{
  "schema": "ferrofinder.endpoint_parent_recovery.v4_variable_cell",
  "status": "complete",
  "input_atom_count": 24,
  "input_formula": "Ag8Ge4S12",
  "input_spacegroup": "Cmc2_1",
  "input_pointgroup": "mm2",
  "input_is_polar_point_group": true,
  "input_energy_eV": -94.8963370430871,
  "input_cartesian_polarization_e_A2": [
    -1.0596255768183467e-16,
    2.2477902974206738e-17,
    -0.002070780940885716
  ],
  "input_reduced_polarization": [
    -4.879432997147898e-15,
    1.7567258521752122e-15,
    -0.1747086401692938
  ],
  "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": "Cmcm",
      "spacegroup_number": 63,
      "pointgroup": "mmm",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 2.886962431967058e-16,
      "parent_symmetrization_rmsd_A": 0.6217259228349089,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -89.31411062955732,
      "reduced_polarization": [
        -3.689376841394348e-18,
        2.283251527757139e-16,
        1.7663389806138738e-16
      ],
      "cartesian_polarization_e_A2": [
        -8.011910535399944e-20,
        2.9214977535103437e-18,
        2.093600575595104e-18
      ],
      "ranking_score": 0.6217259228349095
    },
    {
      "candidate_id": "inversion_parent_endpoint_01",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "Fmmm",
      "spacegroup_number": 69,
      "pointgroup": "mmm",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 2.8702509519744483e-16,
      "parent_symmetrization_rmsd_A": 0.8712645063637869,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -60.93751828422193,
      "reduced_polarization": [
        2.8595934951478653e-16,
        8.693080734768988e-18,
        -2.313192697379994e-17
      ],
      "cartesian_polarization_e_A2": [
        6.20993957398982e-18,
        1.1123091577500968e-19,
        -2.741773586978216e-19
      ],
      "ranking_score": 0.8712645063637875
    },
    {
      "candidate_id": "bec_projection_00",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cmc2_1",
      "spacegroup_number": 36,
      "pointgroup": "mm2",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 6.6864808600671205e-06,
      "parent_symmetrization_rmsd_A": 0.016884511346226243,
      "parent_cell_rmsd_A": 0.07018659017714188,
      "energy_eV": -94.83750035196344,
      "reduced_polarization": [
        4.705597275540713e-15,
        7.093163954019392e-15,
        -6.6864808600671205e-06
      ],
      "cartesian_polarization_e_A2": [
        1.0213061511267306e-16,
        9.080467627158118e-17,
        -7.826772600024418e-08
      ],
      "ranking_score": 0.5344445318522318
    },
    {
      "candidate_id": "inversion_parent_bec_00_00",
      "source": "same_species_inversion_center_projection_after_BEC",
      "spacegroup": "Cmcm",
      "spacegroup_number": 63,
      "pointgroup": "mmm",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 5.2656312316672284e-15,
      "parent_symmetrization_rmsd_A": 0.6217323500246412,
      "parent_cell_rmsd_A": 0.07018659017714188,
      "energy_eV": -89.44004458359737,
      "reduced_polarization": [
        -3.7878817301599045e-15,
        3.442856435989196e-15,
        -1.2351371694665793e-15
      ],
      "cartesian_polarization_e_A2": [
        -8.221316780880697e-17,
        4.407277197388671e-17,
        -1.4457736375181384e-17
      ],
      "ranking_score": 0.6392789975689372
    },
    {
      "candidate_id": "bec_projection_01",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cmc2_1",
      "spacegroup_number": 36,
      "pointgroup": "mm2",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        -0.5
      ],
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_residual": 0.0003843441105559342,
      "parent_symmetrization_rmsd_A": 0.03233106288868975,
      "parent_cell_rmsd_A": 0.13501045238872508,
      "energy_eV": -94.64589036091775,
      "reduced_polarization": [
        7.9826210407991405e-16,
        -2.030703967204185e-15,
        -0.49961565588944407
      ],
      "cartesian_polarization_e_A2": [
        1.4430488376695213e-16,
        -5.232483370144968e-16,
        -0.006068229419545775
      ],
      "ranking_score": 0.5668523642069829
    },
    {
      "candidate_id": "bec_projection_02",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cc",
      "spacegroup_number": 9,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        -0.5,
        0.0,
        0.0
      ],
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_residual": 7.591196971008174e-05,
      "parent_symmetrization_rmsd_A": 0.09678422285565397,
      "parent_cell_rmsd_A": 0.4950264208960275,
      "energy_eV": -92.20200967565573,
      "reduced_polarization": [
        -0.5000667073620186,
        -6.3226148940986605e-15,
        3.623196099825322e-05
      ],
      "cartesian_polarization_e_A2": [
        -0.010871408077216569,
        -2.5596455855691785e-16,
        0.0006262063501102166
      ],
      "ranking_score": 0.7206926520190811
    },
    {
      "candidate_id": "bec_projection_03",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cm",
      "spacegroup_number": 8,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.0
      ],
      "formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_residual": 6.615788263431807e-05,
      "parent_symmetrization_rmsd_A": 0.06645422760089406,
      "parent_cell_rmsd_A": 0.2057488695042099,
      "energy_eV": -93.87363091649561,
      "reduced_polarization": [
        -4.084651907292994e-15,
        0.4999632022049059,
        -5.4979884602192295e-05
      ],
      "cartesian_polarization_e_A2": [
        -6.89409932768272e-16,
        0.00640544512031804,
        0.0002378906216813398
      ],
      "ranking_score": 0.6180237607422152
    },
    {
      "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": [
        -0.5,
        0.0,
        -0.5
      ],
      "formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_residual": 0.0007135625380727158,
      "parent_symmetrization_rmsd_A": 0.10580665687051072,
      "parent_cell_rmsd_A": 0.5144267860224429,
      "energy_eV": -91.26392520637745,
      "reduced_polarization": [
        -0.4997825727241848,
        6.3261486355626376e-15,
        -0.499320370045192
      ],
      "cartesian_polarization_e_A2": [
        -0.01052451225731663,
        -4.744424443837075e-16,
        -0.005418611778772956
      ],
      "ranking_score": 0.7358404784522669
    },
    {
      "candidate_id": "bec_projection_05",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cm",
      "spacegroup_number": 8,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.5,
        -0.5
      ],
      "formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_residual": 0.00034541957307233744,
      "parent_symmetrization_rmsd_A": 0.07081187738623436,
      "parent_cell_rmsd_A": 0.21612638660061922,
      "energy_eV": -93.48080409886781,
      "reduced_polarization": [
        7.301080297764729e-15,
        0.4999364602130426,
        -0.49966047477717423
      ],
      "cartesian_polarization_e_A2": [
        -2.3479248895799537e-16,
        0.006184658884032715,
        -0.0058402348178686475
      ],
      "ranking_score": 0.6255343131825338
    },
    {
      "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": 5.006973319280873e-06,
      "parent_symmetrization_rmsd_A": 0.11782526554694775,
      "parent_cell_rmsd_A": 0.5443089502395897,
      "energy_eV": -91.0331027848066,
      "reduced_polarization": [
        -0.4999981954161753,
        0.4999958888438547,
        -2.2162252116221746e-06
      ],
      "cartesian_polarization_e_A2": [
        -0.010875992455455294,
        0.006420011529715925,
        0.0008810109018758393
      ],
      "ranking_score": 0.7539125170534837
    },
    {
      "candidate_id": "bec_projection_07",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        -0.5,
        0.5,
        -0.5
      ],
      "formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "target_residual": 0.0007735581362881001,
      "parent_symmetrization_rmsd_A": 0.1238159932164054,
      "parent_cell_rmsd_A": 0.5447809287488591,
      "energy_eV": -89.91809004287163,
      "reduced_polarization": [
        -0.4997381503217278,
        0.49988565590141876,
        -0.4992811451027322
      ],
      "cartesian_polarization_e_A2": [
        -0.010528964842174363,
        0.006193570787950108,
        -0.005185745605425964
      ],
      "ranking_score": 0.7615583416761964
    }
  ],
  "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": [
              -4.879432997147898e-15,
              1.7567258521752122e-15,
              -0.1747086401692938
            ],
            "branch_aligned_reduced_polarization": [
              -4.879432997147898e-15,
              1.7567258521752122e-15,
              -0.1747086401692938
            ],
            "target_residual": 0.1747086401692938,
            "energy_eV": -94.8963370430871,
            "max_atomic_step_A": 0.023973699337505643,
            "max_log_strain_component": 0.006818911430432611,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 7.584529553787404,
            "cell_principal_stretches": [
              1.0068422131409702,
              1.0058191565391672,
              0.99375363440914
            ],
            "cell_volume_ratio": 1.0063754837499905,
            "cell_rmsd_from_input_A": 0.07079209806485551
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              5.3980969006755025e-14,
              -7.810662974836446e-14,
              0.0015075577530743107
            ],
            "branch_aligned_reduced_polarization": [
              5.3980969006755025e-14,
              -7.810662974836446e-14,
              0.0015075577530743107
            ],
            "target_residual": 0.0015075577530743107,
            "energy_eV": -94.8363801225373,
            "max_atomic_step_A": 0.00020803476841220684,
