{
  "schema": "ferrofinder.endpoint_parent_recovery.v4_variable_cell",
  "status": "complete",
  "input_atom_count": 24,
  "input_formula": "Na8O12Si4",
  "input_spacegroup": "Cmc2_1",
  "input_pointgroup": "mm2",
  "input_is_polar_point_group": true,
  "input_energy_eV": -142.25662949346005,
  "input_cartesian_polarization_e_A2": [
    -5.404111045691518e-18,
    -1.2639691531472912e-17,
    0.002541494802361694
  ],
  "input_reduced_polarization": [
    -1.6226367489713629e-16,
    -6.551438639322251e-16,
    0.166345949055587
  ],
  "input_formal_targets": [
    {
      "orbit_id": 0,
      "representative_formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ]
    },
    {
      "orbit_id": 1,
      "representative_formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.5
      ]
    },
    {
      "orbit_id": 2,
      "representative_formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        -0.5,
        0.0
      ]
    },
    {
      "orbit_id": 3,
      "representative_formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        -0.5,
        0.0,
        0.0
      ]
    },
    {
      "orbit_id": 4,
      "representative_formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        -0.5,
        0.5
      ]
    },
    {
      "orbit_id": 5,
      "representative_formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        -0.5,
        0.0,
        0.5
      ]
    },
    {
      "orbit_id": 6,
      "representative_formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        -0.5,
        -0.5,
        0.0
      ]
    },
    {
      "orbit_id": 7,
      "representative_formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "target_reduced_polarization": [
        -0.5,
        -0.5,
        0.5
      ]
    }
  ],
  "parent_candidates": [
    {
      "candidate_id": "inversion_parent_endpoint_00",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "Cmcm",
      "spacegroup_number": 63,
      "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": 7.525047103179227e-16,
      "parent_symmetrization_rmsd_A": 0.27086232774654817,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -137.42963904858175,
      "reduced_polarization": [
        -1.8218047499531855e-16,
        -7.257151552308803e-16,
        -8.006951385739904e-17
      ],
      "cartesian_polarization_e_A2": [
        -6.067430174101793e-18,
        -1.400122355840646e-17,
        -1.2233315836756923e-18
      ],
      "ranking_score": 0.27086232774654967
    },
    {
      "candidate_id": "inversion_parent_endpoint_01",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "Cmcm",
      "spacegroup_number": 63,
      "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": 1.8339826513629057e-15,
      "parent_symmetrization_rmsd_A": 0.33314837838123823,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -139.63942050246368,
      "reduced_polarization": [
        -1.3713583178006173e-15,
        -9.805328174278274e-16,
        -7.22097032015934e-16
      ],
      "cartesian_polarization_e_A2": [
        -4.5672407194803696e-17,
        -1.8917421090363614e-17,
        -1.1032464956847494e-17
      ],
      "ranking_score": 0.3331483783812419
    },
    {
      "candidate_id": "bec_projection_00",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cmc2_1",
      "spacegroup_number": 36,
      "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": 3.038830269791456e-06,
      "parent_symmetrization_rmsd_A": 0.01712507968601378,
      "parent_cell_rmsd_A": 0.009816711701983005,
      "energy_eV": -142.16896344245754,
      "reduced_polarization": [
        -1.2473480330765167e-15,
        6.696567536932994e-16,
        3.038830269791456e-06
      ],
      "cartesian_polarization_e_A2": [
        -4.161233719004375e-17,
        1.294917696694909e-17,
        4.634021871587959e-08
      ],
      "ranking_score": 0.5195853352720491
    },
    {
      "candidate_id": "inversion_parent_bec_00_00",
      "source": "same_species_inversion_center_projection_after_BEC",
      "spacegroup": "Cmcm",
      "spacegroup_number": 63,
      "pointgroup": "mmm",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 9.366831059839064e-15,
      "parent_symmetrization_rmsd_A": 0.27087365065435975,
      "parent_cell_rmsd_A": 0.009816711701983005,
      "energy_eV": -137.642058808417,
      "reduced_polarization": [
        -1.4412692814710733e-15,
        -6.437816332372641e-16,
        9.232865869845614e-15
      ],
      "cartesian_polarization_e_A2": [
        -4.8081804081800775e-17,
        -1.2448620546377948e-17,
        1.4079530141457593e-16
      ],
      "ranking_score": 0.2733278285798742
    },
    {
      "candidate_id": "inversion_parent_bec_00_01",
      "source": "same_species_inversion_center_projection_after_BEC",
      "spacegroup": "Cmcm",
      "spacegroup_number": 63,
      "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": 2.3539193036588307e-15,
      "parent_symmetrization_rmsd_A": 0.33314974494094235,
      "parent_cell_rmsd_A": 0.009816711701983005,
      "energy_eV": -139.61132877207655,
      "reduced_polarization": [
        -1.3273332466703564e-15,
        1.651471131683178e-15,
        1.0255562596163554e-15
      ],
      "cartesian_polarization_e_A2": [
        -4.428081409778239e-17,
        3.193402296714103e-17,
        1.5639077262226584e-17
      ],
      "ranking_score": 0.3356039228664428
    },
    {
      "candidate_id": "bec_projection_01",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cmc2_1",
      "spacegroup_number": 36,
      "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": 4.614406368191881e-05,
      "parent_symmetrization_rmsd_A": 0.03561327206400865,
      "parent_cell_rmsd_A": 0.020653124495777532,
      "energy_eV": -141.841640614529,
      "reduced_polarization": [
        -2.7179661844899787e-17,
        3.0722638886679285e-16,
        0.4999538559363181
      ],
      "cartesian_polarization_e_A2": [
        -3.909947498332267e-17,
        -6.916140881081721e-17,
        0.007669023495812792
      ],
      "ranking_score": 0.5408688413153169
    },
    {
      "candidate_id": "bec_projection_02",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cm",
      "spacegroup_number": 8,
      "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": 3.479009347297704e-05,
      "parent_symmetrization_rmsd_A": 0.07256127065393464,
      "parent_cell_rmsd_A": 0.03161655994779575,
      "energy_eV": -140.34132962200755,
      "reduced_polarization": [
        -2.766117834580141e-15,
        -0.5000236439543034,
        -2.5520854781055314e-05
      ],
      "cartesian_polarization_e_A2": [
        -8.415159114944894e-17,
        -0.009670643410212737,
        -7.807742152006181e-05
      ],
      "ranking_score": 0.5805349908278296
    },
    {
      "candidate_id": "bec_projection_03",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cc",
      "spacegroup_number": 9,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        -0.5,
        0.0,
        0.0
      ],
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_residual": 7.743205480838562e-06,
      "parent_symmetrization_rmsd_A": 0.1261300322746924,
      "parent_cell_rmsd_A": 0.06132312968943011,
      "energy_eV": -133.959332427237,
      "reduced_polarization": [
        -0.49999822760015394,
        -8.817913809695166e-17,
        -7.537627604504515e-06
      ],
      "cartesian_polarization_e_A2": [
        -0.016682064565451876,
        3.949317855677114e-16,
        -0.00015747878008390612
      ],
      "ranking_score": 0.6414763011080116
    },
    {
      "candidate_id": "bec_projection_04",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cm",
      "spacegroup_number": 8,
      "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": 2.6785557384764326e-05,
      "parent_symmetrization_rmsd_A": 0.07863189219058192,
      "parent_cell_rmsd_A": 0.03588474423125924,
      "energy_eV": -139.42682823880472,
      "reduced_polarization": [
        2.362822146660716e-15,
        -0.4999831604917022,
        0.4999791698044968
      ],
      "cartesian_polarization_e_A2": [
        8.028230457740067e-17,
        -0.009540810839361468,
        0.007592573461596775
      ],
      "ranking_score": 0.5876566493631663
    },
    {
      "candidate_id": "bec_projection_05",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cc",
      "spacegroup_number": 9,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        -0.5,
        0.0,
        0.5
      ],
      "formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_residual": 2.7538483550113138e-05,
      "parent_symmetrization_rmsd_A": 0.13137296567152745,
      "parent_cell_rmsd_A": 0.06481192797235028,
      "energy_eV": -132.25075757992,
      "reduced_polarization": [
        -0.5000026219056287,
        2.4526319338830706e-15,
        0.4999725866148184
      ],
      "cartesian_polarization_e_A2": [
        -0.016516575936930837,
        2.676555091448627e-16,
        0.007514709251447359
      ],
      "ranking_score": 0.6476310246317152
    },
    {
      "candidate_id": "bec_projection_06",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        -0.5,
        -0.5,
        0.0
      ],
      "formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_residual": 2.3547216731382614e-05,
      "parent_symmetrization_rmsd_A": 0.14564832197692823,
      "parent_cell_rmsd_A": 0.06909109450033926,
      "energy_eV": -130.94330129300678,
