{
  "schema": "ferrofinder.endpoint_parent_recovery.v4_variable_cell",
  "status": "complete",
  "input_atom_count": 42,
  "input_formula": "Al2Ca22Sb18",
  "input_spacegroup": "Iba2",
  "input_pointgroup": "mm2",
  "input_is_polar_point_group": true,
  "input_energy_eV": -164.05825579371248,
  "input_cartesian_polarization_e_A2": [
    -5.7474472037341815e-09,
    0.0006006855845136821,
    0.0004484253856669676
  ],
  "input_reduced_polarization": [
    -0.05580895135023365,
    0.05580788818339866,
    0.05580880219520701
  ],
  "input_formal_targets": [
    {
      "orbit_id": 0,
      "representative_formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ]
    },
    {
      "orbit_id": 1,
      "representative_formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        -0.5,
        0.0,
        0.0
      ]
    },
    {
      "orbit_id": 2,
      "representative_formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.5
      ]
    },
    {
      "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": [
        0.0,
        0.5,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.5
      ]
    },
    {
      "orbit_id": 5,
      "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": "Ibam",
      "spacegroup_number": 72,
      "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": 6.555793737145348e-15,
      "parent_symmetrization_rmsd_A": 0.47345739439541484,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -155.32385810376934,
      "reduced_polarization": [
        1.5938000717375517e-15,
        -1.0755467381861623e-15,
        -6.2674900932750306e-15
      ],
      "cartesian_polarization_e_A2": [
        -1.9699671851960607e-17,
        -2.3946772510165454e-17,
        -5.0359469325470083e-17
      ],
      "ranking_score": 0.47345739439542794
    },
    {
      "candidate_id": "bec_projection_00",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Iba2",
      "spacegroup_number": 45,
      "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": 6.5588475984675e-05,
      "parent_symmetrization_rmsd_A": 0.009133487578209346,
      "parent_cell_rmsd_A": 0.005093568934568803,
      "energy_eV": -164.02667257269584,
      "reduced_polarization": [
        -3.780299754562386e-05,
        3.505550479315823e-05,
        4.0544952118046775e-05
      ],
      "cartesian_polarization_e_A2": [
        -2.6244954627257506e-11,
        3.9025805647897473e-07,
        3.256682357473388e-07
      ],
      "ranking_score": 0.5105380567638209
    },
    {
      "candidate_id": "inversion_parent_bec_00_00",
      "source": "same_species_inversion_center_projection_after_BEC",
      "spacegroup": "Ibam",
      "spacegroup_number": 72,
      "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": 4.156973794924281e-15,
      "parent_symmetrization_rmsd_A": 0.47345760360288824,
      "parent_cell_rmsd_A": 0.005093568934568803,
      "energy_eV": -155.35618658879181,
      "reduced_polarization": [
        2.4730122052395194e-15,
        -2.3917772867405317e-15,
        -2.333247345451323e-15
      ],
      "cartesian_polarization_e_A2": [
        1.047058659484028e-18,
        -2.5594767231831794e-17,
        -1.8741796005473365e-17
      ],
      "ranking_score": 0.47473099583653877
    },
    {
      "candidate_id": "bec_projection_01",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cc",
      "spacegroup_number": 9,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        -0.5,
        0.0,
        0.0
      ],
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_residual": 2.8457249777482757e-06,
      "parent_symmetrization_rmsd_A": 0.06449926028336411,
      "parent_cell_rmsd_A": 0.010787986531333733,
      "energy_eV": -163.76874771691132,
      "reduced_polarization": [
        -0.5000026467358347,
        -7.143128033718626e-07,
        -7.633461135817793e-07
      ],
      "cartesian_polarization_e_A2": [
        -0.004737901134340287,
        3.559090125450717e-06,
        2.6566389431360174e-06
      ],
      "ranking_score": 0.567201948366153
    },
    {
      "candidate_id": "bec_projection_02",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.5
      ],
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_residual": 1.5464416100039492e-06,
      "parent_symmetrization_rmsd_A": 0.059795746686042935,
      "parent_cell_rmsd_A": 0.030179582358787423,
      "energy_eV": -163.9304359768305,
      "reduced_polarization": [
        -1.12478346415428e-07,
        1.1867505966545079e-07,
        0.49999846222677063
      ],
      "cartesian_polarization_e_A2": [
        0.0023769078909759685,
        0.00118884159395853,
        0.004012734726830467
      ],
      "ranking_score": 0.5673437351589597
    },
    {
      "candidate_id": "bec_projection_03",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.0
      ],
      "formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_residual": 4.994817190185444e-06,
      "parent_symmetrization_rmsd_A": 0.05977546375121364,
      "parent_cell_rmsd_A": 0.025180037837855038,
      "energy_eV": -163.92366749169605,
      "reduced_polarization": [
        1.2644848754179868e-07,
        0.49999594946050413,
        2.919818373763497e-06
      ],
      "cartesian_polarization_e_A2": [
        0.002376925519358292,
        0.004187569688344447,
        4.759462358783686e-06
      ],
      "ranking_score": 0.5660804628450578
    },
    {
      "candidate_id": "bec_projection_04",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cc",
      "spacegroup_number": 9,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.5
      ],
      "formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_residual": 9.563315267189855e-06,
      "parent_symmetrization_rmsd_A": 0.09734925465633014,
      "parent_cell_rmsd_A": 0.029198311271770586,
      "energy_eV": -163.53856162583523,
      "reduced_polarization": [
        2.3970655677447076e-06,
        0.5000070900461515,
        0.5000059533453732
      ],
      "cartesian_polarization_e_A2": [
        0.0047702034220916635,
        0.00540123519458607,
        0.004030560898579144
      ],
      "ranking_score": 0.6046679591048072
    },
    {
      "candidate_id": "bec_projection_05",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Iba2",
      "spacegroup_number": 45,
      "pointgroup": "mm2",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        -0.5,
        0.5,
        0.5
      ],
      "formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "target_residual": 0.00047830769936242645,
      "parent_symmetrization_rmsd_A": 0.07299795046642933,
      "parent_cell_rmsd_A": 0.04040575887417367,
      "energy_eV": -163.81415268817744,
      "reduced_polarization": [
        -0.4997675453298344,
        0.4995850043628894,
        0.49994978344130925
      ],
      "cartesian_polarization_e_A2": [
        -7.479545266049302e-10,
        0.005393865542319165,
        0.0040273538615585355
      ],
      "ranking_score": 0.5840560055836976
    }
  ],
  "formal_branches": [
    {
      "orbit_id": 0,
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.0,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -0.05580895135023365,
              0.05580788818339866,
              0.05580880219520701
            ],
            "branch_aligned_reduced_polarization": [
              -0.05580895135023365,
              0.05580788818339866,
