{
  "schema": "ferrofinder.endpoint_parent_recovery.v4_variable_cell",
  "status": "complete",
  "input_atom_count": 36,
  "input_formula": "H12Cl4O20",
  "input_spacegroup": "Pna2_1",
  "input_pointgroup": "mm2",
  "input_is_polar_point_group": true,
  "input_energy_eV": -159.78332416305955,
  "input_cartesian_polarization_e_A2": [
    -3.2023801127078394e-17,
    6.390867036206534e-18,
    0.0032135990246438696
  ],
  "input_reduced_polarization": [
    -1.3418586882314678e-15,
    3.4346528915001677e-16,
    0.22781970261893789
  ],
  "input_formal_targets": [
    {
      "orbit_id": 0,
      "representative_formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ]
    },
    {
      "orbit_id": 1,
      "representative_formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.5
      ]
    },
    {
      "orbit_id": 2,
      "representative_formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        -0.5,
        0.0,
        0.0
      ]
    },
    {
      "orbit_id": 3,
      "representative_formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.0
      ]
    },
    {
      "orbit_id": 4,
      "representative_formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        -0.5,
        0.0,
        0.5
      ]
    },
    {
      "orbit_id": 5,
      "representative_formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.5
      ]
    },
    {
      "orbit_id": 6,
      "representative_formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        -0.5,
        0.5,
        0.0
      ]
    },
    {
      "orbit_id": 7,
      "representative_formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "target_reduced_polarization": [
        -0.5,
        0.5,
        0.5
      ]
    }
  ],
  "parent_candidates": [
    {
      "candidate_id": "inversion_parent_endpoint_00",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "Pnma",
      "spacegroup_number": 62,
      "pointgroup": "mmm",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 1.2043166082503844e-15,
      "parent_symmetrization_rmsd_A": 0.36029375334185326,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -157.25898096251393,
      "reduced_polarization": [
        1.5499777689441575e-16,
        -5.599977540489404e-17,
        1.1929870943225247e-15
      ],
      "cartesian_polarization_e_A2": [
        3.69906162693476e-18,
        -1.041989190685848e-18,
        1.682814137081092e-17
      ],
      "ranking_score": 0.36029375334185565
    },
    {
      "candidate_id": "bec_projection_00",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Pna2_1",
      "spacegroup_number": 33,
      "pointgroup": "mm2",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 2.577244886172839e-06,
      "parent_symmetrization_rmsd_A": 0.02342117015822679,
      "parent_cell_rmsd_A": 0.005167891182581915,
      "energy_eV": -159.2599665893464,
      "reduced_polarization": [
        5.207533458928931e-16,
        2.1780563988718646e-15,
        2.577244886172839e-06
      ],
      "cartesian_polarization_e_A2": [
        1.2437287155900642e-17,
        4.0508035820614936e-17,
        3.6361948298167385e-08
      ],
      "ranking_score": 0.5247182974436446
    },
    {
      "candidate_id": "inversion_parent_bec_00_00",
      "source": "same_species_inversion_center_projection_after_BEC",
      "spacegroup": "Pnma",
      "spacegroup_number": 62,
      "pointgroup": "mmm",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 3.66354473875763e-15,
      "parent_symmetrization_rmsd_A": 0.36031264421789083,
      "parent_cell_rmsd_A": 0.005167891182581915,
      "energy_eV": -157.17367746431214,
      "reduced_polarization": [
        1.092446236897477e-15,
        -2.7627397863324212e-15,
        -2.1436861116738018e-15
      ],
      "cartesian_polarization_e_A2": [
        2.6090510206931234e-17,
        -5.1381976825634216e-17,
        -3.024493480552961e-17
      ],
      "ranking_score": 0.3616046170135436
    },
    {
      "candidate_id": "bec_projection_01",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Pna2_1",
      "spacegroup_number": 33,
      "pointgroup": "mm2",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.5
      ],
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_residual": 5.719421104999345e-06,
      "parent_symmetrization_rmsd_A": 0.028217969172267522,
      "parent_cell_rmsd_A": 0.006230304165004902,
      "energy_eV": -159.16671523604026,
      "reduced_polarization": [
        1.0786743666396492e-15,
        1.4254812426159192e-15,
        0.499994280578895
      ],
      "cartesian_polarization_e_A2": [
        -4.85952134189163e-17,
        -3.819559468439295e-19,
        0.007051080558666531
      ],
      "ranking_score": 0.5297869840557288
    },
    {
      "candidate_id": "bec_projection_02",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Pc",
      "spacegroup_number": 7,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        -0.5,
        0.0,
        0.0
      ],
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_residual": 1.992153292145028e-05,
      "parent_symmetrization_rmsd_A": 0.1170153997786924,
      "parent_cell_rmsd_A": 0.040163992195526826,
      "energy_eV": -144.43288213552438,
      "reduced_polarization": [
        -0.5000000085136473,
        2.5354731810299498e-15,
        -1.9921531102258087e-05
      ],
      "cartesian_polarization_e_A2": [
        -0.011940628727133888,
        8.591245733294714e-17,
        -7.260470612765941e-05
      ],
      "ranking_score": 0.627096240893417
    },
    {
      "candidate_id": "bec_projection_03",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Pc",
      "spacegroup_number": 7,
      "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": 6.027968707447811e-05,
      "parent_symmetrization_rmsd_A": 0.08148091521837529,
      "parent_cell_rmsd_A": 0.008535396245682319,
      "energy_eV": -153.76663401895001,
      "reduced_polarization": [
        2.8305567610212925e-16,
        0.4999509976855128,
        3.51057523590741e-05
      ],
      "cartesian_polarization_e_A2": [
        8.250955443423616e-17,
        0.009298283784102657,
        1.2969729414895116e-05
      ],
      "ranking_score": 0.5837353236539449
    },
    {
      "candidate_id": "bec_projection_04",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Pc",
      "spacegroup_number": 7,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        -0.5,
        0.0,
        0.5
      ],
      "formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_residual": 2.2521911019397436e-05,
      "parent_symmetrization_rmsd_A": 0.1232599957187359,
      "parent_cell_rmsd_A": 0.043482714542191686,
      "energy_eV": -145.1482097548304,
      "reduced_polarization": [
        -0.5000114766915381,
        1.034706294506631e-15,
        0.4999806216092695
      ],
      "cartesian_polarization_e_A2": [
        -0.011869081055683527,
        6.72714684855964e-16,
        0.0069733023215379835
      ],
      "ranking_score": 0.6341757181763226
    },
    {
      "candidate_id": "bec_projection_05",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Pc",
      "spacegroup_number": 7,
      "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": 0.00011825610175650038,
      "parent_symmetrization_rmsd_A": 0.09160151605030402,
      "parent_cell_rmsd_A": 0.01237193501560081,
      "energy_eV": -152.97603631874944,
      "reduced_polarization": [
        9.079615844684817e-16,
        0.49990876659473726,
        0.49992476057305635
      ],
      "cartesian_polarization_e_A2": [
        -3.863758282437963e-16,
        0.00932068461491235,
        0.00706311568476855
      ],
      "ranking_score": 0.5949310120077173
    },
    {
      "candidate_id": "bec_projection_06",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        -0.5,
        0.5,
        0.0
      ],
      "formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_residual": 0.0001488865538243346,
      "parent_symmetrization_rmsd_A": 0.15762901993555603,
      "parent_cell_rmsd_A": 0.04867010727093897,
      "energy_eV": -134.27126825087618,
      "reduced_polarization": [
        -0.5001196126990495,
        0.5000882694479928,
        -8.27723908288187e-06
      ],
      "cartesian_polarization_e_A2": [
        -0.011942963108419049,
        0.009301411009416553,
        -6.685587311744202e-05
      ],
      "ranking_score": 0.6700943198609395
    },
    {
      "candidate_id": "bec_projection_07",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        -0.5,
        0.5,
        0.5
      ],
      "formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "target_residual": 1.2276389391569019e-06,
      "parent_symmetrization_rmsd_A": 0.17423751147786398,
      "parent_cell_rmsd_A": 0.0577867693620745,
      "energy_eV": -130.92706332486182,
      "reduced_polarization": [
        -0.5000006313993071,
        0.5000000313031545,
        0.49999894764436026
      ],
      "cartesian_polarization_e_A2": [
        -0.011846742387809594,
        0.009335859141884407,
        0.006974826575898252
      ],
      "ranking_score": 0.6886866590962609
    }
  ],
  "formal_branches": [
    {
      "orbit_id": 0,
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.0,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -1.3418586882314678e-15,
              3.4346528915001677e-16,
              0.22781970261893789
            ],
            "branch_aligned_reduced_polarization": [
              -1.3418586882314678e-15,
              3.4346528915001677e-16,
              0.22781970261893789
            ],
            "target_residual": 0.22781970261893789,
            "energy_eV": -159.78332416305955,
            "max_atomic_step_A": 0.04313509080129096,
            "max_log_strain_component": 0.0006958665367491622,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.3914466120456609,
            "cell_principal_stretches": [
              1.0004894518480643,
              0.9999781705035298,
              0.9993043755222193