      "reduced_polarization": [
        -0.4999862846485918,
        -0.500008584390441,
        -1.7107565352784946e-05
      ],
      "cartesian_polarization_e_A2": [
        -0.016684831245080262,
        -0.009672464736913643,
        -0.0002386596084264563
      ],
      "ranking_score": 0.6629681900354758
    },
    {
      "candidate_id": "bec_projection_07",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        -0.5,
        -0.5,
        0.5
      ],
      "formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "target_residual": 1.6862972431155255e-05,
      "parent_symmetrization_rmsd_A": 0.14966111775726135,
      "parent_cell_rmsd_A": 0.07161870030053386,
      "energy_eV": -128.5896008939925,
      "reduced_polarization": [
        -0.5000018573737153,
        -0.49999718143917543,
        0.4999834783258423
      ],
      "cartesian_polarization_e_A2": [
        -0.01651868534505123,
        -0.00953717897760064,
        0.007434597884920497
      ],
      "ranking_score": 0.6675995187772571
    }
  ],
  "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": [
              -1.6226367489713629e-16,
              -6.551438639322251e-16,
              0.166345949055587
            ],
            "branch_aligned_reduced_polarization": [
              -1.6226367489713629e-16,
              -6.551438639322251e-16,
              0.166345949055587
            ],
            "target_residual": 0.166345949055587,
            "energy_eV": -142.25662949346005,
            "max_atomic_step_A": 0.026181096877749797,
            "max_log_strain_component": 0.0029668733249721656,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.5313608647413024,
            "cell_principal_stretches": [
              1.0012566546156567,
              1.0006718372637522,
              0.9970375234943477
            ],
            "cell_volume_ratio": 0.9989611440281481,
            "cell_rmsd_from_input_A": 0.009956159758739622
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              2.2932338036499554e-15,
              3.2532419281371547e-15,
              -0.0024519622918213672
            ],
            "branch_aligned_reduced_polarization": [
              2.2932338036499554e-15,
              3.2532419281371547e-15,
              -0.0024519622918213672
            ],
            "target_residual": 0.0024519622918213672,
            "energy_eV": -142.16599893165653,
            "max_atomic_step_A": 0.0003792642048017658,
            "max_log_strain_component": 4.1579699050583366e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.5313608647413024,
            "cell_principal_stretches": [
              1.0012390321316198,
              1.0006624185800463,
              0.9970789808764031
            ],
            "cell_volume_ratio": 0.9989756957746343,
            "cell_rmsd_from_input_A": 0.009816711701983005
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -1.2473480330765167e-15,
              6.696567536932994e-16,
              3.038830269791456e-06
            ],
            "branch_aligned_reduced_polarization": [
              -1.2473480330765167e-15,
              6.696567536932994e-16,
              3.038830269791456e-06
            ],
            "target_residual": 3.038830269791456e-06,
            "energy_eV": -142.16896344245754
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "inversion_parent_endpoint_00",
        "source": "same_species_inversion_center_projection_from_endpoint",
        "spacegroup": "Cmcm",
        "spacegroup_number": 63,
        "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": 7.525047103179227e-16,
        "parent_symmetrization_rmsd_A": 0.27086232774654817,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -137.42963904858175,
        "reduced_polarization": [
          -1.8218047499531855e-16,
          -7.257151552308803e-16,
          -8.006951385739904e-17
        ],
        "cartesian_polarization_e_A2": [
          -6.067430174101793e-18,
          -1.400122355840646e-17,
          -1.2233315836756923e-18
        ],
        "ranking_score": 0.27086232774654967
      },
      "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": [
          -142.25662949346005,
          -141.95926066137585,
          -141.2710881869591,
          -140.38863138321463,
          -139.47172472588886,
          -138.63961203593706,
          -137.9760648240164,
          -137.56316761759985,
          -137.42963904858178
        ],
        "cartesian_polarizations_e_A2": [
          [
            -2.0374517478671964e-17,
            -1.3032388892534583e-17,
            0.00254149480236168
          ],
          [
            -2.8370872085644275e-18,
            4.630839468851826e-18,
            0.006359025602924456
          ],
          [
            -1.2969074085931882e-17,
            -2.6350128808677992e-17,
            0.009972583125588701
          ],
          [
            -3.8160431452951505e-17,
            -1.4262115922848814e-17,
            0.013233608085324896
          ],
          [
            -1.1703285692565323e-17,
            6.000524382174196e-18,
            0.015747366946902295
          ],
          [
            -3.940829905376841e-17,
            -1.9219070847253587e-17,
            0.01665142165244034
          ],
          [
            -5.804285173990019e-17,
            -2.3393348678331288e-17,
            0.014626352169470036
          ],
          [
            -3.9552253114363675e-17,
            -7.65284269030912e-18,
            0.008773132619192752
          ],
          [
            -4.645491848245446e-17,
            -1.6523183081349237e-17,
            -2.2815266775204675e-18
          ]
        ],
        "raw_reduced_polarization": [
          [
            -6.117646459136005e-16,
            -6.754982583287433e-16,
            0.1663459490555861
          ],
          [
            -8.518629476208595e-17,
            2.400269069319526e-16,
            0.4162110219561661
          ],
          [
            -3.894090264622315e-16,
            -1.3657869070494204e-15,
            0.6527256333635807
          ],
          [
            -1.1458039612551732e-15,
            -7.392377978749338e-16,
            0.8661662791273229
          ],
          [
            -3.5140250242650685e-16,
            3.110207808132343e-16,
            1.0306968550456421
          ],
          [
            -1.1832723961155293e-15,
            -9.961680081119537e-16,
            1.089869054749198
          ],
          [
            -1.7427929117656897e-15,
            -1.2125302904168122e-15,
            0.9573241820486237
          ],
          [
            -1.1875947563873773e-15,
            -3.9666418422557427e-16,
            0.5742191840699482
          ],
          [
            -1.3948539780690965e-15,
            -8.564340341233989e-16,
            -1.4933051215178934e-16
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -6.117646459136005e-16,
            -6.754982583287433e-16,
            0.1663459490555861
          ],
          [
            -8.518629476208595e-17,
            2.4002690693195254e-16,
            0.4162110219561661
          ],
          [
            -3.894090264622315e-16,
            -1.3657869070494204e-15,
            0.6527256333635807
          ],
          [
            -1.1458039612551732e-15,
            -7.392377978749338e-16,
            0.8661662791273229
          ],
          [
            -3.5140250242650685e-16,
            3.1102078081323437e-16,
            1.0306968550456421
          ],
          [
            -1.1832723961155293e-15,
            -9.961680081119539e-16,
            1.089869054749198
          ],
          [
            -1.7427929117656897e-15,
            -1.2125302904168122e-15,
            0.9573241820486237
          ],
          [
            -1.1875947563873773e-15,
            -3.966641842255743e-16,
            0.5742191840699482
          ],
          [
            -1.3948539780690965e-15,
            -8.564340341233989e-16,
            0.9999999999999999
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            1
          ]
        ],
        "folded_reduced_polarization": [
          [
            -6.106226635438361e-16,
            -6.661338147750939e-16,
            0.16634594905558608
          ],
          [
            -1.1102230246251565e-16,
            2.220446049250313e-16,
            0.4162110219561661
          ],
          [
            -3.885780586188048e-16,
            -1.3877787807814457e-15,
            -0.3472743666364193
          ],
          [
            -1.1657341758564144e-15,
            -7.216449660063518e-16,
            -0.1338337208726772
          ],
          [
            -3.3306690738754696e-16,
            3.3306690738754696e-16,
            0.030696855045642124
          ],
          [
            -1.1657341758564144e-15,
            -9.992007221626409e-16,
            0.08986905474919804
          ],
          [
            -1.7208456881689926e-15,
            -1.2212453270876722e-15,
            -0.04267581795137643
          ],
          [
            -1.1657341758564144e-15,
            -3.885780586188048e-16,
            -0.4257808159300518
          ],
          [
            -1.3877787807814457e-15,
            -8.326672684688674e-16,
            0.0
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -137.42963904858178,
          -137.56316761759982,
