{
  "schema": "ferrofinder.endpoint_parent_recovery.v4_variable_cell",
  "status": "complete",
  "input_atom_count": 24,
  "input_formula": "Ba2Ga8S14",
  "input_spacegroup": "Pmn2_1",
  "input_pointgroup": "mm2",
  "input_is_polar_point_group": true,
  "input_energy_eV": -107.0680771856922,
  "input_cartesian_polarization_e_A2": [
    6.353355797411894e-18,
    -6.7332393279234886e-18,
    0.0035130527198101
  ],
  "input_reduced_polarization": [
    2.4181289885305324e-16,
    -6.12515692688517e-16,
    0.33551813719845464
  ],
  "input_formal_targets": [
    {
      "orbit_id": 0,
      "representative_formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.5
      ]
    },
    {
      "orbit_id": 1,
      "representative_formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ]
    },
    {
      "orbit_id": 2,
      "representative_formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        -0.5,
        0.5
      ]
    },
    {
      "orbit_id": 3,
      "representative_formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.5
      ]
    },
    {
      "orbit_id": 4,
      "representative_formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        -0.5,
        0.0
      ]
    },
    {
      "orbit_id": 5,
      "representative_formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.0
      ]
    },
    {
      "orbit_id": 6,
      "representative_formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "target_reduced_polarization": [
        0.5,
        -0.5,
        0.5
      ]
    },
    {
      "orbit_id": 7,
      "representative_formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        0.5,
        -0.5,
        0.0
      ]
    }
  ],
  "parent_candidates": [
    {
      "candidate_id": "inversion_parent_endpoint_00",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "Pmmn",
      "spacegroup_number": 59,
      "pointgroup": "mmm",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 9.472992722983578e-16,
      "parent_symmetrization_rmsd_A": 0.3905317834213815,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -103.26498995629336,
      "reduced_polarization": [
        8.300560438537244e-16,
        4.215161756136031e-16,
        1.7523409786620924e-16
      ],
      "cartesian_polarization_e_A2": [
        2.1808767867257443e-17,
        4.6336270643774544e-18,
        1.8347938780675582e-18
      ],
      "ranking_score": 0.3905317834213834
    },
    {
      "candidate_id": "inversion_parent_endpoint_01",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "Immm",
      "spacegroup_number": 71,
      "pointgroup": "mmm",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 1.53498016252203e-15,
      "parent_symmetrization_rmsd_A": 0.6262396784163091,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -88.23668475377065,
      "reduced_polarization": [
        -9.091201563691386e-17,
        -1.532275923649616e-15,
        5.4404551930960374e-18
      ],
      "cartesian_polarization_e_A2": [
        -2.3886086488388107e-18,
        -1.684394478950025e-17,
        5.696444929236764e-20
      ],
      "ranking_score": 0.6262396784163122
    },
    {
      "candidate_id": "bec_projection_00",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Pmn2_1",
      "spacegroup_number": 31,
      "pointgroup": "mm2",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.5
      ],
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_residual": 0.0006116747950493107,
      "parent_symmetrization_rmsd_A": 0.024384404405486622,
      "parent_cell_rmsd_A": 0.04219114178398463,
      "energy_eV": -107.0193816335056,
      "reduced_polarization": [
        3.857078885958238e-15,
        5.479938146069854e-15,
        0.5006116747950493
      ],
      "cartesian_polarization_e_A2": [
        1.1027751302454548e-16,
        7.34309577778851e-17,
        0.005266532675531349
      ],
      "ranking_score": 0.5361555394415813
    },
    {
      "candidate_id": "inversion_parent_bec_00_00",
      "source": "same_species_inversion_center_projection_after_BEC",
      "spacegroup": "Pmmn",
      "spacegroup_number": 59,
      "pointgroup": "mmm",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.5
      ],
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_residual": 0.49999999999999845,
      "parent_symmetrization_rmsd_A": 0.39054091170056,
      "parent_cell_rmsd_A": 0.04219114178398463,
      "energy_eV": -103.1103046835934,
      "reduced_polarization": [
        1.1851678031109614e-15,
        -4.356186348018027e-16,
        1.5588152543296045e-15
      ],
      "cartesian_polarization_e_A2": [
        3.1014411699595395e-17,
        -4.771686787010584e-18,
        1.6399041183777003e-17
      ],
      "ranking_score": 1.401088697146553
    },
    {
      "candidate_id": "bec_projection_01",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Pmn2_1",
      "spacegroup_number": 31,
      "pointgroup": "mm2",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 2.8887591688623464e-05,
      "parent_symmetrization_rmsd_A": 0.05130474373425968,
      "parent_cell_rmsd_A": 0.08754137215569033,
      "energy_eV": -106.84426613489197,
      "reduced_polarization": [
        -2.6188780684298568e-15,
        2.4459891119751585e-15,
        2.8887591688623464e-05
      ],
      "cartesian_polarization_e_A2": [
        -6.938097827966397e-17,
        2.7084205115858857e-17,
        2.995269011444596e-07
      ],
      "ranking_score": 0.5732478619565595
    },
    {
      "candidate_id": "bec_projection_02",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Pm",
      "spacegroup_number": 6,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        -0.5,
        0.5
      ],
      "formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_residual": 1.3396956670629705e-05,
      "parent_symmetrization_rmsd_A": 0.09229058005804586,
      "parent_cell_rmsd_A": 0.07845485762294996,
      "energy_eV": -106.43837977197549,
      "reduced_polarization": [
        -8.719531774017019e-16,
        -0.4999886816858792,
        0.49999283241927167
      ],
      "cartesian_polarization_e_A2": [
        1.083721886788131e-16,
        -0.005380853811653781,
        0.0051588353625121024
      ],
      "ranking_score": 0.6119310883771246
    },
    {
      "candidate_id": "bec_projection_03",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Pc",
      "spacegroup_number": 7,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.5
      ],
      "formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_residual": 6.933480369445076e-05,
      "parent_symmetrization_rmsd_A": 0.23143378211756757,
      "parent_cell_rmsd_A": 0.411675055385699,
      "energy_eV": -102.67934949917978,
      "reduced_polarization": [
        0.4999309999033945,
        -4.1114154534385163e-16,
        0.5000068045331788
      ],
      "cartesian_polarization_e_A2": [
        0.012839066682149078,
        4.090567952556676e-16,
        0.0046386124317193385
      ],
      "ranking_score": 0.8344912155713813
    },
    {
      "candidate_id": "bec_projection_04",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Pm",
      "spacegroup_number": 6,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        -0.5,
        0.0
      ],
      "formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_residual": 8.740335631012327e-05,
      "parent_symmetrization_rmsd_A": 0.10035768638329418,
      "parent_cell_rmsd_A": 0.11018671405404154,
      "energy_eV": -106.35520121927144,
      "reduced_polarization": [
        2.600918710408665e-15,
        -0.49993373906126287,
        5.699854991093111e-05
      ],
      "cartesian_polarization_e_A2": [
        2.6784458410365955e-16,
        -0.005537547600024278,
        -0.00010129622924190703
      ],
      "ranking_score": 0.6280791716094248
    },
    {
      "candidate_id": "bec_projection_05",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Pc",
      "spacegroup_number": 7,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.0
      ],
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_residual": 0.0005408712616163536,
      "parent_symmetrization_rmsd_A": 0.22860659942621728,
      "parent_cell_rmsd_A": 0.4330785592989187,
      "energy_eV": -102.9835416707585,
      "reduced_polarization": [
        0.49954142969654514,
        -4.3136861247813514e-15,
        0.00028680132222808915
      ],
      "cartesian_polarization_e_A2": [
        0.013253617129562198,
        1.8711645108068702e-17,
        -0.0006401627355825729
      ],
      "ranking_score": 0.8379579817741797
    },
    {
      "candidate_id": "bec_projection_06",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.5,
        -0.5,
        0.5
      ],
      "formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "target_residual": 0.0001682997693954662,
      "parent_symmetrization_rmsd_A": 0.2491422314826539,
      "parent_cell_rmsd_A": 0.4189574720392979,
      "energy_eV": -101.93528958350052,
      "reduced_polarization": [
        0.4998733817403369,
        -0.49989468728688125,
        0.5000346678691878
      ],
      "cartesian_polarization_e_A2": [
        0.012840208128809772,
        -0.005383349593933539,
        0.0045347458677749
      ],
      "ranking_score": 0.8542181990312694
    },
    {
      "candidate_id": "bec_projection_07",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.5,
        -0.5,
        0.0
      ],
      "formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_residual": 3.256634272939057e-07,
      "parent_symmetrization_rmsd_A": 0.24733174950433134,
      "parent_cell_rmsd_A": 0.4442737157485769,
      "energy_eV": -102.21905001968447,
      "reduced_polarization": [
        0.4999999472549152,
        -0.500000147476613,
        2.855263079204327e-07
      ],
      "cartesian_polarization_e_A2": [
        0.013273760439317195,
        -0.005546982843053344,
        -0.0007565732892705213
      ],
      "ranking_score": 0.8584008297683301
    }
  ],
  "formal_branches": [
    {
      "orbit_id": 0,
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.0,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              2.4181289885305324e-16,
              -6.12515692688517e-16,
              0.33551813719845464
            ],
            "branch_aligned_reduced_polarization": [
