1.0740290064810404e-14,
              -0.3041571901268906,
              0.351078535759116
            ],
            "target_residual": 0.24603253583752652,
            "energy_eV": -260.9227623234291,
            "max_atomic_step_A": 0.04027632947429554,
            "max_log_strain_component": 0.013244214723906524,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.1390938929902044,
            "cell_principal_stretches": [
              1.0325314215679504,
              1.0025951806158377,
              0.9626286486950865
            ],
            "cell_volume_ratio": 0.9965237921300307,
            "cell_rmsd_from_input_A": 0.19328015573349566
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -9.02701682853399e-15,
              -0.4959217776003926,
              0.5029264097188407
            ],
            "branch_aligned_reduced_polarization": [
              -9.02701682853399e-15,
              -0.4959217776003926,
              0.5029264097188407
            ],
            "target_residual": 0.005019539001062268,
            "energy_eV": -260.09955776085155,
            "max_atomic_step_A": 0.0007736131600020699,
            "max_log_strain_component": 0.0002949238350516342,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.1390938929902044,
            "cell_principal_stretches": [
              1.0328169093075388,
              1.0025752425726875,
              0.9624074146016399
            ],
            "cell_volume_ratio": 0.9965504184859754,
            "cell_rmsd_from_input_A": 0.1942390157958263
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -4.507657100150469e-16,
              -0.49997687394045043,
              0.5002234466166272
            ],
            "branch_aligned_reduced_polarization": [
              -4.507657100150469e-16,
              -0.49997687394045043,
              0.5002234466166272
            ],
            "target_residual": 0.00022464016807427297,
            "energy_eV": -260.0824289827576
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_04",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Pc",
        "spacegroup_number": 7,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          -0.5,
          0.5
        ],
        "formal_class": [
          0.0,
          0.5,
          0.5
        ],
        "target_residual": 0.00022464016807427297,
        "parent_symmetrization_rmsd_A": 0.08160538927224345,
        "parent_cell_rmsd_A": 0.1942390157958263,
        "energy_eV": -260.0824289827576,
        "reduced_polarization": [
          -4.507657100150469e-16,
          -0.49997687394045043,
          0.5002234466166272
        ],
        "cartesian_polarization_e_A2": [
          1.27387404417896e-16,
          -0.0024035734708526438,
          0.0014312863760575338
        ],
        "ranking_score": 0.6306144235573485
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 5,
      "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": [
              -7.994351906310773e-16,
              -1.3783925634411432e-15,
              0.10939763593528573
            ],
            "branch_aligned_reduced_polarization": [
              -7.771561172376096e-16,
              -1.3783925634411432e-15,
              0.10939763593528573
            ],
            "target_residual": 0.6344842053297646,
            "energy_eV": -261.41035421167356,
            "max_atomic_step_A": 0.11999999999999998,
            "max_log_strain_component": 0.017252308062466675,
            "step_scale": 0.7247869339171125,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.1390938929902044,
            "cell_principal_stretches": [
              1.0142052420570118,
              1.0058541618418724,
              0.9777891663895534
            ],
            "cell_volume_ratio": 0.997484346943949,
            "cell_rmsd_from_input_A": 0.20204950360455318
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.3527824472682135,
              3.506259145305947e-14,
              0.3800926777464314
            ],
            "branch_aligned_reduced_polarization": [
              -0.3527824472682135,
              3.506259145305947e-14,
              0.3800926777464314
            ],
            "target_residual": 0.18987041307786076,
            "energy_eV": -259.79154809313167,
            "max_atomic_step_A": 0.05144330697114479,
            "max_log_strain_component": 0.007986708284935551,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.1390938929902044,
            "cell_principal_stretches": [
              1.0207110294142838,
              1.0089498985091019,
              0.9672924120721742
            ],
            "cell_volume_ratio": 0.9961625014675625,
            "cell_rmsd_from_input_A": 0.29804166552913114
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.4936926471385557,
