{
  "schema": "ferrofinder.endpoint_parent_recovery.v4_variable_cell",
  "status": "complete",
  "input_atom_count": 44,
  "input_formula": "Na4Nb4O28Se8",
  "input_spacegroup": "Cmc2_1",
  "input_pointgroup": "mm2",
  "input_is_polar_point_group": true,
  "input_energy_eV": -271.5235314984117,
  "input_cartesian_polarization_e_A2": [
    -5.447530140535724e-18,
    1.9723474981745934e-17,
    0.008669736646929835
  ],
  "input_reduced_polarization": [
    -3.223427018373004e-16,
    1.6776588443760973e-15,
    0.7728852223925118
  ],
  "input_formal_targets": [
    {
      "orbit_id": 0,
      "representative_formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        1.0
      ]
    },
    {
      "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,
        1.0
      ]
    },
    {
      "orbit_id": 3,
      "representative_formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        -0.5,
        0.0,
        1.0
      ]
    },
    {
      "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,
        1.0
      ]
    },
    {
      "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": 2.181853451486512e-15,
      "parent_symmetrization_rmsd_A": 0.12843549030090334,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -271.0549331414626,
      "reduced_polarization": [
        -7.229638405116645e-16,
        -2.046849524939955e-15,
        2.1957866774646308e-16
      ],
      "cartesian_polarization_e_A2": [
        -1.2217950923835745e-17,
        -2.406388255388435e-17,
        2.4630943476349035e-18
      ],
      "ranking_score": 0.1284354903009077
    },
    {
      "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,
        1.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 1.1580272110123246e-06,
      "parent_symmetrization_rmsd_A": 0.009819740134447046,
      "parent_cell_rmsd_A": 0.000925445754094436,
      "energy_eV": -271.50729874467163,
      "reduced_polarization": [
        -2.0938650086662543e-15,
        1.1544899854856243e-15,
        0.999998841972789
      ],
      "cartesian_polarization_e_A2": [
        -4.6464596647103797e-17,
        3.83901653583902e-17,
        0.011216433171151714
      ],
      "ranking_score": 0.5100534176273926
    },
    {
      "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,
        1.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 1.5282854237966527e-15,
      "parent_symmetrization_rmsd_A": 0.12843594984443857,
      "parent_cell_rmsd_A": 0.000925445754094436,
      "energy_eV": -271.0550989135803,
      "reduced_polarization": [
        6.177067121382976e-16,
        8.494113196566064e-16,
        -1.152968818045766e-15
      ],
      "cartesian_polarization_e_A2": [
        1.0440039175955495e-17,
        9.986000918912077e-18,
        -1.2932212671886276e-17
      ],
      "ranking_score": 0.12866731128296524
    },
    {
      "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": 1.1348795598276062e-06,
      "parent_symmetrization_rmsd_A": 0.011401391507279921,
      "parent_cell_rmsd_A": 0.0010744815747419974,
      "energy_eV": -271.45390504076516,
      "reduced_polarization": [
        -3.316741293910291e-15,
        9.350982438849127e-17,
        0.4999988651204402
      ],
      "cartesian_polarization_e_A2": [
        -4.958947770843681e-17,
        -1.3300983195580462e-17,
        0.005609204707850548
      ],
      "ranking_score": 0.511672281660085
    },
    {
      "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,
        1.0
      ],
      "formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_residual": 5.483917869626606e-06,
      "parent_symmetrization_rmsd_A": 0.03326026459036355,
      "parent_cell_rmsd_A": 0.0022113817303230825,
      "energy_eV": -270.8707576434424,
      "reduced_polarization": [
        -1.072690944889344e-15,
        0.4999982607177121,
        0.9999947992065679
      ],
      "cartesian_polarization_e_A2": [
        -1.5852325258063897e-17,
        0.005881815049699216,
        0.011218283108196416
      ],
      "ranking_score": 0.5338240778586836
    },
    {
      "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,
        1.0
      ],
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_residual": 0.00010197398683440508,
      "parent_symmetrization_rmsd_A": 0.05330529236044086,
      "parent_cell_rmsd_A": 0.028320848028816622,
      "energy_eV": -270.37111377029134,
      "reduced_polarization": [
        -0.4999274726040247,
        -2.01387960661173e-15,
        0.999928316872111
      ],
      "cartesian_polarization_e_A2": [
        -0.008485433905810042,
        -2.1298450961573736e-16,
        0.011242624589215575
      ],
      "ranking_score": 0.5605894523413139
    },
    {
      "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": 7.990740510059496e-07,
      "parent_symmetrization_rmsd_A": 0.033357789907457865,
      "parent_cell_rmsd_A": 0.002250045106346459,
      "energy_eV": -270.84348907938613,
      "reduced_polarization": [
        -2.999917181548237e-15,
        0.5000000049392572,
        0.49999920094121447
      ],
      "cartesian_polarization_e_A2": [
        -4.477433913353024e-17,
        0.005880172320479445,
        0.005611097168920296
      ],
      "ranking_score": 0.5339218993321465
    },
    {
      "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": 1.0794663157257817e-05,
      "parent_symmetrization_rmsd_A": 0.051932845376592526,
      "parent_cell_rmsd_A": 0.02738593145031381,
      "energy_eV": -270.39469886490554,
      "reduced_polarization": [
        -0.4999926831066031,
        -6.726226392635566e-16,
        0.49999206351313885
      ],
      "cartesian_polarization_e_A2": [
        -0.008466348961821852,
        -1.1354521002165205e-16,
        0.005635282476191803
      ],
      "ranking_score": 0.5588009175654854
    },
    {
      "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,
        1.0
      ],
      "formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_residual": 0.0008304573768850229,
      "parent_symmetrization_rmsd_A": 0.062070222918388235,
      "parent_cell_rmsd_A": 0.02864291936491005,
      "energy_eV": -269.6815599476037,
      "reduced_polarization": [
        -0.4993492417998312,
        0.49985147714486045,
        0.99950592087553
      ],
      "cartesian_polarization_e_A2": [
        -0.008476006994631177,
        0.005880064011865376,
        0.011239950522565375
      ],
      "ranking_score": 0.5708918675133858
    },
    {
      "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": 0.0003812701069171464,
      "parent_symmetrization_rmsd_A": 0.060707754391965275,
      "parent_cell_rmsd_A": 0.027665261046611347,
      "energy_eV": -269.72852250488484,
      "reduced_polarization": [
        -0.49962640105057304,
        0.49993869498967647,
        0.5000450823149907
      ],
      "cartesian_polarization_e_A2": [
        -0.008460318618268391,
        0.005879441699273235,
        0.005637925269371474
      ],
      "ranking_score": 0.5683866098674524
    }
  ],
  "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,
        1.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -3.223427018373004e-16,
              1.6776588443760973e-15,
              0.7728852223925118
            ],
            "branch_aligned_reduced_polarization": [
              -3.223427018373004e-16,
              1.6776588443760973e-15,
              0.7728852223925118
            ],
            "target_residual": 0.22711477760748822,
            "energy_eV": -271.5235314984117,
            "max_atomic_step_A": 0.02028378266431429,
            "max_log_strain_component": 9.034604396680457e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.431616143152727,
            "cell_principal_stretches": [
              1.0000903501252936,
              0.9999902622875134,
              0.9999237427786721
            ],
            "cell_volume_ratio": 1.0000043481644638,
            "cell_rmsd_from_input_A": 0.0009093888845742389
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -7.223455129987117e-16,