              0.05580880219520701
            ],
            "target_residual": 0.0966632393248189,
            "energy_eV": -164.05825579371248,
            "max_atomic_step_A": 0.009208259204830193,
            "max_log_strain_component": 0.00032747491244718033,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.1325477357718252,
            "cell_principal_stretches": [
              1.000467641950544,
              1.0002101803198125,
              1.0001387595647577
            ],
            "cell_volume_ratio": 1.0008167741922112,
            "cell_rmsd_from_input_A": 0.005093568934568803
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -3.780299754562386e-05,
              3.505550479315823e-05,
              4.0544952118046775e-05
            ],
            "branch_aligned_reduced_polarization": [
              -3.780299754562386e-05,
              3.505550479315823e-05,
              4.0544952118046775e-05
            ],
            "target_residual": 6.5588475984675e-05,
            "energy_eV": -164.02667257269584
          }
        ],
        "iterations": 1
      },
      "parent": {
        "candidate_id": "inversion_parent_endpoint_00",
        "source": "same_species_inversion_center_projection_from_endpoint",
        "spacegroup": "Ibam",
        "spacegroup_number": 72,
        "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": 6.555793737145348e-15,
        "parent_symmetrization_rmsd_A": 0.47345739439541484,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -155.32385810376934,
        "reduced_polarization": [
          1.5938000717375517e-15,
          -1.0755467381861623e-15,
          -6.2674900932750306e-15
        ],
        "cartesian_polarization_e_A2": [
          -1.9699671851960607e-17,
          -2.3946772510165454e-17,
          -5.0359469325470083e-17
        ],
        "ranking_score": 0.47345739439542794
      },
      "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": [
          -164.0582557937125,
          -163.8980332512329,
          -163.21095775777422,
          -161.9894892855931,
          -160.36421694623954,
          -158.57985398698662,
          -156.93879407934642,
          -155.7589456185613,
          -155.32385810376945
        ],
        "cartesian_polarizations_e_A2": [
          [
            -5.747447170001335e-09,
            0.0006006855845137009,
            0.00044842538566694924
          ],
          [
            -5.164488514013767e-09,
            0.001538286575182125,
            0.0011483573413940415
          ],
          [
            -4.811552410861102e-09,
            0.0022266256060041135,
            0.001662211668384324
          ],
          [
            -4.384322907375304e-09,
            0.0025114828949302213,
            0.0018748610129516907
          ],
          [
            -3.678746714582349e-09,
            0.002414114921650012,
            0.0018021736729442136
          ],
          [
            -2.7459997978434427e-09,
            0.0020266604481076786,
            0.0015129328203187216
          ],
          [
            -1.7726101729324521e-09,
            0.0014487738510848974,
            0.0010815316124050912
          ],
          [
            -8.624360521088898e-10,
            0.0007572189199551965,
            0.0005652753670146676
          ],
          [
            4.7061867345747714e-17,
            -4.440049878708149e-17,
            -3.1387515438769773e-17
          ]
        ],
        "raw_reduced_polarization": [
          [
            -0.05580895135023039,
            0.055807888183401544,
            0.05580880219520472
          ],
          [
            -0.14291891241325475,
            0.14291786929217254,
            0.14291886624561098
          ],
          [
            -0.20687062231308498,
            0.20686959946137667,
            0.2068706303713153
          ],
          [
            -0.23333588988359466,
            0.23333494068921082,
            0.2333359144235308
          ],
          [
            -0.2242895787954612,
            0.2242887736158557,
            0.2242896081477622
          ],
          [
            -0.1882920771174884,
            0.1882914507304595,
            0.1882921244037499
          ],
          [
            -0.13460201971535327,
            0.13460159857525805,
            0.1346020670413291
          ],
          [
            -0.07035134216231079,
            0.0703511304051236,
            0.0703513720496054
          ],
          [
            9.010434594410423e-15,
            -4.187333097489239e-15,
            -3.906334691368798e-15
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -0.05580895135023039,
            0.055807888183401544,
            0.05580880219520472
          ],
          [
            -0.14291891241325475,
            0.14291786929217254,
            0.14291886624561098
          ],
          [
            -0.20687062231308498,
            0.20686959946137667,
            0.2068706303713153
          ],
          [
            -0.23333588988359466,
            0.23333494068921082,
            0.2333359144235308
          ],
          [
            -0.2242895787954612,
            0.2242887736158557,
            0.2242896081477622
          ],
          [
            -0.1882920771174884,
            0.1882914507304595,
            0.1882921244037499
          ],
          [
            -0.13460201971535327,
            0.13460159857525805,
            0.1346020670413291
          ],
          [
            -0.07035134216231079,
            0.0703511304051236,
            0.0703513720496054
          ],
          [
            9.006684287271582e-15,
            -4.191091917959966e-15,
            -3.899658373995862e-15
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            -0.055808951350230396,
            0.055807888183401544,
            0.055808802195204676
          ],
          [
            -0.14291891241325472,
            0.14291786929217254,
            0.142918866245611
          ],
          [
            -0.20687062231308495,
            0.20686959946137673,
            0.20687063037131526
          ],
          [
            -0.23333588988359466,
            0.2333349406892108,
            0.23333591442353074
          ],
          [
            -0.2242895787954612,
            0.22428877361585564,
            0.22428960814776222
          ],
          [
            -0.1882920771174884,
            0.1882914507304595,
            0.18829212440374987
          ],
          [
            -0.13460201971535324,
            0.134601598575258,
            0.13460206704132904
          ],
          [
            -0.07035134216231076,
            0.07035113040512364,
            0.0703513720496054
          ],
          [
            8.992806499463768e-15,
            -4.218847493575595e-15,
            -3.885780586188048e-15
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -155.3238581037694,
          -155.75894561856134,
          -156.93879407934642,
          -158.57985398698662,
          -160.36421694623962,
          -161.98948928559315,
          -163.21095775777422,
          -163.89803325123285,
          -164.05825579371248
        ],
        "cartesian_polarizations_e_A2": [
          [
            2.7201404476701023e-17,
            -5.879961159303187e-17,
            -5.179688557304137e-17
          ],
          [
