{
  "schema": "ferrofinder.endpoint_parent_recovery.v4_variable_cell",
  "status": "complete",
  "input_atom_count": 4,
  "input_formula": "Al2N2",
  "input_spacegroup": "P6_3mc",
  "input_pointgroup": "6mm",
  "input_is_polar_point_group": true,
  "input_energy_eV": -29.480228614867915,
  "input_cartesian_polarization_e_A2": [
    3.175177563812562e-19,
    -7.386042484330268e-17,
    -0.036477392171465624
  ],
  "input_reduced_polarization": [
    -5.749581211039838e-16,
    -1.158542627684507e-15,
    -0.3090087043664729
  ],
  "input_formal_targets": [
    {
      "orbit_id": 0,
      "representative_formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        -0.5
      ]
    },
    {
      "orbit_id": 1,
      "representative_formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ]
    },
    {
      "orbit_id": 2,
      "representative_formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        -0.5,
        -0.5
      ]
    },
    {
      "orbit_id": 3,
      "representative_formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        -0.5,
        0.0
      ]
    }
  ],
  "parent_candidates": [
    {
      "candidate_id": "inversion_parent_endpoint_00",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "P6_3/mmc",
      "spacegroup_number": 194,
      "pointgroup": "6/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": 2.5593199456415832e-17,
      "parent_symmetrization_rmsd_A": 0.4204863365913037,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -28.592995172375616,
      "reduced_polarization": [
        6.980509571939833e-18,
        1.646508671000056e-17,
        1.830806554948127e-17
      ],
      "cartesian_polarization_e_A2": [
        -9.216906867704053e-20,
        1.0496966364656116e-18,
        2.1612028318700866e-18
      ],
      "ranking_score": 0.42048633659130374
    },
    {
      "candidate_id": "bec_projection_00",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P6_3mc",
      "spacegroup_number": 186,
      "pointgroup": "6mm",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        -0.5
      ],
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_residual": 0.13430263716147683,
      "parent_symmetrization_rmsd_A": 0.02919495721038319,
      "parent_cell_rmsd_A": 0.1398102204665007,
      "energy_eV": -30.00806140220742,
      "reduced_polarization": [
        -4.222592424752394e-14,
        -6.290818806203628e-14,
        -0.36569736283852317
      ],
      "cartesian_polarization_e_A2": [
        -2.1289111855750274e-15,
        -3.3494222113932967e-15,
        -0.04576465642593323
      ],
      "ranking_score": 0.832752786649962
    },
    {
      "candidate_id": "inversion_parent_bec_00_00",
      "source": "same_species_inversion_center_projection_after_BEC",
      "spacegroup": "P6_3/mmc",
      "spacegroup_number": 194,
      "pointgroup": "6/mmm",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        -0.5
      ],
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_residual": 0.4999999999999998,
      "parent_symmetrization_rmsd_A": 0.4204863365936624,
      "parent_cell_rmsd_A": 0.1398102204665007,
      "energy_eV": -28.120758355948226,
      "reduced_polarization": [
        5.319094558113198e-17,
        -4.1083841554330347e-16,
        -2.1504569682839353e-16
      ],
      "cartesian_polarization_e_A2": [
        2.0154580447867945e-17,
        -2.7728723452152134e-17,
        -2.6911576159142313e-17
      ],
      "ranking_score": 1.4554388917102872
    },
    {
      "candidate_id": "bec_projection_01",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P6_3mc",
      "spacegroup_number": 186,
      "pointgroup": "6mm",
      "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": 5.6072805732491545e-05,
      "parent_symmetrization_rmsd_A": 0.11570272667774889,
      "parent_cell_rmsd_A": 0.05793297599749956,
      "energy_eV": -28.916683079558318,
      "reduced_polarization": [
        -9.741032372232339e-15,
        -2.2269784592381667e-15,
        5.6072805732491545e-05
      ],
      "cartesian_polarization_e_A2": [
        -6.22218218037308e-16,
        -1.3901172113059264e-16,
        6.506900072467731e-06
      ],
      "ranking_score": 0.6302981162885888
    },
    {
      "candidate_id": "bec_projection_02",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cc",
      "spacegroup_number": 9,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        -0.5,
        -0.5
      ],
      "formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_residual": 0.22219936747664434,
      "parent_symmetrization_rmsd_A": 0.11032575996991364,
      "parent_cell_rmsd_A": 0.2827639423211678,
      "energy_eV": -29.03690769276662,
      "reduced_polarization": [
        0.0005521790937703161,
        -0.36571170914769624,
        -0.3229720108422504
      ],
      "cartesian_polarization_e_A2": [
        0.014714063681410625,
        -0.0253742889143253,
        -0.04083757117768829
      ],
      "ranking_score": 1.1254154805034942
    },
    {
      "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": [
        0.0,
        -0.5,
        0.0
      ],
      "formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_residual": 0.00012739579857041827,
      "parent_symmetrization_rmsd_A": 0.25333515036346443,
      "parent_cell_rmsd_A": 0.06241199550436117,
      "energy_eV": -27.70539851057016,
      "reduced_polarization": [
        4.3310626489228834e-10,
        -0.5000129582165114,
        -0.00012673505481141127
      ],
      "cartesian_polarization_e_A2": [
        0.018076355320826562,
        -0.03130916561192053,
        0.00028610709411412086
      ],
      "ranking_score": 0.7691929408366955
    }
  ],
  "formal_branches": [
    {
      "orbit_id": 0,
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.0,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        -0.5
      ],
      "bec_backprojection": {
        "converged_to_target": false,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -5.749581211039838e-16,
              -1.158542627684507e-15,
              -0.3090087043664729
            ],
            "branch_aligned_reduced_polarization": [
              -5.749581211039838e-16,
              -1.158542627684507e-15,
              -0.3090087043664729
            ],
            "target_residual": 0.19099129563352713,
            "energy_eV": -29.480228614867915,
            "max_atomic_step_A": 0.06944006473466137,
            "max_log_strain_component": 0.008929745184223094,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.075186094965824,
            "cell_principal_stretches": [
              0.993700921023405,
              0.9937009173429094,
              0.9911100065779371
            ],
            "cell_volume_ratio": 0.9786631681965571,
            "cell_rmsd_from_input_A": 0.04193917658975038
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              4.246276487956471e-14,
              2.065292544019146e-14,
              -0.322643234124204
            ],
            "branch_aligned_reduced_polarization": [
              4.246276487956471e-14,
              2.065292544019146e-14,
              -0.322643234124204
            ],
            "target_residual": 0.17735676587579602,
            "energy_eV": -29.19424143710976,
            "max_atomic_step_A": 0.054438647898132186,
            "max_log_strain_component": 0.005529018555681517,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.075186094965824,
            "cell_principal_stretches": [
              0.9898206340955973,
              0.9898206281595254,
              0.9856452622187784
            ],
            "cell_volume_ratio": 0.9656809009349485,
            "cell_rmsd_from_input_A": 0.06755100019140885
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              2.0756947842619806e-14,
              1.2581693181571504e-14,
              -0.3784848277871907
            ],
            "branch_aligned_reduced_polarization": [
