{
  "schema": "ferrofinder.endpoint_parent_recovery.v4_variable_cell",
  "status": "complete",
  "input_atom_count": 22,
  "input_formula": "Br12O2Sr8",
  "input_spacegroup": "P6_3mc",
  "input_pointgroup": "6mm",
  "input_is_polar_point_group": true,
  "input_energy_eV": -91.03895516074655,
  "input_cartesian_polarization_e_A2": [
    4.9047156406599574e-17,
    0.0007023360098445774,
    7.465734303574807e-18
  ],
  "input_reduced_polarization": [
    3.5437628776493192e-15,
    0.06078290182861926,
    5.725468948456793e-16
  ],
  "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,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.0
      ]
    },
    {
      "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": [
        0.5,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        0.5,
        0.5,
        0.0
      ]
    }
  ],
  "parent_candidates": [
    {
      "candidate_id": "inversion_parent_endpoint_00",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "P6_3/mmc",
      "spacegroup_number": 194,
      "pointgroup": "6/mmm",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 1.3983505172154003e-15,
      "parent_symmetrization_rmsd_A": 0.6039648084399772,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -87.82138335689254,
      "reduced_polarization": [
        1.3200119727963446e-15,
        3.2097744870637413e-16,
        -3.315509585159225e-16
      ],
      "cartesian_polarization_e_A2": [
        2.2371108520001074e-17,
        3.708839390560046e-18,
        -4.323263974809609e-18
      ],
      "ranking_score": 0.60396480843998
    },
    {
      "candidate_id": "inversion_parent_endpoint_01",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "Cmce",
      "spacegroup_number": 64,
      "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": 2.196998228519678e-15,
      "parent_symmetrization_rmsd_A": 0.980015208928202,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -82.88164981497005,
      "reduced_polarization": [
        -1.630063210898175e-15,
        -1.4384848906364095e-16,
        1.465947733307379e-15
      ],
      "cartesian_polarization_e_A2": [
        -3.5579624006456194e-17,
        -1.6621446293562704e-18,
        1.9115248686748204e-17
      ],
      "ranking_score": 0.9800152089282065
    },
    {
      "candidate_id": "inversion_parent_endpoint_02",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "Cmce",
      "spacegroup_number": 64,
      "pointgroup": "mmm",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 4.542192685918682e-16,
      "parent_symmetrization_rmsd_A": 0.9800168469829784,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -82.88163950169897,
      "reduced_polarization": [
        -3.5323343486653814e-16,
        -2.3326525899348114e-16,
        -1.6470763005769675e-16
      ],
      "cartesian_polarization_e_A2": [
        -4.078562760191523e-18,
        -2.6953400760426486e-18,
        -2.147707750844918e-18
      ],
      "ranking_score": 0.9800168469829793
    },
    {
      "candidate_id": "bec_projection_00",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P6_3mc",
      "spacegroup_number": 186,
      "pointgroup": "6mm",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 7.093311259182705e-05,
      "parent_symmetrization_rmsd_A": 0.015685487650349144,
      "parent_cell_rmsd_A": 0.009663495351995682,
      "energy_eV": -91.02817368283577,
      "reduced_polarization": [
        -1.7585236705943975e-14,
        7.093311259182705e-05,
        -1.2973109318405298e-14
      ],
      "cartesian_polarization_e_A2": [
        -1.6675467347455967e-16,
        8.198631875038579e-07,
        -1.688036367020376e-16
      ],
      "ranking_score": 0.5182432277135317
    },
    {
      "candidate_id": "inversion_parent_bec_00_00",
      "source": "same_species_inversion_center_projection_after_BEC",
      "spacegroup": "P6_3/mmc",
      "spacegroup_number": 194,
      "pointgroup": "6/mmm",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 4.659032920008484e-16,
      "parent_symmetrization_rmsd_A": 0.6039649501725929,
      "parent_cell_rmsd_A": 0.009663495351995682,
      "energy_eV": -87.81874257041257,
      "reduced_polarization": [
        3.293131705768173e-16,
        -2.4389384396470847e-16,
        2.216630462165271e-16
      ],
      "cartesian_polarization_e_A2": [
        3.2827231341267354e-18,
        -2.8189878749027476e-18,
        2.8843186467698297e-18
      ],
      "ranking_score": 0.6063808240105927
    },
    {
      "candidate_id": "bec_projection_01",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P6_3mc",
      "spacegroup_number": 186,
      "pointgroup": "6mm",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.5,
        0.0
      ],
      "formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_residual": 0.0007101866622251651,
      "parent_symmetrization_rmsd_A": 0.11545411755726663,
      "parent_cell_rmsd_A": 0.0685940511806855,
      "energy_eV": -90.77569363700849,
      "reduced_polarization": [