              2.4181289885305324e-16,
              -6.12515692688517e-16,
              0.33551813719845464
            ],
            "target_residual": 0.16448186280154536,
            "energy_eV": -107.0680771856922,
            "max_atomic_step_A": 0.01948971845797616,
            "max_log_strain_component": 0.0061438810916485415,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 5.452412360693887,
            "cell_principal_stretches": [
              1.0061627934409862,
              0.9978649244409069,
              0.9974085773526575
            ],
            "cell_volume_ratio": 1.0014127337835788,
            "cell_rmsd_from_input_A": 0.04219114178398463
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              3.857078885958238e-15,
              5.479938146069854e-15,
              0.5006116747950493
            ],
            "branch_aligned_reduced_polarization": [
              3.857078885958238e-15,
              5.479938146069854e-15,
              0.5006116747950493
            ],
            "target_residual": 0.0006116747950493107,
            "energy_eV": -107.0193816335056
          }
        ],
        "iterations": 1
      },
      "parent": {
        "candidate_id": "bec_projection_00",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Pmn2_1",
        "spacegroup_number": 31,
        "pointgroup": "mm2",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.5
        ],
        "formal_class": [
          0.0,
          0.0,
          0.5
        ],
        "target_residual": 0.0006116747950493107,
        "parent_symmetrization_rmsd_A": 0.024384404405486622,
        "parent_cell_rmsd_A": 0.04219114178398463,
        "energy_eV": -107.0193816335056,
        "reduced_polarization": [
          3.857078885958238e-15,
          5.479938146069854e-15,
          0.5006116747950493
        ],
        "cartesian_polarization_e_A2": [
          1.1027751302454548e-16,
          7.34309577778851e-17,
          0.005266532675531349
        ],
        "ranking_score": 0.5361555394415813
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 1,
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.0,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              2.4181289885305324e-16,
              -6.12515692688517e-16,
              0.33551813719845464
            ],
            "branch_aligned_reduced_polarization": [
              2.4181289885305324e-16,
              -6.12515692688517e-16,
              0.33551813719845464
            ],
            "target_residual": 0.33551813719845464,
            "energy_eV": -107.0680771856922,
            "max_atomic_step_A": 0.03975607960758733,
            "max_log_strain_component": 0.012532588723936552,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 5.452412360693887,
            "cell_principal_stretches": [
              1.0053070041340795,
              1.0043694055438914,
              0.9875456171179857
            ],
            "cell_volume_ratio": 0.9971244127403134,
            "cell_rmsd_from_input_A": 0.08646568672772385
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -7.0819871141080526e-15,
              -1.4078990898909922e-14,
              0.003951656975704122
            ],
            "branch_aligned_reduced_polarization": [
              -7.0819871141080526e-15,
              -1.4078990898909922e-14,
              0.003951656975704122
            ],
            "target_residual": 0.003951656975704122,
            "energy_eV": -106.8498846279799,
            "max_atomic_step_A": 0.0005196195513099669,
            "max_log_strain_component": 0.0001554112026233749,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 5.452412360693887,
            "cell_principal_stretches": [
              1.005372990476928,
              1.0044237083187333,
              0.9873921533912842
            ],
            "cell_volume_ratio": 0.9970888057837872,
            "cell_rmsd_from_input_A": 0.08754137215569033
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -2.6188780684298568e-15,
              2.4459891119751585e-15,
              2.8887591688623464e-05
            ],
            "branch_aligned_reduced_polarization": [
              -2.6188780684298568e-15,
              2.4459891119751585e-15,
              2.8887591688623464e-05
            ],
            "target_residual": 2.8887591688623464e-05,
            "energy_eV": -106.84426613489197
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "inversion_parent_endpoint_00",
        "source": "same_species_inversion_center_projection_from_endpoint",
        "spacegroup": "Pmmn",
        "spacegroup_number": 59,
        "pointgroup": "mmm",
        "has_inversion": true,
        "is_polar_point_group": false,
        "nonpolar_parent_hypothesis": true,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.0
        ],
        "formal_class": [
          0.0,
          0.0,
          0.0
        ],
        "target_residual": 9.472992722983578e-16,
        "parent_symmetrization_rmsd_A": 0.3905317834213815,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -103.26498995629336,
        "reduced_polarization": [
          8.300560438537244e-16,
          4.215161756136031e-16,
          1.7523409786620924e-16
        ],
        "cartesian_polarization_e_A2": [
          2.1808767867257443e-17,
          4.6336270643774544e-18,
          1.8347938780675582e-18
        ],
        "ranking_score": 0.3905317834213834
      },
      "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": [
          -107.06807718569219,
          -106.86982472124551,
          -106.42370795446936,
          -105.83517397465664,
          -105.17728445279265,
          -104.5043741927053,
          -103.88612871208949,
          -103.43336979946974,
          -103.26498995629338
        ],
        "cartesian_polarizations_e_A2": [
          [
            1.2294989089960147e-17,
            -2.751216069474114e-17,
            0.0035130527198101048
          ],
          [
            -1.5872927997109573e-17,
            -1.6362495571082888e-17,
            0.00638247996739285
          ],
          [
            5.519169802492045e-18,
            -8.639783797120462e-18,
            0.009196196729327723
          ],
          [
            9.81435166316978e-18,
            -1.6893432005542804e-17,
            0.011519109275546936
          ],
          [
            4.909557807191862e-18,
            -8.929385488644053e-18,
            0.012725145752402293
          ],
          [
            2.6241985636116836e-18,
            -1.414221593606869e-17,
            0.012205027073139028
          ],
          [
            2.463184397257427e-17,
            -2.5629749699837796e-17,
            0.009660453773592287
          ],
          [
            6.986646703604942e-18,
            -1.8100105720224432e-17,
            0.005339039830416236
          ],
          [
            -1.5011822835226295e-18,
            -1.2163271043990818e-17,
            -9.325627093997761e-19
          ]
        ],
        "raw_reduced_polarization": [
          [
            4.679553684717365e-16,
            -2.5027522927057687e-15,
            0.3355181371984551
          ],
          [
            -6.041340757006583e-16,
            -1.4884789951355362e-15,
            0.6095660840187616
          ],
          [
            2.100632314259026e-16,
            -7.859520357795308e-16,
            0.8782933368848922
          ],
          [
            3.7354067703891724e-16,
            -1.5367777235912614e-15,
            1.1001457690978989
          ],
          [
            1.86860998077161e-16,
            -8.122967967553809e-16,
            1.2153296687946191
          ],
          [
            9.987872268879642e-17,
            -1.2865024943206847e-15,
            1.1656551366122598
          ],
          [
            9.375041765377993e-16,
            -2.3315113463627423e-15,
            0.9226327394206237
          ],
          [
            2.6591636711878455e-16,
            -1.6465475609906373e-15,
            0.5099111346175416
          ],
          [
            -5.713598470800692e-17,
            -1.1064799609857081e-15,
            -8.906547326038141e-17
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            4.679553684717365e-16,
            -2.5027522927057687e-15,
            0.3355181371984551
          ],
          [
            -6.041340757006582e-16,
            -1.4884789951355362e-15,
            0.6095660840187616
          ],
          [
            2.1006323142590259e-16,
            -7.859520357795308e-16,
            0.8782933368848922
          ],
          [
            3.7354067703891724e-16,
            -1.5367777235912614e-15,
            1.1001457690978989
          ],
          [
            1.86860998077161e-16,
            -8.122967967553809e-16,
            1.2153296687946191
          ],
          [
            9.987872268879642e-17,
            -1.2865024943206847e-15,
            1.1656551366122598
          ],
          [
            9.375041765377993e-16,
            -2.3315113463627423e-15,
            0.9226327394206237
          ],
          [
            2.659163671187846e-16,
            -1.6465475609906373e-15,
            0.5099111346175416
          ],
          [
            -5.713598470800689e-17,
            -1.1064799609857081e-15,
            0.9999999999999999
          ]
        ],
        "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,
            1
          ]
        ],
        "folded_reduced_polarization": [
          [
            4.440892098500626e-16,
            -2.4980018054066022e-15,
            0.335518137198455
          ],
          [
            -6.106226635438361e-16,
            -1.4988010832439613e-15,
            -0.39043391598123844
          ],
          [
            2.220446049250313e-16,
            -7.771561172376096e-16,
            -0.1217066631151078
          ],
          [
            3.3306690738754696e-16,
            -1.5543122344752192e-15,
            0.10014576909789885
          ],
          [
            2.220446049250313e-16,
            -8.326672684688674e-16,
            0.21532966879461912
          ],
          [
            1.1102230246251565e-16,
            -1.27675647831893e-15,
            0.16565513661225983
          ],