              2.0756947842619806e-14,
              1.2581693181571504e-14,
              -0.3784848277871907
            ],
            "target_residual": 0.12151517221280927,
            "energy_eV": -29.612559379217004,
            "max_atomic_step_A": 0.05817206790729458,
            "max_log_strain_component": 0.018606723575056352,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.075186094965824,
            "cell_principal_stretches": [
              0.9768733154622218,
              0.9768733020646938,
              0.9674752001612852
            ],
            "cell_volume_ratio": 0.9232436478534657,
            "cell_rmsd_from_input_A": 0.15178682871830004
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              5.676427427522302e-14,
              4.800262261897597e-14,
              -0.21160481838252548
            ],
            "branch_aligned_reduced_polarization": [
              5.676427427522302e-14,
              4.800262261897597e-14,
              -0.21160481838252548
            ],
            "target_residual": 0.2883951816174745,
            "energy_eV": -29.292777829953433,
            "max_atomic_step_A": 0.04688646595535666,
            "max_log_strain_component": 0.0023013062088525064,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.075186094965824,
            "cell_principal_stretches": [
              0.975283786296301,
              0.9752837719896429,
              0.9652513033914468
            ],
            "cell_volume_ratio": 0.9181262384846391,
            "cell_rmsd_from_input_A": 0.16199931398267242
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              4.8416686478757915e-15,
              1.2954956089798337e-14,
              -0.3966318295773566
            ],
            "branch_aligned_reduced_polarization": [
              4.8416686478757915e-15,
              1.2954956089798337e-14,
              -0.3966318295773566
            ],
            "target_residual": 0.1033681704226434,
            "energy_eV": -29.720006184753622,
            "max_atomic_step_A": 0.04573850580800297,
            "max_log_strain_component": 0.007548358458234453,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": true,
            "strain_jacobian_frobenius_norm": 2.3222279584713954,
            "cell_principal_stretches": [
              0.9725649344600591,
              0.9712305862333562,
              0.971230563336132
            ],
            "cell_volume_ratio": 0.9174096385391108,
            "cell_rmsd_from_input_A": 0.1398102204665007
          },
          {
            "iteration": 5,
            "reduced_polarization": [
              -4.222592424752394e-14,
              -6.290818806203628e-14,
              -0.36569736283852317
            ],
            "branch_aligned_reduced_polarization": [
              -4.222592424752394e-14,
              -6.290818806203628e-14,
              -0.36569736283852317
            ],
            "target_residual": 0.13430263716147683,
            "energy_eV": -30.00806140220742
          }
        ],
        "iterations": 5
      },
      "parent": {
        "candidate_id": "bec_projection_00",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P6_3mc",
        "spacegroup_number": 186,
        "pointgroup": "6mm",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          -0.5
        ],
        "formal_class": [
          0.0,
          0.0,
          0.5
        ],
        "target_residual": 0.13430263716147683,
        "parent_symmetrization_rmsd_A": 0.02919495721038319,
        "parent_cell_rmsd_A": 0.1398102204665007,
        "energy_eV": -30.00806140220742,
        "reduced_polarization": [
          -4.222592424752394e-14,
          -6.290818806203628e-14,
          -0.36569736283852317
        ],
        "cartesian_polarization_e_A2": [
          -2.1289111855750274e-15,
          -3.3494222113932967e-15,
          -0.04576465642593323
        ],
        "ranking_score": 0.832752786649962
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 1,
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.0,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -5.749581211039838e-16,
              -1.158542627684507e-15,
              -0.3090087043664729
            ],
            "branch_aligned_reduced_polarization": [
              -5.749581211039838e-16,
              -1.158542627684507e-15,
              -0.3090087043664729
            ],
            "target_residual": 0.3090087043664729,
            "energy_eV": -29.480228614867915,
            "max_atomic_step_A": 0.1123484940169964,
            "max_log_strain_component": 0.014447616476691107,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.075186094965824,
            "cell_principal_stretches": [
              1.0145524877255025,
              1.0102760877899795,
              1.0102760817359044
            ],
            "cell_volume_ratio": 1.035510877076606,
            "cell_rmsd_from_input_A": 0.06938513146026089
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -3.7564836719136084e-14,
              -5.891718115494293e-15,
              0.11210982862800586
            ],
            "branch_aligned_reduced_polarization": [
              -3.7564836719136084e-14,
              -5.891718115494293e-15,
              0.11210982862800586
            ],
            "target_residual": 0.11210982862800586,
            "energy_eV": -28.45346448020185,
            "max_atomic_step_A": 0.02848541810259286,
            "max_log_strain_component": 0.0022931201162712626,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.075186094965824,
            "cell_principal_stretches": [
              1.0122286624304515,
              1.0086380487987363,
              1.0086380437138198
            ],
            "cell_volume_ratio": 1.0297915467415437,
            "cell_rmsd_from_input_A": 0.058244278522912446
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              1.7428758388255335e-14,
              -4.328514042326122e-15,
              0.0030910006520495003
            ],
            "branch_aligned_reduced_polarization": [
              1.7428758388255335e-14,
              -4.328514042326122e-15,
              0.0030910006520495003
            ],
            "target_residual": 0.0030910006520495003,
            "energy_eV": -28.906424543683396,
            "max_atomic_step_A": 0.000791031024492133,
            "max_log_strain_component": 6.421966133173493e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.075186094965824,
            "cell_principal_stretches": [
              1.012163659535814,
              1.0085922131731668,
              1.0085922081153469
            ],
            "cell_volume_ratio": 1.0296318303533043,
            "cell_rmsd_from_input_A": 0.05793297599749956
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -9.741032372232339e-15,
              -2.2269784592381667e-15,
              5.6072805732491545e-05
            ],
            "branch_aligned_reduced_polarization": [
              -9.741032372232339e-15,
              -2.2269784592381667e-15,
              5.6072805732491545e-05
            ],
            "target_residual": 5.6072805732491545e-05,
            "energy_eV": -28.916683079558318
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "inversion_parent_endpoint_00",
        "source": "same_species_inversion_center_projection_from_endpoint",
        "spacegroup": "P6_3/mmc",
        "spacegroup_number": 194,
        "pointgroup": "6/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": 2.5593199456415832e-17,
        "parent_symmetrization_rmsd_A": 0.4204863365913037,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -28.592995172375616,
        "reduced_polarization": [
          6.980509571939833e-18,
          1.646508671000056e-17,
          1.830806554948127e-17
        ],
        "cartesian_polarization_e_A2": [
          -9.216906867704053e-20,
          1.0496966364656116e-18,
          2.1612028318700866e-18
        ],
