{
  "schema": "ferrofinder.endpoint_parent_recovery.v4_variable_cell",
  "status": "complete",
  "input_atom_count": 18,
  "input_formula": "Ba4In4O10",
  "input_spacegroup": "Ima2",
  "input_pointgroup": "mm2",
  "input_is_polar_point_group": true,
  "input_energy_eV": -100.42846735670695,
  "input_cartesian_polarization_e_A2": [
    -0.00019999175603941502,
    0.0003887071721268062,
    0.0004501415987047225
  ],
  "input_reduced_polarization": [
    7.826928562200735e-07,
    0.03310242546674642,
    0.033103399517096496
  ],
  "input_formal_targets": [
    {
      "orbit_id": 0,
      "representative_formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ]
    },
    {
      "orbit_id": 1,
      "representative_formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.5
      ]
    },
    {
      "orbit_id": 2,
      "representative_formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.0
      ]
    },
    {
      "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,
        0.5
      ],
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.5
      ]
    },
    {
      "orbit_id": 5,
      "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": "Imma",
      "spacegroup_number": 74,
      "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": 2.1161032228417783e-15,
      "parent_symmetrization_rmsd_A": 0.2779358973689132,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -98.9373483514394,
      "reduced_polarization": [
        1.1837805233014866e-15,
        -9.14362837009987e-16,
        1.4968290231915158e-15
      ],
      "cartesian_polarization_e_A2": [
        -1.552840954140931e-17,
        -4.075800575648733e-17,
        2.0353952141352605e-17
      ],
      "ranking_score": 0.27793589736891744
    },
    {
      "candidate_id": "inversion_parent_endpoint_01",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "Cmmm",
      "spacegroup_number": 65,
      "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": 8.830351923389443e-16,
      "parent_symmetrization_rmsd_A": 0.4499530808914252,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -96.68106081479922,
      "reduced_polarization": [
        3.7666926909641145e-16,
        -2.57868311980513e-16,
        -7.558937400877007e-16
      ],
      "cartesian_polarization_e_A2": [
        2.4377453313083882e-17,
        3.1725718966458475e-18,
        -1.0278678974896224e-17
      ],
      "ranking_score": 0.449953080891427
    },
    {
      "candidate_id": "inversion_parent_endpoint_02",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "P-1",
      "spacegroup_number": 2,
      "pointgroup": "-1",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 1.5695927917987528e-15,
      "parent_symmetrization_rmsd_A": 0.7102560969688655,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -84.50970338680581,
      "reduced_polarization": [
        5.82590712167647e-16,
        1.0557237461532551e-15,
        1.0048168818101806e-15
      ],
      "cartesian_polarization_e_A2": [
        1.213315469260218e-17,
        1.3031104219177779e-17,
        1.3663547677329336e-17
      ],
      "ranking_score": 0.7102560969688686
    },
    {
      "candidate_id": "bec_projection_00",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Ima2",
      "spacegroup_number": 46,
      "pointgroup": "mm2",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 0.00010129206202454897,
      "parent_symmetrization_rmsd_A": 0.005574654426037342,
      "parent_cell_rmsd_A": 0.011989112949216988,
      "energy_eV": -100.42772216701829,
      "reduced_polarization": [
        8.272554217436707e-06,
        -7.370178359491213e-05,
        -6.8990533921933e-05
      ],
      "cartesian_polarization_e_A2": [
        5.805723156327532e-07,
        -9.228618561529758e-07,
        -9.367978282232908e-07
      ],
      "ranking_score": 0.5087745167873907
    },
    {
      "candidate_id": "inversion_parent_bec_00_00",
      "source": "same_species_inversion_center_projection_after_BEC",
      "spacegroup": "Imma",
      "spacegroup_number": 74,
      "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": 2.9927774126098467e-15,
      "parent_symmetrization_rmsd_A": 0.2779362618409551,
      "parent_cell_rmsd_A": 0.011989112949216988,
      "energy_eV": -98.95977838936118,
      "reduced_polarization": [
        1.2926624313468888e-15,
        5.859865940501308e-16,
        2.6348358946252354e-15
      ],
      "cartesian_polarization_e_A2": [
        -1.2900358346103567e-17,
        -1.8661578095288593e-17,
        3.5825778788703873e-17
      ],
      "ranking_score": 0.2809335400782653
    },
    {
      "candidate_id": "inversion_parent_bec_00_01",
      "source": "same_species_inversion_center_projection_after_BEC",
      "spacegroup": "Imma",
      "spacegroup_number": 74,
      "pointgroup": "mmm",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 1.4551117804070392e-15,
      "parent_symmetrization_rmsd_A": 0.3646869010282432,
      "parent_cell_rmsd_A": 0.011989112949216988,
      "energy_eV": -98.48474673235278,
      "reduced_polarization": [
        7.019210633107431e-16,
        -1.134200350923387e-15,
        -5.815897852656325e-16
      ],
      "cartesian_polarization_e_A2": [
        1.482076492916524e-17,
        -2.018054375420743e-17,
        -7.882834185642826e-18
      ],
      "ranking_score": 0.3676841792655503
    },
    {
      "candidate_id": "bec_projection_01",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.5
      ],
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_residual": 0.0002369567659949672,
      "parent_symmetrization_rmsd_A": 0.14225603865910302,
      "parent_cell_rmsd_A": 0.13338486961102008,
      "energy_eV": -99.34078877819726,
      "reduced_polarization": [
        7.207077200264147e-05,
        0.0001899900454967135,
        0.4998781062126854
      ],
      "cartesian_polarization_e_A2": [
        -0.011538440016224751,
        -0.0062167525458313305,
        0.006624269122376529
      ],
      "ranking_score": 0.676076169593848
    },
    {
      "candidate_id": "bec_projection_02",
      "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,
        0.0,
        0.0
      ],
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_residual": 0.00032905833926888005,
      "parent_symmetrization_rmsd_A": 0.14990132553183125,
      "parent_cell_rmsd_A": 0.14848398768817292,
      "energy_eV": -99.32574905419035,
      "reduced_polarization": [
        0.499754536691589,
        -0.00021894848684406764,
        9.418862723431772e-06
      ],
      "cartesian_polarization_e_A2": [
        0.014976386239444143,
        -6.856443103586931e-05,
        -0.00012282882668977188
      ],
      "ranking_score": 0.6876804391324123
    },
    {
      "candidate_id": "bec_projection_03",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.5
      ],
      "formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_residual": 0.00037769573199519774,
      "parent_symmetrization_rmsd_A": 0.07977437711372475,
      "parent_cell_rmsd_A": 0.17288729702055358,
      "energy_eV": -100.0288862637298,
      "reduced_polarization": [
        3.692066362437414e-05,
        0.49972159141565275,
        0.4997474537849686
      ],
      "cartesian_polarization_e_A2": [
        -0.0030991168999349506,
        0.005991460804654941,
        0.006921483437201825
      ],
      "ranking_score": 0.6237515928328535
    },
    {
      "candidate_id": "bec_projection_04",
      "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,
        0.0,
        0.5
      ],
      "formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_residual": 9.187514680805092e-05,
      "parent_symmetrization_rmsd_A": 0.09888330634950383,
      "parent_cell_rmsd_A": 0.020618770390017555,
      "energy_eV": -99.98574685319379,
      "reduced_polarization": [
        0.49994683556334113,
        -1.3969788386924213e-05,
        0.49992638322006383
      ],
      "cartesian_polarization_e_A2": [
