{
  "schema": "ferrofinder.endpoint_parent_recovery.v4_variable_cell",
  "status": "complete",
  "input_atom_count": 28,
  "input_formula": "H8O16S4",
  "input_spacegroup": "Cc",
  "input_pointgroup": "m",
  "input_is_polar_point_group": true,
  "input_energy_eV": -150.3762291196781,
  "input_cartesian_polarization_e_A2": [
    -0.008680120684424055,
    -2.2306392397283113e-17,
    -0.006765754278951063
  ],
  "input_reduced_polarization": [
    -0.35225289770624046,
    -1.5575840844983896e-15,
    -0.4188276055531586
  ],
  "input_formal_targets": [
    {
      "orbit_id": 0,
      "representative_formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        -0.5,
        0.0,
        -0.5
      ]
    },
    {
      "orbit_id": 1,
      "representative_formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        -0.5
      ]
    },
    {
      "orbit_id": 2,
      "representative_formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        -0.5,
        0.0,
        0.0
      ]
    },
    {
      "orbit_id": 3,
      "representative_formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "target_reduced_polarization": [
        -0.5,
        -0.5,
        -0.5
      ]
    },
    {
      "orbit_id": 4,
      "representative_formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ]
    },
    {
      "orbit_id": 5,
      "representative_formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        -0.5,
        -0.5
      ]
    },
    {
      "orbit_id": 6,
      "representative_formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        -0.5,
        -0.5,
        0.0
      ]
    },
    {
      "orbit_id": 7,
      "representative_formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        -0.5,
        0.0
      ]
    }
  ],
  "parent_candidates": [
    {
      "candidate_id": "inversion_parent_endpoint_00",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "P-1",
      "spacegroup_number": 2,
      "pointgroup": "-1",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 3.845089323296571e-15,
      "parent_symmetrization_rmsd_A": 0.6797384836434879,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -126.91734363836476,
      "reduced_polarization": [
        -3.2176302051205835e-15,
        1.9228711587240903e-15,
        8.568163596547558e-16
      ],
      "cartesian_polarization_e_A2": [
        -8.077173982505893e-17,
        2.753772269683356e-17,
        5.771203586464054e-17
      ],
      "ranking_score": 0.6797384836434955
    },
    {
      "candidate_id": "inversion_parent_endpoint_01",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "P-1",
      "spacegroup_number": 2,
      "pointgroup": "-1",
      "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": 9.434433819301456e-15,
      "parent_symmetrization_rmsd_A": 0.679738483643488,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -126.91734363836474,
      "reduced_polarization": [
        -3.975493630048677e-15,
        -4.61138402502525e-15,
        -7.206880688755946e-15
      ],
      "cartesian_polarization_e_A2": [
        -9.717719164444914e-17,
        -6.604031370152486e-17,
        -1.3965559367679878e-16
      ],
      "ranking_score": 0.6797384836435069
    },
    {
      "candidate_id": "inversion_parent_endpoint_02",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "C2/c",
      "spacegroup_number": 15,
      "pointgroup": "2/m",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 1.1199062502681926e-14,
      "parent_symmetrization_rmsd_A": 0.8784452770482531,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -125.4404293241079,
      "reduced_polarization": [
        9.586066412041129e-15,
        3.720814138062991e-15,
        4.436425794815445e-15
      ],
      "cartesian_polarization_e_A2": [
        2.3842310973231126e-16,
        5.328633043122087e-17,
        6.444998929046153e-18
      ],
      "ranking_score": 0.8784452770482756
    },
    {
      "candidate_id": "bec_projection_00",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cc",
      "spacegroup_number": 9,
      "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": 1.5431788205566627e-05,
      "parent_symmetrization_rmsd_A": 0.02942824423002309,
      "parent_cell_rmsd_A": 0.041045310169658,
      "energy_eV": -149.80132324688725,
      "reduced_polarization": [
        -0.4999859831154504,
        4.253776268878606e-15,
        -0.4999935449992452
      ],
      "cartesian_polarization_e_A2": [
        -0.012380115354970167,
        6.495397924644464e-17,
        -0.0072509364162873504
      ],
      "ranking_score": 0.5397204353488487
    },
    {
      "candidate_id": "inversion_parent_bec_00_00",
      "source": "same_species_inversion_center_projection_after_BEC",
      "spacegroup": "C2/c",
      "spacegroup_number": 15,
      "pointgroup": "2/m",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        -0.5,
        0.0,
        -0.5
      ],
      "formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_residual": 0.70710678118654,
      "parent_symmetrization_rmsd_A": 0.8784567955302923,
      "parent_cell_rmsd_A": 0.041045310169658,
      "energy_eV": -125.44123411039676,
      "reduced_polarization": [
        6.256816265701369e-15,
        4.802290260192318e-15,
        4.292407471839628e-15
      ],
      "cartesian_polarization_e_A2": [
        1.5544362261373896e-16,
        6.908722306831199e-17,
        4.0364859512282146e-17
      ],
      "ranking_score": 2.302931685445787
    },
    {
      "candidate_id": "bec_projection_01",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cc",
      "spacegroup_number": 9,
      "pointgroup": "m",
      "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": 8.989221122792885e-07,
      "parent_symmetrization_rmsd_A": 0.07784156295999603,
      "parent_cell_rmsd_A": 0.10115026183992194,
      "energy_eV": -144.7839478034428,
      "reduced_polarization": [
        -3.151894245621376e-07,
        -2.7994458129680356e-15,
        -0.4999991581469305
      ],
      "cartesian_polarization_e_A2": [
        0.00022921327897073502,
        1.271352391666536e-16,
        -0.012653014209117762
      ],
      "ranking_score": 0.6031309262642011
    },
    {
      "candidate_id": "bec_projection_02",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cc",
      "spacegroup_number": 9,
      "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": 6.253037719124905e-05,
      "parent_symmetrization_rmsd_A": 0.09880901366836431,
      "parent_cell_rmsd_A": 0.06472597637919596,
      "energy_eV": -141.88564496787114,
      "reduced_polarization": [
        -0.49995084948037516,
        -4.620119142985121e-15,
        3.8655846805987875e-05
      ],
      "cartesian_polarization_e_A2": [
        -0.012484240280147572,
        -3.510557794394037e-16,
        0.0055321129456498
      ],
      "ranking_score": 0.6151155685175458
    },
    {
      "candidate_id": "bec_projection_03",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        -0.5,
        -0.5,
        -0.5
      ],
      "formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "target_residual": 0.00016638703897827942,
      "parent_symmetrization_rmsd_A": 0.06587275455809231,
      "parent_cell_rmsd_A": 0.04913406093967958,
      "energy_eV": -146.9892584751757,
      "reduced_polarization": [
        -0.4998585497101905,
        -0.5000089989840617,
        -0.4999128479458726
      ],
      "cartesian_polarization_e_A2": [
        -0.012359567331154207,
        -0.007182509839787979,
        -0.007274102899724846
      ],
      "ranking_score": 0.5784890438709688
    },
    {
      "candidate_id": "bec_projection_04",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cc",
      "spacegroup_number": 9,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 0.0008217527072584599,
      "parent_symmetrization_rmsd_A": 0.08369334445920523,
      "parent_cell_rmsd_A": 0.08617951958569046,
      "energy_eV": -144.13737315661234,
      "reduced_polarization": [
        -0.00024130633567597603,
        -4.472394969967462e-15,
        0.0007855245153712526
      ],
      "cartesian_polarization_e_A2": [
        -6.352357057722509e-06,
        -6.308777643718799e-17,
        2.2500206031710706e-05
      ],
      "ranking_score": 0.6068817297701448
    },
    {
      "candidate_id": "bec_projection_05",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        -0.5,
        -0.5
      ],
      "formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_residual": 4.09253943656784e-05,
      "parent_symmetrization_rmsd_A": 0.09848063820122709,
      "parent_cell_rmsd_A": 0.10507412888820274,
      "energy_eV": -140.29872207155947,
      "reduced_polarization": [
        -2.259699612418153e-05,
        -0.49996725106886153,
        -0.4999904202724758
      ],
      "cartesian_polarization_e_A2": [
        0.0002500168588776979,
        -0.007128132834815183,
        -0.012674135062408675
      ],
      "ranking_score": 0.6248310212120092
    },
    {
      "candidate_id": "bec_projection_06",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        -0.5,
        -0.5,
        0.0
      ],
      "formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_residual": 0.00023732403270663798,
      "parent_symmetrization_rmsd_A": 0.11351180075081888,
      "parent_cell_rmsd_A": 0.06920739036197392,
      "energy_eV": -139.0574839165585,
      "reduced_polarization": [
        -0.49979681431383494,
        -0.5000816198951886,
