{
  "schema": "ferrofinder.endpoint_parent_recovery.v4_variable_cell",
  "status": "complete",
  "input_atom_count": 41,
  "input_formula": "O25P6Sr10",
  "input_spacegroup": "P3",
  "input_pointgroup": "3",
  "input_is_polar_point_group": true,
  "input_energy_eV": -281.3133995268154,
  "input_cartesian_polarization_e_A2": [
    0.0005331410973125741,
    2.608609956437169e-07,
    -1.46563041949124e-07
  ],
  "input_reduced_polarization": [
    0.045329627732870845,
    1.1104170817146763e-05,
    -1.0662734622030895e-05
  ],
  "input_formal_targets": [
    {
      "orbit_id": 0,
      "representative_formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ]
    },
    {
      "orbit_id": 1,
      "representative_formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.0
      ]
    },
    {
      "orbit_id": 2,
      "representative_formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.0
      ]
    },
    {
      "orbit_id": 3,
      "representative_formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        0.5,
        0.5,
        0.0
      ]
    }
  ],
  "parent_candidates": [
    {
      "candidate_id": "inversion_parent_endpoint_00",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "P-3",
      "spacegroup_number": 147,
      "pointgroup": "-3",
      "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": 3.0519549931218083e-15,
      "parent_symmetrization_rmsd_A": 0.26438444083380425,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -280.1841310192091,
      "reduced_polarization": [
        2.3610084866122187e-15,
        -1.897338345212931e-15,
        -3.7440006673460156e-16
      ],
      "cartesian_polarization_e_A2": [
        2.776882843015173e-17,
        -2.7142913076899118e-17,
        -5.146260751271209e-18
      ],
      "ranking_score": 0.26438444083381035
    },
    {
      "candidate_id": "bec_projection_00",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P3",
      "spacegroup_number": 143,
      "pointgroup": "3",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 1.8178087388893934e-06,
      "parent_symmetrization_rmsd_A": 0.005114781061663013,
      "parent_cell_rmsd_A": 0.0007267876347200959,
      "energy_eV": -281.3016744005894,
      "reduced_polarization": [
        1.8178031671026696e-06,
        3.3715169994475867e-09,
        -2.981564567962105e-09
      ],
      "cartesian_polarization_e_A2": [
        2.137727784860933e-08,
        7.716689975473446e-11,
        -4.0979213732849034e-11
      ],
      "ranking_score": 0.5053001135878208
    },
    {
      "candidate_id": "inversion_parent_bec_00_00",
      "source": "same_species_inversion_center_projection_after_BEC",
      "spacegroup": "P-3",
      "spacegroup_number": 147,
      "pointgroup": "-3",
      "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": 2.1298381686357667e-15,
      "parent_symmetrization_rmsd_A": 0.2643845041264767,
      "parent_cell_rmsd_A": 0.0007267876347200959,
      "energy_eV": -280.181798775675,
      "reduced_polarization": [
        -1.4904494763428111e-15,
        -1.4521137506628401e-15,
        -4.540227287075996e-16
      ],
      "cartesian_polarization_e_A2": [
        -1.7527615311849208e-17,
        -1.9442560246058372e-17,
        -6.240067206722935e-18
      ],
      "ranking_score": 0.264566201035161
    },
    {
      "candidate_id": "bec_projection_01",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P3",
      "spacegroup_number": 143,
      "pointgroup": "3",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.0
      ],
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_residual": 0.0009144935734106156,
      "parent_symmetrization_rmsd_A": 0.051324931319516355,
      "parent_cell_rmsd_A": 0.007283688461098557,
      "energy_eV": -280.22340533398904,
      "reduced_polarization": [
        0.4990855064267359,
        1.3426358722982112e-08,
        9.363383579046275e-09
      ],
      "cartesian_polarization_e_A2": [
        0.005877345855512004,
        5.365558251280825e-10,
        -2.0278793750235728e-10
      ],
      "ranking_score": 0.5549748405816122
    },
    {
      "candidate_id": "bec_projection_02",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.0
      ],
      "formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_residual": 2.2332025383016465e-05,
      "parent_symmetrization_rmsd_A": 0.07564119048590087,
      "parent_cell_rmsd_A": 0.07508165918749873,
      "energy_eV": -278.6264867809,
      "reduced_polarization": [
        -1.9404709163100914e-06,
        0.4999779030168049,
        -2.5840402484802474e-06
      ],
      "cartesian_polarization_e_A2": [
        -1.6693140813264492e-05,
        0.00798614508731826,
        -1.9983300225437025e-05
      ],
      "ranking_score": 0.5944562693335416
    },
    {
      "candidate_id": "bec_projection_03",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.5,
        0.5,
        0.0
      ],
      "formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_residual": 2.3256131066687294e-05,
      "parent_symmetrization_rmsd_A": 0.09164866970795964,
      "parent_cell_rmsd_A": 0.06988812597158002,
      "energy_eV": -277.4657985550607,
      "reduced_polarization": [
        0.49999563358202326,
        0.4999784763383461,
        -7.649445421128574e-06
      ],
      "cartesian_polarization_e_A2": [
        0.0058714466349685515,
        0.007982828109219704,
        -2.0452050789032942e-05
      ],
      "ranking_score": 0.609167213462988
    }
  ],
  "formal_branches": [
    {
      "orbit_id": 0,
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.0,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              0.045329627732870845,
              1.1104170817146763e-05,
              -1.0662734622030895e-05
            ],
            "branch_aligned_reduced_polarization": [
              0.045329627732870845,
              1.1104170817146763e-05,
              -1.0662734622030895e-05
            ],
            "target_residual": 0.045329630347016654,
            "energy_eV": -281.3133995268154,
            "max_atomic_step_A": 0.005265867796184182,
            "max_log_strain_component": 6.293303542481772e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.0652102727932755,
            "cell_principal_stretches": [
              1.0000629781762906,
              1.0000624316248015,
              1.0000387455885735