            8.624360649721712e-10,
            -0.0007572189199553122,
            -0.0005652753670148058
          ],
          [
            1.7726101666754638e-09,
            -0.0014487738510849816,
            -0.001081531612405113
          ],
          [
            2.745999758469569e-09,
            -0.0020266604481077926,
            -0.0015129328203187392
          ],
          [
            3.678746649356641e-09,
            -0.002414114921650037,
            -0.0018021736729441934
          ],
          [
            4.38432287515611e-09,
            -0.0025114828949302564,
            -0.0018748610129516517
          ],
          [
            4.8115525052981025e-09,
            -0.0022266256060042367,
            -0.001662211668384319
          ],
          [
            5.164488506695004e-09,
            -0.0015382865751823833,
            -0.0011483573413941597
          ],
          [
            5.747447264191604e-09,
            -0.0006006855845138134,
            -0.0004484253856669541
          ]
        ],
        "raw_reduced_polarization": [
          [
            8.683778211986362e-15,
            -5.1833250699043505e-15,
            -6.44638379911099e-15
          ],
          [
            0.0703513421623252,
            -0.07035113040513252,
            -0.07035137204962259
          ],
          [
            0.1346020197153586,
            -0.1346015985752673,
            -0.13460206704133182
          ],
          [
            0.18829207711749185,
            -0.1882914507304725,
            -0.1882921244037521
          ],
          [
            0.22428957879545489,
            -0.22428877361585936,
            -0.2242896081477597
          ],
          [
            0.23333588988359164,
            -0.2333349406892164,
            -0.23333591442352594
          ],
          [
            0.20687062231310202,
            -0.20686959946139152,
            -0.20687063037131467
          ],
          [
            0.14291891241327465,
            -0.14291786929219918,
            -0.1429188662456257
          ],
          [
            0.05580895135024727,
            -0.055807888183414804,
            -0.05580880219520533
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            8.683778211986362e-15,
            -5.1833250699043505e-15,
            -6.44638379911099e-15
          ],
          [
            0.0703513421623252,
            -0.07035113040513252,
            -0.07035137204962259
          ],
          [
            0.1346020197153586,
            -0.1346015985752673,
            -0.13460206704133182
          ],
          [
            0.18829207711749185,
            -0.1882914507304725,
            -0.1882921244037521
          ],
          [
            0.22428957879545489,
            -0.22428877361585936,
            -0.2242896081477597
          ],
          [
            0.23333588988359164,
            -0.2333349406892164,
            -0.23333591442352594
          ],
          [
            0.20687062231310202,
            -0.20686959946139152,
            -0.20687063037131467
          ],
          [
            0.14291891241327465,
            -0.14291786929219918,
            -0.1429188662456257
          ],
          [
            0.05580895135024727,
            -0.05580788818341481,
            -0.05580880219520533
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          0.055808951350248416,
          -0.05580788818340992,
          -0.05580880219521253
        ],
        "actual_opposite_endpoint_branch_residual": 8.781728810925229e-15
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            -0.05580895135023039,
            0.055807888183401544,
            0.05580880219520472
          ],
          [
            -0.14291891241325475,
            0.14291786929217254,
            0.14291886624561098
          ],
          [
            -0.20687062231308498,
            0.20686959946137667,
            0.2068706303713153
          ],
          [
            -0.23333588988359466,
            0.23333494068921082,
            0.2333359144235308
          ],
          [
            -0.2242895787954612,
            0.2242887736158557,
            0.2242896081477622
          ],
          [
            -0.1882920771174884,
            0.1882914507304595,
            0.1882921244037499
          ],
          [
            -0.13460201971535327,
            0.13460159857525805,
            0.1346020670413291
          ],
          [
            -0.07035134216231079,
            0.0703511304051236,
            0.0703513720496054
          ],
          [
            9.010434594410423e-15,
            -4.187333097489239e-15,
            -3.906334691368798e-15
          ],
          [
            0.0703513421623252,
            -0.07035113040513252,
            -0.07035137204962259
          ],
          [
            0.1346020197153586,
            -0.1346015985752673,
            -0.13460206704133182
          ],
          [
            0.18829207711749185,
            -0.1882914507304725,
            -0.1882921244037521
          ],
          [
            0.22428957879545489,
            -0.22428877361585936,
            -0.2242896081477597
          ],
          [
            0.23333588988359164,
            -0.2333349406892164,
            -0.23333591442352594
          ],
          [
            0.20687062231310202,
            -0.20686959946139152,
            -0.20687063037131467
          ],
          [
            0.14291891241327465,
            -0.14291786929219918,
            -0.1429188662456257
          ],
          [
            0.05580895135024727,
            -0.055807888183414804,
            -0.05580880219520533
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -0.05580895135023039,
            0.055807888183401544,
            0.05580880219520472
          ],
          [
            -0.14291891241325475,
            0.14291786929217254,
            0.14291886624561098
          ],
          [
            -0.20687062231308498,
            0.20686959946137667,
            0.2068706303713153
          ],
          [
            -0.23333588988359466,
            0.23333494068921082,
            0.2333359144235308
          ],
          [
            -0.2242895787954612,
            0.2242887736158557,
            0.2242896081477622
          ],
          [
            -0.1882920771174884,
            0.1882914507304595,
            0.1882921244037499
          ],
          [
            -0.13460201971535327,
            0.13460159857525805,
            0.1346020670413291
          ],
          [
            -0.07035134216231079,
            0.0703511304051236,
            0.0703513720496054
          ],
          [
            9.006684287271582e-15,
            -4.191091917959966e-15,
            -3.899658373995862e-15
          ],
          [
            0.0703513421623252,
            -0.07035113040513252,
            -0.07035137204962259
          ],
          [
            0.1346020197153586,
            -0.1346015985752673,
            -0.13460206704133182
          ],
          [
            0.18829207711749185,
            -0.1882914507304725,
            -0.1882921244037521
          ],
          [
            0.22428957879545489,
            -0.22428877361585936,
            -0.2242896081477597
          ],
          [
            0.23333588988359164,
            -0.2333349406892164,