              1.3557094063153483e-14,
              0.4957423881612791
            ],
            "branch_aligned_reduced_polarization": [
              -0.4936926471385557,
              1.3557094063153483e-14,
              0.4957423881612791
            ],
            "target_residual": 0.007609859308028372,
            "energy_eV": -258.1991242749827,
            "max_atomic_step_A": 0.002423060211552942,
            "max_log_strain_component": 0.00039678407867392915,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.1390938929902044,
            "cell_principal_stretches": [
              1.0210382339470476,
              1.0090961807717294,
              0.9667817707235682
            ],
            "cell_volume_ratio": 0.9961001842320877,
            "cell_rmsd_from_input_A": 0.3027981957585437
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -0.4999102683248172,
              5.743095572142653e-15,
              0.5001767600226181
            ],
            "branch_aligned_reduced_polarization": [
              -0.4999102683248172,
              5.743095572142653e-15,
              0.5001767600226181
            ],
            "target_residual": 0.00019823188221643106,
            "energy_eV": -258.1173650853939
          }
        ],
        "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,
          0.5
        ],
        "formal_class": [
          0.5,
          0.0,
          0.5
        ],
        "target_residual": 0.00019823188221643106,
        "parent_symmetrization_rmsd_A": 0.1825211508467364,
        "parent_cell_rmsd_A": 0.3027981957585437,
        "energy_eV": -258.1173650853939,
        "reduced_polarization": [
          -0.4999102683248172,
          5.743095572142653e-15,
          0.5001767600226181
        ],
        "cartesian_polarization_e_A2": [
          -0.005129081946528705,
          -7.712348979550196e-16,
          0.0014800762338428594
        ],
        "ranking_score": 0.7586171635508052
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 6,
      "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": [
              -7.994351906310773e-16,
              -1.3783925634411432e-15,
              0.10939763593528573
            ],
            "branch_aligned_reduced_polarization": [
              -7.771561172376096e-16,
              -1.3877787807814457e-15,
              0.10939763593528573
            ],
            "target_residual": 0.7155192818843019,
            "energy_eV": -261.41035421167356,
            "max_atomic_step_A": 0.1140308332273899,
            "max_log_strain_component": 0.02,
            "step_scale": 0.6140920871560228,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.1390938929902044,
            "cell_principal_stretches": [
              1.0258505716011466,
              0.9992290847344738,
              0.9761361861241036
            ],
            "cell_volume_ratio": 1.0005978931809971,
            "cell_rmsd_from_input_A": 0.1902776669518071
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.2997940022010497,
              -0.29815477648962396,
              0.04279446553257047
            ],
            "branch_aligned_reduced_polarization": [
              -0.2997940022010497,
              -0.29815477648962396,
              0.04279446553257047
            ],
            "target_residual": 0.287498351454135,
            "energy_eV": -259.75360842421685,
            "max_atomic_step_A": 0.0765041636587886,
            "max_log_strain_component": 0.015189945410468416,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.1390938929902044,
            "cell_principal_stretches": [
              1.0454432900326645,
              0.9988340082934821,
              0.9585234621390805
            ],
            "cell_volume_ratio": 1.0009135026220728,
            "cell_rmsd_from_input_A": 0.3310227999855949
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.4870402718086119,
              -0.48470250169841145,
              0.001828928728665644
            ],
            "branch_aligned_reduced_polarization": [
              -0.4870402718086119,
              -0.48470250169841145,
              0.001828928728665644
            ],
            "target_residual": 0.020132386579248422,
            "energy_eV": -256.8281195653161,
            "max_atomic_step_A": 0.005699366448119974,
            "max_log_strain_component": 0.0014063942156581641,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.1390938929902044,
            "cell_principal_stretches": [
              1.0471260944313352,
              0.9988615882484331,
              0.9569387268685143
            ],
            "cell_volume_ratio": 1.000894782673943,
            "cell_rmsd_from_input_A": 0.34278952437092153
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -0.4994440760606725,