            ],
            "cell_volume_ratio": 1.0001641641807244,
            "cell_rmsd_from_input_A": 0.0007267876347200959
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              1.8178031671026696e-06,
              3.3715169994475867e-09,
              -2.981564567962105e-09
            ],
            "branch_aligned_reduced_polarization": [
              1.8178031671026696e-06,
              3.3715169994475867e-09,
              -2.981564567962105e-09
            ],
            "target_residual": 1.8178087388893934e-06,
            "energy_eV": -281.3016744005894
          }
        ],
        "iterations": 1
      },
      "parent": {
        "candidate_id": "inversion_parent_endpoint_00",
        "source": "same_species_inversion_center_projection_from_endpoint",
        "spacegroup": "P-3",
        "spacegroup_number": 147,
        "pointgroup": "-3",
        "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": 3.0519549931218083e-15,
        "parent_symmetrization_rmsd_A": 0.26438444083380425,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -280.1841310192091,
        "reduced_polarization": [
          2.3610084866122187e-15,
          -1.897338345212931e-15,
          -3.7440006673460156e-16
        ],
        "cartesian_polarization_e_A2": [
          2.776882843015173e-17,
          -2.7142913076899118e-17,
          -5.146260751271209e-18
        ],
        "ranking_score": 0.26438444083381035
      },
      "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": [
          -281.3133995268154,
          -281.24820485937505,
          -281.11071418939827,
          -280.92354299237354,
          -280.7114559208742,
          -280.50177067197944,
          -280.3299461264422,
          -280.22151245569677,
          -280.184131019209
        ],
        "cartesian_polarizations_e_A2": [
          [
            0.0005331410973125724,
            2.6086099564686247e-07,
            -1.4656304195145816e-07
          ],
          [
            0.0006659566582940638,
            2.2869450289811914e-07,
            -1.2819826917316052e-07
          ],
          [
            0.0006778188044855476,
            1.9658160226500444e-07,
            -1.100098182169697e-07
          ],
          [
            0.0005991476170476859,
            1.6440998653278637e-07,
            -9.187936103084843e-08
          ],
          [
            0.00047616723272417397,
            1.3204495995286426e-07,
            -7.367040961601661e-08
          ],
          [
            0.00033595791923851024,
            9.939791934603632e-08,
            -5.534762760955746e-08
          ],
          [
            0.0002114672639571939,
            6.649378101206919e-08,
            -3.6939765771611353e-08
          ],
          [
            0.0001066603167203137,
            3.333662179713353e-08,
            -1.8478426679708873e-08
          ],
          [
            7.042068741311588e-18,
            -3.484563165277589e-17,
            -1.6250179737275392e-17
          ]
        ],
        "raw_reduced_polarization": [
          [
            0.0453296277328707,
            1.1104170817260041e-05,
            -1.066273462220071e-05
          ],
          [
            0.05662209790028245,
            9.745557773081661e-06,
            -9.326663154764473e-06
          ],
          [
            0.05763066143755859,
            8.38390742763411e-06,
            -8.003419428702835e-06
          ],
          [
            0.05094174614320755,
            7.016448161910936e-06,
            -6.684394857564289e-06
          ],
          [
            0.0404854990672823,
            5.6396583530889634e-06,
            -5.359659684905939e-06
          ],
          [
            0.02856438471870997,
            4.249240954036384e-06,
            -4.026643124428058e-06
          ],
          [
            0.01797972882073343,
            2.845719979661626e-06,
            -2.6874368475471336e-06
          ],
          [
            0.00906865457413292,
            1.428202718293978e-06,
            -1.3443400007130434e-06
          ],
          [
            5.987427270604674e-16,
            -2.7865632727871464e-15,
            -1.1822308802721112e-15
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            0.0453296277328707,
            1.1104170817260041e-05,
            -1.066273462220071e-05
          ],
          [
            0.05662209790028245,
            9.745557773081661e-06,
            -9.326663154764473e-06
          ],
          [
            0.05763066143755859,
            8.38390742763411e-06,
            -8.003419428702835e-06
          ],
          [
            0.05094174614320755,
            7.016448161910936e-06,
            -6.684394857564289e-06
          ],
          [
            0.0404854990672823,
            5.6396583530889634e-06,
            -5.359659684905939e-06
          ],
          [
            0.02856438471870997,
            4.249240954036384e-06,
            -4.026643124428058e-06
          ],
          [
            0.01797972882073343,
            2.845719979661626e-06,
            -2.6874368475471336e-06
          ],
          [
            0.00906865457413292,
            1.428202718293978e-06,
            -1.3443400007130434e-06
          ],
          [
            5.984795992119984e-16,
            -2.7865632724048033e-15,
            -1.1822307777789023e-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": [
          [
            0.04532962773287075,
            1.1104170817288761e-05,
            -1.0662734622191028e-05
          ],
          [
            0.0566220979002825,
            9.745557773110924e-06,
            -9.326663154785031e-06
          ],
          [
            0.05763066143755857,
            8.38390742763373e-06,
            -8.003419428692649e-06
          ],
          [
            0.05094174614320757,
            7.016448161922817e-06,
            -6.6843948575701084e-06
          ],
          [
            0.04048549906728227,
            5.639658353095989e-06,
            -5.359659684900375e-06
          ],
          [
            0.028564384718709923,
            4.249240953990707e-06,
            -4.026643124432905e-06
          ],
          [
            0.0179797288207334,
            2.8457199796605437e-06,
            -2.6874368475593435e-06
          ],
          [