        0.003228735608058725,
        -0.006261545752796714,
        0.006769783513958446
      ],
      "ranking_score": 0.6042217492406243
    },
    {
      "candidate_id": "bec_projection_05",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.5,
        0.5,
        0.0
      ],
      "formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_residual": 0.0009203188614173949,
      "parent_symmetrization_rmsd_A": 0.2647531318585627,
      "parent_cell_rmsd_A": 0.22797624067571853,
      "energy_eV": -96.03689197028288,
      "reduced_polarization": [
        0.4994747377268428,
        0.49931432590060676,
        0.0003177064376112326
      ],
      "cartesian_polarization_e_A2": [
        0.02360916174294947,
        0.011644561971464358,
        -0.0007107233754838323
      ],
      "ranking_score": 0.8235878297503272
    }
  ],
  "formal_branches": [
    {
      "orbit_id": 0,
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.0,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              7.826928562200735e-07,
              0.03310242546674642,
              0.033103399517096496
            ],
            "branch_aligned_reduced_polarization": [
              7.826928562200735e-07,
              0.03310242546674642,
              0.033103399517096496
            ],
            "target_residual": 0.04681458781173465,
            "energy_eV": -100.42846735670695,
            "max_atomic_step_A": 0.00516665085583716,
            "max_log_strain_component": 0.0008237028785536282,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 5.083266025229094,
            "cell_principal_stretches": [
              1.0008296568586408,
              1.000564692654764,
              0.9987621678735755
            ],
            "cell_volume_ratio": 1.0001552593375655,
            "cell_rmsd_from_input_A": 0.011989112949216988
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              8.272554217436707e-06,
              -7.370178359491213e-05,
              -6.8990533921933e-05
            ],
            "branch_aligned_reduced_polarization": [
              8.272554217436707e-06,
              -7.370178359491213e-05,
              -6.8990533921933e-05
            ],
            "target_residual": 0.00010129206202454897,
            "energy_eV": -100.42772216701829
          }
        ],
        "iterations": 1
      },
      "parent": {
        "candidate_id": "inversion_parent_endpoint_00",
        "source": "same_species_inversion_center_projection_from_endpoint",
        "spacegroup": "Imma",
        "spacegroup_number": 74,
        "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": 2.1161032228417783e-15,
        "parent_symmetrization_rmsd_A": 0.2779358973689132,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -98.9373483514394,
        "reduced_polarization": [
          1.1837805233014866e-15,
          -9.14362837009987e-16,
          1.4968290231915158e-15
        ],
        "cartesian_polarization_e_A2": [
          -1.552840954140931e-17,
          -4.075800575648733e-17,
          2.0353952141352605e-17
        ],
        "ranking_score": 0.27793589736891744
      },
      "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": [
          -100.42846735670693,
          -100.34394650351406,
          -100.14009042226368,
          -99.89024809693875,
          -99.63336941159908,
          -99.3815376004035,
          -99.15569993387946,
          -98.99549134376554,
          -98.9373483514394
        ],
        "cartesian_polarizations_e_A2": [
          [
            -0.0001999917560394099,
            0.0003887071721268055,
            0.0004501415987047483
          ],
          [
            -0.0008817611843705982,
            0.0017138454762215714,
            0.0019846184807806957
          ],
          [
            -0.0015136801006450954,
            0.0029420917609874293,
            0.003406896872426671
          ],
          [
            -0.001986753900629875,
            0.003861595875071735,
            0.004471659413694149
          ],
          [
            -0.0021690125020566624,
            0.004215850623323048,
            0.004881876183384296
          ],
          [
            -0.001987989613639669,
            0.0038640042479319136,
            0.0044744430664191695
          ],
          [
            -0.0014840309646657899,
            0.002884474550380102,
            0.0033401656811409856
          ],
          [
            -0.0007816282417937888,
            0.0015192322619049028,
            0.0017592412968673236
          ],
          [
            4.489240410399044e-17,
            5.354642689174301e-17,
            1.1639375819116936e-17
          ]
        ],
        "raw_reduced_polarization": [
          [
            7.826928573284947e-07,
            0.03310242546674737,
            0.03310339951709839
          ],
          [
            6.867240093014213e-07,
            0.1459479506303055,
            0.14594878288818594
          ],
          [
            6.194861208151681e-07,
            0.2505423905931832,
            0.25054309267574776
          ],
          [
            5.882312196278978e-07,
            0.32884509876555035,
            0.3288456976690206
          ],
          [
            5.708902747144725e-07,
            0.35901251307195053,
            0.3590130264712037
          ],
          [
            5.163643070254155e-07,
            0.3290499937495118,
            0.32905040740599756
          ],
          [
            3.9028496059141277e-07,
            0.24563539970044795,
            0.24563568289238563
          ],
          [
            2.0777456049215998e-07,
            0.12937441129996582,
            0.12937455161831266
          ],
          [
            6.383795565236459e-16,
            2.653755058835058e-15,
            8.559593447452203e-16
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            7.826928573284947e-07,
            0.03310242546674737,
            0.03310339951709839
          ],
          [
            6.867240093014213e-07,
            0.1459479506303055,
            0.14594878288818594
          ],
          [
            6.194861208151681e-07,
            0.2505423905931832,
            0.25054309267574776
          ],
          [
            5.882312196278978e-07,
            0.32884509876555035,
            0.3288456976690206
          ],
          [
            5.708902747144725e-07,
            0.35901251307195053,
            0.3590130264712037
          ],
          [
            5.163643070254155e-07,
            0.3290499937495118,
            0.32905040740599756
          ],
          [
            3.9028496059141277e-07,
            0.24563539970044795,
            0.24563568289238563
          ],
          [
            2.0777456049215998e-07,
            0.12937441129996582,
            0.12937455161831266
          ],
          [
            6.383795626484451e-16,
            2.6645352591003757e-15,
            8.604228440844963e-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": [
          [
            7.826928573040348e-07,
            0.033102425466747354,
            0.0331033995170984
          ],
          [
            6.867240093244575e-07,
            0.14594795063030552,
            0.1459487828881859
          ],
          [
            6.194861208452807e-07,
            0.2505423905931832,
            0.2505430926757477
          ],
          [
            5.882312196225925e-07,
            0.32884509876555035,
            0.3288456976690206
          ],
          [
            5.708902747203481e-07,
            0.3590125130719506,
            0.3590130264712037
          ],
          [
            5.163643069794333e-07,
            0.3290499937495118,
            0.32905040740599756
          ],
          [
            3.902849605719183e-07,
            0.2456353997004479,
            0.24563568289238558
          ],
          [
