{
  "schema": "ferrofinder.endpoint_parent_recovery.v4_variable_cell",
  "status": "complete",
  "input_atom_count": 28,
  "input_formula": "Li4Mn4O16P4",
  "input_spacegroup": "Pna2_1",
  "input_pointgroup": "mm2",
  "input_is_polar_point_group": true,
  "input_energy_eV": -191.1157371973619,
  "input_cartesian_polarization_e_A2": [
    -8.93805385105057e-18,
    3.0828009810336454e-18,
    -0.00783305958192582
  ],
  "input_reduced_polarization": [
    -2.812484176727314e-16,
    1.8215345741382065e-16,
    -0.4738647820989374
  ],
  "input_formal_targets": [
    {
      "orbit_id": 0,
      "representative_formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        -0.5
      ]
    },
    {
      "orbit_id": 1,
      "representative_formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ]
    },
    {
      "orbit_id": 2,
      "representative_formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        -0.5,
        0.0,
        -0.5
      ]
    },
    {
      "orbit_id": 3,
      "representative_formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        -0.5
      ]
    },
    {
      "orbit_id": 4,
      "representative_formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        -0.5,
        0.0,
        0.0
      ]
    },
    {
      "orbit_id": 5,
      "representative_formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.0
      ]
    },
    {
      "orbit_id": 6,
      "representative_formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "target_reduced_polarization": [
        -0.5,
        0.5,
        -0.5
      ]
    },
    {
      "orbit_id": 7,
      "representative_formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        -0.5,
        0.5,
        0.0
      ]
    }
  ],
  "parent_candidates": [
    {
      "candidate_id": "inversion_parent_endpoint_00",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "Pnma",
      "spacegroup_number": 62,
      "pointgroup": "mmm",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 2.9680162135398697e-15,
      "parent_symmetrization_rmsd_A": 0.49061406323375295,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -191.14847436752288,
      "reduced_polarization": [
        -1.9921762918485143e-16,
        1.4608951785873539e-15,
        -2.5758916625583724e-15
      ],
      "cartesian_polarization_e_A2": [
        -6.331121477827487e-18,
        2.472447766667924e-17,
        -4.257989542931035e-17
      ],
      "ranking_score": 0.4906140632337589
    },
    {
      "candidate_id": "bec_projection_00",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Pna2_1",
      "spacegroup_number": 33,
      "pointgroup": "mm2",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        -0.5
      ],
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_residual": 2.5097748676705667e-05,
      "parent_symmetrization_rmsd_A": 0.0029409816178110944,
      "parent_cell_rmsd_A": 0.002188130975716242,
      "energy_eV": -191.10270436638487,
      "reduced_polarization": [
        5.307074172597019e-16,
        5.8539347451325645e-16,
        -0.4999749022513233
      ],
      "cartesian_polarization_e_A2": [
        2.0513837923434482e-17,
        1.3544923225654824e-17,
        -0.008263998886060536
      ],
      "ranking_score": 0.5035382098590936
    },
    {
      "candidate_id": "inversion_parent_bec_00_00",
      "source": "same_species_inversion_center_projection_after_BEC",
      "spacegroup": "Pnma",
      "spacegroup_number": 62,
      "pointgroup": "mmm",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        -0.5
      ],
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_residual": 0.49999999999999967,
      "parent_symmetrization_rmsd_A": 0.4906142677862359,
      "parent_cell_rmsd_A": 0.002188130975716242,
      "energy_eV": -191.14682620317242,
      "reduced_polarization": [
        7.602714614823095e-16,
        -2.714248889293833e-16,
        3.165291584548896e-16
      ],
      "cartesian_polarization_e_A2": [
        2.4153389813076085e-17,
        -4.590798406252475e-18,
        5.231855841359802e-18
      ],
      "ranking_score": 1.4911613005301643
    },
    {
      "candidate_id": "bec_projection_01",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Pna2_1",
      "spacegroup_number": 33,
      "pointgroup": "mm2",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 1.0027692701203884e-05,
      "parent_symmetrization_rmsd_A": 0.05357737380139948,
      "parent_cell_rmsd_A": 0.039363585423607815,
      "energy_eV": -189.72895568406935,
      "reduced_polarization": [
        5.565060504972579e-16,
        -2.3008411504058175e-16,
        1.0027692701203884e-05
      ],
      "cartesian_polarization_e_A2": [
        1.7792921519615804e-17,
        -3.936579467661477e-18,
        1.6600064733818317e-07
      ],
      "ranking_score": 0.5634383255427038
    },
    {
      "candidate_id": "bec_projection_02",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Pc",
      "spacegroup_number": 7,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        -0.5,
        0.0,
        -0.5
      ],
      "formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_residual": 0.0004244021103984908,
      "parent_symmetrization_rmsd_A": 0.09981242318093726,
      "parent_cell_rmsd_A": 0.09163792239350453,
      "energy_eV": -184.24702743039882,
      "reduced_polarization": [
        -0.49994234814717364,
        -5.445372440071823e-16,
        -0.4995795319094433
      ],
      "cartesian_polarization_e_A2": [
        -0.015974466461401958,
        -1.6109195962015764e-16,
        -0.008455409675464499
      ],
      "ranking_score": 0.6235707080001104
    },
    {
      "candidate_id": "bec_projection_03",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Pc",
      "spacegroup_number": 7,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.5,
        -0.5
      ],
      "formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_residual": 1.5919970777135915e-05,
      "parent_symmetrization_rmsd_A": 0.05699877940091624,
      "parent_cell_rmsd_A": 0.021034128366430288,
      "energy_eV": -189.19648945844136,
      "reduced_polarization": [
        7.370030769383154e-16,
        0.49998774278550245,
        -0.5000101590433755
      ],
      "cartesian_polarization_e_A2": [
        -2.1257058705449455e-17,
        0.008411565079925423,
        -0.008218954382368387
      ],
      "ranking_score": 0.5622891514340781
    },
    {
      "candidate_id": "bec_projection_04",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Pc",
      "spacegroup_number": 7,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        -0.5,
        0.0,
        0.0
      ],
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_residual": 0.0005351055890960403,
      "parent_symmetrization_rmsd_A": 0.11494288928447707,
      "parent_cell_rmsd_A": 0.09967600783647936,
      "energy_eV": -180.5281211945927,
      "reduced_polarization": [
        -0.49985735047296903,
        4.327331475805271e-15,
        0.0005157413149241209
      ],
      "cartesian_polarization_e_A2": [
        -0.01598186905996578,
        -1.875164529166639e-16,
        -0.00019625368418735414
      ],
      "ranking_score": 0.640932102421789
    },
    {
      "candidate_id": "bec_projection_05",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Pc",
      "spacegroup_number": 7,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.0
      ],
      "formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_residual": 0.00011637124861724985,
      "parent_symmetrization_rmsd_A": 0.0793649602910887,
      "parent_cell_rmsd_A": 0.04513144251151021,
      "energy_eV": -187.75677408461556,
      "reduced_polarization": [
        -1.2485202632264785e-16,
        0.49990911561600465,
        -7.267940733470352e-05
      ],
      "cartesian_polarization_e_A2": [
        6.825310677227438e-17,
        0.008556903451049827,
        4.656617008447081e-05
      ],
      "ranking_score": 0.5908805634162008
    },
    {
      "candidate_id": "bec_projection_06",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        -0.5,
        0.5,
        -0.5
      ],
      "formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "target_residual": 0.0009065017528282896,
      "parent_symmetrization_rmsd_A": 0.11828879412508075,
      "parent_cell_rmsd_A": 0.09692795382153938,
      "energy_eV": -181.39703358595617,
      "reduced_polarization": [
        -0.4998825955616944,
        0.49997545479301175,
        -0.4991014683319099
      ],
      "cartesian_polarization_e_A2": [
        -0.015974704690435465,
        0.008393869325210693,
        -0.008403100443469725
      ],
      "ranking_score": 0.6443337860861222
    },
    {
      "candidate_id": "bec_projection_07",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        -0.5,
        0.5,
        0.0
      ],
      "formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_residual": 0.0008823935118989463,
      "parent_symmetrization_rmsd_A": 0.1310075609556345,
      "parent_cell_rmsd_A": 0.10414002382644905,
      "energy_eV": -177.50584135554297,
      "reduced_polarization": [
        -0.49973975829207823,
        0.4998816046598996,
        0.0008347904567865096
      ],
      "cartesian_polarization_e_A2": [
        -0.015977239028959724,
        0.008554696473725002,
        -0.00014363361151254692
      ],
      "ranking_score": 0.6588073539360446
    }
  ],
  "formal_branches": [
    {
      "orbit_id": 0,