              -5.504483351539614e-15,
              0.9962535410386698
            ],
            "branch_aligned_reduced_polarization": [
              -7.223455129987117e-16,
              -5.504483351539614e-15,
              0.9962535410386698
            ],
            "target_residual": 0.00374645896133019,
            "energy_eV": -271.50831471722904,
            "max_atomic_step_A": 0.00034179342647576357,
            "max_log_strain_component": 1.59510573084664e-06,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.431616143152727,
            "cell_principal_stretches": [
              1.0000919453764145,
              0.999990090364058,
              0.9999223964705716
            ],
            "cell_volume_ratio": 1.0000044249337068,
            "cell_rmsd_from_input_A": 0.000925445754094436
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -2.0938650086662543e-15,
              1.1544899854856243e-15,
              0.999998841972789
            ],
            "branch_aligned_reduced_polarization": [
              -2.0938650086662543e-15,
              1.1544899854856243e-15,
              0.999998841972789
            ],
            "target_residual": 1.1580272110123246e-06,
            "energy_eV": -271.50729874467163
          }
        ],
        "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": 2.181853451486512e-15,
        "parent_symmetrization_rmsd_A": 0.12843549030090334,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -271.0549331414626,
        "reduced_polarization": [
          -7.229638405116645e-16,
          -2.046849524939955e-15,
          2.1957866774646308e-16
        ],
        "cartesian_polarization_e_A2": [
          -1.2217950923835745e-17,
          -2.406388255388435e-17,
          2.4630943476349035e-18
        ],
        "ranking_score": 0.1284354903009077
      },
      "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": [
          -271.5235314984118,
          -271.46253016391387,
          -271.38686313964814,
          -271.3052862727486,
          -271.2258456464486,
          -271.1558063648043,
          -271.101263191978,
          -271.0667369182183,
          -271.0549331414626
        ],
        "cartesian_polarizations_e_A2": [
          [
            -4.0018730240586764e-17,
            1.8221424628619274e-17,
            0.008669736646929877
          ],
          [
            -5.636536885846555e-17,
            -1.7092297121786128e-18,
            0.007657347752098718
          ],
          [
            -4.154548835472774e-17,
            7.085534079576795e-18,
            0.006615744495304915
          ],
          [
            2.0903315615707516e-18,
            1.1073736741326892e-17,
            0.0055491397331135775
          ],
          [
            1.213998928785438e-17,
            2.2064601739033004e-18,
            0.0044623363416100075
          ],
          [
            5.969959280520764e-18,
            -1.0887275318180133e-17,
            0.0033599962274983254
          ],
          [
            3.710994668751922e-17,
            -4.01927956560789e-18,
            0.0022463078742440963
          ],
          [
            -2.3313007971820707e-17,
            -3.822459174508534e-18,
            0.0011250730994031746
          ],
          [
            -2.768458068382846e-17,
            -1.9267680391831636e-18,
            -3.0511154286152424e-17
          ]
        ],
        "raw_reduced_polarization": [
          [
            -2.367998945771821e-15,
            1.549895959694094e-15,
            0.7728852223925156
          ],
          [
            -3.3352665922298203e-15,
            -1.4538535153469327e-16,
            0.6826332980268107
          ],
          [
            -2.4583406828284287e-15,
            6.026883663620013e-16,
            0.5897769867503977
          ],
          [
            1.2368965492795526e-16,
            9.419208532762856e-16,
            0.4946918541330083
          ],
          [
            7.183506738593332e-16,
            1.8767927198114955e-16,
            0.3978060645010213
          ],
          [
            3.5325601780928956e-16,
            -9.260606331088645e-16,
            0.29953521511494424
          ],
          [
            2.1958796319971782e-15,
            -3.418758569421879e-16,
            0.20025269874397023
          ],
          [
            -1.3794835060521916e-15,
            -3.251345134321323e-16,
            0.1002974378636962
          ],
          [
            -1.6381593688585633e-15,
            -1.6388894173001792e-16,
            -2.7199926856205008e-15
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -2.367998945771821e-15,
            1.549895959694094e-15,
            0.7728852223925156
          ],
          [
            -3.3352665922298203e-15,
            -1.4538535153469323e-16,
            0.6826332980268107
          ],
          [
            -2.4583406828284287e-15,
            6.026883663620013e-16,
            0.5897769867503977
          ],
          [
            1.2368965492795521e-16,
            9.419208532762856e-16,
            0.4946918541330083
          ],
          [
            7.183506738593332e-16,
            1.8767927198114957e-16,
            0.3978060645010213
          ],
          [
            3.5325601780928956e-16,
            -9.260606331088643e-16,
            0.29953521511494424
          ],
          [
            2.1958796319971782e-15,
            -3.418758569421879e-16,
            0.20025269874397023
          ],
          [
            -1.379483506052192e-15,
            -3.251345134321323e-16,
            0.1002974378636962
          ],
          [
            -1.6381593688585633e-15,
            -1.6388894173001792e-16,
            -2.7200464103316335e-15
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            -2.3869795029440866e-15,
            1.5543122344752192e-15,
            -0.22711477760748444
          ],
          [
            -3.3306690738754696e-15,
            -1.6653345369377348e-16,
            -0.31736670197318917
          ],
          [
            -2.4424906541753444e-15,
            5.551115123125783e-16,
            -0.4102230132496023
          ],
          [
            1.1102230246251565e-16,
            8.881784197001252e-16,
            0.4946918541330083
          ],
          [
            6.661338147750939e-16,
            2.220446049250313e-16,
            0.3978060645010213
          ],
          [
            3.3306690738754696e-16,
            -9.43689570931383e-16,
            0.2995352151149442
          ],
          [
            2.220446049250313e-15,
            -3.3306690738754696e-16,
            0.20025269874397023
          ],
          [
            -1.3877787807814457e-15,
            -3.3306690738754696e-16,
            0.10029743786369616
          ],
          [
            -1.6653345369377348e-15,
            -1.6653345369377348e-16,
            -2.7200464103316335e-15
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -271.05493314146264,
          -271.0667369182183,
          -271.101263191978,
          -271.15580636480433,
          -271.22584564644853,
          -271.3052862727487,
          -271.3868631396482,
          -271.46253016391387,
          -271.52353149841184
        ],
        "cartesian_polarizations_e_A2": [
          [
            -2.0831412085888373e-17,
            -2.238572974556353e-17,
            6.4792476590554714e-18
          ],
          [
            -5.4301347833908076e-17,
            8.887994503328786e-18,
            -0.0011250730994032782
          ],
          [
            -6.727413680627337e-17,
            2.8176392831065617e-18,
            -0.00224630787424424
          ],
          [
            -3.4550149582392283e-17,
            -8.691174112229431e-18,
            -0.00335999622749844
          ],
          [
            -2.5793470068813933e-17,
            -2.4706138566945404e-17,
            -0.004462336341610028
          ],
          [
            -3.139038412528925e-17,
            -3.5220491038832024e-17,