            ],
            "cell_volume_ratio": 0.9997716619072041,
            "cell_rmsd_from_input_A": 0.005090965713165462
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              1.1868705833416751e-15,
              -3.108330620105991e-15,
              0.0031773818926434804
            ],
            "branch_aligned_reduced_polarization": [
              1.1868705833416751e-15,
              -3.108330620105991e-15,
              0.0031773818926434804
            ],
            "target_residual": 0.0031773818926434804,
            "energy_eV": -159.27343904853294,
            "max_atomic_step_A": 0.0006238286982305802,
            "max_log_strain_component": 1.0514855779303644e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.3914466120456609,
            "cell_principal_stretches": [
              1.000496849522235,
              0.9999778406536924,
              0.9992938680360733
            ],
            "cell_volume_ratio": 0.9997682120160086,
            "cell_rmsd_from_input_A": 0.005167891182581915
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              5.207533458928931e-16,
              2.1780563988718646e-15,
              2.577244886172839e-06
            ],
            "branch_aligned_reduced_polarization": [
              5.207533458928931e-16,
              2.1780563988718646e-15,
              2.577244886172839e-06
            ],
            "target_residual": 2.577244886172839e-06,
            "energy_eV": -159.2599665893464
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "inversion_parent_endpoint_00",
        "source": "same_species_inversion_center_projection_from_endpoint",
        "spacegroup": "Pnma",
        "spacegroup_number": 62,
        "pointgroup": "mmm",
        "has_inversion": true,
        "is_polar_point_group": false,
        "nonpolar_parent_hypothesis": true,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.0
        ],
        "formal_class": [
          0.0,
          0.0,
          0.0
        ],
        "target_residual": 1.2043166082503844e-15,
        "parent_symmetrization_rmsd_A": 0.36029375334185326,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -157.25898096251393,
        "reduced_polarization": [
          1.5499777689441575e-16,
          -5.599977540489404e-17,
          1.1929870943225247e-15
        ],
        "cartesian_polarization_e_A2": [
          3.69906162693476e-18,
          -1.041989190685848e-18,
          1.682814137081092e-17
        ],
        "ranking_score": 0.36029375334185565
      },
      "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": [
          -159.7833241630595,
          -159.75772054966373,
          -159.5180436829251,
          -159.1172840454729,
          -158.62092937203914,
          -158.10969387171673,
          -157.66705307876842,
          -157.36600556578026,
          -157.258980962514
        ],
        "cartesian_polarizations_e_A2": [
          [
            -5.843822711096465e-17,
            6.564531901320842e-18,
            0.00321359902464387
          ],
          [
            9.690499473378387e-18,
            -4.001238492233656e-17,
            0.002897620314695384
          ],
          [
            7.988583795258168e-18,
            -1.7053889754225045e-17,
            0.0024735290826691514
          ],
          [
            -8.162248660372476e-18,
            -2.410468327786595e-17,
            0.002041709232171087
          ],
          [
            3.1780670315918366e-18,
            -6.94659460457232e-19,
            0.0016285121700310697
          ],
          [
            7.293924334800936e-18,
            -2.1847040031379947e-17,
            0.0012233308723525735
          ],
          [
            -1.931153300071105e-17,
            -1.5074110291921935e-17,
            0.000818046655625706
          ],
          [
            -1.5977167590516335e-18,
            2.2229102734631426e-18,
            0.0004106826821644775
          ],
          [
            1.1896043260330098e-17,
            1.3545859478916024e-18,
            9.059192994909209e-18
          ]
        ],
        "raw_reduced_polarization": [
          [
            -2.4486737992944086e-15,
            3.527985850508324e-16,
            0.22781970261893794
          ],
          [
            4.0605051411776525e-16,
            -2.150391375547931e-15,
            0.20541921793421372
          ],
          [
            3.3473698296446596e-16,
            -9.16529657460099e-16,
            0.1753543785990629
          ],
          [
            -3.420138738984761e-16,
            -1.2954614710332154e-15,
            0.14474163905968448
          ],
          [
            1.3316710409238539e-16,
            -3.7333183603262696e-17,
            0.11544911342164552
          ],
          [
            3.0562941922842546e-16,
            -1.1741286243226117e-15,
            0.08672484445218381
          ],
          [
            -8.091902718619264e-16,
            -8.101300841908005e-16,
            0.05799327930581452
          ],
          [
            -6.694739659289319e-17,
            1.1946618753044063e-16,
            0.02911427524217261
          ],
          [
            4.984670289796938e-16,
            7.279970802636226e-17,
            6.422278069668316e-16
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -2.4486737992944086e-15,
            3.527985850508324e-16,
            0.22781970261893794
          ],
          [
            4.0605051411776505e-16,
            -2.1503913755479305e-15,
            0.20541921793421372
          ],
          [
            3.3473698296446596e-16,
            -9.16529657460099e-16,
            0.1753543785990629
          ],
          [
            -3.4201387389847605e-16,
            -1.2954614710332154e-15,
            0.14474163905968448
          ],
          [
            1.3316710409238534e-16,
            -3.7333183603262776e-17,
            0.11544911342164552
          ],
          [
            3.0562941922842546e-16,
            -1.1741286243226117e-15,
            0.08672484445218381
          ],
          [
            -8.091902718619263e-16,
            -8.101300841908005e-16,
            0.05799327930581452
          ],
          [
            -6.694739659289319e-17,
            1.194661875304406e-16,
            0.02911427524217261
          ],
          [
            4.984670289796938e-16,
            7.279970802636226e-17,
            6.418476861114186e-16
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            -2.4424906541753444e-15,
            3.3306690738754696e-16,
            0.2278197026189379
          ],
          [
            4.440892098500626e-16,
            -2.1649348980190553e-15,
            0.2054192179342137
          ],
          [
            3.3306690738754696e-16,
            -9.43689570931383e-16,
            0.1753543785990629
          ],
          [
            -3.3306690738754696e-16,
            -1.27675647831893e-15,
            0.1447416390596845
          ],
          [
            1.1102230246251565e-16,
            -5.551115123125783e-17,
            0.11544911342164554
          ],
          [
            3.3306690738754696e-16,
            -1.1657341758564144e-15,
            0.08672484445218376
          ],
          [
            -8.326672684688674e-16,
            -8.326672684688674e-16,
            0.05799327930581455
          ],
          [
            -5.551115123125783e-17,
            1.1102230246251565e-16,
            0.029114275242172583
          ],
          [
            4.440892098500626e-16,
            1.1102230246251565e-16,
            6.661338147750939e-16
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -157.258980962514,
          -157.36600556578026,
          -157.66705307876845,
          -158.10969387171676,
          -158.62092937203917,
          -159.11728404547287,
          -159.5180436829251,
          -159.75772054966367,
          -159.7833241630595
        ],
        "cartesian_polarizations_e_A2": [
          [
            1.1896043260330098e-17,
            1.3545859478916024e-18,
            9.059192994909209e-18
          ],
          [
            2.849840436525794e-17,
            -3.5636030321456004e-17,
            -0.00041068268216446933
          ],
          [
            1.630713083423352e-17,
            2.5077206522506077e-17,
            -0.0008180466556257182
          ],
          [
            -3.2805293020092784e-17,
            -8.370646498509646e-18,
            -0.0012233308723525987
          ],
          [
            -1.0089928663141294e-17,
            -1.2816467045435931e-17,
            -0.001628512170031126
          ],
          [
            3.47329730228616e-18,
            -1.8095878944910893e-17,
            -0.0020417092321711365
          ],
          [
            -5.640634818912724e-17,
            2.2854296249042934e-17,
            -0.0024735290826691896
          ],
          [
            7.207091902243782e-18,
            1.455311569657901e-17,
            -0.0028976203146953415
          ],
          [
            8.075416227815322e-18,
            -7.703773416470703e-17,
            -0.00321359902464388
          ]
        ],
        "raw_reduced_polarization": [
          [
            4.984670289796938e-16,
            7.279970802636226e-17,
            6.422278069668316e-16
          ],
          [
            1.1941378022710622e-15,
            -1.9151923188473762e-15,
            -0.02911427524217203
          ],
          [
            6.833000587035512e-16,
            1.3477279280777833e-15,
            -0.05799327930581538
          ],
          [
            -1.3746046974345137e-15,
            -4.498648624193155e-16,
            -0.08672484445218559
          ],
          [
            -4.227873632659885e-16,
            -6.887972374801967e-16,
            -0.11544911342164953
          ],
          [
            1.455378186802026e-16,
            -9.72529432864993e-16,
            -0.144741639059688