          -137.97606482401636,
          -138.6396120359371,
          -139.47172472588883,
          -140.38863138321466,
          -141.2710881869591,
          -141.95926066137582,
          -142.25662949346003
        ],
        "cartesian_polarizations_e_A2": [
          [
            -4.645491848245446e-17,
            -1.6523183081349237e-17,
            -2.2815266775204675e-18
          ],
          [
            -2.6882584132515074e-17,
            -7.565878568828334e-18,
            -0.008773132619192731
          ],
          [
            -7.338814192514701e-17,
            -2.2262815099081076e-17,
            -0.014626352169470027
          ],
          [
            -5.1674146502236644e-17,
            -1.6175326595426095e-17,
            -0.01665142165244036
          ],
          [
            -7.240316292890735e-17,
            -4.696062559962414e-18,
            -0.015747366946902253
          ],
          [
            -3.5533134690838395e-17,
            -4.087313709596916e-18,
            -0.013233608085324878
          ],
          [
            -5.052928425019816e-17,
            1.8436393753926518e-17,
            -0.009972583125588732
          ],
          [
            -4.9045053004557297e-17,
            -1.3501179859891942e-17,
            -0.006359025602924497
          ],
          [
            -6.673864775671803e-17,
            -4.459628854686529e-18,
            -0.0025414948023616936
          ]
        ],
        "raw_reduced_polarization": [
          [
            -1.3948539780690965e-15,
            -8.564340341233989e-16,
            -1.4933051215178934e-16
          ],
          [
            -8.071756585296378e-16,
            -3.9215663667755636e-16,
            -0.5742191840699469
          ],
          [
            -2.203550130995348e-15,
            -1.1539321722925797e-15,
            -0.9573241820486231
          ],
          [
            -1.5515663608191054e-15,
            -8.384038439313274e-16,
            -1.0898690547491992
          ],
          [
            -2.1739751814291726e-15,
            -2.43407567592966e-16,
            -1.0306968550456395
          ],
          [
            -1.066916828096482e-15,
            -2.1185473475684077e-16,
            -0.8661662791273218
          ],
          [
            -1.517190761447423e-15,
            9.556000801797926e-16,
            -0.6527256333635826
          ],
          [
            -1.472625278932616e-15,
            -6.997967568297773e-16,
            -0.41621102195616877
          ],
          [
            -2.0038926201015657e-15,
            -2.311526726967924e-16,
            -0.16634594905558697
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -1.3948539780690965e-15,
            -8.564340341233989e-16,
            0.9999999999999999
          ],
          [
            -8.071756585296378e-16,
            -3.9215663667755636e-16,
            1.4257808159300531
          ],
          [
            -2.203550130995348e-15,
            -1.1539321722925797e-15,
            1.0426758179513769
          ],
          [
            -1.5515663608191054e-15,
            -8.384038439313274e-16,
            0.9101309452508008
          ],
          [
            -2.1739751814291726e-15,
            -2.4340756759296606e-16,
            0.9693031449543605
          ],
          [
            -1.066916828096482e-15,
            -2.1185473475684077e-16,
            1.1338337208726783
          ],
          [
            -1.517190761447423e-15,
            9.556000801797926e-16,
            1.3472743666364175
          ],
          [
            -1.472625278932616e-15,
            -6.997967568297773e-16,
            1.5837889780438312
          ],
          [
            -2.0038926201015657e-15,
            -2.3115267269679233e-16,
            1.833654050944413
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          1
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          -2.177943310224593e-15,
          -1.0373698099180547e-15,
          -0.16634594905558642
        ],
        "actual_opposite_endpoint_branch_residual": 9.367469996678947e-16
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            -6.117646459136005e-16,
            -6.754982583287433e-16,
            0.1663459490555861
          ],
          [
            -8.518629476208595e-17,
            2.400269069319526e-16,
            0.4162110219561661
          ],
          [
            -3.894090264622315e-16,
            -1.3657869070494204e-15,
            0.6527256333635807
          ],
          [
            -1.1458039612551732e-15,
            -7.392377978749338e-16,
            0.8661662791273229
          ],
          [
            -3.5140250242650685e-16,
            3.110207808132343e-16,
            1.0306968550456421
          ],
          [
            -1.1832723961155293e-15,
            -9.961680081119537e-16,
            1.089869054749198
          ],
          [
            -1.7427929117656897e-15,
            -1.2125302904168122e-15,
            0.9573241820486237
          ],
          [
            -1.1875947563873773e-15,
            -3.9666418422557427e-16,
            0.5742191840699482
          ],
          [
            -1.3948539780690965e-15,
            -8.564340341233989e-16,
            -1.4933051215178934e-16
          ],
          [
            -8.071756585296378e-16,
            -3.9215663667755636e-16,
            -0.5742191840699469
          ],
          [
            -2.203550130995348e-15,
            -1.1539321722925797e-15,
            -0.9573241820486231
          ],
          [
            -1.5515663608191054e-15,
            -8.384038439313274e-16,
            -1.0898690547491992
          ],
          [
            -2.1739751814291726e-15,
            -2.43407567592966e-16,
            -1.0306968550456395
          ],
          [
            -1.066916828096482e-15,
            -2.1185473475684077e-16,
            -0.8661662791273218
          ],
          [
            -1.517190761447423e-15,
            9.556000801797926e-16,
            -0.6527256333635826
          ],
          [
            -1.472625278932616e-15,
            -6.997967568297773e-16,
            -0.41621102195616877
          ],
          [
            -2.0038926201015657e-15,
            -2.311526726967924e-16,
            -0.16634594905558697
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -6.117646459136005e-16,
            -6.754982583287433e-16,
            0.1663459490555861
          ],
          [
            -8.518629476208595e-17,
            2.4002690693195254e-16,
            0.4162110219561661
          ],
          [
            -3.894090264622315e-16,
            -1.3657869070494204e-15,
            0.6527256333635807
          ],
          [
            -1.1458039612551732e-15,
            -7.392377978749338e-16,
            0.8661662791273229
          ],
          [
            -3.5140250242650685e-16,
            3.1102078081323437e-16,
            1.0306968550456421
          ],
          [
            -1.1832723961155293e-15,
            -9.961680081119539e-16,
            1.089869054749198
          ],
          [
            -1.7427929117656897e-15,
            -1.2125302904168122e-15,
            0.9573241820486237
          ],
          [
            -1.1875947563873773e-15,
            -3.966641842255743e-16,
            0.5742191840699482
          ],
          [
            -1.3948539780690965e-15,
            -8.564340341233989e-16,
            0.9999999999999999
          ],
          [
            -8.071756585296378e-16,
            -3.9215663667755636e-16,
            1.4257808159300533
          ],
          [
            -2.203550130995348e-15,
            -1.1539321722925797e-15,
            1.0426758179513769
          ],
          [
            -1.5515663608191054e-15,
            -8.384038439313274e-16,
            0.9101309452508008
          ],
          [
            -2.1739751814291726e-15,
            -2.4340756759296606e-16,
            0.9693031449543605
          ],
          [
            -1.066916828096482e-15,
            -2.1185473475684077e-16,
            1.133833720872678
          ],
          [
            -1.517190761447423e-15,
            9.556000801797926e-16,
            1.3472743666364173
          ],
          [
            -1.472625278932616e-15,
            -6.997967568297773e-16,
            1.5837889780438312
          ],
          [
            -2.0038926201015657e-15,
            -2.3115267269679233e-16,
            1.833654050944413
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            1
          ],
          [
            0,
            0,
            2
          ],
          [
            0,
            0,
            2
          ],
          [
            0,
            0,
            2
          ],
          [
            0,
            0,
            2
          ],
          [
            0,
            0,
            2
          ],
          [
            0,
            0,
            2
          ],
          [
            0,
            0,
            2
          ],
          [
            0,
            0,
            2
          ]
        ],
        "folded_reduced_polarization": [
          [
            -6.106226635438361e-16,
            -6.661338147750939e-16,
            0.16634594905558608
          ],
          [
            -1.1102230246251565e-16,
            2.220446049250313e-16,
            0.4162110219561661