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.0,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        -0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -2.812484176727314e-16,
              1.8215345741382065e-16,
              -0.4738647820989374
            ],
            "branch_aligned_reduced_polarization": [
              -2.812484176727314e-16,
              1.8215345741382065e-16,
              -0.4738647820989374
            ],
            "target_residual": 0.026135217901062602,
            "energy_eV": -191.1157371973619,
            "max_atomic_step_A": 0.004515760161763748,
            "max_log_strain_component": 0.00043523705283379777,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.9049449056060717,
            "cell_principal_stretches": [
              1.0004353317822225,
              1.0001853641066387,
              0.9998951369302963
            ],
            "cell_volume_ratio": 1.0005158484175065,
            "cell_rmsd_from_input_A": 0.002188130975716242
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              5.307074172597019e-16,
              5.8539347451325645e-16,
              -0.4999749022513233
            ],
            "branch_aligned_reduced_polarization": [
              5.307074172597019e-16,
              5.8539347451325645e-16,
              -0.4999749022513233
            ],
            "target_residual": 2.5097748676705667e-05,
            "energy_eV": -191.10270436638487
          }
        ],
        "iterations": 1
      },
      "parent": {
        "candidate_id": "bec_projection_00",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Pna2_1",
        "spacegroup_number": 33,
        "pointgroup": "mm2",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          -0.5
        ],
        "formal_class": [
          0.0,
          0.0,
          0.5
        ],
        "target_residual": 2.5097748676705667e-05,
        "parent_symmetrization_rmsd_A": 0.0029409816178110944,
        "parent_cell_rmsd_A": 0.002188130975716242,
        "energy_eV": -191.10270436638487,
        "reduced_polarization": [
          5.307074172597019e-16,
          5.8539347451325645e-16,
          -0.4999749022513233
        ],
        "cartesian_polarization_e_A2": [
          2.0513837923434482e-17,
          1.3544923225654824e-17,
          -0.008263998886060536
        ],
        "ranking_score": 0.5035382098590936
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 1,
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.0,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -2.812484176727314e-16,
              1.8215345741382065e-16,
              -0.4738647820989374
            ],
            "branch_aligned_reduced_polarization": [
              -2.812484176727314e-16,
              1.8215345741382065e-16,
              -0.4738647820989374
            ],
            "target_residual": 0.4738647820989374,
            "energy_eV": -191.1157371973619,
            "max_atomic_step_A": 0.08187648226871046,
            "max_log_strain_component": 0.007891402014830183,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.9049449056060717,
            "cell_principal_stretches": [
              1.0019032094938565,
              0.9966450645674795,
              0.9921396533542233
            ],
            "cell_volume_ratio": 0.9906930035291582,
            "cell_rmsd_from_input_A": 0.03948414610242742
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -9.156365937117952e-15,
              -6.630693076377183e-15,
              0.0014469316977826273
            ],
            "branch_aligned_reduced_polarization": [
              -9.156365937117952e-15,
              -6.630693076377183e-15,
              0.0014469316977826273
            ],
            "target_residual": 0.0014469316977826273,
            "energy_eV": -189.7190722325275,
            "max_atomic_step_A": 0.00025028931027616127,
            "max_log_strain_component": 2.4204803779618144e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.9049449056060717,
            "cell_principal_stretches": [
              1.0018973663639015,
              0.996655337722898,
              0.9921636681904906
            ],
            "cell_volume_ratio": 0.9907214174483404,
            "cell_rmsd_from_input_A": 0.039363585423607815
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              5.565060504972579e-16,
              -2.3008411504058175e-16,
              1.0027692701203884e-05
            ],
            "branch_aligned_reduced_polarization": [
              5.565060504972579e-16,
              -2.3008411504058175e-16,
              1.0027692701203884e-05
            ],
            "target_residual": 1.0027692701203884e-05,
            "energy_eV": -189.72895568406935
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "inversion_parent_endpoint_00",
        "source": "same_species_inversion_center_projection_from_endpoint",
        "spacegroup": "Pnma",
        "spacegroup_number": 62,
        "pointgroup": "mmm",
        "has_inversion": true,
        "is_polar_point_group": false,
        "nonpolar_parent_hypothesis": true,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.0
        ],
        "formal_class": [
          0.0,
          0.0,
          0.0
        ],
        "target_residual": 2.9680162135398697e-15,
        "parent_symmetrization_rmsd_A": 0.49061406323375295,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -191.14847436752288,
        "reduced_polarization": [
          -1.9921762918485143e-16,
          1.4608951785873539e-15,
          -2.5758916625583724e-15
        ],
        "cartesian_polarization_e_A2": [
          -6.331121477827487e-18,
          2.472447766667924e-17,
          -4.257989542931035e-17
        ],
        "ranking_score": 0.4906140632337589
      },
      "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": [
          -191.11573719736188,
          -190.92716779130896,
          -190.7589853731847,
          -190.68131960316,
          -190.72967930606242,
          -190.8656328642779,
          -191.01193724139105,
          -191.11328442459575,
          -191.14847436752285
        ],
        "cartesian_polarizations_e_A2": [
          [
            -3.3186662909919243e-17,
            -1.2931212168765292e-17,
            -0.007833059581925877
          ],
          [
            -1.986234189122349e-17,
            -2.1103738259424958e-18,
            -0.008331298863010332
          ],
          [
            2.3607220935297917e-17,
            -1.2289824045194533e-17,
            -0.008010128474970984
          ],
          [
            3.947640450880668e-17,
            -4.841445835985725e-18,
            -0.006755538521432893
          ],
          [
            1.2331203924134582e-17,
            1.4482957629017126e-18,
            -0.004969518752631123
          ],
          [
            -1.84347360677918e-17,
            -6.372501356767536e-18,
            -0.003268263465076447
          ],
          [
            -1.671747109177977e-17,
            3.4883237946461255e-17,
            -0.0019398547704509255
          ],
          [
            -2.404170966416843e-17,
            2.8965915258034256e-19,
            -0.0009061322194764996
          ],
          [
            1.3655360050216148e-18,
            5.42076414114641e-18,
            -6.910439782988172e-18
          ]
        ],
        "raw_reduced_polarization": [
          [
            -1.0442649582107897e-15,
            -7.640665159975699e-16,
            -0.47386478209894084
          ],
          [
            -6.24996483717181e-16,
            -1.246956554108034e-16,
            -0.5040060118310618
          ],
          [
            7.428343624180243e-16,
            -7.261688168040904e-16,
            -0.4845766516489859
          ],
          [
            1.2421805113878971e-15,
            -2.860665035894902e-16,
            -0.40867961694129384
          ],
          [
            3.880186503077498e-16,
            8.557544979172782e-17,
            -0.30063347485391706
          ],
          [
            -5.800748614500086e-16,
            -3.765319790836025e-16,
            -0.19771520164277936
          ],
          [
            -5.260387071286274e-16,
            2.0611458335550446e-15,
            -0.11735246597949563
          ],
          [
            -7.565061604993378e-16,
            1.711508995834557e-17,
            -0.054816913141555665
          ],
          [
            4.296850825555619e-17,
            3.202966835061813e-16,
            -4.180504447495123e-16
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -1.0442649582107897e-15,
            -7.640665159975699e-16,
            -0.47386478209894084
          ],
          [
            -6.24996483717181e-16,
            -1.2469565541080339e-16,
            -0.5040060118310618
          ],
          [
            7.428343624180244e-16,
            -7.261688168040904e-16,
            -0.4845766516489859
          ],
          [
            1.2421805113878971e-15,
            -2.860665035894902e-16,
            -0.40867961694129384
          ],
          [
            3.880186503077498e-16,
            8.557544979172784e-17,
            -0.30063347485391706
          ],
          [
            -5.800748614500087e-16,
            -3.7653197908360244e-16,
            -0.19771520164277936
          ],
          [
            -5.260387071286274e-16,
            2.0611458335550442e-15,
            -0.11735246597949563