            0.009068654574132973,
            1.4282027183121215e-06,
            -1.3443400007084882e-06
          ],
          [
            5.551115123125783e-16,
            -2.7755575615628914e-15,
            -1.1657341758564144e-15
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -280.184131019209,
          -280.22151245569677,
          -280.3299461264422,
          -280.50177067197944,
          -280.7114559208741,
          -280.92354299237354,
          -281.1107141893983,
          -281.2482048593751,
          -281.3133995268153
        ],
        "cartesian_polarizations_e_A2": [
          [
            8.559965574671143e-18,
            -2.691505487948862e-17,
            -1.9801433106673128e-17
          ],
          [
            -0.00010666031672026773,
            -3.333662184201326e-08,
            1.8478426720295423e-08
          ],
          [
            -0.00021146726395716172,
            -6.649378104726494e-08,
            3.693976580184425e-08
          ],
          [
            -0.00033595791923848216,
            -9.93979194125973e-08,
            5.5347627604436203e-08
          ],
          [
            -0.00047616723272412794,
            -1.3204495999303678e-07,
            7.367040966686511e-08
          ],
          [
            -0.0005991476170476316,
            -1.6440998655137348e-07,
            9.187936107730928e-08
          ],
          [
            -0.0006778188044855175,
            -1.965816023201378e-07,
            1.100098182455784e-07
          ],
          [
            -0.0006659566582940063,
            -2.2869450292728497e-07,
            1.2819826924255584e-07
          ],
          [
            -0.0005331410973125109,
            -2.6086099570668915e-07,
            1.4656304194348036e-07
          ]
        ],
        "raw_reduced_polarization": [
          [
            7.2779992925313985e-16,
            -2.416077706458806e-15,
            -1.440591185502576e-15
          ],
          [
            -0.00906865457412901,
            -1.4282027196452504e-06,
            1.3443400036657905e-06
          ],
          [
            -0.017979728820730696,
            -2.8457199807793836e-06,
            2.687436849746633e-06
          ],
          [
            -0.028564384718707585,
            -4.249240958416348e-06,
            4.026643124055478e-06
          ],
          [
            -0.040485499067278385,
            -5.639658353770371e-06,
            5.359659688605263e-06
          ],
          [
            -0.05094174614320293,
            -7.0164481613919585e-06,
            6.684394860944402e-06
          ],
          [
            -0.05763066143755604,
            -8.383907430067117e-06,
            8.003419430784173e-06
          ],
          [
            -0.056622097900277564,
            -9.745557772394934e-06,
            9.326663159813112e-06
          ],
          [
            -0.04532962773286547,
            -1.1104170821319616e-05,
            1.0662734621620309e-05
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            7.2779992925313985e-16,
            -2.416077706458806e-15,
            -1.440591185502576e-15
          ],
          [
            -0.00906865457412901,
            -1.4282027196452504e-06,
            1.3443400036657905e-06
          ],
          [
            -0.017979728820730696,
            -2.8457199807793836e-06,
            2.687436849746633e-06
          ],
          [
            -0.028564384718707585,
            -4.249240958416348e-06,
            4.026643124055478e-06
          ],
          [
            -0.040485499067278385,
            -5.639658353770371e-06,
            5.359659688605263e-06
          ],
          [
            -0.05094174614320293,
            -7.0164481613919585e-06,
            6.684394860944402e-06
          ],
          [
            -0.05763066143755604,
            -8.383907430067117e-06,
            8.003419430784173e-06
          ],
          [
            -0.056622097900277564,
            -9.745557772394934e-06,
            9.326663159813112e-06
          ],
          [
            -0.04532962773286547,
            -1.1104170821319616e-05,
            1.0662734621620309e-05
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          -0.0453296277328695,
          -1.1104170822833168e-05,
          1.0662734619836248e-05
        ],
        "actual_opposite_endpoint_branch_residual": 4.66118909649594e-15
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            0.0453296277328707,
            1.1104170817260041e-05,
            -1.066273462220071e-05
          ],
          [
            0.05662209790028245,
            9.745557773081661e-06,
            -9.326663154764473e-06
          ],
          [
            0.05763066143755859,
            8.38390742763411e-06,
            -8.003419428702835e-06
          ],
          [
            0.05094174614320755,
            7.016448161910936e-06,
            -6.684394857564289e-06
          ],
          [
            0.0404854990672823,
            5.6396583530889634e-06,
            -5.359659684905939e-06
          ],
          [
            0.02856438471870997,
            4.249240954036384e-06,
            -4.026643124428058e-06
          ],
          [
            0.01797972882073343,
            2.845719979661626e-06,
            -2.6874368475471336e-06
          ],
          [
            0.00906865457413292,
            1.428202718293978e-06,
            -1.3443400007130434e-06
          ],
          [
            5.987427270604674e-16,
            -2.7865632727871464e-15,
            -1.1822308802721112e-15
          ],
          [
            -0.00906865457412901,
            -1.4282027196452504e-06,
            1.3443400036657905e-06
          ],
          [
            -0.017979728820730696,
            -2.8457199807793836e-06,
            2.687436849746633e-06
          ],
          [
            -0.028564384718707585,
            -4.249240958416348e-06,
            4.026643124055478e-06
          ],
          [
            -0.040485499067278385,
            -5.639658353770371e-06,
            5.359659688605263e-06
          ],
          [
            -0.05094174614320293,
            -7.0164481613919585e-06,
            6.684394860944402e-06
          ],
          [
            -0.05763066143755604,
            -8.383907430067117e-06,
            8.003419430784173e-06