              -0.4992520737452544,
              0.0012373734466651334
            ],
            "branch_aligned_reduced_polarization": [
              -0.4994440760606725,
              -0.4992520737452544,
              0.0012373734466651334
            ],
            "target_residual": 0.0015490442715969074,
            "energy_eV": -256.57039297644343,
            "max_atomic_step_A": 0.0002714183068880285,
            "max_log_strain_component": 6.706585929146846e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.1390938929902044,
            "cell_principal_stretches": [
              1.0472197684313354,
              0.9988482246094373,
              0.9568762129644509
            ],
            "cell_volume_ratio": 1.0009055384716934,
            "cell_rmsd_from_input_A": 0.343327006438142
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              -0.4999771243977137,
              -0.4999701425207914,
              4.946272766849215e-05
            ],
            "branch_aligned_reduced_polarization": [
              -0.4999771243977137,
              -0.4999701425207914,
              4.946272766849215e-05
            ],
            "target_residual": 6.213954999080574e-05,
            "energy_eV": -256.5576053641264
          }
        ],
        "iterations": 4
      },
      "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,
          0.0
        ],
        "formal_class": [
          0.5,
          0.5,
          0.0
        ],
        "target_residual": 6.213954999080574e-05,
        "parent_symmetrization_rmsd_A": 0.20268831778638263,
        "parent_cell_rmsd_A": 0.343327006438142,
        "energy_eV": -256.5576053641264,
        "reduced_polarization": [
          -0.4999771243977137,
          -0.4999701425207914,
          4.946272766849215e-05
        ],
        "cartesian_polarization_e_A2": [
          -0.005053397360509836,
          -0.0023265619856463276,
          0.00021784618906070448
        ],
        "ranking_score": 0.7886443484958998
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 7,
      "formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.5,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        -0.5,
        -0.5,
        0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -7.994351906310773e-16,
              -1.3783925634411432e-15,
              0.10939763593528573
            ],
            "branch_aligned_reduced_polarization": [
              -7.771561172376096e-16,
              -1.3877787807814457e-15,
              0.10939763593528573
            ],
            "target_residual": 0.8078181768275219,
            "energy_eV": -261.41035421167356,
            "max_atomic_step_A": 0.11664966756299103,
            "max_log_strain_component": 0.02,
            "step_scale": 0.6140920871565899,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.1390938929902044,
            "cell_principal_stretches": [
              1.023444722092431,
              1.002714496679924,
              0.9723698290131515
            ],
            "cell_volume_ratio": 0.9978681463170054,
            "cell_rmsd_from_input_A": 0.19889288122890422
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.29839323844059673,
              -0.2968087859045906,
              0.3422724797336632
            ],
            "branch_aligned_reduced_polarization": [
              -0.29839323844059673,
              -0.2968087859045906,
              0.3422724797336632
            ],
            "target_residual": 0.3268178796231997,
            "energy_eV": -259.8182325216778,
            "max_atomic_step_A": 0.08028113559950381,
            "max_log_strain_component": 0.015645657785826158,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.1390938929902044,
            "cell_principal_stretches": [
              1.0418758437183373,
              1.0048572647525371,
              0.9514881509897966
            ],
            "cell_volume_ratio": 0.9961476846084227,
            "cell_rmsd_from_input_A": 0.35214134408114395
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.483513998813236,
              -0.4807481155672807,
              0.4866145907420125
            ],
            "branch_aligned_reduced_polarization": [
              -0.483513998813236,
              -0.4807481155672807,
              0.4866145907420125
            ],
            "target_residual": 0.02866343437804656,
            "energy_eV": -256.95154667950817,
            "max_atomic_step_A": 0.007972500654793593,
            "max_log_strain_component": 0.0019595387879268447,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.1390938929902044,
            "cell_principal_stretches": [
              1.0440976651570153,
              1.005125605960101,
              0.9489881774532276
            ],
            "cell_volume_ratio": 0.9959149769920606,