          [
            8.881784197001252e-16,
            -2.3314683517128287e-15,
            -0.07736726057937626
          ],
          [
            2.220446049250313e-16,
            -1.6653345369377348e-15,
            -0.49008886538245844
          ],
          [
            -5.551115123125783e-17,
            -1.1102230246251565e-15,
            0.0
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -103.26498995629336,
          -103.43336979946974,
          -103.88612871208949,
          -104.50437419270528,
          -105.17728445279265,
          -105.83517397465661,
          -106.42370795446935,
          -106.8698247212455,
          -107.0680771856922
        ],
        "cartesian_polarizations_e_A2": [
          [
            -1.4300043012270203e-18,
            -1.1246199020832781e-17,
            2.6416779907723603e-17
          ],
          [
            9.311894636136835e-18,
            -1.5252355753575788e-17,
            -0.005339039830416234
          ],
          [
            2.27804362520658e-17,
            -2.640202087723404e-17,
            -0.009660453773592275
          ],
          [
            3.2404081070738776e-18,
            -1.5252355753575788e-17,
            -0.012205027073139028
          ],
          [
            9.286544437185795e-18,
            -1.114966512365825e-17,
            -0.012725145752402283
          ],
          [
            2.186059577006608e-17,
            -2.068238746964312e-17,
            -0.011519109275546937
          ],
          [
            1.2564851483204239e-17,
            -2.4664410728092495e-17,
            -0.00919619672932773
          ],
          [
            -4.205742325969617e-18,
            -9.894724460389356e-19,
            -0.006382479967392853
          ],
          [
            1.3540647441801615e-17,
            -3.016684286704072e-17,
            -0.003513052719810105
          ]
        ],
        "raw_reduced_polarization": [
          [
            -5.442690390374534e-17,
            -1.0230548845621826e-15,
            2.5229649231965123e-15
          ],
          [
            3.5441683223466153e-16,
            -1.3874907447281103e-15,
            -0.5099111346175415
          ],
          [
            8.670383814319358e-16,
            -2.401764042298343e-15,
            -0.9226327394206226
          ],
          [
            1.233320630583393e-16,
            -1.3874907447281103e-15,
            -1.1656551366122598
          ],
          [
            3.5345198699533934e-16,
            -1.0142732975702325e-15,
            -1.215329668794618
          ],
          [
            8.320286479104241e-16,
            -1.8814550130253014e-15,
            -1.100145769097899
          ],
          [
            4.782265085876984e-16,
            -2.243695476443242e-15,
            -0.8782933368848928
          ],
          [
            -1.6007331811732983e-16,
            -9.001126666748817e-17,
            -0.6095660840187619
          ],
          [
            5.153659443381165e-16,
            -2.7442459349843955e-15,
            -0.33551813719845514
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -5.442690390374534e-17,
            -1.0230548845621826e-15,
            1.0000000000000024
          ],
          [
            3.5441683223466153e-16,
            -1.3874907447281103e-15,
            1.4900888653824584
          ],
          [
            8.670383814319358e-16,
            -2.401764042298343e-15,
            1.0773672605793774
          ],
          [
            1.2333206305833928e-16,
            -1.3874907447281103e-15,
            0.8343448633877402
          ],
          [
            3.5345198699533934e-16,
            -1.0142732975702325e-15,
            0.784670331205382
          ],
          [
            8.320286479104241e-16,
            -1.8814550130253014e-15,
            0.8998542309021009
          ],
          [
            4.782265085876984e-16,
            -2.243695476443242e-15,
            1.1217066631151071
          ],
          [
            -1.6007331811732986e-16,
            -9.001126666748809e-17,
            1.390433915981238
          ],
          [
            5.153659443381165e-16,
            -2.7442459349843955e-15,
            1.6644818628015448
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          1
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          -5.822273378877504e-16,
          2.897923707343523e-16,
          -0.33551813719845525
        ],
        "actual_opposite_endpoint_branch_residual": 3.2264685731858664e-15
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            4.679553684717365e-16,
            -2.5027522927057687e-15,
            0.3355181371984551
          ],
          [
            -6.041340757006583e-16,
            -1.4884789951355362e-15,
            0.6095660840187616
          ],
          [
            2.100632314259026e-16,
            -7.859520357795308e-16,
            0.8782933368848922
          ],
          [
            3.7354067703891724e-16,
            -1.5367777235912614e-15,
            1.1001457690978989
          ],
          [
            1.86860998077161e-16,
            -8.122967967553809e-16,
            1.2153296687946191
          ],
          [
            9.987872268879642e-17,
            -1.2865024943206847e-15,
            1.1656551366122598
          ],
          [
            9.375041765377993e-16,
            -2.3315113463627423e-15,
            0.9226327394206237
          ],
          [
            2.6591636711878455e-16,
            -1.6465475609906373e-15,
            0.5099111346175416
          ],
          [
            -5.713598470800692e-17,
            -1.1064799609857081e-15,
            -8.906547326038141e-17
          ],
          [
            3.5441683223466153e-16,
            -1.3874907447281103e-15,
            -0.5099111346175415
          ],
          [
            8.670383814319358e-16,
            -2.401764042298343e-15,
            -0.9226327394206226
          ],
          [
            1.233320630583393e-16,
            -1.3874907447281103e-15,
            -1.1656551366122598
          ],
          [
            3.5345198699533934e-16,
            -1.0142732975702325e-15,
            -1.215329668794618
          ],
          [
            8.320286479104241e-16,
            -1.8814550130253014e-15,
            -1.100145769097899
          ],
          [
            4.782265085876984e-16,
            -2.243695476443242e-15,
            -0.8782933368848928
          ],
          [
            -1.6007331811732983e-16,
            -9.001126666748817e-17,
            -0.6095660840187619
          ],
          [
            5.153659443381165e-16,
            -2.7442459349843955e-15,
            -0.33551813719845514
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            4.679553684717365e-16,
            -2.5027522927057687e-15,
            0.3355181371984551
          ],
          [
            -6.041340757006582e-16,
            -1.4884789951355362e-15,
            0.6095660840187616
          ],
          [
            2.1006323142590259e-16,
            -7.859520357795308e-16,
            0.8782933368848922
          ],
          [
            3.7354067703891724e-16,
            -1.5367777235912614e-15,
            1.1001457690978989
          ],
          [
            1.86860998077161e-16,
            -8.122967967553809e-16,
            1.2153296687946191
          ],
          [
            9.987872268879642e-17,
            -1.2865024943206847e-15,
            1.1656551366122598
          ],
          [
            9.375041765377993e-16,
            -2.3315113463627423e-15,
            0.9226327394206237
          ],
          [
            2.659163671187846e-16,
            -1.6465475609906373e-15,
            0.5099111346175416
          ],
          [
            -5.713598470800689e-17,
            -1.1064799609857081e-15,
            0.9999999999999999
          ],
          [
            3.5441683223466153e-16,
            -1.3874907447281103e-15,
            1.4900888653824587
          ],
          [
            8.670383814319358e-16,
            -2.401764042298343e-15,
            1.0773672605793774
          ],
          [
            1.2333206305833928e-16,
            -1.3874907447281103e-15,
            0.8343448633877402
          ],
          [
            3.5345198699533934e-16,
            -1.0142732975702325e-15,
            0.784670331205382
          ],
          [
            8.320286479104241e-16,
            -1.8814550130253014e-15,
            0.8998542309021009
          ],
          [
            4.782265085876984e-16,
            -2.243695476443242e-15,
            1.1217066631151074
          ],
          [
            -1.6007331811732986e-16,
            -9.001126666748809e-17,
            1.3904339159812382
          ],
          [
            5.153659443381165e-16,
            -2.7442459349843955e-15,
            1.6644818628015448
          ]
        ],
        "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,
            1
          ],
          [
            0,
            0,
            2
          ],
          [
            0,
            0,
            2
          ],
          [
            0,
            0,
            2
          ],
          [
            0,
            0,
            2
          ],
          [
            0,
            0,
            2
          ],
          [
            0,
            0,
            2
          ],
          [
            0,
            0,
            2
          ],
          [
            0,
            0,
            2
          ]
        ],
        "folded_reduced_polarization": [
          [
            4.440892098500626e-16,
            -2.4980018054066022e-15,
            0.335518137198455
          ],
          [
            -6.106226635438361e-16,
            -1.4988010832439613e-15,
            -0.39043391598123844
          ],
          [
            2.220446049250313e-16,
            -7.771561172376096e-16,
            -0.1217066631151078
          ],
          [
            3.3306690738754696e-16,
            -1.5543122344752192e-15,
            0.10014576909789885
          ],
          [
            2.220446049250313e-16,
            -8.326672684688674e-16,
            0.21532966879461912