          ],
          [
            -2.36353417536649e-15,
            1.2282617405473427e-15,
            -0.1753543785990656
          ],
          [
            3.0199097376142036e-16,
            7.8213019648835345e-16,
            -0.2054192179342107
          ],
          [
            3.38375428431471e-16,
            -4.140250061601833e-15,
            -0.22781970261893864
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            4.984670289796938e-16,
            7.279970802636226e-17,
            6.422278069668316e-16
          ],
          [
            1.1941378022710622e-15,
            -1.9151923188473762e-15,
            -0.02911427524217203
          ],
          [
            6.833000587035512e-16,
            1.3477279280777833e-15,
            -0.05799327930581538
          ],
          [
            -1.3746046974345137e-15,
            -4.498648624193154e-16,
            -0.08672484445218559
          ],
          [
            -4.2278736326598847e-16,
            -6.887972374801967e-16,
            -0.11544911342164953
          ],
          [
            1.4553781868020257e-16,
            -9.72529432864993e-16,
            -0.144741639059688
          ],
          [
            -2.36353417536649e-15,
            1.228261740547343e-15,
            -0.1753543785990656
          ],
          [
            3.0199097376142036e-16,
            7.8213019648835345e-16,
            -0.2054192179342107
          ],
          [
            3.38375428431471e-16,
            -4.140250061601833e-15,
            -0.22781970261893864
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          3.4456078572537965e-15,
          -2.071991689981079e-16,
          -0.22781970261893664
        ],
        "actual_opposite_endpoint_branch_residual": 5.396053282095852e-15
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            -2.4486737992944086e-15,
            3.527985850508324e-16,
            0.22781970261893794
          ],
          [
            4.0605051411776525e-16,
            -2.150391375547931e-15,
            0.20541921793421372
          ],
          [
            3.3473698296446596e-16,
            -9.16529657460099e-16,
            0.1753543785990629
          ],
          [
            -3.420138738984761e-16,
            -1.2954614710332154e-15,
            0.14474163905968448
          ],
          [
            1.3316710409238539e-16,
            -3.7333183603262696e-17,
            0.11544911342164552
          ],
          [
            3.0562941922842546e-16,
            -1.1741286243226117e-15,
            0.08672484445218381
          ],
          [
            -8.091902718619264e-16,
            -8.101300841908005e-16,
            0.05799327930581452
          ],
          [
            -6.694739659289319e-17,
            1.1946618753044063e-16,
            0.02911427524217261
          ],
          [
            4.984670289796938e-16,
            7.279970802636226e-17,
            6.422278069668316e-16
          ],
          [
            1.1941378022710622e-15,
            -1.9151923188473762e-15,
            -0.02911427524217203
          ],
          [
            6.833000587035512e-16,
            1.3477279280777833e-15,
            -0.05799327930581538
          ],
          [
            -1.3746046974345137e-15,
            -4.498648624193155e-16,
            -0.08672484445218559
          ],
          [
            -4.227873632659885e-16,
            -6.887972374801967e-16,
            -0.11544911342164953
          ],
          [
            1.455378186802026e-16,
            -9.72529432864993e-16,
            -0.144741639059688
          ],
          [
            -2.36353417536649e-15,
            1.2282617405473427e-15,
            -0.1753543785990656
          ],
          [
            3.0199097376142036e-16,
            7.8213019648835345e-16,
            -0.2054192179342107
          ],
          [
            3.38375428431471e-16,
            -4.140250061601833e-15,
            -0.22781970261893864
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -2.4486737992944086e-15,
            3.527985850508324e-16,
            0.22781970261893794
          ],
          [
            4.0605051411776505e-16,
            -2.1503913755479305e-15,
            0.20541921793421372
          ],
          [
            3.3473698296446596e-16,
            -9.16529657460099e-16,
            0.1753543785990629
          ],
          [
            -3.4201387389847605e-16,
            -1.2954614710332154e-15,
            0.14474163905968448
          ],
          [
            1.3316710409238534e-16,
            -3.7333183603262776e-17,
            0.11544911342164552
          ],
          [
            3.0562941922842546e-16,
            -1.1741286243226117e-15,
            0.08672484445218381
          ],
          [
            -8.091902718619263e-16,
            -8.101300841908005e-16,
            0.05799327930581452
          ],
          [
            -6.694739659289319e-17,
            1.194661875304406e-16,
            0.02911427524217261
          ],
          [
            4.984670289796938e-16,
            7.279970802636226e-17,
            6.418476861114186e-16
          ],
          [
            1.1941378022710622e-15,
            -1.9151923188473762e-15,
            -0.02911427524217203
          ],
          [
            6.833000587035512e-16,
            1.3477279280777833e-15,
            -0.05799327930581538
          ],
          [
            -1.3746046974345137e-15,
            -4.498648624193154e-16,
            -0.08672484445218559
          ],
          [
            -4.2278736326598847e-16,
            -6.887972374801967e-16,
            -0.11544911342164953
          ],
          [
            1.4553781868020257e-16,
            -9.72529432864993e-16,
            -0.144741639059688
          ],
          [
            -2.36353417536649e-15,
            1.228261740547343e-15,
            -0.1753543785990656
          ],
          [
            3.0199097376142036e-16,
            7.8213019648835345e-16,
            -0.2054192179342107
          ],
          [
            3.38375428431471e-16,
            -4.140250061601833e-15,
            -0.22781970261893864
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            -2.4424906541753444e-15,
            3.3306690738754696e-16,
            0.2278197026189379
          ],
          [
            4.440892098500626e-16,
            -2.1649348980190553e-15,
            0.2054192179342137
          ],
          [
            3.3306690738754696e-16,
            -9.43689570931383e-16,
            0.1753543785990629
          ],
          [
            -3.3306690738754696e-16,
            -1.27675647831893e-15,
            0.1447416390596845
          ],
          [
            1.1102230246251565e-16,
            -5.551115123125783e-17,
            0.11544911342164554
          ],
          [
            3.3306690738754696e-16,
            -1.1657341758564144e-15,
            0.08672484445218376
          ],
          [
            -8.326672684688674e-16,
            -8.326672684688674e-16,
            0.05799327930581455
          ],
          [
            -5.551115123125783e-17,
            1.1102230246251565e-16,
            0.029114275242172583
          ],
          [
            4.440892098500626e-16,
            1.1102230246251565e-16,
            6.661338147750939e-16
          ],
          [
            1.2212453270876722e-15,
            -1.942890293094024e-15,
            -0.029114275242172027
          ],
          [
            6.661338147750939e-16,
            1.3322676295501878e-15,
            -0.05799327930581538
          ],
          [
            -1.3877787807814457e-15,
            -4.440892098500626e-16,
            -0.08672484445218559
          ],
          [
            -4.440892098500626e-16,
            -6.661338147750939e-16,
            -0.11544911342164954
          ],
          [
            1.1102230246251565e-16,
            -9.992007221626409e-16,
            -0.144741639059688
          ],
          [
            -2.3869795029440866e-15,
            1.2212453270876722e-15,
            -0.1753543785990656
          ],
          [
            3.3306690738754696e-16,
            7.771561172376096e-16,
            -0.2054192179342107
          ],
          [
            3.3306690738754696e-16,
            -4.163336342344337e-15,
            -0.22781970261893864
          ]
        ]
      },
      "incoming_structure_ids": [
        "incoming_00_000",
        "incoming_00_001",
        "incoming_00_002",
        "incoming_00_003",
        "incoming_00_004",
        "incoming_00_005",
        "incoming_00_006",
        "incoming_00_007",
        "incoming_00_008"
      ],
      "reflected_structure_ids": [
        "reflected_00_001",
        "reflected_00_002",
        "reflected_00_003",
        "reflected_00_004",
        "reflected_00_005",
        "reflected_00_006",
        "reflected_00_007",
        "reflected_00_008"
      ]
    },
    {
      "orbit_id": 1,
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.0,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -1.3418586882314678e-15,
              3.4346528915001677e-16,
              0.22781970261893789
            ],
            "branch_aligned_reduced_polarization": [
              -1.3418586882314678e-15,
              3.4346528915001677e-16,
              0.2278197026189379
            ],
            "target_residual": 0.2721802973810621,
            "energy_eV": -159.78332416305955,
            "max_atomic_step_A": 0.05153426901575865,
            "max_log_strain_component": 0.000831364270660638,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.3914466120456609,
            "cell_principal_stretches": [
              1.0008317099497244,
              1.0000260807169212,
              0.9994155569833737
            ],
            "cell_volume_ratio": 1.0002728679991688,
            "cell_rmsd_from_input_A": 0.006082503775016625