            2.0777456044562825e-07,
            0.12937441129996585,
            0.12937455161831268
          ],
          [
            6.661338147750939e-16,
            2.6645352591003757e-15,
            8.881784197001252e-16
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -98.9373483514394,
          -98.99549134376554,
          -99.15569993387948,
          -99.3815376004035,
          -99.63336941159906,
          -99.89024809693875,
          -100.14009042226367,
          -100.34394650351406,
          -100.42846735670693
        ],
        "cartesian_polarizations_e_A2": [
          [
            7.465790191816636e-18,
            1.3358121694950988e-17,
            9.76073431073152e-18
          ],
          [
            0.0007816282417939065,
            -0.0015192322619048903,
            -0.0017592412968673173
          ],
          [
            0.0014840309646658959,
            -0.002884474550380042,
            -0.0033401656811409704
          ],
          [
            0.001987989613639704,
            -0.0038640042479318793,
            -0.004474443066419194
          ],
          [
            0.0021690125020567127,
            -0.004215850623322968,
            -0.004881876183384385
          ],
          [
            0.0019867539006300007,
            -0.003861595875071745,
            -0.004471659413694176
          ],
          [
            0.0015136801006452438,
            -0.0029420917609874076,
            -0.003406896872426754
          ],
          [
            0.0008817611843707442,
            -0.0017138454762215748,
            -0.001984618480780733
          ],
          [
            0.0001999917560394697,
            -0.00038870717212683234,
            -0.00045014159870478685
          ]
        ],
        "raw_reduced_polarization": [
          [
            2.78461785488296e-16,
            9.215366394491006e-16,
            7.1780410519297145e-16
          ],
          [
            -2.0777455661268574e-07,
            -0.12937441129996508,
            -0.12937455161831218
          ],
          [
            -3.9028495793703566e-07,
            -0.2456353997004449,
            -0.24563568289238452
          ],
          [
            -5.163643075796262e-07,
            -0.3290499937495113,
            -0.32905040740599933
          ],
          [
            -5.70890278156412e-07,
            -0.35901251307195053,
            -0.3590130264712102
          ],
          [
            -5.882312161567892e-07,
            -0.3288450987655518,
            -0.3288456976690226
          ],
          [
            -6.194861193275501e-07,
            -0.2505423905931854,
            -0.25054309267575386
          ],
          [
            -6.867240056115454e-07,
            -0.14594795063030708,
            -0.14594878288818866
          ],
          [
            -7.826928560523519e-07,
            -0.03310242546674993,
            -0.03310339951710123
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            2.78461785488296e-16,
            9.215366394491006e-16,
            7.1780410519297145e-16
          ],
          [
            -2.0777455661268574e-07,
            -0.12937441129996508,
            -0.12937455161831218
          ],
          [
            -3.9028495793703566e-07,
            -0.2456353997004449,
            -0.24563568289238452
          ],
          [
            -5.163643075796262e-07,
            -0.3290499937495113,
            -0.32905040740599933
          ],
          [
            -5.70890278156412e-07,
            -0.35901251307195053,
            -0.3590130264712102
          ],
          [
            -5.882312161567892e-07,
            -0.3288450987655518,
            -0.3288456976690226
          ],
          [
            -6.194861193275501e-07,
            -0.2505423905931854,
            -0.25054309267575386
          ],
          [
            -6.867240056115454e-07,
            -0.14594795063030708,
            -0.14594878288818866
          ],
          [
            -7.826928560523519e-07,
            -0.033102425466749935,
            -0.03310339951710123
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          -7.826928560559979e-07,
          -0.03310242546674206,
          -0.033103399517096684
        ],
        "actual_opposite_endpoint_branch_residual": 9.092996932732318e-15
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            7.826928573284947e-07,
            0.03310242546674737,
            0.03310339951709839
          ],
          [
            6.867240093014213e-07,
            0.1459479506303055,
            0.14594878288818594
          ],
          [
            6.194861208151681e-07,
            0.2505423905931832,
            0.25054309267574776
          ],
          [
            5.882312196278978e-07,
            0.32884509876555035,
            0.3288456976690206
          ],
          [
            5.708902747144725e-07,
            0.35901251307195053,
            0.3590130264712037
          ],
          [
            5.163643070254155e-07,
            0.3290499937495118,
            0.32905040740599756
          ],
          [
            3.9028496059141277e-07,
            0.24563539970044795,
            0.24563568289238563
          ],
          [
            2.0777456049215998e-07,
            0.12937441129996582,
            0.12937455161831266
          ],
          [
            6.383795565236459e-16,
            2.653755058835058e-15,
            8.559593447452203e-16
          ],
          [
            -2.0777455661268574e-07,
            -0.12937441129996508,
            -0.12937455161831218
          ],
          [
            -3.9028495793703566e-07,
            -0.2456353997004449,
            -0.24563568289238452
          ],
          [
            -5.163643075796262e-07,
            -0.3290499937495113,
            -0.32905040740599933
          ],
          [
            -5.70890278156412e-07,
            -0.35901251307195053,
            -0.3590130264712102
          ],
          [
            -5.882312161567892e-07,
            -0.3288450987655518,
            -0.3288456976690226
          ],
          [
            -6.194861193275501e-07,
            -0.2505423905931854,
            -0.25054309267575386
          ],
          [
            -6.867240056115454e-07,
            -0.14594795063030708,
            -0.14594878288818866
          ],
          [
            -7.826928560523519e-07,
            -0.03310242546674993,
            -0.03310339951710123
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            7.826928573284947e-07,
            0.03310242546674737,
            0.03310339951709839
          ],
          [
            6.867240093014213e-07,
            0.1459479506303055,
            0.14594878288818594
          ],
          [
            6.194861208151681e-07,
            0.2505423905931832,
            0.25054309267574776
          ],
          [
            5.882312196278978e-07,
            0.32884509876555035,
            0.3288456976690206
          ],
          [
            5.708902747144725e-07,
            0.35901251307195053,
            0.3590130264712037
          ],
          [
            5.163643070254155e-07,
            0.3290499937495118,
            0.32905040740599756
          ],
          [
            3.9028496059141277e-07,
            0.24563539970044795,
            0.24563568289238563
          ],
          [
            2.0777456049215998e-07,
            0.12937441129996582,
            0.12937455161831266
          ],
          [
            6.383795626484451e-16,
            2.6645352591003757e-15,
            8.604228440844963e-16
          ],
          [
            -2.0777455661268574e-07,
            -0.12937441129996508,
            -0.12937455161831218
          ],
          [
            -3.9028495793703566e-07,
            -0.2456353997004449,
            -0.24563568289238452
          ],
          [