          ],
          [
            -3.885780586188048e-16,
            -1.3877787807814457e-15,
            -0.3472743666364193
          ],
          [
            -1.1657341758564144e-15,
            -7.216449660063518e-16,
            -0.1338337208726772
          ],
          [
            -3.3306690738754696e-16,
            3.3306690738754696e-16,
            0.030696855045642124
          ],
          [
            -1.1657341758564144e-15,
            -9.992007221626409e-16,
            0.08986905474919804
          ],
          [
            -1.7208456881689926e-15,
            -1.2212453270876722e-15,
            -0.04267581795137643
          ],
          [
            -1.1657341758564144e-15,
            -3.885780586188048e-16,
            -0.4257808159300518
          ],
          [
            -1.3877787807814457e-15,
            -8.326672684688674e-16,
            0.0
          ],
          [
            -8.326672684688674e-16,
            -3.885780586188048e-16,
            0.42578081593005335
          ],
          [
            -2.220446049250313e-15,
            -1.1657341758564144e-15,
            0.04267581795137687
          ],
          [
            -1.5543122344752192e-15,
            -8.326672684688674e-16,
            -0.08986905474919915
          ],
          [
            -2.1649348980190553e-15,
            -2.220446049250313e-16,
            -0.03069685504563946
          ],
          [
            -1.0547118733938987e-15,
            -2.220446049250313e-16,
            0.13383372087267809
          ],
          [
            -1.4988010832439613e-15,
            9.992007221626409e-16,
            0.3472743666364173
          ],
          [
            -1.4988010832439613e-15,
            -7.216449660063518e-16,
            -0.416211021956169
          ],
          [
            -1.9984014443252818e-15,
            -2.220446049250313e-16,
            -0.16634594905558675
          ]
        ]
      },
      "incoming_structure_ids": [
        "incoming_00_000",
        "incoming_00_001",
        "incoming_00_002",
        "incoming_00_003",
        "incoming_00_004",
        "incoming_00_005",
        "incoming_00_006",
        "incoming_00_007",
        "incoming_00_008"
      ],
      "reflected_structure_ids": [
        "reflected_00_001",
        "reflected_00_002",
        "reflected_00_003",
        "reflected_00_004",
        "reflected_00_005",
        "reflected_00_006",
        "reflected_00_007",
        "reflected_00_008"
      ]
    },
    {
      "orbit_id": 1,
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.0,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -1.6226367489713629e-16,
              -6.551438639322251e-16,
              0.166345949055587
            ],
            "branch_aligned_reduced_polarization": [
              -1.6226367489713629e-16,
              -6.551438639322251e-16,
              0.16634594905558697
            ],
            "target_residual": 0.333654050944413,
            "energy_eV": -142.25662949346005,
            "max_atomic_step_A": 0.0525136264575356,
            "max_log_strain_component": 0.005950907185513066,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.5313608647413024,
            "cell_principal_stretches": [
              1.0059686490095343,
              0.9986537989447077,
              0.9974841746477732
            ],
            "cell_volume_ratio": 1.0020869785433288,
            "cell_rmsd_from_input_A": 0.020007355221065472
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -2.4419136044760694e-15,
              -7.02533376346805e-15,
              0.49029647494377165
            ],
            "branch_aligned_reduced_polarization": [
              -2.4419136044760694e-15,
              -7.02533376346805e-15,
              0.49029647494377165
            ],
            "target_residual": 0.009703525056228346,
            "energy_eV": -141.86340265468965,
            "max_atomic_step_A": 0.0015794346829383539,
            "max_log_strain_component": 0.0001918224428934604,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.5313608647413024,
            "cell_principal_stretches": [
              1.006161634882181,
              0.9986104354590365,
              0.9974031845374529
            ],
            "cell_volume_ratio": 1.0021543229371797,
            "cell_rmsd_from_input_A": 0.020653124495777532
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -2.7179661844899787e-17,
              3.0722638886679285e-16,
              0.4999538559363181
            ],
            "branch_aligned_reduced_polarization": [
              -2.7179661844899787e-17,
              3.0722638886679285e-16,
              0.4999538559363181
            ],
            "target_residual": 4.614406368191881e-05,
            "energy_eV": -141.841640614529
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_01",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cmc2_1",
        "spacegroup_number": 36,
        "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": 4.614406368191881e-05,
        "parent_symmetrization_rmsd_A": 0.03561327206400865,
        "parent_cell_rmsd_A": 0.020653124495777532,
        "energy_eV": -141.841640614529,
        "reduced_polarization": [
          -2.7179661844899787e-17,
          3.0722638886679285e-16,
          0.4999538559363181
        ],
        "cartesian_polarization_e_A2": [
          -3.909947498332267e-17,
          -6.916140881081721e-17,
          0.007669023495812792
        ],
        "ranking_score": 0.5408688413153169
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 2,
      "formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.5,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        -0.5,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -1.6226367489713629e-16,
              -6.551438639322251e-16,
              0.166345949055587
            ],
            "branch_aligned_reduced_polarization": [
              -1.6226367489713629e-16,
              -6.661338147750939e-16,
              0.166345949055587
            ],
            "target_residual": 0.526944944721176,
            "energy_eV": -142.25662949346005,
            "max_atomic_step_A": 0.10331750972883383,
            "max_log_strain_component": 0.007956876691626497,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.5313608647413024,
            "cell_principal_stretches": [
              1.007404010863315,
              1.000671837263757,
              0.9909534253737119
            ],
            "cell_volume_ratio": 0.9989611440281423,
            "cell_rmsd_from_input_A": 0.031109439981067643
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -2.7310409603126592e-15,
              -0.49459518744679154,
              0.008959048817390854
            ],
            "branch_aligned_reduced_polarization": [
              -2.7310409603126592e-15,
              -0.49459518744679154,
              0.008959048817390854
            ],
            "target_residual": 0.010463104436433395,
            "energy_eV": -140.38582556882287,
            "max_atomic_step_A": 0.0019260223183102782,
            "max_log_strain_component": 0.00016075757388244523,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.5313608647413024,
            "cell_principal_stretches": [
              1.0074801327188498,
              1.000708253097748,
              0.9907866925928749
            ],
            "cell_volume_ratio": 0.9989048853104359,
            "cell_rmsd_from_input_A": 0.03161655994779575
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -2.766117834580141e-15,
              -0.5000236439543034,
              -2.5520854781055314e-05
            ],
            "branch_aligned_reduced_polarization": [
              -2.766117834580141e-15,
              -0.5000236439543034,
              -2.5520854781055314e-05
            ],
            "target_residual": 3.479009347297704e-05,
            "energy_eV": -140.34132962200755
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_02",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cm",
        "spacegroup_number": 8,
        "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": 3.479009347297704e-05,
        "parent_symmetrization_rmsd_A": 0.07256127065393464,
        "parent_cell_rmsd_A": 0.03161655994779575,
        "energy_eV": -140.34132962200755,
        "reduced_polarization": [
          -2.766117834580141e-15,
          -0.5000236439543034,
          -2.5520854781055314e-05
        ],
        "cartesian_polarization_e_A2": [
          -8.415159114944894e-17,
          -0.009670643410212737,
          -7.807742152006181e-05
        ],
        "ranking_score": 0.5805349908278296
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 3,
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.0,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        -0.5,
        0.0,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -1.6226367489713629e-16,
              -6.551438639322251e-16,
              0.166345949055587
            ],
            "branch_aligned_reduced_polarization": [
              -1.6653345369377348e-16,
              -6.551438639322251e-16,
              0.166345949055587
            ],
            "target_residual": 0.5269449447211765,
            "energy_eV": -142.25662949346005,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.006383505588475391,