          ],
          [
            -7.565061604993378e-16,
            1.7115089958345646e-17,
            -0.054816913141555665
          ],
          [
            4.296850825555624e-17,
            3.202966835061813e-16,
            -4.163336342344337e-16
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            -1.0547118733938987e-15,
            -7.771561172376096e-16,
            -0.47386478209894084
          ],
          [
            -6.106226635438361e-16,
            -1.1102230246251565e-16,
            0.49599398816893825
          ],
          [
            7.771561172376096e-16,
            -7.216449660063518e-16,
            -0.4845766516489859
          ],
          [
            1.2212453270876722e-15,
            -2.7755575615628914e-16,
            -0.40867961694129384
          ],
          [
            3.3306690738754696e-16,
            1.1102230246251565e-16,
            -0.30063347485391706
          ],
          [
            -5.551115123125783e-16,
            -3.885780586188048e-16,
            -0.19771520164277934
          ],
          [
            -4.996003610813204e-16,
            2.1094237467877974e-15,
            -0.11735246597949561
          ],
          [
            -7.771561172376096e-16,
            0.0,
            -0.05481691314155568
          ],
          [
            0.0,
            3.3306690738754696e-16,
            -4.440892098500626e-16
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -191.14847436752285,
          -191.1132844245958,
          -191.01193724139105,
          -190.8656328642779,
          -190.72967930606242,
          -190.68131960316003,
          -190.7589853731847,
          -190.92716779130896,
          -191.11573719736194
        ],
        "cartesian_polarizations_e_A2": [
          [
            1.3655360050216148e-18,
            5.42076414114641e-18,
            -6.910439782988172e-18
          ],
          [
            -9.600131914091353e-18,
            -4.4069571071152114e-18,
            0.0009061322194765763
          ],
          [
            1.8703705280902117e-17,
            1.2165684408374387e-17,
            0.0019398547704509593
          ],
          [
            -3.3931500730840127e-18,
            -1.1638090951888763e-17,
            0.0032682634650765263
          ],
          [
            3.3600461699319737e-17,
            -8.379425485359909e-18,
            0.004969518752631118
          ],
          [
            -5.925598664215007e-17,
            1.718299472985532e-17,
            0.00675553852143292
          ],
          [
            2.813831767923328e-17,
            2.6808989068284204e-17,
            0.008010128474971009
          ],
          [
            6.455261114647634e-18,
            -1.210878707483182e-17,
            0.008331298863010372
          ],
          [
            -2.4993446879789556e-17,
            2.865556616598389e-18,
            0.007833059581925848
          ]
        ],
        "raw_reduced_polarization": [
          [
            4.296850825555619e-17,
            3.202966835061813e-16,
            -4.180504447495123e-16
          ],
          [
            -3.020816337966375e-16,
            -2.6039386865197183e-16,
            0.0548169131415603
          ],
          [
            5.885383555003453e-16,
            7.188337782505138e-16,
            0.11735246597949767
          ],
          [
            -1.067702326350184e-16,
            -6.876598643978129e-16,
            0.19771520164278417
          ],
          [
            1.057285718288231e-15,
            -4.951151023664253e-16,
            0.3006334748539168
          ],
          [
            -1.8645728430895896e-15,
            1.0152915864575709e-15,
            0.40867961694129545
          ],
          [
            8.854116852660065e-16,
            1.584062700966162e-15,
            0.48457665164898733
          ],
          [
            2.0312385720808383e-16,
            -7.154718855801246e-16,
            0.5040060118310641
          ],
          [
            -7.864539086774527e-16,
            1.6931713994506151e-16,
            0.47386478209893906
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            4.296850825555619e-17,
            3.202966835061813e-16,
            -4.180504447495123e-16
          ],
          [
            -3.020816337966375e-16,
            -2.6039386865197183e-16,
            0.0548169131415603
          ],
          [
            5.885383555003453e-16,
            7.188337782505138e-16,
            0.11735246597949767
          ],
          [
            -1.0677023263501839e-16,
            -6.876598643978128e-16,
            0.19771520164278417
          ],
          [
            1.057285718288231e-15,
            -4.951151023664253e-16,
            0.3006334748539168
          ],
          [
            -1.8645728430895892e-15,
            1.0152915864575709e-15,
            0.40867961694129545
          ],
          [
            8.854116852660063e-16,
            1.584062700966162e-15,
            0.48457665164898733
          ],
          [
            2.0312385720808383e-16,
            -7.154718855801246e-16,
            0.5040060118310641
          ],
          [
            -7.864539086774526e-16,
            1.6931713994506154e-16,
            0.47386478209893906
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          1.1302019747219022e-15,
          1.4046598830099326e-15,
          0.47386478209894
        ],
        "actual_opposite_endpoint_branch_residual": 2.4678313302365418e-15
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            -1.0442649582107897e-15,
            -7.640665159975699e-16,
            -0.47386478209894084
          ],
          [
            -6.24996483717181e-16,
            -1.246956554108034e-16,
            -0.5040060118310618
          ],
          [
            7.428343624180243e-16,
            -7.261688168040904e-16,
            -0.4845766516489859
          ],
          [
            1.2421805113878971e-15,
            -2.860665035894902e-16,
            -0.40867961694129384
          ],
          [
            3.880186503077498e-16,
            8.557544979172782e-17,
            -0.30063347485391706
          ],
          [
            -5.800748614500086e-16,
            -3.765319790836025e-16,
            -0.19771520164277936
          ],
          [
            -5.260387071286274e-16,
            2.0611458335550446e-15,
            -0.11735246597949563
          ],
          [
            -7.565061604993378e-16,
            1.711508995834557e-17,
            -0.054816913141555665
          ],
          [
            4.296850825555619e-17,
            3.202966835061813e-16,
            -4.180504447495123e-16
          ],
          [
            -3.020816337966375e-16,
            -2.6039386865197183e-16,
            0.0548169131415603
          ],
          [
            5.885383555003453e-16,
            7.188337782505138e-16,
            0.11735246597949767
          ],
          [
            -1.067702326350184e-16,
            -6.876598643978129e-16,
            0.19771520164278417
          ],
          [
            1.057285718288231e-15,
            -4.951151023664253e-16,
            0.3006334748539168
          ],
          [
            -1.8645728430895896e-15,
            1.0152915864575709e-15,
            0.40867961694129545
          ],
          [
            8.854116852660065e-16,
            1.584062700966162e-15,
            0.48457665164898733
          ],
          [
            2.0312385720808383e-16,
            -7.154718855801246e-16,
            0.5040060118310641
          ],
          [
            -7.864539086774527e-16,
            1.6931713994506151e-16,
            0.47386478209893906
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -1.0442649582107897e-15,
            -7.640665159975699e-16,
            -0.47386478209894084
          ],
          [
            -6.24996483717181e-16,
            -1.2469565541080339e-16,
            -0.5040060118310618
          ],
          [
            7.428343624180244e-16,
            -7.261688168040904e-16,
            -0.4845766516489859
          ],
          [
            1.2421805113878971e-15,
            -2.860665035894902e-16,
            -0.40867961694129384
          ],
          [
            3.880186503077498e-16,
            8.557544979172784e-17,
            -0.30063347485391706
          ],
          [
            -5.800748614500087e-16,
            -3.7653197908360244e-16,
            -0.19771520164277936
          ],
          [
            -5.260387071286274e-16,
            2.0611458335550442e-15,
            -0.11735246597949563
          ],
          [
            -7.565061604993378e-16,
            1.7115089958345646e-17,
            -0.054816913141555665
          ],
          [
            4.296850825555624e-17,
            3.202966835061813e-16,
            -4.163336342344337e-16
          ],
          [
            -3.020816337966375e-16,
            -2.6039386865197183e-16,
            0.0548169131415603
          ],
          [
            5.885383555003453e-16,
            7.188337782505138e-16,
            0.11735246597949767
          ],
          [
            -1.0677023263501839e-16,
            -6.876598643978128e-16,
            0.19771520164278417
          ],
          [
            1.057285718288231e-15,
            -4.951151023664253e-16,
            0.3006334748539168