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -2.925260740810744e-16,
              -1.678892909190492e-15,
              0.494128493434324
            ],
            "branch_aligned_reduced_polarization": [
              -2.925260740810744e-16,
              -1.678892909190492e-15,
              0.494128493434324
            ],
            "target_residual": 0.005871506565675977,
            "energy_eV": -159.19703267822257,
            "max_atomic_step_A": 0.001139410607662086,
            "max_log_strain_component": 2.020108523007088e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.3914466120456609,
            "cell_principal_stretches": [
              1.0008519280406114,
              1.0000267144533486,
              0.9994013600193905
            ],
            "cell_volume_ratio": 1.0002794992679922,
            "cell_rmsd_from_input_A": 0.006230304165004902
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              1.0786743666396492e-15,
              1.4254812426159192e-15,
              0.499994280578895
            ],
            "branch_aligned_reduced_polarization": [
              1.0786743666396492e-15,
              1.4254812426159192e-15,
              0.499994280578895
            ],
            "target_residual": 5.719421104999345e-06,
            "energy_eV": -159.16671523604026
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_01",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Pna2_1",
        "spacegroup_number": 33,
        "pointgroup": "mm2",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.5
        ],
        "formal_class": [
          0.0,
          0.0,
          0.5
        ],
        "target_residual": 5.719421104999345e-06,
        "parent_symmetrization_rmsd_A": 0.028217969172267522,
        "parent_cell_rmsd_A": 0.006230304165004902,
        "energy_eV": -159.16671523604026,
        "reduced_polarization": [
          1.0786743666396492e-15,
          1.4254812426159192e-15,
          0.499994280578895
        ],
        "cartesian_polarization_e_A2": [
          -4.85952134189163e-17,
          -3.819559468439295e-19,
          0.007051080558666531
        ],
        "ranking_score": 0.5297869840557288
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 2,
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.0,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        -0.5,
        0.0,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -1.3418586882314678e-15,
              3.4346528915001677e-16,
              0.22781970261893789
            ],
            "branch_aligned_reduced_polarization": [
              -1.3322676295501878e-15,
              3.4346528915001677e-16,
              0.22781970261893789
            ],
            "target_residual": 0.5494559280792045,
            "energy_eV": -159.78332416305955,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.0024241111323537816,
            "step_scale": 0.6478153062867911,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.3914466120456609,
            "cell_principal_stretches": [
              1.0025845205515247,
              0.9995493085982403,
              0.9977242621964283
            ],
            "cell_volume_ratio": 0.9998520731401679,
            "cell_rmsd_from_input_A": 0.01629689469674629
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.287997226573934,
              1.96123215036262e-15,
              0.06506210871211386
            ],
            "branch_aligned_reduced_polarization": [
              -0.287997226573934,
              1.96123215036262e-15,
              0.06506210871211386
            ],
            "target_residual": 0.22176170528387176,
            "energy_eV": -155.928686308328,
            "max_atomic_step_A": 0.09581411724120216,
            "max_log_strain_component": 0.002775686699677784,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.3914466120456609,
            "cell_principal_stretches": [
              1.0054552124067533,
              0.999302793909968,
              0.995040518096669
            ],
            "cell_volume_ratio": 0.999771142622784,
            "cell_rmsd_from_input_A": 0.03462726068588612
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.4654757286367049,
              -6.951885059361101e-15,
              -0.015350782413030666
            ],
            "branch_aligned_reduced_polarization": [
              -0.4654757286367049,
              -6.951885059361101e-15,
              -0.015350782413030666
            ],
            "target_residual": 0.03778322159184749,
            "energy_eV": -146.25635974902133,
            "max_atomic_step_A": 0.018208226883021254,
            "max_log_strain_component": 0.0008340067641564777,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.3914466120456609,
            "cell_principal_stretches": [
              1.0062729445990992,
              0.9993602472015204,
              0.9941935127649528
            ],
            "cell_volume_ratio": 0.9997900056776381,
            "cell_rmsd_from_input_A": 0.04001414439618516
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -0.4991345624661174,
              2.390538301919956e-16,
              -0.0020640808106172936
            ],
            "branch_aligned_reduced_polarization": [
              -0.4991345624661174,
              2.390538301919956e-16,
              -0.0020640808106172936
            ],
            "target_residual": 0.002238171512152564,
            "energy_eV": -144.46500971749245,
            "max_atomic_step_A": 0.0006680960078163022,
            "max_log_strain_component": 2.4026541519483758e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.3914466120456609,
            "cell_principal_stretches": [
              1.0062942785619358,
              0.9993682625070187,
              0.994167078430569
            ],
            "cell_volume_ratio": 0.9997926372034572,
            "cell_rmsd_from_input_A": 0.040163992195526826
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              -0.5000000085136473,
              2.5354731810299498e-15,
              -1.9921531102258087e-05
            ],
            "branch_aligned_reduced_polarization": [
              -0.5000000085136473,
              2.5354731810299498e-15,
              -1.9921531102258087e-05
            ],
            "target_residual": 1.992153292145028e-05,
            "energy_eV": -144.43288213552438
          }
        ],
        "iterations": 4
      },
      "parent": {
        "candidate_id": "bec_projection_02",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Pc",
        "spacegroup_number": 7,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          -0.5,
          0.0,
          0.0
        ],
        "formal_class": [
          0.5,
          0.0,
          0.0
        ],
        "target_residual": 1.992153292145028e-05,
        "parent_symmetrization_rmsd_A": 0.1170153997786924,
        "parent_cell_rmsd_A": 0.040163992195526826,
        "energy_eV": -144.43288213552438,
        "reduced_polarization": [
          -0.5000000085136473,
          2.5354731810299498e-15,
          -1.9921531102258087e-05
        ],
        "cartesian_polarization_e_A2": [
          -0.011940628727133888,
          8.591245733294714e-17,
          -7.260470612765941e-05
        ],
        "ranking_score": 0.627096240893417
      },
      "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
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -1.3418586882314678e-15,
              3.4346528915001677e-16,
              0.22781970261893789
            ],
            "branch_aligned_reduced_polarization": [
              -1.3418586882314678e-15,
              3.3306690738754696e-16,
              0.22781970261893789
            ],
            "target_residual": 0.5494559280792054,
            "energy_eV": -159.78332416305955,
            "max_atomic_step_A": 0.12000000000000001,
            "max_log_strain_component": 0.0009495915161668493,
            "step_scale": 0.8459127689294081,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.3914466120456609,
            "cell_principal_stretches": [
              1.000688145660983,
              1.0004140179581484,
              0.9987058207356526
            ],
            "cell_volume_ratio": 0.9998068424934261,
            "cell_rmsd_from_input_A": 0.006497407418489314
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              2.6183573984730756e-15,
              0.3934495599571231,
              0.029018412141146994
            ],
            "branch_aligned_reduced_polarization": [
              2.6183573984730756e-15,
              0.3934495599571231,
              0.029018412141146994
            ],
            "target_residual": 0.11043126602789706,
            "energy_eV": -156.2949047583886,
            "max_atomic_step_A": 0.034013858098636066,
            "max_log_strain_component": 0.00036308376414404675,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.3914466120456609,
            "cell_principal_stretches": [
              1.0010013102899766,
              1.0004816213922485,
              0.9982944297980058
            ],
            "cell_volume_ratio": 0.9997753136660829,
            "cell_rmsd_from_input_A": 0.008385140327921604
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              1.0861877388669202e-15,
              0.4935056481480977,
              0.0018981690819693075
            ],
            "branch_aligned_reduced_polarization": [
              1.0861877388669202e-15,
              0.4935056481480977,
              0.0018981690819693075
            ],
            "target_residual": 0.006766066201276099,
            "energy_eV": -153.94870795440073,
            "max_atomic_step_A": 0.00234090587817583,
            "max_log_strain_component": 2.852388523837678e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.3914466120456609,
            "cell_principal_stretches": [
              1.0010259916675701,
              1.0004869421485085,