        "ranking_score": 0.42048633659130374
      },
      "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": [
          -29.480228614867915,
          -29.328955289356472,
          -29.08168765474605,
          -28.84384870054543,
          -28.685240434354046,
          -28.616326128437098,
          -28.59917042371732,
          -28.594704991826553,
          -28.592995172375616
        ],
        "cartesian_polarizations_e_A2": [
          [
            3.175177563812562e-19,
            -7.386042484330268e-17,
            -0.036477392171465624
          ],
          [
            -5.556750138824792e-18,
            1.9490956867039383e-17,
            -0.04254286945428433
          ],
          [
            6.672020791152878e-17,
            -7.326634505395134e-17,
            -0.03848567158408761
          ],
          [
            -1.6506337806020496e-17,
            -1.946798936387781e-17,
            -0.023583008807430632
          ],
          [
            -9.989412456681563e-17,
            2.322780153073721e-17,
            -0.0019551637432881795
          ],
          [
            -7.027218610555154e-18,
            1.0071400661218449e-16,
            0.017613926291464615
          ],
          [
            -2.3730773900320683e-17,
            -1.2276419527357011e-17,
            0.02524827024062758
          ],
          [
            1.199752984161425e-18,
            7.941584418279064e-17,
            0.01762387120482821
          ],
          [
            -1.0669920435772995e-18,
            -7.051631551198682e-18,
            2.9481487941813578e-18
          ]
        ],
        "raw_reduced_polarization": [
          [
            -5.749581211039838e-16,
            -1.158542627684507e-15,
            -0.3090087043664729
          ],
          [
            7.73799071801246e-17,
            3.057267059149978e-16,
            -0.36039081161026426
          ],
          [
            3.3172185613073597e-16,
            -1.1492241494646818e-15,
            -0.32602131909460647
          ],
          [
            -3.7690695595703476e-16,
            -3.0536644760994997e-16,
            -0.19977730212709058
          ],
          [
            -1.1748010932604498e-15,
            3.6434123250503633e-16,
            -0.016562659202660562
          ],
          [
            6.944197036137794e-16,
            1.5797562783135705e-15,
            0.14921177798421945
          ],
          [
            -4.186424888563764e-16,
            -1.925625985492993e-16,
            0.21388412959668626
          ],
          [
            6.391388281106088e-16,
            1.2456825288306797e-15,
            0.14929602372138936
          ],
          [
            -6.979854476191767e-17,
            -1.1060883773848859e-16,
            2.4974472815581144e-17
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -5.749581211039838e-16,
            -1.158542627684507e-15,
            -0.3090087043664729
          ],
          [
            7.73799071801246e-17,
            3.0572670591499773e-16,
            -0.36039081161026426
          ],
          [
            3.3172185613073597e-16,
            -1.1492241494646818e-15,
            -0.32602131909460647
          ],
          [
            -3.7690695595703476e-16,
            -3.0536644760994997e-16,
            -0.19977730212709058
          ],
          [
            -1.1748010932604498e-15,
            3.643412325050364e-16,
            -0.016562659202660562
          ],
          [
            6.944197036137795e-16,
            1.5797562783135705e-15,
            0.14921177798421945
          ],
          [
            -4.186424888563763e-16,
            -1.9256259854929923e-16,
            0.21388412959668626
          ],
          [
            6.391388281106087e-16,
            1.2456825288306797e-15,
            0.14929602372138936
          ],
          [
            -6.979854476191767e-17,
            -1.1060883773848867e-16,
            2.7755575615628914e-17
          ]
        ],
        "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": [
          [
            -5.551115123125783e-16,
            -1.1657341758564144e-15,
            -0.3090087043664729
          ],
          [
            1.1102230246251565e-16,
            3.3306690738754696e-16,
            -0.36039081161026426
          ],
          [
            3.3306690738754696e-16,
            -1.1657341758564144e-15,
            -0.32602131909460647
          ],
          [
            -3.885780586188048e-16,
            -3.3306690738754696e-16,
            -0.19977730212709055
          ],
          [
            -1.1657341758564144e-15,
            3.3306690738754696e-16,
            -0.016562659202660535
          ],
          [
            6.661338147750939e-16,
            1.5543122344752192e-15,
            0.14921177798421947
          ],
          [
            -4.440892098500626e-16,
            -1.6653345369377348e-16,
            0.21388412959668623
          ],
          [
            6.661338147750939e-16,
            1.2212453270876722e-15,
            0.1492960237213894
          ],
          [
            -5.551115123125783e-17,
            -1.1102230246251565e-16,
            0.0
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -28.592995172375616,
          -28.594704991826543,
          -28.599170423717332,
          -28.61632612843711,
          -28.685240434354046,
          -28.843848700545422,
          -29.081687654746062,
          -29.328955289356472,
          -29.4802286148679
        ],
        "cartesian_polarizations_e_A2": [
          [
            -1.0669920435772995e-18,
            -7.051631551198682e-18,
            2.9481487941813578e-18
          ],
          [
            -6.0757419431220836e-18,
            -8.191344052919938e-18,
            -0.017623871204827724
          ],
          [
            -1.7734560924309286e-17,
            -5.326311517477217e-17,
            -0.025248270240628357
          ],
          [
            -5.65808029057713e-18,
            -7.0756407662007e-17,
            -0.017613926291464656
          ],
          [
            -1.5191627683638908e-17,
            -8.315369566845866e-17,
            0.0019551637432889332
          ],
          [
            -2.782465159059615e-17,
            -1.527576410733001e-16,
            0.023583008807430424
          ],
          [
            6.868991055245824e-17,
            -1.9830358546897464e-16,
            0.038485671584088166
          ],
          [
            -5.221069712842674e-18,
            -1.272294806169679e-16,
            0.04254286945428418
          ],
          [
            -4.7916451897549005e-18,
            -4.811399335866068e-17,
            0.03647739217146544
          ]
        ],
        "raw_reduced_polarization": [
          [
            -6.979854476191767e-17,
            -1.1060883773848859e-16,
            2.4974472815581144e-17
          ],
          [
            -1.4677641915072674e-16,
            -1.284858743159292e-16,
            -0.14929602372138523
          ],
          [
            -6.586391124761558e-16,
            -8.354621509984241e-16,
            -0.21388412959669284
          ],
          [
            -6.317871040437757e-16,
            -1.1098543588419507e-15,
            -0.14921177798421978
          ],
          [
            -8.585210032707586e-16,
            -1.3043128479939862e-15,
            0.01656265920266695
          ],
          [
            -1.576017922285693e-15,
            -2.3960901831178037e-15,
            0.19977730212708886
          ],
          [
            -6.221615010139654e-16,
            -3.1105041363611535e-15,
            0.3260213190946112
          ],
          [
            -1.068756788043145e-15,
            -1.9956665170235976e-15,
            0.36039081161026293
          ],
          [
            -4.4243781255737957e-16,
            -7.546952567954543e-16,
            0.3090087043664713