            "cell_rmsd_from_input_A": 0.3698321946449058
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -0.4990030205069255,
              -0.4988964448173032,
              0.5005476457075796
            ],
            "branch_aligned_reduced_polarization": [
              -0.4990030205069255,
              -0.4988964448173032,
              0.5005476457075796
            ],
            "target_residual": 0.0015848400461555485,
            "energy_eV": -256.61576811817355,
            "max_atomic_step_A": 0.0004599459699881195,
            "max_log_strain_component": 0.0001129350591209933,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.1390938929902044,
            "cell_principal_stretches": [
              1.0442314537887964,
              1.0051252574541394,
              0.9488667261436821
            ],
            "cell_volume_ratio": 0.9959147729523623,
            "cell_rmsd_from_input_A": 0.3707598404023569
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              -0.4999503316539696,
              -0.49994564941650194,
              0.5000457085047356
            ],
            "branch_aligned_reduced_polarization": [
              -0.4999503316539696,
              -0.49994564941650194,
              0.5000457085047356
            ],
            "target_residual": 8.666139814899797e-05,
            "energy_eV": -256.59642428063546
          }
        ],
        "iterations": 4
      },
      "parent": {
        "candidate_id": "bec_projection_07",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          -0.5,
          -0.5,
          0.5
        ],
        "formal_class": [
          0.5,
          0.5,
          0.5
        ],
        "target_residual": 8.666139814899797e-05,
        "parent_symmetrization_rmsd_A": 0.20594845043136215,
        "parent_cell_rmsd_A": 0.3707598404023569,
        "energy_eV": -256.59642428063546,
        "reduced_polarization": [
          -0.4999503316539696,
          -0.49994564941650194,
          0.5000457085047356
        ],
        "cartesian_polarization_e_A2": [
          -0.005133993240228124,
          -0.0024171093657227405,
          0.0015736370571121387
        ],
        "ranking_score": 0.7988117333282494
      },
      "branch_status": "awaiting_branch_sampling"
    }
  ],
  "sampled_polarization_branches": [
    {
      "orbit_id": 0,
      "candidate_id": "inversion_parent_endpoint_01",
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "construction": "MACEField-BEC-parent plus variable-cell P-N-P path and symmetric log-strain continuation beyond both polar endpoints",
      "geometry_diagnostics": {
        "collision_aware": false,
        "permutations_tested": 1,
        "selected_order": [
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          10,
          11,
          12,
          13,
          14,
          15,
          16,
          17,
          18,
          19,
          20,
          21,
          22,
          23,
          24,
          25,
          26,
          27,
          28,
          29,
          30,
          31,
          32,
          33,
          34,
          35,
          36,
          37,
          38,
          39,
          40,
          41,
          42,
          43,
          44,
          45,
          46,
          47,
          48,
          49,
          50,
          51,
          52,
          53,
          54,
          55,
          56,
          57,
          58,
          59,
          60,
          61,
          62,
          63,
          64,
          65,
          66,
          67,
          68,
          69,
          70,
          71,
          72,
          73,
          74,
          75,
          76,
          77,
          78,
          79,
          80,
          81,
          82,
          83
        ],
        "endpoint_rmsd_A": 0.2321058704340009,
        "minimum_distance_A_by_image": [
          2.2598269888049827,
          2.2517760617397484,
          2.2448775029488157,
          2.23914196343063,
          2.2345783986414496,
          2.2311939998760173,
          2.228994138309757,
          2.2279823227046713,
          2.228160171549274
        ],
        "minimum_distance_A": 2.2279823227046713,
        "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": [
          2786.424470895011,
          2786.424470895011,
          2786.424470895011,
          2786.424470895011,
          2786.424470895011,
          2786.424470895011,
          2786.424470895011,
          2786.424470895011,
          2786.424470895011
        ],
        "cell_deformation_log_strain_norm": 0.0
      },
      "parent_reduced_polarization": [
        -6.433878042825234e-16,
        2.1891802791217227e-15,
        6.52600899198893e-16
      ],