          ],
          [
            -1.8645728430895892e-15,
            1.0152915864575709e-15,
            0.40867961694129545
          ],
          [
            8.854116852660063e-16,
            1.584062700966162e-15,
            0.48457665164898733
          ],
          [
            2.0312385720808383e-16,
            -7.154718855801246e-16,
            0.5040060118310641
          ],
          [
            -7.864539086774526e-16,
            1.6931713994506154e-16,
            0.47386478209893906
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            -1.0547118733938987e-15,
            -7.771561172376096e-16,
            -0.47386478209894084
          ],
          [
            -6.106226635438361e-16,
            -1.1102230246251565e-16,
            0.49599398816893825
          ],
          [
            7.771561172376096e-16,
            -7.216449660063518e-16,
            -0.4845766516489859
          ],
          [
            1.2212453270876722e-15,
            -2.7755575615628914e-16,
            -0.40867961694129384
          ],
          [
            3.3306690738754696e-16,
            1.1102230246251565e-16,
            -0.30063347485391706
          ],
          [
            -5.551115123125783e-16,
            -3.885780586188048e-16,
            -0.19771520164277934
          ],
          [
            -4.996003610813204e-16,
            2.1094237467877974e-15,
            -0.11735246597949561
          ],
          [
            -7.771561172376096e-16,
            0.0,
            -0.05481691314155568
          ],
          [
            0.0,
            3.3306690738754696e-16,
            -4.440892098500626e-16
          ],
          [
            -2.7755575615628914e-16,
            -2.7755575615628914e-16,
            0.05481691314156034
          ],
          [
            5.551115123125783e-16,
            6.661338147750939e-16,
            0.11735246597949767
          ],
          [
            -1.1102230246251565e-16,
            -6.661338147750939e-16,
            0.1977152016427841
          ],
          [
            1.1102230246251565e-15,
            -4.996003610813204e-16,
            0.3006334748539168
          ],
          [
            -1.887379141862766e-15,
            9.992007221626409e-16,
            0.4086796169412954
          ],
          [
            8.881784197001252e-16,
            1.5543122344752192e-15,
            0.48457665164898733
          ],
          [
            2.220446049250313e-16,
            -7.216449660063518e-16,
            -0.4959939881689359
          ],
          [
            -7.771561172376096e-16,
            2.220446049250313e-16,
            0.473864782098939
          ]
        ]
      },
      "incoming_structure_ids": [
        "incoming_01_000",
        "incoming_01_001",
        "incoming_01_002",
        "incoming_01_003",
        "incoming_01_004",
        "incoming_01_005",
        "incoming_01_006",
        "incoming_01_007",
        "incoming_01_008"
      ],
      "reflected_structure_ids": [
        "reflected_01_001",
        "reflected_01_002",
        "reflected_01_003",
        "reflected_01_004",
        "reflected_01_005",
        "reflected_01_006",
        "reflected_01_007",
        "reflected_01_008"
      ]
    },
    {
      "orbit_id": 2,
      "formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.0,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        -0.5,
        0.0,
        -0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -2.812484176727314e-16,
              1.8215345741382065e-16,
              -0.4738647820989374
            ],
            "branch_aligned_reduced_polarization": [
              -2.7755575615628914e-16,
              1.8215345741382065e-16,
              -0.4738647820989374
            ],
            "target_residual": 0.5006825836942361,
            "energy_eV": -191.1157371973619,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.00905618693522973,
            "step_scale": 0.7820493970143884,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.9049449056060717,
            "cell_principal_stretches": [
              1.0093427512884237,
              0.9999179909623885,
              0.9912246794678196
            ],
            "cell_volume_ratio": 1.000403396270536,
            "cell_rmsd_from_input_A": 0.06584815239666499
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.37960084346467715,
              -6.3482804034640584e-15,
              -0.45914724460253775
            ],
            "branch_aligned_reduced_polarization": [
              -0.37960084346467715,
              -6.3482804034640584e-15,
              -0.45914724460253775
            ],
            "target_residual": 0.12714127778963863,
            "energy_eV": -187.3830200454605,
            "max_atomic_step_A": 0.04089226005634534,
            "max_log_strain_component": 0.0033356683404774912,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.9049449056060717,
            "cell_principal_stretches": [
              1.0133991687599957,
              0.9996915214433194,
              0.9885812751546991
            ],
            "cell_volume_ratio": 1.0015184002099649,
            "cell_rmsd_from_input_A": 0.09051053740740991
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.4962189059438244,
              -1.1302903341961648e-16,
              -0.4877075781302712
            ],
            "branch_aligned_reduced_polarization": [
              -0.4962189059438244,
              -1.1302903341961648e-16,
              -0.4877075781302712
            ],
            "target_residual": 0.01286080509474555,
            "energy_eV": -184.35279780143452,
            "max_atomic_step_A": 0.0031982968055325766,
            "max_log_strain_component": 0.0002351843611406015,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.9049449056060717,
            "cell_principal_stretches": [
              1.0137087274704704,
              0.9996348738294596,
              0.9886108531653506
            ],
            "cell_volume_ratio": 1.0017975338230165,
            "cell_rmsd_from_input_A": 0.09163792239350453
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -0.49994234814717364,
              -5.445372440071823e-16,
              -0.4995795319094433
            ],
            "branch_aligned_reduced_polarization": [
              -0.49994234814717364,
              -5.445372440071823e-16,
              -0.4995795319094433
            ],
            "target_residual": 0.0004244021103984908,
            "energy_eV": -184.24702743039882
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_02",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Pc",
        "spacegroup_number": 7,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          -0.5,
          0.0,
          -0.5
        ],
        "formal_class": [
          0.5,
          0.0,
          0.5
        ],
        "target_residual": 0.0004244021103984908,
        "parent_symmetrization_rmsd_A": 0.09981242318093726,
        "parent_cell_rmsd_A": 0.09163792239350453,
        "energy_eV": -184.24702743039882,
        "reduced_polarization": [
          -0.49994234814717364,
          -5.445372440071823e-16,
          -0.4995795319094433
        ],
        "cartesian_polarization_e_A2": [
          -0.015974466461401958,
          -1.6109195962015764e-16,
          -0.008455409675464499
        ],
        "ranking_score": 0.6235707080001104
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 3,
      "formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.5,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        -0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -2.812484176727314e-16,
              1.8215345741382065e-16,
              -0.4738647820989374
            ],
            "branch_aligned_reduced_polarization": [
              -2.812484176727314e-16,
              1.6653345369377348e-16,
              -0.4738647820989374
            ],
            "target_residual": 0.5006825836942362,
            "energy_eV": -191.1157371973619,
            "max_atomic_step_A": 0.07867750846537999,
            "max_log_strain_component": 0.005300520468880154,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.9049449056060717,
            "cell_principal_stretches": [
              1.0054875815440425,
              1.0001853641066398,
              0.9948709873931676
            ],
            "cell_volume_ratio": 1.0005158484175052,
            "cell_rmsd_from_input_A": 0.02062533880896053
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              1.0634522945574478e-15,
              0.4914655229677089,
              -0.49707992103148446
            ],
            "branch_aligned_reduced_polarization": [
              1.0634522945574478e-15,
              0.4914655229677089,
              -0.49707992103148446
            ],
            "target_residual": 0.009020208389891614,
            "energy_eV": -189.26466049990296,
            "max_atomic_step_A": 0.0014724109389346236,
            "max_log_strain_component": 9.89055482580691e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.9049449056060717,
            "cell_principal_stretches": [
              1.0056072020459275,
              1.000206214411141,
              0.9947896067084856
            ],
            "cell_volume_ratio": 1.000573883240609,
            "cell_rmsd_from_input_A": 0.021034128366430288
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              7.370030769383154e-16,