            "max_log_strain_component": 5.80374570202569e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 7.584529553787404,
            "cell_principal_stretches": [
              1.0067837802749635,
              1.0057694856443122,
              0.9938066338100028
            ],
            "cell_volume_ratio": 1.0063210492777883,
            "cell_rmsd_from_input_A": 0.07018659017714188
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              4.705597275540713e-15,
              7.093163954019392e-15,
              -6.6864808600671205e-06
            ],
            "branch_aligned_reduced_polarization": [
              4.705597275540713e-15,
              7.093163954019392e-15,
              -6.6864808600671205e-06
            ],
            "target_residual": 6.6864808600671205e-06,
            "energy_eV": -94.83750035196344
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_00",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cmc2_1",
        "spacegroup_number": 36,
        "pointgroup": "mm2",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.0
        ],
        "formal_class": [
          0.0,
          0.0,
          0.0
        ],
        "target_residual": 6.6864808600671205e-06,
        "parent_symmetrization_rmsd_A": 0.016884511346226243,
        "parent_cell_rmsd_A": 0.07018659017714188,
        "energy_eV": -94.83750035196344,
        "reduced_polarization": [
          4.705597275540713e-15,
          7.093163954019392e-15,
          -6.6864808600671205e-06
        ],
        "cartesian_polarization_e_A2": [
          1.0213061511267306e-16,
          9.080467627158118e-17,
          -7.826772600024418e-08
        ],
        "ranking_score": 0.5344445318522318
      },
      "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": [
          -94.8963370430871,
          -94.89649627623737,
          -94.89456181919341,
          -94.89050787535645,
          -94.8843079867422,
          -94.87593463777736,
          -94.86536063492134,
          -94.85255873102449,
          -94.83750035196346
        ],
        "cartesian_polarizations_e_A2": [
          [
            8.271375780368784e-18,
            -2.2289013033247018e-17,
            -0.0020707809408857013
          ],
          [
            1.15351786617488e-17,
            1.471552389760145e-16,
            -0.001810125577992313
          ],
          [
            2.01440375330655e-17,
            -5.586113374633774e-17,
            -0.001549876367455267
          ],
          [
            -4.4112448210467076e-17,
            -1.036442734571868e-17,
            -0.0012900958928749766
          ],
          [
            -1.178059392123856e-16,
            7.13138827422317e-17,
            -0.0010308401163985226
          ],
          [
            -6.402559883847391e-17,
            7.350296186894862e-17,
            -0.0007721599322883394
          ],
          [
            -4.30616270630206e-18,
            8.230612783149267e-17,
            -0.0005141064775988717
          ],
          [
            -1.0191956899289698e-16,
            1.3161492450629834e-16,
            -0.00025673041157832046
          ],
          [
            1.8447366264667324e-17,
            2.0954588389798974e-16,
            -7.826772610672208e-08
          ]
        ],
        "raw_reduced_polarization": [
          [
            3.808857090419242e-16,
            -1.741963450056093e-15,
            -0.17470864016929255
          ],
          [
            6.485917008901831e-16,
            1.0703342031432438e-14,
            -0.15295661457329102
          ],
          [
            1.128897652601585e-15,
            -5.730557375384739e-15,
            -0.1311704313923218
          ],
          [
            -1.7803610748250833e-15,
            -2.5158703598242894e-15,
            -0.10935539571817086
          ],
          [
            -5.1582606503755295e-15,
            3.7532276292575865e-15,
            -0.08751628388110669
          ],
          [
            -2.6981336925225003e-15,
            4.038479322165981e-15,
            -0.06565747128185594
          ],
          [
            2.4647016888289166e-18,
            5.067524497020203e-15,
            -0.04378338141457942
          ],
          [
            -4.578406001251395e-15,
            9.487476392035847e-15,
            -0.02189842467069506
          ],
          [
            8.499831704018832e-16,
            1.636893474365615e-14,
            -6.686480869163622e-06
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            3.808857090419242e-16,
            -1.741963450056093e-15,
            -0.17470864016929255
          ],
          [
            6.485917008901831e-16,
            1.0703342031432438e-14,
            -0.15295661457329102
          ],
          [
            1.128897652601585e-15,
            -5.730557375384738e-15,
            -0.1311704313923218
          ],
          [
            -1.7803610748250833e-15,
            -2.5158703598242894e-15,
            -0.10935539571817086
          ],
          [
            -5.1582606503755295e-15,
            3.7532276292575865e-15,
            -0.08751628388110669
          ],
          [
            -2.6981336925225003e-15,
            4.038479322165981e-15,
            -0.06565747128185594
          ],
          [
            2.4647016888289112e-18,
            5.067524497020203e-15,
            -0.04378338141457942
          ],
          [
            -4.578406001251395e-15,
            9.487476392035847e-15,
            -0.02189842467069506
          ],
          [
            8.499831704018835e-16,
            1.636893474365615e-14,
            -6.6864808691627364e-06
          ]
        ],
        "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": [
          [
            3.3306690738754696e-16,
            -1.7208456881689926e-15,
            -0.17470864016929255
          ],
          [
            6.661338147750939e-16,
            1.0658141036401503e-14,
            -0.15295661457329102
          ],
          [
            1.1102230246251565e-15,
            -5.717648576819556e-15,
            -0.13117043139232176
          ],
          [
            -1.7763568394002505e-15,
            -2.4980018054066022e-15,
            -0.10935539571817088
          ],
          [
            -5.162537064506978e-15,
            3.774758283725532e-15,
            -0.08751628388110666
          ],
          [
            -2.7200464103316335e-15,
            3.9968028886505635e-15,
            -0.06565747128185595
          ],
          [
            0.0,
            5.10702591327572e-15,
            -0.043783381414579436
          ],
          [
            -4.551914400963142e-15,
            9.43689570931383e-15,
            -0.021898424670695082
          ],
          [
            8.881784197001252e-16,
            1.63202784619898e-14,
            -6.6864808691557975e-06
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -94.83750035196344,
          -94.83977461778407,
          -94.84100417818689,
          -94.84118231676675,
          -94.84030235430127,
          -94.83835775617777,
          -94.83534208434573,
          -94.83124892927296,
          -94.82607210903245
        ],
        "cartesian_polarizations_e_A2": [
          [
            6.512568814652786e-17,
            1.3180536831372764e-16,
            -7.826772616279537e-08
          ],
          [
            -2.1964675435268556e-16,
            8.373975307579237e-16,
            7.570909974450616e-05
          ],
          [
            -3.677548117944506e-16,
            1.3083566068819e-15,
            0.0001524314362995002
          ],
          [
            -5.444246756907339e-16,
            1.852500416113485e-15,
            0.00023008116666726287
          ],
          [
            -7.135304235156747e-16,
            2.3263565177883934e-15,
            0.0003086506576761436
          ],
          [
            -9.732265629607932e-16,
            3.0120659049149328e-15,
            0.00038813232151178173
          ],
          [
            -1.1196827846809458e-15,
            3.45410524899775e-15,
            0.000468518543234008
          ],
          [
            -1.2433987956352329e-15,
            4.168494576915556e-15,
            0.0005498015882990379
          ],
          [
            -1.2627796299756554e-15,
            4.806033805471379e-15,
            0.0006319737650334281
          ]
        ],
        "raw_reduced_polarization": [
          [
            3.0006357649110174e-15,
            1.0296037069441529e-14,
            -6.686480873954012e-06
          ],
          [
            -1.0153824193831656e-14,
            6.565350269229488e-14,
            0.006457785844102969
          ],
          [
            -1.7001126652547318e-14,
            1.0262140126183266e-13,
            0.012981675987129853
          ],
          [
            -2.515345569664631e-14,
            1.4524557724758928e-13,
            0.01956401382830448
          ],
          [
            -3.294637575340242e-14,
            1.8231563472977736e-13,
            0.026203829427640202
          ],
          [
            -4.49006142296932e-14,
            2.3587604582314003e-13,
            0.032900161797543605
          ],
          [
            -5.1627761784865384e-14,
            2.703319746593217e-13,
            0.039652052719670074
          ],
          [
            -5.729641443545325e-14,
            3.2600552986387197e-13,
            0.046458538929941735
          ],
          [
            -5.814930037014128e-14,
            3.7560816247795653e-13,
            0.05331866588671316
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            3.0006357649110174e-15,
            1.0296037069441529e-14,
            -6.686480873954012e-06
          ],
          [