          ],
          [
            -0.056622097900277564,
            -9.745557772394934e-06,
            9.326663159813112e-06
          ],
          [
            -0.04532962773286547,
            -1.1104170821319616e-05,
            1.0662734621620309e-05
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            0.0453296277328707,
            1.1104170817260041e-05,
            -1.066273462220071e-05
          ],
          [
            0.05662209790028245,
            9.745557773081661e-06,
            -9.326663154764473e-06
          ],
          [
            0.05763066143755859,
            8.38390742763411e-06,
            -8.003419428702835e-06
          ],
          [
            0.05094174614320755,
            7.016448161910936e-06,
            -6.684394857564289e-06
          ],
          [
            0.0404854990672823,
            5.6396583530889634e-06,
            -5.359659684905939e-06
          ],
          [
            0.02856438471870997,
            4.249240954036384e-06,
            -4.026643124428058e-06
          ],
          [
            0.01797972882073343,
            2.845719979661626e-06,
            -2.6874368475471336e-06
          ],
          [
            0.00906865457413292,
            1.428202718293978e-06,
            -1.3443400007130434e-06
          ],
          [
            5.984795992119984e-16,
            -2.7865632724048033e-15,
            -1.1822307777789023e-15
          ],
          [
            -0.00906865457412901,
            -1.4282027196452504e-06,
            1.3443400036657905e-06
          ],
          [
            -0.017979728820730696,
            -2.8457199807793836e-06,
            2.687436849746633e-06
          ],
          [
            -0.028564384718707585,
            -4.249240958416348e-06,
            4.026643124055478e-06
          ],
          [
            -0.040485499067278385,
            -5.639658353770371e-06,
            5.359659688605263e-06
          ],
          [
            -0.05094174614320293,
            -7.0164481613919585e-06,
            6.684394860944402e-06
          ],
          [
            -0.05763066143755604,
            -8.383907430067117e-06,
            8.003419430784173e-06
          ],
          [
            -0.056622097900277564,
            -9.745557772394934e-06,
            9.326663159813112e-06
          ],
          [
            -0.04532962773286547,
            -1.1104170821319616e-05,
            1.0662734621620309e-05
          ]
        ],
        "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": [
          [
            0.04532962773287075,
            1.1104170817288761e-05,
            -1.0662734622191028e-05
          ],
          [
            0.0566220979002825,
            9.745557773110924e-06,
            -9.326663154785031e-06
          ],
          [
            0.05763066143755857,
            8.38390742763373e-06,
            -8.003419428692649e-06
          ],
          [
            0.05094174614320757,
            7.016448161922817e-06,
            -6.6843948575701084e-06
          ],
          [
            0.04048549906728227,
            5.639658353095989e-06,
            -5.359659684900375e-06
          ],
          [
            0.028564384718709923,
            4.249240953990707e-06,
            -4.026643124432905e-06
          ],
          [
            0.0179797288207334,
            2.8457199796605437e-06,
            -2.6874368475593435e-06
          ],
          [
            0.009068654574132973,
            1.4282027183121215e-06,
            -1.3443400007084882e-06
          ],
          [
            5.551115123125783e-16,
            -2.7755575615628914e-15,
            -1.1657341758564144e-15
          ],
          [
            -0.009068654574129031,
            -1.4282027196443892e-06,
            1.3443400036505793e-06
          ],
          [
            -0.017979728820730678,
            -2.8457199807707667e-06,
            2.6874368497242784e-06
          ],
          [
            -0.02856438471870759,
            -4.249240958431599e-06,
            4.026643124044327e-06
          ],
          [
            -0.040485499067278385,
            -5.6396583537621225e-06,
            5.359659688619622e-06
          ],
          [
            -0.050941746143202904,
            -7.0164481613677054e-06,
            6.684394860956289e-06
          ],
          [
            -0.05763066143755602,
            -8.38390743007622e-06,
            8.003419430746561e-06
          ],
          [
            -0.05662209790027756,
            -9.74555777238928e-06,
            9.326663159781035e-06
          ],
          [
            -0.045329627732865474,
            -1.1104170821341075e-05,
            1.0662734621580405e-05
          ]
        ]
      },
      "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": [
        0.5,
        0.0,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.0,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              0.045329627732870845,
              1.1104170817146763e-05,
              -1.0662734622030895e-05
            ],
            "branch_aligned_reduced_polarization": [
              0.04532962773287086,
              1.1104170817146763e-05,
              -1.0662734622030895e-05
            ],
            "target_residual": 0.4546703725277537,
            "energy_eV": -281.3133995268154,
            "max_atomic_step_A": 0.05281788962761493,
            "max_log_strain_component": 0.0006291554284368748,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.0652102727932755,
            "cell_principal_stretches": [
              0.9996114502594772,
              0.9993715384922524,
              0.9993709992153647
            ],
            "cell_volume_ratio": 0.9983548717029289,
            "cell_rmsd_from_input_A": 0.007283688461098557
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.4990855064267359,
              1.3426358722982112e-08,
              9.363383579046275e-09
            ],
            "branch_aligned_reduced_polarization": [
              0.4990855064267359,
              1.3426358722982112e-08,
              9.363383579046275e-09
            ],
            "target_residual": 0.0009144935734106156,
            "energy_eV": -280.22340533398904
          }
        ],
        "iterations": 1
      },
      "parent": {