            -5.163643075796262e-07,
            -0.3290499937495113,
            -0.32905040740599933
          ],
          [
            -5.70890278156412e-07,
            -0.35901251307195053,
            -0.3590130264712102
          ],
          [
            -5.882312161567892e-07,
            -0.3288450987655518,
            -0.3288456976690226
          ],
          [
            -6.194861193275501e-07,
            -0.2505423905931854,
            -0.25054309267575386
          ],
          [
            -6.867240056115454e-07,
            -0.14594795063030708,
            -0.14594878288818866
          ],
          [
            -7.826928560523519e-07,
            -0.033102425466749935,
            -0.03310339951710123
          ]
        ],
        "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": [
          [
            7.826928573040348e-07,
            0.033102425466747354,
            0.0331033995170984
          ],
          [
            6.867240093244575e-07,
            0.14594795063030552,
            0.1459487828881859
          ],
          [
            6.194861208452807e-07,
            0.2505423905931832,
            0.2505430926757477
          ],
          [
            5.882312196225925e-07,
            0.32884509876555035,
            0.3288456976690206
          ],
          [
            5.708902747203481e-07,
            0.3590125130719506,
            0.3590130264712037
          ],
          [
            5.163643069794333e-07,
            0.3290499937495118,
            0.32905040740599756
          ],
          [
            3.902849605719183e-07,
            0.2456353997004479,
            0.24563568289238558
          ],
          [
            2.0777456044562825e-07,
            0.12937441129996585,
            0.12937455161831268
          ],
          [
            6.661338147750939e-16,
            2.6645352591003757e-15,
            8.881784197001252e-16
          ],
          [
            -2.0777455661535882e-07,
            -0.12937441129996508,
            -0.12937455161831218
          ],
          [
            -3.902849579628942e-07,
            -0.2456353997004449,
            -0.24563568289238452
          ],
          [
            -5.163643075900559e-07,
            -0.3290499937495113,
            -0.32905040740599933
          ],
          [
            -5.708902781620395e-07,
            -0.35901251307195053,
            -0.3590130264712102
          ],
          [
            -5.882312161809011e-07,
            -0.3288450987655518,
            -0.3288456976690226
          ],
          [
            -6.194861193464796e-07,
            -0.2505423905931854,
            -0.25054309267575386
          ],
          [
            -6.867240056052104e-07,
            -0.14594795063030708,
            -0.1459487828881887
          ],
          [
            -7.826928560272783e-07,
            -0.03310242546674991,
            -0.03310339951710123
          ]
        ]
      },
      "incoming_structure_ids": [
        "incoming_00_000",
        "incoming_00_001",
        "incoming_00_002",
        "incoming_00_003",
        "incoming_00_004",
        "incoming_00_005",
        "incoming_00_006",
        "incoming_00_007",
        "incoming_00_008"
      ],
      "reflected_structure_ids": [
        "reflected_00_001",
        "reflected_00_002",
        "reflected_00_003",
        "reflected_00_004",
        "reflected_00_005",
        "reflected_00_006",
        "reflected_00_007",
        "reflected_00_008"
      ]
    },
    {
      "orbit_id": 1,
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.0,
          0.5
        ],
        [
          0.0,
          0.5,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              7.826928562200735e-07,
              0.03310242546674642,
              0.033103399517096496
            ],
            "branch_aligned_reduced_polarization": [
              7.826928562200735e-07,
              0.03310242546674642,
              0.03310339951709651
            ],
            "target_residual": 0.46806859125013517,
            "energy_eV": -100.42846735670695,
            "max_atomic_step_A": 0.11187027247947759,
            "max_log_strain_component": 0.011638303051277547,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 5.083266025229094,
            "cell_principal_stretches": [
              1.017448695678987,
              0.9968357075975235,
              0.9849488711526779
            ],
            "cell_volume_ratio": 0.9989638962743901,
            "cell_rmsd_from_input_A": 0.13778112350566338
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.007465654871138737,
              0.011218434708791272,
              0.5243352823205093
            ],
            "branch_aligned_reduced_polarization": [
              0.007465654871138737,
              0.011218434708791272,
              0.5243352823205093
            ],
            "target_residual": 0.027817175370430096,
            "energy_eV": -99.29568580384164,
            "max_atomic_step_A": 0.00292639540944588,
            "max_log_strain_component": 0.0004132281933617386,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 5.083266025229094,
            "cell_principal_stretches": [
              1.0171321397025548,
              0.9969347112914518,
              0.9852223106737558
            ],
            "cell_volume_ratio": 0.9990295472092714,
            "cell_rmsd_from_input_A": 0.13338486961102008
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              7.207077200264147e-05,
              0.0001899900454967135,
              0.4998781062126854
            ],
            "branch_aligned_reduced_polarization": [
              7.207077200264147e-05,
              0.0001899900454967135,
              0.4998781062126854
            ],
            "target_residual": 0.0002369567659949672,
            "energy_eV": -99.34078877819726
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_01",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.5
        ],
        "formal_class": [
          0.0,
          0.0,
          0.5
        ],
        "target_residual": 0.0002369567659949672,
        "parent_symmetrization_rmsd_A": 0.14225603865910302,
        "parent_cell_rmsd_A": 0.13338486961102008,
        "energy_eV": -99.34078877819726,
        "reduced_polarization": [
          7.207077200264147e-05,
          0.0001899900454967135,
          0.4998781062126854
        ],
        "cartesian_polarization_e_A2": [
          -0.011538440016224751,
          -0.0062167525458313305,
          0.006624269122376529
        ],
        "ranking_score": 0.676076169593848
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 2,
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.0,
          0.0
        ],
        [
          0.5,
          0.5,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              7.826928562200735e-07,
              0.03310242546674642,
              0.033103399517096496
            ],
            "branch_aligned_reduced_polarization": [
              7.826928561938118e-07,
              0.03310242546674642,
              0.033103399517096496
            ],
            "target_residual": 0.5021860441501003,
            "energy_eV": -100.42846735670695,
            "max_atomic_step_A": 0.11480871999936934,
            "max_log_strain_component": 0.013110543798035489,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 5.083266025229094,
            "cell_principal_stretches": [
              1.0133396694932137,
              1.007787877896273,
              0.9805451496265499
            ],
            "cell_volume_ratio": 1.0013635303400124,
            "cell_rmsd_from_input_A": 0.1414163223833841
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.4912667628685291,
              0.005790355436180456,
              0.014322659577660497
            ],
            "branch_aligned_reduced_polarization": [
              0.4912667628685291,