        9.152303615577785e-05
      ],
      "cartesian_polarization_e_A2": [
        -0.012462096244175144,
        -0.007152922785394179,
        0.005512496899703665
      ],
      "ranking_score": 0.6312882964067257
    },
    {
      "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": [
        0.0,
        -0.5,
        0.0
      ],
      "formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_residual": 4.0047905063132544e-05,
      "parent_symmetrization_rmsd_A": 0.10143880845510511,
      "parent_cell_rmsd_A": 0.09075345707087593,
      "energy_eV": -139.73140608306545,
      "reduced_polarization": [
        -3.156531858136661e-05,
        -0.4999813872237351,
        -1.6156420473444575e-05
      ],
      "cartesian_polarization_e_A2": [
        1.9133677018289694e-05,
        -0.007088740497723289,
        -2.09962921371148e-05
      ],
      "ranking_score": 0.6242072685329504
    }
  ],
  "formal_branches": [
    {
      "orbit_id": 0,
      "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": [
              -0.35225289770624046,
              -1.5575840844983896e-15,
              -0.4188276055531586
            ],
            "branch_aligned_reduced_polarization": [
              -0.35225289770624046,
              -1.5575840844983896e-15,
              -0.4188276055531586
            ],
            "target_residual": 0.16857687817858133,
            "energy_eV": -150.3762291196781,
            "max_atomic_step_A": 0.05236752816937822,
            "max_log_strain_component": 0.0039170756364325385,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.1353500585683762,
            "cell_principal_stretches": [
              1.0004257367311986,
              0.9993629129994047,
              0.9951467566259442
            ],
            "cell_volume_ratio": 0.9949361621758566,
            "cell_rmsd_from_input_A": 0.04016999941928947
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.49700346300316556,
              1.2522248802908218e-14,
              -0.4975880197116309
            ],
            "branch_aligned_reduced_polarization": [
              -0.49700346300316556,
              1.2522248802908218e-14,
              -0.4975880197116309
            ],
            "target_residual": 0.0038466716632536498,
            "energy_eV": -149.8293088564493,
            "max_atomic_step_A": 0.00119308342443483,
            "max_log_strain_component": 8.978893096408738e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.1353500585683762,
            "cell_principal_stretches": [
              1.0004337686757527,
              0.999344338046127,
              0.99503913913711
            ],
            "cell_volume_ratio": 0.9948180636459479,
            "cell_rmsd_from_input_A": 0.041045310169658
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.4999859831154504,
              4.253776268878606e-15,
              -0.4999935449992452
            ],
            "branch_aligned_reduced_polarization": [
              -0.4999859831154504,
              4.253776268878606e-15,
              -0.4999935449992452
            ],
            "target_residual": 1.5431788205566627e-05,
            "energy_eV": -149.80132324688725
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_00",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cc",
        "spacegroup_number": 9,
        "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": 1.5431788205566627e-05,
        "parent_symmetrization_rmsd_A": 0.02942824423002309,
        "parent_cell_rmsd_A": 0.041045310169658,
        "energy_eV": -149.80132324688725,
        "reduced_polarization": [
          -0.4999859831154504,
          4.253776268878606e-15,
          -0.4999935449992452
        ],
        "cartesian_polarization_e_A2": [
          -0.012380115354970167,
          6.495397924644464e-17,
          -0.0072509364162873504
        ],
        "ranking_score": 0.5397204353488487
      },
      "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": [
          -150.37622911967816,
          -150.38204846193565,
          -150.3656083660322,
          -150.32697252429438,
          -150.266179009918,
          -150.1832408140191,
          -150.0781463890042,
          -149.95086018710396,
          -149.80132324688728
        ],
        "cartesian_polarizations_e_A2": [
          [
            -0.008680120684424064,
            -5.5347474569243745e-18,
            -0.006765754278951041
          ],
          [
            -0.009152242243775076,
            -1.668831530479777e-17,
            -0.006828047793544649
          ],
          [
            -0.009621904699435345,
            -9.41815673214879e-18,
            -0.006890104310897067
          ],
          [
            -0.01008895300606789,
            6.183959834089128e-17,
            -0.006951794892994817
          ],
          [
            -0.010553237975078891,
            1.1613340426917424e-16,
            -0.007012999626847136
          ],
          [
            -0.01101461893679038,
            1.152326567149703e-16,
            -0.007073608834619477
          ],
          [
            -0.011472966406837667,
            4.733931273028425e-17,
            -0.007133523972872476
          ],
          [
            -0.011928164719756254,
            1.8845025187896998e-17,
            -0.007192658110998687
          ],
          [
            -0.012380115354970158,
            4.587585127477194e-17,
            -0.007250936416287339
          ]
        ],
        "raw_reduced_polarization": [
          [
            -0.35225289770624085,
            -3.864737245307917e-16,
            -0.4188276055531579
          ],
          [
            -0.37113094825790544,
            -1.2126270090011377e-15,
            -0.4292590591306608
          ],
          [
            -0.3899030759091519,
            -7.472868418218892e-16,
            -0.4396228179225817
          ],
          [
            -0.408563050739675,
            4.183484029321474e-15,
            -0.44991122880647555
          ],
          [
            -0.4271048914096907,
            7.93228358224777e-15,
            -0.4601171175774972
          ],
          [
            -0.445522971942807,
            7.839134057034412e-15,
            -0.47023388134007105
          ],
          [
            -0.46381212837024055,
            3.0895262748165297e-15,
            -0.4802555683766362
          ],
          [
            -0.48196776372615496,
            1.0909015336700885e-15,
            -0.4901769405982211
          ],
          [
            -0.49998598311545,
            2.927645269945913e-15,
            -0.4999935449992446
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -0.35225289770624085,
            -3.864737245307917e-16,
            -0.4188276055531579
          ],
          [
            -0.37113094825790544,
            -1.2126270090011377e-15,
            -0.4292590591306608
          ],
          [
            -0.3899030759091519,
            -7.472868418218892e-16,
            -0.4396228179225817
          ],
          [
            -0.408563050739675,
            4.183484029321474e-15,
            -0.44991122880647555
          ],
          [
            -0.4271048914096907,
            7.93228358224777e-15,
            -0.4601171175774972
          ],
          [
            -0.445522971942807,
            7.839134057034412e-15,
            -0.47023388134007105
          ],
          [
            -0.46381212837024055,
            3.08952627481653e-15,
            -0.4802555683766362
          ],
          [
            -0.48196776372615496,
            1.0909015336700887e-15,
            -0.4901769405982211
          ],
          [
            -0.49998598311545,
            2.927645269945913e-15,
            -0.4999935449992446
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            -0.35225289770624085,
            -3.885780586188048e-16,
            -0.4188276055531579
          ],
          [
            -0.37113094825790544,
            -1.2212453270876722e-15,
            -0.4292590591306608
          ],
          [
            -0.3899030759091519,
            -7.216449660063518e-16,
            -0.4396228179225817
          ],
          [
            -0.408563050739675,
            4.218847493575595e-15,
            -0.44991122880647555
          ],
          [
            -0.4271048914096907,
            7.882583474838611e-15,
            -0.4601171175774972
          ],
          [
            -0.445522971942807,
            7.882583474838611e-15,
            -0.47023388134007105
          ],
          [
            -0.46381212837024055,
            3.1086244689504383e-15,
            -0.4802555683766362
          ],
          [
            -0.48196776372615496,
            1.1102230246251565e-15,
            -0.4901769405982211
          ],
          [
            -0.49998598311545,
            2.886579864025407e-15,
            -0.4999935449992446
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -149.80132324688725,
          -149.62836372667056,
          -149.43327167435467,
          -149.2161786791982,
          -148.97719768282138,
          -148.71642264883224,
          -148.43392827051377,
          -148.12976972199112,
          -147.8039824428117
        ],
        "cartesian_polarizations_e_A2": [
          [
            -0.012380115354970137,
            1.2394472885676006e-16,
            -0.007250936416287324
          ],
          [
            -0.012800096673678187,