              0.9982620291977402
            ],
            "cell_volume_ratio": 0.9997728323093199,
            "cell_rmsd_from_input_A": 0.008535396245682319
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              2.8305567610212925e-16,
              0.4999509976855128,
              3.51057523590741e-05
            ],
            "branch_aligned_reduced_polarization": [
              2.8305567610212925e-16,
              0.4999509976855128,
              3.51057523590741e-05
            ],
            "target_residual": 6.027968707447811e-05,
            "energy_eV": -153.76663401895001
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_03",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Pc",
        "spacegroup_number": 7,
        "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": 6.027968707447811e-05,
        "parent_symmetrization_rmsd_A": 0.08148091521837529,
        "parent_cell_rmsd_A": 0.008535396245682319,
        "energy_eV": -153.76663401895001,
        "reduced_polarization": [
          2.8305567610212925e-16,
          0.4999509976855128,
          3.51057523590741e-05
        ],
        "cartesian_polarization_e_A2": [
          8.250955443423616e-17,
          0.009298283784102657,
          1.2969729414895116e-05
        ],
        "ranking_score": 0.5837353236539449
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 4,
      "formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.0,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        -0.5,
        0.0,
        0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -1.3418586882314678e-15,
              3.4346528915001677e-16,
              0.22781970261893789
            ],
            "branch_aligned_reduced_polarization": [
              -1.3322676295501878e-15,
              3.4346528915001677e-16,
              0.2278197026189379
            ],
            "target_residual": 0.5692821043054507,
            "energy_eV": -159.78332416305955,
            "max_atomic_step_A": 0.12000000000000001,
            "max_log_strain_component": 0.002392578211435216,
            "step_scale": 0.6393885025225099,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.3914466120456609,
            "cell_principal_stretches": [
              1.002224441103803,
              1.0005317060616337,
              0.997424232405414
            ],
            "cell_volume_ratio": 1.0001744600786293,
            "cell_rmsd_from_input_A": 0.01619996194490575
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.2894963547467061,
              -4.59355925982953e-16,
              0.3680539992469307
            ],
            "branch_aligned_reduced_polarization": [
              -0.2894963547467061,
              -4.59355925982953e-16,
              0.3680539992469307
            ],
            "target_residual": 0.24843818502728915,
            "energy_eV": -156.39049657945844,
            "max_atomic_step_A": 0.10533021280656292,
            "max_log_strain_component": 0.0027738033503490224,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.3914466120456609,
            "cell_principal_stretches": [
              1.0047964235068518,
              1.0011911729624479,
              0.9944308217062912
            ],
            "cell_volume_ratio": 1.000390753734524,
            "cell_rmsd_from_input_A": 0.035022159441438966
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.46307030440625263,
              -1.7318663225488902e-15,
              0.4513657706031658
            ],
            "branch_aligned_reduced_polarization": [
              -0.46307030440625263,
              -1.7318663225488902e-15,
              0.4513657706031658
            ],
            "target_residual": 0.06106628108597032,
            "energy_eV": -147.81009399340994,
            "max_atomic_step_A": 0.027372827150653152,
            "max_log_strain_component": 0.001196541947993175,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.3914466120456609,
            "cell_principal_stretches": [
              1.005889943106921,
              1.0015347217389263,
              0.993120827297326
            ],
            "cell_volume_ratio": 1.0005033938314103,
            "cell_rmsd_from_input_A": 0.04323623386494848
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -0.49901495121317707,
              -2.210591574777384e-15,
              0.4987091244604455
            ],
            "branch_aligned_reduced_polarization": [
              -0.49901495121317707,
              -2.210591574777384e-15,
              0.4987091244604455
            ],
            "target_residual": 0.001623785937567325,
            "energy_eV": -145.2253396654698,
            "max_atomic_step_A": 0.0007812257905735493,
            "max_log_strain_component": 3.597697113021521e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.3914466120456609,
            "cell_principal_stretches": [
              1.005922914675963,
              1.0015448150357207,
              0.993081551635944
            ],
            "cell_volume_ratio": 1.000506702750396,
            "cell_rmsd_from_input_A": 0.043482714542191686
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              -0.5000114766915381,
              1.034706294506631e-15,
              0.4999806216092695
            ],
            "branch_aligned_reduced_polarization": [
              -0.5000114766915381,
              1.034706294506631e-15,
              0.4999806216092695
            ],
            "target_residual": 2.2521911019397436e-05,
            "energy_eV": -145.1482097548304
          }
        ],
        "iterations": 4
      },
      "parent": {
        "candidate_id": "bec_projection_04",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Pc",
        "spacegroup_number": 7,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          -0.5,
          0.0,
          0.5
        ],
        "formal_class": [
          0.5,
          0.0,
          0.5
        ],
        "target_residual": 2.2521911019397436e-05,
        "parent_symmetrization_rmsd_A": 0.1232599957187359,
        "parent_cell_rmsd_A": 0.043482714542191686,
        "energy_eV": -145.1482097548304,
        "reduced_polarization": [
          -0.5000114766915381,
          1.034706294506631e-15,
          0.4999806216092695
        ],
        "cartesian_polarization_e_A2": [
          -0.011869081055683527,
          6.72714684855964e-16,
          0.0069733023215379835
        ],
        "ranking_score": 0.6341757181763226
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 5,
      "formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.5,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -1.3418586882314678e-15,
              3.4346528915001677e-16,
              0.22781970261893789
            ],
            "branch_aligned_reduced_polarization": [
              -1.3418586882314678e-15,
              3.3306690738754696e-16,
              0.2278197026189379
            ],
            "target_residual": 0.5692821043054516,
            "energy_eV": -159.78332416305955,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.0009289360779354066,
            "step_scale": 0.8275125424683025,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.3914466120456609,
            "cell_principal_stretches": [
              1.0013425568265737,
              0.9995163416904711,
              0.9993680895368654
            ],
            "cell_volume_ratio": 1.0002257963785097,
            "cell_rmsd_from_input_A": 0.006935183028436477
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              4.576182098170447e-15,
              0.37259754788685145,
              0.40439405638317844
            ],
            "branch_aligned_reduced_polarization": [
              4.576182098170447e-15,
              0.37259754788685145,
              0.40439405638317844
            ],
            "target_residual": 0.1592855337414731,
            "energy_eV": -156.75677420661566,
            "max_atomic_step_A": 0.05116482622251222,
            "max_log_strain_component": 0.0005660900645475223,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.3914466120456609,
            "cell_principal_stretches": [
              1.002218130491449,
              0.999118539882325,
              0.9990781459337602
            ],
            "cell_volume_ratio": 1.0004116307013537,
            "cell_rmsd_from_input_A": 0.011811317321493707
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              3.554370138426737e-15,
              0.4901800132998225,
              0.49120362621040126
            ],
            "branch_aligned_reduced_polarization": [
              3.554370138426737e-15,
              0.4901800132998225,
              0.49120362621040126
            ],
            "target_residual": 0.013183638748008921,
            "energy_eV": -153.36111470118132,
            "max_atomic_step_A": 0.004670519855944811,
            "max_log_strain_component": 6.609601416006399e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.3914466120456609,
            "cell_principal_stretches": [
              1.0023172746682565,
              0.9990721033314315,
              0.99904742438165
            ],
            "cell_volume_ratio": 1.0004333307505067,
            "cell_rmsd_from_input_A": 0.01237193501560081
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              9.079615844684817e-16,
              0.49990876659473726,
              0.49992476057305635
            ],
            "branch_aligned_reduced_polarization": [
              9.079615844684817e-16,
              0.49990876659473726,
              0.49992476057305635
            ],
            "target_residual": 0.00011825610175650038,
            "energy_eV": -152.97603631874944
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_05",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Pc",
        "spacegroup_number": 7,
        "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": 0.00011825610175650038,