            -1.0153824193831656e-14,
            6.565350269229488e-14,
            0.006457785844102969
          ],
          [
            -1.7001126652547318e-14,
            1.0262140126183266e-13,
            0.012981675987129853
          ],
          [
            -2.515345569664631e-14,
            1.4524557724758928e-13,
            0.01956401382830448
          ],
          [
            -3.294637575340242e-14,
            1.8231563472977736e-13,
            0.026203829427640202
          ],
          [
            -4.49006142296932e-14,
            2.3587604582314003e-13,
            0.032900161797543605
          ],
          [
            -5.1627761784865384e-14,
            2.703319746593217e-13,
            0.039652052719670074
          ],
          [
            -5.729641443545325e-14,
            3.2600552986387197e-13,
            0.046458538929941735
          ],
          [
            -5.814930037014128e-14,
            3.7560816247795653e-13,
            0.05331866588671316
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          1.3180670084371053e-15,
          3.449543443735536e-14,
          0.17469543351114034
        ],
        "actual_opposite_endpoint_branch_residual": 0.12137676762442717
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            3.808857090419242e-16,
            -1.741963450056093e-15,
            -0.17470864016929255
          ],
          [
            6.485917008901831e-16,
            1.0703342031432438e-14,
            -0.15295661457329102
          ],
          [
            1.128897652601585e-15,
            -5.730557375384739e-15,
            -0.1311704313923218
          ],
          [
            -1.7803610748250833e-15,
            -2.5158703598242894e-15,
            -0.10935539571817086
          ],
          [
            -5.1582606503755295e-15,
            3.7532276292575865e-15,
            -0.08751628388110669
          ],
          [
            -2.6981336925225003e-15,
            4.038479322165981e-15,
            -0.06565747128185594
          ],
          [
            2.4647016888289166e-18,
            5.067524497020203e-15,
            -0.04378338141457942
          ],
          [
            -4.578406001251395e-15,
            9.487476392035847e-15,
            -0.02189842467069506
          ],
          [
            8.499831704018832e-16,
            1.636893474365615e-14,
            -6.686480869163622e-06
          ],
          [
            -1.0153824193831656e-14,
            6.565350269229488e-14,
            0.006457785844102969
          ],
          [
            -1.7001126652547318e-14,
            1.0262140126183266e-13,
            0.012981675987129853
          ],
          [
            -2.515345569664631e-14,
            1.4524557724758928e-13,
            0.01956401382830448
          ],
          [
            -3.294637575340242e-14,
            1.8231563472977736e-13,
            0.026203829427640202
          ],
          [
            -4.49006142296932e-14,
            2.3587604582314003e-13,
            0.032900161797543605
          ],
          [
            -5.1627761784865384e-14,
            2.703319746593217e-13,
            0.039652052719670074
          ],
          [
            -5.729641443545325e-14,
            3.2600552986387197e-13,
            0.046458538929941735
          ],
          [
            -5.814930037014128e-14,
            3.7560816247795653e-13,
            0.05331866588671316
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            3.808857090419242e-16,
            -1.741963450056093e-15,
            -0.17470864016929255
          ],
          [
            6.485917008901831e-16,
            1.0703342031432438e-14,
            -0.15295661457329102
          ],
          [
            1.128897652601585e-15,
            -5.730557375384738e-15,
            -0.1311704313923218
          ],
          [
            -1.7803610748250833e-15,
            -2.5158703598242894e-15,
            -0.10935539571817086
          ],
          [
            -5.1582606503755295e-15,
            3.7532276292575865e-15,
            -0.08751628388110669
          ],
          [
            -2.6981336925225003e-15,
            4.038479322165981e-15,
            -0.06565747128185594
          ],
          [
            2.4647016888289112e-18,
            5.067524497020203e-15,
            -0.04378338141457942
          ],
          [
            -4.578406001251395e-15,
            9.487476392035847e-15,
            -0.02189842467069506
          ],
          [
            8.499831704018835e-16,
            1.636893474365615e-14,
            -6.6864808691627364e-06
          ],
          [
            -1.0153824193831656e-14,
            6.565350269229488e-14,
            0.006457785844102969
          ],
          [
            -1.7001126652547318e-14,
            1.0262140126183266e-13,
            0.012981675987129853
          ],
          [
            -2.515345569664631e-14,
            1.4524557724758928e-13,
            0.01956401382830448
          ],
          [
            -3.294637575340242e-14,
            1.8231563472977736e-13,
            0.026203829427640202
          ],
          [
            -4.49006142296932e-14,
            2.3587604582314003e-13,
            0.032900161797543605
          ],
          [
            -5.1627761784865384e-14,
            2.703319746593217e-13,
            0.039652052719670074
          ],
          [
            -5.729641443545325e-14,
            3.2600552986387197e-13,
            0.046458538929941735
          ],
          [
            -5.814930037014128e-14,
            3.7560816247795653e-13,
            0.05331866588671316
          ]
        ],
        "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": [
          [
            3.3306690738754696e-16,
            -1.7208456881689926e-15,
            -0.17470864016929255
          ],
          [
            6.661338147750939e-16,
            1.0658141036401503e-14,
            -0.15295661457329102
          ],
          [
            1.1102230246251565e-15,
            -5.717648576819556e-15,
            -0.13117043139232176
          ],
          [
            -1.7763568394002505e-15,
            -2.4980018054066022e-15,
            -0.10935539571817088
          ],
          [
            -5.162537064506978e-15,
            3.774758283725532e-15,
            -0.08751628388110666
          ],
          [
            -2.7200464103316335e-15,
            3.9968028886505635e-15,
            -0.06565747128185595
          ],
          [
            0.0,
            5.10702591327572e-15,
            -0.043783381414579436
          ],
          [
            -4.551914400963142e-15,
            9.43689570931383e-15,
            -0.021898424670695082
          ],
          [
            8.881784197001252e-16,
            1.63202784619898e-14,
            -6.6864808691557975e-06
          ],
          [
            -1.0158540675320182e-14,
            6.561418075534675e-14,
            0.006457785844102948
          ],
          [
            -1.6986412276764895e-14,
            1.0258460747536446e-13,
            0.012981675987129848
          ],
          [
            -2.5146551507759796e-14,
            1.4521717162097048e-13,
            0.019564013828304527
          ],
          [
            -3.297362383136715e-14,
            1.822986206434507e-13,
            0.026203829427640213
          ],
          [
            -4.490852134608758e-14,
            2.3592239273284576e-13,
            0.032900161797543626
          ],
          [
            -5.162537064506978e-14,
            2.703393064962256e-13,
            0.039652052719670094
          ],
          [
            -5.728750807065808e-14,
            3.2596148002994596e-13,
            0.046458538929941784
          ],
          [
            -5.81756864903582e-14,
            3.7558844923069046e-13,
            0.05331866588671319
          ]
        ]
      },
      "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": [
              -4.879432997147898e-15,
              1.7567258521752122e-15,
              -0.1747086401692938
            ],
            "branch_aligned_reduced_polarization": [
              -4.879432997147898e-15,
              1.7567258521752122e-15,
              -0.17470864016929377
            ],
            "target_residual": 0.32529135983070623,
            "energy_eV": -94.8963370430871,
            "max_atomic_step_A": 0.044636815043108215,
            "max_log_strain_component": 0.01269618359813908,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 7.584529553787404,
            "cell_principal_stretches": [
              1.0117349517463428,
              0.9892548168376901,
              0.9873840729312449
            ],
            "cell_volume_ratio": 0.9882368512563966,
            "cell_rmsd_from_input_A": 0.1299591073619933
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -8.859099668226817e-14,
              1.9480518653550322e-13,
              -0.4885594165659415
            ],
            "branch_aligned_reduced_polarization": [
              -8.859099668226817e-14,
              1.9480518653550322e-13,
              -0.4885594165659415
            ],
            "target_residual": 0.011440583434058516,
            "energy_eV": -94.66239242915127,
            "max_atomic_step_A": 0.0015403447361693487,
            "max_log_strain_component": 0.0004981934137984193,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 7.584529553787404,
            "cell_principal_stretches": [
              1.0121982241407865,
              0.9888355422544532,
              0.9868922872015984
            ],
            "cell_volume_ratio": 0.9877781018201274,
            "cell_rmsd_from_input_A": 0.13501045238872508
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              7.9826210407991405e-16,