      "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": [
          -261.4103542116735,
          -261.3815360153594,
          -261.3429603201879,
          -261.3010688475945,
          -261.26087485335955,
          -261.2260739932791,
          -261.19878273337685,
          -261.1809537948966,
          -261.1746939927553
        ],
        "cartesian_polarizations_e_A2": [
          [
            -8.925056469811825e-18,
            -5.376450033014434e-18,
            0.00029889335723400713
          ],
          [
            -1.5418136432461237e-06,
            1.8452753471346437e-18,
            0.0002505330514522355
          ],
          [
            -3.387579072556929e-06,
            1.6858993387451468e-18,
            0.00020429736781036467
          ],
          [
            -5.19700601115136e-06,
            1.09944543287442e-17,
            0.0001607593573947349
          ],
          [
            -6.320350135368222e-06,
            2.154066363389294e-18,
            0.0001210945239590707
          ],
          [
            -6.3878696227923015e-06,
            7.039937120579808e-18,
            8.587953190910275e-05
          ],
          [
            -5.2567603855410524e-06,
            -8.108254426815654e-18,
            5.4783775489087e-05
          ],
          [
            -2.9896812481751424e-06,
            -7.981251670130273e-18,
            2.663876736729289e-05
          ],
          [
            -6.509513842658513e-18,
            1.02000645369278e-17,
            1.7830190938574965e-18
          ]
        ],
        "raw_reduced_polarization": [
          [
            -8.821353827653266e-16,
            -1.1539160699765134e-15,
            0.10939763593528774
          ],
          [
            -0.0001523898894016071,
            3.960406706125968e-16,
            0.09169733247390485
          ],
          [
            -0.0003348217876184285,
            3.6183472875131985e-16,
            0.07477465967488212
          ],
          [
            -0.0005136620594376325,
            2.359675520586525e-15,
            0.05883935934946586
          ],
          [
            -0.0006246912279751079,
            4.623146829688209e-16,
            0.04432167636117723
          ],
          [
            -0.0006313647240010903,
            1.5109405881535913e-15,
            0.03143267502840312
          ],
          [
            -0.0005195680666547796,
            -1.7402272921924631e-15,
            0.020051350694366622
          ],
          [
            -0.0002954943334113048,
            -1.712969432271758e-15,
            0.00975002656860773
          ],
          [
            -6.433878042825234e-16,
            2.1891802791217227e-15,
            6.52600899198893e-16
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -8.821353827653266e-16,
            -1.1539160699765134e-15,
            0.10939763593528774
          ],
          [
            -0.0001523898894016071,
            3.9604067061259674e-16,
            0.09169733247390485
          ],
          [
            -0.0003348217876184285,
            3.6183472875131985e-16,
            0.07477465967488212
          ],
          [
            -0.0005136620594376325,
            2.359675520586525e-15,
            0.05883935934946586
          ],
          [
            -0.0006246912279751079,
            4.62314682968821e-16,
            0.04432167636117723
          ],
          [
            -0.0006313647240010903,
            1.5109405881535913e-15,
            0.03143267502840312
          ],
          [
            -0.0005195680666547796,
            -1.740227292192463e-15,
            0.020051350694366622
          ],
          [
            -0.0002954943334113048,
            -1.712969432271758e-15,
            0.00975002656860773
          ],
          [
            -6.433655691528983e-16,
            2.1891802791217227e-15,
            6.522560269672795e-16
          ]
        ],
        "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": [
          [
            -8.881784197001252e-16,
            -1.1657341758564144e-15,
            0.10939763593528773
          ],
          [
            -0.00015238988940158293,
            4.440892098500626e-16,
            0.09169733247390488
          ],
          [
            -0.0003348217876184556,
            3.3306690738754696e-16,
            0.07477465967488217
          ],
          [
            -0.0005136620594376473,
            2.3314683517128287e-15,
            0.058839359349465825
          ],
          [
            -0.0006246912279750938,
            4.440892098500626e-16,
            0.04432167636117723
          ],
          [
            -0.0006313647240011044,
            1.5543122344752192e-15,
            0.03143267502840308
          ],
          [
            -0.0005195680666547631,