            -0.005549139733113678
          ],
          [
            -1.3468665637871718e-17,
            -3.725084875754116e-17,
            -0.006615744495305005
          ],
          [
            -2.0909096395743707e-17,
            -2.4623266823324622e-17,
            -0.007657347752098838
          ],
          [
            8.249584236390963e-18,
            -4.657391991487905e-17,
            -0.008669736646929962
          ]
        ],
        "raw_reduced_polarization": [
          [
            -1.2326418544957506e-15,
            -1.904107543433165e-15,
            5.776086370142053e-16
          ],
          [
            -3.213133791393326e-15,
            7.560038279804052e-16,
            -0.10029743786370544
          ],
          [
            -3.98076310960507e-15,
            2.396655491965853e-16,
            -0.200252698743983
          ],
          [
            -2.0444106371068127e-15,
            -7.392624844703496e-16,
            -0.29953521511495446
          ],
          [
            -1.526258068748082e-15,
            -2.1014791721832938e-15,
            -0.3978060645010231
          ],
          [
            -1.8574401553767935e-15,
            -2.9958193649573167e-15,
            -0.49469185413301725
          ],
          [
            -7.969714641042481e-16,
            -3.1685195401136793e-15,
            -0.5897769867504057
          ],
          [
            -1.2372386111328183e-15,
            -2.094430185442218e-15,
            -0.6826332980268215
          ],
          [
            4.881465917930935e-16,
            -3.961530548484734e-15,
            -0.7728852223925231
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -1.2326418544957506e-15,
            -1.904107543433165e-15,
            5.776086370142053e-16
          ],
          [
            -3.213133791393326e-15,
            7.560038279804054e-16,
            -0.10029743786370544
          ],
          [
            -3.98076310960507e-15,
            2.396655491965853e-16,
            -0.200252698743983
          ],
          [
            -2.0444106371068127e-15,
            -7.392624844703497e-16,
            -0.29953521511495446
          ],
          [
            -1.526258068748082e-15,
            -2.1014791721832938e-15,
            -0.3978060645010231
          ],
          [
            -1.8574401553767935e-15,
            -2.9958193649573167e-15,
            -0.49469185413301725
          ],
          [
            -7.969714641042482e-16,
            -3.1685195401136793e-15,
            -0.5897769867504057
          ],
          [
            -1.2372386111328183e-15,
            -2.094430185442218e-15,
            -0.6826332980268215
          ],
          [
            4.881465917930935e-16,
            -3.961530548484734e-15,
            -0.7728852223925231
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          -9.083197919453055e-16,
          -1.87767384315413e-15,
          -0.7728852223925209
        ],
        "actual_opposite_endpoint_branch_residual": 3.35006832570532e-15
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            -2.367998945771821e-15,
            1.549895959694094e-15,
            0.7728852223925156
          ],
          [
            -3.3352665922298203e-15,
            -1.4538535153469327e-16,
            0.6826332980268107
          ],
          [
            -2.4583406828284287e-15,
            6.026883663620013e-16,
            0.5897769867503977
          ],
          [
            1.2368965492795526e-16,
            9.419208532762856e-16,
            0.4946918541330083
          ],
          [
            7.183506738593332e-16,
            1.8767927198114955e-16,
            0.3978060645010213
          ],
          [
            3.5325601780928956e-16,
            -9.260606331088645e-16,
            0.29953521511494424
          ],
          [
            2.1958796319971782e-15,
            -3.418758569421879e-16,
            0.20025269874397023
          ],
          [
            -1.3794835060521916e-15,
            -3.251345134321323e-16,
            0.1002974378636962
          ],
          [
            -1.6381593688585633e-15,
            -1.6388894173001792e-16,
            -2.7199926856205008e-15
          ],
          [
            -3.213133791393326e-15,
            7.560038279804052e-16,
            -0.10029743786370544
          ],
          [
            -3.98076310960507e-15,
            2.396655491965853e-16,
            -0.200252698743983
          ],
          [
            -2.0444106371068127e-15,
            -7.392624844703496e-16,
            -0.29953521511495446
          ],
          [
            -1.526258068748082e-15,
            -2.1014791721832938e-15,
            -0.3978060645010231
          ],
          [
            -1.8574401553767935e-15,
            -2.9958193649573167e-15,
            -0.49469185413301725
          ],
          [
            -7.969714641042481e-16,
            -3.1685195401136793e-15,
            -0.5897769867504057
          ],
          [
            -1.2372386111328183e-15,
            -2.094430185442218e-15,
            -0.6826332980268215
          ],
          [
            4.881465917930935e-16,
            -3.961530548484734e-15,
            -0.7728852223925231
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -2.367998945771821e-15,
            1.549895959694094e-15,
            0.7728852223925156
          ],
          [
            -3.3352665922298203e-15,
            -1.4538535153469323e-16,
            0.6826332980268107
          ],
          [
            -2.4583406828284287e-15,
            6.026883663620013e-16,
            0.5897769867503977
          ],
          [
            1.2368965492795521e-16,
            9.419208532762856e-16,
            0.4946918541330083
          ],
          [
            7.183506738593332e-16,
            1.8767927198114957e-16,
            0.3978060645010213
          ],
          [
            3.5325601780928956e-16,
            -9.260606331088643e-16,
            0.29953521511494424
          ],
          [
            2.1958796319971782e-15,
            -3.418758569421879e-16,
            0.20025269874397023
          ],
          [
            -1.379483506052192e-15,
            -3.251345134321323e-16,
            0.1002974378636962
          ],
          [
            -1.6381593688585633e-15,
            -1.6388894173001792e-16,
            -2.7200464103316335e-15
          ],
          [
            -3.213133791393326e-15,
            7.560038279804052e-16,
            -0.10029743786370544
          ],
          [
            -3.98076310960507e-15,
            2.396655491965853e-16,
            -0.200252698743983
          ],
          [
            -2.0444106371068127e-15,
            -7.392624844703497e-16,
            -0.29953521511495446
          ],
          [
            -1.526258068748082e-15,
            -2.1014791721832938e-15,
            -0.3978060645010231
          ],
          [
            -1.8574401553767935e-15,
            -2.9958193649573167e-15,
            -0.49469185413301725
          ],
          [
            -7.969714641042482e-16,
            -3.1685195401136793e-15,
            -0.5897769867504057
          ],
          [
            -1.2372386111328183e-15,
            -2.094430185442218e-15,
            -0.6826332980268215
          ],
          [
            4.881465917930935e-16,
            -3.961530548484734e-15,
            -0.7728852223925231
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            -2.3869795029440866e-15,
            1.5543122344752192e-15,
            -0.22711477760748444
          ],
          [
            -3.3306690738754696e-15,
            -1.6653345369377348e-16,
            -0.31736670197318917
          ],
          [
            -2.4424906541753444e-15,
            5.551115123125783e-16,
            -0.4102230132496023
          ],
          [
            1.1102230246251565e-16,
            8.881784197001252e-16,
            0.4946918541330083
          ],
          [
            6.661338147750939e-16,