        1.1610741962677757e-13,
        0.49928981333777483,
        8.507795794633917e-14
      ],
      "cartesian_polarization_e_A2": [
        8.743775996906336e-16,
        0.005756851760651353,
        8.828615602958381e-16
      ],
      "ranking_score": 0.6340230036768884
    },
    {
      "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": 4.26912163872417e-06,
      "parent_symmetrization_rmsd_A": 0.19232695657284257,
      "parent_cell_rmsd_A": 0.02029289783189068,
      "energy_eV": -90.44573506474107,
      "reduced_polarization": [
        0.49999597124007966,
        -1.4122652263625666e-06,
        3.011840992408741e-11
      ],
      "cartesian_polarization_e_A2": [
        0.007509531765608518,
        1.4382011255318628e-05,
        -2.984243711855167e-11
      ],
      "ranking_score": 0.6974087192740928
    },
    {
      "candidate_id": "bec_projection_03",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cc",
      "spacegroup_number": 9,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.5,
        0.5,
        0.0
      ],
      "formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_residual": 1.2126551227767472e-05,
      "parent_symmetrization_rmsd_A": 0.22031948421804376,
      "parent_cell_rmsd_A": 0.07151593446653497,
      "energy_eV": -90.07458722942775,
      "reduced_polarization": [
        0.5000046735125949,
        0.5000111897955601,
        -1.644454352957916e-10
      ],
      "cartesian_polarization_e_A2": [
        0.007656286321234583,
        0.005779144965244842,
        3.0279745585854644e-10
      ],
      "ranking_score": 0.738222720937133
    }
  ],
  "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": [
              3.5437628776493192e-15,
              0.06078290182861926,
              5.725468948456793e-16
            ],
            "branch_aligned_reduced_polarization": [
              3.5437628776493192e-15,
              0.06078290182861926,
              5.725468948456793e-16
            ],
            "target_residual": 0.06078290182861926,
            "energy_eV": -91.03895516074655,
            "max_atomic_step_A": 0.013627292098076992,
            "max_log_strain_component": 0.002247220059495451,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.5906290845812385,
            "cell_principal_stretches": [
              1.0022497469509657,
              0.9998516553289456,
              0.9998516482019292
            ],
            "cell_volume_ratio": 1.0019524050465733,
            "cell_rmsd_from_input_A": 0.009663495351995682
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -1.7585236705943975e-14,
              7.093311259182705e-05,
              -1.2973109318405298e-14
            ],
            "branch_aligned_reduced_polarization": [
              -1.7585236705943975e-14,
              7.093311259182705e-05,
              -1.2973109318405298e-14
            ],
            "target_residual": 7.093311259182705e-05,
            "energy_eV": -91.02817368283577
          }
        ],
        "iterations": 1
      },
      "parent": {
        "candidate_id": "bec_projection_00",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P6_3mc",
        "spacegroup_number": 186,
        "pointgroup": "6mm",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.0
        ],
        "formal_class": [
          0.0,
          0.0,
          0.0
        ],
        "target_residual": 7.093311259182705e-05,
        "parent_symmetrization_rmsd_A": 0.015685487650349144,
        "parent_cell_rmsd_A": 0.009663495351995682,
        "energy_eV": -91.02817368283577,
        "reduced_polarization": [
          -1.7585236705943975e-14,
          7.093311259182705e-05,
          -1.2973109318405298e-14
        ],
        "cartesian_polarization_e_A2": [
          -1.6675467347455967e-16,
          8.198631875038579e-07,
          -1.688036367020376e-16
        ],
        "ranking_score": 0.5182432277135317
      },
      "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": [
          -91.03895516074655,
          -91.0382049247404,
          -91.03728341703923,
          -91.03619089093682,
          -91.03492762603854,
          -91.03349392865105,
          -91.03189013086846,
          -91.03011658907984,
          -91.02817368283576
        ],
        "cartesian_polarizations_e_A2": [
          [
            1.0386687329998324e-17,
            0.0007023360098446114,
            -3.34964676372776e-17
          ],
          [
            1.3570706255093951e-17,
            0.0006147395687809545,
            -5.369020025873565e-19
          ],
          [
            -2.4260401242888213e-17,
            0.0005271139732711738,
            -4.176705490901607e-17
          ],
          [
            -3.102381902826615e-17,
            0.0004394605369779431,
            -9.51728464502952e-17
          ],
          [
            -9.225956256439333e-18,
            0.0003517805453451088,
            -6.020454763174789e-17
          ],
          [