            -0.23333591442352594
          ],
          [
            0.20687062231310202,
            -0.20686959946139152,
            -0.20687063037131467
          ],
          [
            0.14291891241327465,
            -0.14291786929219918,
            -0.1429188662456257
          ],
          [
            0.05580895135024727,
            -0.05580788818341481,
            -0.05580880219520533
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            -0.055808951350230396,
            0.055807888183401544,
            0.055808802195204676
          ],
          [
            -0.14291891241325472,
            0.14291786929217254,
            0.142918866245611
          ],
          [
            -0.20687062231308495,
            0.20686959946137673,
            0.20687063037131526
          ],
          [
            -0.23333588988359466,
            0.2333349406892108,
            0.23333591442353074
          ],
          [
            -0.2242895787954612,
            0.22428877361585564,
            0.22428960814776222
          ],
          [
            -0.1882920771174884,
            0.1882914507304595,
            0.18829212440374987
          ],
          [
            -0.13460201971535324,
            0.134601598575258,
            0.13460206704132904
          ],
          [
            -0.07035134216231076,
            0.07035113040512364,
            0.0703513720496054
          ],
          [
            8.992806499463768e-15,
            -4.218847493575595e-15,
            -3.885780586188048e-15
          ],
          [
            0.07035134216232519,
            -0.07035113040513252,
            -0.0703513720496226
          ],
          [
            0.13460201971535857,
            -0.13460159857526732,
            -0.13460206704133182
          ],
          [
            0.18829207711749185,
            -0.1882914507304725,
            -0.1882921244037521
          ],
          [
            0.22428957879545486,
            -0.22428877361585936,
            -0.22428960814775967
          ],
          [
            0.23333588988359166,
            -0.2333349406892164,
            -0.23333591442352597
          ],
          [
            0.20687062231310205,
            -0.2068695994613915,
            -0.2068706303713147
          ],
          [
            0.1429189124132746,
            -0.14291786929219918,
            -0.14291886624562566
          ],
          [
            0.05580895135024733,
            -0.05580788818341481,
            -0.05580880219520534
          ]
        ]
      },
      "incoming_structure_ids": [
        "incoming_00_000",
        "incoming_00_001",
        "incoming_00_002",
        "incoming_00_003",
        "incoming_00_004",
        "incoming_00_005",
        "incoming_00_006",
        "incoming_00_007",
        "incoming_00_008"
      ],
      "reflected_structure_ids": [
        "reflected_00_001",
        "reflected_00_002",
        "reflected_00_003",
        "reflected_00_004",
        "reflected_00_005",
        "reflected_00_006",
        "reflected_00_007",
        "reflected_00_008"
      ]
    },
    {
      "orbit_id": 1,
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.0,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        -0.5,
        0.0,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -0.05580895135023365,
              0.05580788818339866,
              0.05580880219520701
            ],
            "branch_aligned_reduced_polarization": [
              -0.05580895135023367,
              0.05580788818339866,
              0.05580880219520701
            ],
            "target_residual": 0.45114834643001134,
            "energy_eV": -164.05825579371248,
            "max_atomic_step_A": 0.06315294729314778,
            "max_log_strain_component": 0.0007507169690489928,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.1325477357718252,
            "cell_principal_stretches": [
              1.0012846668768,
              1.000140457673986,
              0.9993924583657635
            ],
            "cell_volume_ratio": 1.0008168974257472,
            "cell_rmsd_from_input_A": 0.0106978056170639
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.4978574365710303,
              -0.0008091738252838812,
              -0.0008028594917898963
            ],
            "branch_aligned_reduced_polarization": [
              -0.4978574365710303,
              -0.0008091738252838812,
              -0.0008028594917898963
            ],
            "target_residual": 0.0024269164984069783,
            "energy_eV": -163.76961762491624,
            "max_atomic_step_A": 0.00020311376998644179,
            "max_log_strain_component": 4.819541654453299e-06,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.1325477357718252,
            "cell_principal_stretches": [
              1.0012819906783272,
              1.0001383946600233,
              0.9993852637697204
            ],
            "cell_volume_ratio": 1.0008049532573393,
            "cell_rmsd_from_input_A": 0.010787986531333733
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.5000026467358347,
              -7.143128033718626e-07,
              -7.633461135817793e-07
            ],
            "branch_aligned_reduced_polarization": [
              -0.5000026467358347,
              -7.143128033718626e-07,
              -7.633461135817793e-07
            ],
            "target_residual": 2.8457249777482757e-06,
            "energy_eV": -163.76874771691132
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_01",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cc",
        "spacegroup_number": 9,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          -0.5,
          0.0,
          0.0
        ],
        "formal_class": [
          0.5,
          0.0,
          0.0
        ],
        "target_residual": 2.8457249777482757e-06,
        "parent_symmetrization_rmsd_A": 0.06449926028336411,
        "parent_cell_rmsd_A": 0.010787986531333733,
        "energy_eV": -163.76874771691132,
        "reduced_polarization": [
          -0.5000026467358347,
          -7.143128033718626e-07,
          -7.633461135817793e-07
        ],
        "cartesian_polarization_e_A2": [
          -0.004737901134340287,
          3.559090125450717e-06,
          2.6566389431360174e-06
        ],
        "ranking_score": 0.567201948366153
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 2,
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.0,
          0.5
        ],
        [
          0.5,
          0.5,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -0.05580895135023365,
              0.05580788818339866,
              0.05580880219520701
            ],
            "branch_aligned_reduced_polarization": [
              -0.05580895135023365,
              0.05580788818339866,
              0.05580880219520701
            ],
            "target_residual": 0.45114851173594733,
            "energy_eV": -164.05825579371248,
            "max_atomic_step_A": 0.06298940960938215,
            "max_log_strain_component": 0.0035677689858975062,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.1325477357718252,
            "cell_principal_stretches": [
              1.0022498779005928,
              0.9992890915480097,
              0.9956337560351558
            ],
            "cell_volume_ratio": 0.9971644134940967,