            "step_scale": 0.6890728775400162,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.5313608647413024,
            "cell_principal_stretches": [
              1.005730989423453,
              1.0008657575340207,
              0.9927303205617581
            ],
            "cell_volume_ratio": 0.9992840368612018,
            "cell_rmsd_from_input_A": 0.04142810794426429
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.3415445769317093,
              5.26438391652745e-15,
              0.049714788691679536
            ],
            "branch_aligned_reduced_polarization": [
              -0.3415445769317093,
              5.26438391652745e-15,
              0.049714788691679536
            ],
            "target_residual": 0.1660713139419609,
            "energy_eV": -138.65373251201132,
            "max_atomic_step_A": 0.05511726295510937,
            "max_log_strain_component": 0.0030495168101146502,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.5313608647413024,
            "cell_principal_stretches": [
              1.0084874076575965,
              1.0012686188737254,
              0.9892890823298
            ],
            "cell_volume_ratio": 0.9989512648221908,
            "cell_rmsd_from_input_A": 0.06119080596211069
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.4991046089596243,
              -1.1129741154222245e-15,
              0.0018411088313631063
            ],
            "branch_aligned_reduced_polarization": [
              -0.4991046089596243,
              -1.1129741154222245e-15,
              0.0018411088313631063
            ],
            "target_residual": 0.002047292564366009,
            "energy_eV": -133.98976475496409,
            "max_atomic_step_A": 0.0004245319501397624,
            "max_log_strain_component": 3.5232932185517265e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.5313608647413024,
            "cell_principal_stretches": [
              1.0084956448551463,
              1.0012835518653667,
              0.9892540372990195
            ],
            "cell_volume_ratio": 0.998938934556696,
            "cell_rmsd_from_input_A": 0.06132312968943011
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -0.49999822760015394,
              -8.817913809695166e-17,
              -7.537627604504515e-06
            ],
            "branch_aligned_reduced_polarization": [
              -0.49999822760015394,
              -8.817913809695166e-17,
              -7.537627604504515e-06
            ],
            "target_residual": 7.743205480838562e-06,
            "energy_eV": -133.959332427237
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_03",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cc",
        "spacegroup_number": 9,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          -0.5,
          0.0,
          0.0
        ],
        "formal_class": [
          0.5,
          0.0,
          0.0
        ],
        "target_residual": 7.743205480838562e-06,
        "parent_symmetrization_rmsd_A": 0.1261300322746924,
        "parent_cell_rmsd_A": 0.06132312968943011,
        "energy_eV": -133.959332427237,
        "reduced_polarization": [
          -0.49999822760015394,
          -8.817913809695166e-17,
          -7.537627604504515e-06
        ],
        "cartesian_polarization_e_A2": [
          -0.016682064565451876,
          3.949317855677114e-16,
          -0.00015747878008390612
        ],
        "ranking_score": 0.6414763011080116
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 4,
      "formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.5,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        -0.5,
        0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -1.6226367489713629e-16,
              -6.551438639322251e-16,
              0.166345949055587
            ],
            "branch_aligned_reduced_polarization": [
              -1.6226367489713629e-16,
              -6.661338147750939e-16,
              0.16634594905558697
            ],
            "target_residual": 0.6011031739324093,
            "energy_eV": -142.25662949346005,
            "max_atomic_step_A": 0.11314452250180343,
            "max_log_strain_component": 0.0079568766916124,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.5313608647413024,
            "cell_principal_stretches": [
              1.0107874201261284,
              0.9986537989447126,
              0.992728824675706
            ],
            "cell_volume_ratio": 1.0020869785433226,
            "cell_rmsd_from_input_A": 0.035743879919373986
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -9.060893585595516e-15,
              -0.5007438297664822,
              0.49534089897754385
            ],
            "branch_aligned_reduced_polarization": [
              -9.060893585595516e-15,
              -0.5007438297664822,
              0.49534089897754385
            ],
            "target_residual": 0.004718103968646403,
            "energy_eV": -139.43744263185164,
            "max_atomic_step_A": 0.0008191983618771861,
            "max_log_strain_component": 9.565780699574735e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.5313608647413024,
            "cell_principal_stretches": [
              1.0108357542147217,
              0.9986321742535161,
              0.9927361203934689
            ],
            "cell_volume_ratio": 1.0021205612066295,
            "cell_rmsd_from_input_A": 0.03588474423125924
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              2.362822146660716e-15,
              -0.4999831604917022,
              0.4999791698044968
            ],
            "branch_aligned_reduced_polarization": [
              2.362822146660716e-15,
              -0.4999831604917022,
              0.4999791698044968
            ],
            "target_residual": 2.6785557384764326e-05,
            "energy_eV": -139.42682823880472
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_04",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cm",
        "spacegroup_number": 8,
        "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": 2.6785557384764326e-05,
        "parent_symmetrization_rmsd_A": 0.07863189219058192,
        "parent_cell_rmsd_A": 0.03588474423125924,
        "energy_eV": -139.42682823880472,
        "reduced_polarization": [
          2.362822146660716e-15,
          -0.4999831604917022,
          0.4999791698044968
        ],
        "cartesian_polarization_e_A2": [
          8.028230457740067e-17,
          -0.009540810839361468,
          0.007592573461596775
        ],
        "ranking_score": 0.5876566493631663
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 5,
      "formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.0,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        -0.5,
        0.0,
        0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -1.6226367489713629e-16,
              -6.551438639322251e-16,
              0.166345949055587
            ],
            "branch_aligned_reduced_polarization": [
              -1.6653345369377348e-16,
              -6.551438639322251e-16,
              0.16634594905558697
            ],
            "target_residual": 0.6011031739324098,
            "energy_eV": -142.25662949346005,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.006175991701801192,
            "step_scale": 0.6666726165807473,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.5313608647413024,
            "cell_principal_stretches": [
              1.0082059353596458,
              0.9983220640842133,
              0.9949097764356548
            ],
            "cell_volume_ratio": 1.0013908479567137,
            "cell_rmsd_from_input_A": 0.04179283531369453
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.33158827286752884,
              -3.3460425936602595e-15,
              0.37663712841241914
            ],
            "branch_aligned_reduced_polarization": [
              -0.33158827286752884,
              -3.3460425936602595e-15,
              0.37663712841241914
            ],
            "target_residual": 0.2087604079371275,
            "energy_eV": -138.36769874351876,
            "max_atomic_step_A": 0.06159245231135157,
            "max_log_strain_component": 0.0032707980769033224,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.5313608647413024,
            "cell_principal_stretches": [
              1.0129178909875678,
              0.9972067743141558,
              0.9923067138986897
            ],
            "cell_volume_ratio": 1.0023176822623032,
            "cell_rmsd_from_input_A": 0.06459021596260256
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.4990889718519801,
              1.1719411312335772e-15,
              0.49583010025446556
            ],
            "branch_aligned_reduced_polarization": [
              -0.4990889718519801,
              1.1719411312335772e-15,
              0.49583010025446556
            ],
            "target_residual": 0.004268259150320281,
            "energy_eV": -132.31035981694077,
            "max_atomic_step_A": 0.0007659374122360367,
            "max_log_strain_component": 9.006719559636315e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.5313608647413024,
            "cell_principal_stretches": [
              1.0129930965843426,
              0.9971687564449383,
              0.99230218396409
            ],
            "cell_volume_ratio": 1.0023493094738436,
            "cell_rmsd_from_input_A": 0.06481192797235028