            8.327336004668595e-17,
            -0.007292471516187683
          ],
          [
            -0.013217489702184403,
            1.1495039683164652e-16,
            -0.007332240248655266
          ],
          [
            -0.013632327260220784,
            6.740973960862993e-17,
            -0.0073701520713636915
          ],
          [
            -0.014044658307103514,
            1.1809501086282753e-16,
            -0.007406120187379103
          ],
          [
            -0.014454550350875013,
            5.753105877179375e-17,
            -0.007440059578460058
          ],
          [
            -0.014862091551361815,
            1.0041494135444511e-16,
            -0.007471885260828678
          ],
          [
            -0.015267392420522052,
            1.0270537838147185e-16,
            -0.007501510844113643
          ],
          [
            -0.015670586978311307,
            6.267133698861437e-17,
            -0.0075288475594842185
          ]
        ],
        "raw_reduced_polarization": [
          [
            -0.49998598311544923,
            8.35425519556741e-15,
            -0.49999354499924364
          ],
          [
            -0.5170181910745614,
            5.609481272119842e-15,
            -0.5093079950910054
          ],
          [
            -0.5339517879282843,
            7.859110937748452e-15,
            -0.5185211694445249
          ],
          [
            -0.5507879510211351,
            4.590149761475174e-15,
            -0.5276298596326211
          ],
          [
            -0.5675285069066521,
            8.155408772484844e-15,
            -0.5366312750377308
          ],
          [
            -0.5841760255012878,
            3.964399760250094e-15,
            -0.5455230122852966
          ],
          [
            -0.6007339044078872,
            6.978481868442465e-15,
            -0.5543030248763491
          ],
          [
            -0.617206437169957,
            7.157647304290115e-15,
            -0.562969597573687
          ],
          [
            -0.6335988598468122,
            4.376139149223899e-15,
            -0.571521329617479
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -0.49998598311544923,
            8.35425519556741e-15,
            -0.49999354499924364
          ],
          [
            -0.5170181910745614,
            5.609481272119842e-15,
            -0.5093079950910054
          ],
          [
            -0.5339517879282843,
            7.859110937748452e-15,
            -0.5185211694445249
          ],
          [
            -0.5507879510211351,
            4.590149761475174e-15,
            -0.5276298596326211
          ],
          [
            -0.5675285069066521,
            8.155408772484844e-15,
            -0.5366312750377308
          ],
          [
            -0.5841760255012878,
            3.964399760250094e-15,
            -0.5455230122852966
          ],
          [
            -0.6007339044078872,
            6.978481868442465e-15,
            -0.5543030248763491
          ],
          [
            -0.617206437169957,
            7.157647304290115e-15,
            -0.562969597573687
          ],
          [
            -0.6335988598468122,
            4.376139149223899e-15,
            -0.571521329617479
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          -0.6501620926802313,
          6.793201853020372e-15,
          -0.5868714125527015
        ],
        "actual_opposite_endpoint_branch_residual": 0.022582420773961758
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            -0.35225289770624085,
            -3.864737245307917e-16,
            -0.4188276055531579
          ],
          [
            -0.37113094825790544,
            -1.2126270090011377e-15,
            -0.4292590591306608
          ],
          [
            -0.3899030759091519,
            -7.472868418218892e-16,
            -0.4396228179225817
          ],
          [
            -0.408563050739675,
            4.183484029321474e-15,
            -0.44991122880647555
          ],
          [
            -0.4271048914096907,
            7.93228358224777e-15,
            -0.4601171175774972
          ],
          [
            -0.445522971942807,
            7.839134057034412e-15,
            -0.47023388134007105
          ],
          [
            -0.46381212837024055,
            3.0895262748165297e-15,
            -0.4802555683766362
          ],
          [
            -0.48196776372615496,
            1.0909015336700885e-15,
            -0.4901769405982211
          ],
          [
            -0.49998598311545,
            2.927645269945913e-15,
            -0.4999935449992446
          ],
          [
            -0.5170181910745614,
            5.609481272119842e-15,
            -0.5093079950910054
          ],
          [
            -0.5339517879282843,
            7.859110937748452e-15,
            -0.5185211694445249
          ],
          [
            -0.5507879510211351,
            4.590149761475174e-15,
            -0.5276298596326211
          ],
          [
            -0.5675285069066521,
            8.155408772484844e-15,
            -0.5366312750377308
          ],
          [
            -0.5841760255012878,
            3.964399760250094e-15,
            -0.5455230122852966
          ],
          [
            -0.6007339044078872,
            6.978481868442465e-15,
            -0.5543030248763491
          ],
          [
            -0.617206437169957,
            7.157647304290115e-15,
            -0.562969597573687
          ],
          [
            -0.6335988598468122,
            4.376139149223899e-15,
            -0.571521329617479
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -0.35225289770624085,
            -3.864737245307917e-16,
            -0.4188276055531579
          ],
          [
            -0.37113094825790544,
            -1.2126270090011377e-15,
            -0.4292590591306608
          ],
          [
            -0.3899030759091519,
            -7.472868418218892e-16,
            -0.4396228179225817
          ],
          [
            -0.408563050739675,
            4.183484029321474e-15,
            -0.44991122880647555
          ],
          [
            -0.4271048914096907,
            7.93228358224777e-15,
            -0.4601171175774972
          ],
          [
            -0.445522971942807,
            7.839134057034412e-15,
            -0.47023388134007105
          ],
          [
            -0.46381212837024055,
            3.08952627481653e-15,
            -0.4802555683766362
          ],
          [
            -0.48196776372615496,
            1.0909015336700887e-15,
            -0.4901769405982211
          ],
          [
            -0.49998598311545,
            2.927645269945913e-15,
            -0.4999935449992446
          ],
          [
            -0.5170181910745614,
            5.609481272119842e-15,
            -0.5093079950910054
          ],
          [
            -0.5339517879282843,
            7.859110937748452e-15,
            -0.5185211694445249
          ],
          [
            -0.5507879510211351,
            4.590149761475174e-15,
            -0.5276298596326211
          ],
          [
            -0.5675285069066521,
            8.155408772484844e-15,
            -0.5366312750377308
          ],
          [
            -0.5841760255012878,
            3.964399760250094e-15,
            -0.5455230122852966
          ],
          [
            -0.6007339044078872,
            6.978481868442465e-15,
            -0.5543030248763491
          ],
          [
            -0.617206437169957,
            7.157647304290115e-15,
            -0.562969597573687
          ],
          [
            -0.6335988598468122,
            4.376139149223899e-15,
            -0.571521329617479
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            -0.35225289770624085,
            -3.885780586188048e-16,
            -0.4188276055531579
          ],
          [
            -0.37113094825790544,
            -1.2212453270876722e-15,
            -0.4292590591306608
          ],
          [
            -0.3899030759091519,
            -7.216449660063518e-16,
            -0.4396228179225817
          ],
          [
            -0.408563050739675,
            4.218847493575595e-15,
            -0.44991122880647555
          ],
          [
            -0.4271048914096907,
            7.882583474838611e-15,
            -0.4601171175774972
          ],
          [
            -0.445522971942807,
            7.882583474838611e-15,
            -0.47023388134007105
          ],
          [
            -0.46381212837024055,
            3.1086244689504383e-15,
            -0.4802555683766362
          ],
          [
            -0.48196776372615496,
            1.1102230246251565e-15,
            -0.4901769405982211
          ],
          [
            -0.49998598311545,
            2.886579864025407e-15,
            -0.4999935449992446
          ],
          [
            0.4829818089254386,
            5.662137425588298e-15,
            0.49069200490899456
          ],
          [
            0.46604821207171565,
            7.882583474838611e-15,
            0.48147883055547513
          ],
          [
            0.4492120489788649,
            4.551914400963142e-15,
            0.4723701403673789
          ],
          [
            0.43247149309334787,
            8.104628079763643e-15,
            0.4633687249622692
          ],
          [