              0.49998774278550245,
              -0.5000101590433755
            ],
            "branch_aligned_reduced_polarization": [
              7.370030769383154e-16,
              0.49998774278550245,
              -0.5000101590433755
            ],
            "target_residual": 1.5919970777135915e-05,
            "energy_eV": -189.19648945844136
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_03",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Pc",
        "spacegroup_number": 7,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.5,
          -0.5
        ],
        "formal_class": [
          0.0,
          0.5,
          0.5
        ],
        "target_residual": 1.5919970777135915e-05,
        "parent_symmetrization_rmsd_A": 0.05699877940091624,
        "parent_cell_rmsd_A": 0.021034128366430288,
        "energy_eV": -189.19648945844136,
        "reduced_polarization": [
          7.370030769383154e-16,
          0.49998774278550245,
          -0.5000101590433755
        ],
        "cartesian_polarization_e_A2": [
          -2.1257058705449455e-17,
          0.008411565079925423,
          -0.008218954382368387
        ],
        "ranking_score": 0.5622891514340781
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 4,
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.0,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        -0.5,
        0.0,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -2.812484176727314e-16,
              1.8215345741382065e-16,
              -0.4738647820989374
            ],
            "branch_aligned_reduced_polarization": [
              -2.7755575615628914e-16,
              1.8215345741382065e-16,
              -0.4738647820989374
            ],
            "target_residual": 0.6888743221471338,
            "energy_eV": -191.1157371973619,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.0076691857350581535,
            "step_scale": 0.6622745447487958,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.9049449056060717,
            "cell_principal_stretches": [
              1.0040969829684325,
              1.0012600424605391,
              0.9885258245723807
            ],
            "cell_volume_ratio": 0.9938264856903382,
            "cell_rmsd_from_input_A": 0.06093120427156878
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.3193091277548252,
              -6.753427296980384e-15,
              -0.14591177259196078
            ],
            "branch_aligned_reduced_polarization": [
              -0.3193091277548252,
              -6.753427296980384e-15,
              -0.14591177259196078
            ],
            "target_residual": 0.232248652727309,
            "energy_eV": -187.51389346595818,
            "max_atomic_step_A": 0.06902381954961104,
            "max_log_strain_component": 0.004864291745760313,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.9049449056060717,
            "cell_principal_stretches": [
              1.0071093055644535,
              1.0019128495036207,
              0.9817750503843949
            ],
            "cell_volume_ratio": 0.9906461283208838,
            "cell_rmsd_from_input_A": 0.09776583753027526
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.4900106506195713,
              -4.440262292873475e-15,
              0.003977112180989843
            ],
            "branch_aligned_reduced_polarization": [
              -0.4900106506195713,
              -4.440262292873475e-15,
              0.003977112180989843
            ],
            "target_residual": 0.010751954349998401,
            "energy_eV": -180.855437074152,
            "max_atomic_step_A": 0.0037817645072635176,
            "max_log_strain_component": 0.0003079045750123367,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.9049449056060717,
            "cell_principal_stretches": [
              1.0074525538282453,
              1.0018991204923626,
              0.981520138960077
            ],
            "cell_volume_ratio": 0.9907128873854706,
            "cell_rmsd_from_input_A": 0.09967600783647936
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -0.49985735047296903,
              4.327331475805271e-15,
              0.0005157413149241209
            ],
            "branch_aligned_reduced_polarization": [
              -0.49985735047296903,
              4.327331475805271e-15,
              0.0005157413149241209
            ],
            "target_residual": 0.0005351055890960403,
            "energy_eV": -180.5281211945927
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_04",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Pc",
        "spacegroup_number": 7,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          -0.5,
          0.0,
          0.0
        ],
        "formal_class": [
          0.5,
          0.0,
          0.0
        ],
        "target_residual": 0.0005351055890960403,
        "parent_symmetrization_rmsd_A": 0.11494288928447707,
        "parent_cell_rmsd_A": 0.09967600783647936,
        "energy_eV": -180.5281211945927,
        "reduced_polarization": [
          -0.49985735047296903,
          4.327331475805271e-15,
          0.0005157413149241209
        ],
        "cartesian_polarization_e_A2": [
          -0.01598186905996578,
          -1.875164529166639e-16,
          -0.00019625368418735414
        ],
        "ranking_score": 0.640932102421789
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 5,
      "formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.5,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -2.812484176727314e-16,
              1.8215345741382065e-16,
              -0.4738647820989374
            ],
            "branch_aligned_reduced_polarization": [
              -2.812484176727314e-16,
              1.6653345369377348e-16,
              -0.4738647820989374
            ],
            "target_residual": 0.688874322147134,
            "energy_eV": -191.1157371973619,
            "max_atomic_step_A": 0.11697794711756206,
            "max_log_strain_component": 0.007891402014833435,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.9049449056060717,
            "cell_principal_stretches": [
              1.0042298929833116,
              0.9966450645674806,
              0.9898409815393084
            ],
            "cell_volume_ratio": 0.990693003529157,
            "cell_rmsd_from_input_A": 0.04440658403490827
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -8.195217515430192e-15,
              0.4747254915027338,
              -0.0013888890185116552
            ],
            "branch_aligned_reduced_polarization": [
              -8.195217515430192e-15,
              0.4747254915027338,
              -0.0013888890185116552
            ],
            "target_residual": 0.025312640962256855,
            "energy_eV": -187.96960170561,
            "max_atomic_step_A": 0.004300447078117567,
            "max_log_strain_component": 0.0003082189412405506,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.9049449056060717,
            "cell_principal_stretches": [
              1.004461381545863,
              0.9966283610925137,
              0.9895832998418033
            ],
            "cell_volume_ratio": 0.9906468054800146,
            "cell_rmsd_from_input_A": 0.04513144251151021
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -1.2485202632264785e-16,
              0.49990911561600465,
              -7.267940733470352e-05
            ],
            "branch_aligned_reduced_polarization": [
              -1.2485202632264785e-16,
              0.49990911561600465,
              -7.267940733470352e-05
            ],
            "target_residual": 0.00011637124861724985,
            "energy_eV": -187.75677408461556
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_05",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Pc",
        "spacegroup_number": 7,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.5,
          0.0
        ],
        "formal_class": [
          0.0,
          0.5,
          0.0
        ],
        "target_residual": 0.00011637124861724985,
        "parent_symmetrization_rmsd_A": 0.0793649602910887,
        "parent_cell_rmsd_A": 0.04513144251151021,
        "energy_eV": -187.75677408461556,
        "reduced_polarization": [
          -1.2485202632264785e-16,
          0.49990911561600465,
          -7.267940733470352e-05
        ],
        "cartesian_polarization_e_A2": [
          6.825310677227438e-17,
          0.008556903451049827,
          4.656617008447081e-05
        ],
        "ranking_score": 0.5908805634162008
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 6,
      "formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.5,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        -0.5,
        0.5,
        -0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -2.812484176727314e-16,
              1.8215345741382065e-16,
              -0.4738647820989374
            ],
            "branch_aligned_reduced_polarization": [
              -2.7755575615628914e-16,
              1.6653345369377348e-16,
              -0.4738647820989374
            ],
            "target_residual": 0.7075896053608586,
            "energy_eV": -191.1157371973619,
            "max_atomic_step_A": 0.11999999999999998,
            "max_log_strain_component": 0.007712104473263726,
            "step_scale": 0.6659808036383865,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.9049449056060717,