          ],
          [
            1.1102230246251565e-16,
            -1.27675647831893e-15,
            0.16565513661225983
          ],
          [
            8.881784197001252e-16,
            -2.3314683517128287e-15,
            -0.07736726057937626
          ],
          [
            2.220446049250313e-16,
            -1.6653345369377348e-15,
            -0.49008886538245844
          ],
          [
            -5.551115123125783e-17,
            -1.1102230246251565e-15,
            0.0
          ],
          [
            3.3306690738754696e-16,
            -1.3877787807814457e-15,
            0.49008886538245866
          ],
          [
            8.881784197001252e-16,
            -2.3869795029440866e-15,
            0.07736726057937737
          ],
          [
            1.1102230246251565e-16,
            -1.3877787807814457e-15,
            -0.16565513661225983
          ],
          [
            3.3306690738754696e-16,
            -9.992007221626409e-16,
            -0.215329668794618
          ],
          [
            7.771561172376096e-16,
            -1.887379141862766e-15,
            -0.10014576909789907
          ],
          [
            4.440892098500626e-16,
            -2.220446049250313e-15,
            0.12170666311510736
          ],
          [
            -1.6653345369377348e-16,
            -1.1102230246251565e-16,
            0.3904339159812382
          ],
          [
            5.551115123125783e-16,
            -2.7200464103316335e-15,
            -0.33551813719845525
          ]
        ]
      },
      "incoming_structure_ids": [
        "incoming_01_000",
        "incoming_01_001",
        "incoming_01_002",
        "incoming_01_003",
        "incoming_01_004",
        "incoming_01_005",
        "incoming_01_006",
        "incoming_01_007",
        "incoming_01_008"
      ],
      "reflected_structure_ids": [
        "reflected_01_001",
        "reflected_01_002",
        "reflected_01_003",
        "reflected_01_004",
        "reflected_01_005",
        "reflected_01_006",
        "reflected_01_007",
        "reflected_01_008"
      ]
    },
    {
      "orbit_id": 2,
      "formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.5,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        -0.5,
        0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              2.4181289885305324e-16,
              -6.12515692688517e-16,
              0.33551813719845464
            ],
            "branch_aligned_reduced_polarization": [
              2.4181289885305324e-16,
              -6.106226635438361e-16,
              0.33551813719845464
            ],
            "target_residual": 0.5263594619560532,
            "energy_eV": -107.0680771856922,
            "max_atomic_step_A": 0.0734170824385903,
            "max_log_strain_component": 0.018477298127569205,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 5.452412360693887,
            "cell_principal_stretches": [
              1.0211595725175726,
              0.997408577352673,
              0.9832102512410564
            ],
            "cell_volume_ratio": 1.0014127337835652,
            "cell_rmsd_from_input_A": 0.0785129559456862
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -3.1291400181834373e-15,
              -0.4987259943739242,
              0.5014650603885455
            ],
            "branch_aligned_reduced_polarization": [
              -3.1291400181834373e-15,
              -0.4987259943739242,
              0.5014650603885455
            ],
            "target_residual": 0.0019415180342603267,
            "energy_eV": -106.44021212831107,
            "max_atomic_step_A": 0.00022848877661649485,
            "max_log_strain_component": 5.323604741968472e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 5.452412360693887,
            "cell_principal_stretches": [
              1.0211799567594888,
              0.9974310028746811,
              0.9831564930009126
            ],
            "cell_volume_ratio": 1.0014004840344322,
            "cell_rmsd_from_input_A": 0.07845485762294996
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -8.719531774017019e-16,
              -0.4999886816858792,
              0.49999283241927167
            ],
            "branch_aligned_reduced_polarization": [
              -8.719531774017019e-16,
              -0.4999886816858792,
              0.49999283241927167
            ],
            "target_residual": 1.3396956670629705e-05,
            "energy_eV": -106.43837977197549
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_02",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Pm",
        "spacegroup_number": 6,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          -0.5,
          0.5
        ],
        "formal_class": [
          0.0,
          0.5,
          0.5
        ],
        "target_residual": 1.3396956670629705e-05,
        "parent_symmetrization_rmsd_A": 0.09229058005804586,
        "parent_cell_rmsd_A": 0.07845485762294996,
        "energy_eV": -106.43837977197549,
        "reduced_polarization": [
          -8.719531774017019e-16,
          -0.4999886816858792,
          0.49999283241927167
        ],
        "cartesian_polarization_e_A2": [
          1.083721886788131e-16,
          -0.005380853811653781,
          0.0051588353625121024
        ],
        "ranking_score": 0.6119310883771246
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 3,
      "formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.0,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              2.4181289885305324e-16,
              -6.12515692688517e-16,
              0.33551813719845464
            ],
            "branch_aligned_reduced_polarization": [
              2.220446049250313e-16,
              -6.12515692688517e-16,
              0.33551813719845464
            ],
            "target_residual": 0.5263594619560535,
            "energy_eV": -107.0680771856922,
            "max_atomic_step_A": 0.07932993595604362,
            "max_log_strain_component": 0.02,
            "step_scale": 0.4215134527590791,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 5.452412360693887,
            "cell_principal_stretches": [
              1.0210511298222675,
              0.999099480526158,
              0.9808491284578588
            ],
            "cell_volume_ratio": 1.000595243145814,
            "cell_rmsd_from_input_A": 0.1710546802178107
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.21026813543242312,
              -3.75758046674789e-14,
              0.40436750895016227
            ],
            "branch_aligned_reduced_polarization": [
              0.21026813543242312,
              -3.75758046674789e-14,
              0.40436750895016227
            ],
            "target_residual": 0.30510674638591984,
            "energy_eV": -106.37628746856767,
            "max_atomic_step_A": 0.07831038581264954,
            "max_log_strain_component": 0.02,
            "step_scale": 0.724918955377119,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 5.452412360693887,
            "cell_principal_stretches": [
              1.0428540255869116,
              0.9979136631755592,
              0.9622382314298752
            ],
            "cell_volume_ratio": 1.0013804284341252,
            "cell_rmsd_from_input_A": 0.3429058863156643
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.4193445313225473,
              -4.653111579977681e-14,
              0.4778273346962471
            ],
            "branch_aligned_reduced_polarization": [
              0.4193445313225473,
              -4.653111579977681e-14,
              0.4778273346962471
            ],
            "target_residual": 0.08364766412908255,
            "energy_eV": -104.11398549751699,
            "max_atomic_step_A": 0.02929366475962501,
            "max_log_strain_component": 0.007809373903274617,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 5.452412360693887,
            "cell_principal_stretches": [
              1.0513893402151993,
              0.9975459713694683,
              0.9550108909658355
            ],
            "cell_volume_ratio": 1.0016242091873861,
            "cell_rmsd_from_input_A": 0.4101138405936999
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.4981381867167632,
              -1.4250885333445138e-14,
              0.5019135835292645
            ],
            "branch_aligned_reduced_polarization": [
              0.4981381867167632,
              -1.4250885333445138e-14,
              0.5019135835292645
            ],
            "target_residual": 0.002669859663935445,
            "energy_eV": -102.71180089167606,
            "max_atomic_step_A": 0.0006499551658889341,
            "max_log_strain_component": 0.00018746797837440967,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 5.452412360693887,
            "cell_principal_stretches": [
              1.0515562522886879,
              0.9975724971051774,
              0.9548171435730223
            ],
            "cell_volume_ratio": 1.001606617552758,
            "cell_rmsd_from_input_A": 0.411675055385699
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              0.4999309999033945,
              -4.1114154534385163e-16,
              0.5000068045331788
            ],
            "branch_aligned_reduced_polarization": [
              0.4999309999033945,
              -4.1114154534385163e-16,
              0.5000068045331788
            ],
            "target_residual": 6.933480369445076e-05,
            "energy_eV": -102.67934949917978
          }
        ],
        "iterations": 4
      },
      "parent": {
        "candidate_id": "bec_projection_03",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Pc",
        "spacegroup_number": 7,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.5,
          0.0,
          0.5
        ],
        "formal_class": [
          0.5,
          0.0,
          0.5
        ],
        "target_residual": 6.933480369445076e-05,
        "parent_symmetrization_rmsd_A": 0.23143378211756757,
        "parent_cell_rmsd_A": 0.411675055385699,
        "energy_eV": -102.67934949917978,
        "reduced_polarization": [
          0.4999309999033945,
          -4.1114154534385163e-16,
          0.5000068045331788
        ],
        "cartesian_polarization_e_A2": [