            0.4158239744987122,
            3.9968028886505635e-15,
            0.45447698771470335
          ],
          [
            0.3992660955921128,
            6.994405055138486e-15,
            0.4456969751236509
          ],
          [
            0.38279356283004295,
            7.105427357601002e-15,
            0.43703040242631297
          ],
          [
            0.3664011401531878,
            4.3298697960381105e-15,
            0.42847867038252097
          ]
        ]
      },
      "incoming_structure_ids": [
        "incoming_00_000",
        "incoming_00_001",
        "incoming_00_002",
        "incoming_00_003",
        "incoming_00_004",
        "incoming_00_005",
        "incoming_00_006",
        "incoming_00_007",
        "incoming_00_008"
      ],
      "reflected_structure_ids": [
        "reflected_00_001",
        "reflected_00_002",
        "reflected_00_003",
        "reflected_00_004",
        "reflected_00_005",
        "reflected_00_006",
        "reflected_00_007",
        "reflected_00_008"
      ]
    },
    {
      "orbit_id": 1,
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.0,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        -0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -0.35225289770624046,
              -1.5575840844983896e-15,
              -0.4188276055531586
            ],
            "branch_aligned_reduced_polarization": [
              -0.35225289770624046,
              -1.5575840844983896e-15,
              -0.4188276055531586
            ],
            "target_residual": 0.3614845246517155,
            "energy_eV": -150.3762291196781,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.0064853751535268395,
            "step_scale": 0.7554213825167826,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.1353500585683762,
            "cell_principal_stretches": [
              1.0089315358088242,
              1.0001329288152072,
              0.9988396870236763
            ],
            "cell_volume_ratio": 1.0078948199126627,
            "cell_rmsd_from_input_A": 0.07733103664210314
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.08274334735019809,
              -1.3490480791586765e-14,
              -0.4785675400437739
            ],
            "branch_aligned_reduced_polarization": [
              -0.08274334735019809,
              -1.3490480791586765e-14,
              -0.4785675400437739
            ],
            "target_residual": 0.0854740420858331,
            "energy_eV": -147.03454031381335,
            "max_atomic_step_A": 0.03782848735491166,
            "max_log_strain_component": 0.001944606019925633,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.1353500585683762,
            "cell_principal_stretches": [
              1.0116364703057472,
              1.0001611068367584,
              0.9984856515645228
            ],
            "cell_volume_ratio": 1.0102672349404906,
            "cell_rmsd_from_input_A": 0.10091793013419349
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.0008181388837104036,
              7.749085182483431e-16,
              -0.5009585498413369
            ],
            "branch_aligned_reduced_polarization": [
              -0.0008181388837104036,
              7.749085182483431e-16,
              -0.5009585498413369
            ],
            "target_residual": 0.0012602257858677307,
            "energy_eV": -144.79185939163813,
            "max_atomic_step_A": 0.00041696718601782156,
            "max_log_strain_component": 2.464990572743647e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.1353500585683762,
            "cell_principal_stretches": [
              1.0116648990297985,
              1.0001675434567774,
              0.9984844878077281
            ],
            "cell_volume_ratio": 1.0103009494990751,
            "cell_rmsd_from_input_A": 0.10115026183992194
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -3.151894245621376e-07,
              -2.7994458129680356e-15,
              -0.4999991581469305
            ],
            "branch_aligned_reduced_polarization": [
              -3.151894245621376e-07,
              -2.7994458129680356e-15,
              -0.4999991581469305
            ],
            "target_residual": 8.989221122792885e-07,
            "energy_eV": -144.7839478034428
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_01",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cc",
        "spacegroup_number": 9,
        "pointgroup": "m",
        "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": 8.989221122792885e-07,
        "parent_symmetrization_rmsd_A": 0.07784156295999603,
        "parent_cell_rmsd_A": 0.10115026183992194,
        "energy_eV": -144.7839478034428,
        "reduced_polarization": [
          -3.151894245621376e-07,
          -2.7994458129680356e-15,
          -0.4999991581469305
        ],
        "cartesian_polarization_e_A2": [
          0.00022921327897073502,
          1.271352391666536e-16,
          -0.012653014209117762
        ],
        "ranking_score": 0.6031309262642011
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 2,
      "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": [
              -0.35225289770624046,
              -1.5575840844983896e-15,
              -0.4188276055531586
            ],
            "branch_aligned_reduced_polarization": [
              -0.35225289770624046,
              -1.5575840844983896e-15,
              -0.4188276055531586
            ],
            "target_residual": 0.4441235969970464,
            "energy_eV": -150.3762291196781,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.002017115777684624,
            "step_scale": 0.5666374587097441,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.1353500585683762,
            "cell_principal_stretches": [
              1.001025008332168,
              1.0009732673372962,
              0.9968779303662466
            ],
            "cell_volume_ratio": 0.9988709617724547,
            "cell_rmsd_from_input_A": 0.029074204830438745
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.4152628500793063,
              2.7590539997066188e-14,
              -0.1621311769278792
            ],
            "branch_aligned_reduced_polarization": [
              -0.4152628500793063,
              2.7590539997066188e-14,
              -0.1621311769278792
            ],
            "target_residual": 0.18293961601769418,
            "energy_eV": -147.391690054548,
            "max_atomic_step_A": 0.08628933434302949,
            "max_log_strain_component": 0.0024890055481100737,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.1353500585683762,
            "cell_principal_stretches": [
              1.0016912477105275,
              1.001470819436201,
              0.993008685532612
            ],
            "cell_volume_ratio": 0.9961511158025202,
            "cell_rmsd_from_input_A": 0.06351937869007374
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.4939446087513986,
              2.5080193845635094e-14,
              0.007912918823637614
            ],
            "branch_aligned_reduced_polarization": [
              -0.4939446087513986,
              2.5080193845635094e-14,
              0.007912918823637614
            ],
            "target_residual": 0.009964037709840157,
            "energy_eV": -141.76360905398167,
            "max_atomic_step_A": 0.002605972425711061,
            "max_log_strain_component": 0.00013481165258267234,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.1353500585683762,
            "cell_principal_stretches": [
              1.001690974829456,
              1.0014375434198342,
              0.9928618764296432
            ],
            "cell_volume_ratio": 0.9959704764271111,
            "cell_rmsd_from_input_A": 0.06472597637919596
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -0.49995084948037516,
              -4.620119142985121e-15,
              3.8655846805987875e-05
            ],
            "branch_aligned_reduced_polarization": [
              -0.49995084948037516,
              -4.620119142985121e-15,
              3.8655846805987875e-05
            ],
            "target_residual": 6.253037719124905e-05,
            "energy_eV": -141.88564496787114
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_02",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cc",
        "spacegroup_number": 9,
        "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": 6.253037719124905e-05,
        "parent_symmetrization_rmsd_A": 0.09880901366836431,
        "parent_cell_rmsd_A": 0.06472597637919596,
        "energy_eV": -141.88564496787114,
        "reduced_polarization": [
          -0.49995084948037516,
          -4.620119142985121e-15,
          3.8655846805987875e-05
        ],
        "cartesian_polarization_e_A2": [
          -0.012484240280147572,
          -3.510557794394037e-16,
          0.0055321129456498
        ],
        "ranking_score": 0.6151155685175458
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 3,
      "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": [
              -0.35225289770624046,
              -1.5575840844983896e-15,
              -0.4188276055531586
            ],
            "branch_aligned_reduced_polarization": [
              -0.35225289770624046,
              -1.5543122344752192e-15,
              -0.4188276055531586
            ],
            "target_residual": 0.5276534505302081,