            "cell_principal_stretches": [
              1.0087101290713691,
              0.9999636645054956,
              0.9917416669261692
            ],
            "cell_volume_ratio": 1.0003435155534697,
            "cell_rmsd_from_input_A": 0.05770667445307701
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.3230619032449051,
              0.32387956001397766,
              -0.464539804836888
            ],
            "branch_aligned_reduced_polarization": [
              -0.3230619032449051,
              0.32387956001397766,
              -0.464539804836888
            ],
            "target_residual": 0.2521565484083081,
            "energy_eV": -187.51124918404528,
            "max_atomic_step_A": 0.07088890268219378,
            "max_log_strain_component": 0.004838751443770892,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.9049449056060717,
            "cell_principal_stretches": [
              1.0146911111402028,
              0.9998551175267497,
              0.987027434446425
            ],
            "cell_volume_ratio": 1.0013828603358264,
            "cell_rmsd_from_input_A": 0.09428966940676219
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.491241153406584,
              0.4904904606090633,
              -0.4804025801457379
            ],
            "branch_aligned_reduced_polarization": [
              -0.491241153406584,
              0.4904904606090633,
              -0.4804025801457379
            ],
            "target_residual": 0.02347781075865036,
            "energy_eV": -181.75183063822027,
            "max_atomic_step_A": 0.006590417590123553,
            "max_log_strain_component": 0.00038018732564610566,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.9049449056060717,
            "cell_principal_stretches": [
              1.0153112667925974,
              0.9998084825290051,
              0.986915057266626
            ],
            "cell_volume_ratio": 1.001834071529079,
            "cell_rmsd_from_input_A": 0.09692795382153938
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -0.4998825955616944,
              0.49997545479301175,
              -0.4991014683319099
            ],
            "branch_aligned_reduced_polarization": [
              -0.4998825955616944,
              0.49997545479301175,
              -0.4991014683319099
            ],
            "target_residual": 0.0009065017528282896,
            "energy_eV": -181.39703358595617
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_06",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          -0.5,
          0.5,
          -0.5
        ],
        "formal_class": [
          0.5,
          0.5,
          0.5
        ],
        "target_residual": 0.0009065017528282896,
        "parent_symmetrization_rmsd_A": 0.11828879412508075,
        "parent_cell_rmsd_A": 0.09692795382153938,
        "energy_eV": -181.39703358595617,
        "reduced_polarization": [
          -0.4998825955616944,
          0.49997545479301175,
          -0.4991014683319099
        ],
        "cartesian_polarization_e_A2": [
          -0.015974704690435465,
          0.008393869325210693,
          -0.008403100443469725
        ],
        "ranking_score": 0.6443337860861222
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 7,
      "formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.5,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        -0.5,
        0.5,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -2.812484176727314e-16,
              1.8215345741382065e-16,
              -0.4738647820989374
            ],
            "branch_aligned_reduced_polarization": [
              -2.7755575615628914e-16,
              1.6653345369377348e-16,
              -0.4738647820989374
            ],
            "target_residual": 0.8512037545227775,
            "energy_eV": -191.1157371973619,
            "max_atomic_step_A": 0.12000000000000001,
            "max_log_strain_component": 0.006735560123723422,
            "step_scale": 0.5816510603169276,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.9049449056060717,
            "cell_principal_stretches": [
              1.0047742106368467,
              1.000428162114743,
              0.9894266017050319
            ],
            "cell_volume_ratio": 0.9945759902200974,
            "cell_rmsd_from_input_A": 0.054880007775388824
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.28083375260741,
              0.2795604731164778,
              -0.18597074472074296
            ],
            "branch_aligned_reduced_polarization": [
              -0.28083375260741,
              0.2795604731164778,
              -0.18597074472074296
            ],
            "target_residual": 0.3622327247789311,
            "energy_eV": -187.7547794972918,
            "max_atomic_step_A": 0.09598017174011947,
            "max_log_strain_component": 0.005868320281484465,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.9049449056060717,
            "cell_principal_stretches": [
              1.009320486138842,
              1.000758050362163,
              0.9807565619074601
            ],
            "cell_volume_ratio": 0.9906480821505903,
            "cell_rmsd_from_input_A": 0.10075814112058373
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.4840701344465387,
              0.4853194966696322,
              0.0066458323796105305
            ],
            "branch_aligned_reduced_polarization": [
              -0.4840701344465387,
              0.4853194966696322,
              0.0066458323796105305
            ],
            "target_residual": 0.02265932220085529,
            "energy_eV": -178.21921126202085,
            "max_atomic_step_A": 0.007820715520510535,
            "max_log_strain_component": 0.0005242548844820239,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.9049449056060717,
            "cell_principal_stretches": [
              1.0099166508645119,
              1.0007749109848338,
              0.9802749558360091
            ],
            "cell_volume_ratio": 0.990763159099853,
            "cell_rmsd_from_input_A": 0.10414002382644905
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -0.49973975829207823,
              0.4998816046598996,
              0.0008347904567865096
            ],
            "branch_aligned_reduced_polarization": [
              -0.49973975829207823,
              0.4998816046598996,
              0.0008347904567865096
            ],
            "target_residual": 0.0008823935118989463,
            "energy_eV": -177.50584135554297
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_07",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          -0.5,
          0.5,
          0.0
        ],
        "formal_class": [
          0.5,
          0.5,
          0.0
        ],
        "target_residual": 0.0008823935118989463,
        "parent_symmetrization_rmsd_A": 0.1310075609556345,
        "parent_cell_rmsd_A": 0.10414002382644905,
        "energy_eV": -177.50584135554297,
        "reduced_polarization": [
          -0.49973975829207823,
          0.4998816046598996,
          0.0008347904567865096
        ],
        "cartesian_polarization_e_A2": [
          -0.015977239028959724,
          0.008554696473725002,
          -0.00014363361151254692
        ],
        "ranking_score": 0.6588073539360446
      },
      "branch_status": "awaiting_branch_sampling"
    }
  ],
  "sampled_polarization_branches": [
    {
      "orbit_id": 1,
      "candidate_id": "inversion_parent_endpoint_00",
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "construction": "MACEField-BEC-parent plus variable-cell P-N-P path and symmetric log-strain continuation beyond both polar endpoints",
      "geometry_diagnostics": {
        "collision_aware": false,
        "permutations_tested": 1,
        "selected_order": [
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          10,
          11,
          12,
          13,
          14,
          15,
          16,
          17,
          18,
          19,
          20,
          21,
          22,
          23,
          24,
          25,
          26,
          27
        ],
        "endpoint_rmsd_A": 0.49061406323375295,
        "minimum_distance_A_by_image": [
          1.527484025618387,
          1.5274711368442877,
          1.52745996648543,
          1.5274505145795148,
          1.5274427811584437,
          1.5274367662483186,
          1.5274324698694417,
          1.527429892036315,
          1.5274290327576392
        ],
        "minimum_distance_A": 1.5274290327576392,
        "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": [
          335.37526361352013,
          335.37526361352013,
          335.37526361352013,
          335.37526361352013,
          335.37526361352013,
          335.37526361352013,
          335.37526361352013,
          335.37526361352013,
          335.37526361352013
        ],
        "cell_deformation_log_strain_norm": 0.0
      },
      "parent_reduced_polarization": [
        4.296850825555619e-17,
        3.202966835061813e-16,
        -4.180504447495123e-16
      ],
      "incoming": {
        "reached": true,
        "construction": "variable_cell_linear_interpolation",
        "continuation_fractions": [
          0.0,
          0.125,
          0.25,
          0.375,
          0.5,
          0.625,
          0.75,
          0.875,
          1.0
        ],
        "energies_eV": [
          -191.11573719736188,
          -190.92716779130896,