        "candidate_id": "bec_projection_01",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P3",
        "spacegroup_number": 143,
        "pointgroup": "3",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.5,
          0.0,
          0.0
        ],
        "formal_class": [
          0.5,
          0.0,
          0.0
        ],
        "target_residual": 0.0009144935734106156,
        "parent_symmetrization_rmsd_A": 0.051324931319516355,
        "parent_cell_rmsd_A": 0.007283688461098557,
        "energy_eV": -280.22340533398904,
        "reduced_polarization": [
          0.4990855064267359,
          1.3426358722982112e-08,
          9.363383579046275e-09
        ],
        "cartesian_polarization_e_A2": [
          0.005877345855512004,
          5.365558251280825e-10,
          -2.0278793750235728e-10
        ],
        "ranking_score": 0.5549748405816122
      },
      "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
        ],
        [
          0.0,
          0.0,
          0.5
        ],
        [
          0.0,
          0.5,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              0.045329627732870845,
              1.1104170817146763e-05,
              -1.0662734622030895e-05
            ],
            "branch_aligned_reduced_polarization": [
              0.045329627732870845,
              1.1104170817122228e-05,
              -1.0662734622030895e-05
            ],
            "target_residual": 0.5020395116089769,
            "energy_eV": -281.3133995268154,
            "max_atomic_step_A": 0.08746181558452304,
            "max_log_strain_component": 0.006350592935308455,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.0652102727932755,
            "cell_principal_stretches": [
              1.0073878706530424,
              0.9995275651156615,
              0.9932984891240667
            ],
            "cell_volume_ratio": 1.0001641141271391,
            "cell_rmsd_from_input_A": 0.07324060435638087
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.0015344848284190242,
              0.48856572166343165,
              0.000904217206981384
            ],
            "branch_aligned_reduced_polarization": [
              0.0015344848284190242,
              0.48856572166343165,
              0.000904217206981384
            ],
            "target_residual": 0.011572163735627215,
            "energy_eV": -278.7580729417737,
            "max_atomic_step_A": 0.0022470420389131365,
            "max_log_strain_component": 0.00016939391767761553,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.0652102727932755,
            "cell_principal_stretches": [
              1.0075788811528275,
              0.9995137542966578,
              0.9931298704111363
            ],
            "cell_volume_ratio": 1.0001701186553509,
            "cell_rmsd_from_input_A": 0.07508165918749873
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -1.9404709163100914e-06,
              0.4999779030168049,
              -2.5840402484802474e-06
            ],
            "branch_aligned_reduced_polarization": [
              -1.9404709163100914e-06,
              0.4999779030168049,
              -2.5840402484802474e-06
            ],
            "target_residual": 2.2332025383016465e-05,
            "energy_eV": -278.6264867809
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_02",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.5,
          0.0
        ],
        "formal_class": [
          0.0,
          0.5,
          0.0
        ],
        "target_residual": 2.2332025383016465e-05,
        "parent_symmetrization_rmsd_A": 0.07564119048590087,
        "parent_cell_rmsd_A": 0.07508165918749873,
        "energy_eV": -278.6264867809,
        "reduced_polarization": [
          -1.9404709163100914e-06,
          0.4999779030168049,
          -2.5840402484802474e-06
        ],
        "cartesian_polarization_e_A2": [
          -1.6693140813264492e-05,
          0.00798614508731826,
          -1.9983300225437025e-05
        ],
        "ranking_score": 0.5944562693335416
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 3,
      "formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.5,
          0.0
        ],
        [
          0.5,
          0.0,
          0.5
        ],
        [
          0.5,
          0.5,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.5,
        0.5,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              0.045329627732870845,
              1.1104170817146763e-05,
              -1.0662734622030895e-05
            ],
            "branch_aligned_reduced_polarization": [
              0.04532962773287086,
              1.1104170817122228e-05,
              -1.0662734622030895e-05
            ],
            "target_residual": 0.6758062174053366,
            "energy_eV": -281.3133995268154,
            "max_atomic_step_A": 0.10285683331628041,
            "max_log_strain_component": 0.0069168455054310135,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.0652102727932755,
            "cell_principal_stretches": [
              1.0067103547685385,
              0.9990804262795877,
              0.9926129426065566
            ],
            "cell_volume_ratio": 0.9983548217398909,
            "cell_rmsd_from_input_A": 0.06814987234870844
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.4971285612746032,
              0.48889686878729205,
              0.0009889035005131955
            ],
            "branch_aligned_reduced_polarization": [
              0.4971285612746032,
              0.48889686878729205,
              0.0009889035005131955
            ],
            "target_residual": 0.011510977943408857,
            "energy_eV": -277.6094104609898,
            "max_atomic_step_A": 0.0022083762086352824,
            "max_log_strain_component": 0.0001673678914576959,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 2.0652102727932755,
            "cell_principal_stretches": [
              1.0068896056189731,
              0.999062561521795,
              0.9924428274230193
            ],
            "cell_volume_ratio": 0.9983436032367043,
            "cell_rmsd_from_input_A": 0.06988812597158002
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.49999563358202326,
              0.4999784763383461,
              -7.649445421128574e-06
            ],
            "branch_aligned_reduced_polarization": [