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -6.979854476191767e-17,
            -1.1060883773848859e-16,
            2.4974472815581144e-17
          ],
          [
            -1.4677641915072674e-16,
            -1.284858743159292e-16,
            -0.14929602372138523
          ],
          [
            -6.586391124761558e-16,
            -8.354621509984241e-16,
            -0.21388412959669284
          ],
          [
            -6.317871040437757e-16,
            -1.1098543588419507e-15,
            -0.14921177798421978
          ],
          [
            -8.585210032707586e-16,
            -1.3043128479939862e-15,
            0.016562659202666946
          ],
          [
            -1.576017922285693e-15,
            -2.3960901831178037e-15,
            0.19977730212708886
          ],
          [
            -6.221615010139653e-16,
            -3.1105041363611535e-15,
            0.3260213190946112
          ],
          [
            -1.068756788043145e-15,
            -1.9956665170235976e-15,
            0.36039081161026293
          ],
          [
            -4.424378125573795e-16,
            -7.546952567954544e-16,
            0.3090087043664713
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          4.353610315801485e-16,
          9.3732495220753e-16,
          0.30900870436647293
        ],
        "actual_opposite_endpoint_branch_residual": 2.494993894102979e-15
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            -5.749581211039838e-16,
            -1.158542627684507e-15,
            -0.3090087043664729
          ],
          [
            7.73799071801246e-17,
            3.057267059149978e-16,
            -0.36039081161026426
          ],
          [
            3.3172185613073597e-16,
            -1.1492241494646818e-15,
            -0.32602131909460647
          ],
          [
            -3.7690695595703476e-16,
            -3.0536644760994997e-16,
            -0.19977730212709058
          ],
          [
            -1.1748010932604498e-15,
            3.6434123250503633e-16,
            -0.016562659202660562
          ],
          [
            6.944197036137794e-16,
            1.5797562783135705e-15,
            0.14921177798421945
          ],
          [
            -4.186424888563764e-16,
            -1.925625985492993e-16,
            0.21388412959668626
          ],
          [
            6.391388281106088e-16,
            1.2456825288306797e-15,
            0.14929602372138936
          ],
          [
            -6.979854476191767e-17,
            -1.1060883773848859e-16,
            2.4974472815581144e-17
          ],
          [
            -1.4677641915072674e-16,
            -1.284858743159292e-16,
            -0.14929602372138523
          ],
          [
            -6.586391124761558e-16,
            -8.354621509984241e-16,
            -0.21388412959669284
          ],
          [
            -6.317871040437757e-16,
            -1.1098543588419507e-15,
            -0.14921177798421978
          ],
          [
            -8.585210032707586e-16,
            -1.3043128479939862e-15,
            0.01656265920266695
          ],
          [
            -1.576017922285693e-15,
            -2.3960901831178037e-15,
            0.19977730212708886
          ],
          [
            -6.221615010139654e-16,
            -3.1105041363611535e-15,
            0.3260213190946112
          ],
          [
            -1.068756788043145e-15,
            -1.9956665170235976e-15,
            0.36039081161026293
          ],
          [
            -4.4243781255737957e-16,
            -7.546952567954543e-16,
            0.3090087043664713
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -5.749581211039838e-16,
            -1.158542627684507e-15,
            -0.3090087043664729
          ],
          [
            7.73799071801246e-17,
            3.0572670591499773e-16,
            -0.36039081161026426
          ],
          [
            3.3172185613073597e-16,
            -1.1492241494646818e-15,
            -0.32602131909460647
          ],
          [
            -3.7690695595703476e-16,
            -3.0536644760994997e-16,
            -0.19977730212709058
          ],
          [
            -1.1748010932604498e-15,
            3.643412325050364e-16,
            -0.016562659202660562
          ],
          [
            6.944197036137795e-16,
            1.5797562783135705e-15,
            0.14921177798421945
          ],
          [
            -4.186424888563763e-16,
            -1.9256259854929923e-16,
            0.21388412959668626
          ],
          [
            6.391388281106087e-16,
            1.2456825288306797e-15,
            0.14929602372138936
          ],
          [
            -6.979854476191767e-17,
            -1.1060883773848867e-16,
            2.7755575615628914e-17
          ],
          [
            -1.4677641915072674e-16,
            -1.284858743159292e-16,
            -0.14929602372138523
          ],
          [
            -6.586391124761558e-16,
            -8.354621509984241e-16,
            -0.21388412959669284
          ],
          [
            -6.317871040437757e-16,
            -1.1098543588419507e-15,
            -0.14921177798421978
          ],
          [
            -8.585210032707586e-16,
            -1.3043128479939862e-15,
            0.016562659202666946
          ],
          [
            -1.576017922285693e-15,
            -2.3960901831178037e-15,
            0.19977730212708886
          ],
          [
            -6.221615010139653e-16,
            -3.1105041363611535e-15,
            0.3260213190946112
          ],
          [
            -1.068756788043145e-15,
            -1.9956665170235976e-15,
            0.36039081161026293
          ],
          [
            -4.424378125573795e-16,
            -7.546952567954544e-16,
            0.3090087043664713
          ]
        ],
        "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": [
          [
            -5.551115123125783e-16,
            -1.1657341758564144e-15,
            -0.3090087043664729
          ],
          [
            1.1102230246251565e-16,
            3.3306690738754696e-16,
            -0.36039081161026426
          ],
          [
            3.3306690738754696e-16,
            -1.1657341758564144e-15,
            -0.32602131909460647
          ],
          [
            -3.885780586188048e-16,
            -3.3306690738754696e-16,
            -0.19977730212709055
          ],
          [
            -1.1657341758564144e-15,
            3.3306690738754696e-16,
            -0.016562659202660535
          ],
          [
            6.661338147750939e-16,
            1.5543122344752192e-15,
            0.14921177798421947
          ],
          [
            -4.440892098500626e-16,
            -1.6653345369377348e-16,
            0.21388412959668623
          ],
          [
            6.661338147750939e-16,
            1.2212453270876722e-15,
            0.1492960237213894
          ],
          [
            -5.551115123125783e-17,
            -1.1102230246251565e-16,
            0.0
          ],
          [
            -1.6653345369377348e-16,
            -1.1102230246251565e-16,
            -0.14929602372138523
          ],
          [
            -6.661338147750939e-16,
            -8.326672684688674e-16,
            -0.21388412959669284
          ],
          [
            -6.106226635438361e-16,
            -1.1102230246251565e-15,
            -0.1492117779842198
          ],
          [
            -8.326672684688674e-16,
            -1.27675647831893e-15,
            0.016562659202666974
          ],
          [
            -1.5543122344752192e-15,
            -2.3869795029440866e-15,
            0.19977730212708888
          ],
          [
            -6.106226635438361e-16,
            -3.1086244689504383e-15,
            0.3260213190946112
          ],
          [
            -1.0547118733938987e-15,
            -1.9984014443252818e-15,