            -1.7208456881689926e-15,
            0.020051350694366588
          ],
          [
            -0.0002954943334113058,
            -1.7208456881689926e-15,
            0.009750026568607684
          ],
          [
            -6.661338147750939e-16,
            2.220446049250313e-15,
            6.661338147750939e-16
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -261.1746939927553,
          -261.1809537948966,
          -261.1987827333769,
          -261.2260739932789,
          -261.2608748533595,
          -261.30106884759454,
          -261.34296032018784,
          -261.38153601535936,
          -261.4103542116736
        ],
        "cartesian_polarizations_e_A2": [
          [
            -4.905792758239201e-18,
            7.777051159381232e-18,
            2.6994311420971034e-18
          ],
          [
            2.9896812481585075e-06,
            7.119625124774557e-18,
            -2.663876736729532e-05
          ],
          [
            5.256760385524612e-06,
            8.43198694385682e-18,
            -5.478377548908013e-05
          ],
          [
            6.387869622778829e-06,
            1.8353143466103002e-17,
            -8.587953190912228e-05
          ],
          [
            6.3203501353734015e-06,
            1.0175162035616942e-17,
            -0.00012109452395907441
          ],
          [
            5.1970060111420214e-06,
            4.472489235430256e-18,
            -0.00016075935739477467
          ],
          [
            3.387579072549887e-06,
            -7.445847891946807e-18,
            -0.00020429736781037858
          ],
          [
            1.5418136432377565e-06,
            -1.1604565610860242e-17,
            -0.00025053305145224074
          ],
          [
            -1.7770424935428904e-17,
            -2.9036316528461466e-18,
            -0.00029889335723399586
          ]
        ],
        "raw_reduced_polarization": [
          [
            -4.848791026918787e-16,
            1.6691430692619973e-15,
            9.880158864966482e-16
          ],
          [
            0.00029549433340966065,
            1.52804355908423e-15,
            -0.009750026568608619
          ],
          [
            0.0005195680666531547,
            1.8097081115981816e-15,
            -0.020051350694364107
          ],
          [
            0.0006313647239997588,
            3.93902799246267e-15,
            -0.03143267502841027
          ],
          [
            0.0006246912279756197,
            2.183835600705898e-15,
            -0.04432167636117859
          ],
          [
            0.0005136620594367095,
            9.599042434820834e-16,
            -0.05883935934948042
          ],
          [
            0.0003348217876177325,
            -1.5980588463315307e-15,
            -0.0747746596748872
          ],
          [
            0.0001523898894007801,
            -2.4906201417742253e-15,
            -0.09169733247390678
          ],
          [
            -1.7563945567559629e-15,
            -6.231895032851388e-16,
            -0.10939763593528361
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -4.848791026918787e-16,
            1.6691430692619973e-15,
            9.880158864966482e-16
          ],
          [
            0.00029549433340966065,
            1.52804355908423e-15,
            -0.009750026568608619
          ],
          [
            0.0005195680666531547,
            1.8097081115981816e-15,
            -0.020051350694364107
          ],
          [
            0.0006313647239997588,
            3.93902799246267e-15,
            -0.03143267502841027
          ],
          [
            0.0006246912279756197,
            2.183835600705898e-15,
            -0.04432167636117859
          ],
          [
            0.0005136620594367095,
            9.599042434820834e-16,
            -0.05883935934948042
          ],
          [
            0.0003348217876177325,
            -1.5980588463315305e-15,
            -0.0747746596748872
          ],
          [
            0.0001523898894007801,
            -2.4906201417742253e-15,
            -0.09169733247390678
          ],
          [
            -1.7564075194265172e-15,
            -6.231895032851389e-16,
            -0.10939763593528361
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          -4.0464022579972003e-16,
          5.532276628219959e-15,
          -0.10939763593528642
        ],
        "actual_opposite_endpoint_branch_residual": 6.90315890155013e-15
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            -8.821353827653266e-16,
            -1.1539160699765134e-15,
            0.10939763593528774
          ],
          [
            -0.0001523898894016071,
            3.960406706125968e-16,
            0.09169733247390485
          ],
          [