          0.012839066682149078,
          4.090567952556676e-16,
          0.0046386124317193385
        ],
        "ranking_score": 0.8344912155713813
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 4,
      "formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.5,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        -0.5,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              2.4181289885305324e-16,
              -6.12515692688517e-16,
              0.33551813719845464
            ],
            "branch_aligned_reduced_polarization": [
              2.4181289885305324e-16,
              -6.106226635438361e-16,
              0.33551813719845464
            ],
            "target_residual": 0.6021398677957808,
            "energy_eV": -107.0680771856922,
            "max_atomic_step_A": 0.0822922147521881,
            "max_log_strain_component": 0.018477298127561367,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 5.452412360693887,
            "cell_principal_stretches": [
              1.0163623063070986,
              1.005307004134095,
              0.9758927483410065
            ],
            "cell_volume_ratio": 0.9971244127402998,
            "cell_rmsd_from_input_A": 0.10823249795135788
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -2.1980386536998673e-14,
              -0.4976493468321106,
              0.00805891794727107
            ],
            "branch_aligned_reduced_polarization": [
              -2.1980386536998673e-14,
              -0.4976493468321106,
              0.00805891794727107
            ],
            "target_residual": 0.008394744117396089,
            "energy_eV": -106.37020970797025,
            "max_atomic_step_A": 0.0010878531958582942,
            "max_log_strain_component": 0.00032097126823055135,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 5.452412360693887,
            "cell_principal_stretches": [
              1.016428623872726,
              1.0054432907098563,
              0.9756248456766737
            ],
            "cell_volume_ratio": 0.997050874974578,
            "cell_rmsd_from_input_A": 0.11018671405404154
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              2.600918710408665e-15,
              -0.49993373906126287,
              5.699854991093111e-05
            ],
            "branch_aligned_reduced_polarization": [
              2.600918710408665e-15,
              -0.49993373906126287,
              5.699854991093111e-05
            ],
            "target_residual": 8.740335631012327e-05,
            "energy_eV": -106.35520121927144
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_04",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Pm",
        "spacegroup_number": 6,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          -0.5,
          0.0
        ],
        "formal_class": [
          0.0,
          0.5,
          0.0
        ],
        "target_residual": 8.740335631012327e-05,
        "parent_symmetrization_rmsd_A": 0.10035768638329418,
        "parent_cell_rmsd_A": 0.11018671405404154,
        "energy_eV": -106.35520121927144,
        "reduced_polarization": [
          2.600918710408665e-15,
          -0.49993373906126287,
          5.699854991093111e-05
        ],
        "cartesian_polarization_e_A2": [
          2.6784458410365955e-16,
          -0.005537547600024278,
          -0.00010129622924190703
        ],
        "ranking_score": 0.6280791716094248
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 5,
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.0,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              2.4181289885305324e-16,
              -6.12515692688517e-16,
              0.33551813719845464
            ],
            "branch_aligned_reduced_polarization": [
              2.220446049250313e-16,
              -6.12515692688517e-16,
              0.33551813719845464
            ],
            "target_residual": 0.6021398677957811,
            "energy_eV": -107.0680771856922,
            "max_atomic_step_A": 0.08066331781019155,
            "max_log_strain_component": 0.02,
            "step_scale": 0.4215134527590316,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 5.452412360693887,
            "cell_principal_stretches": [
              1.019002280765973,
              1.001839440894285,
              0.9783619469741974
            ],
            "cell_volume_ratio": 0.9987868916010959,
            "cell_rmsd_from_input_A": 0.17485641891287304
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.21088105548097735,
              -4.0301408049402895e-14,
              0.19512986144275662
            ],
            "branch_aligned_reduced_polarization": [
              0.21088105548097735,
              -4.0301408049402895e-14,
              0.19512986144275662
            ],
            "target_residual": 0.34880571512872766,
            "energy_eV": -106.40578741444195,
            "max_atomic_step_A": 0.07579537870990545,
            "max_log_strain_component": 0.02,
            "step_scale": 0.7424798495578687,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 5.452412360693887,
            "cell_principal_stretches": [
              1.038431886637361,
              1.003543015491943,
              0.9573515844032193
            ],
            "cell_volume_ratio": 0.9976666810199298,
            "cell_rmsd_from_input_A": 0.35119254625790153
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.4187276823855412,
              -4.888561683975231e-14,
              0.06193230205709108
            ],
            "branch_aligned_reduced_polarization": [
              0.4187276823855412,
              -4.888561683975231e-14,
              0.06193230205709108
            ],
            "target_residual": 0.10218023120210797,
            "energy_eV": -104.36718350375894,
            "max_atomic_step_A": 0.02883661198071928,
            "max_log_strain_component": 0.008337936982947531,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 5.452412360693887,
            "cell_principal_stretches": [
              1.0465343467912522,
              1.0044772505192894,
              0.9484729690365091
            ],
            "cell_volume_ratio": 0.9970537006741688,
            "cell_rmsd_from_input_A": 0.42660185590498195
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.49400900324726593,
              -1.0844850234698019e-14,
              0.00610414780815477
            ],
            "branch_aligned_reduced_polarization": [
              0.49400900324726593,
              -1.0844850234698019e-14,
              0.00610414780815477
            ],
            "target_residual": 0.008552932979690115,
            "energy_eV": -103.09803510465599,
            "max_atomic_step_A": 0.0023332132158409144,
            "max_log_strain_component": 0.0006958744162561703,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 5.452412360693887,
            "cell_principal_stretches": [
              1.0471989658670766,
              1.0045864381519927,
              0.9476999431710551
            ],
            "cell_volume_ratio": 0.9969821210927964,
            "cell_rmsd_from_input_A": 0.4330785592989187
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              0.49954142969654514,
              -4.3136861247813514e-15,
              0.00028680132222808915
            ],
            "branch_aligned_reduced_polarization": [
              0.49954142969654514,
              -4.3136861247813514e-15,
              0.00028680132222808915
            ],
            "target_residual": 0.0005408712616163536,
            "energy_eV": -102.9835416707585
          }
        ],
        "iterations": 4
      },
      "parent": {
        "candidate_id": "bec_projection_05",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Pc",
        "spacegroup_number": 7,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.5,
          0.0,
          0.0
        ],
        "formal_class": [
          0.5,
          0.0,
          0.0
        ],
        "target_residual": 0.0005408712616163536,
        "parent_symmetrization_rmsd_A": 0.22860659942621728,
        "parent_cell_rmsd_A": 0.4330785592989187,
        "energy_eV": -102.9835416707585,
        "reduced_polarization": [
          0.49954142969654514,
          -4.3136861247813514e-15,
          0.00028680132222808915
        ],
        "cartesian_polarization_e_A2": [
          0.013253617129562198,
          1.8711645108068702e-17,
          -0.0006401627355825729
        ],
        "ranking_score": 0.8379579817741797
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 6,
      "formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.5,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.5,
        -0.5,
        0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              2.4181289885305324e-16,
              -6.12515692688517e-16,
              0.33551813719845464
            ],
            "branch_aligned_reduced_polarization": [
              2.220446049250313e-16,
              -6.106226635438361e-16,
              0.33551813719845464
            ],
            "target_residual": 0.7259850433656782,
            "energy_eV": -107.0680771856922,
            "max_atomic_step_A": 0.08475507250949288,
            "max_log_strain_component": 0.02,
            "step_scale": 0.4215134527591624,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 5.452412360693887,
            "cell_principal_stretches": [
              1.0225520883723926,
              0.9990741466030739,
              0.9794342190962315
            ],
            "cell_volume_ratio": 1.0005952431458087,
            "cell_rmsd_from_input_A": 0.1733148887636126
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.21024351080271628,
              -0.21118109028533544,
              0.4047117221276951
            ],
            "branch_aligned_reduced_polarization": [
              0.2102435108027163,
              -0.21118109028533544,
              0.4047117221276951
            ],
            "target_residual": 0.4200655205328958,
            "energy_eV": -106.27464387397073,
            "max_atomic_step_A": 0.08874822761447301,
            "max_log_strain_component": 0.02,
            "step_scale": 0.7263434508939213,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 5.452412360693887,