            "energy_eV": -150.3762291196781,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.0038090413558671005,
            "step_scale": 0.9724196593019078,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.1353500585683762,
            "cell_principal_stretches": [
              1.0022842376749974,
              0.999659961776569,
              0.9931453787924966
            ],
            "cell_volume_ratio": 0.9950754800893273,
            "cell_rmsd_from_input_A": 0.045409365795196374
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.4846855416421343,
              -0.4949793309551136,
              -0.4833679651964853
            ],
            "branch_aligned_reduced_polarization": [
              -0.4846855416421343,
              -0.4949793309551136,
              -0.4833679651964853
            ],
            "target_residual": 0.023159540888333868,
            "energy_eV": -147.17789829786025,
            "max_atomic_step_A": 0.007432089952037973,
            "max_log_strain_component": 0.00044501945993105147,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.1353500585683762,
            "cell_principal_stretches": [
              1.0022152680084038,
              0.9995743275039931,
              0.992703659915759
            ],
            "cell_volume_ratio": 0.9944792618323149,
            "cell_rmsd_from_input_A": 0.04913406093967958
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.4998585497101905,
              -0.5000089989840617,
              -0.4999128479458726
            ],
            "branch_aligned_reduced_polarization": [
              -0.4998585497101905,
              -0.5000089989840617,
              -0.4999128479458726
            ],
            "target_residual": 0.00016638703897827942,
            "energy_eV": -146.9892584751757
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_03",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          -0.5,
          -0.5,
          -0.5
        ],
        "formal_class": [
          0.5,
          0.5,
          0.5
        ],
        "target_residual": 0.00016638703897827942,
        "parent_symmetrization_rmsd_A": 0.06587275455809231,
        "parent_cell_rmsd_A": 0.04913406093967958,
        "energy_eV": -146.9892584751757,
        "reduced_polarization": [
          -0.4998585497101905,
          -0.5000089989840617,
          -0.4999128479458726
        ],
        "cartesian_polarization_e_A2": [
          -0.012359567331154207,
          -0.007182509839787979,
          -0.007274102899724846
        ],
        "ranking_score": 0.5784890438709688
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 4,
      "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": [
              -0.35225289770624046,
              -1.5575840844983896e-15,
              -0.4188276055531586
            ],
            "branch_aligned_reduced_polarization": [
              -0.35225289770624046,
              -1.5575840844983896e-15,
              -0.4188276055531586
            ],
            "target_residual": 0.5472647139326958,
            "energy_eV": -150.3762291196781,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.007138149996045275,
            "step_scale": 0.7168829650468257,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.1353500585683762,
            "cell_principal_stretches": [
              1.0083298883030392,
              1.0018808959967376,
              0.9994984389067768
            ],
            "cell_volume_ratio": 1.0097197616696945,
            "cell_rmsd_from_input_A": 0.06684838227895322
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.08268181223488257,
              -2.1935101791249066e-14,
              -0.10197069810368123
            ],
            "branch_aligned_reduced_polarization": [
              -0.08268181223488257,
              -2.1935101791249066e-14,
              -0.10197069810368123
            ],
            "target_residual": 0.13127949324321936,
            "energy_eV": -146.6307452121535,
            "max_atomic_step_A": 0.03736656762536591,
            "max_log_strain_component": 0.0020179687318213546,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.1353500585683762,
            "cell_principal_stretches": [
              1.0107144591965436,
              1.0023902303109844,
              0.9993492272444228
            ],
            "cell_volume_ratio": 1.0124709819358795,
            "cell_rmsd_from_input_A": 0.08617951958569046
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.00024130633567597603,
              -4.472394969967462e-15,
              0.0007855245153712526
            ],
            "branch_aligned_reduced_polarization": [
              -0.00024130633567597603,
              -4.472394969967462e-15,
              0.0007855245153712526
            ],
            "target_residual": 0.0008217527072584599,
            "energy_eV": -144.13737315661234
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_04",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cc",
        "spacegroup_number": 9,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.0
        ],
        "formal_class": [
          0.0,
          0.0,
          0.0
        ],
        "target_residual": 0.0008217527072584599,
        "parent_symmetrization_rmsd_A": 0.08369334445920523,
        "parent_cell_rmsd_A": 0.08617951958569046,
        "energy_eV": -144.13737315661234,
        "reduced_polarization": [
          -0.00024130633567597603,
          -4.472394969967462e-15,
          0.0007855245153712526
        ],
        "cartesian_polarization_e_A2": [
          -6.352357057722509e-06,
          -6.308777643718799e-17,
          2.2500206031710706e-05
        ],
        "ranking_score": 0.6068817297701448
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 5,
      "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": [
              -0.35225289770624046,
              -1.5575840844983896e-15,
              -0.4188276055531586
            ],
            "branch_aligned_reduced_polarization": [
              -0.35225289770624046,
              -1.5543122344752192e-15,
              -0.4188276055531586
            ],
            "target_residual": 0.6169854630075778,
            "energy_eV": -150.3762291196781,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.004819931850093041,
            "step_scale": 0.5614292921614429,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.1353500585683762,
            "cell_principal_stretches": [
              1.0072711500306073,
              0.9999539493663259,
              0.9986465172615729
            ],
            "cell_volume_ratio": 1.0058615032233245,
            "cell_rmsd_from_input_A": 0.05898230100484932
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.15063666732379216,
              -0.2685876530396134,
              -0.46203608129030965
            ],
            "branch_aligned_reduced_polarization": [
              -0.15063666732379216,
              -0.2685876530396134,
              -0.46203608129030965
            ],
            "target_residual": 0.2787191041029107,
            "energy_eV": -147.4411011041807,
            "max_atomic_step_A": 0.10095705852586462,
            "max_log_strain_component": 0.0035471026923355703,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.1353500585683762,
            "cell_principal_stretches": [
              1.012894045701921,
              0.9998649234340705,
              0.9974542179767112
            ],
            "cell_volume_ratio": 1.0101789683089726,
            "cell_rmsd_from_input_A": 0.10387137248197195
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.003619481148584168,
              -0.4930053535295258,
              -0.5064487463446277
            ],
            "branch_aligned_reduced_polarization": [
              -0.003619481148584168,
              -0.4930053535295258,
              -0.5064487463446277
            ],
            "target_residual": 0.010179000562394234,
            "energy_eV": -140.4305180550815,
            "max_atomic_step_A": 0.00315281538589711,
            "max_log_strain_component": 0.00012910428323714503,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.1353500585683762,
            "cell_principal_stretches": [
              1.0130590656363652,
              0.9998981727482449,
              0.997436772126596
            ],
            "cell_volume_ratio": 1.0103594717963518,
            "cell_rmsd_from_input_A": 0.10507412888820274
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -2.259699612418153e-05,
              -0.49996725106886153,
              -0.4999904202724758
            ],
            "branch_aligned_reduced_polarization": [
              -2.259699612418153e-05,
              -0.49996725106886153,
              -0.4999904202724758
            ],
            "target_residual": 4.09253943656784e-05,
            "energy_eV": -140.29872207155947
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_05",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          -0.5,
          -0.5
        ],
        "formal_class": [
          0.0,
          0.5,
          0.5
        ],
        "target_residual": 4.09253943656784e-05,
        "parent_symmetrization_rmsd_A": 0.09848063820122709,
        "parent_cell_rmsd_A": 0.10507412888820274,
        "energy_eV": -140.29872207155947,
        "reduced_polarization": [
          -2.259699612418153e-05,
          -0.49996725106886153,
          -0.4999904202724758
        ],