              0.49999563358202326,
              0.4999784763383461,
              -7.649445421128574e-06
            ],
            "target_residual": 2.3256131066687294e-05,
            "energy_eV": -277.4657985550607
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_03",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.5,
          0.5,
          0.0
        ],
        "formal_class": [
          0.5,
          0.5,
          0.0
        ],
        "target_residual": 2.3256131066687294e-05,
        "parent_symmetrization_rmsd_A": 0.09164866970795964,
        "parent_cell_rmsd_A": 0.06988812597158002,
        "energy_eV": -277.4657985550607,
        "reduced_polarization": [
          0.49999563358202326,
          0.4999784763383461,
          -7.649445421128574e-06
        ],
        "cartesian_polarization_e_A2": [
          0.0058714466349685515,
          0.007982828109219704,
          -2.0452050789032942e-05
        ],
        "ranking_score": 0.609167213462988
      },
      "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
        ],
        "endpoint_rmsd_A": 0.26438444083380425,
        "minimum_distance_A_by_image": [
          1.5518427072979841,
          1.5521830846733031,
          1.5525259033876022,
          1.5528711618239988,
          1.553218858355548,
          1.5535689913452746,
          1.5539215591462132,
          1.5542765601014483,
          1.5546339743608681
        ],
        "minimum_distance_A": 1.5518427072979841,
        "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": [
          624.280041914988,
          624.280041914988,
          624.280041914988,
          624.280041914988,
          624.280041914988,
          624.280041914988,
          624.280041914988,
          624.280041914988,
          624.280041914988
        ],
        "cell_deformation_log_strain_norm": 0.0
      },
      "parent_reduced_polarization": [
        5.987427270604674e-16,
        -2.7865632727871464e-15,
        -1.1822308802721112e-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": [
          -281.3133995268154,
          -281.24820485937505,
          -281.11071418939827,
          -280.92354299237354,
          -280.7114559208742,
          -280.50177067197944,
          -280.3299461264422,
          -280.22151245569677,
          -280.184131019209
        ],
        "cartesian_polarizations_e_A2": [
          [
            0.0005331410973125724,
            2.6086099564686247e-07,
            -1.4656304195145816e-07
          ],
          [
            0.0006659566582940638,
            2.2869450289811914e-07,
            -1.2819826917316052e-07
          ],
          [
            0.0006778188044855476,
            1.9658160226500444e-07,
            -1.100098182169697e-07
          ],
          [
            0.0005991476170476859,
            1.6440998653278637e-07,
            -9.187936103084843e-08
          ],
          [
            0.00047616723272417397,
            1.3204495995286426e-07,
            -7.367040961601661e-08
          ],
          [
            0.00033595791923851024,
            9.939791934603632e-08,
            -5.534762760955746e-08
          ],
          [
            0.0002114672639571939,
            6.649378101206919e-08,
            -3.6939765771611353e-08
          ],
          [
            0.0001066603167203137,
            3.333662179713353e-08,
            -1.8478426679708873e-08
          ],
          [
            7.042068741311588e-18,
            -3.484563165277589e-17,
            -1.6250179737275392e-17
          ]
        ],
        "raw_reduced_polarization": [
          [
            0.0453296277328707,
            1.1104170817260041e-05,
            -1.066273462220071e-05
          ],
          [
            0.05662209790028245,
            9.745557773081661e-06,
            -9.326663154764473e-06
          ],
          [
            0.05763066143755859,
            8.38390742763411e-06,
            -8.003419428702835e-06
          ],
          [
            0.05094174614320755,
            7.016448161910936e-06,
            -6.684394857564289e-06
          ],
          [
            0.0404854990672823,
            5.6396583530889634e-06,
            -5.359659684905939e-06
          ],
          [
            0.02856438471870997,
            4.249240954036384e-06,
            -4.026643124428058e-06
          ],
          [
            0.01797972882073343,
            2.845719979661626e-06,
            -2.6874368475471336e-06
          ],
          [
            0.00906865457413292,
            1.428202718293978e-06,
            -1.3443400007130434e-06
          ],
          [
            5.987427270604674e-16,
            -2.7865632727871464e-15,
            -1.1822308802721112e-15
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            0.0453296277328707,
            1.1104170817260041e-05,
            -1.066273462220071e-05
          ],
          [
            0.05662209790028245,
            9.745557773081661e-06,
            -9.326663154764473e-06
          ],
          [
            0.05763066143755859,
            8.38390742763411e-06,
            -8.003419428702835e-06
          ],
          [
            0.05094174614320755,
            7.016448161910936e-06,
            -6.684394857564289e-06
          ],
          [
            0.0404854990672823,
            5.6396583530889634e-06,
            -5.359659684905939e-06
          ],
          [
            0.02856438471870997,
            4.249240954036384e-06,
            -4.026643124428058e-06
          ],
          [
            0.01797972882073343,
            2.845719979661626e-06,
            -2.6874368475471336e-06
          ],
          [
            0.00906865457413292,
            1.428202718293978e-06,
            -1.3443400007130434e-06
          ],
          [
            5.984795992119984e-16,
            -2.7865632724048033e-15,
            -1.1822307777789023e-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": [
          [
            0.04532962773287075,
            1.1104170817288761e-05,
            -1.0662734622191028e-05
          ],
          [
            0.0566220979002825,
            9.745557773110924e-06,
            -9.326663154785031e-06
          ],
          [
            0.05763066143755857,
            8.38390742763373e-06,
            -8.003419428692649e-06