            "cell_rmsd_from_input_A": 0.03022951988676282
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.0006938660437477638,
              0.0001954833249423564,
              0.5007169425085599
            ],
            "branch_aligned_reduced_polarization": [
              -0.0006938660437477638,
              0.0001954833249423564,
              0.5007169425085599
            ],
            "target_residual": 0.001016695813691035,
            "energy_eV": -163.93020981145077,
            "max_atomic_step_A": 9.011760765797346e-05,
            "max_log_strain_component": 4.986701073565621e-06,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.1325477357718252,
            "cell_principal_stretches": [
              1.002248615472383,
              0.9992908616837309,
              0.995639889188782
            ],
            "cell_volume_ratio": 0.9971710664270569,
            "cell_rmsd_from_input_A": 0.030179582358787423
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -1.12478346415428e-07,
              1.1867505966545079e-07,
              0.49999846222677063
            ],
            "branch_aligned_reduced_polarization": [
              -1.12478346415428e-07,
              1.1867505966545079e-07,
              0.49999846222677063
            ],
            "target_residual": 1.5464416100039492e-06,
            "energy_eV": -163.9304359768305
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_02",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.5
        ],
        "formal_class": [
          0.0,
          0.0,
          0.5
        ],
        "target_residual": 1.5464416100039492e-06,
        "parent_symmetrization_rmsd_A": 0.059795746686042935,
        "parent_cell_rmsd_A": 0.030179582358787423,
        "energy_eV": -163.9304359768305,
        "reduced_polarization": [
          -1.12478346415428e-07,
          1.1867505966545079e-07,
          0.49999846222677063
        ],
        "cartesian_polarization_e_A2": [
          0.0023769078909759685,
          0.00118884159395853,
          0.004012734726830467
        ],
        "ranking_score": 0.5673437351589597
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 3,
      "formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.5,
          0.0
        ],
        [
          0.5,
          0.0,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -0.05580895135023365,
              0.05580788818339866,
              0.05580880219520701
            ],
            "branch_aligned_reduced_polarization": [
              -0.05580895135023365,
              0.05580788818339866,
              0.05580880219520701
            ],
            "target_residual": 0.45114952471810116,
            "energy_eV": -164.05825579371248,
            "max_atomic_step_A": 0.063022024616586,
            "max_log_strain_component": 0.003738155531450066,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.1325477357718252,
            "cell_principal_stretches": [
              1.0018463316996753,
              0.999255460220377,
              0.9960656366486702
            ],
            "cell_volume_ratio": 0.9971617244600157,
            "cell_rmsd_from_input_A": 0.025270141944261724
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.00019011629097261652,
              0.5011006442738025,
              -0.0008573059148235363
            ],
            "branch_aligned_reduced_polarization": [
              -0.00019011629097261652,
              0.5011006442738025,
              -0.0008573059148235363
            ],
            "target_residual": 0.001408025373755346,
            "energy_eV": -163.9230781460962,
            "max_atomic_step_A": 0.00016008952195703841,
            "max_log_strain_component": 1.0908562687617838e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.1325477357718252,
            "cell_principal_stretches": [
              1.0018355532202,
              0.999255867182615,
              0.9960776726011553
            ],
            "cell_volume_ratio": 0.9971634515579206,
            "cell_rmsd_from_input_A": 0.025180037837855038
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              1.2644848754179868e-07,
              0.49999594946050413,
              2.919818373763497e-06
            ],
            "branch_aligned_reduced_polarization": [
              1.2644848754179868e-07,
              0.49999594946050413,
              2.919818373763497e-06
            ],
            "target_residual": 4.994817190185444e-06,
            "energy_eV": -163.92366749169605
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_03",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.5,
          0.0
        ],
        "formal_class": [
          0.0,
          0.5,
          0.0
        ],
        "target_residual": 4.994817190185444e-06,
        "parent_symmetrization_rmsd_A": 0.05977546375121364,
        "parent_cell_rmsd_A": 0.025180037837855038,
        "energy_eV": -163.92366749169605,
        "reduced_polarization": [
          1.2644848754179868e-07,
          0.49999594946050413,
          2.919818373763497e-06
        ],
        "cartesian_polarization_e_A2": [
          0.002376925519358292,
          0.004187569688344447,
          4.759462358783686e-06
        ],
        "ranking_score": 0.5660804628450578
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 4,
      "formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.5,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -0.05580895135023365,
              0.05580788818339866,
              0.05580880219520701
            ],
            "branch_aligned_reduced_polarization": [
              -0.05580895135023365,
              0.05580788818339866,
              0.05580880219520701
            ],
            "target_residual": 0.6306560801721978,
            "energy_eV": -164.05825579371248,
            "max_atomic_step_A": 0.09024438475858838,
            "max_log_strain_component": 0.0026064824359437397,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.1325477357718252,
            "cell_principal_stretches": [
              0.9989130391670966,
              0.9986737521377671,
              0.9959246407253876
            ],
            "cell_volume_ratio": 0.9935227024272152,
            "cell_rmsd_from_input_A": 0.0289876396783596
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.001086688354206588,
              0.49707415938295324,
              0.49744003148628346
            ],
            "branch_aligned_reduced_polarization": [
              0.001086688354206588,
              0.49707415938295324,
              0.49744003148628346
            ],
            "target_residual": 0.0040366909327751175,
            "energy_eV": -163.54497986438085,
            "max_atomic_step_A": 0.000484429216439185,
            "max_log_strain_component": 1.8679578331580835e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.1325477357718252,
            "cell_principal_stretches": [
              0.9989047176896135,
              0.9986640365769028,
              0.9959010608143292
            ],
            "cell_volume_ratio": 0.9934812378685555,
            "cell_rmsd_from_input_A": 0.029198311271770586
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              2.3970655677447076e-06,
              0.5000070900461515,
              0.5000059533453732
            ],