            2.220446049250313e-16,
            0.3978060645010213
          ],
          [
            3.3306690738754696e-16,
            -9.43689570931383e-16,
            0.2995352151149442
          ],
          [
            2.220446049250313e-15,
            -3.3306690738754696e-16,
            0.20025269874397023
          ],
          [
            -1.3877787807814457e-15,
            -3.3306690738754696e-16,
            0.10029743786369616
          ],
          [
            -1.6653345369377348e-15,
            -1.6653345369377348e-16,
            -2.7200464103316335e-15
          ],
          [
            -3.219646771412954e-15,
            7.771561172376096e-16,
            -0.10029743786370543
          ],
          [
            -3.9968028886505635e-15,
            2.220446049250313e-16,
            -0.200252698743983
          ],
          [
            -2.0539125955565396e-15,
            -7.216449660063518e-16,
            -0.29953521511495446
          ],
          [
            -1.4988010832439613e-15,
            -2.1094237467877974e-15,
            -0.3978060645010231
          ],
          [
            -1.8318679906315083e-15,
            -2.9976021664879227e-15,
            -0.49469185413301725
          ],
          [
            -7.771561172376096e-16,
            -3.164135620181696e-15,
            0.4102230132495943
          ],
          [
            -1.2212453270876722e-15,
            -2.1094237467877974e-15,
            0.3173667019731785
          ],
          [
            4.440892098500626e-16,
            -3.941291737419306e-15,
            0.2271147776074769
          ]
        ]
      },
      "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": [
              -3.223427018373004e-16,
              1.6776588443760973e-15,
              0.7728852223925118
            ],
            "branch_aligned_reduced_polarization": [
              -3.223427018373004e-16,
              1.6776588443760973e-15,
              0.7728852223925118
            ],
            "target_residual": 0.2728852223925118,
            "energy_eV": -271.5235314984117,
            "max_atomic_step_A": 0.02437157371097577,
            "max_log_strain_component": 0.00010855348366090751,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.431616143152727,
            "cell_principal_stretches": [
              1.0000916330321434,
              1.0000117002792557,
              0.9998914524080553
            ],
            "cell_volume_ratio": 0.9999947755748876,
            "cell_rmsd_from_input_A": 0.0010924898769235742
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              8.436726942353607e-16,
              -5.124810418568069e-17,
              0.495188533860736
            ],
            "branch_aligned_reduced_polarization": [
              8.436726942353607e-16,
              -5.124810418568069e-17,
              0.495188533860736
            ],
            "target_residual": 0.004811466139263976,
            "energy_eV": -271.4520454543492,
            "max_atomic_step_A": 0.0004207889229869242,
            "max_log_strain_component": 1.7895135473284418e-06,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.431616143152727,
            "cell_principal_stretches": [
              1.0000901223856333,
              1.0000115073980327,
              0.9998932417289563
            ],
            "cell_volume_ratio": 0.9999948616997651,
            "cell_rmsd_from_input_A": 0.0010744815747419974
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -3.316741293910291e-15,
              9.350982438849127e-17,
              0.4999988651204402
            ],
            "branch_aligned_reduced_polarization": [
              -3.316741293910291e-15,
              9.350982438849127e-17,
              0.4999988651204402
            ],
            "target_residual": 1.1348795598276062e-06,
            "energy_eV": -271.45390504076516
          }
        ],
        "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": 1.1348795598276062e-06,
        "parent_symmetrization_rmsd_A": 0.011401391507279921,
        "parent_cell_rmsd_A": 0.0010744815747419974,
        "energy_eV": -271.45390504076516,
        "reduced_polarization": [
          -3.316741293910291e-15,
          9.350982438849127e-17,
          0.4999988651204402
        ],
        "cartesian_polarization_e_A2": [
          -4.958947770843681e-17,
          -1.3300983195580462e-17,
          0.005609204707850548
        ],
        "ranking_score": 0.511672281660085
      },
      "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,
        1.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -3.223427018373004e-16,
              1.6776588443760973e-15,
              0.7728852223925118
            ],
            "branch_aligned_reduced_polarization": [
              -3.223427018373004e-16,
              1.6653345369377348e-15,
              0.7728852223925118
            ],
            "target_residual": 0.5491640212247131,
            "energy_eV": -271.5235314984117,
            "max_atomic_step_A": 0.07021016906077156,
            "max_log_strain_component": 0.0003219990368867415,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.431616143152727,
            "cell_principal_stretches": [
              1.000280752810161,
              1.00009035012531,
              0.9996333559349411
            ],
            "cell_volume_ratio": 1.0000043481644745,
            "cell_rmsd_from_input_A": 0.0021797647286161933
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -2.9257384441809853e-15,
              0.49535822775550015,
              0.9926688819748066
            ],
            "branch_aligned_reduced_polarization": [
              -2.9257384441809853e-15,
              0.49535822775550015,
              0.9926688819748066
            ],
            "target_residual": 0.008677058318873072,
            "energy_eV": -270.88512949333676,
            "max_atomic_step_A": 0.0010093290734954677,
            "max_log_strain_component": 3.266147290642249e-06,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.431616143152727,
            "cell_principal_stretches": [
              1.0002824905979986,
              1.0000936165730319,
              0.9996285114700981
            ],
            "cell_volume_ratio": 1.0000045053576063,
            "cell_rmsd_from_input_A": 0.0022113817303230825
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -1.072690944889344e-15,
              0.4999982607177121,
              0.9999947992065679
            ],
            "branch_aligned_reduced_polarization": [
              -1.072690944889344e-15,
              0.4999982607177121,
              0.9999947992065679
            ],
            "target_residual": 5.483917869626606e-06,
            "energy_eV": -270.8707576434424
          }
        ],
        "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,
          1.0
        ],
        "formal_class": [
          0.0,
          0.5,
          0.0
        ],
        "target_residual": 5.483917869626606e-06,
        "parent_symmetrization_rmsd_A": 0.03326026459036355,
        "parent_cell_rmsd_A": 0.0022113817303230825,
        "energy_eV": -270.8707576434424,
        "reduced_polarization": [
          -1.072690944889344e-15,
          0.4999982607177121,
          0.9999947992065679
        ],
        "cartesian_polarization_e_A2": [
          -1.5852325258063897e-17,
          0.005881815049699216,
          0.011218283108196416
        ],
        "ranking_score": 0.5338240778586836
      },
      "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,
        1.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -3.223427018373004e-16,
              1.6776588443760973e-15,
              0.7728852223925118
            ],
            "branch_aligned_reduced_polarization": [
              -3.3306690738754696e-16,
              1.6776588443760973e-15,
              0.7728852223925118
            ],
            "target_residual": 0.5491640212247143,
            "energy_eV": -271.5235314984117,
            "max_atomic_step_A": 0.11214211612833846,