          ],
          [
            0.05094174614320757,
            7.016448161922817e-06,
            -6.6843948575701084e-06
          ],
          [
            0.04048549906728227,
            5.639658353095989e-06,
            -5.359659684900375e-06
          ],
          [
            0.028564384718709923,
            4.249240953990707e-06,
            -4.026643124432905e-06
          ],
          [
            0.0179797288207334,
            2.8457199796605437e-06,
            -2.6874368475593435e-06
          ],
          [
            0.009068654574132973,
            1.4282027183121215e-06,
            -1.3443400007084882e-06
          ],
          [
            5.551115123125783e-16,
            -2.7755575615628914e-15,
            -1.1657341758564144e-15
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -280.184131019209,
          -280.22151245569677,
          -280.3299461264422,
          -280.50177067197944,
          -280.7114559208741,
          -280.92354299237354,
          -281.1107141893983,
          -281.2482048593751,
          -281.3133995268153
        ],
        "cartesian_polarizations_e_A2": [
          [
            8.559965574671143e-18,
            -2.691505487948862e-17,
            -1.9801433106673128e-17
          ],
          [
            -0.00010666031672026773,
            -3.333662184201326e-08,
            1.8478426720295423e-08
          ],
          [
            -0.00021146726395716172,
            -6.649378104726494e-08,
            3.693976580184425e-08
          ],
          [
            -0.00033595791923848216,
            -9.93979194125973e-08,
            5.5347627604436203e-08
          ],
          [
            -0.00047616723272412794,
            -1.3204495999303678e-07,
            7.367040966686511e-08
          ],
          [
            -0.0005991476170476316,
            -1.6440998655137348e-07,
            9.187936107730928e-08
          ],
          [
            -0.0006778188044855175,
            -1.965816023201378e-07,
            1.100098182455784e-07
          ],
          [
            -0.0006659566582940063,
            -2.2869450292728497e-07,
            1.2819826924255584e-07
          ],
          [
            -0.0005331410973125109,
            -2.6086099570668915e-07,
            1.4656304194348036e-07
          ]
        ],
        "raw_reduced_polarization": [
          [
            7.2779992925313985e-16,
            -2.416077706458806e-15,
            -1.440591185502576e-15
          ],
          [
            -0.00906865457412901,
            -1.4282027196452504e-06,
            1.3443400036657905e-06
          ],
          [
            -0.017979728820730696,
            -2.8457199807793836e-06,
            2.687436849746633e-06
          ],
          [
            -0.028564384718707585,
            -4.249240958416348e-06,
            4.026643124055478e-06
          ],
          [
            -0.040485499067278385,
            -5.639658353770371e-06,
            5.359659688605263e-06
          ],
          [
            -0.05094174614320293,
            -7.0164481613919585e-06,
            6.684394860944402e-06
          ],
          [
            -0.05763066143755604,
            -8.383907430067117e-06,
            8.003419430784173e-06
          ],
          [
            -0.056622097900277564,
            -9.745557772394934e-06,
            9.326663159813112e-06
          ],
          [
            -0.04532962773286547,
            -1.1104170821319616e-05,
            1.0662734621620309e-05
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            7.2779992925313985e-16,
            -2.416077706458806e-15,
            -1.440591185502576e-15
          ],
          [
            -0.00906865457412901,
            -1.4282027196452504e-06,
            1.3443400036657905e-06
          ],
          [
            -0.017979728820730696,
            -2.8457199807793836e-06,
            2.687436849746633e-06
          ],
          [
            -0.028564384718707585,
            -4.249240958416348e-06,
            4.026643124055478e-06
          ],
          [
            -0.040485499067278385,
            -5.639658353770371e-06,
            5.359659688605263e-06
          ],
          [
            -0.05094174614320293,
            -7.0164481613919585e-06,
            6.684394860944402e-06
          ],
          [
            -0.05763066143755604,
            -8.383907430067117e-06,
            8.003419430784173e-06
          ],
          [
            -0.056622097900277564,
            -9.745557772394934e-06,
            9.326663159813112e-06
          ],
          [
            -0.04532962773286547,
            -1.1104170821319616e-05,
            1.0662734621620309e-05
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          -0.0453296277328695,
          -1.1104170822833168e-05,
          1.0662734619836248e-05
        ],
        "actual_opposite_endpoint_branch_residual": 4.66118909649594e-15
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            0.0453296277328707,
            1.1104170817260041e-05,
            -1.066273462220071e-05
          ],
          [
            0.05662209790028245,
            9.745557773081661e-06,
            -9.326663154764473e-06
          ],
          [
            0.05763066143755859,
            8.38390742763411e-06,
            -8.003419428702835e-06
          ],
          [
            0.05094174614320755,
            7.016448161910936e-06,
            -6.684394857564289e-06
          ],
          [
            0.0404854990672823,
            5.6396583530889634e-06,
            -5.359659684905939e-06
          ],
          [
            0.02856438471870997,
            4.249240954036384e-06,
            -4.026643124428058e-06
          ],
          [
            0.01797972882073343,
            2.845719979661626e-06,
            -2.6874368475471336e-06
          ],
          [
            0.00906865457413292,
            1.428202718293978e-06,
            -1.3443400007130434e-06
          ],
          [
            5.987427270604674e-16,
            -2.7865632727871464e-15,
            -1.1822308802721112e-15
          ],
          [
            -0.00906865457412901,
            -1.4282027196452504e-06,
            1.3443400036657905e-06
          ],
          [
            -0.017979728820730696,
            -2.8457199807793836e-06,