            0.360390811610263
          ],
          [
            -4.440892098500626e-16,
            -7.771561172376096e-16,
            0.3090087043664713
          ]
        ]
      },
      "incoming_structure_ids": [
        "incoming_01_000",
        "incoming_01_001",
        "incoming_01_002",
        "incoming_01_003",
        "incoming_01_004",
        "incoming_01_005",
        "incoming_01_006",
        "incoming_01_007",
        "incoming_01_008"
      ],
      "reflected_structure_ids": [
        "reflected_01_001",
        "reflected_01_002",
        "reflected_01_003",
        "reflected_01_004",
        "reflected_01_005",
        "reflected_01_006",
        "reflected_01_007",
        "reflected_01_008"
      ]
    },
    {
      "orbit_id": 2,
      "formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.5,
          0.5
        ],
        [
          0.5,
          0.0,
          0.5
        ],
        [
          0.5,
          0.5,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        -0.5,
        -0.5
      ],
      "bec_backprojection": {
        "converged_to_target": false,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -5.749581211039838e-16,
              -1.158542627684507e-15,
              -0.3090087043664729
            ],
            "branch_aligned_reduced_polarization": [
              -5.749581211039838e-16,
              -1.1657341758564144e-15,
              -0.3090087043664729
            ],
            "target_residual": 0.5352360927738078,
            "energy_eV": -29.480228614867915,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.006607810746584234,
            "step_scale": 0.7399775257042296,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.075186094965824,
            "cell_principal_stretches": [
              0.9996779088546914,
              0.9953349945236121,
              0.9890982706535693
            ],
            "cell_volume_ratio": 0.9841670281859543,
            "cell_rmsd_from_input_A": 0.038081129093078175
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -2.423590934593954e-07,
              -0.40123508927403034,
              -0.32938411341435714
            ],
            "branch_aligned_reduced_polarization": [
              -2.423590934593954e-07,
              -0.40123508927403034,
              -0.32938411341435714
            ],
            "target_residual": 0.19714027580931412,
            "energy_eV": -28.295394836721346,
            "max_atomic_step_A": 0.029779984346797763,
            "max_log_strain_component": 0.02,
            "step_scale": 0.455319204613756,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.075186094965824,
            "cell_principal_stretches": [
              0.985768994299551,
              0.9813475234327753,
              0.9693755259251594
            ],
            "cell_volume_ratio": 0.9377563974404434,
            "cell_rmsd_from_input_A": 0.1263521439623905
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -6.760116395568899e-08,
              -0.4802267141227788,
              -0.3275195306199578
            ],
            "branch_aligned_reduced_polarization": [
              -6.760116395568899e-08,
              -0.4802267141227788,
              -0.3275195306199578
            ],
            "target_residual": 0.1736101815906733,
            "energy_eV": -28.129694602241717,
            "max_atomic_step_A": 0.005669010944131136,
            "max_log_strain_component": 0.02,
            "step_scale": 0.41942036820696854,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.075186094965824,
            "cell_principal_stretches": [
              0.972639009333388,
              0.9675566186724496,
              0.9494742440561802
            ],
            "cell_volume_ratio": 0.8935343653621379,
            "cell_rmsd_from_input_A": 0.21445062669142356
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              7.543697642435716e-08,
              -0.5370071425162584,
              -0.30450075528094855
            ],
            "branch_aligned_reduced_polarization": [
              7.543697642435716e-08,
              -0.5370071425162584,
              -0.30450075528094855
            ],
            "target_residual": 0.19897106142086068,
            "energy_eV": -27.900453549498348,
            "max_atomic_step_A": 0.08760395385562093,
            "max_log_strain_component": 0.01961933999833981,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.075186094965824,
            "cell_principal_stretches": [
              0.9600153012061808,
              0.9542165191276452,
              0.9302650137673754
            ],
            "cell_volume_ratio": 0.8521808560578205,
            "cell_rmsd_from_input_A": 0.2978712553482054
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              1.0452146341210816e-06,
              -0.5703700593268002,
              -0.15653304559684628
            ],
            "branch_aligned_reduced_polarization": [
              1.0452146341210816e-06,
              -0.5703700593268002,
              -0.15653304559684628
            ],
            "target_residual": 0.35060161724916206,
            "energy_eV": -27.923602510906704,
            "max_atomic_step_A": 0.0911985999720099,
            "max_log_strain_component": 0.00798108230111632,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": true,
            "strain_jacobian_frobenius_norm": 5.784947901035365,
            "cell_principal_stretches": [
              0.9696861399857953,
              0.9590447320628667,
              0.9321896884355712
            ],
            "cell_volume_ratio": 0.8669106671815289,
            "cell_rmsd_from_input_A": 0.2827639423211678
          },
          {
            "iteration": 5,
            "reduced_polarization": [
              0.0005521790937703161,
              -0.36571170914769624,
              -0.3229720108422504
            ],
            "branch_aligned_reduced_polarization": [
              0.0005521790937703161,
              -0.36571170914769624,
              -0.3229720108422504
            ],
            "target_residual": 0.22219936747664434,
            "energy_eV": -29.03690769276662
          }
        ],
        "iterations": 5
      },
      "parent": {
        "candidate_id": "bec_projection_02",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cc",
        "spacegroup_number": 9,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          -0.5,
          -0.5
        ],
        "formal_class": [
          0.0,
          0.5,
          0.5
        ],
        "target_residual": 0.22219936747664434,
        "parent_symmetrization_rmsd_A": 0.11032575996991364,
        "parent_cell_rmsd_A": 0.2827639423211678,
        "energy_eV": -29.03690769276662,
        "reduced_polarization": [
          0.0005521790937703161,
          -0.36571170914769624,
          -0.3229720108422504
        ],
        "cartesian_polarization_e_A2": [
          0.014714063681410625,
          -0.0253742889143253,
          -0.04083757117768829
        ],
        "ranking_score": 1.1254154805034942
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 3,
      "formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.5,
          0.0
        ],
        [
          0.5,
          0.0,
          0.0
        ],
        [
          0.5,
          0.5,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        -0.5,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -5.749581211039838e-16,
              -1.158542627684507e-15,
              -0.3090087043664729
            ],
            "branch_aligned_reduced_polarization": [
              -5.749581211039838e-16,
              -1.1657341758564144e-15,
              -0.3090087043664729
            ],
            "target_residual": 0.5877808940193999,
            "energy_eV": -29.480228614867915,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.009388796727898881,