            "max_log_strain_component": 0.0030724361638303976,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.431616143152727,
            "cell_principal_stretches": [
              1.0030853581635977,
              0.999990262287515,
              0.9969381746782412
            ],
            "cell_volume_ratio": 1.0000043481644358,
            "cell_rmsd_from_input_A": 0.027193350509705453
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.48307134926833345,
              1.4792424568507102e-15,
              0.9769047613450412
            ],
            "branch_aligned_reduced_polarization": [
              -0.48307134926833345,
              1.4792424568507102e-15,
              0.9769047613450412
            ],
            "target_residual": 0.028635105449853964,
            "energy_eV": -270.4602470257679,
            "max_atomic_step_A": 0.0046182511895167385,
            "max_log_strain_component": 0.0001270079207384274,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.431616143152727,
            "cell_principal_stretches": [
              1.0032139869504875,
              0.9999889491831031,
              0.9968122439568242
            ],
            "cell_volume_ratio": 1.0000049345074373,
            "cell_rmsd_from_input_A": 0.028320848028816622
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.4999274726040247,
              -2.01387960661173e-15,
              0.999928316872111
            ],
            "branch_aligned_reduced_polarization": [
              -0.4999274726040247,
              -2.01387960661173e-15,
              0.999928316872111
            ],
            "target_residual": 0.00010197398683440508,
            "energy_eV": -270.37111377029134
          }
        ],
        "iterations": 2
      },
      "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,
          1.0
        ],
        "formal_class": [
          0.5,
          0.0,
          0.0
        ],
        "target_residual": 0.00010197398683440508,
        "parent_symmetrization_rmsd_A": 0.05330529236044086,
        "parent_cell_rmsd_A": 0.028320848028816622,
        "energy_eV": -270.37111377029134,
        "reduced_polarization": [
          -0.4999274726040247,
          -2.01387960661173e-15,
          0.999928316872111
        ],
        "cartesian_polarization_e_A2": [
          -0.008485433905810042,
          -2.1298450961573736e-16,
          0.011242624589215575
        ],
        "ranking_score": 0.5605894523413139
      },
      "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": [
              -3.223427018373004e-16,
              1.6776588443760973e-15,
              0.7728852223925118
            ],
            "branch_aligned_reduced_polarization": [
              -3.223427018373004e-16,
              1.6653345369377348e-15,
              0.7728852223925118
            ],
            "target_residual": 0.569619473508595,
            "energy_eV": -271.5235314984117,
            "max_atomic_step_A": 0.0723277757654145,
            "max_log_strain_component": 0.0003219990368819605,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.431616143152727,
            "cell_principal_stretches": [
              1.0003762048769003,
              0.9998914524080715,
              0.9997272321232301
            ],
            "cell_volume_ratio": 0.999994775574898,
            "cell_rmsd_from_input_A": 0.002262763591423892
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -4.337669816547339e-16,
              0.5016205315530289,
              0.49602821791465185
            ],
            "branch_aligned_reduced_polarization": [
              -4.337669816547339e-16,
              0.5016205315530289,
              0.49602821791465185
            ],
            "target_residual": 0.004289659129564342,
            "energy_eV": -270.8380872786535,
            "max_atomic_step_A": 0.00043229618792718546,
            "max_log_strain_component": 1.4877384687228435e-06,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.431616143152727,
            "cell_principal_stretches": [
              1.0003744144814934,
              0.9998929399861565,
              0.9997276056081926
            ],
            "cell_volume_ratio": 0.9999948471760841,
            "cell_rmsd_from_input_A": 0.002250045106346459
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -2.999917181548237e-15,
              0.5000000049392572,
              0.49999920094121447
            ],
            "branch_aligned_reduced_polarization": [
              -2.999917181548237e-15,
              0.5000000049392572,
              0.49999920094121447
            ],
            "target_residual": 7.990740510059496e-07,
            "energy_eV": -270.84348907938613
          }
        ],
        "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": 7.990740510059496e-07,
        "parent_symmetrization_rmsd_A": 0.033357789907457865,
        "parent_cell_rmsd_A": 0.002250045106346459,
        "energy_eV": -270.84348907938613,
        "reduced_polarization": [
          -2.999917181548237e-15,
          0.5000000049392572,
          0.49999920094121447
        ],
        "cartesian_polarization_e_A2": [
          -4.477433913353024e-17,
          0.005880172320479445,
          0.005611097168920296
        ],
        "ranking_score": 0.5339218993321465
      },
      "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": [
              -3.223427018373004e-16,
              1.6776588443760973e-15,
              0.7728852223925118
            ],
            "branch_aligned_reduced_polarization": [
              -3.3306690738754696e-16,
              1.6776588443760973e-15,
              0.7728852223925118
            ],
            "target_residual": 0.5696194735085962,
            "energy_eV": -271.5235314984117,
            "max_atomic_step_A": 0.1129530697932469,
            "max_log_strain_component": 0.0030724361638282474,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.431616143152727,
            "cell_principal_stretches": [
              1.003070307516728,
              1.0000117002792568,
              0.9969222177149805
            ],
            "cell_volume_ratio": 0.9999947755748593,
            "cell_rmsd_from_input_A": 0.027194122490839537
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.4971641912628502,
              -1.243474085479728e-15,
              0.4860009410428777
            ],
            "branch_aligned_reduced_polarization": [
              -0.4971641912628502,
              -1.243474085479728e-15,
              0.4860009410428777
            ],
            "target_residual": 0.014283398155854948,
            "energy_eV": -270.40279453555286,
            "max_atomic_step_A": 0.0014358166329886033,
            "max_log_strain_component": 2.1936198030401442e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.431616143152727,
            "cell_principal_stretches": [
              1.0030925773472594,
              1.000011090511107,
              0.9969009641747493
            ],
            "cell_volume_ratio": 0.9999950478472049,
            "cell_rmsd_from_input_A": 0.02738593145031381
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.4999926831066031,
              -6.726226392635566e-16,
              0.49999206351313885
            ],
            "branch_aligned_reduced_polarization": [
              -0.4999926831066031,
              -6.726226392635566e-16,
              0.49999206351313885
            ],
            "target_residual": 1.0794663157257817e-05,
            "energy_eV": -270.39469886490554
          }
        ],
        "iterations": 2
      },
      "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": 1.0794663157257817e-05,
        "parent_symmetrization_rmsd_A": 0.051932845376592526,
        "parent_cell_rmsd_A": 0.02738593145031381,
        "energy_eV": -270.39469886490554,
        "reduced_polarization": [
          -0.4999926831066031,
          -6.726226392635566e-16,
          0.49999206351313885
        ],
        "cartesian_polarization_e_A2": [
          -0.008466348961821852,