            2.687436849746633e-06
          ],
          [
            -0.028564384718707585,
            -4.249240958416348e-06,
            4.026643124055478e-06
          ],
          [
            -0.040485499067278385,
            -5.639658353770371e-06,
            5.359659688605263e-06
          ],
          [
            -0.05094174614320293,
            -7.0164481613919585e-06,
            6.684394860944402e-06
          ],
          [
            -0.05763066143755604,
            -8.383907430067117e-06,
            8.003419430784173e-06
          ],
          [
            -0.056622097900277564,
            -9.745557772394934e-06,
            9.326663159813112e-06
          ],
          [
            -0.04532962773286547,
            -1.1104170821319616e-05,
            1.0662734621620309e-05
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            0.0453296277328707,
            1.1104170817260041e-05,
            -1.066273462220071e-05
          ],
          [
            0.05662209790028245,
            9.745557773081661e-06,
            -9.326663154764473e-06
          ],
          [
            0.05763066143755859,
            8.38390742763411e-06,
            -8.003419428702835e-06
          ],
          [
            0.05094174614320755,
            7.016448161910936e-06,
            -6.684394857564289e-06
          ],
          [
            0.0404854990672823,
            5.6396583530889634e-06,
            -5.359659684905939e-06
          ],
          [
            0.02856438471870997,
            4.249240954036384e-06,
            -4.026643124428058e-06
          ],
          [
            0.01797972882073343,
            2.845719979661626e-06,
            -2.6874368475471336e-06
          ],
          [
            0.00906865457413292,
            1.428202718293978e-06,
            -1.3443400007130434e-06
          ],
          [
            5.984795992119984e-16,
            -2.7865632724048033e-15,
            -1.1822307777789023e-15
          ],
          [
            -0.00906865457412901,
            -1.4282027196452504e-06,
            1.3443400036657905e-06
          ],
          [
            -0.017979728820730696,
            -2.8457199807793836e-06,
            2.687436849746633e-06
          ],
          [
            -0.028564384718707585,
            -4.249240958416348e-06,
            4.026643124055478e-06
          ],
          [
            -0.040485499067278385,
            -5.639658353770371e-06,
            5.359659688605263e-06
          ],
          [
            -0.05094174614320293,
            -7.0164481613919585e-06,
            6.684394860944402e-06
          ],
          [
            -0.05763066143755604,
            -8.383907430067117e-06,
            8.003419430784173e-06
          ],
          [
            -0.056622097900277564,
            -9.745557772394934e-06,
            9.326663159813112e-06
          ],
          [
            -0.04532962773286547,
            -1.1104170821319616e-05,
            1.0662734621620309e-05
          ]
        ],
        "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": [
          [
            0.04532962773287075,
            1.1104170817288761e-05,
            -1.0662734622191028e-05
          ],
          [
            0.0566220979002825,
            9.745557773110924e-06,
            -9.326663154785031e-06
          ],
          [
            0.05763066143755857,
            8.38390742763373e-06,
            -8.003419428692649e-06
          ],
          [
            0.05094174614320757,
            7.016448161922817e-06,
            -6.6843948575701084e-06
          ],
          [
            0.04048549906728227,
            5.639658353095989e-06,
            -5.359659684900375e-06
          ],
          [
            0.028564384718709923,
            4.249240953990707e-06,
            -4.026643124432905e-06
          ],
          [
            0.0179797288207334,
            2.8457199796605437e-06,
            -2.6874368475593435e-06
          ],
          [
            0.009068654574132973,
            1.4282027183121215e-06,
            -1.3443400007084882e-06
          ],
          [
            5.551115123125783e-16,
            -2.7755575615628914e-15,
            -1.1657341758564144e-15
          ],
          [
            -0.009068654574129031,
            -1.4282027196443892e-06,
            1.3443400036505793e-06
          ],
          [
            -0.017979728820730678,
            -2.8457199807707667e-06,
            2.6874368497242784e-06
          ],
          [
            -0.02856438471870759,
            -4.249240958431599e-06,
            4.026643124044327e-06
          ],
          [
            -0.040485499067278385,
            -5.6396583537621225e-06,
            5.359659688619622e-06
          ],
          [
            -0.050941746143202904,
            -7.0164481613677054e-06,
            6.684394860956289e-06
          ],
          [
            -0.05763066143755602,
            -8.38390743007622e-06,
            8.003419430746561e-06
          ],
          [
            -0.05662209790027756,
            -9.74555777238928e-06,
            9.326663159781035e-06
          ],
          [
            -0.045329627732865474,
            -1.1104170821341075e-05,
            1.0662734621580405e-05
          ]
        ]
      },
      "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": "P-3",
        "spacegroup_number": 147,
        "pointgroup": "-3",
        "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": 3.0519549931218083e-15,
        "parent_symmetrization_rmsd_A": 0.26438444083380425,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -280.1841310192091,
        "reduced_polarization": [
          2.3610084866122187e-15,
          -1.897338345212931e-15,
          -3.7440006673460156e-16
        ],
        "cartesian_polarization_e_A2": [
          2.776882843015173e-17,
          -2.7142913076899118e-17,
          -5.146260751271209e-18
        ],
        "ranking_score": 0.26438444083381035
      }
    }
  ],
  "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": 39,
      "full_response": 7,
      "energy_polarization": 32
    },
    "model_evaluations_for_recovery_and_path_properties": {
      "total": 64,
      "full_response": 32,
      "energy_polarization": 32
    },
    "elapsed_seconds": 420.2054420739878
  }
}