          -190.7589853731847,
          -190.68131960316,
          -190.72967930606242,
          -190.8656328642779,
          -191.01193724139105,
          -191.11328442459575,
          -191.14847436752285
        ],
        "cartesian_polarizations_e_A2": [
          [
            -3.3186662909919243e-17,
            -1.2931212168765292e-17,
            -0.007833059581925877
          ],
          [
            -1.986234189122349e-17,
            -2.1103738259424958e-18,
            -0.008331298863010332
          ],
          [
            2.3607220935297917e-17,
            -1.2289824045194533e-17,
            -0.008010128474970984
          ],
          [
            3.947640450880668e-17,
            -4.841445835985725e-18,
            -0.006755538521432893
          ],
          [
            1.2331203924134582e-17,
            1.4482957629017126e-18,
            -0.004969518752631123
          ],
          [
            -1.84347360677918e-17,
            -6.372501356767536e-18,
            -0.003268263465076447
          ],
          [
            -1.671747109177977e-17,
            3.4883237946461255e-17,
            -0.0019398547704509255
          ],
          [
            -2.404170966416843e-17,
            2.8965915258034256e-19,
            -0.0009061322194764996
          ],
          [
            1.3655360050216148e-18,
            5.42076414114641e-18,
            -6.910439782988172e-18
          ]
        ],
        "raw_reduced_polarization": [
          [
            -1.0442649582107897e-15,
            -7.640665159975699e-16,
            -0.47386478209894084
          ],
          [
            -6.24996483717181e-16,
            -1.246956554108034e-16,
            -0.5040060118310618
          ],
          [
            7.428343624180243e-16,
            -7.261688168040904e-16,
            -0.4845766516489859
          ],
          [
            1.2421805113878971e-15,
            -2.860665035894902e-16,
            -0.40867961694129384
          ],
          [
            3.880186503077498e-16,
            8.557544979172782e-17,
            -0.30063347485391706
          ],
          [
            -5.800748614500086e-16,
            -3.765319790836025e-16,
            -0.19771520164277936
          ],
          [
            -5.260387071286274e-16,
            2.0611458335550446e-15,
            -0.11735246597949563
          ],
          [
            -7.565061604993378e-16,
            1.711508995834557e-17,
            -0.054816913141555665
          ],
          [
            4.296850825555619e-17,
            3.202966835061813e-16,
            -4.180504447495123e-16
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -1.0442649582107897e-15,
            -7.640665159975699e-16,
            -0.47386478209894084
          ],
          [
            -6.24996483717181e-16,
            -1.2469565541080339e-16,
            -0.5040060118310618
          ],
          [
            7.428343624180244e-16,
            -7.261688168040904e-16,
            -0.4845766516489859
          ],
          [
            1.2421805113878971e-15,
            -2.860665035894902e-16,
            -0.40867961694129384
          ],
          [
            3.880186503077498e-16,
            8.557544979172784e-17,
            -0.30063347485391706
          ],
          [
            -5.800748614500087e-16,
            -3.7653197908360244e-16,
            -0.19771520164277936
          ],
          [
            -5.260387071286274e-16,
            2.0611458335550442e-15,
            -0.11735246597949563
          ],
          [
            -7.565061604993378e-16,
            1.7115089958345646e-17,
            -0.054816913141555665
          ],
          [
            4.296850825555624e-17,
            3.202966835061813e-16,
            -4.163336342344337e-16
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            -1.0547118733938987e-15,
            -7.771561172376096e-16,
            -0.47386478209894084
          ],
          [
            -6.106226635438361e-16,
            -1.1102230246251565e-16,
            0.49599398816893825
          ],
          [
            7.771561172376096e-16,
            -7.216449660063518e-16,
            -0.4845766516489859
          ],
          [
            1.2212453270876722e-15,
            -2.7755575615628914e-16,
            -0.40867961694129384
          ],
          [
            3.3306690738754696e-16,
            1.1102230246251565e-16,
            -0.30063347485391706
          ],
          [
            -5.551115123125783e-16,
            -3.885780586188048e-16,
            -0.19771520164277934
          ],
          [
            -4.996003610813204e-16,
            2.1094237467877974e-15,
            -0.11735246597949561
          ],
          [
            -7.771561172376096e-16,
            0.0,
            -0.05481691314155568
          ],
          [
            0.0,
            3.3306690738754696e-16,
            -4.440892098500626e-16
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -191.14847436752285,
          -191.1132844245958,
          -191.01193724139105,
          -190.8656328642779,
          -190.72967930606242,
          -190.68131960316003,
          -190.7589853731847,
          -190.92716779130896,
          -191.11573719736194
        ],
        "cartesian_polarizations_e_A2": [
          [
            1.3655360050216148e-18,
            5.42076414114641e-18,
            -6.910439782988172e-18
          ],
          [
            -9.600131914091353e-18,
            -4.4069571071152114e-18,
            0.0009061322194765763
          ],
          [
            1.8703705280902117e-17,
            1.2165684408374387e-17,
            0.0019398547704509593
          ],
          [
            -3.3931500730840127e-18,
            -1.1638090951888763e-17,
            0.0032682634650765263
          ],
          [
            3.3600461699319737e-17,
            -8.379425485359909e-18,
            0.004969518752631118
          ],
          [
            -5.925598664215007e-17,
            1.718299472985532e-17,
            0.00675553852143292
          ],
          [
            2.813831767923328e-17,
            2.6808989068284204e-17,
            0.008010128474971009
          ],
          [
            6.455261114647634e-18,
            -1.210878707483182e-17,
            0.008331298863010372
          ],
          [
            -2.4993446879789556e-17,
            2.865556616598389e-18,
            0.007833059581925848
          ]
        ],
        "raw_reduced_polarization": [
          [
            4.296850825555619e-17,
            3.202966835061813e-16,
            -4.180504447495123e-16
          ],
          [
            -3.020816337966375e-16,
            -2.6039386865197183e-16,
            0.0548169131415603
          ],
          [
            5.885383555003453e-16,
            7.188337782505138e-16,
            0.11735246597949767
          ],
          [
            -1.067702326350184e-16,
            -6.876598643978129e-16,
            0.19771520164278417
          ],
          [
            1.057285718288231e-15,
            -4.951151023664253e-16,
            0.3006334748539168
          ],
          [
            -1.8645728430895896e-15,
            1.0152915864575709e-15,
            0.40867961694129545
          ],
          [
            8.854116852660065e-16,
            1.584062700966162e-15,
            0.48457665164898733
          ],
          [
            2.0312385720808383e-16,
            -7.154718855801246e-16,
            0.5040060118310641
          ],
          [
            -7.864539086774527e-16,
            1.6931713994506151e-16,
            0.47386478209893906
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            4.296850825555619e-17,
            3.202966835061813e-16,
            -4.180504447495123e-16
          ],
          [
            -3.020816337966375e-16,
            -2.6039386865197183e-16,
            0.0548169131415603
          ],
          [
            5.885383555003453e-16,
            7.188337782505138e-16,
            0.11735246597949767
          ],
          [
            -1.0677023263501839e-16,
            -6.876598643978128e-16,
            0.19771520164278417
          ],
          [
            1.057285718288231e-15,
            -4.951151023664253e-16,
            0.3006334748539168
          ],
          [
            -1.8645728430895892e-15,
            1.0152915864575709e-15,
            0.40867961694129545
          ],
          [
            8.854116852660063e-16,
            1.584062700966162e-15,
            0.48457665164898733
          ],
          [
            2.0312385720808383e-16,
            -7.154718855801246e-16,
            0.5040060118310641
          ],
          [
            -7.864539086774526e-16,
            1.6931713994506154e-16,
            0.47386478209893906
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          1.1302019747219022e-15,
          1.4046598830099326e-15,
          0.47386478209894
        ],
        "actual_opposite_endpoint_branch_residual": 2.4678313302365418e-15
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            -1.0442649582107897e-15,
            -7.640665159975699e-16,
            -0.47386478209894084
          ],
          [
            -6.24996483717181e-16,
            -1.246956554108034e-16,
            -0.5040060118310618
          ],
          [
            7.428343624180243e-16,
            -7.261688168040904e-16,