        "cartesian_polarization_e_A2": [
          0.0002500168588776979,
          -0.007128132834815183,
          -0.012674135062408675
        ],
        "ranking_score": 0.6248310212120092
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 6,
      "formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.5,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        -0.5,
        -0.5,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -0.35225289770624046,
              -1.5575840844983896e-15,
              -0.4188276055531586
            ],
            "branch_aligned_reduced_polarization": [
              -0.35225289770624046,
              -1.5543122344752192e-15,
              -0.4188276055531586
            ],
            "target_residual": 0.6687643601520593,
            "energy_eV": -150.3762291196781,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.001589679832953237,
            "step_scale": 0.446564421672459,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.1353500585683762,
            "cell_principal_stretches": [
              1.0016159314947735,
              1.000726526747574,
              0.9967740318072
            ],
            "cell_volume_ratio": 0.9991101035838745,
            "cell_rmsd_from_input_A": 0.025302096198156415
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.40235597331424094,
              -0.21937453732554033,
              -0.21640086832738453
            ],
            "branch_aligned_reduced_polarization": [
              -0.40235597331424094,
              -0.21937453732554035,
              -0.21640086832738453
            ],
            "target_residual": 0.36757902832113504,
            "energy_eV": -147.90744586533535,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.002594396463068092,
            "step_scale": 0.9448373102809676,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.1353500585683762,
            "cell_principal_stretches": [
              1.0031467932845823,
              1.0013807747674492,
              0.9918666806539532
            ],
            "cell_volume_ratio": 0.9963617342225458,
            "cell_rmsd_from_input_A": 0.06473748122039405
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.4822754771043376,
              -0.49165567164350554,
              0.005480899818544417
            ],
            "branch_aligned_reduced_polarization": [
              -0.4822754771043376,
              -0.49165567164350554,
              0.005480899818544417
            ],
            "target_residual": 0.020342733110887,
            "energy_eV": -139.24861978477543,
            "max_atomic_step_A": 0.0064010615893042655,
            "max_log_strain_component": 0.0004396855439390305,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.1353500585683762,
            "cell_principal_stretches": [
              1.003120722613003,
              1.001366792953147,
              0.991356875472905
            ],
            "cell_volume_ratio": 0.9958098333986507,
            "cell_rmsd_from_input_A": 0.06920739036197392
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -0.49979681431383494,
              -0.5000816198951886,
              9.152303615577785e-05
            ],
            "branch_aligned_reduced_polarization": [
              -0.49979681431383494,
              -0.5000816198951886,
              9.152303615577785e-05
            ],
            "target_residual": 0.00023732403270663798,
            "energy_eV": -139.0574839165585
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_06",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          -0.5,
          -0.5,
          0.0
        ],
        "formal_class": [
          0.5,
          0.5,
          0.0
        ],
        "target_residual": 0.00023732403270663798,
        "parent_symmetrization_rmsd_A": 0.11351180075081888,
        "parent_cell_rmsd_A": 0.06920739036197392,
        "energy_eV": -139.0574839165585,
        "reduced_polarization": [
          -0.49979681431383494,
          -0.5000816198951886,
          9.152303615577785e-05
        ],
        "cartesian_polarization_e_A2": [
          -0.012462096244175144,
          -0.007152922785394179,
          0.005512496899703665
        ],
        "ranking_score": 0.6312882964067257
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 7,
      "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": [
              -0.35225289770624046,
              -1.5575840844983896e-15,
              -0.4188276055531586
            ],
            "branch_aligned_reduced_polarization": [
              -0.35225289770624046,
              -1.5543122344752192e-15,
              -0.4188276055531586
            ],
            "target_residual": 0.741281773090256,
            "energy_eV": -150.3762291196781,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.005487296685470629,
            "step_scale": 0.5510880998805581,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.1353500585683762,
            "cell_principal_stretches": [
              1.0071080509634498,
              1.0012277807644114,
              0.9991262219342026
            ],
            "cell_volume_ratio": 1.0074634894978118,
            "cell_rmsd_from_input_A": 0.05304770841243406
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.14507047039577287,
              -0.26569631135582467,
              -0.1741591339530149
            ],
            "branch_aligned_reduced_polarization": [
              -0.14507047039577287,
              -0.26569631135582467,
              -0.1741591339530149
            ],
            "target_residual": 0.3259985641569325,
            "energy_eV": -147.046228128039,
            "max_atomic_step_A": 0.08540788001250413,
            "max_log_strain_component": 0.003607115183088475,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.1353500585683762,
            "cell_principal_stretches": [
              1.0121209809722296,
              1.0019178768793564,
              0.9983237383871211
            ],
            "cell_volume_ratio": 1.0123622710220652,
            "cell_rmsd_from_input_A": 0.08971081066091738
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.002651647205399482,
              -0.5014394274326966,
              0.007226416666356167
            ],
            "branch_aligned_reduced_polarization": [
              -0.002651647205399482,
              -0.5014394274326966,
              0.007226416666356167
            ],
            "target_residual": 0.007830982190740363,
            "energy_eV": -139.64800666478212,
            "max_atomic_step_A": 0.0034885094059886783,
            "max_log_strain_component": 7.506475552918492e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.1353500585683762,
            "cell_principal_stretches": [
              1.0122209143347611,
              1.001903889763842,
              0.9983186902354115
            ],
            "cell_volume_ratio": 1.0124429743171728,
            "cell_rmsd_from_input_A": 0.09075345707087593
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -3.156531858136661e-05,
              -0.4999813872237351,
              -1.6156420473444575e-05
            ],
            "branch_aligned_reduced_polarization": [
              -3.156531858136661e-05,
              -0.4999813872237351,
              -1.6156420473444575e-05
            ],
            "target_residual": 4.0047905063132544e-05,
            "energy_eV": -139.73140608306545
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_07",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          -0.5,
          0.0
        ],
        "formal_class": [
          0.0,
          0.5,
          0.0
        ],
        "target_residual": 4.0047905063132544e-05,
        "parent_symmetrization_rmsd_A": 0.10143880845510511,
        "parent_cell_rmsd_A": 0.09075345707087593,
        "energy_eV": -139.73140608306545,
        "reduced_polarization": [
          -3.156531858136661e-05,
          -0.4999813872237351,
          -1.6156420473444575e-05
        ],
        "cartesian_polarization_e_A2": [
          1.9133677018289694e-05,
          -0.007088740497723289,
          -2.09962921371148e-05
        ],
        "ranking_score": 0.6242072685329504
      },
      "branch_status": "awaiting_branch_sampling"
    }
  ],
  "sampled_polarization_branches": [
    {
      "orbit_id": 0,
      "candidate_id": "bec_projection_00",
      "formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "construction": "MACEField-BEC-parent plus variable-cell P-N-P path and symmetric log-strain continuation beyond both polar endpoints",
      "geometry_diagnostics": {
        "collision_aware": false,
        "permutations_tested": 1,
        "selected_order": [
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          10,
          11,
          12,
          13,
          14,
          15,
          16,
          17,
          18,
          19,
          20,
          21,
          22,
          23,
          24,
          25,
          26,
          27
        ],
        "endpoint_rmsd_A": 0.02942824423002309,
        "minimum_distance_A_by_image": [
          0.9833548058584708,
          0.986526912809606,
          0.9892629555661503,
          0.992003547018489,
          0.9947486219677589,
          0.9974981159522419,
          1.0002519652399384,
          1.0030101068211907,
          1.0057724784166293
        ],
        "minimum_distance_A": 0.9833548058584708,
        "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": [