            "branch_aligned_reduced_polarization": [
              2.3970655677447076e-06,
              0.5000070900461515,
              0.5000059533453732
            ],
            "target_residual": 9.563315267189855e-06,
            "energy_eV": -163.53856162583523
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_04",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cc",
        "spacegroup_number": 9,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.5,
          0.5
        ],
        "formal_class": [
          0.0,
          0.5,
          0.5
        ],
        "target_residual": 9.563315267189855e-06,
        "parent_symmetrization_rmsd_A": 0.09734925465633014,
        "parent_cell_rmsd_A": 0.029198311271770586,
        "energy_eV": -163.53856162583523,
        "reduced_polarization": [
          2.3970655677447076e-06,
          0.5000070900461515,
          0.5000059533453732
        ],
        "cartesian_polarization_e_A2": [
          0.0047702034220916635,
          0.00540123519458607,
          0.004030560898579144
        ],
        "ranking_score": 0.6046679591048072
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 5,
      "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": [
              -0.05580895135023365,
              0.05580788818339866,
              0.05580880219520701
            ],
            "branch_aligned_reduced_polarization": [
              -0.05580895135023367,
              0.05580788818339866,
              0.05580880219520701
            ],
            "target_residual": 0.769362164463478,
            "energy_eV": -164.05825579371248,
            "max_atomic_step_A": 0.07329074342937453,
            "max_log_strain_component": 0.0026064918780186862,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.1325477357718252,
            "cell_principal_stretches": [
              0.9988962477509976,
              0.9983286996942998,
              0.9962857321791526
            ],
            "cell_volume_ratio": 0.9935228247626113,
            "cell_rmsd_from_input_A": 0.04040575887417367
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.4997675453298344,
              0.4995850043628894,
              0.49994978344130925
            ],
            "branch_aligned_reduced_polarization": [
              -0.4997675453298344,
              0.4995850043628894,
              0.49994978344130925
            ],
            "target_residual": 0.00047830769936242645,
            "energy_eV": -163.81415268817744
          }
        ],
        "iterations": 1
      },
      "parent": {
        "candidate_id": "bec_projection_05",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Iba2",
        "spacegroup_number": 45,
        "pointgroup": "mm2",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          -0.5,
          0.5,
          0.5
        ],
        "formal_class": [
          0.5,
          0.5,
          0.5
        ],
        "target_residual": 0.00047830769936242645,
        "parent_symmetrization_rmsd_A": 0.07299795046642933,
        "parent_cell_rmsd_A": 0.04040575887417367,
        "energy_eV": -163.81415268817744,
        "reduced_polarization": [
          -0.4997675453298344,
          0.4995850043628894,
          0.49994978344130925
        ],
        "cartesian_polarization_e_A2": [
          -7.479545266049302e-10,
          0.005393865542319165,
          0.0040273538615585355
        ],
        "ranking_score": 0.5840560055836976
      },
      "branch_status": "awaiting_branch_sampling"
    }
  ],
  "sampled_polarization_branches": [
    {
      "orbit_id": 0,
      "candidate_id": "inversion_parent_endpoint_00",
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "construction": "MACEField-BEC-parent plus variable-cell P-N-P path and symmetric log-strain continuation beyond both polar endpoints",
      "geometry_diagnostics": {
        "collision_aware": false,
        "permutations_tested": 1,
        "selected_order": [
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          10,
          11,
          12,
          13,
          14,
          15,
          16,
          17,
          18,
          19,
          20,
          21,
          22,
          23,
          24,
          25,
          26,
          27,
          28,
          29,
          30,
          31,
          32,
          33,
          34,
          35,
          36,
          37,
          38,
          39,
          40,
          41
        ],
        "endpoint_rmsd_A": 0.47345739439541484,
        "minimum_distance_A_by_image": [
          2.7732754513850835,
          2.6323341989761606,
          2.5037757608537223,
          2.389599528346265,
          2.2919559050735763,
          2.2130343321840797,
          2.154892841823954,
          2.119242431567866,
          2.107224935185162
        ],
        "minimum_distance_A": 2.107224935185162,
        "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": [
          1251.4873458731597,
          1251.4873458731597,
          1251.4873458731597,
          1251.4873458731597,
          1251.4873458731597,
          1251.4873458731597,
          1251.4873458731597,
          1251.4873458731597,
          1251.4873458731597
        ],
        "cell_deformation_log_strain_norm": 0.0
      },
      "parent_reduced_polarization": [
        9.010434594410423e-15,
        -4.187333097489239e-15,
        -3.906334691368798e-15
      ],
      "incoming": {
        "reached": true,
        "construction": "variable_cell_linear_interpolation",
        "continuation_fractions": [
          0.0,
          0.125,
          0.25,
          0.375,
          0.5,
          0.625,
          0.75,
          0.875,
          1.0
        ],
        "energies_eV": [
          -164.0582557937125,
          -163.8980332512329,
          -163.21095775777422,
          -161.9894892855931,
          -160.36421694623954,
          -158.57985398698662,
          -156.93879407934642,
          -155.7589456185613,
          -155.32385810376945
        ],
        "cartesian_polarizations_e_A2": [
          [
            -5.747447170001335e-09,
            0.0006006855845137009,
            0.00044842538566694924
          ],
          [
            -5.164488514013767e-09,
            0.001538286575182125,
            0.0011483573413940415
          ],
          [
            -4.811552410861102e-09,
            0.0022266256060041135,
            0.001662211668384324
          ],
          [
            -4.384322907375304e-09,
            0.0025114828949302213,
            0.0018748610129516907
          ],
          [
            -3.678746714582349e-09,
            0.002414114921650012,
            0.0018021736729442136
          ],
          [
            -2.7459997978434427e-09,
            0.0020266604481076786,
            0.0015129328203187216
          ],
          [
            -1.7726101729324521e-09,
            0.0014487738510848974,
            0.0010815316124050912
          ],
          [
            -8.624360521088898e-10,
            0.0007572189199551965,
            0.0005652753670146676
          ],
          [
            4.7061867345747714e-17,
            -4.440049878708149e-17,
            -3.1387515438769773e-17
          ]
        ],
        "raw_reduced_polarization": [
          [
            -0.05580895135023039,
            0.055807888183401544,