            -0.4845766516489859
          ],
          [
            1.2421805113878971e-15,
            -2.860665035894902e-16,
            -0.40867961694129384
          ],
          [
            3.880186503077498e-16,
            8.557544979172782e-17,
            -0.30063347485391706
          ],
          [
            -5.800748614500086e-16,
            -3.765319790836025e-16,
            -0.19771520164277936
          ],
          [
            -5.260387071286274e-16,
            2.0611458335550446e-15,
            -0.11735246597949563
          ],
          [
            -7.565061604993378e-16,
            1.711508995834557e-17,
            -0.054816913141555665
          ],
          [
            4.296850825555619e-17,
            3.202966835061813e-16,
            -4.180504447495123e-16
          ],
          [
            -3.020816337966375e-16,
            -2.6039386865197183e-16,
            0.0548169131415603
          ],
          [
            5.885383555003453e-16,
            7.188337782505138e-16,
            0.11735246597949767
          ],
          [
            -1.067702326350184e-16,
            -6.876598643978129e-16,
            0.19771520164278417
          ],
          [
            1.057285718288231e-15,
            -4.951151023664253e-16,
            0.3006334748539168
          ],
          [
            -1.8645728430895896e-15,
            1.0152915864575709e-15,
            0.40867961694129545
          ],
          [
            8.854116852660065e-16,
            1.584062700966162e-15,
            0.48457665164898733
          ],
          [
            2.0312385720808383e-16,
            -7.154718855801246e-16,
            0.5040060118310641
          ],
          [
            -7.864539086774527e-16,
            1.6931713994506151e-16,
            0.47386478209893906
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -1.0442649582107897e-15,
            -7.640665159975699e-16,
            -0.47386478209894084
          ],
          [
            -6.24996483717181e-16,
            -1.2469565541080339e-16,
            -0.5040060118310618
          ],
          [
            7.428343624180244e-16,
            -7.261688168040904e-16,
            -0.4845766516489859
          ],
          [
            1.2421805113878971e-15,
            -2.860665035894902e-16,
            -0.40867961694129384
          ],
          [
            3.880186503077498e-16,
            8.557544979172784e-17,
            -0.30063347485391706
          ],
          [
            -5.800748614500087e-16,
            -3.7653197908360244e-16,
            -0.19771520164277936
          ],
          [
            -5.260387071286274e-16,
            2.0611458335550442e-15,
            -0.11735246597949563
          ],
          [
            -7.565061604993378e-16,
            1.7115089958345646e-17,
            -0.054816913141555665
          ],
          [
            4.296850825555624e-17,
            3.202966835061813e-16,
            -4.163336342344337e-16
          ],
          [
            -3.020816337966375e-16,
            -2.6039386865197183e-16,
            0.0548169131415603
          ],
          [
            5.885383555003453e-16,
            7.188337782505138e-16,
            0.11735246597949767
          ],
          [
            -1.0677023263501839e-16,
            -6.876598643978128e-16,
            0.19771520164278417
          ],
          [
            1.057285718288231e-15,
            -4.951151023664253e-16,
            0.3006334748539168
          ],
          [
            -1.8645728430895892e-15,
            1.0152915864575709e-15,
            0.40867961694129545
          ],
          [
            8.854116852660063e-16,
            1.584062700966162e-15,
            0.48457665164898733
          ],
          [
            2.0312385720808383e-16,
            -7.154718855801246e-16,
            0.5040060118310641
          ],
          [
            -7.864539086774526e-16,
            1.6931713994506154e-16,
            0.47386478209893906
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            -1.0547118733938987e-15,
            -7.771561172376096e-16,
            -0.47386478209894084
          ],
          [
            -6.106226635438361e-16,
            -1.1102230246251565e-16,
            0.49599398816893825
          ],
          [
            7.771561172376096e-16,
            -7.216449660063518e-16,
            -0.4845766516489859
          ],
          [
            1.2212453270876722e-15,
            -2.7755575615628914e-16,
            -0.40867961694129384
          ],
          [
            3.3306690738754696e-16,
            1.1102230246251565e-16,
            -0.30063347485391706
          ],
          [
            -5.551115123125783e-16,
            -3.885780586188048e-16,
            -0.19771520164277934
          ],
          [
            -4.996003610813204e-16,
            2.1094237467877974e-15,
            -0.11735246597949561
          ],
          [
            -7.771561172376096e-16,
            0.0,
            -0.05481691314155568
          ],
          [
            0.0,
            3.3306690738754696e-16,
            -4.440892098500626e-16
          ],
          [
            -2.7755575615628914e-16,
            -2.7755575615628914e-16,
            0.05481691314156034
          ],
          [
            5.551115123125783e-16,
            6.661338147750939e-16,
            0.11735246597949767
          ],
          [
            -1.1102230246251565e-16,
            -6.661338147750939e-16,
            0.1977152016427841
          ],
          [
            1.1102230246251565e-15,
            -4.996003610813204e-16,
            0.3006334748539168
          ],
          [
            -1.887379141862766e-15,
            9.992007221626409e-16,
            0.4086796169412954
          ],
          [
            8.881784197001252e-16,
            1.5543122344752192e-15,
            0.48457665164898733
          ],
          [
            2.220446049250313e-16,
            -7.216449660063518e-16,
            -0.4959939881689359
          ],
          [
            -7.771561172376096e-16,
            2.220446049250313e-16,
            0.473864782098939
          ]
        ]
      },
      "incoming_structure_ids": [
        "incoming_01_000",
        "incoming_01_001",
        "incoming_01_002",
        "incoming_01_003",
        "incoming_01_004",
        "incoming_01_005",
        "incoming_01_006",
        "incoming_01_007",
        "incoming_01_008"
      ],
      "reflected_structure_ids": [
        "reflected_01_001",
        "reflected_01_002",
        "reflected_01_003",
        "reflected_01_004",
        "reflected_01_005",
        "reflected_01_006",
        "reflected_01_007",
        "reflected_01_008"
      ],
      "positive_extension_structure_ids": [
        "extension_plus_01_000",
        "extension_plus_01_001",
        "extension_plus_01_002",
        "extension_plus_01_003"
      ],
      "negative_extension_structure_ids": [
        "extension_minus_01_000",
        "extension_minus_01_001",
        "extension_minus_01_002",
        "extension_minus_01_003"
      ],
      "extension": {
        "enabled": true,
        "fraction_beyond_polar_endpoint": 0.35,
        "images_per_side": 4,
        "construction": "continue fractional atomic displacements and symmetric log strain beyond +P; reflect these structures about N for the -P side",
        "positive_path_coordinates": [
          1.35,
          1.2625,
          1.175,
          1.0875
        ],
        "negative_path_coordinates": [
          -1.0875,
          -1.175,
          -1.2625,
          -1.35
        ]
      },
      "branch_coordinates": [
        1.35,
        1.2625,
        1.175,
        1.0875,
        1.0,
        0.875,
        0.75,
        0.625,
        0.5,
        0.375,
        0.25,
        0.125,
        0.0,
        -0.125,
        -0.25,
        -0.375,
        -0.5,
        -0.625,
        -0.75,
        -0.875,
        -1.0,
        -1.0875,
        -1.175,
        -1.2625,
        -1.35
      ],
      "parent": {
        "candidate_id": "inversion_parent_endpoint_00",
        "source": "same_species_inversion_center_projection_from_endpoint",
        "spacegroup": "Pnma",
        "spacegroup_number": 62,
        "pointgroup": "mmm",
        "has_inversion": true,
        "is_polar_point_group": false,
        "nonpolar_parent_hypothesis": true,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.0
        ],
        "formal_class": [
          0.0,
          0.0,
          0.0
        ],
        "target_residual": 2.9680162135398697e-15,
        "parent_symmetrization_rmsd_A": 0.49061406323375295,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -191.14847436752288,
        "reduced_polarization": [
          -1.9921762918485143e-16,
          1.4608951785873539e-15,
          -2.5758916625583724e-15
        ],
        "cartesian_polarization_e_A2": [
          -6.331121477827487e-18,
          2.472447766667924e-17,
          -4.257989542931035e-17
        ],
        "ranking_score": 0.4906140632337589
      }
    }
  ],
  "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": 52,
      "full_response": 20,
      "energy_polarization": 32
    },
    "model_evaluations_for_recovery_and_path_properties": {
      "total": 77,
      "full_response": 45,
      "energy_polarization": 32
    },
    "elapsed_seconds": 597.885092956014
  }
}