          331.60274282927224,
          331.3874612510552,
          331.17231943693514,
          330.95731729617484,
          330.742454738097,
          330.52773167208136,
          330.3131480075684,
          330.09870365405607,
          329.88439852110173
        ],
        "cell_deformation_log_strain_norm": 0.005034981032593909
      },
      "parent_reduced_polarization": [
        -0.49998598311545,
        2.927645269945913e-15,
        -0.4999935449992446
      ],
      "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": [
          -150.37622911967816,
          -150.38204846193565,
          -150.3656083660322,
          -150.32697252429438,
          -150.266179009918,
          -150.1832408140191,
          -150.0781463890042,
          -149.95086018710396,
          -149.80132324688728
        ],
        "cartesian_polarizations_e_A2": [
          [
            -0.008680120684424064,
            -5.5347474569243745e-18,
            -0.006765754278951041
          ],
          [
            -0.009152242243775076,
            -1.668831530479777e-17,
            -0.006828047793544649
          ],
          [
            -0.009621904699435345,
            -9.41815673214879e-18,
            -0.006890104310897067
          ],
          [
            -0.01008895300606789,
            6.183959834089128e-17,
            -0.006951794892994817
          ],
          [
            -0.010553237975078891,
            1.1613340426917424e-16,
            -0.007012999626847136
          ],
          [
            -0.01101461893679038,
            1.152326567149703e-16,
            -0.007073608834619477
          ],
          [
            -0.011472966406837667,
            4.733931273028425e-17,
            -0.007133523972872476
          ],
          [
            -0.011928164719756254,
            1.8845025187896998e-17,
            -0.007192658110998687
          ],
          [
            -0.012380115354970158,
            4.587585127477194e-17,
            -0.007250936416287339
          ]
        ],
        "raw_reduced_polarization": [
          [
            -0.35225289770624085,
            -3.864737245307917e-16,
            -0.4188276055531579
          ],
          [
            -0.37113094825790544,
            -1.2126270090011377e-15,
            -0.4292590591306608
          ],
          [
            -0.3899030759091519,
            -7.472868418218892e-16,
            -0.4396228179225817
          ],
          [
            -0.408563050739675,
            4.183484029321474e-15,
            -0.44991122880647555
          ],
          [
            -0.4271048914096907,
            7.93228358224777e-15,
            -0.4601171175774972
          ],
          [
            -0.445522971942807,
            7.839134057034412e-15,
            -0.47023388134007105
          ],
          [
            -0.46381212837024055,
            3.0895262748165297e-15,
            -0.4802555683766362
          ],
          [
            -0.48196776372615496,
            1.0909015336700885e-15,
            -0.4901769405982211
          ],
          [
            -0.49998598311545,
            2.927645269945913e-15,
            -0.4999935449992446
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -0.35225289770624085,
            -3.864737245307917e-16,
            -0.4188276055531579
          ],
          [
            -0.37113094825790544,
            -1.2126270090011377e-15,
            -0.4292590591306608
          ],
          [
            -0.3899030759091519,
            -7.472868418218892e-16,
            -0.4396228179225817
          ],
          [
            -0.408563050739675,
            4.183484029321474e-15,
            -0.44991122880647555
          ],
          [
            -0.4271048914096907,
            7.93228358224777e-15,
            -0.4601171175774972
          ],
          [
            -0.445522971942807,
            7.839134057034412e-15,
            -0.47023388134007105
          ],
          [
            -0.46381212837024055,
            3.08952627481653e-15,
            -0.4802555683766362
          ],
          [
            -0.48196776372615496,
            1.0909015336700887e-15,
            -0.4901769405982211
          ],
          [
            -0.49998598311545,
            2.927645269945913e-15,
            -0.4999935449992446
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            -0.35225289770624085,
            -3.885780586188048e-16,
            -0.4188276055531579
          ],
          [
            -0.37113094825790544,
            -1.2212453270876722e-15,
            -0.4292590591306608
          ],
          [
            -0.3899030759091519,
            -7.216449660063518e-16,
            -0.4396228179225817
          ],
          [
            -0.408563050739675,
            4.218847493575595e-15,
            -0.44991122880647555
          ],
          [
            -0.4271048914096907,
            7.882583474838611e-15,
            -0.4601171175774972
          ],
          [
            -0.445522971942807,
            7.882583474838611e-15,
            -0.47023388134007105
          ],
          [
            -0.46381212837024055,
            3.1086244689504383e-15,
            -0.4802555683766362
          ],
          [
            -0.48196776372615496,
            1.1102230246251565e-15,
            -0.4901769405982211
          ],
          [
            -0.49998598311545,
            2.886579864025407e-15,
            -0.4999935449992446
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -149.80132324688725,
          -149.62836372667056,
          -149.43327167435467,
          -149.2161786791982,
          -148.97719768282138,
          -148.71642264883224,
          -148.43392827051377,
          -148.12976972199112,
          -147.8039824428117
        ],
        "cartesian_polarizations_e_A2": [
          [
            -0.012380115354970137,
            1.2394472885676006e-16,
            -0.007250936416287324
          ],
          [
            -0.012800096673678187,
            8.327336004668595e-17,
            -0.007292471516187683
          ],
          [
            -0.013217489702184403,
            1.1495039683164652e-16,
            -0.007332240248655266
          ],
          [
            -0.013632327260220784,
            6.740973960862993e-17,
            -0.0073701520713636915
          ],
          [
            -0.014044658307103514,
            1.1809501086282753e-16,
            -0.007406120187379103
          ],
          [
            -0.014454550350875013,
            5.753105877179375e-17,
            -0.007440059578460058
          ],
          [
            -0.014862091551361815,
            1.0041494135444511e-16,
            -0.007471885260828678
          ],
          [
            -0.015267392420522052,
            1.0270537838147185e-16,
            -0.007501510844113643
          ],
          [
            -0.015670586978311307,
            6.267133698861437e-17,
            -0.0075288475594842185
          ]
        ],
        "raw_reduced_polarization": [
          [
            -0.49998598311544923,
            8.35425519556741e-15,
            -0.49999354499924364
          ],
          [
            -0.5170181910745614,
            5.609481272119842e-15,
            -0.5093079950910054
          ],
          [
            -0.5339517879282843,
            7.859110937748452e-15,
            -0.5185211694445249
          ],
          [
            -0.5507879510211351,
            4.590149761475174e-15,
            -0.5276298596326211
          ],
          [
            -0.5675285069066521,
            8.155408772484844e-15,
            -0.5366312750377308
          ],
          [
            -0.5841760255012878,
            3.964399760250094e-15,
            -0.5455230122852966
          ],
          [
            -0.6007339044078872,
            6.978481868442465e-15,
            -0.5543030248763491
          ],
          [
            -0.617206437169957,
            7.157647304290115e-15,
            -0.562969597573687
          ],
          [
            -0.6335988598468122,
            4.376139149223899e-15,
            -0.571521329617479
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -0.49998598311544923,
            8.35425519556741e-15,
            -0.49999354499924364
          ],
          [
            -0.5170181910745614,
            5.609481272119842e-15,
            -0.5093079950910054
          ],
          [
            -0.5339517879282843,
            7.859110937748452e-15,
            -0.5185211694445249
          ],
          [
            -0.5507879510211351,
            4.590149761475174e-15,
            -0.5276298596326211
          ],
          [
            -0.5675285069066521,
            8.155408772484844e-15,
            -0.5366312750377308
          ],
          [
            -0.5841760255012878,
            3.964399760250094e-15,
            -0.5455230122852966
          ],
          [
            -0.6007339044078872,
            6.978481868442465e-15,
            -0.5543030248763491
          ],
          [
            -0.617206437169957,
            7.157647304290115e-15,
            -0.562969597573687
          ],
          [
            -0.6335988598468122,
            4.376139149223899e-15,
            -0.571521329617479
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          -0.6501620926802313,
          6.793201853020372e-15,
          -0.5868714125527015