            -0.0003348217876184285,
            3.6183472875131985e-16,
            0.07477465967488212
          ],
          [
            -0.0005136620594376325,
            2.359675520586525e-15,
            0.05883935934946586
          ],
          [
            -0.0006246912279751079,
            4.623146829688209e-16,
            0.04432167636117723
          ],
          [
            -0.0006313647240010903,
            1.5109405881535913e-15,
            0.03143267502840312
          ],
          [
            -0.0005195680666547796,
            -1.7402272921924631e-15,
            0.020051350694366622
          ],
          [
            -0.0002954943334113048,
            -1.712969432271758e-15,
            0.00975002656860773
          ],
          [
            -6.433878042825234e-16,
            2.1891802791217227e-15,
            6.52600899198893e-16
          ],
          [
            0.00029549433340966065,
            1.52804355908423e-15,
            -0.009750026568608619
          ],
          [
            0.0005195680666531547,
            1.8097081115981816e-15,
            -0.020051350694364107
          ],
          [
            0.0006313647239997588,
            3.93902799246267e-15,
            -0.03143267502841027
          ],
          [
            0.0006246912279756197,
            2.183835600705898e-15,
            -0.04432167636117859
          ],
          [
            0.0005136620594367095,
            9.599042434820834e-16,
            -0.05883935934948042
          ],
          [
            0.0003348217876177325,
            -1.5980588463315307e-15,
            -0.0747746596748872
          ],
          [
            0.0001523898894007801,
            -2.4906201417742253e-15,
            -0.09169733247390678
          ],
          [
            -1.7563945567559629e-15,
            -6.231895032851388e-16,
            -0.10939763593528361
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -8.821353827653266e-16,
            -1.1539160699765134e-15,
            0.10939763593528774
          ],
          [
            -0.0001523898894016071,
            3.9604067061259674e-16,
            0.09169733247390485
          ],
          [
            -0.0003348217876184285,
            3.6183472875131985e-16,
            0.07477465967488212
          ],
          [
            -0.0005136620594376325,
            2.359675520586525e-15,
            0.05883935934946586
          ],
          [
            -0.0006246912279751079,
            4.62314682968821e-16,
            0.04432167636117723
          ],
          [
            -0.0006313647240010903,
            1.5109405881535913e-15,
            0.03143267502840312
          ],
          [
            -0.0005195680666547796,
            -1.740227292192463e-15,
            0.020051350694366622
          ],
          [
            -0.0002954943334113048,
            -1.712969432271758e-15,
            0.00975002656860773
          ],
          [
            -6.433655691528983e-16,
            2.1891802791217227e-15,
            6.522560269672795e-16
          ],
          [
            0.00029549433340966065,
            1.52804355908423e-15,
            -0.009750026568608619
          ],
          [
            0.0005195680666531547,
            1.8097081115981816e-15,
            -0.020051350694364107
          ],
          [
            0.0006313647239997588,
            3.93902799246267e-15,
            -0.03143267502841027
          ],
          [
            0.0006246912279756197,
            2.183835600705898e-15,
            -0.04432167636117859
          ],
          [
            0.0005136620594367095,
            9.599042434820834e-16,
            -0.05883935934948042
          ],
          [
            0.0003348217876177325,
            -1.5980588463315305e-15,
            -0.0747746596748872
          ],
          [
            0.0001523898894007801,
            -2.4906201417742253e-15,
            -0.09169733247390678
          ],
          [
            -1.7564075194265172e-15,
            -6.231895032851389e-16,
            -0.10939763593528361
          ]
        ],
        "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": [
          [
            -8.881784197001252e-16,
            -1.1657341758564144e-15,
            0.10939763593528773
          ],
          [
            -0.00015238988940158293,
            4.440892098500626e-16,
            0.09169733247390488
          ],
          [
            -0.0003348217876184556,
            3.3306690738754696e-16,
            0.07477465967488217
          ],
          [
            -0.0005136620594376473,
            2.3314683517128287e-15,
            0.058839359349465825
          ],
          [
            -0.0006246912279750938,
            4.440892098500626e-16,
            0.04432167636117723