              0.005790355436180456,
              0.014322659577660497
            ],
            "target_residual": 0.017746442580116064,
            "energy_eV": -99.40104256662454,
            "max_atomic_step_A": 0.004509925693027356,
            "max_log_strain_component": 0.000629259582703935,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 5.083266025229094,
            "cell_principal_stretches": [
              1.0139255212585665,
              1.0080711111453933,
              0.9797768114372515
            ],
            "cell_volume_ratio": 1.001438723252448,
            "cell_rmsd_from_input_A": 0.14848398768817292
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.499754536691589,
              -0.00021894848684406764,
              9.418862723431772e-06
            ],
            "branch_aligned_reduced_polarization": [
              0.499754536691589,
              -0.00021894848684406764,
              9.418862723431772e-06
            ],
            "target_residual": 0.00032905833926888005,
            "energy_eV": -99.32574905419035
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_02",
        "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,
          0.0,
          0.0
        ],
        "formal_class": [
          0.5,
          0.0,
          0.0
        ],
        "target_residual": 0.00032905833926888005,
        "parent_symmetrization_rmsd_A": 0.14990132553183125,
        "parent_cell_rmsd_A": 0.14848398768817292,
        "energy_eV": -99.32574905419035,
        "reduced_polarization": [
          0.499754536691589,
          -0.00021894848684406764,
          9.418862723431772e-06
        ],
        "cartesian_polarization_e_A2": [
          0.014976386239444143,
          -6.856443103586931e-05,
          -0.00012282882668977188
        ],
        "ranking_score": 0.6876804391324123
      },
      "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": [
              7.826928562200735e-07,
              0.03310242546674642,
              0.033103399517096496
            ],
            "branch_aligned_reduced_polarization": [
              7.826928562200735e-07,
              0.03310242546674641,
              0.03310339951709651
            ],
            "target_residual": 0.6602921933872457,
            "energy_eV": -100.42846735670695,
            "max_atomic_step_A": 0.07287351105640341,
            "max_log_strain_component": 0.01161795091784018,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 5.083266025229094,
            "cell_principal_stretches": [
              1.0176233960062442,
              0.9920690876729253,
              0.988371069890879
            ],
            "cell_volume_ratio": 0.9978126961171391,
            "cell_rmsd_from_input_A": 0.1671438926720836
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.0019105478097694078,
              0.48515858291118663,
              0.48635125285884734
            ],
            "branch_aligned_reduced_polarization": [
              0.0019105478097694078,
              0.48515858291118663,
              0.48635125285884734
            ],
            "target_residual": 0.02025354666868643,
            "energy_eV": -100.05359295110287,
            "max_atomic_step_A": 0.0025530531936183145,
            "max_log_strain_component": 0.0004174512090981833,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 5.083266025229094,
            "cell_principal_stretches": [
              1.018239994459025,
              0.9917960121406495,
              0.9879682214522169
            ],
            "cell_volume_ratio": 0.9977356367935641,
            "cell_rmsd_from_input_A": 0.17288729702055358
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              3.692066362437414e-05,
              0.49972159141565275,
              0.4997474537849686
            ],
            "branch_aligned_reduced_polarization": [
              3.692066362437414e-05,
              0.49972159141565275,
              0.4997474537849686
            ],
            "target_residual": 0.00037769573199519774,
            "energy_eV": -100.0288862637298
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_03",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.5,
          0.5
        ],
        "formal_class": [
          0.0,
          0.5,
          0.5
        ],
        "target_residual": 0.00037769573199519774,
        "parent_symmetrization_rmsd_A": 0.07977437711372475,
        "parent_cell_rmsd_A": 0.17288729702055358,
        "energy_eV": -100.0288862637298,
        "reduced_polarization": [
          3.692066362437414e-05,
          0.49972159141565275,
          0.4997474537849686
        ],
        "cartesian_polarization_e_A2": [
          -0.0030991168999349506,
          0.005991460804654941,
          0.006921483437201825
        ],
        "ranking_score": 0.6237515928328535
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 4,
      "formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.0,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              7.826928562200735e-07,
              0.03310242546674642,
              0.033103399517096496
            ],
            "branch_aligned_reduced_polarization": [
              7.826928561938118e-07,
              0.03310242546674642,
              0.03310339951709651
            ],
            "target_residual": 0.6848995717782498,
            "energy_eV": -100.42846735670695,
            "max_atomic_step_A": 0.08982591682849381,
            "max_log_strain_component": 0.004865032422520443,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 5.083266025229094,
            "cell_principal_stretches": [
              1.005920201060284,
              0.9991855898263576,
              0.9950947799735134
            ],
            "cell_volume_ratio": 1.000170728010854,
            "cell_rmsd_from_input_A": 0.02200520645291938
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.49870868040519606,
              0.00606240961836085,
              0.5052148016467976
            ],
            "branch_aligned_reduced_polarization": [
              0.49870868040519606,
              0.00606240961836085,
              0.5052148016467976
            ],
            "target_residual": 0.008100276099748773,
            "energy_eV": -99.98766540186108,
            "max_atomic_step_A": 0.0010032804619070693,
            "max_log_strain_component": 0.00016254626298816302,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 5.083266025229094,
            "cell_principal_stretches": [
              1.005885860985232,
              0.9993279345785752,
              0.9950165968475663
            ],
            "cell_volume_ratio": 1.0002004739952473,
            "cell_rmsd_from_input_A": 0.020618770390017555
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.49994683556334113,
              -1.3969788386924213e-05,
              0.49992638322006383
            ],
            "branch_aligned_reduced_polarization": [
              0.49994683556334113,
              -1.3969788386924213e-05,
              0.49992638322006383
            ],
            "target_residual": 9.187514680805092e-05,
            "energy_eV": -99.98574685319379
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_04",
        "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,
          0.0,
          0.5
        ],
        "formal_class": [
          0.5,
          0.0,
          0.5
        ],
        "target_residual": 9.187514680805092e-05,
        "parent_symmetrization_rmsd_A": 0.09888330634950383,
        "parent_cell_rmsd_A": 0.020618770390017555,
        "energy_eV": -99.98574685319379,
        "reduced_polarization": [
          0.49994683556334113,
          -1.3969788386924213e-05,
          0.49992638322006383
        ],
        "cartesian_polarization_e_A2": [
          0.003228735608058725,
          -0.006261545752796714,
          0.006769783513958446
        ],
        "ranking_score": 0.6042217492406243