            0.05580880219520472
          ],
          [
            -0.14291891241325475,
            0.14291786929217254,
            0.14291886624561098
          ],
          [
            -0.20687062231308498,
            0.20686959946137667,
            0.2068706303713153
          ],
          [
            -0.23333588988359466,
            0.23333494068921082,
            0.2333359144235308
          ],
          [
            -0.2242895787954612,
            0.2242887736158557,
            0.2242896081477622
          ],
          [
            -0.1882920771174884,
            0.1882914507304595,
            0.1882921244037499
          ],
          [
            -0.13460201971535327,
            0.13460159857525805,
            0.1346020670413291
          ],
          [
            -0.07035134216231079,
            0.0703511304051236,
            0.0703513720496054
          ],
          [
            9.010434594410423e-15,
            -4.187333097489239e-15,
            -3.906334691368798e-15
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -0.05580895135023039,
            0.055807888183401544,
            0.05580880219520472
          ],
          [
            -0.14291891241325475,
            0.14291786929217254,
            0.14291886624561098
          ],
          [
            -0.20687062231308498,
            0.20686959946137667,
            0.2068706303713153
          ],
          [
            -0.23333588988359466,
            0.23333494068921082,
            0.2333359144235308
          ],
          [
            -0.2242895787954612,
            0.2242887736158557,
            0.2242896081477622
          ],
          [
            -0.1882920771174884,
            0.1882914507304595,
            0.1882921244037499
          ],
          [
            -0.13460201971535327,
            0.13460159857525805,
            0.1346020670413291
          ],
          [
            -0.07035134216231079,
            0.0703511304051236,
            0.0703513720496054
          ],
          [
            9.006684287271582e-15,
            -4.191091917959966e-15,
            -3.899658373995862e-15
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            -0.055808951350230396,
            0.055807888183401544,
            0.055808802195204676
          ],
          [
            -0.14291891241325472,
            0.14291786929217254,
            0.142918866245611
          ],
          [
            -0.20687062231308495,
            0.20686959946137673,
            0.20687063037131526
          ],
          [
            -0.23333588988359466,
            0.2333349406892108,
            0.23333591442353074
          ],
          [
            -0.2242895787954612,
            0.22428877361585564,
            0.22428960814776222
          ],
          [
            -0.1882920771174884,
            0.1882914507304595,
            0.18829212440374987
          ],
          [
            -0.13460201971535324,
            0.134601598575258,
            0.13460206704132904
          ],
          [
            -0.07035134216231076,
            0.07035113040512364,
            0.0703513720496054
          ],
          [
            8.992806499463768e-15,
            -4.218847493575595e-15,
            -3.885780586188048e-15
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -155.3238581037694,
          -155.75894561856134,
          -156.93879407934642,
          -158.57985398698662,
          -160.36421694623962,
          -161.98948928559315,
          -163.21095775777422,
          -163.89803325123285,
          -164.05825579371248
        ],
        "cartesian_polarizations_e_A2": [
          [
            2.7201404476701023e-17,
            -5.879961159303187e-17,
            -5.179688557304137e-17
          ],
          [
            8.624360649721712e-10,
            -0.0007572189199553122,
            -0.0005652753670148058
          ],
          [
            1.7726101666754638e-09,
            -0.0014487738510849816,
            -0.001081531612405113
          ],
          [
            2.745999758469569e-09,
            -0.0020266604481077926,
            -0.0015129328203187392
          ],
          [
            3.678746649356641e-09,
            -0.002414114921650037,
            -0.0018021736729441934
          ],
          [
            4.38432287515611e-09,
            -0.0025114828949302564,
            -0.0018748610129516517
          ],
          [
            4.8115525052981025e-09,
            -0.0022266256060042367,
            -0.001662211668384319
          ],
          [
            5.164488506695004e-09,
            -0.0015382865751823833,
            -0.0011483573413941597
          ],
          [
            5.747447264191604e-09,
            -0.0006006855845138134,
            -0.0004484253856669541
          ]
        ],
        "raw_reduced_polarization": [
          [
            8.683778211986362e-15,
            -5.1833250699043505e-15,
            -6.44638379911099e-15
          ],
          [
            0.0703513421623252,
            -0.07035113040513252,
            -0.07035137204962259
          ],
          [
            0.1346020197153586,
            -0.1346015985752673,
            -0.13460206704133182
          ],
          [
            0.18829207711749185,
            -0.1882914507304725,
            -0.1882921244037521
          ],
          [
            0.22428957879545489,
            -0.22428877361585936,
            -0.2242896081477597
          ],
          [
            0.23333588988359164,
            -0.2333349406892164,
            -0.23333591442352594
          ],
          [
            0.20687062231310202,
            -0.20686959946139152,
            -0.20687063037131467
          ],
          [
            0.14291891241327465,
            -0.14291786929219918,
            -0.1429188662456257
          ],
          [
            0.05580895135024727,
            -0.055807888183414804,
            -0.05580880219520533
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            8.683778211986362e-15,
            -5.1833250699043505e-15,
            -6.44638379911099e-15
          ],
          [
            0.0703513421623252,
            -0.07035113040513252,
            -0.07035137204962259
          ],
          [
            0.1346020197153586,
            -0.1346015985752673,
            -0.13460206704133182
          ],
          [
            0.18829207711749185,
            -0.1882914507304725,
            -0.1882921244037521
          ],
          [
            0.22428957879545489,
            -0.22428877361585936,
            -0.2242896081477597
          ],
          [
            0.23333588988359164,
            -0.2333349406892164,
            -0.23333591442352594
          ],
          [
            0.20687062231310202,
            -0.20686959946139152,
            -0.20687063037131467
          ],
          [
            0.14291891241327465,
            -0.14291786929219918,
            -0.1429188662456257
          ],
          [
            0.05580895135024727,
            -0.05580788818341481,
            -0.05580880219520533
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          0.055808951350248416,
          -0.05580788818340992,
          -0.05580880219521253
        ],
        "actual_opposite_endpoint_branch_residual": 8.781728810925229e-15