        "parent_symmetrization_rmsd_A": 0.09160151605030402,
        "parent_cell_rmsd_A": 0.01237193501560081,
        "energy_eV": -152.97603631874944,
        "reduced_polarization": [
          9.079615844684817e-16,
          0.49990876659473726,
          0.49992476057305635
        ],
        "cartesian_polarization_e_A2": [
          -3.863758282437963e-16,
          0.00932068461491235,
          0.00706311568476855
        ],
        "ranking_score": 0.5949310120077173
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 6,
      "formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.5,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        -0.5,
        0.5,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -1.3418586882314678e-15,
              3.4346528915001677e-16,
              0.22781970261893789
            ],
            "branch_aligned_reduced_polarization": [
              -1.3322676295501878e-15,
              3.3306690738754696e-16,
              0.22781970261893789
            ],
            "target_residual": 0.7429009468976194,
            "energy_eV": -159.78332416305955,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.0019598339416639706,
            "step_scale": 0.5237426651988464,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.3914466120456609,
            "cell_principal_stretches": [
              1.0021543409492426,
              0.9996890133704763,
              0.9980413279612189
            ],
            "cell_volume_ratio": 0.9998804030953979,
            "cell_rmsd_from_input_A": 0.01351407061807093
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.23212480278706912,
              0.23983420705939457,
              0.09287185959368885
            ],
            "branch_aligned_reduced_polarization": [
              -0.23212480278706915,
              0.23983420705939457,
              0.09287185959368885
            ],
            "target_residual": 0.38479675596692653,
            "energy_eV": -156.02084043413038,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.002713901285505976,
            "step_scale": 0.7658800397225372,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.3914466120456609,
            "cell_principal_stretches": [
              1.005036332742812,
              0.9994941762702597,
              0.9953029774027993
            ],
            "cell_volume_ratio": 0.9998096709816968,
            "cell_rmsd_from_input_A": 0.031793524591495904
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.3964917548424128,
              0.4045380650270311,
              0.018427650389705605
            ],
            "branch_aligned_reduced_polarization": [
              -0.3964917548424128,
              0.4045380650270311,
              0.018427650389705605
            ],
            "target_residual": 0.14200885938303898,
            "energy_eV": -143.86176068440938,
            "max_atomic_step_A": 0.08419015266530427,
            "max_log_strain_component": 0.0025928575731022727,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.3914466120456609,
            "cell_principal_stretches": [
              1.0077556356918305,
              0.9994544194593173,
              0.9926423787595973
            ],
            "cell_volume_ratio": 0.9997951848643849,
            "cell_rmsd_from_input_A": 0.04920011185353676
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -0.5083417133326623,
              0.4990352209262018,
              -0.011953087366253536
            ],
            "branch_aligned_reduced_polarization": [
              -0.5083417133326623,
              0.4990352209262018,
              -0.011953087366253536
            ],
            "target_residual": 0.014607918317503184,
            "energy_eV": -133.63377670009686,
            "max_atomic_step_A": 0.005785449225845167,
            "max_log_strain_component": 8.023430951541691e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.3914466120456609,
            "cell_principal_stretches": [
              1.0076687754144318,
              0.9994882081018349,
              0.9927061862428204
            ],
            "cell_volume_ratio": 0.9998070718640154,
            "cell_rmsd_from_input_A": 0.04867010727093897
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              -0.5001196126990495,
              0.5000882694479928,
              -8.27723908288187e-06
            ],
            "branch_aligned_reduced_polarization": [
              -0.5001196126990495,
              0.5000882694479928,
              -8.27723908288187e-06
            ],
            "target_residual": 0.0001488865538243346,
            "energy_eV": -134.27126825087618
          }
        ],
        "iterations": 4
      },
      "parent": {
        "candidate_id": "bec_projection_06",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          -0.5,
          0.5,
          0.0
        ],
        "formal_class": [
          0.5,
          0.5,
          0.0
        ],
        "target_residual": 0.0001488865538243346,
        "parent_symmetrization_rmsd_A": 0.15762901993555603,
        "parent_cell_rmsd_A": 0.04867010727093897,
        "energy_eV": -134.27126825087618,
        "reduced_polarization": [
          -0.5001196126990495,
          0.5000882694479928,
          -8.27723908288187e-06
        ],
        "cartesian_polarization_e_A2": [
          -0.011942963108419049,
          0.009301411009416553,
          -6.685587311744202e-05
        ],
        "ranking_score": 0.6700943198609395
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 7,
      "formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.5,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        -0.5,
        0.5,
        0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -1.3418586882314678e-15,
              3.4346528915001677e-16,
              0.22781970261893789
            ],
            "branch_aligned_reduced_polarization": [
              -1.3322676295501878e-15,
              3.3306690738754696e-16,
              0.2278197026189379
            ],
            "target_residual": 0.7576820667552069,
            "energy_eV": -159.78332416305955,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.0019410643656145431,
            "step_scale": 0.5187267158519839,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.3914466120456609,
            "cell_principal_stretches": [
              1.0019302204602532,
              1.000366962929136,
              0.9978485866344572
            ],
            "cell_volume_ratio": 1.0001415346282652,
            "cell_rmsd_from_input_A": 0.013480449086164364
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.2333847914810445,
              0.2322829696536232,
              0.3339699940259382
            ],
            "branch_aligned_reduced_polarization": [
              -0.23338479148104452,
              0.23228296965362316,
              0.3339699940259382
            ],
            "target_residual": 0.41270090941847454,
            "energy_eV": -156.3911594029075,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.0024386863340597072,
            "step_scale": 0.6840373542234297,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.3914466120456609,
            "cell_principal_stretches": [
              1.0043403976126701,
              1.0009294025266116,
              0.9951117058812894
            ],
            "cell_volume_ratio": 1.0003597599447882,
            "cell_rmsd_from_input_A": 0.030616719904340367
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.37983114220960595,
              0.3815607813354571,
              0.41038880762079927
            ],
            "branch_aligned_reduced_polarization": [
              -0.37983114220960595,
              0.3815607813354571,
              0.41038880762079927
            ],
            "target_residual": 0.19104598582576257,
            "energy_eV": -146.27273858586824,
            "max_atomic_step_A": 0.10957305926194678,
            "max_log_strain_component": 0.003667356097788891,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.3914466120456609,
            "cell_principal_stretches": [
              1.007967282669941,
              1.0018696025436964,
              0.9909653223065747
            ],
            "cell_volume_ratio": 1.0007280955073314,
            "cell_rmsd_from_input_A": 0.05660851228538375
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -0.4970984349642955,
              0.4684900700404463,
              0.4934518566162349
            ],
            "branch_aligned_reduced_polarization": [
              -0.4970984349642955,
              0.4684900700404463,
              0.4934518566162349
            ],
            "target_residual": 0.03231366502714833,
            "energy_eV": -132.6869468841922,
            "max_atomic_step_A": 0.012120787917523704,
            "max_log_strain_component": 0.00015269094686940542,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 0.3914466120456609,
            "cell_principal_stretches": [
              1.0081129489547627,
              1.001935650576661,
              0.9907959027940697
            ],
            "cell_volume_ratio": 1.000767573333328,
            "cell_rmsd_from_input_A": 0.057662426216960966
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              -0.4998723669437242,
              0.49875520025181647,
              0.49928358448997096
            ],
            "branch_aligned_reduced_polarization": [
              -0.4998723669437242,
              0.49875520025181647,
              0.49928358448997096
            ],
            "target_residual": 0.001441897289387237,
            "energy_eV": -131.017679437391,
            "max_atomic_step_A": 0.0005057805733106556,
            "max_log_strain_component": 7.750832854191242e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": true,
            "strain_jacobian_frobenius_norm": 2.015434653980677,
            "cell_principal_stretches": [