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 5,
      "formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.5,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.5,
        0.5,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              7.826928562200735e-07,
              0.03310242546674642,
              0.033103399517096496
            ],
            "branch_aligned_reduced_polarization": [
              7.826928561938118e-07,
              0.03310242546674641,
              0.033103399517096496
            ],
            "target_residual": 0.6849002828677909,
            "energy_eV": -100.42846735670695,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.01399672176738996,
            "step_scale": 0.6141373593714037,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 5.083266025229094,
            "cell_principal_stretches": [
              1.0180042757403076,
              1.002999200560052,
              0.9795028400982072
            ],
            "cell_volume_ratio": 1.0001286964056952,
            "cell_rmsd_from_input_A": 0.12929954749666708
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.3093228461756331,
              0.3443530209839298,
              0.044800183983778004
            ],
            "branch_aligned_reduced_polarization": [
              0.3093228461756331,
              0.3443530209839298,
              0.044800183983778004
            ],
            "target_residual": 0.25018156517291723,
            "energy_eV": -99.04875973031601,
            "max_atomic_step_A": 0.0889820838525075,
            "max_log_strain_component": 0.00829194086037601,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 5.083266025229094,
            "cell_principal_stretches": [
              1.0292840272183614,
              1.0060842018821679,
              0.9662139719043971
            ],
            "cell_volume_ratio": 1.0005593993019835,
            "cell_rmsd_from_input_A": 0.2219371023980837
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.498562231365596,
              0.51452472604354,
              0.02477684988780643
            ],
            "branch_aligned_reduced_polarization": [
              0.498562231365596,
              0.51452472604354,
              0.02477684988780643
            ],
            "target_residual": 0.02875634079031718,
            "energy_eV": -96.14547366522584,
            "max_atomic_step_A": 0.004475216096448617,
            "max_log_strain_component": 0.0008203356778247881,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 5.083266025229094,
            "cell_principal_stretches": [
              1.0295807904542207,
              1.0065037878936278,
              0.9656453797507298
            ],
            "cell_volume_ratio": 1.000676063910678,
            "cell_rmsd_from_input_A": 0.22797624067571853
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.4994747377268428,
              0.49931432590060676,
              0.0003177064376112326
            ],
            "branch_aligned_reduced_polarization": [
              0.4994747377268428,
              0.49931432590060676,
              0.0003177064376112326
            ],
            "target_residual": 0.0009203188614173949,
            "energy_eV": -96.03689197028288
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_05",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.5,
          0.5,
          0.0
        ],
        "formal_class": [
          0.5,
          0.5,
          0.0
        ],
        "target_residual": 0.0009203188614173949,
        "parent_symmetrization_rmsd_A": 0.2647531318585627,
        "parent_cell_rmsd_A": 0.22797624067571853,
        "energy_eV": -96.03689197028288,
        "reduced_polarization": [
          0.4994747377268428,
          0.49931432590060676,
          0.0003177064376112326
        ],
        "cartesian_polarization_e_A2": [
          0.02360916174294947,
          0.011644561971464358,
          -0.0007107233754838323
        ],
        "ranking_score": 0.8235878297503272
      },
      "branch_status": "awaiting_branch_sampling"
    }
  ],
  "sampled_polarization_branches": [
    {
      "orbit_id": 0,
      "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
        ],
        "endpoint_rmsd_A": 0.2779358973689132,
        "minimum_distance_A_by_image": [
          2.070255648770652,
          2.0637934682160495,
          2.023020013611512,
          1.9849456690575644,
          1.953241994202967,
          1.9282232526073118,
          1.910152135575335,
          1.8992269731025948,
          1.8955713267634695
        ],
        "minimum_distance_A": 1.8955713267634695,
        "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": [
          319.7222854669143,
          319.7222854669143,
          319.722285466914,
          319.722285466914,
          319.722285466914,
          319.722285466914,
          319.722285466914,
          319.7222854669137,
          319.7222854669143
        ],
        "cell_deformation_log_strain_norm": 4.965068306494545e-16
      },
      "parent_reduced_polarization": [
        6.383795565236459e-16,
        2.653755058835058e-15,
        8.559593447452203e-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": [
          -100.42846735670693,
          -100.34394650351406,
          -100.14009042226368,
          -99.89024809693875,
          -99.63336941159908,
          -99.3815376004035,
          -99.15569993387946,
          -98.99549134376554,
          -98.9373483514394
        ],
        "cartesian_polarizations_e_A2": [
          [
            -0.0001999917560394099,
            0.0003887071721268055,
            0.0004501415987047483
          ],
          [
            -0.0008817611843705982,
            0.0017138454762215714,
            0.0019846184807806957
          ],
          [
            -0.0015136801006450954,
            0.0029420917609874293,
            0.003406896872426671
          ],
          [
            -0.001986753900629875,
            0.003861595875071735,
            0.004471659413694149
          ],
          [
            -0.0021690125020566624,
            0.004215850623323048,
            0.004881876183384296
          ],
          [
            -0.001987989613639669,
            0.0038640042479319136,
            0.0044744430664191695
          ],
          [
            -0.0014840309646657899,
            0.002884474550380102,
            0.0033401656811409856
          ],
          [
            -0.0007816282417937888,
            0.0015192322619049028,
            0.0017592412968673236
          ],
          [
            4.489240410399044e-17,
            5.354642689174301e-17,
            1.1639375819116936e-17
          ]
        ],
        "raw_reduced_polarization": [
          [
            7.826928573284947e-07,
            0.03310242546674737,
            0.03310339951709839
          ],
          [
            6.867240093014213e-07,
            0.1459479506303055,
            0.14594878288818594
          ],
          [
            6.194861208151681e-07,
            0.2505423905931832,
            0.25054309267574776
          ],
          [
            5.882312196278978e-07,
            0.32884509876555035,
            0.3288456976690206
          ],
          [
            5.708902747144725e-07,
            0.35901251307195053,
            0.3590130264712037
          ],
          [
            5.163643070254155e-07,
            0.3290499937495118,
            0.32905040740599756
          ],
          [
            3.9028496059141277e-07,
            0.24563539970044795,
            0.24563568289238563
          ],
          [
            2.0777456049215998e-07,
            0.12937441129996582,
            0.12937455161831266
          ],
          [
            6.383795565236459e-16,
            2.653755058835058e-15,
            8.559593447452203e-16
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            7.826928573284947e-07,