            "step_scale": 0.6498509109125743,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.075186094965824,
            "cell_principal_stretches": [
              1.0128935019095053,
              1.0066659638994997,
              1.0032267482527422
            ],
            "cell_volume_ratio": 1.022935552483465,
            "cell_rmsd_from_input_A": 0.049217400924231144
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -1.4927412422564951e-07,
              -0.2879151999617471,
              -0.03178421465906772
            ],
            "branch_aligned_reduced_polarization": [
              -1.4927412422564951e-07,
              -0.2879151999617471,
              -0.03178421465906772
            ],
            "target_residual": 0.21445325530003434,
            "energy_eV": -28.639255361987754,
            "max_atomic_step_A": 0.07120586130692771,
            "max_log_strain_component": 0.0032979080384702274,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.075186094965824,
            "cell_principal_stretches": [
              1.0176674779252342,
              1.007463388862714,
              1.0004303247985318
            ],
            "cell_volume_ratio": 1.025703922021955,
            "cell_rmsd_from_input_A": 0.062482359146847015
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              2.24648133213568e-07,
              -0.506281437430977,
              -0.0023012080982102454
            ],
            "branch_aligned_reduced_polarization": [
              2.24648133213568e-07,
              -0.506281437430977,
              -0.0023012080982102454
            ],
            "target_residual": 0.006689694683691764,
            "energy_eV": -27.676296736111752,
            "max_atomic_step_A": 0.0019405651967935246,
            "max_log_strain_component": 7.713367818204243e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 3.075186094965824,
            "cell_principal_stretches": [
              1.0176150070565204,
              1.0074925721317598,
              1.0005518468092434
            ],
            "cell_volume_ratio": 1.0258053360796449,
            "cell_rmsd_from_input_A": 0.06241199550436117
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              4.3310626489228834e-10,
              -0.5000129582165114,
              -0.00012673505481141127
            ],
            "branch_aligned_reduced_polarization": [
              4.3310626489228834e-10,
              -0.5000129582165114,
              -0.00012673505481141127
            ],
            "target_residual": 0.00012739579857041827,
            "energy_eV": -27.70539851057016
          }
        ],
        "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": [
          0.0,
          -0.5,
          0.0
        ],
        "formal_class": [
          0.0,
          0.5,
          0.0
        ],
        "target_residual": 0.00012739579857041827,
        "parent_symmetrization_rmsd_A": 0.25333515036346443,
        "parent_cell_rmsd_A": 0.06241199550436117,
        "energy_eV": -27.70539851057016,
        "reduced_polarization": [
          4.3310626489228834e-10,
          -0.5000129582165114,
          -0.00012673505481141127
        ],
        "cartesian_polarization_e_A2": [
          0.018076355320826562,
          -0.03130916561192053,
          0.00028610709411412086
        ],
        "ranking_score": 0.7691929408366955
      },
      "branch_status": "awaiting_branch_sampling"
    }
  ],
  "sampled_polarization_branches": [
    {
      "orbit_id": 1,
      "candidate_id": "inversion_parent_endpoint_00",
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "construction": "MACEField-BEC-parent plus variable-cell P-N-P path and symmetric log-strain continuation beyond both polar endpoints",
      "geometry_diagnostics": {
        "collision_aware": false,
        "permutations_tested": 1,
        "selected_order": [
          0,
          1,
          2,
          3
        ],
        "endpoint_rmsd_A": 0.4204863365913037,
        "minimum_distance_A_by_image": [
          1.901102941084718,
          1.8791788862952488,
          1.8599690127119017,
          1.8435581675805268,
          1.8300216538912872,
          1.8194236278620992,
          1.811815655354736,
          1.8072354987128514,
          1.805706198162097
        ],
        "minimum_distance_A": 1.805706198162097,
        "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": [
          42.48533018031972,
          42.48533018031972,
          42.48533018031972,
          42.48533018031972,
          42.48533018031972,
          42.48533018031972,
          42.48533018031972,
          42.48533018031972,
          42.48533018031972
        ],
        "cell_deformation_log_strain_norm": 0.0
      },
      "parent_reduced_polarization": [
        -6.979854476191767e-17,
        -1.1060883773848859e-16,
        2.4974472815581144e-17
      ],
      "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": [
          -29.480228614867915,
          -29.328955289356472,
          -29.08168765474605,
          -28.84384870054543,
          -28.685240434354046,
          -28.616326128437098,
          -28.59917042371732,
          -28.594704991826553,
          -28.592995172375616
        ],
        "cartesian_polarizations_e_A2": [
          [
            3.175177563812562e-19,
            -7.386042484330268e-17,
            -0.036477392171465624
          ],
          [
            -5.556750138824792e-18,
            1.9490956867039383e-17,
            -0.04254286945428433
          ],
          [
            6.672020791152878e-17,
            -7.326634505395134e-17,
            -0.03848567158408761
          ],
          [
            -1.6506337806020496e-17,
            -1.946798936387781e-17,
            -0.023583008807430632
          ],
          [
            -9.989412456681563e-17,
            2.322780153073721e-17,
            -0.0019551637432881795
          ],
          [
            -7.027218610555154e-18,
            1.0071400661218449e-16,
            0.017613926291464615
          ],
          [
            -2.3730773900320683e-17,
            -1.2276419527357011e-17,
            0.02524827024062758
          ],
          [
            1.199752984161425e-18,
            7.941584418279064e-17,
            0.01762387120482821
          ],
          [
            -1.0669920435772995e-18,
            -7.051631551198682e-18,
            2.9481487941813578e-18
          ]
        ],
        "raw_reduced_polarization": [
          [
            -5.749581211039838e-16,
            -1.158542627684507e-15,
            -0.3090087043664729
          ],
          [
            7.73799071801246e-17,
            3.057267059149978e-16,
            -0.36039081161026426
          ],
          [
            3.3172185613073597e-16,
            -1.1492241494646818e-15,
            -0.32602131909460647
          ],
          [
            -3.7690695595703476e-16,
            -3.0536644760994997e-16,
            -0.19977730212709058
          ],
          [
            -1.1748010932604498e-15,
            3.6434123250503633e-16,
            -0.016562659202660562
          ],
          [
            6.944197036137794e-16,
            1.5797562783135705e-15,
            0.14921177798421945
          ],
          [
            -4.186424888563764e-16,
            -1.925625985492993e-16,
            0.21388412959668626
          ],
          [
            6.391388281106088e-16,
            1.2456825288306797e-15,
            0.14929602372138936
          ],
          [
            -6.979854476191767e-17,
            -1.1060883773848859e-16,
            2.4974472815581144e-17
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -5.749581211039838e-16,
            -1.158542627684507e-15,
            -0.3090087043664729
          ],
          [
            7.73799071801246e-17,
            3.0572670591499773e-16,
            -0.36039081161026426
          ],
          [
            3.3172185613073597e-16,
            -1.1492241494646818e-15,