              -2.030703967204185e-15,
              -0.49961565588944407
            ],
            "branch_aligned_reduced_polarization": [
              7.9826210407991405e-16,
              -2.030703967204185e-15,
              -0.49961565588944407
            ],
            "target_residual": 0.0003843441105559342,
            "energy_eV": -94.64589036091775
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_01",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cmc2_1",
        "spacegroup_number": 36,
        "pointgroup": "mm2",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          -0.5
        ],
        "formal_class": [
          0.0,
          0.0,
          0.5
        ],
        "target_residual": 0.0003843441105559342,
        "parent_symmetrization_rmsd_A": 0.03233106288868975,
        "parent_cell_rmsd_A": 0.13501045238872508,
        "energy_eV": -94.64589036091775,
        "reduced_polarization": [
          7.9826210407991405e-16,
          -2.030703967204185e-15,
          -0.49961565588944407
        ],
        "cartesian_polarization_e_A2": [
          1.4430488376695213e-16,
          -5.232483370144968e-16,
          -0.006068229419545775
        ],
        "ranking_score": 0.5668523642069829
      },
      "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": [
              -4.879432997147898e-15,
              1.7567258521752122e-15,
              -0.1747086401692938
            ],
            "branch_aligned_reduced_polarization": [
              -4.884981308350689e-15,
              1.7567258521752122e-15,
              -0.1747086401692938
            ],
            "target_residual": 0.5296443230601069,
            "energy_eV": -94.8963370430871,
            "max_atomic_step_A": 0.043604250258609645,
            "max_log_strain_component": 0.02,
            "step_scale": 0.3244122563894228,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 7.584529553787404,
            "cell_principal_stretches": [
              1.0202221133213913,
              1.0022145870267136,
              0.9800312888863595
            ],
            "cell_volume_ratio": 1.0020638466053176,
            "cell_rmsd_from_input_A": 0.168427801980959
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.1635739134816623,
              -6.453079319956849e-14,
              -0.12124016552053143
            ],
            "branch_aligned_reduced_polarization": [
              -0.16357391348166228,
              -6.453079319956849e-14,
              -0.12124016552053143
            ],
            "target_residual": 0.35760549412095155,
            "energy_eV": -94.60000832529194,
            "max_atomic_step_A": 0.045473661878460345,
            "max_log_strain_component": 0.02,
            "step_scale": 0.4993492102375159,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 7.584529553787404,
            "cell_principal_stretches": [
              1.0408614693908547,
              1.0045835741214988,
              0.9604439407478378
            ],
            "cell_volume_ratio": 1.004271240483381,
            "cell_rmsd_from_input_A": 0.3386637019816726
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.33550407125126314,
              -8.042362518353163e-14,
              -0.06597625081084815
            ],
            "branch_aligned_reduced_polarization": [
              -0.33550407125126314,
              -8.042362518353163e-14,
              -0.06597625081084815
            ],
            "target_residual": 0.17723367695211162,
            "energy_eV": -93.67149686182562,
            "max_atomic_step_A": 0.04561931049715449,
            "max_log_strain_component": 0.01832598111676465,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 7.584529553787404,
            "cell_principal_stretches": [
              1.0601561948867442,
              1.0070287908344544,
              0.9428081010894506
            ],
            "cell_volume_ratio": 1.0065492930277729,
            "cell_rmsd_from_input_A": 0.49715139460501845
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -0.5027235071614292,
              -4.502651280698552e-14,
              -0.005097645766953684
            ],
            "branch_aligned_reduced_polarization": [
              -0.5027235071614292,
              -4.502651280698552e-14,
              -0.005097645766953684
            ],
            "target_residual": 0.005779574692284636,
            "energy_eV": -92.16964476165897,
            "max_atomic_step_A": 0.0010435076402872346,
            "max_log_strain_component": 0.00030416386199227864,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 7.584529553787404,
            "cell_principal_stretches": [
              1.0598488715441403,
              1.0072343243298172,
              0.9430683994789884
            ],
            "cell_volume_ratio": 1.0067407583355512,
            "cell_rmsd_from_input_A": 0.4950264208960275
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              -0.5000667073620186,
              -6.3226148940986605e-15,
              3.623196099825322e-05
            ],
            "branch_aligned_reduced_polarization": [
              -0.5000667073620186,
              -6.3226148940986605e-15,
              3.623196099825322e-05
            ],
            "target_residual": 7.591196971008174e-05,
            "energy_eV": -92.20200967565573
          }
        ],
        "iterations": 4
      },
      "parent": {
        "candidate_id": "bec_projection_02",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cc",
        "spacegroup_number": 9,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          -0.5,
          0.0,
          0.0
        ],
        "formal_class": [
          0.5,
          0.0,
          0.0
        ],
        "target_residual": 7.591196971008174e-05,
        "parent_symmetrization_rmsd_A": 0.09678422285565397,
        "parent_cell_rmsd_A": 0.4950264208960275,
        "energy_eV": -92.20200967565573,
        "reduced_polarization": [
          -0.5000667073620186,
          -6.3226148940986605e-15,
          3.623196099825322e-05
        ],
        "cartesian_polarization_e_A2": [
          -0.010871408077216569,
          -2.5596455855691785e-16,
          0.0006262063501102166
        ],
        "ranking_score": 0.7206926520190811
      },
      "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": [
              -4.879432997147898e-15,
              1.7567258521752122e-15,
              -0.1747086401692938
            ],
            "branch_aligned_reduced_polarization": [
              -4.879432997147898e-15,
              1.7763568394002505e-15,
              -0.1747086401692938
            ],
            "target_residual": 0.5296443230601098,
            "energy_eV": -94.8963370430871,
            "max_atomic_step_A": 0.05108575226425102,
            "max_log_strain_component": 0.02,
            "step_scale": 0.5553563044135517,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 7.584529553787404,
            "cell_principal_stretches": [
              1.020692074072795,
              1.0032275360048197,
              0.9800283160679881
            ],
            "cell_volume_ratio": 1.0035356618702307,
            "cell_rmsd_from_input_A": 0.10568906132030571
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -1.6104083221260403e-14,
              0.27468839685206975,
              -0.0888896872689172
            ],
            "branch_aligned_reduced_polarization": [
              -1.6104083221260403e-14,
              0.27468839685206975,
              -0.0888896872689172
            ],
            "target_residual": 0.2422120868492246,
            "energy_eV": -94.60346711950416,
            "max_atomic_step_A": 0.04229022335695768,
            "max_log_strain_component": 0.01674534239774875,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 7.584529553787404,
            "cell_principal_stretches": [
              1.0385542569045285,
              1.006709459750483,
              0.9634908041018982
            ],
            "cell_volume_ratio": 1.0073512129590336,
            "cell_rmsd_from_input_A": 0.19831314782729983
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -9.240553108202289e-15,
              0.4914724562286246,
              -0.017203889113917004
            ],
            "branch_aligned_reduced_polarization": [
              -9.240553108202289e-15,
              0.4914724562286246,
              -0.017203889113917004
            ],
            "target_residual": 0.01920137503973804,
            "energy_eV": -93.91980581270266,
            "max_atomic_step_A": 0.0033418369557694665,
            "max_log_strain_component": 0.0008031934241813745,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 7.584529553787404,
            "cell_principal_stretches": [
              1.0395606140144096,
              1.0073619148433326,
              0.96261752141262
            ],
            "cell_volume_ratio": 1.00806632436857,
            "cell_rmsd_from_input_A": 0.2053180291640949
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -3.151639883166879e-16,
              0.4993642343410973,
              -0.0008274885428099205
            ],
            "branch_aligned_reduced_polarization": [
              -3.151639883166879e-16,
              0.4993642343410973,
              -0.0008274885428099205
            ],
            "target_residual": 0.001043520609054606,
            "energy_eV": -93.87666863625606,
            "max_atomic_step_A": 0.00019096779290516503,
            "max_log_strain_component": 5.712037084114924e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 7.584529553787404,
            "cell_principal_stretches": [
              1.0396284578416315,
              1.0073947829681322,
              0.9625576960953712
            ],
            "cell_volume_ratio": 1.0081023500405502,