            0.03310242546674737,
            0.03310339951709839
          ],
          [
            6.867240093014213e-07,
            0.1459479506303055,
            0.14594878288818594
          ],
          [
            6.194861208151681e-07,
            0.2505423905931832,
            0.25054309267574776
          ],
          [
            5.882312196278978e-07,
            0.32884509876555035,
            0.3288456976690206
          ],
          [
            5.708902747144725e-07,
            0.35901251307195053,
            0.3590130264712037
          ],
          [
            5.163643070254155e-07,
            0.3290499937495118,
            0.32905040740599756
          ],
          [
            3.9028496059141277e-07,
            0.24563539970044795,
            0.24563568289238563
          ],
          [
            2.0777456049215998e-07,
            0.12937441129996582,
            0.12937455161831266
          ],
          [
            6.383795626484451e-16,
            2.6645352591003757e-15,
            8.604228440844963e-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": [
          [
            7.826928573040348e-07,
            0.033102425466747354,
            0.0331033995170984
          ],
          [
            6.867240093244575e-07,
            0.14594795063030552,
            0.1459487828881859
          ],
          [
            6.194861208452807e-07,
            0.2505423905931832,
            0.2505430926757477
          ],
          [
            5.882312196225925e-07,
            0.32884509876555035,
            0.3288456976690206
          ],
          [
            5.708902747203481e-07,
            0.3590125130719506,
            0.3590130264712037
          ],
          [
            5.163643069794333e-07,
            0.3290499937495118,
            0.32905040740599756
          ],
          [
            3.902849605719183e-07,
            0.2456353997004479,
            0.24563568289238558
          ],
          [
            2.0777456044562825e-07,
            0.12937441129996585,
            0.12937455161831268
          ],
          [
            6.661338147750939e-16,
            2.6645352591003757e-15,
            8.881784197001252e-16
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -98.9373483514394,
          -98.99549134376554,
          -99.15569993387948,
          -99.3815376004035,
          -99.63336941159906,
          -99.89024809693875,
          -100.14009042226367,
          -100.34394650351406,
          -100.42846735670693
        ],
        "cartesian_polarizations_e_A2": [
          [
            7.465790191816636e-18,
            1.3358121694950988e-17,
            9.76073431073152e-18
          ],
          [
            0.0007816282417939065,
            -0.0015192322619048903,
            -0.0017592412968673173
          ],
          [
            0.0014840309646658959,
            -0.002884474550380042,
            -0.0033401656811409704
          ],
          [
            0.001987989613639704,
            -0.0038640042479318793,
            -0.004474443066419194
          ],
          [
            0.0021690125020567127,
            -0.004215850623322968,
            -0.004881876183384385
          ],
          [
            0.0019867539006300007,
            -0.003861595875071745,
            -0.004471659413694176
          ],
          [
            0.0015136801006452438,
            -0.0029420917609874076,
            -0.003406896872426754
          ],
          [
            0.0008817611843707442,
            -0.0017138454762215748,
            -0.001984618480780733
          ],
          [
            0.0001999917560394697,
            -0.00038870717212683234,
            -0.00045014159870478685
          ]
        ],
        "raw_reduced_polarization": [
          [
            2.78461785488296e-16,
            9.215366394491006e-16,
            7.1780410519297145e-16
          ],
          [
            -2.0777455661268574e-07,
            -0.12937441129996508,
            -0.12937455161831218
          ],
          [
            -3.9028495793703566e-07,
            -0.2456353997004449,
            -0.24563568289238452
          ],
          [
            -5.163643075796262e-07,
            -0.3290499937495113,
            -0.32905040740599933
          ],
          [
            -5.70890278156412e-07,
            -0.35901251307195053,
            -0.3590130264712102
          ],
          [
            -5.882312161567892e-07,
            -0.3288450987655518,
            -0.3288456976690226
          ],
          [
            -6.194861193275501e-07,
            -0.2505423905931854,
            -0.25054309267575386
          ],
          [
            -6.867240056115454e-07,
            -0.14594795063030708,
            -0.14594878288818866
          ],
          [
            -7.826928560523519e-07,
            -0.03310242546674993,
            -0.03310339951710123
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            2.78461785488296e-16,
            9.215366394491006e-16,
            7.1780410519297145e-16
          ],
          [
            -2.0777455661268574e-07,
            -0.12937441129996508,
            -0.12937455161831218
          ],
          [
            -3.9028495793703566e-07,
            -0.2456353997004449,
            -0.24563568289238452
          ],
          [
            -5.163643075796262e-07,
            -0.3290499937495113,
            -0.32905040740599933
          ],
          [
            -5.70890278156412e-07,
            -0.35901251307195053,
            -0.3590130264712102
          ],
          [
            -5.882312161567892e-07,
            -0.3288450987655518,
            -0.3288456976690226
          ],
          [
            -6.194861193275501e-07,
            -0.2505423905931854,
            -0.25054309267575386
          ],
          [
            -6.867240056115454e-07,
            -0.14594795063030708,
            -0.14594878288818866
          ],
          [
            -7.826928560523519e-07,
            -0.033102425466749935,
            -0.03310339951710123
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          -7.826928560559979e-07,
          -0.03310242546674206,
          -0.033103399517096684
        ],
        "actual_opposite_endpoint_branch_residual": 9.092996932732318e-15
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            7.826928573284947e-07,
            0.03310242546674737,
            0.03310339951709839
          ],
          [
            6.867240093014213e-07,
            0.1459479506303055,
            0.14594878288818594
          ],
          [
            6.194861208151681e-07,
            0.2505423905931832,
            0.25054309267574776
          ],
          [
            5.882312196278978e-07,
            0.32884509876555035,
            0.3288456976690206
          ],
          [
            5.708902747144725e-07,
            0.35901251307195053,
            0.3590130264712037
          ],
          [
            5.163643070254155e-07,
            0.3290499937495118,
            0.32905040740599756
          ],
          [
            3.9028496059141277e-07,
            0.24563539970044795,
            0.24563568289238563
          ],
          [
            2.0777456049215998e-07,
            0.12937441129996582,
            0.12937455161831266
          ],
          [
            6.383795565236459e-16,
            2.653755058835058e-15,
            8.559593447452203e-16
          ],
          [
            -2.0777455661268574e-07,
            -0.12937441129996508,
            -0.12937455161831218
          ],
          [
            -3.9028495793703566e-07,
            -0.2456353997004449,
            -0.24563568289238452
          ],
          [
            -5.163643075796262e-07,
            -0.3290499937495113,
            -0.32905040740599933
          ],
          [
            -5.70890278156412e-07,