        ],
        "actual_opposite_endpoint_branch_residual": 0.022582420773961758
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            -0.35225289770624085,
            -3.864737245307917e-16,
            -0.4188276055531579
          ],
          [
            -0.37113094825790544,
            -1.2126270090011377e-15,
            -0.4292590591306608
          ],
          [
            -0.3899030759091519,
            -7.472868418218892e-16,
            -0.4396228179225817
          ],
          [
            -0.408563050739675,
            4.183484029321474e-15,
            -0.44991122880647555
          ],
          [
            -0.4271048914096907,
            7.93228358224777e-15,
            -0.4601171175774972
          ],
          [
            -0.445522971942807,
            7.839134057034412e-15,
            -0.47023388134007105
          ],
          [
            -0.46381212837024055,
            3.0895262748165297e-15,
            -0.4802555683766362
          ],
          [
            -0.48196776372615496,
            1.0909015336700885e-15,
            -0.4901769405982211
          ],
          [
            -0.49998598311545,
            2.927645269945913e-15,
            -0.4999935449992446
          ],
          [
            -0.5170181910745614,
            5.609481272119842e-15,
            -0.5093079950910054
          ],
          [
            -0.5339517879282843,
            7.859110937748452e-15,
            -0.5185211694445249
          ],
          [
            -0.5507879510211351,
            4.590149761475174e-15,
            -0.5276298596326211
          ],
          [
            -0.5675285069066521,
            8.155408772484844e-15,
            -0.5366312750377308
          ],
          [
            -0.5841760255012878,
            3.964399760250094e-15,
            -0.5455230122852966
          ],
          [
            -0.6007339044078872,
            6.978481868442465e-15,
            -0.5543030248763491
          ],
          [
            -0.617206437169957,
            7.157647304290115e-15,
            -0.562969597573687
          ],
          [
            -0.6335988598468122,
            4.376139149223899e-15,
            -0.571521329617479
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -0.35225289770624085,
            -3.864737245307917e-16,
            -0.4188276055531579
          ],
          [
            -0.37113094825790544,
            -1.2126270090011377e-15,
            -0.4292590591306608
          ],
          [
            -0.3899030759091519,
            -7.472868418218892e-16,
            -0.4396228179225817
          ],
          [
            -0.408563050739675,
            4.183484029321474e-15,
            -0.44991122880647555
          ],
          [
            -0.4271048914096907,
            7.93228358224777e-15,
            -0.4601171175774972
          ],
          [
            -0.445522971942807,
            7.839134057034412e-15,
            -0.47023388134007105
          ],
          [
            -0.46381212837024055,
            3.08952627481653e-15,
            -0.4802555683766362
          ],
          [
            -0.48196776372615496,
            1.0909015336700887e-15,
            -0.4901769405982211
          ],
          [
            -0.49998598311545,
            2.927645269945913e-15,
            -0.4999935449992446
          ],
          [
            -0.5170181910745614,
            5.609481272119842e-15,
            -0.5093079950910054
          ],
          [
            -0.5339517879282843,
            7.859110937748452e-15,
            -0.5185211694445249
          ],
          [
            -0.5507879510211351,
            4.590149761475174e-15,
            -0.5276298596326211
          ],
          [
            -0.5675285069066521,
            8.155408772484844e-15,
            -0.5366312750377308
          ],
          [
            -0.5841760255012878,
            3.964399760250094e-15,
            -0.5455230122852966
          ],
          [
            -0.6007339044078872,
            6.978481868442465e-15,
            -0.5543030248763491
          ],
          [
            -0.617206437169957,
            7.157647304290115e-15,
            -0.562969597573687
          ],
          [
            -0.6335988598468122,
            4.376139149223899e-15,
            -0.571521329617479
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            -0.35225289770624085,
            -3.885780586188048e-16,
            -0.4188276055531579
          ],
          [
            -0.37113094825790544,
            -1.2212453270876722e-15,
            -0.4292590591306608
          ],
          [
            -0.3899030759091519,
            -7.216449660063518e-16,
            -0.4396228179225817
          ],
          [
            -0.408563050739675,
            4.218847493575595e-15,
            -0.44991122880647555
          ],
          [
            -0.4271048914096907,
            7.882583474838611e-15,
            -0.4601171175774972
          ],
          [
            -0.445522971942807,
            7.882583474838611e-15,
            -0.47023388134007105
          ],
          [
            -0.46381212837024055,
            3.1086244689504383e-15,
            -0.4802555683766362
          ],
          [
            -0.48196776372615496,
            1.1102230246251565e-15,
            -0.4901769405982211
          ],
          [
            -0.49998598311545,
            2.886579864025407e-15,
            -0.4999935449992446
          ],
          [
            0.4829818089254386,
            5.662137425588298e-15,
            0.49069200490899456
          ],
          [
            0.46604821207171565,
            7.882583474838611e-15,
            0.48147883055547513
          ],
          [
            0.4492120489788649,
            4.551914400963142e-15,
            0.4723701403673789
          ],
          [
            0.43247149309334787,
            8.104628079763643e-15,
            0.4633687249622692
          ],
          [
            0.4158239744987122,
            3.9968028886505635e-15,
            0.45447698771470335
          ],
          [
            0.3992660955921128,
            6.994405055138486e-15,
            0.4456969751236509
          ],
          [
            0.38279356283004295,
            7.105427357601002e-15,
            0.43703040242631297
          ],
          [
            0.3664011401531878,
            4.3298697960381105e-15,
            0.42847867038252097
          ]
        ]
      },
      "incoming_structure_ids": [
        "incoming_00_000",
        "incoming_00_001",
        "incoming_00_002",
        "incoming_00_003",
        "incoming_00_004",
        "incoming_00_005",
        "incoming_00_006",
        "incoming_00_007",
        "incoming_00_008"
      ],
      "reflected_structure_ids": [
        "reflected_00_001",
        "reflected_00_002",
        "reflected_00_003",
        "reflected_00_004",
        "reflected_00_005",
        "reflected_00_006",
        "reflected_00_007",
        "reflected_00_008"
      ],
      "positive_extension_structure_ids": [
        "extension_plus_00_000",
        "extension_plus_00_001",
        "extension_plus_00_002",
        "extension_plus_00_003"
      ],
      "negative_extension_structure_ids": [
        "extension_minus_00_000",
        "extension_minus_00_001",
        "extension_minus_00_002",
        "extension_minus_00_003"
      ],
      "extension": {
        "enabled": true,
        "fraction_beyond_polar_endpoint": 0.35,
        "images_per_side": 4,
        "construction": "continue fractional atomic displacements and symmetric log strain beyond +P; reflect these structures about N for the -P side",
        "positive_path_coordinates": [
          1.35,
          1.2625,
          1.175,
          1.0875
        ],
        "negative_path_coordinates": [
          -1.0875,
          -1.175,
          -1.2625,
          -1.35
        ]
      },
      "branch_coordinates": [
        1.35,
        1.2625,
        1.175,
        1.0875,
        1.0,
        0.875,
        0.75,
        0.625,
        0.5,
        0.375,
        0.25,
        0.125,
        0.0,
        -0.125,
        -0.25,
        -0.375,
        -0.5,
        -0.625,
        -0.75,
        -0.875,
        -1.0,
        -1.0875,
        -1.175,
        -1.2625,
        -1.35
      ],
      "parent": {
        "candidate_id": "bec_projection_00",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cc",
        "spacegroup_number": 9,
        "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": 1.5431788205566627e-05,
        "parent_symmetrization_rmsd_A": 0.02942824423002309,
        "parent_cell_rmsd_A": 0.041045310169658,
        "energy_eV": -149.80132324688725,
        "reduced_polarization": [
          -0.4999859831154504,
          4.253776268878606e-15,
          -0.4999935449992452
        ],
        "cartesian_polarization_e_A2": [
          -0.012380115354970167,
          6.495397924644464e-17,
          -0.0072509364162873504
        ],
        "ranking_score": 0.5397204353488487
      }
    }
  ],
  "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": 56,
      "full_response": 22,
      "energy_polarization": 34
    },
    "model_evaluations_for_recovery_and_path_properties": {
      "total": 81,
      "full_response": 47,
      "energy_polarization": 34
    },
    "elapsed_seconds": 602.8870532389847
  }
}