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -0.5000026219056287,
              2.4526319338830706e-15,
              0.4999725866148184
            ],
            "branch_aligned_reduced_polarization": [
              -0.5000026219056287,
              2.4526319338830706e-15,
              0.4999725866148184
            ],
            "target_residual": 2.7538483550113138e-05,
            "energy_eV": -132.25075757992
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_05",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cc",
        "spacegroup_number": 9,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          -0.5,
          0.0,
          0.5
        ],
        "formal_class": [
          0.5,
          0.0,
          0.5
        ],
        "target_residual": 2.7538483550113138e-05,
        "parent_symmetrization_rmsd_A": 0.13137296567152745,
        "parent_cell_rmsd_A": 0.06481192797235028,
        "energy_eV": -132.25075757992,
        "reduced_polarization": [
          -0.5000026219056287,
          2.4526319338830706e-15,
          0.4999725866148184
        ],
        "cartesian_polarization_e_A2": [
          -0.016516575936930837,
          2.676555091448627e-16,
          0.007514709251447359
        ],
        "ranking_score": 0.6476310246317152
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 6,
      "formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.5,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        -0.5,
        -0.5,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -1.6226367489713629e-16,
              -6.551438639322251e-16,
              0.166345949055587
            ],
            "branch_aligned_reduced_polarization": [
              -1.6653345369377348e-16,
              -6.661338147750939e-16,
              0.166345949055587
            ],
            "target_residual": 0.726409646664472,
            "energy_eV": -142.25662949346005,
            "max_atomic_step_A": 0.11999999999999998,
            "max_log_strain_component": 0.005536499640213707,
            "step_scale": 0.5976421083530602,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.5313608647413024,
            "cell_principal_stretches": [
              1.0068042841093858,
              1.000601170785695,
              0.9920285256748408
            ],
            "cell_volume_ratio": 0.9993790061055743,
            "cell_rmsd_from_input_A": 0.04002472876928297
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.2961025066174141,
              -0.29439217319602873,
              0.06881352139846038
            ],
            "branch_aligned_reduced_polarization": [
              -0.2961025066174141,
              -0.29439217319602873,
              0.06881352139846038
            ],
            "target_residual": 0.2976307561022716,
            "energy_eV": -138.8066080120062,
            "max_atomic_step_A": 0.08507878088935106,
            "max_log_strain_component": 0.003952652060556332,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.5313608647413024,
            "cell_principal_stretches": [
              1.0117320181328322,
              1.0010719154110392,
              0.9862485940261995
            ],
            "cell_volume_ratio": 0.9988888582789041,
            "cell_rmsd_from_input_A": 0.06882231171115075
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.4988537263489529,
              -0.49839091767917415,
              0.007537945604212687
            ],
            "branch_aligned_reduced_polarization": [
              -0.4988537263489529,
              -0.49839091767917415,
              0.007537945604212687
            ],
            "target_residual": 0.007792542148127816,
            "energy_eV": -130.99371280017044,
            "max_atomic_step_A": 0.0013872454833258766,
            "max_log_strain_component": 0.00014547879731969133,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.5313608647413024,
            "cell_principal_stretches": [
              1.0117388181465232,
              1.001120392883305,
              0.9861439470955795
            ],
            "cell_volume_ratio": 0.9988379500693484,
            "cell_rmsd_from_input_A": 0.06909109450033926
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -0.4999862846485918,
              -0.500008584390441,
              -1.7107565352784946e-05
            ],
            "branch_aligned_reduced_polarization": [
              -0.4999862846485918,
              -0.500008584390441,
              -1.7107565352784946e-05
            ],
            "target_residual": 2.3547216731382614e-05,
            "energy_eV": -130.94330129300678
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_06",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          -0.5,
          -0.5,
          0.0
        ],
        "formal_class": [
          0.5,
          0.5,
          0.0
        ],
        "target_residual": 2.3547216731382614e-05,
        "parent_symmetrization_rmsd_A": 0.14564832197692823,
        "parent_cell_rmsd_A": 0.06909109450033926,
        "energy_eV": -130.94330129300678,
        "reduced_polarization": [
          -0.4999862846485918,
          -0.500008584390441,
          -1.7107565352784946e-05
        ],
        "cartesian_polarization_e_A2": [
          -0.016684831245080262,
          -0.009672464736913643,
          -0.0002386596084264563
        ],
        "ranking_score": 0.6629681900354758
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 7,
      "formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.5,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        -0.5,
        -0.5,
        0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -1.6226367489713629e-16,
              -6.551438639322251e-16,
              0.166345949055587
            ],
            "branch_aligned_reduced_polarization": [
              -1.6653345369377348e-16,
              -6.661338147750939e-16,
              0.16634594905558697
            ],
            "target_residual": 0.7818727682376565,
            "energy_eV": -142.25662949346005,
            "max_atomic_step_A": 0.11999999999999998,
            "max_log_strain_component": 0.00539597747979804,
            "step_scale": 0.5824733256065302,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.5313608647413024,
            "cell_principal_stretches": [
              1.0087042629057166,
              0.9988337312301998,
              0.9937344040264581
            ],
            "cell_volume_ratio": 1.0012150802319362,
            "cell_rmsd_from_input_A": 0.04036963361785444
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.2894557184421186,
              -0.28885499524174646,
              0.35443121394514854
            ],
            "branch_aligned_reduced_polarization": [
              -0.2894557184421186,
              -0.28885499524174646,
              0.35443121394514854
            ],
            "target_residual": 0.33181527843752234,
            "energy_eV": -138.49604746362738,
            "max_atomic_step_A": 0.08994080777339902,
            "max_log_strain_component": 0.0041098201928985965,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.5313608647413024,
            "cell_principal_stretches": [
              1.0155475777975695,
              0.9978409919200051,
              0.9890434578686667
            ],
            "cell_volume_ratio": 1.0022521355940053,
            "cell_rmsd_from_input_A": 0.07148557746045944
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.4990303420428074,
              -0.5006173245984891,
              0.4979690652428033
            ],
            "branch_aligned_reduced_polarization": [
              -0.4990303420428074,
              -0.5006173245984891,
              0.4979690652428033
            ],
            "target_residual": 0.002333671399712516,
            "energy_eV": -128.6435609971412,
            "max_atomic_step_A": 0.0004929504602636907,
            "max_log_strain_component": 4.5725831952332695e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.5313608647413024,
            "cell_principal_stretches": [
              1.0155808999237104,
              0.99782384901896,
              0.9890438416206034
            ],
            "cell_volume_ratio": 1.0022681911039535,
            "cell_rmsd_from_input_A": 0.07161870030053386
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -0.5000018573737153,
              -0.49999718143917543,
              0.4999834783258423
            ],
            "branch_aligned_reduced_polarization": [
              -0.5000018573737153,
              -0.49999718143917543,
              0.4999834783258423
            ],
            "target_residual": 1.6862972431155255e-05,
            "energy_eV": -128.5896008939925
          }
        ],
        "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,
          0.5
        ],
        "formal_class": [
          0.5,
          0.5,
          0.5
        ],
        "target_residual": 1.6862972431155255e-05,
        "parent_symmetrization_rmsd_A": 0.14966111775726135,
        "parent_cell_rmsd_A": 0.07161870030053386,
        "energy_eV": -128.5896008939925,
        "reduced_polarization": [
          -0.5000018573737153,
          -0.49999718143917543,
          0.4999834783258423
        ],
        "cartesian_polarization_e_A2": [
          -0.01651868534505123,
          -0.00953717897760064,
          0.007434597884920497