            "cell_principal_stretches": [
              1.0458928831186085,
              0.9978376854654661,
              0.9595267206350577
            ],
            "cell_volume_ratio": 1.0013921512115755,
            "cell_rmsd_from_input_A": 0.34748864578169464
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.4188755751947455,
              -0.42049218506067726,
              0.4800912710376294
            ],
            "branch_aligned_reduced_polarization": [
              0.4188755751947455,
              -0.42049218506067726,
              0.4800912710376294
            ],
            "target_residual": 0.11532138754500884,
            "energy_eV": -103.6594612976609,
            "max_atomic_step_A": 0.03491884792280124,
            "max_log_strain_component": 0.007940796484178315,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 5.452412360693887,
            "cell_principal_stretches": [
              1.0550965024163643,
              0.9975149908580482,
              0.9516626758120595
            ],
            "cell_volume_ratio": 1.0016007730876932,
            "cell_rmsd_from_input_A": 0.4166406096366697
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.4973447128416786,
              -0.49775652249075203,
              0.502882776513957
            ],
            "branch_aligned_reduced_polarization": [
              0.4973447128416786,
              -0.49775652249075203,
              0.502882776513957
            ],
            "target_residual": 0.004515987340224723,
            "energy_eV": -101.99101071779792,
            "max_atomic_step_A": 0.0010742736066430513,
            "max_log_strain_component": 0.00027556548061150147,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 5.452412360693887,
            "cell_principal_stretches": [
              1.0553541338443666,
              0.9975583324335084,
              0.9513625069856815
            ],
            "cell_volume_ratio": 1.0015728608294514,
            "cell_rmsd_from_input_A": 0.4189574720392979
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              0.4998733817403369,
              -0.49989468728688125,
              0.5000346678691878
            ],
            "branch_aligned_reduced_polarization": [
              0.4998733817403369,
              -0.49989468728688125,
              0.5000346678691878
            ],
            "target_residual": 0.0001682997693954662,
            "energy_eV": -101.93528958350052
          }
        ],
        "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,
          0.5
        ],
        "formal_class": [
          0.5,
          0.5,
          0.5
        ],
        "target_residual": 0.0001682997693954662,
        "parent_symmetrization_rmsd_A": 0.2491422314826539,
        "parent_cell_rmsd_A": 0.4189574720392979,
        "energy_eV": -101.93528958350052,
        "reduced_polarization": [
          0.4998733817403369,
          -0.49989468728688125,
          0.5000346678691878
        ],
        "cartesian_polarization_e_A2": [
          0.012840208128809772,
          -0.005383349593933539,
          0.0045347458677749
        ],
        "ranking_score": 0.8542181990312694
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 7,
      "formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.5,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.5,
        -0.5,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              2.4181289885305324e-16,
              -6.12515692688517e-16,
              0.33551813719845464
            ],
            "branch_aligned_reduced_polarization": [
              2.220446049250313e-16,
              -6.106226635438361e-16,
              0.33551813719845464
            ],
            "target_residual": 0.7826700584468018,
            "energy_eV": -107.0680771856922,
            "max_atomic_step_A": 0.08619139555378676,
            "max_log_strain_component": 0.02,
            "step_scale": 0.42151345275911495,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 5.452412360693887,
            "cell_principal_stretches": [
              1.020439811177488,
              1.001891053568901,
              0.9769333636039144
            ],
            "cell_volume_ratio": 0.9987868916010901,
            "cell_rmsd_from_input_A": 0.17703691434984536
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.21079360759373916,
              -0.21107916844431943,
              0.1956790010616112
            ],
            "branch_aligned_reduced_polarization": [
              0.21079360759373916,
              -0.2110791684443194,
              0.1956790010616112
            ],
            "target_residual": 0.45321722801758113,
            "energy_eV": -106.31185095711427,
            "max_atomic_step_A": 0.08533200823008023,
            "max_log_strain_component": 0.02,
            "step_scale": 0.7425016656704124,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 5.452412360693887,
            "cell_principal_stretches": [
              1.0413684761428053,
              1.0036449075368554,
              0.9545535549175019
            ],
            "cell_volume_ratio": 0.9976651719892011,
            "cell_rmsd_from_input_A": 0.3555932134635843
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.41704308407919555,
              -0.4195796306711687,
              0.06564567756409517
            ],
            "branch_aligned_reduced_polarization": [
              0.41704308407919555,
              -0.4195796306711687,
              0.06564567756409517
            ],
            "target_residual": 0.13288581822348913,
            "energy_eV": -103.96252014567474,
            "max_atomic_step_A": 0.03501286968447953,
            "max_log_strain_component": 0.008713817240494233,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 5.452412360693887,
            "cell_principal_stretches": [
              1.050400360671933,
              1.0047262490788822,
              0.9446722977270052
            ],
            "cell_volume_ratio": 0.9969739041679991,
            "cell_rmsd_from_input_A": 0.4356725617613311
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.4925905408809874,
              -0.4943451312946739,
              0.008087403406066413
            ],
            "branch_aligned_reduced_polarization": [
              0.4925905408809874,
              -0.4943451312946739,
              0.008087403406066413
            ],
            "target_residual": 0.01234032894064214,
            "energy_eV": -102.4065903494747,
            "max_atomic_step_A": 0.0033302497950357,
            "max_log_strain_component": 0.0008934719495357706,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 5.452412360693887,
            "cell_principal_stretches": [
              1.0512830282521972,
              1.00488375121761,
              0.9436355203681821
            ],
            "cell_volume_ratio": 0.9968728254081362,
            "cell_rmsd_from_input_A": 0.444117538007046
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              0.49928793658212495,
              -0.4994610202955192,
              0.0004915323267288333
            ],
            "branch_aligned_reduced_polarization": [
              0.49928793658212495,
              -0.4994610202955192,
              0.0004915323267288333
            ],
            "target_residual": 0.0010193809205285213,
            "energy_eV": -102.23569375975846,
            "max_atomic_step_A": 0.0003257607787855536,
            "max_log_strain_component": 4.6939096019862016e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": true,
            "strain_jacobian_frobenius_norm": 5.346882328606429,
            "cell_principal_stretches": [
              1.051272747913234,
              1.0048794664083183,
              0.9435429663747767
            ],
            "cell_volume_ratio": 0.9967610522685486,
            "cell_rmsd_from_input_A": 0.4442737157485769
          },
          {
            "iteration": 5,
            "reduced_polarization": [
              0.4999999472549152,
              -0.500000147476613,
              2.855263079204327e-07
            ],
            "branch_aligned_reduced_polarization": [
              0.4999999472549152,
              -0.500000147476613,
              2.855263079204327e-07
            ],
            "target_residual": 3.256634272939057e-07,
            "energy_eV": -102.21905001968447
          }
        ],
        "iterations": 5
      },
      "parent": {
        "candidate_id": "bec_projection_07",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.5,
          -0.5,
          0.0
        ],
        "formal_class": [
          0.5,
          0.5,
          0.0
        ],
        "target_residual": 3.256634272939057e-07,
        "parent_symmetrization_rmsd_A": 0.24733174950433134,
        "parent_cell_rmsd_A": 0.4442737157485769,
        "energy_eV": -102.21905001968447,
        "reduced_polarization": [
          0.4999999472549152,
          -0.500000147476613,
          2.855263079204327e-07
        ],
        "cartesian_polarization_e_A2": [
          0.013273760439317195,
          -0.005546982843053344,
          -0.0007565732892705213
        ],
        "ranking_score": 0.8584008297683301
      },
      "branch_status": "awaiting_branch_sampling"
    }
  ],
  "sampled_polarization_branches": [
    {
      "orbit_id": 1,
      "candidate_id": "inversion_parent_endpoint_00",
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "construction": "MACEField-BEC-parent plus variable-cell P-N-P path and symmetric log-strain continuation beyond both polar endpoints",
      "geometry_diagnostics": {
        "collision_aware": false,
        "permutations_tested": 1,
        "selected_order": [
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          10,
          11,
          12,
          13,
          14,
          15,
          16,
          17,
          18,
          19,
          20,
          21,
          22,
          23
        ],
        "endpoint_rmsd_A": 0.3905317834213815,
        "minimum_distance_A_by_image": [
          2.2522276870342357,
          2.232215296614135,
          2.2147249557917434,
          2.1998168224534993,
          2.1875436905502355,
          2.1779501066270837,
          2.1710715923298745,