            -0.32602131909460647
          ],
          [
            -3.7690695595703476e-16,
            -3.0536644760994997e-16,
            -0.19977730212709058
          ],
          [
            -1.1748010932604498e-15,
            3.643412325050364e-16,
            -0.016562659202660562
          ],
          [
            6.944197036137795e-16,
            1.5797562783135705e-15,
            0.14921177798421945
          ],
          [
            -4.186424888563763e-16,
            -1.9256259854929923e-16,
            0.21388412959668626
          ],
          [
            6.391388281106087e-16,
            1.2456825288306797e-15,
            0.14929602372138936
          ],
          [
            -6.979854476191767e-17,
            -1.1060883773848867e-16,
            2.7755575615628914e-17
          ]
        ],
        "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": [
          [
            -5.551115123125783e-16,
            -1.1657341758564144e-15,
            -0.3090087043664729
          ],
          [
            1.1102230246251565e-16,
            3.3306690738754696e-16,
            -0.36039081161026426
          ],
          [
            3.3306690738754696e-16,
            -1.1657341758564144e-15,
            -0.32602131909460647
          ],
          [
            -3.885780586188048e-16,
            -3.3306690738754696e-16,
            -0.19977730212709055
          ],
          [
            -1.1657341758564144e-15,
            3.3306690738754696e-16,
            -0.016562659202660535
          ],
          [
            6.661338147750939e-16,
            1.5543122344752192e-15,
            0.14921177798421947
          ],
          [
            -4.440892098500626e-16,
            -1.6653345369377348e-16,
            0.21388412959668623
          ],
          [
            6.661338147750939e-16,
            1.2212453270876722e-15,
            0.1492960237213894
          ],
          [
            -5.551115123125783e-17,
            -1.1102230246251565e-16,
            0.0
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -28.592995172375616,
          -28.594704991826543,
          -28.599170423717332,
          -28.61632612843711,
          -28.685240434354046,
          -28.843848700545422,
          -29.081687654746062,
          -29.328955289356472,
          -29.4802286148679
        ],
        "cartesian_polarizations_e_A2": [
          [
            -1.0669920435772995e-18,
            -7.051631551198682e-18,
            2.9481487941813578e-18
          ],
          [
            -6.0757419431220836e-18,
            -8.191344052919938e-18,
            -0.017623871204827724
          ],
          [
            -1.7734560924309286e-17,
            -5.326311517477217e-17,
            -0.025248270240628357
          ],
          [
            -5.65808029057713e-18,
            -7.0756407662007e-17,
            -0.017613926291464656
          ],
          [
            -1.5191627683638908e-17,
            -8.315369566845866e-17,
            0.0019551637432889332
          ],
          [
            -2.782465159059615e-17,
            -1.527576410733001e-16,
            0.023583008807430424
          ],
          [
            6.868991055245824e-17,
            -1.9830358546897464e-16,
            0.038485671584088166
          ],
          [
            -5.221069712842674e-18,
            -1.272294806169679e-16,
            0.04254286945428418
          ],
          [
            -4.7916451897549005e-18,
            -4.811399335866068e-17,
            0.03647739217146544
          ]
        ],
        "raw_reduced_polarization": [
          [
            -6.979854476191767e-17,
            -1.1060883773848859e-16,
            2.4974472815581144e-17
          ],
          [
            -1.4677641915072674e-16,
            -1.284858743159292e-16,
            -0.14929602372138523
          ],
          [
            -6.586391124761558e-16,
            -8.354621509984241e-16,
            -0.21388412959669284
          ],
          [
            -6.317871040437757e-16,
            -1.1098543588419507e-15,
            -0.14921177798421978
          ],
          [
            -8.585210032707586e-16,
            -1.3043128479939862e-15,
            0.01656265920266695
          ],
          [
            -1.576017922285693e-15,
            -2.3960901831178037e-15,
            0.19977730212708886
          ],
          [
            -6.221615010139654e-16,
            -3.1105041363611535e-15,
            0.3260213190946112
          ],
          [
            -1.068756788043145e-15,
            -1.9956665170235976e-15,
            0.36039081161026293
          ],
          [
            -4.4243781255737957e-16,
            -7.546952567954543e-16,
            0.3090087043664713
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -6.979854476191767e-17,
            -1.1060883773848859e-16,
            2.4974472815581144e-17
          ],
          [
            -1.4677641915072674e-16,
            -1.284858743159292e-16,
            -0.14929602372138523
          ],
          [
            -6.586391124761558e-16,
            -8.354621509984241e-16,
            -0.21388412959669284
          ],
          [
            -6.317871040437757e-16,
            -1.1098543588419507e-15,
            -0.14921177798421978
          ],
          [
            -8.585210032707586e-16,
            -1.3043128479939862e-15,
            0.016562659202666946
          ],
          [
            -1.576017922285693e-15,
            -2.3960901831178037e-15,
            0.19977730212708886
          ],
          [
            -6.221615010139653e-16,
            -3.1105041363611535e-15,
            0.3260213190946112
          ],
          [
            -1.068756788043145e-15,
            -1.9956665170235976e-15,
            0.36039081161026293
          ],
          [
            -4.424378125573795e-16,
            -7.546952567954544e-16,
            0.3090087043664713
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          4.353610315801485e-16,
          9.3732495220753e-16,
          0.30900870436647293
        ],
        "actual_opposite_endpoint_branch_residual": 2.494993894102979e-15
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            -5.749581211039838e-16,
            -1.158542627684507e-15,
            -0.3090087043664729
          ],
          [
            7.73799071801246e-17,
            3.057267059149978e-16,
            -0.36039081161026426
          ],
          [
            3.3172185613073597e-16,
            -1.1492241494646818e-15,
            -0.32602131909460647
          ],
          [
            -3.7690695595703476e-16,
            -3.0536644760994997e-16,
            -0.19977730212709058
          ],
          [
            -1.1748010932604498e-15,
            3.6434123250503633e-16,
            -0.016562659202660562
          ],
          [
            6.944197036137794e-16,
            1.5797562783135705e-15,
            0.14921177798421945
          ],
          [
            -4.186424888563764e-16,
            -1.925625985492993e-16,
            0.21388412959668626
          ],
          [
            6.391388281106088e-16,
            1.2456825288306797e-15,
            0.14929602372138936
          ],
          [
            -6.979854476191767e-17,
            -1.1060883773848859e-16,
            2.4974472815581144e-17
          ],
          [
            -1.4677641915072674e-16,
            -1.284858743159292e-16,
            -0.14929602372138523
          ],
          [
            -6.586391124761558e-16,
            -8.354621509984241e-16,
            -0.21388412959669284
          ],
          [
            -6.317871040437757e-16,
            -1.1098543588419507e-15,
            -0.14921177798421978
          ],
          [
            -8.585210032707586e-16,
            -1.3043128479939862e-15,
            0.01656265920266695
          ],
          [
            -1.576017922285693e-15,