          -1.1354521002165205e-16,
          0.005635282476191803
        ],
        "ranking_score": 0.5588009175654854
      },
      "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,
        1.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -3.223427018373004e-16,
              1.6776588443760973e-15,
              0.7728852223925118
            ],
            "branch_aligned_reduced_polarization": [
              -3.3306690738754696e-16,
              1.6653345369377348e-15,
              0.7728852223925118
            ],
            "target_residual": 0.7426850760636683,
            "energy_eV": -271.5235314984117,
            "max_atomic_step_A": 0.11999999999999998,
            "max_log_strain_component": 0.0028199646175642436,
            "step_scale": 0.9178269188338678,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.431616143152727,
            "cell_principal_stretches": [
              1.0028464512495867,
              0.9999920597386933,
              0.9971735253903053
            ],
            "cell_volume_ratio": 1.0000039908616634,
            "cell_rmsd_from_input_A": 0.02502468050113404
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.44375489888450426,
              0.4580371127534487,
              0.9593661571329005
            ],
            "branch_aligned_reduced_polarization": [
              -0.44375489888450426,
              0.4580371127534487,
              0.9593661571329005
            ],
            "target_residual": 0.08108948447059734,
            "energy_eV": -270.07064310776116,
            "max_atomic_step_A": 0.01500441581909676,
            "max_log_strain_component": 0.00040784153861612695,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.431616143152727,
            "cell_principal_stretches": [
              1.003258602498139,
              0.9999896079805807,
              0.9967674924133759
            ],
            "cell_volume_ratio": 1.0000051692730834,
            "cell_rmsd_from_input_A": 0.02864291936491005
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.4993492417998312,
              0.49985147714486045,
              0.99950592087553
            ],
            "branch_aligned_reduced_polarization": [
              -0.4993492417998312,
              0.49985147714486045,
              0.99950592087553
            ],
            "target_residual": 0.0008304573768850229,
            "energy_eV": -269.6815599476037
          }
        ],
        "iterations": 2
      },
      "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,
          1.0
        ],
        "formal_class": [
          0.5,
          0.5,
          0.0
        ],
        "target_residual": 0.0008304573768850229,
        "parent_symmetrization_rmsd_A": 0.062070222918388235,
        "parent_cell_rmsd_A": 0.02864291936491005,
        "energy_eV": -269.6815599476037,
        "reduced_polarization": [
          -0.4993492417998312,
          0.49985147714486045,
          0.99950592087553
        ],
        "cartesian_polarization_e_A2": [
          -0.008476006994631177,
          0.005880064011865376,
          0.011239950522565375
        ],
        "ranking_score": 0.5708918675133858
      },
      "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": [
              -3.223427018373004e-16,
              1.6776588443760973e-15,
              0.7728852223925118
            ],
            "branch_aligned_reduced_polarization": [
              -3.3306690738754696e-16,
              1.6653345369377348e-15,
              0.7728852223925118
            ],
            "target_residual": 0.757935580772013,
            "energy_eV": -271.5235314984117,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.00279539247144356,
            "step_scale": 0.9098293088564889,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.431616143152727,
            "cell_principal_stretches": [
              1.0028090131510712,
              1.0000094577816705,
              0.9971846841247567
            ],
            "cell_volume_ratio": 0.9999952466637752,
            "cell_rmsd_from_input_A": 0.0248078226715933
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.4516142061898333,
              0.4589016502183765,
              0.5129574032846069
            ],
            "branch_aligned_reduced_polarization": [
              -0.4516142061898333,
              0.4589016502183765,
              0.5129574032846069
            ],
            "target_residual": 0.0647931608836348,
            "energy_eV": -270.05022524282924,
            "max_atomic_step_A": 0.012212314013695037,
            "max_log_strain_component": 0.00032276490965223945,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.431616143152727,
            "cell_principal_stretches": [
              1.0031335102309702,
              1.0000096639462193,
              0.9968618286851104
            ],
            "cell_volume_ratio": 0.9999951692303032,
            "cell_rmsd_from_input_A": 0.027665261046611347
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.49962640105057304,
              0.49993869498967647,
              0.5000450823149907
            ],
            "branch_aligned_reduced_polarization": [
              -0.49962640105057304,
              0.49993869498967647,
              0.5000450823149907
            ],
            "target_residual": 0.0003812701069171464,
            "energy_eV": -269.72852250488484
          }
        ],
        "iterations": 2
      },
      "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": 0.0003812701069171464,
        "parent_symmetrization_rmsd_A": 0.060707754391965275,
        "parent_cell_rmsd_A": 0.027665261046611347,
        "energy_eV": -269.72852250488484,
        "reduced_polarization": [
          -0.49962640105057304,
          0.49993869498967647,
          0.5000450823149907
        ],
        "cartesian_polarization_e_A2": [
          -0.008460318618268391,
          0.005879441699273235,
          0.005637925269371474
        ],
        "ranking_score": 0.5683866098674524
      },
      "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,
          24,
          25,
          26,
          27,
          28,
          29,
          30,
          31,
          32,
          33,
          34,
          35,
          36,
          37,
          38,
          39,
          40,
          41,
          42,
          43
        ],
        "endpoint_rmsd_A": 0.12843549030090334,
        "minimum_distance_A_by_image": [
          1.6721594373769273,
          1.672098636052267,
          1.6720459397824863,
          1.672001349333923,
          1.6719648653551118,
          1.6719364883767358,
          1.6719162188115888,
          1.671904056954545,
          1.6719000029825375
        ],
        "minimum_distance_A": 1.6719000029825375,
        "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": [
          669.8441327031237,
          669.8441327031237,
          669.8441327031237,
          669.8441327031237,
          669.8441327031237,
          669.8441327031237,
          669.8441327031237,
          669.8441327031237,
          669.8441327031237
        ],
        "cell_deformation_log_strain_norm": 0.0
      },
      "parent_reduced_polarization": [
        -1.6381593688585633e-15,
        -1.6388894173001792e-16,
        -2.7199926856205008e-15
      ],
      "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": [
          -271.5235314984118,
          -271.46253016391387,
          -271.38686313964814,
          -271.3052862727486,
          -271.2258456464486,
          -271.1558063648043,
          -271.101263191978,
          -271.0667369182183,
          -271.0549331414626
        ],
        "cartesian_polarizations_e_A2": [
          [
            -4.0018730240586764e-17,
            1.8221424628619274e-17,
            0.008669736646929877
          ],
          [
            -5.636536885846555e-17,
            -1.7092297121786128e-18,
            0.007657347752098718
          ],
          [
            -4.154548835472774e-17,