          2.166934003208378,
          2.1655530500714257
        ],
        "minimum_distance_A": 2.1655530500714257,
        "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": [
          575.0430973577644,
          575.0430973577644,
          575.0430973577644,
          575.0430973577644,
          575.0430973577644,
          575.0430973577644,
          575.0430973577644,
          575.0430973577644,
          575.0430973577644
        ],
        "cell_deformation_log_strain_norm": 0.0
      },
      "parent_reduced_polarization": [
        -5.713598470800692e-17,
        -1.1064799609857081e-15,
        -8.906547326038141e-17
      ],
      "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": [
          -107.06807718569219,
          -106.86982472124551,
          -106.42370795446936,
          -105.83517397465664,
          -105.17728445279265,
          -104.5043741927053,
          -103.88612871208949,
          -103.43336979946974,
          -103.26498995629338
        ],
        "cartesian_polarizations_e_A2": [
          [
            1.2294989089960147e-17,
            -2.751216069474114e-17,
            0.0035130527198101048
          ],
          [
            -1.5872927997109573e-17,
            -1.6362495571082888e-17,
            0.00638247996739285
          ],
          [
            5.519169802492045e-18,
            -8.639783797120462e-18,
            0.009196196729327723
          ],
          [
            9.81435166316978e-18,
            -1.6893432005542804e-17,
            0.011519109275546936
          ],
          [
            4.909557807191862e-18,
            -8.929385488644053e-18,
            0.012725145752402293
          ],
          [
            2.6241985636116836e-18,
            -1.414221593606869e-17,
            0.012205027073139028
          ],
          [
            2.463184397257427e-17,
            -2.5629749699837796e-17,
            0.009660453773592287
          ],
          [
            6.986646703604942e-18,
            -1.8100105720224432e-17,
            0.005339039830416236
          ],
          [
            -1.5011822835226295e-18,
            -1.2163271043990818e-17,
            -9.325627093997761e-19
          ]
        ],
        "raw_reduced_polarization": [
          [
            4.679553684717365e-16,
            -2.5027522927057687e-15,
            0.3355181371984551
          ],
          [
            -6.041340757006583e-16,
            -1.4884789951355362e-15,
            0.6095660840187616
          ],
          [
            2.100632314259026e-16,
            -7.859520357795308e-16,
            0.8782933368848922
          ],
          [
            3.7354067703891724e-16,
            -1.5367777235912614e-15,
            1.1001457690978989
          ],
          [
            1.86860998077161e-16,
            -8.122967967553809e-16,
            1.2153296687946191
          ],
          [
            9.987872268879642e-17,
            -1.2865024943206847e-15,
            1.1656551366122598
          ],
          [
            9.375041765377993e-16,
            -2.3315113463627423e-15,
            0.9226327394206237
          ],
          [
            2.6591636711878455e-16,
            -1.6465475609906373e-15,
            0.5099111346175416
          ],
          [
            -5.713598470800692e-17,
            -1.1064799609857081e-15,
            -8.906547326038141e-17
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            4.679553684717365e-16,
            -2.5027522927057687e-15,
            0.3355181371984551
          ],
          [
            -6.041340757006582e-16,
            -1.4884789951355362e-15,
            0.6095660840187616
          ],
          [
            2.1006323142590259e-16,
            -7.859520357795308e-16,
            0.8782933368848922
          ],
          [
            3.7354067703891724e-16,
            -1.5367777235912614e-15,
            1.1001457690978989
          ],
          [
            1.86860998077161e-16,
            -8.122967967553809e-16,
            1.2153296687946191
          ],
          [
            9.987872268879642e-17,
            -1.2865024943206847e-15,
            1.1656551366122598
          ],
          [
            9.375041765377993e-16,
            -2.3315113463627423e-15,
            0.9226327394206237
          ],
          [
            2.659163671187846e-16,
            -1.6465475609906373e-15,
            0.5099111346175416
          ],
          [
            -5.713598470800689e-17,
            -1.1064799609857081e-15,
            0.9999999999999999
          ]
        ],
        "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,
            1
          ]
        ],
        "folded_reduced_polarization": [
          [
            4.440892098500626e-16,
            -2.4980018054066022e-15,
            0.335518137198455
          ],
          [
            -6.106226635438361e-16,
            -1.4988010832439613e-15,
            -0.39043391598123844
          ],
          [
            2.220446049250313e-16,
            -7.771561172376096e-16,
            -0.1217066631151078
          ],
          [
            3.3306690738754696e-16,
            -1.5543122344752192e-15,
            0.10014576909789885
          ],
          [
            2.220446049250313e-16,
            -8.326672684688674e-16,
            0.21532966879461912
          ],
          [
            1.1102230246251565e-16,
            -1.27675647831893e-15,
            0.16565513661225983
          ],
          [
            8.881784197001252e-16,
            -2.3314683517128287e-15,
            -0.07736726057937626
          ],
          [
            2.220446049250313e-16,
            -1.6653345369377348e-15,
            -0.49008886538245844
          ],
          [
            -5.551115123125783e-17,
            -1.1102230246251565e-15,
            0.0
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -103.26498995629336,
          -103.43336979946974,
          -103.88612871208949,
          -104.50437419270528,
          -105.17728445279265,
          -105.83517397465661,
          -106.42370795446935,
          -106.8698247212455,
          -107.0680771856922
        ],
        "cartesian_polarizations_e_A2": [
          [
            -1.4300043012270203e-18,
            -1.1246199020832781e-17,
            2.6416779907723603e-17
          ],
          [
            9.311894636136835e-18,
            -1.5252355753575788e-17,
            -0.005339039830416234
          ],
          [
            2.27804362520658e-17,
            -2.640202087723404e-17,
            -0.009660453773592275
          ],
          [
            3.2404081070738776e-18,
            -1.5252355753575788e-17,
            -0.012205027073139028
          ],
          [
            9.286544437185795e-18,
            -1.114966512365825e-17,
            -0.012725145752402283
          ],
          [
            2.186059577006608e-17,
            -2.068238746964312e-17,
            -0.011519109275546937
          ],
          [
            1.2564851483204239e-17,
            -2.4664410728092495e-17,
            -0.00919619672932773
          ],
          [
            -4.205742325969617e-18,
            -9.894724460389356e-19,
            -0.006382479967392853
          ],
          [
            1.3540647441801615e-17,
            -3.016684286704072e-17,
            -0.003513052719810105
          ]
        ],
        "raw_reduced_polarization": [
          [
            -5.442690390374534e-17,
            -1.0230548845621826e-15,
            2.5229649231965123e-15
          ],
          [
            3.5441683223466153e-16,
            -1.3874907447281103e-15,
            -0.5099111346175415
          ],
          [
            8.670383814319358e-16,
            -2.401764042298343e-15,
            -0.9226327394206226
          ],
          [
            1.233320630583393e-16,
            -1.3874907447281103e-15,
            -1.1656551366122598
          ],
          [
            3.5345198699533934e-16,
            -1.0142732975702325e-15,
            -1.215329668794618
          ],
          [
            8.320286479104241e-16,
            -1.8814550130253014e-15,
            -1.100145769097899
          ],
          [
            4.782265085876984e-16,
            -2.243695476443242e-15,
            -0.8782933368848928
          ],
          [
            -1.6007331811732983e-16,
            -9.001126666748817e-17,
            -0.6095660840187619
          ],
          [
            5.153659443381165e-16,
            -2.7442459349843955e-15,
            -0.33551813719845514
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -5.442690390374534e-17,
            -1.0230548845621826e-15,
            1.0000000000000024
          ],
          [
            3.5441683223466153e-16,
            -1.3874907447281103e-15,
            1.4900888653824584
          ],
          [
            8.670383814319358e-16,
            -2.401764042298343e-15,
            1.0773672605793774
          ],
          [
            1.2333206305833928e-16,
            -1.3874907447281103e-15,
            0.8343448633877402
          ],
          [
            3.5345198699533934e-16,
            -1.0142732975702325e-15,
            0.784670331205382
          ],
          [
            8.320286479104241e-16,
            -1.8814550130253014e-15,
            0.8998542309021009
          ],
          [
            4.782265085876984e-16,
            -2.243695476443242e-15,
            1.1217066631151071
          ],
          [
            -1.6007331811732986e-16,
            -9.001126666748809e-17,
            1.390433915981238
          ],
          [
            5.153659443381165e-16,
            -2.7442459349843955e-15,
            1.6644818628015448
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          1
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          -5.822273378877504e-16,
          2.897923707343523e-16,
          -0.33551813719845525
        ],
        "actual_opposite_endpoint_branch_residual": 3.2264685731858664e-15
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            4.679553684717365e-16,
            -2.5027522927057687e-15,
            0.3355181371984551
          ],
          [
            -6.041340757006583e-16,