        ],
        "ranking_score": 0.6675995187772571
      },
      "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,
          18,
          19,
          20,
          21,
          22,
          23
        ],
        "endpoint_rmsd_A": 0.27086232774654817,
        "minimum_distance_A_by_image": [
          1.6174303709734108,
          1.6122592832549067,
          1.6046962474984567,
          1.5701139699793423,
          1.541242331068885,
          1.5184071192531692,
          1.5018837001860241,
          1.4918818084338707,
          1.48853291
        ],
        "minimum_distance_A": 1.48853291,
        "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": [
          319.16122583681175,
          319.16122583681175,
          319.16122583681175,
          319.16122583681175,
          319.16122583681175,
          319.16122583681175,
          319.16122583681175,
          319.16122583681175,
          319.16122583681175
        ],
        "cell_deformation_log_strain_norm": 0.0
      },
      "parent_reduced_polarization": [
        -1.3948539780690965e-15,
        -8.564340341233989e-16,
        -1.4933051215178934e-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": [
          -142.25662949346005,
          -141.95926066137585,
          -141.2710881869591,
          -140.38863138321463,
          -139.47172472588886,
          -138.63961203593706,
          -137.9760648240164,
          -137.56316761759985,
          -137.42963904858178
        ],
        "cartesian_polarizations_e_A2": [
          [
            -2.0374517478671964e-17,
            -1.3032388892534583e-17,
            0.00254149480236168
          ],
          [
            -2.8370872085644275e-18,
            4.630839468851826e-18,
            0.006359025602924456
          ],
          [
            -1.2969074085931882e-17,
            -2.6350128808677992e-17,
            0.009972583125588701
          ],
          [
            -3.8160431452951505e-17,
            -1.4262115922848814e-17,
            0.013233608085324896
          ],
          [
            -1.1703285692565323e-17,
            6.000524382174196e-18,
            0.015747366946902295
          ],
          [
            -3.940829905376841e-17,
            -1.9219070847253587e-17,
            0.01665142165244034
          ],
          [
            -5.804285173990019e-17,
            -2.3393348678331288e-17,
            0.014626352169470036
          ],
          [
            -3.9552253114363675e-17,
            -7.65284269030912e-18,
            0.008773132619192752
          ],
          [
            -4.645491848245446e-17,
            -1.6523183081349237e-17,
            -2.2815266775204675e-18
          ]
        ],
        "raw_reduced_polarization": [
          [
            -6.117646459136005e-16,
            -6.754982583287433e-16,
            0.1663459490555861
          ],
          [
            -8.518629476208595e-17,
            2.400269069319526e-16,
            0.4162110219561661
          ],
          [
            -3.894090264622315e-16,
            -1.3657869070494204e-15,
            0.6527256333635807
          ],
          [
            -1.1458039612551732e-15,
            -7.392377978749338e-16,
            0.8661662791273229
          ],
          [
            -3.5140250242650685e-16,
            3.110207808132343e-16,
            1.0306968550456421
          ],
          [
            -1.1832723961155293e-15,
            -9.961680081119537e-16,
            1.089869054749198
          ],
          [
            -1.7427929117656897e-15,
            -1.2125302904168122e-15,
            0.9573241820486237
          ],
          [
            -1.1875947563873773e-15,
            -3.9666418422557427e-16,
            0.5742191840699482
          ],
          [
            -1.3948539780690965e-15,
            -8.564340341233989e-16,
            -1.4933051215178934e-16
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -6.117646459136005e-16,
            -6.754982583287433e-16,
            0.1663459490555861
          ],
          [
            -8.518629476208595e-17,
            2.4002690693195254e-16,
            0.4162110219561661
          ],
          [
            -3.894090264622315e-16,
            -1.3657869070494204e-15,
            0.6527256333635807
          ],
          [
            -1.1458039612551732e-15,
            -7.392377978749338e-16,
            0.8661662791273229
          ],
          [
            -3.5140250242650685e-16,
            3.1102078081323437e-16,
            1.0306968550456421
          ],
          [
            -1.1832723961155293e-15,
            -9.961680081119539e-16,
            1.089869054749198
          ],
          [
            -1.7427929117656897e-15,
            -1.2125302904168122e-15,
            0.9573241820486237
          ],
          [
            -1.1875947563873773e-15,
            -3.966641842255743e-16,
            0.5742191840699482
          ],
          [
            -1.3948539780690965e-15,
            -8.564340341233989e-16,
            0.9999999999999999
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            1
          ]
        ],
        "folded_reduced_polarization": [
          [
            -6.106226635438361e-16,
            -6.661338147750939e-16,
            0.16634594905558608
          ],
          [
            -1.1102230246251565e-16,
            2.220446049250313e-16,
            0.4162110219561661
          ],
          [
            -3.885780586188048e-16,
            -1.3877787807814457e-15,
            -0.3472743666364193
          ],
          [
            -1.1657341758564144e-15,
            -7.216449660063518e-16,
            -0.1338337208726772
          ],
          [
            -3.3306690738754696e-16,
            3.3306690738754696e-16,
            0.030696855045642124
          ],
          [
            -1.1657341758564144e-15,
            -9.992007221626409e-16,
            0.08986905474919804
          ],
          [
            -1.7208456881689926e-15,
            -1.2212453270876722e-15,
            -0.04267581795137643
          ],
          [
            -1.1657341758564144e-15,
            -3.885780586188048e-16,
            -0.4257808159300518
          ],
          [
            -1.3877787807814457e-15,
            -8.326672684688674e-16,
            0.0
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -137.42963904858178,
          -137.56316761759982,
          -137.97606482401636,
          -138.6396120359371,
          -139.47172472588883,
          -140.38863138321466,
          -141.2710881869591,
          -141.95926066137582,
          -142.25662949346003
        ],
        "cartesian_polarizations_e_A2": [
          [
            -4.645491848245446e-17,
            -1.6523183081349237e-17,
            -2.2815266775204675e-18
          ],
          [
            -2.6882584132515074e-17,
            -7.565878568828334e-18,
            -0.008773132619192731
          ],
          [
            -7.338814192514701e-17,
            -2.2262815099081076e-17,
            -0.014626352169470027
          ],
          [
            -5.1674146502236644e-17,
            -1.6175326595426095e-17,
            -0.01665142165244036
          ],
          [
            -7.240316292890735e-17,
            -4.696062559962414e-18,
            -0.015747366946902253
          ],
          [
            -3.5533134690838395e-17,
            -4.087313709596916e-18,
            -0.013233608085324878
          ],
          [
            -5.052928425019816e-17,
            1.8436393753926518e-17,
            -0.009972583125588732
          ],
          [
            -4.9045053004557297e-17,
            -1.3501179859891942e-17,
            -0.006359025602924497
          ],
          [
            -6.673864775671803e-17,
            -4.459628854686529e-18,
            -0.0025414948023616936
          ]
        ],
        "raw_reduced_polarization": [
          [
            -1.3948539780690965e-15,
            -8.564340341233989e-16,
            -1.4933051215178934e-16
          ],
          [
            -8.071756585296378e-16,
            -3.9215663667755636e-16,
            -0.5742191840699469
          ],
          [
            -2.203550130995348e-15,
            -1.1539321722925797e-15,
            -0.9573241820486231
          ],
          [
            -1.5515663608191054e-15,
            -8.384038439313274e-16,
            -1.0898690547491992
          ],
          [
            -2.1739751814291726e-15,
            -2.43407567592966e-16,
            -1.0306968550456395
          ],
          [
            -1.066916828096482e-15,
            -2.1185473475684077e-16,
            -0.8661662791273218
          ],
          [
            -1.517190761447423e-15,
            9.556000801797926e-16,
            -0.6527256333635826
          ],
          [
            -1.472625278932616e-15,
            -6.997967568297773e-16,
            -0.41621102195616877
          ],
          [
            -2.0038926201015657e-15,
            -2.311526726967924e-16,
            -0.16634594905558697
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -1.3948539780690965e-15,
            -8.564340341233989e-16,
            0.9999999999999999
          ],
          [
            -8.071756585296378e-16,
            -3.9215663667755636e-16,
            1.4257808159300531
          ],
          [
            -2.203550130995348e-15,