            -2.3960901831178037e-15,
            0.19977730212708886
          ],
          [
            -6.221615010139654e-16,
            -3.1105041363611535e-15,
            0.3260213190946112
          ],
          [
            -1.068756788043145e-15,
            -1.9956665170235976e-15,
            0.36039081161026293
          ],
          [
            -4.4243781255737957e-16,
            -7.546952567954543e-16,
            0.3090087043664713
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -5.749581211039838e-16,
            -1.158542627684507e-15,
            -0.3090087043664729
          ],
          [
            7.73799071801246e-17,
            3.0572670591499773e-16,
            -0.36039081161026426
          ],
          [
            3.3172185613073597e-16,
            -1.1492241494646818e-15,
            -0.32602131909460647
          ],
          [
            -3.7690695595703476e-16,
            -3.0536644760994997e-16,
            -0.19977730212709058
          ],
          [
            -1.1748010932604498e-15,
            3.643412325050364e-16,
            -0.016562659202660562
          ],
          [
            6.944197036137795e-16,
            1.5797562783135705e-15,
            0.14921177798421945
          ],
          [
            -4.186424888563763e-16,
            -1.9256259854929923e-16,
            0.21388412959668626
          ],
          [
            6.391388281106087e-16,
            1.2456825288306797e-15,
            0.14929602372138936
          ],
          [
            -6.979854476191767e-17,
            -1.1060883773848867e-16,
            2.7755575615628914e-17
          ],
          [
            -1.4677641915072674e-16,
            -1.284858743159292e-16,
            -0.14929602372138523
          ],
          [
            -6.586391124761558e-16,
            -8.354621509984241e-16,
            -0.21388412959669284
          ],
          [
            -6.317871040437757e-16,
            -1.1098543588419507e-15,
            -0.14921177798421978
          ],
          [
            -8.585210032707586e-16,
            -1.3043128479939862e-15,
            0.016562659202666946
          ],
          [
            -1.576017922285693e-15,
            -2.3960901831178037e-15,
            0.19977730212708886
          ],
          [
            -6.221615010139653e-16,
            -3.1105041363611535e-15,
            0.3260213190946112
          ],
          [
            -1.068756788043145e-15,
            -1.9956665170235976e-15,
            0.36039081161026293
          ],
          [
            -4.424378125573795e-16,
            -7.546952567954544e-16,
            0.3090087043664713
          ]
        ],
        "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": [
          [
            -5.551115123125783e-16,
            -1.1657341758564144e-15,
            -0.3090087043664729
          ],
          [
            1.1102230246251565e-16,
            3.3306690738754696e-16,
            -0.36039081161026426
          ],
          [
            3.3306690738754696e-16,
            -1.1657341758564144e-15,
            -0.32602131909460647
          ],
          [
            -3.885780586188048e-16,
            -3.3306690738754696e-16,
            -0.19977730212709055
          ],
          [
            -1.1657341758564144e-15,
            3.3306690738754696e-16,
            -0.016562659202660535
          ],
          [
            6.661338147750939e-16,
            1.5543122344752192e-15,
            0.14921177798421947
          ],
          [
            -4.440892098500626e-16,
            -1.6653345369377348e-16,
            0.21388412959668623
          ],
          [
            6.661338147750939e-16,
            1.2212453270876722e-15,
            0.1492960237213894
          ],
          [
            -5.551115123125783e-17,
            -1.1102230246251565e-16,
            0.0
          ],
          [
            -1.6653345369377348e-16,
            -1.1102230246251565e-16,
            -0.14929602372138523
          ],
          [
            -6.661338147750939e-16,
            -8.326672684688674e-16,
            -0.21388412959669284
          ],
          [
            -6.106226635438361e-16,
            -1.1102230246251565e-15,
            -0.1492117779842198
          ],
          [
            -8.326672684688674e-16,
            -1.27675647831893e-15,
            0.016562659202666974
          ],
          [
            -1.5543122344752192e-15,
            -2.3869795029440866e-15,
            0.19977730212708888
          ],
          [
            -6.106226635438361e-16,
            -3.1086244689504383e-15,
            0.3260213190946112
          ],
          [
            -1.0547118733938987e-15,
            -1.9984014443252818e-15,
            0.360390811610263
          ],
          [
            -4.440892098500626e-16,
            -7.771561172376096e-16,
            0.3090087043664713
          ]
        ]
      },
      "incoming_structure_ids": [
        "incoming_01_000",
        "incoming_01_001",
        "incoming_01_002",
        "incoming_01_003",
        "incoming_01_004",
        "incoming_01_005",
        "incoming_01_006",
        "incoming_01_007",
        "incoming_01_008"
      ],
      "reflected_structure_ids": [
        "reflected_01_001",
        "reflected_01_002",
        "reflected_01_003",
        "reflected_01_004",
        "reflected_01_005",
        "reflected_01_006",
        "reflected_01_007",
        "reflected_01_008"
      ],
      "positive_extension_structure_ids": [
        "extension_plus_01_000",
        "extension_plus_01_001",
        "extension_plus_01_002",
        "extension_plus_01_003"
      ],
      "negative_extension_structure_ids": [
        "extension_minus_01_000",
        "extension_minus_01_001",
        "extension_minus_01_002",
        "extension_minus_01_003"
      ],
      "extension": {
        "enabled": true,
        "fraction_beyond_polar_endpoint": 0.35,
        "images_per_side": 4,
        "construction": "continue fractional atomic displacements and symmetric log strain beyond +P; reflect these structures about N for the -P side",
        "positive_path_coordinates": [
          1.35,
          1.2625,
          1.175,
          1.0875
        ],
        "negative_path_coordinates": [
          -1.0875,
          -1.175,
          -1.2625,
          -1.35
        ]
      },
      "branch_coordinates": [
        1.35,
        1.2625,
        1.175,
        1.0875,
        1.0,
        0.875,
        0.75,
        0.625,
        0.5,
        0.375,
        0.25,
        0.125,
        0.0,
        -0.125,
        -0.25,
        -0.375,
        -0.5,
        -0.625,
        -0.75,
        -0.875,
        -1.0,
        -1.0875,
        -1.175,
        -1.2625,
        -1.35
      ],
      "parent": {
        "candidate_id": "inversion_parent_endpoint_00",
        "source": "same_species_inversion_center_projection_from_endpoint",
        "spacegroup": "P6_3/mmc",
        "spacegroup_number": 194,
        "pointgroup": "6/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": 2.5593199456415832e-17,
        "parent_symmetrization_rmsd_A": 0.4204863365913037,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -28.592995172375616,
        "reduced_polarization": [
          6.980509571939833e-18,
          1.646508671000056e-17,
          1.830806554948127e-17
        ],
        "cartesian_polarization_e_A2": [
          -9.216906867704053e-20,
          1.0496966364656116e-18,
          2.1612028318700866e-18
        ],
        "ranking_score": 0.42048633659130374
      }
    }
  ],
  "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": 73,
      "full_response": 17,
      "energy_polarization": 56
    },
    "model_evaluations_for_recovery_and_path_properties": {
      "total": 98,
      "full_response": 42,
      "energy_polarization": 56
    },
    "elapsed_seconds": 112.71816419402603
  }
}