            -0.35901251307195053,
            -0.3590130264712102
          ],
          [
            -5.882312161567892e-07,
            -0.3288450987655518,
            -0.3288456976690226
          ],
          [
            -6.194861193275501e-07,
            -0.2505423905931854,
            -0.25054309267575386
          ],
          [
            -6.867240056115454e-07,
            -0.14594795063030708,
            -0.14594878288818866
          ],
          [
            -7.826928560523519e-07,
            -0.03310242546674993,
            -0.03310339951710123
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            7.826928573284947e-07,
            0.03310242546674737,
            0.03310339951709839
          ],
          [
            6.867240093014213e-07,
            0.1459479506303055,
            0.14594878288818594
          ],
          [
            6.194861208151681e-07,
            0.2505423905931832,
            0.25054309267574776
          ],
          [
            5.882312196278978e-07,
            0.32884509876555035,
            0.3288456976690206
          ],
          [
            5.708902747144725e-07,
            0.35901251307195053,
            0.3590130264712037
          ],
          [
            5.163643070254155e-07,
            0.3290499937495118,
            0.32905040740599756
          ],
          [
            3.9028496059141277e-07,
            0.24563539970044795,
            0.24563568289238563
          ],
          [
            2.0777456049215998e-07,
            0.12937441129996582,
            0.12937455161831266
          ],
          [
            6.383795626484451e-16,
            2.6645352591003757e-15,
            8.604228440844963e-16
          ],
          [
            -2.0777455661268574e-07,
            -0.12937441129996508,
            -0.12937455161831218
          ],
          [
            -3.9028495793703566e-07,
            -0.2456353997004449,
            -0.24563568289238452
          ],
          [
            -5.163643075796262e-07,
            -0.3290499937495113,
            -0.32905040740599933
          ],
          [
            -5.70890278156412e-07,
            -0.35901251307195053,
            -0.3590130264712102
          ],
          [
            -5.882312161567892e-07,
            -0.3288450987655518,
            -0.3288456976690226
          ],
          [
            -6.194861193275501e-07,
            -0.2505423905931854,
            -0.25054309267575386
          ],
          [
            -6.867240056115454e-07,
            -0.14594795063030708,
            -0.14594878288818866
          ],
          [
            -7.826928560523519e-07,
            -0.033102425466749935,
            -0.03310339951710123
          ]
        ],
        "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": [
          [
            7.826928573040348e-07,
            0.033102425466747354,
            0.0331033995170984
          ],
          [
            6.867240093244575e-07,
            0.14594795063030552,
            0.1459487828881859
          ],
          [
            6.194861208452807e-07,
            0.2505423905931832,
            0.2505430926757477
          ],
          [
            5.882312196225925e-07,
            0.32884509876555035,
            0.3288456976690206
          ],
          [
            5.708902747203481e-07,
            0.3590125130719506,
            0.3590130264712037
          ],
          [
            5.163643069794333e-07,
            0.3290499937495118,
            0.32905040740599756
          ],
          [
            3.902849605719183e-07,
            0.2456353997004479,
            0.24563568289238558
          ],
          [
            2.0777456044562825e-07,
            0.12937441129996585,
            0.12937455161831268
          ],
          [
            6.661338147750939e-16,
            2.6645352591003757e-15,
            8.881784197001252e-16
          ],
          [
            -2.0777455661535882e-07,
            -0.12937441129996508,
            -0.12937455161831218
          ],
          [
            -3.902849579628942e-07,
            -0.2456353997004449,
            -0.24563568289238452
          ],
          [
            -5.163643075900559e-07,
            -0.3290499937495113,
            -0.32905040740599933
          ],
          [
            -5.708902781620395e-07,
            -0.35901251307195053,
            -0.3590130264712102
          ],
          [
            -5.882312161809011e-07,
            -0.3288450987655518,
            -0.3288456976690226
          ],
          [
            -6.194861193464796e-07,
            -0.2505423905931854,
            -0.25054309267575386
          ],
          [
            -6.867240056052104e-07,
            -0.14594795063030708,
            -0.1459487828881887
          ],
          [
            -7.826928560272783e-07,
            -0.03310242546674991,
            -0.03310339951710123
          ]
        ]
      },
      "incoming_structure_ids": [
        "incoming_00_000",
        "incoming_00_001",
        "incoming_00_002",
        "incoming_00_003",
        "incoming_00_004",
        "incoming_00_005",
        "incoming_00_006",
        "incoming_00_007",
        "incoming_00_008"
      ],
      "reflected_structure_ids": [
        "reflected_00_001",
        "reflected_00_002",
        "reflected_00_003",
        "reflected_00_004",
        "reflected_00_005",
        "reflected_00_006",
        "reflected_00_007",
        "reflected_00_008"
      ],
      "positive_extension_structure_ids": [
        "extension_plus_00_000",
        "extension_plus_00_001",
        "extension_plus_00_002",
        "extension_plus_00_003"
      ],
      "negative_extension_structure_ids": [
        "extension_minus_00_000",
        "extension_minus_00_001",
        "extension_minus_00_002",
        "extension_minus_00_003"
      ],
      "extension": {
        "enabled": true,
        "fraction_beyond_polar_endpoint": 0.35,
        "images_per_side": 4,
        "construction": "continue fractional atomic displacements and symmetric log strain beyond +P; reflect these structures about N for the -P side",
        "positive_path_coordinates": [
          1.35,
          1.2625,
          1.175,
          1.0875
        ],
        "negative_path_coordinates": [
          -1.0875,
          -1.175,
          -1.2625,
          -1.35
        ]
      },
      "branch_coordinates": [
        1.35,
        1.2625,
        1.175,
        1.0875,
        1.0,
        0.875,
        0.75,
        0.625,
        0.5,
        0.375,
        0.25,
        0.125,
        0.0,
        -0.125,
        -0.25,
        -0.375,
        -0.5,
        -0.625,
        -0.75,
        -0.875,
        -1.0,
        -1.0875,
        -1.175,
        -1.2625,
        -1.35
      ],
      "parent": {
        "candidate_id": "inversion_parent_endpoint_00",
        "source": "same_species_inversion_center_projection_from_endpoint",
        "spacegroup": "Imma",
        "spacegroup_number": 74,
        "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": 2.1161032228417783e-15,
        "parent_symmetrization_rmsd_A": 0.2779358973689132,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -98.9373483514394,
        "reduced_polarization": [
          1.1837805233014866e-15,
          -9.14362837009987e-16,
          1.4968290231915158e-15
        ],
        "cartesian_polarization_e_A2": [
          -1.552840954140931e-17,
          -4.075800575648733e-17,
          2.0353952141352605e-17
        ],
        "ranking_score": 0.27793589736891744
      }
    }
  ],
  "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": 48,
      "full_response": 13,
      "energy_polarization": 35
    },
    "model_evaluations_for_recovery_and_path_properties": {
      "total": 73,
      "full_response": 38,
      "energy_polarization": 35
    },
    "elapsed_seconds": 181.77207302994793
  }
}