          ],
          [
            -0.0006313647240011044,
            1.5543122344752192e-15,
            0.03143267502840308
          ],
          [
            -0.0005195680666547631,
            -1.7208456881689926e-15,
            0.020051350694366588
          ],
          [
            -0.0002954943334113058,
            -1.7208456881689926e-15,
            0.009750026568607684
          ],
          [
            -6.661338147750939e-16,
            2.220446049250313e-15,
            6.661338147750939e-16
          ],
          [
            0.000295494333409696,
            1.5543122344752192e-15,
            -0.009750026568608627
          ],
          [
            0.0005195680666532088,
            1.7763568394002505e-15,
            -0.02005135069436409
          ],
          [
            0.0006313647239997167,
            3.885780586188048e-15,
            -0.031432675028410295
          ],
          [
            0.0006246912279755934,
            2.220446049250313e-15,
            -0.044321676361178564
          ],
          [
            0.0005136620594367036,
            9.992007221626409e-16,
            -0.058839359349480425
          ],
          [
            0.00033482178761767845,
            -1.609823385706477e-15,
            -0.07477465967488717
          ],
          [
            0.00015238988940080578,
            -2.4980018054066022e-15,
            -0.09169733247390677
          ],
          [
            -1.7763568394002505e-15,
            -6.106226635438361e-16,
            -0.10939763593528362
          ]
        ]
      },
      "incoming_structure_ids": [
        "incoming_00_000",
        "incoming_00_001",
        "incoming_00_002",
        "incoming_00_003",
        "incoming_00_004",
        "incoming_00_005",
        "incoming_00_006",
        "incoming_00_007",
        "incoming_00_008"
      ],
      "reflected_structure_ids": [
        "reflected_00_001",
        "reflected_00_002",
        "reflected_00_003",
        "reflected_00_004",
        "reflected_00_005",
        "reflected_00_006",
        "reflected_00_007",
        "reflected_00_008"
      ],
      "positive_extension_structure_ids": [
        "extension_plus_00_000",
        "extension_plus_00_001",
        "extension_plus_00_002",
        "extension_plus_00_003"
      ],
      "negative_extension_structure_ids": [
        "extension_minus_00_000",
        "extension_minus_00_001",
        "extension_minus_00_002",
        "extension_minus_00_003"
      ],
      "extension": {
        "enabled": true,
        "fraction_beyond_polar_endpoint": 0.35,
        "images_per_side": 4,
        "construction": "continue fractional atomic displacements and symmetric log strain beyond +P; reflect these structures about N for the -P side",
        "positive_path_coordinates": [
          1.35,
          1.2625,
          1.175,
          1.0875
        ],
        "negative_path_coordinates": [
          -1.0875,
          -1.175,
          -1.2625,
          -1.35
        ]
      },
      "branch_coordinates": [
        1.35,
        1.2625,
        1.175,
        1.0875,
        1.0,
        0.875,
        0.75,
        0.625,
        0.5,
        0.375,
        0.25,
        0.125,
        0.0,
        -0.125,
        -0.25,
        -0.375,
        -0.5,
        -0.625,
        -0.75,
        -0.875,
        -1.0,
        -1.0875,
        -1.175,
        -1.2625,
        -1.35
      ],
      "parent": {
        "candidate_id": "inversion_parent_endpoint_01",
        "source": "same_species_inversion_center_projection_from_endpoint",
        "spacegroup": "P2_1/c",
        "spacegroup_number": 14,
        "pointgroup": "2/m",
        "has_inversion": true,
        "is_polar_point_group": false,
        "nonpolar_parent_hypothesis": true,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.0
        ],
        "formal_class": [
          0.0,
          0.0,
          0.0
        ],
        "target_residual": 3.2759532360285765e-15,
        "parent_symmetrization_rmsd_A": 0.2321058704340009,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -261.17469399275535,
        "reduced_polarization": [
          -1.3020357630660092e-15,
          2.77923277622875e-16,
          -2.9932141801245324e-15
        ],
        "cartesian_polarization_e_A2": [
          -1.3173423193444352e-17,
          1.2949300681646622e-18,
          -8.177981430486059e-18
        ],
        "ranking_score": 0.23210587043400746
      }
    }
  ],
  "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": 58,
      "full_response": 24,
      "energy_polarization": 34
    },
    "model_evaluations_for_recovery_and_path_properties": {
      "total": 83,
      "full_response": 49,
      "energy_polarization": 34
    },
    "elapsed_seconds": 741.8727951350156
  }
}