              1.008093093949984,
              1.0019039564412746,
              0.9907654045875461
            ],
            "cell_volume_ratio": 1.000685402866538,
            "cell_rmsd_from_input_A": 0.0577867693620745
          },
          {
            "iteration": 5,
            "reduced_polarization": [
              -0.5000006313993071,
              0.5000000313031545,
              0.49999894764436026
            ],
            "branch_aligned_reduced_polarization": [
              -0.5000006313993071,
              0.5000000313031545,
              0.49999894764436026
            ],
            "target_residual": 1.2276389391569019e-06,
            "energy_eV": -130.92706332486182
          }
        ],
        "iterations": 5
      },
      "parent": {
        "candidate_id": "bec_projection_07",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          -0.5,
          0.5,
          0.5
        ],
        "formal_class": [
          0.5,
          0.5,
          0.5
        ],
        "target_residual": 1.2276389391569019e-06,
        "parent_symmetrization_rmsd_A": 0.17423751147786398,
        "parent_cell_rmsd_A": 0.0577867693620745,
        "energy_eV": -130.92706332486182,
        "reduced_polarization": [
          -0.5000006313993071,
          0.5000000313031545,
          0.49999894764436026
        ],
        "cartesian_polarization_e_A2": [
          -0.011846742387809594,
          0.009335859141884407,
          0.006974826575898252
        ],
        "ranking_score": 0.6886866590962609
      },
      "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
        ],
        "endpoint_rmsd_A": 0.36029375334185326,
        "minimum_distance_A_by_image": [
          0.9985565194827442,
          0.9775081397767182,
          0.9591710059683126,
          0.9437031782732694,
          0.9278774155459742,
          0.9135517213732671,
          0.9031799757434309,
          0.8968993595492257,
          0.8947960244389669
        ],
        "minimum_distance_A": 0.8947960244389669,
        "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": [
          399.556576935696,
          399.556576935696,
          399.556576935696,
          399.556576935696,
          399.556576935696,
          399.556576935696,
          399.556576935696,
          399.556576935696,
          399.556576935696
        ],
        "cell_deformation_log_strain_norm": 0.0
      },
      "parent_reduced_polarization": [
        4.984670289796938e-16,
        7.279970802636226e-17,
        6.422278069668316e-16
      ],
      "incoming": {
        "reached": true,
        "construction": "variable_cell_linear_interpolation",
        "continuation_fractions": [
          0.0,
          0.125,
          0.25,
          0.375,
          0.5,
          0.625,
          0.75,
          0.875,
          1.0
        ],
        "energies_eV": [
          -159.7833241630595,
          -159.75772054966373,
          -159.5180436829251,
          -159.1172840454729,
          -158.62092937203914,
          -158.10969387171673,
          -157.66705307876842,
          -157.36600556578026,
          -157.258980962514
        ],
        "cartesian_polarizations_e_A2": [
          [
            -5.843822711096465e-17,
            6.564531901320842e-18,
            0.00321359902464387
          ],
          [
            9.690499473378387e-18,
            -4.001238492233656e-17,
            0.002897620314695384
          ],
          [
            7.988583795258168e-18,
            -1.7053889754225045e-17,
            0.0024735290826691514
          ],
          [
            -8.162248660372476e-18,
            -2.410468327786595e-17,
            0.002041709232171087
          ],
          [
            3.1780670315918366e-18,
            -6.94659460457232e-19,
            0.0016285121700310697
          ],
          [
            7.293924334800936e-18,
            -2.1847040031379947e-17,
            0.0012233308723525735
          ],
          [
            -1.931153300071105e-17,
            -1.5074110291921935e-17,
            0.000818046655625706
          ],
          [
            -1.5977167590516335e-18,
            2.2229102734631426e-18,
            0.0004106826821644775
          ],
          [
            1.1896043260330098e-17,
            1.3545859478916024e-18,
            9.059192994909209e-18
          ]
        ],
        "raw_reduced_polarization": [
          [
            -2.4486737992944086e-15,
            3.527985850508324e-16,
            0.22781970261893794
          ],
          [
            4.0605051411776525e-16,
            -2.150391375547931e-15,
            0.20541921793421372
          ],
          [
            3.3473698296446596e-16,
            -9.16529657460099e-16,
            0.1753543785990629
          ],
          [
            -3.420138738984761e-16,
            -1.2954614710332154e-15,
            0.14474163905968448
          ],
          [
            1.3316710409238539e-16,
            -3.7333183603262696e-17,
            0.11544911342164552
          ],
          [
            3.0562941922842546e-16,
            -1.1741286243226117e-15,
            0.08672484445218381
          ],
          [
            -8.091902718619264e-16,
            -8.101300841908005e-16,
            0.05799327930581452
          ],
          [
            -6.694739659289319e-17,
            1.1946618753044063e-16,
            0.02911427524217261
          ],
          [
            4.984670289796938e-16,
            7.279970802636226e-17,
            6.422278069668316e-16
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -2.4486737992944086e-15,
            3.527985850508324e-16,
            0.22781970261893794
          ],
          [
            4.0605051411776505e-16,
            -2.1503913755479305e-15,
            0.20541921793421372
          ],
          [
            3.3473698296446596e-16,
            -9.16529657460099e-16,
            0.1753543785990629
          ],
          [
            -3.4201387389847605e-16,
            -1.2954614710332154e-15,
            0.14474163905968448
          ],
          [
            1.3316710409238534e-16,
            -3.7333183603262776e-17,
            0.11544911342164552
          ],
          [
            3.0562941922842546e-16,
            -1.1741286243226117e-15,
            0.08672484445218381
          ],
          [
            -8.091902718619263e-16,
            -8.101300841908005e-16,
            0.05799327930581452
          ],
          [
            -6.694739659289319e-17,
            1.194661875304406e-16,
            0.02911427524217261
          ],
          [
            4.984670289796938e-16,
            7.279970802636226e-17,
            6.418476861114186e-16
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            -2.4424906541753444e-15,
            3.3306690738754696e-16,
            0.2278197026189379
          ],
          [
            4.440892098500626e-16,
            -2.1649348980190553e-15,
            0.2054192179342137
          ],
          [
            3.3306690738754696e-16,
            -9.43689570931383e-16,
            0.1753543785990629
          ],
          [
            -3.3306690738754696e-16,
            -1.27675647831893e-15,
            0.1447416390596845
          ],
          [
            1.1102230246251565e-16,
            -5.551115123125783e-17,
            0.11544911342164554
          ],
          [
            3.3306690738754696e-16,
            -1.1657341758564144e-15,
            0.08672484445218376
          ],
          [
            -8.326672684688674e-16,
            -8.326672684688674e-16,
            0.05799327930581455
          ],
          [
            -5.551115123125783e-17,
            1.1102230246251565e-16,
            0.029114275242172583
          ],
          [
            4.440892098500626e-16,
            1.1102230246251565e-16,
            6.661338147750939e-16
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -157.258980962514,
          -157.36600556578026,
          -157.66705307876845,
          -158.10969387171676,
          -158.62092937203917,
          -159.11728404547287,
          -159.5180436829251,
          -159.75772054966367,
          -159.7833241630595
        ],
        "cartesian_polarizations_e_A2": [
          [
            1.1896043260330098e-17,
            1.3545859478916024e-18,
            9.059192994909209e-18
          ],
          [
            2.849840436525794e-17,
            -3.5636030321456004e-17,
            -0.00041068268216446933
          ],
          [
            1.630713083423352e-17,
            2.5077206522506077e-17,
            -0.0008180466556257182
          ],
          [
            -3.2805293020092784e-17,
            -8.370646498509646e-18,
            -0.0012233308723525987
          ],
          [
            -1.0089928663141294e-17,
            -1.2816467045435931e-17,
            -0.001628512170031126
          ],
          [
            3.47329730228616e-18,
            -1.8095878944910893e-17,
            -0.0020417092321711365
          ],
          [
            -5.640634818912724e-17,
            2.2854296249042934e-17,
            -0.0024735290826691896
          ],
          [
            7.207091902243782e-18,
            1.455311569657901e-17,
            -0.0028976203146953415
          ],
          [
            8.075416227815322e-18,
            -7.703773416470703e-17,
            -0.00321359902464388
          ]
        ],
        "raw_reduced_polarization": [
          [
            4.984670289796938e-16,
            7.279970802636226e-17,
            6.422278069668316e-16
          ],
          [
            1.1941378022710622e-15,
            -1.9151923188473762e-15,
            -0.02911427524217203
          ],
          [
            6.833000587035512e-16,
            1.3477279280777833e-15,
            -0.05799327930581538
          ],
          [
            -1.3746046974345137e-15,
            -4.498648624193155e-16,
            -0.08672484445218559