            -1.1539321722925797e-15,
            1.0426758179513769
          ],
          [
            -1.5515663608191054e-15,
            -8.384038439313274e-16,
            0.9101309452508008
          ],
          [
            -2.1739751814291726e-15,
            -2.4340756759296606e-16,
            0.9693031449543605
          ],
          [
            -1.066916828096482e-15,
            -2.1185473475684077e-16,
            1.1338337208726783
          ],
          [
            -1.517190761447423e-15,
            9.556000801797926e-16,
            1.3472743666364175
          ],
          [
            -1.472625278932616e-15,
            -6.997967568297773e-16,
            1.5837889780438312
          ],
          [
            -2.0038926201015657e-15,
            -2.3115267269679233e-16,
            1.833654050944413
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          1
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          -2.177943310224593e-15,
          -1.0373698099180547e-15,
          -0.16634594905558642
        ],
        "actual_opposite_endpoint_branch_residual": 9.367469996678947e-16
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            -6.117646459136005e-16,
            -6.754982583287433e-16,
            0.1663459490555861
          ],
          [
            -8.518629476208595e-17,
            2.400269069319526e-16,
            0.4162110219561661
          ],
          [
            -3.894090264622315e-16,
            -1.3657869070494204e-15,
            0.6527256333635807
          ],
          [
            -1.1458039612551732e-15,
            -7.392377978749338e-16,
            0.8661662791273229
          ],
          [
            -3.5140250242650685e-16,
            3.110207808132343e-16,
            1.0306968550456421
          ],
          [
            -1.1832723961155293e-15,
            -9.961680081119537e-16,
            1.089869054749198
          ],
          [
            -1.7427929117656897e-15,
            -1.2125302904168122e-15,
            0.9573241820486237
          ],
          [
            -1.1875947563873773e-15,
            -3.9666418422557427e-16,
            0.5742191840699482
          ],
          [
            -1.3948539780690965e-15,
            -8.564340341233989e-16,
            -1.4933051215178934e-16
          ],
          [
            -8.071756585296378e-16,
            -3.9215663667755636e-16,
            -0.5742191840699469
          ],
          [
            -2.203550130995348e-15,
            -1.1539321722925797e-15,
            -0.9573241820486231
          ],
          [
            -1.5515663608191054e-15,
            -8.384038439313274e-16,
            -1.0898690547491992
          ],
          [
            -2.1739751814291726e-15,
            -2.43407567592966e-16,
            -1.0306968550456395
          ],
          [
            -1.066916828096482e-15,
            -2.1185473475684077e-16,
            -0.8661662791273218
          ],
          [
            -1.517190761447423e-15,
            9.556000801797926e-16,
            -0.6527256333635826
          ],
          [
            -1.472625278932616e-15,
            -6.997967568297773e-16,
            -0.41621102195616877
          ],
          [
            -2.0038926201015657e-15,
            -2.311526726967924e-16,
            -0.16634594905558697
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -6.117646459136005e-16,
            -6.754982583287433e-16,
            0.1663459490555861
          ],
          [
            -8.518629476208595e-17,
            2.4002690693195254e-16,
            0.4162110219561661
          ],
          [
            -3.894090264622315e-16,
            -1.3657869070494204e-15,
            0.6527256333635807
          ],
          [
            -1.1458039612551732e-15,
            -7.392377978749338e-16,
            0.8661662791273229
          ],
          [
            -3.5140250242650685e-16,
            3.1102078081323437e-16,
            1.0306968550456421
          ],
          [
            -1.1832723961155293e-15,
            -9.961680081119539e-16,
            1.089869054749198
          ],
          [
            -1.7427929117656897e-15,
            -1.2125302904168122e-15,
            0.9573241820486237
          ],
          [
            -1.1875947563873773e-15,
            -3.966641842255743e-16,
            0.5742191840699482
          ],
          [
            -1.3948539780690965e-15,
            -8.564340341233989e-16,
            0.9999999999999999
          ],
          [
            -8.071756585296378e-16,
            -3.9215663667755636e-16,
            1.4257808159300533
          ],
          [
            -2.203550130995348e-15,
            -1.1539321722925797e-15,
            1.0426758179513769
          ],
          [
            -1.5515663608191054e-15,
            -8.384038439313274e-16,
            0.9101309452508008
          ],
          [
            -2.1739751814291726e-15,
            -2.4340756759296606e-16,
            0.9693031449543605
          ],
          [
            -1.066916828096482e-15,
            -2.1185473475684077e-16,
            1.133833720872678
          ],
          [
            -1.517190761447423e-15,
            9.556000801797926e-16,
            1.3472743666364173
          ],
          [
            -1.472625278932616e-15,
            -6.997967568297773e-16,
            1.5837889780438312
          ],
          [
            -2.0038926201015657e-15,
            -2.3115267269679233e-16,
            1.833654050944413
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            1
          ],
          [
            0,
            0,
            2
          ],
          [
            0,
            0,
            2
          ],
          [
            0,
            0,
            2
          ],
          [
            0,
            0,
            2
          ],
          [
            0,
            0,
            2
          ],
          [
            0,
            0,
            2
          ],
          [
            0,
            0,
            2
          ],
          [
            0,
            0,
            2
          ]
        ],
        "folded_reduced_polarization": [
          [
            -6.106226635438361e-16,
            -6.661338147750939e-16,
            0.16634594905558608
          ],
          [
            -1.1102230246251565e-16,
            2.220446049250313e-16,
            0.4162110219561661
          ],
          [
            -3.885780586188048e-16,
            -1.3877787807814457e-15,
            -0.3472743666364193
          ],
          [
            -1.1657341758564144e-15,
            -7.216449660063518e-16,
            -0.1338337208726772
          ],
          [
            -3.3306690738754696e-16,
            3.3306690738754696e-16,
            0.030696855045642124
          ],
          [
            -1.1657341758564144e-15,
            -9.992007221626409e-16,
            0.08986905474919804
          ],
          [
            -1.7208456881689926e-15,
            -1.2212453270876722e-15,
            -0.04267581795137643
          ],
          [
            -1.1657341758564144e-15,
            -3.885780586188048e-16,
            -0.4257808159300518
          ],
          [
            -1.3877787807814457e-15,
            -8.326672684688674e-16,
            0.0
          ],
          [
            -8.326672684688674e-16,
            -3.885780586188048e-16,
            0.42578081593005335
          ],
          [
            -2.220446049250313e-15,
            -1.1657341758564144e-15,
            0.04267581795137687
          ],
          [
            -1.5543122344752192e-15,
            -8.326672684688674e-16,
            -0.08986905474919915
          ],
          [
            -2.1649348980190553e-15,
            -2.220446049250313e-16,
            -0.03069685504563946
          ],
          [
            -1.0547118733938987e-15,
            -2.220446049250313e-16,
            0.13383372087267809
          ],
          [
            -1.4988010832439613e-15,
            9.992007221626409e-16,
            0.3472743666364173
          ],
          [
            -1.4988010832439613e-15,
            -7.216449660063518e-16,
            -0.416211021956169
          ],
          [
            -1.9984014443252818e-15,
            -2.220446049250313e-16,
            -0.16634594905558675
          ]
        ]
      },
      "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": "Cmcm",
        "spacegroup_number": 63,
        "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": 7.525047103179227e-16,
        "parent_symmetrization_rmsd_A": 0.27086232774654817,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -137.42963904858175,
        "reduced_polarization": [
          -1.8218047499531855e-16,
          -7.257151552308803e-16,
          -8.006951385739904e-17
        ],
        "cartesian_polarization_e_A2": [
          -6.067430174101793e-18,
          -1.400122355840646e-17,
          -1.2233315836756923e-18
        ],
        "ranking_score": 0.27086232774654967
      }
    }
  ],
  "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": 55,
      "full_response": 21,
      "energy_polarization": 34
    },
    "model_evaluations_for_recovery_and_path_properties": {
      "total": 80,
      "full_response": 46,
      "energy_polarization": 34
    },
    "elapsed_seconds": 340.0900874400395
  }
}