            "cell_rmsd_from_input_A": 0.2057488695042099
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              -4.084651907292994e-15,
              0.4999632022049059,
              -5.4979884602192295e-05
            ],
            "branch_aligned_reduced_polarization": [
              -4.084651907292994e-15,
              0.4999632022049059,
              -5.4979884602192295e-05
            ],
            "target_residual": 6.615788263431807e-05,
            "energy_eV": -93.87363091649561
          }
        ],
        "iterations": 4
      },
      "parent": {
        "candidate_id": "bec_projection_03",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cm",
        "spacegroup_number": 8,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.5,
          0.0
        ],
        "formal_class": [
          0.0,
          0.5,
          0.0
        ],
        "target_residual": 6.615788263431807e-05,
        "parent_symmetrization_rmsd_A": 0.06645422760089406,
        "parent_cell_rmsd_A": 0.2057488695042099,
        "energy_eV": -93.87363091649561,
        "reduced_polarization": [
          -4.084651907292994e-15,
          0.4999632022049059,
          -5.4979884602192295e-05
        ],
        "cartesian_polarization_e_A2": [
          -6.89409932768272e-16,
          0.00640544512031804,
          0.0002378906216813398
        ],
        "ranking_score": 0.6180237607422152
      },
      "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": [
              -4.879432997147898e-15,
              1.7567258521752122e-15,
              -0.1747086401692938
            ],
            "branch_aligned_reduced_polarization": [
              -4.884981308350689e-15,
              1.7567258521752122e-15,
              -0.17470864016929377
            ],
            "target_residual": 0.5965018598298794,
            "energy_eV": -94.8963370430871,
            "max_atomic_step_A": 0.045282831410876946,
            "max_log_strain_component": 0.02,
            "step_scale": 0.3244122563891628,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 7.584529553787404,
            "cell_principal_stretches": [
              1.0206803636688024,
              0.9958896730445304,
              0.980013077997269
            ],
            "cell_volume_ratio": 0.996168626572448,
            "cell_rmsd_from_input_A": 0.17092934008245111
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.16311391398849565,
              2.4426913504491657e-14,
              -0.2823460718136139
            ],
            "branch_aligned_reduced_polarization": [
              -0.16311391398849562,
              2.4426913504491657e-14,
              -0.2823460718136139
            ],
            "target_residual": 0.4010803752405685,
            "energy_eV": -94.5533608290087,
            "max_atomic_step_A": 0.046387648271690625,
            "max_log_strain_component": 0.02,
            "step_scale": 0.4854786922956215,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 7.584529553787404,
            "cell_principal_stretches": [
              1.0418090234274229,
              0.9916948579636223,
              0.9604133009829421
            ],
            "cell_volume_ratio": 0.9922573901121592,
            "cell_rmsd_from_input_A": 0.3410400214938752
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.32855244804090916,
              6.203587308659907e-15,
              -0.3869917755292307
            ],
            "branch_aligned_reduced_polarization": [
              -0.32855244804090916,
              6.203587308659907e-15,
              -0.3869917755292307
            ],
            "target_residual": 0.2053414762555313,
            "energy_eV": -93.43854246313207,
            "max_atomic_step_A": 0.049439792558704856,
            "max_log_strain_component": 0.02,
            "step_scale": 0.9842053677293844,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 7.584529553787404,
            "cell_principal_stretches": [
              1.063521011727857,
              0.9868387680707906,
              0.9411203537004771
            ],
            "cell_volume_ratio": 0.987728176962956,
            "cell_rmsd_from_input_A": 0.512134096791337
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -0.49876849167245296,
              1.618291129566479e-14,
              -0.49034106919181786
            ],
            "branch_aligned_reduced_polarization": [
              -0.49876849167245296,
              1.618291129566479e-14,
              -0.49034106919181786
            ],
            "target_residual": 0.009737122630329139,
            "energy_eV": -91.30861812096332,
            "max_atomic_step_A": 0.0013640578439573408,
            "max_log_strain_component": 0.00045413145223993813,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 7.584529553787404,
            "cell_principal_stretches": [
              1.0637914189483213,
              0.9863907152930499,
              0.9409101829112307
            ],
            "cell_volume_ratio": 0.9873102075913919,
            "cell_rmsd_from_input_A": 0.5144267860224429
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              -0.4997825727241848,
              6.3261486355626376e-15,
              -0.499320370045192
            ],
            "branch_aligned_reduced_polarization": [
              -0.4997825727241848,
              6.3261486355626376e-15,
              -0.499320370045192
            ],
            "target_residual": 0.0007135625380727158,
            "energy_eV": -91.26392520637745
          }
        ],
        "iterations": 4
      },
      "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": [
          -0.5,
          0.0,
          -0.5
        ],
        "formal_class": [
          0.5,
          0.0,
          0.5
        ],
        "target_residual": 0.0007135625380727158,
        "parent_symmetrization_rmsd_A": 0.10580665687051072,
        "parent_cell_rmsd_A": 0.5144267860224429,
        "energy_eV": -91.26392520637745,
        "reduced_polarization": [
          -0.4997825727241848,
          6.3261486355626376e-15,
          -0.499320370045192
        ],
        "cartesian_polarization_e_A2": [
          -0.01052451225731663,
          -4.744424443837075e-16,
          -0.005418611778772956
        ],
        "ranking_score": 0.7358404784522669
      },
      "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": [
              -4.879432997147898e-15,
              1.7567258521752122e-15,
              -0.1747086401692938
            ],
            "branch_aligned_reduced_polarization": [
              -4.879432997147898e-15,
              1.7763568394002505e-15,
              -0.17470864016929377
            ],
            "target_residual": 0.596501859829882,
            "energy_eV": -94.8963370430871,
            "max_atomic_step_A": 0.05964006504778584,
            "max_log_strain_component": 0.02,
            "step_scale": 0.5553563044113268,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 7.584529553787404,
            "cell_principal_stretches": [
              1.0210456768315848,
              0.9940182650698933,
              0.9788282911100608
            ],
            "cell_volume_ratio": 0.9934500792578732,
            "cell_rmsd_from_input_A": 0.1217710799774266
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -8.998466928432752e-14,
              0.2828803931358614,
              -0.360004446781754
            ],
            "branch_aligned_reduced_polarization": [
              -8.998466928432752e-14,
              0.2828803931358614,
              -0.360004446781754
            ],
            "target_residual": 0.2583402380693353,
            "energy_eV": -94.48307032184314,
            "max_atomic_step_A": 0.04559982412477683,
            "max_log_strain_component": 0.015474017037546528,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 7.584529553787404,
            "cell_principal_stretches": [
              1.0376483539096637,
              0.9893656671621269,
              0.962736210990476
            ],
            "cell_volume_ratio": 0.9883581412760679,
            "cell_rmsd_from_input_A": 0.21600381210513828
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -9.024104827195237e-14,
              0.504117279543549,
              -0.4953812776871828
            ],
            "branch_aligned_reduced_polarization": [
              -9.024104827195237e-14,
              0.504117279543549,
              -0.4953812776871828
            ],
            "target_residual": 0.006187453970951416,
            "energy_eV": -93.4701679764622,
            "max_atomic_step_A": 0.001139990747191184,
            "max_log_strain_component": 0.0003087565539199792,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 7.584529553787404,
            "cell_principal_stretches": [
              1.0374075238736147,
              0.9891804205545035,
              0.9629425221836672
            ],
            "cell_volume_ratio": 0.988155449183784,
            "cell_rmsd_from_input_A": 0.21612638660061922
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              7.301080297764729e-15,
              0.4999364602130426,
              -0.49966047477717423
            ],
            "branch_aligned_reduced_polarization": [
              7.301080297764729e-15,
              0.4999364602130426,
              -0.49966047477717423
            ],
            "target_residual": 0.00034541957307233744,
            "energy_eV": -93.48080409886781
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_05",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cm",
        "spacegroup_number": 8,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.5,
          -0.5
        ],
        "formal_class": [
          0.0,
          0.5,
          0.5
        ],
        "target_residual": 0.00034541957307233744,