            -1.4884789951355362e-15,
            0.6095660840187616
          ],
          [
            2.100632314259026e-16,
            -7.859520357795308e-16,
            0.8782933368848922
          ],
          [
            3.7354067703891724e-16,
            -1.5367777235912614e-15,
            1.1001457690978989
          ],
          [
            1.86860998077161e-16,
            -8.122967967553809e-16,
            1.2153296687946191
          ],
          [
            9.987872268879642e-17,
            -1.2865024943206847e-15,
            1.1656551366122598
          ],
          [
            9.375041765377993e-16,
            -2.3315113463627423e-15,
            0.9226327394206237
          ],
          [
            2.6591636711878455e-16,
            -1.6465475609906373e-15,
            0.5099111346175416
          ],
          [
            -5.713598470800692e-17,
            -1.1064799609857081e-15,
            -8.906547326038141e-17
          ],
          [
            3.5441683223466153e-16,
            -1.3874907447281103e-15,
            -0.5099111346175415
          ],
          [
            8.670383814319358e-16,
            -2.401764042298343e-15,
            -0.9226327394206226
          ],
          [
            1.233320630583393e-16,
            -1.3874907447281103e-15,
            -1.1656551366122598
          ],
          [
            3.5345198699533934e-16,
            -1.0142732975702325e-15,
            -1.215329668794618
          ],
          [
            8.320286479104241e-16,
            -1.8814550130253014e-15,
            -1.100145769097899
          ],
          [
            4.782265085876984e-16,
            -2.243695476443242e-15,
            -0.8782933368848928
          ],
          [
            -1.6007331811732983e-16,
            -9.001126666748817e-17,
            -0.6095660840187619
          ],
          [
            5.153659443381165e-16,
            -2.7442459349843955e-15,
            -0.33551813719845514
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            4.679553684717365e-16,
            -2.5027522927057687e-15,
            0.3355181371984551
          ],
          [
            -6.041340757006582e-16,
            -1.4884789951355362e-15,
            0.6095660840187616
          ],
          [
            2.1006323142590259e-16,
            -7.859520357795308e-16,
            0.8782933368848922
          ],
          [
            3.7354067703891724e-16,
            -1.5367777235912614e-15,
            1.1001457690978989
          ],
          [
            1.86860998077161e-16,
            -8.122967967553809e-16,
            1.2153296687946191
          ],
          [
            9.987872268879642e-17,
            -1.2865024943206847e-15,
            1.1656551366122598
          ],
          [
            9.375041765377993e-16,
            -2.3315113463627423e-15,
            0.9226327394206237
          ],
          [
            2.659163671187846e-16,
            -1.6465475609906373e-15,
            0.5099111346175416
          ],
          [
            -5.713598470800689e-17,
            -1.1064799609857081e-15,
            0.9999999999999999
          ],
          [
            3.5441683223466153e-16,
            -1.3874907447281103e-15,
            1.4900888653824587
          ],
          [
            8.670383814319358e-16,
            -2.401764042298343e-15,
            1.0773672605793774
          ],
          [
            1.2333206305833928e-16,
            -1.3874907447281103e-15,
            0.8343448633877402
          ],
          [
            3.5345198699533934e-16,
            -1.0142732975702325e-15,
            0.784670331205382
          ],
          [
            8.320286479104241e-16,
            -1.8814550130253014e-15,
            0.8998542309021009
          ],
          [
            4.782265085876984e-16,
            -2.243695476443242e-15,
            1.1217066631151074
          ],
          [
            -1.6007331811732986e-16,
            -9.001126666748809e-17,
            1.3904339159812382
          ],
          [
            5.153659443381165e-16,
            -2.7442459349843955e-15,
            1.6644818628015448
          ]
        ],
        "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,
            1
          ],
          [
            0,
            0,
            2
          ],
          [
            0,
            0,
            2
          ],
          [
            0,
            0,
            2
          ],
          [
            0,
            0,
            2
          ],
          [
            0,
            0,
            2
          ],
          [
            0,
            0,
            2
          ],
          [
            0,
            0,
            2
          ],
          [
            0,
            0,
            2
          ]
        ],
        "folded_reduced_polarization": [
          [
            4.440892098500626e-16,
            -2.4980018054066022e-15,
            0.335518137198455
          ],
          [
            -6.106226635438361e-16,
            -1.4988010832439613e-15,
            -0.39043391598123844
          ],
          [
            2.220446049250313e-16,
            -7.771561172376096e-16,
            -0.1217066631151078
          ],
          [
            3.3306690738754696e-16,
            -1.5543122344752192e-15,
            0.10014576909789885
          ],
          [
            2.220446049250313e-16,
            -8.326672684688674e-16,
            0.21532966879461912
          ],
          [
            1.1102230246251565e-16,
            -1.27675647831893e-15,
            0.16565513661225983
          ],
          [
            8.881784197001252e-16,
            -2.3314683517128287e-15,
            -0.07736726057937626
          ],
          [
            2.220446049250313e-16,
            -1.6653345369377348e-15,
            -0.49008886538245844
          ],
          [
            -5.551115123125783e-17,
            -1.1102230246251565e-15,
            0.0
          ],
          [
            3.3306690738754696e-16,
            -1.3877787807814457e-15,
            0.49008886538245866
          ],
          [
            8.881784197001252e-16,
            -2.3869795029440866e-15,
            0.07736726057937737
          ],
          [
            1.1102230246251565e-16,
            -1.3877787807814457e-15,
            -0.16565513661225983
          ],
          [
            3.3306690738754696e-16,
            -9.992007221626409e-16,
            -0.215329668794618
          ],
          [
            7.771561172376096e-16,
            -1.887379141862766e-15,
            -0.10014576909789907
          ],
          [
            4.440892098500626e-16,
            -2.220446049250313e-15,
            0.12170666311510736
          ],
          [
            -1.6653345369377348e-16,
            -1.1102230246251565e-16,
            0.3904339159812382
          ],
          [
            5.551115123125783e-16,
            -2.7200464103316335e-15,
            -0.33551813719845525
          ]
        ]
      },
      "incoming_structure_ids": [
        "incoming_01_000",
        "incoming_01_001",
        "incoming_01_002",
        "incoming_01_003",
        "incoming_01_004",
        "incoming_01_005",
        "incoming_01_006",
        "incoming_01_007",
        "incoming_01_008"
      ],
      "reflected_structure_ids": [
        "reflected_01_001",
        "reflected_01_002",
        "reflected_01_003",
        "reflected_01_004",
        "reflected_01_005",
        "reflected_01_006",
        "reflected_01_007",
        "reflected_01_008"
      ],
      "positive_extension_structure_ids": [
        "extension_plus_01_000",
        "extension_plus_01_001",
        "extension_plus_01_002",
        "extension_plus_01_003"
      ],
      "negative_extension_structure_ids": [
        "extension_minus_01_000",
        "extension_minus_01_001",
        "extension_minus_01_002",
        "extension_minus_01_003"
      ],
      "extension": {
        "enabled": true,
        "fraction_beyond_polar_endpoint": 0.35,
        "images_per_side": 4,
        "construction": "continue fractional atomic displacements and symmetric log strain beyond +P; reflect these structures about N for the -P side",
        "positive_path_coordinates": [
          1.35,
          1.2625,
          1.175,
          1.0875
        ],
        "negative_path_coordinates": [
          -1.0875,
          -1.175,
          -1.2625,
          -1.35
        ]
      },
      "branch_coordinates": [
        1.35,
        1.2625,
        1.175,
        1.0875,
        1.0,
        0.875,
        0.75,
        0.625,
        0.5,
        0.375,
        0.25,
        0.125,
        0.0,
        -0.125,
        -0.25,
        -0.375,
        -0.5,
        -0.625,
        -0.75,
        -0.875,
        -1.0,
        -1.0875,
        -1.175,
        -1.2625,
        -1.35
      ],
      "parent": {
        "candidate_id": "inversion_parent_endpoint_00",
        "source": "same_species_inversion_center_projection_from_endpoint",
        "spacegroup": "Pmmn",
        "spacegroup_number": 59,
        "pointgroup": "mmm",
        "has_inversion": true,
        "is_polar_point_group": false,
        "nonpolar_parent_hypothesis": true,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.0
        ],
        "formal_class": [
          0.0,
          0.0,
          0.0
        ],
        "target_residual": 9.472992722983578e-16,
        "parent_symmetrization_rmsd_A": 0.3905317834213815,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -103.26498995629336,
        "reduced_polarization": [
          8.300560438537244e-16,
          4.215161756136031e-16,
          1.7523409786620924e-16
        ],
        "cartesian_polarization_e_A2": [
          2.1808767867257443e-17,
          4.6336270643774544e-18,
          1.8347938780675582e-18
        ],
        "ranking_score": 0.3905317834213834
      }
    }
  ],
  "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": 70,
      "full_response": 25,
      "energy_polarization": 45
    },
    "model_evaluations_for_recovery_and_path_properties": {
      "total": 95,
      "full_response": 50,
      "energy_polarization": 45
    },
    "elapsed_seconds": 255.16193055099575
  }
}