          ],
          [
            -4.227873632659885e-16,
            -6.887972374801967e-16,
            -0.11544911342164953
          ],
          [
            1.455378186802026e-16,
            -9.72529432864993e-16,
            -0.144741639059688
          ],
          [
            -2.36353417536649e-15,
            1.2282617405473427e-15,
            -0.1753543785990656
          ],
          [
            3.0199097376142036e-16,
            7.8213019648835345e-16,
            -0.2054192179342107
          ],
          [
            3.38375428431471e-16,
            -4.140250061601833e-15,
            -0.22781970261893864
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            4.984670289796938e-16,
            7.279970802636226e-17,
            6.422278069668316e-16
          ],
          [
            1.1941378022710622e-15,
            -1.9151923188473762e-15,
            -0.02911427524217203
          ],
          [
            6.833000587035512e-16,
            1.3477279280777833e-15,
            -0.05799327930581538
          ],
          [
            -1.3746046974345137e-15,
            -4.498648624193154e-16,
            -0.08672484445218559
          ],
          [
            -4.2278736326598847e-16,
            -6.887972374801967e-16,
            -0.11544911342164953
          ],
          [
            1.4553781868020257e-16,
            -9.72529432864993e-16,
            -0.144741639059688
          ],
          [
            -2.36353417536649e-15,
            1.228261740547343e-15,
            -0.1753543785990656
          ],
          [
            3.0199097376142036e-16,
            7.8213019648835345e-16,
            -0.2054192179342107
          ],
          [
            3.38375428431471e-16,
            -4.140250061601833e-15,
            -0.22781970261893864
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          3.4456078572537965e-15,
          -2.071991689981079e-16,
          -0.22781970261893664
        ],
        "actual_opposite_endpoint_branch_residual": 5.396053282095852e-15
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            -2.4486737992944086e-15,
            3.527985850508324e-16,
            0.22781970261893794
          ],
          [
            4.0605051411776525e-16,
            -2.150391375547931e-15,
            0.20541921793421372
          ],
          [
            3.3473698296446596e-16,
            -9.16529657460099e-16,
            0.1753543785990629
          ],
          [
            -3.420138738984761e-16,
            -1.2954614710332154e-15,
            0.14474163905968448
          ],
          [
            1.3316710409238539e-16,
            -3.7333183603262696e-17,
            0.11544911342164552
          ],
          [
            3.0562941922842546e-16,
            -1.1741286243226117e-15,
            0.08672484445218381
          ],
          [
            -8.091902718619264e-16,
            -8.101300841908005e-16,
            0.05799327930581452
          ],
          [
            -6.694739659289319e-17,
            1.1946618753044063e-16,
            0.02911427524217261
          ],
          [
            4.984670289796938e-16,
            7.279970802636226e-17,
            6.422278069668316e-16
          ],
          [
            1.1941378022710622e-15,
            -1.9151923188473762e-15,
            -0.02911427524217203
          ],
          [
            6.833000587035512e-16,
            1.3477279280777833e-15,
            -0.05799327930581538
          ],
          [
            -1.3746046974345137e-15,
            -4.498648624193155e-16,
            -0.08672484445218559
          ],
          [
            -4.227873632659885e-16,
            -6.887972374801967e-16,
            -0.11544911342164953
          ],
          [
            1.455378186802026e-16,
            -9.72529432864993e-16,
            -0.144741639059688
          ],
          [
            -2.36353417536649e-15,
            1.2282617405473427e-15,
            -0.1753543785990656
          ],
          [
            3.0199097376142036e-16,
            7.8213019648835345e-16,
            -0.2054192179342107
          ],
          [
            3.38375428431471e-16,
            -4.140250061601833e-15,
            -0.22781970261893864
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -2.4486737992944086e-15,
            3.527985850508324e-16,
            0.22781970261893794
          ],
          [
            4.0605051411776505e-16,
            -2.1503913755479305e-15,
            0.20541921793421372
          ],
          [
            3.3473698296446596e-16,
            -9.16529657460099e-16,
            0.1753543785990629
          ],
          [
            -3.4201387389847605e-16,
            -1.2954614710332154e-15,
            0.14474163905968448
          ],
          [
            1.3316710409238534e-16,
            -3.7333183603262776e-17,
            0.11544911342164552
          ],
          [
            3.0562941922842546e-16,
            -1.1741286243226117e-15,
            0.08672484445218381
          ],
          [
            -8.091902718619263e-16,
            -8.101300841908005e-16,
            0.05799327930581452
          ],
          [
            -6.694739659289319e-17,
            1.194661875304406e-16,
            0.02911427524217261
          ],
          [
            4.984670289796938e-16,
            7.279970802636226e-17,
            6.418476861114186e-16
          ],
          [
            1.1941378022710622e-15,
            -1.9151923188473762e-15,
            -0.02911427524217203
          ],
          [
            6.833000587035512e-16,
            1.3477279280777833e-15,
            -0.05799327930581538
          ],
          [
            -1.3746046974345137e-15,
            -4.498648624193154e-16,
            -0.08672484445218559
          ],
          [
            -4.2278736326598847e-16,
            -6.887972374801967e-16,
            -0.11544911342164953
          ],
          [
            1.4553781868020257e-16,
            -9.72529432864993e-16,
            -0.144741639059688
          ],
          [
            -2.36353417536649e-15,
            1.228261740547343e-15,
            -0.1753543785990656
          ],
          [
            3.0199097376142036e-16,
            7.8213019648835345e-16,
            -0.2054192179342107
          ],
          [
            3.38375428431471e-16,
            -4.140250061601833e-15,
            -0.22781970261893864
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            -2.4424906541753444e-15,
            3.3306690738754696e-16,
            0.2278197026189379
          ],
          [
            4.440892098500626e-16,
            -2.1649348980190553e-15,
            0.2054192179342137
          ],
          [
            3.3306690738754696e-16,
            -9.43689570931383e-16,
            0.1753543785990629
          ],
          [
            -3.3306690738754696e-16,
            -1.27675647831893e-15,
            0.1447416390596845
          ],
          [
            1.1102230246251565e-16,
            -5.551115123125783e-17,
            0.11544911342164554
          ],
          [
            3.3306690738754696e-16,
            -1.1657341758564144e-15,
            0.08672484445218376
          ],
          [
            -8.326672684688674e-16,
            -8.326672684688674e-16,
            0.05799327930581455
          ],
          [
            -5.551115123125783e-17,
            1.1102230246251565e-16,
            0.029114275242172583
          ],
          [
            4.440892098500626e-16,
            1.1102230246251565e-16,
            6.661338147750939e-16
          ],
          [
            1.2212453270876722e-15,
            -1.942890293094024e-15,
            -0.029114275242172027
          ],
          [
            6.661338147750939e-16,
            1.3322676295501878e-15,
            -0.05799327930581538
          ],
          [
            -1.3877787807814457e-15,
            -4.440892098500626e-16,
            -0.08672484445218559
          ],
          [
            -4.440892098500626e-16,
            -6.661338147750939e-16,
            -0.11544911342164954
          ],
          [
            1.1102230246251565e-16,
            -9.992007221626409e-16,
            -0.144741639059688
          ],
          [
            -2.3869795029440866e-15,
            1.2212453270876722e-15,
            -0.1753543785990656
          ],
          [
            3.3306690738754696e-16,
            7.771561172376096e-16,
            -0.2054192179342107
          ],
          [
            3.3306690738754696e-16,
            -4.163336342344337e-15,
            -0.22781970261893864
          ]
        ]
      },
      "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": "Pnma",
        "spacegroup_number": 62,
        "pointgroup": "mmm",
        "has_inversion": true,
        "is_polar_point_group": false,
        "nonpolar_parent_hypothesis": true,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.0
        ],
        "formal_class": [
          0.0,
          0.0,
          0.0
        ],
        "target_residual": 1.2043166082503844e-15,
        "parent_symmetrization_rmsd_A": 0.36029375334185326,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -157.25898096251393,
        "reduced_polarization": [
          1.5499777689441575e-16,
          -5.599977540489404e-17,
          1.1929870943225247e-15
        ],
        "cartesian_polarization_e_A2": [
          3.69906162693476e-18,
          -1.041989190685848e-18,
          1.682814137081092e-17
        ],
        "ranking_score": 0.36029375334185565
      }
    }
  ],
  "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": 72,
      "full_response": 28,
      "energy_polarization": 44
    },
    "model_evaluations_for_recovery_and_path_properties": {
      "total": 97,
      "full_response": 53,
      "energy_polarization": 44
    },
    "elapsed_seconds": 1087.4079868510016
  }
}