        "parent_symmetrization_rmsd_A": 0.07081187738623436,
        "parent_cell_rmsd_A": 0.21612638660061922,
        "energy_eV": -93.48080409886781,
        "reduced_polarization": [
          7.301080297764729e-15,
          0.4999364602130426,
          -0.49966047477717423
        ],
        "cartesian_polarization_e_A2": [
          -2.3479248895799537e-16,
          0.006184658884032715,
          -0.0058402348178686475
        ],
        "ranking_score": 0.6255343131825338
      },
      "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": [
              -4.879432997147898e-15,
              1.7567258521752122e-15,
              -0.1747086401692938
            ],
            "branch_aligned_reduced_polarization": [
              -4.884981308350689e-15,
              1.7763568394002505e-15,
              -0.1747086401692938
            ],
            "target_residual": 0.7283701730231663,
            "energy_eV": -94.8963370430871,
            "max_atomic_step_A": 0.0520797605766171,
            "max_log_strain_component": 0.02,
            "step_scale": 0.324412256389333,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 7.584529553787404,
            "cell_principal_stretches": [
              1.0234873257784578,
              1.0021303362274607,
              0.9769868434486343
            ],
            "cell_volume_ratio": 1.0020638466052996,
            "cell_rmsd_from_input_A": 0.1779377466438837
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.16395958068232902,
              0.16127818263109017,
              -0.12480049566482226
            ],
            "branch_aligned_reduced_polarization": [
              -0.16395958068232902,
              0.16127818263109017,
              -0.12480049566482226
            ],
            "target_residual": 0.4931843435218504,
            "energy_eV": -94.49949613363964,
            "max_atomic_step_A": 0.057898713347875275,
            "max_log_strain_component": 0.02,
            "step_scale": 0.5036872304442926,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 7.584529553787404,
            "cell_principal_stretches": [
              1.0478697552799277,
              1.0047039357264738,
              0.9541838459305124
            ],
            "cell_volume_ratio": 1.0045636721519837,
            "cell_rmsd_from_input_A": 0.35934001554653994
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.3372943157155898,
              0.32742803877992804,
              -0.07377950676538006
            ],
            "branch_aligned_reduced_polarization": [
              -0.3372943157155898,
              0.32742803877992804,
              -0.07377950676538006
            ],
            "target_residual": 0.24839009061623804,
            "energy_eV": -93.23830898535003,
            "max_atomic_step_A": 0.06012851040196338,
            "max_log_strain_component": 0.0182509903467977,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 7.584529553787404,
            "cell_principal_stretches": [
              1.071711759863598,
              1.007928177202108,
              0.93289286950604
            ],
            "cell_volume_ratio": 1.0077187891367123,
            "cell_rmsd_from_input_A": 0.5322904749199326
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -0.49471989949080164,
              0.4825522359485874,
              -0.01726701962170621
            ],
            "branch_aligned_reduced_polarization": [
              -0.49471989949080164,
              0.4825522359485874,
              -0.01726701962170621
            ],
            "target_residual": 0.02510884104050581,
            "energy_eV": -91.17924778396787,
            "max_atomic_step_A": 0.004593390184136613,
            "max_log_strain_component": 0.0016210491379861733,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 7.584529553787404,
            "cell_principal_stretches": [
              1.073421453745097,
              1.008727328857462,
              0.9314030297040038
            ],
            "cell_volume_ratio": 1.0085134727803016,
            "cell_rmsd_from_input_A": 0.5431459873076669
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              -0.4994950107296431,
              0.49775366477202065,
              -0.0016334163985497622
            ],
            "branch_aligned_reduced_polarization": [
              -0.4994950107296431,
              0.49775366477202065,
              -0.0016334163985497622
            ],
            "target_residual": 0.0028229568276344407,
            "energy_eV": -91.04991539621253,
            "max_atomic_step_A": 0.0006477321204875854,
            "max_log_strain_component": 0.0001782575667326339,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": true,
            "strain_jacobian_frobenius_norm": 7.041811976964329,
            "cell_principal_stretches": [
              1.0736207830497362,
              1.0087658650296003,
              0.9312553067020529
            ],
            "cell_volume_ratio": 1.0085792953975745,
            "cell_rmsd_from_input_A": 0.5443089502395897
          },
          {
            "iteration": 5,
            "reduced_polarization": [
              -0.4999981954161753,
              0.4999958888438547,
              -2.2162252116221746e-06
            ],
            "branch_aligned_reduced_polarization": [
              -0.4999981954161753,
              0.4999958888438547,
              -2.2162252116221746e-06
            ],
            "target_residual": 5.006973319280873e-06,
            "energy_eV": -91.0331027848066
          }
        ],
        "iterations": 5
      },
      "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": 5.006973319280873e-06,
        "parent_symmetrization_rmsd_A": 0.11782526554694775,
        "parent_cell_rmsd_A": 0.5443089502395897,
        "energy_eV": -91.0331027848066,
        "reduced_polarization": [
          -0.4999981954161753,
          0.4999958888438547,
          -2.2162252116221746e-06
        ],
        "cartesian_polarization_e_A2": [
          -0.010875992455455294,
          0.006420011529715925,
          0.0008810109018758393
        ],
        "ranking_score": 0.7539125170534837
      },
      "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": [
              -4.879432997147898e-15,
              1.7567258521752122e-15,
              -0.1747086401692938
            ],
            "branch_aligned_reduced_polarization": [
              -4.884981308350689e-15,
              1.7763568394002505e-15,
              -0.17470864016929377
            ],
            "target_residual": 0.7783408435772232,
            "energy_eV": -94.8963370430871,
            "max_atomic_step_A": 0.05351232926323927,
            "max_log_strain_component": 0.02,
            "step_scale": 0.32441225638907306,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 7.584529553787404,
            "cell_principal_stretches": [
              1.0238014567190359,
              0.9960463050633206,
              0.9768718343650407
            ],
            "cell_volume_ratio": 0.9961686265724315,
            "cell_rmsd_from_input_A": 0.1802767333165996
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.1634903324699256,
              0.16397941413205938,
              -0.28495250568859526
            ],
            "branch_aligned_reduced_polarization": [
              -0.16349033246992561,
              0.1639794141320594,
              -0.28495250568859526
            ],
            "target_residual": 0.5219138006202259,
            "energy_eV": -94.44119676686448,
            "max_atomic_step_A": 0.05769874856208849,
            "max_log_strain_component": 0.02,
            "step_scale": 0.48981777178553565,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 7.584529553787404,
            "cell_principal_stretches": [
              1.0481164784417047,
              0.9921193169596015,
              0.9543282849407351
            ],
            "cell_volume_ratio": 0.9923645701339879,
            "cell_rmsd_from_input_A": 0.3595697116956786
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.3308264711798685,
              0.3292444524219739,
              -0.3907916855963166
            ],
            "branch_aligned_reduced_polarization": [
              -0.3308264711798685,
              0.3292444524219739,
              -0.3907916855963166
            ],
            "target_residual": 0.26401438562514196,
            "energy_eV": -92.92924904590281,
            "max_atomic_step_A": 0.0634780810102513,
            "max_log_strain_component": 0.019875117837746613,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 7.584529553787404,
            "cell_principal_stretches": [
              1.0731743856693903,
              0.9876262325998714,
              0.9321705657937867
            ],
            "cell_volume_ratio": 0.9880030853732604,
            "cell_rmsd_from_input_A": 0.539650192992254
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -0.49612751148659495,
              0.495533584286233,
              -0.49206949260103117
            ],
            "branch_aligned_reduced_polarization": [
              -0.49612751148659495,
              0.495533584286233,
              -0.49206949260103117
            ],
            "target_residual": 0.009891308519085741,
            "energy_eV": -90.02780582251617,
            "max_atomic_step_A": 0.002075147130826809,
            "max_log_strain_component": 0.0005007105940365746,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 7.584529553787404,
            "cell_principal_stretches": [
              1.0738785171525274,
              0.9872536766258027,
              0.9315692744377935
            ],
            "cell_volume_ratio": 0.9876409081800118,
            "cell_rmsd_from_input_A": 0.5447809287488591
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              -0.4997381503217278,