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            -0.05580895135023039,
            0.055807888183401544,
            0.05580880219520472
          ],
          [
            -0.14291891241325475,
            0.14291786929217254,
            0.14291886624561098
          ],
          [
            -0.20687062231308498,
            0.20686959946137667,
            0.2068706303713153
          ],
          [
            -0.23333588988359466,
            0.23333494068921082,
            0.2333359144235308
          ],
          [
            -0.2242895787954612,
            0.2242887736158557,
            0.2242896081477622
          ],
          [
            -0.1882920771174884,
            0.1882914507304595,
            0.1882921244037499
          ],
          [
            -0.13460201971535327,
            0.13460159857525805,
            0.1346020670413291
          ],
          [
            -0.07035134216231079,
            0.0703511304051236,
            0.0703513720496054
          ],
          [
            9.010434594410423e-15,
            -4.187333097489239e-15,
            -3.906334691368798e-15
          ],
          [
            0.0703513421623252,
            -0.07035113040513252,
            -0.07035137204962259
          ],
          [
            0.1346020197153586,
            -0.1346015985752673,
            -0.13460206704133182
          ],
          [
            0.18829207711749185,
            -0.1882914507304725,
            -0.1882921244037521
          ],
          [
            0.22428957879545489,
            -0.22428877361585936,
            -0.2242896081477597
          ],
          [
            0.23333588988359164,
            -0.2333349406892164,
            -0.23333591442352594
          ],
          [
            0.20687062231310202,
            -0.20686959946139152,
            -0.20687063037131467
          ],
          [
            0.14291891241327465,
            -0.14291786929219918,
            -0.1429188662456257
          ],
          [
            0.05580895135024727,
            -0.055807888183414804,
            -0.05580880219520533
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -0.05580895135023039,
            0.055807888183401544,
            0.05580880219520472
          ],
          [
            -0.14291891241325475,
            0.14291786929217254,
            0.14291886624561098
          ],
          [
            -0.20687062231308498,
            0.20686959946137667,
            0.2068706303713153
          ],
          [
            -0.23333588988359466,
            0.23333494068921082,
            0.2333359144235308
          ],
          [
            -0.2242895787954612,
            0.2242887736158557,
            0.2242896081477622
          ],
          [
            -0.1882920771174884,
            0.1882914507304595,
            0.1882921244037499
          ],
          [
            -0.13460201971535327,
            0.13460159857525805,
            0.1346020670413291
          ],
          [
            -0.07035134216231079,
            0.0703511304051236,
            0.0703513720496054
          ],
          [
            9.006684287271582e-15,
            -4.191091917959966e-15,
            -3.899658373995862e-15
          ],
          [
            0.0703513421623252,
            -0.07035113040513252,
            -0.07035137204962259
          ],
          [
            0.1346020197153586,
            -0.1346015985752673,
            -0.13460206704133182
          ],
          [
            0.18829207711749185,
            -0.1882914507304725,
            -0.1882921244037521
          ],
          [
            0.22428957879545489,
            -0.22428877361585936,
            -0.2242896081477597
          ],
          [
            0.23333588988359164,
            -0.2333349406892164,
            -0.23333591442352594
          ],
          [
            0.20687062231310202,
            -0.20686959946139152,
            -0.20687063037131467
          ],
          [
            0.14291891241327465,
            -0.14291786929219918,
            -0.1429188662456257
          ],
          [
            0.05580895135024727,
            -0.05580788818341481,
            -0.05580880219520533
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            -0.055808951350230396,
            0.055807888183401544,
            0.055808802195204676
          ],
          [
            -0.14291891241325472,
            0.14291786929217254,
            0.142918866245611
          ],
          [
            -0.20687062231308495,
            0.20686959946137673,
            0.20687063037131526
          ],
          [
            -0.23333588988359466,
            0.2333349406892108,
            0.23333591442353074
          ],
          [
            -0.2242895787954612,
            0.22428877361585564,
            0.22428960814776222
          ],
          [
            -0.1882920771174884,
            0.1882914507304595,
            0.18829212440374987
          ],
          [
            -0.13460201971535324,
            0.134601598575258,
            0.13460206704132904
          ],
          [
            -0.07035134216231076,
            0.07035113040512364,
            0.0703513720496054
          ],
          [
            8.992806499463768e-15,
            -4.218847493575595e-15,
            -3.885780586188048e-15
          ],
          [
            0.07035134216232519,
            -0.07035113040513252,
            -0.0703513720496226
          ],
          [
            0.13460201971535857,
            -0.13460159857526732,
            -0.13460206704133182
          ],
          [
            0.18829207711749185,
            -0.1882914507304725,
            -0.1882921244037521
          ],
          [
            0.22428957879545486,
            -0.22428877361585936,
            -0.22428960814775967
          ],
          [
            0.23333588988359166,
            -0.2333349406892164,
            -0.23333591442352597
          ],
          [
            0.20687062231310205,
            -0.2068695994613915,
            -0.2068706303713147
          ],
          [
            0.1429189124132746,
            -0.14291786929219918,
            -0.14291886624562566
          ],
          [
            0.05580895135024733,
            -0.05580788818341481,
            -0.05580880219520534
          ]
        ]
      },
      "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": "Ibam",
        "spacegroup_number": 72,
        "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": 6.555793737145348e-15,
        "parent_symmetrization_rmsd_A": 0.47345739439541484,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -155.32385810376934,
        "reduced_polarization": [
          1.5938000717375517e-15,
          -1.0755467381861623e-15,
          -6.2674900932750306e-15
        ],
        "cartesian_polarization_e_A2": [
          -1.9699671851960607e-17,
          -2.3946772510165454e-17,
          -5.0359469325470083e-17
        ],
        "ranking_score": 0.47345739439542794
      }
    }
  ],
  "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": 43,
      "full_response": 11,
      "energy_polarization": 32
    },
    "model_evaluations_for_recovery_and_path_properties": {
      "total": 68,
      "full_response": 36,
      "energy_polarization": 32
    },
    "elapsed_seconds": 296.9975331510068
  }
}