            7.085534079576795e-18,
            0.006615744495304915
          ],
          [
            2.0903315615707516e-18,
            1.1073736741326892e-17,
            0.0055491397331135775
          ],
          [
            1.213998928785438e-17,
            2.2064601739033004e-18,
            0.0044623363416100075
          ],
          [
            5.969959280520764e-18,
            -1.0887275318180133e-17,
            0.0033599962274983254
          ],
          [
            3.710994668751922e-17,
            -4.01927956560789e-18,
            0.0022463078742440963
          ],
          [
            -2.3313007971820707e-17,
            -3.822459174508534e-18,
            0.0011250730994031746
          ],
          [
            -2.768458068382846e-17,
            -1.9267680391831636e-18,
            -3.0511154286152424e-17
          ]
        ],
        "raw_reduced_polarization": [
          [
            -2.367998945771821e-15,
            1.549895959694094e-15,
            0.7728852223925156
          ],
          [
            -3.3352665922298203e-15,
            -1.4538535153469327e-16,
            0.6826332980268107
          ],
          [
            -2.4583406828284287e-15,
            6.026883663620013e-16,
            0.5897769867503977
          ],
          [
            1.2368965492795526e-16,
            9.419208532762856e-16,
            0.4946918541330083
          ],
          [
            7.183506738593332e-16,
            1.8767927198114955e-16,
            0.3978060645010213
          ],
          [
            3.5325601780928956e-16,
            -9.260606331088645e-16,
            0.29953521511494424
          ],
          [
            2.1958796319971782e-15,
            -3.418758569421879e-16,
            0.20025269874397023
          ],
          [
            -1.3794835060521916e-15,
            -3.251345134321323e-16,
            0.1002974378636962
          ],
          [
            -1.6381593688585633e-15,
            -1.6388894173001792e-16,
            -2.7199926856205008e-15
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -2.367998945771821e-15,
            1.549895959694094e-15,
            0.7728852223925156
          ],
          [
            -3.3352665922298203e-15,
            -1.4538535153469323e-16,
            0.6826332980268107
          ],
          [
            -2.4583406828284287e-15,
            6.026883663620013e-16,
            0.5897769867503977
          ],
          [
            1.2368965492795521e-16,
            9.419208532762856e-16,
            0.4946918541330083
          ],
          [
            7.183506738593332e-16,
            1.8767927198114957e-16,
            0.3978060645010213
          ],
          [
            3.5325601780928956e-16,
            -9.260606331088643e-16,
            0.29953521511494424
          ],
          [
            2.1958796319971782e-15,
            -3.418758569421879e-16,
            0.20025269874397023
          ],
          [
            -1.379483506052192e-15,
            -3.251345134321323e-16,
            0.1002974378636962
          ],
          [
            -1.6381593688585633e-15,
            -1.6388894173001792e-16,
            -2.7200464103316335e-15
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            -2.3869795029440866e-15,
            1.5543122344752192e-15,
            -0.22711477760748444
          ],
          [
            -3.3306690738754696e-15,
            -1.6653345369377348e-16,
            -0.31736670197318917
          ],
          [
            -2.4424906541753444e-15,
            5.551115123125783e-16,
            -0.4102230132496023
          ],
          [
            1.1102230246251565e-16,
            8.881784197001252e-16,
            0.4946918541330083
          ],
          [
            6.661338147750939e-16,
            2.220446049250313e-16,
            0.3978060645010213
          ],
          [
            3.3306690738754696e-16,
            -9.43689570931383e-16,
            0.2995352151149442
          ],
          [
            2.220446049250313e-15,
            -3.3306690738754696e-16,
            0.20025269874397023
          ],
          [
            -1.3877787807814457e-15,
            -3.3306690738754696e-16,
            0.10029743786369616
          ],
          [
            -1.6653345369377348e-15,
            -1.6653345369377348e-16,
            -2.7200464103316335e-15
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -271.05493314146264,
          -271.0667369182183,
          -271.101263191978,
          -271.15580636480433,
          -271.22584564644853,
          -271.3052862727487,
          -271.3868631396482,
          -271.46253016391387,
          -271.52353149841184
        ],
        "cartesian_polarizations_e_A2": [
          [
            -2.0831412085888373e-17,
            -2.238572974556353e-17,
            6.4792476590554714e-18
          ],
          [
            -5.4301347833908076e-17,
            8.887994503328786e-18,
            -0.0011250730994032782
          ],
          [
            -6.727413680627337e-17,
            2.8176392831065617e-18,
            -0.00224630787424424
          ],
          [
            -3.4550149582392283e-17,
            -8.691174112229431e-18,
            -0.00335999622749844
          ],
          [
            -2.5793470068813933e-17,
            -2.4706138566945404e-17,
            -0.004462336341610028
          ],
          [
            -3.139038412528925e-17,
            -3.5220491038832024e-17,
            -0.005549139733113678
          ],
          [
            -1.3468665637871718e-17,
            -3.725084875754116e-17,
            -0.006615744495305005
          ],
          [
            -2.0909096395743707e-17,
            -2.4623266823324622e-17,
            -0.007657347752098838
          ],
          [
            8.249584236390963e-18,
            -4.657391991487905e-17,
            -0.008669736646929962
          ]
        ],
        "raw_reduced_polarization": [
          [
            -1.2326418544957506e-15,
            -1.904107543433165e-15,
            5.776086370142053e-16
          ],
          [
            -3.213133791393326e-15,
            7.560038279804052e-16,
            -0.10029743786370544
          ],
          [
            -3.98076310960507e-15,
            2.396655491965853e-16,
            -0.200252698743983
          ],
          [
            -2.0444106371068127e-15,
            -7.392624844703496e-16,
            -0.29953521511495446
          ],
          [
            -1.526258068748082e-15,
            -2.1014791721832938e-15,
            -0.3978060645010231
          ],
          [
            -1.8574401553767935e-15,
            -2.9958193649573167e-15,
            -0.49469185413301725
          ],
          [
            -7.969714641042481e-16,
            -3.1685195401136793e-15,
            -0.5897769867504057
          ],
          [
            -1.2372386111328183e-15,
            -2.094430185442218e-15,
            -0.6826332980268215
          ],
          [
            4.881465917930935e-16,
            -3.961530548484734e-15,
            -0.7728852223925231
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -1.2326418544957506e-15,
            -1.904107543433165e-15,
            5.776086370142053e-16
          ],
          [
            -3.213133791393326e-15,
            7.560038279804054e-16,
            -0.10029743786370544
          ],
          [
            -3.98076310960507e-15,
            2.396655491965853e-16,
            -0.200252698743983
          ],
          [
            -2.0444106371068127e-15,
            -7.392624844703497e-16,
            -0.29953521511495446
          ],
          [
            -1.526258068748082e-15,
            -2.1014791721832938e-15,
            -0.3978060645010231
          ],
          [
            -1.8574401553767935e-15,
            -2.9958193649573167e-15,
            -0.49469185413301725
          ],
          [
            -7.969714641042482e-16,
            -3.1685195401136793e-15,
            -0.5897769867504057