              0.49988565590141876,
              -0.4992811451027322
            ],
            "branch_aligned_reduced_polarization": [
              -0.4997381503217278,
              0.49988565590141876,
              -0.4992811451027322
            ],
            "target_residual": 0.0007735581362881001,
            "energy_eV": -89.91809004287163
          }
        ],
        "iterations": 4
      },
      "parent": {
        "candidate_id": "bec_projection_07",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          -0.5,
          0.5,
          -0.5
        ],
        "formal_class": [
          0.5,
          0.5,
          0.5
        ],
        "target_residual": 0.0007735581362881001,
        "parent_symmetrization_rmsd_A": 0.1238159932164054,
        "parent_cell_rmsd_A": 0.5447809287488591,
        "energy_eV": -89.91809004287163,
        "reduced_polarization": [
          -0.4997381503217278,
          0.49988565590141876,
          -0.4992811451027322
        ],
        "cartesian_polarization_e_A2": [
          -0.010528964842174363,
          0.006193570787950108,
          -0.005185745605425964
        ],
        "ranking_score": 0.7615583416761964
      },
      "branch_status": "awaiting_branch_sampling"
    }
  ],
  "sampled_polarization_branches": [
    {
      "orbit_id": 0,
      "candidate_id": "bec_projection_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
        ],
        "endpoint_rmsd_A": 0.016884511346226243,
        "minimum_distance_A_by_image": [
          2.2036404467973747,
          2.2057629370407423,
          2.207889050105221,
          2.2100187512937293,
          2.2121520061146214,
          2.2142887802810125,
          2.21642903971011,
          2.2185727505225534,
          2.220719879041699
        ],
        "minimum_distance_A": 2.2036404467973747,
        "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": [
          551.0267409147184,
          551.4609250128169,
          551.8954512283061,
          552.330319830759,
          552.7655310899613,
          553.2010852759117,
          553.6369826588203,
          554.0732235091109,
          554.5098080974195
        ],
        "cell_deformation_log_strain_norm": 0.010835222569225018
      },
      "parent_reduced_polarization": [
        8.499831704018832e-16,
        1.636893474365615e-14,
        -6.686480869163622e-06
      ],
      "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": [
          -94.8963370430871,
          -94.89649627623737,
          -94.89456181919341,
          -94.89050787535645,
          -94.8843079867422,
          -94.87593463777736,
          -94.86536063492134,
          -94.85255873102449,
          -94.83750035196346
        ],
        "cartesian_polarizations_e_A2": [
          [
            8.271375780368784e-18,
            -2.2289013033247018e-17,
            -0.0020707809408857013
          ],
          [
            1.15351786617488e-17,
            1.471552389760145e-16,
            -0.001810125577992313
          ],
          [
            2.01440375330655e-17,
            -5.586113374633774e-17,
            -0.001549876367455267
          ],
          [
            -4.4112448210467076e-17,
            -1.036442734571868e-17,
            -0.0012900958928749766
          ],
          [
            -1.178059392123856e-16,
            7.13138827422317e-17,
            -0.0010308401163985226
          ],
          [
            -6.402559883847391e-17,
            7.350296186894862e-17,
            -0.0007721599322883394
          ],
          [
            -4.30616270630206e-18,
            8.230612783149267e-17,
            -0.0005141064775988717
          ],
          [
            -1.0191956899289698e-16,
            1.3161492450629834e-16,
            -0.00025673041157832046
          ],
          [
            1.8447366264667324e-17,
            2.0954588389798974e-16,
            -7.826772610672208e-08
          ]
        ],
        "raw_reduced_polarization": [
          [
            3.808857090419242e-16,
            -1.741963450056093e-15,
            -0.17470864016929255
          ],
          [
            6.485917008901831e-16,
            1.0703342031432438e-14,
            -0.15295661457329102
          ],
          [
            1.128897652601585e-15,
            -5.730557375384739e-15,
            -0.1311704313923218
          ],
          [
            -1.7803610748250833e-15,
            -2.5158703598242894e-15,
            -0.10935539571817086
          ],
          [
            -5.1582606503755295e-15,
            3.7532276292575865e-15,
            -0.08751628388110669
          ],
          [
            -2.6981336925225003e-15,
            4.038479322165981e-15,
            -0.06565747128185594
          ],
          [
            2.4647016888289166e-18,
            5.067524497020203e-15,
            -0.04378338141457942
          ],
          [
            -4.578406001251395e-15,
            9.487476392035847e-15,
            -0.02189842467069506
          ],
          [
            8.499831704018832e-16,
            1.636893474365615e-14,
            -6.686480869163622e-06
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            3.808857090419242e-16,
            -1.741963450056093e-15,
            -0.17470864016929255
          ],
          [
            6.485917008901831e-16,
            1.0703342031432438e-14,
            -0.15295661457329102
          ],
          [
            1.128897652601585e-15,
            -5.730557375384738e-15,
            -0.1311704313923218
          ],
          [
            -1.7803610748250833e-15,
            -2.5158703598242894e-15,
            -0.10935539571817086
          ],
          [
            -5.1582606503755295e-15,
            3.7532276292575865e-15,
            -0.08751628388110669
          ],
          [
            -2.6981336925225003e-15,
            4.038479322165981e-15,
            -0.06565747128185594
          ],
          [
            2.4647016888289112e-18,
            5.067524497020203e-15,
            -0.04378338141457942
          ],
          [
            -4.578406001251395e-15,
            9.487476392035847e-15,
            -0.02189842467069506
          ],
          [
            8.499831704018835e-16,
            1.636893474365615e-14,
            -6.6864808691627364e-06
          ]
        ],
        "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": [
          [
            3.3306690738754696e-16,
            -1.7208456881689926e-15,
            -0.17470864016929255
          ],
          [
            6.661338147750939e-16,
            1.0658141036401503e-14,
            -0.15295661457329102
          ],
          [
            1.1102230246251565e-15,
            -5.717648576819556e-15,
            -0.13117043139232176
          ],
          [
            -1.7763568394002505e-15,
            -2.4980018054066022e-15,
            -0.10935539571817088
          ],
          [
            -5.162537064506978e-15,
            3.774758283725532e-15,
            -0.08751628388110666
          ],
          [
            -2.7200464103316335e-15,
            3.9968028886505635e-15,
            -0.06565747128185595
          ],
          [
            0.0,
            5.10702591327572e-15,
            -0.043783381414579436
          ],
          [
            -4.551914400963142e-15,
            9.43689570931383e-15,
            -0.021898424670695082
          ],
          [
            8.881784197001252e-16,
            1.63202784619898e-14,
            -6.6864808691557975e-06
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -94.83750035196344,
          -94.83977461778407,
          -94.84100417818689,
          -94.84118231676675,
          -94.84030235430127,
          -94.83835775617777,
          -94.83534208434573,
          -94.83124892927296,
          -94.82607210903245
        ],
        "cartesian_polarizations_e_A2": [
          [
            6.512568814652786e-17,
            1.3180536831372764e-16,
            -7.826772616279537e-08
          ],
          [
            -2.1964675435268556e-16,
            8.373975307579237e-16,
            7.570909974450616e-05
          ],
          [
            -3.677548117944506e-16,
            1.3083566068819e-15,
            0.0001524314362995002
          ],
          [
            -5.444246756907339e-16,
            1.852500416113485e-15,
            0.00023008116666726287
          ],
          [
            -7.135304235156747e-16,
            2.3263565177883934e-15,
            0.0003086506576761436
          ],
          [
            -9.732265629607932e-16,
            3.0120659049149328e-15,
            0.00038813232151178173
          ],
          [
            -1.1196827846809458e-15,
            3.45410524899775e-15,
            0.000468518543234008
          ],
          [
            -1.2433987956352329e-15,
            4.168494576915556e-15,
            0.0005498015882990379
          ],
          [
            -1.2627796299756554e-15,
            4.806033805471379e-15,
            0.0006319737650334281
          ]
        ],
        "raw_reduced_polarization": [
          [
            3.0006357649110174e-15,
            1.0296037069441529e-14,
            -6.686480873954012e-06
          ],
          [
            -1.0153824193831656e-14,
            6.565350269229488e-14,
            0.006457785844102969
          ],
          [
            -1.7001126652547318e-14,
            1.0262140126183266e-13,
            0.012981675987129853
          ],
          [
            -2.515345569664631e-14,
            1.4524557724758928e-13,
            0.01956401382830448
          ],
          [
            -3.294637575340242e-14,
            1.8231563472977736e-13,
            0.026203829427640202
          ],
          [
            -4.49006142296932e-14,