          ],
          [
            -1.2372386111328183e-15,
            -2.094430185442218e-15,
            -0.6826332980268215
          ],
          [
            4.881465917930935e-16,
            -3.961530548484734e-15,
            -0.7728852223925231
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          -9.083197919453055e-16,
          -1.87767384315413e-15,
          -0.7728852223925209
        ],
        "actual_opposite_endpoint_branch_residual": 3.35006832570532e-15
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            -2.367998945771821e-15,
            1.549895959694094e-15,
            0.7728852223925156
          ],
          [
            -3.3352665922298203e-15,
            -1.4538535153469327e-16,
            0.6826332980268107
          ],
          [
            -2.4583406828284287e-15,
            6.026883663620013e-16,
            0.5897769867503977
          ],
          [
            1.2368965492795526e-16,
            9.419208532762856e-16,
            0.4946918541330083
          ],
          [
            7.183506738593332e-16,
            1.8767927198114955e-16,
            0.3978060645010213
          ],
          [
            3.5325601780928956e-16,
            -9.260606331088645e-16,
            0.29953521511494424
          ],
          [
            2.1958796319971782e-15,
            -3.418758569421879e-16,
            0.20025269874397023
          ],
          [
            -1.3794835060521916e-15,
            -3.251345134321323e-16,
            0.1002974378636962
          ],
          [
            -1.6381593688585633e-15,
            -1.6388894173001792e-16,
            -2.7199926856205008e-15
          ],
          [
            -3.213133791393326e-15,
            7.560038279804052e-16,
            -0.10029743786370544
          ],
          [
            -3.98076310960507e-15,
            2.396655491965853e-16,
            -0.200252698743983
          ],
          [
            -2.0444106371068127e-15,
            -7.392624844703496e-16,
            -0.29953521511495446
          ],
          [
            -1.526258068748082e-15,
            -2.1014791721832938e-15,
            -0.3978060645010231
          ],
          [
            -1.8574401553767935e-15,
            -2.9958193649573167e-15,
            -0.49469185413301725
          ],
          [
            -7.969714641042481e-16,
            -3.1685195401136793e-15,
            -0.5897769867504057
          ],
          [
            -1.2372386111328183e-15,
            -2.094430185442218e-15,
            -0.6826332980268215
          ],
          [
            4.881465917930935e-16,
            -3.961530548484734e-15,
            -0.7728852223925231
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -2.367998945771821e-15,
            1.549895959694094e-15,
            0.7728852223925156
          ],
          [
            -3.3352665922298203e-15,
            -1.4538535153469323e-16,
            0.6826332980268107
          ],
          [
            -2.4583406828284287e-15,
            6.026883663620013e-16,
            0.5897769867503977
          ],
          [
            1.2368965492795521e-16,
            9.419208532762856e-16,
            0.4946918541330083
          ],
          [
            7.183506738593332e-16,
            1.8767927198114957e-16,
            0.3978060645010213
          ],
          [
            3.5325601780928956e-16,
            -9.260606331088643e-16,
            0.29953521511494424
          ],
          [
            2.1958796319971782e-15,
            -3.418758569421879e-16,
            0.20025269874397023
          ],
          [
            -1.379483506052192e-15,
            -3.251345134321323e-16,
            0.1002974378636962
          ],
          [
            -1.6381593688585633e-15,
            -1.6388894173001792e-16,
            -2.7200464103316335e-15
          ],
          [
            -3.213133791393326e-15,
            7.560038279804052e-16,
            -0.10029743786370544
          ],
          [
            -3.98076310960507e-15,
            2.396655491965853e-16,
            -0.200252698743983
          ],
          [
            -2.0444106371068127e-15,
            -7.392624844703497e-16,
            -0.29953521511495446
          ],
          [
            -1.526258068748082e-15,
            -2.1014791721832938e-15,
            -0.3978060645010231
          ],
          [
            -1.8574401553767935e-15,
            -2.9958193649573167e-15,
            -0.49469185413301725
          ],
          [
            -7.969714641042482e-16,
            -3.1685195401136793e-15,
            -0.5897769867504057
          ],
          [
            -1.2372386111328183e-15,
            -2.094430185442218e-15,
            -0.6826332980268215
          ],
          [
            4.881465917930935e-16,
            -3.961530548484734e-15,
            -0.7728852223925231
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            -2.3869795029440866e-15,
            1.5543122344752192e-15,
            -0.22711477760748444
          ],
          [
            -3.3306690738754696e-15,
            -1.6653345369377348e-16,
            -0.31736670197318917
          ],
          [
            -2.4424906541753444e-15,
            5.551115123125783e-16,
            -0.4102230132496023
          ],
          [
            1.1102230246251565e-16,
            8.881784197001252e-16,
            0.4946918541330083
          ],
          [
            6.661338147750939e-16,
            2.220446049250313e-16,
            0.3978060645010213
          ],
          [
            3.3306690738754696e-16,
            -9.43689570931383e-16,
            0.2995352151149442
          ],
          [
            2.220446049250313e-15,
            -3.3306690738754696e-16,
            0.20025269874397023
          ],
          [
            -1.3877787807814457e-15,
            -3.3306690738754696e-16,
            0.10029743786369616
          ],
          [
            -1.6653345369377348e-15,
            -1.6653345369377348e-16,
            -2.7200464103316335e-15
          ],
          [
            -3.219646771412954e-15,
            7.771561172376096e-16,
            -0.10029743786370543
          ],
          [
            -3.9968028886505635e-15,
            2.220446049250313e-16,
            -0.200252698743983
          ],
          [
            -2.0539125955565396e-15,
            -7.216449660063518e-16,
            -0.29953521511495446
          ],
          [
            -1.4988010832439613e-15,
            -2.1094237467877974e-15,
            -0.3978060645010231
          ],
          [
            -1.8318679906315083e-15,
            -2.9976021664879227e-15,
            -0.49469185413301725
          ],
          [
            -7.771561172376096e-16,
            -3.164135620181696e-15,
            0.4102230132495943
          ],
          [
            -1.2212453270876722e-15,
            -2.1094237467877974e-15,
            0.3173667019731785
          ],
          [
            4.440892098500626e-16,
            -3.941291737419306e-15,
            0.2271147776074769
          ]
        ]
      },
      "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": 2.181853451486512e-15,
        "parent_symmetrization_rmsd_A": 0.12843549030090334,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -271.0549331414626,
        "reduced_polarization": [
          -7.229638405116645e-16,
          -2.046849524939955e-15,
          2.1957866774646308e-16
        ],
        "cartesian_polarization_e_A2": [
          -1.2217950923835745e-17,
          -2.406388255388435e-17,
          2.4630943476349035e-18
        ],
        "ranking_score": 0.1284354903009077
      }
    }
  ],
  "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": 49,
      "full_response": 17,
      "energy_polarization": 32
    },
    "model_evaluations_for_recovery_and_path_properties": {
      "total": 74,
      "full_response": 42,
      "energy_polarization": 32
    },
    "elapsed_seconds": 946.7417144929641
  }
}