            2.3587604582314003e-13,
            0.032900161797543605
          ],
          [
            -5.1627761784865384e-14,
            2.703319746593217e-13,
            0.039652052719670074
          ],
          [
            -5.729641443545325e-14,
            3.2600552986387197e-13,
            0.046458538929941735
          ],
          [
            -5.814930037014128e-14,
            3.7560816247795653e-13,
            0.05331866588671316
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            3.0006357649110174e-15,
            1.0296037069441529e-14,
            -6.686480873954012e-06
          ],
          [
            -1.0153824193831656e-14,
            6.565350269229488e-14,
            0.006457785844102969
          ],
          [
            -1.7001126652547318e-14,
            1.0262140126183266e-13,
            0.012981675987129853
          ],
          [
            -2.515345569664631e-14,
            1.4524557724758928e-13,
            0.01956401382830448
          ],
          [
            -3.294637575340242e-14,
            1.8231563472977736e-13,
            0.026203829427640202
          ],
          [
            -4.49006142296932e-14,
            2.3587604582314003e-13,
            0.032900161797543605
          ],
          [
            -5.1627761784865384e-14,
            2.703319746593217e-13,
            0.039652052719670074
          ],
          [
            -5.729641443545325e-14,
            3.2600552986387197e-13,
            0.046458538929941735
          ],
          [
            -5.814930037014128e-14,
            3.7560816247795653e-13,
            0.05331866588671316
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          1.3180670084371053e-15,
          3.449543443735536e-14,
          0.17469543351114034
        ],
        "actual_opposite_endpoint_branch_residual": 0.12137676762442717
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            3.808857090419242e-16,
            -1.741963450056093e-15,
            -0.17470864016929255
          ],
          [
            6.485917008901831e-16,
            1.0703342031432438e-14,
            -0.15295661457329102
          ],
          [
            1.128897652601585e-15,
            -5.730557375384739e-15,
            -0.1311704313923218
          ],
          [
            -1.7803610748250833e-15,
            -2.5158703598242894e-15,
            -0.10935539571817086
          ],
          [
            -5.1582606503755295e-15,
            3.7532276292575865e-15,
            -0.08751628388110669
          ],
          [
            -2.6981336925225003e-15,
            4.038479322165981e-15,
            -0.06565747128185594
          ],
          [
            2.4647016888289166e-18,
            5.067524497020203e-15,
            -0.04378338141457942
          ],
          [
            -4.578406001251395e-15,
            9.487476392035847e-15,
            -0.02189842467069506
          ],
          [
            8.499831704018832e-16,
            1.636893474365615e-14,
            -6.686480869163622e-06
          ],
          [
            -1.0153824193831656e-14,
            6.565350269229488e-14,
            0.006457785844102969
          ],
          [
            -1.7001126652547318e-14,
            1.0262140126183266e-13,
            0.012981675987129853
          ],
          [
            -2.515345569664631e-14,
            1.4524557724758928e-13,
            0.01956401382830448
          ],
          [
            -3.294637575340242e-14,
            1.8231563472977736e-13,
            0.026203829427640202
          ],
          [
            -4.49006142296932e-14,
            2.3587604582314003e-13,
            0.032900161797543605
          ],
          [
            -5.1627761784865384e-14,
            2.703319746593217e-13,
            0.039652052719670074
          ],
          [
            -5.729641443545325e-14,
            3.2600552986387197e-13,
            0.046458538929941735
          ],
          [
            -5.814930037014128e-14,
            3.7560816247795653e-13,
            0.05331866588671316
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            3.808857090419242e-16,
            -1.741963450056093e-15,
            -0.17470864016929255
          ],
          [
            6.485917008901831e-16,
            1.0703342031432438e-14,
            -0.15295661457329102
          ],
          [
            1.128897652601585e-15,
            -5.730557375384738e-15,
            -0.1311704313923218
          ],
          [
            -1.7803610748250833e-15,
            -2.5158703598242894e-15,
            -0.10935539571817086
          ],
          [
            -5.1582606503755295e-15,
            3.7532276292575865e-15,
            -0.08751628388110669
          ],
          [
            -2.6981336925225003e-15,
            4.038479322165981e-15,
            -0.06565747128185594
          ],
          [
            2.4647016888289112e-18,
            5.067524497020203e-15,
            -0.04378338141457942
          ],
          [
            -4.578406001251395e-15,
            9.487476392035847e-15,
            -0.02189842467069506
          ],
          [
            8.499831704018835e-16,
            1.636893474365615e-14,
            -6.6864808691627364e-06
          ],
          [
            -1.0153824193831656e-14,
            6.565350269229488e-14,
            0.006457785844102969
          ],
          [
            -1.7001126652547318e-14,
            1.0262140126183266e-13,
            0.012981675987129853
          ],
          [
            -2.515345569664631e-14,
            1.4524557724758928e-13,
            0.01956401382830448
          ],
          [
            -3.294637575340242e-14,
            1.8231563472977736e-13,
            0.026203829427640202
          ],
          [
            -4.49006142296932e-14,
            2.3587604582314003e-13,
            0.032900161797543605
          ],
          [
            -5.1627761784865384e-14,
            2.703319746593217e-13,
            0.039652052719670074
          ],
          [
            -5.729641443545325e-14,
            3.2600552986387197e-13,
            0.046458538929941735
          ],
          [
            -5.814930037014128e-14,
            3.7560816247795653e-13,
            0.05331866588671316
          ]
        ],
        "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": [
          [
            3.3306690738754696e-16,
            -1.7208456881689926e-15,
            -0.17470864016929255
          ],
          [
            6.661338147750939e-16,
            1.0658141036401503e-14,
            -0.15295661457329102
          ],
          [
            1.1102230246251565e-15,
            -5.717648576819556e-15,
            -0.13117043139232176
          ],
          [
            -1.7763568394002505e-15,
            -2.4980018054066022e-15,
            -0.10935539571817088
          ],
          [
            -5.162537064506978e-15,
            3.774758283725532e-15,
            -0.08751628388110666
          ],
          [
            -2.7200464103316335e-15,
            3.9968028886505635e-15,
            -0.06565747128185595
          ],
          [
            0.0,
            5.10702591327572e-15,
            -0.043783381414579436
          ],
          [
            -4.551914400963142e-15,
            9.43689570931383e-15,
            -0.021898424670695082
          ],
          [
            8.881784197001252e-16,
            1.63202784619898e-14,
            -6.6864808691557975e-06
          ],
          [
            -1.0158540675320182e-14,
            6.561418075534675e-14,
            0.006457785844102948
          ],
          [
            -1.6986412276764895e-14,
            1.0258460747536446e-13,
            0.012981675987129848
          ],
          [
            -2.5146551507759796e-14,
            1.4521717162097048e-13,
            0.019564013828304527
          ],
          [
            -3.297362383136715e-14,
            1.822986206434507e-13,
            0.026203829427640213
          ],
          [
            -4.490852134608758e-14,
            2.3592239273284576e-13,
            0.032900161797543626
          ],
          [
            -5.162537064506978e-14,
            2.703393064962256e-13,
            0.039652052719670094
          ],
          [
            -5.728750807065808e-14,
            3.2596148002994596e-13,
            0.046458538929941784
          ],
          [
            -5.81756864903582e-14,
            3.7558844923069046e-13,
            0.05331866588671319
          ]
        ]
      },
      "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": "bec_projection_00",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cmc2_1",
        "spacegroup_number": 36,
        "pointgroup": "mm2",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.0
        ],
        "formal_class": [
          0.0,
          0.0,
          0.0
        ],
        "target_residual": 6.6864808600671205e-06,
        "parent_symmetrization_rmsd_A": 0.016884511346226243,
        "parent_cell_rmsd_A": 0.07018659017714188,
        "energy_eV": -94.83750035196344,
        "reduced_polarization": [
          4.705597275540713e-15,
          7.093163954019392e-15,
          -6.6864808600671205e-06
        ],
        "cartesian_polarization_e_A2": [
          1.0213061511267306e-16,
          9.080467627158118e-17,
          -7.826772600024418e-08
        ],
        "ranking_score": 0.5344445318522318
      }
    }
  ],
  "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": 74,
      "full_response": 29,
      "energy_polarization": 45
    },
    "model_evaluations_for_recovery_and_path_properties": {
      "total": 99,
      "full_response": 54,
      "energy_polarization": 45
    },
    "elapsed_seconds": 320.257599072007
  }
}