            -1.087206169504159e-16,
            0.00026407525920080975,
            -1.4093068873243666e-17
          ],
          [
            -7.468952477157193e-17,
            0.00017634591452734194,
            -6.184270592678719e-17
          ],
          [
            -1.2405713898731077e-16,
            8.859372103065043e-05,
            -3.2930564405533635e-17
          ],
          [
            -1.0434743763451508e-16,
            8.198631875065126e-07,
            -8.281489482179892e-17
          ]
        ],
        "raw_reduced_polarization": [
          [
            -5.945848364139635e-16,
            0.060782901828622185,
            -2.568842896651032e-15
          ],
          [
            8.327687960789668e-16,
            0.053199990426686924,
            -7.690470338924945e-17
          ],
          [
            -3.2971421111257284e-15,
            0.045615118475695604,
            -3.2660569952984346e-15
          ],
          [
            -5.817708027268081e-15,
            0.03802839990193341,
            -7.381169792590788e-15
          ],
          [
            -3.0346745493603384e-15,
            0.0304399461729962,
            -4.70371968423438e-15
          ],
          [
            -7.874845429807519e-15,
            0.022849866610015212,
            -1.158969558101285e-15
          ],
          [
            -7.426419278231565e-15,
            0.015258268368141455,
            -4.811699702402312e-15
          ],
          [
            -9.56813722150961e-15,
            0.007665256313175714,
            -2.566144066752262e-15
          ],
          [
            -1.0127558462115183e-14,
            7.093311259205674e-05,
            -6.3647803599723985e-15
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -5.945848364139635e-16,
            0.060782901828622185,
            -2.568842896651032e-15
          ],
          [
            8.327687960789667e-16,
            0.053199990426686924,
            -7.690470338924944e-17
          ],
          [
            -3.2971421111257284e-15,
            0.045615118475695604,
            -3.2660569952984346e-15
          ],
          [
            -5.817708027268081e-15,
            0.03802839990193341,
            -7.381169792590788e-15
          ],
          [
            -3.0346745493603384e-15,
            0.0304399461729962,
            -4.70371968423438e-15
          ],
          [
            -7.874845429807519e-15,
            0.022849866610015212,
            -1.1589695581012852e-15
          ],
          [
            -7.426419278231565e-15,
            0.015258268368141455,
            -4.811699702402312e-15
          ],
          [
            -9.56813722150961e-15,
            0.007665256313175714,
            -2.566144066752262e-15
          ],
          [
            -1.0127558462115183e-14,
            7.093311259205679e-05,
            -6.364780359972398e-15
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            -6.106226635438361e-16,
            0.06078290182862223,
            -2.55351295663786e-15
          ],
          [
            8.881784197001252e-16,
            0.05319999042668688,
            -5.551115123125783e-17
          ],
          [
            -3.2751579226442118e-15,
            0.04561511847569566,
            -3.2751579226442118e-15
          ],
          [
            -5.828670879282072e-15,
            0.03802839990193341,
            -7.382983113757291e-15
          ],
          [
            -3.0531133177191805e-15,
            0.03043994617299617,
            -4.718447854656915e-15
          ],
          [
            -7.882583474838611e-15,
            0.0228498666100152,
            -1.1657341758564144e-15
          ],
          [
            -7.438494264988549e-15,
            0.015258268368141481,
            -4.829470157119431e-15
          ],
          [
            -9.547918011776346e-15,
            0.007665256313175717,
            -2.55351295663786e-15
          ],
          [
            -1.0103029524088925e-14,
            7.093311259209756e-05,
            -6.38378239159465e-15
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -91.02817368283574,
          -91.02777941819993,
          -91.02722238926648,
          -91.02649997591345,
          -91.02560952574055,
          -91.02454835726124,
          -91.02331376010238,
          -91.02190299460932,
          -91.020313292766
        ],
        "cartesian_polarizations_e_A2": [
          [
            -1.3543419166328213e-16,
            8.198631873935357e-07,
            -8.850530264580776e-17
          ],
          [
            -1.3450860211448799e-16,
            -7.71269459944859e-05,
            -9.042174337603423e-17
          ],
          [
            -1.0377174260046159e-16,
            -0.000155173405208611,
            -5.552945625272852e-17
          ],
          [
            -2.0211105982691297e-16,
            -0.00023331839175084405,
            -1.233085840498106e-16
          ],
          [
            -2.687042981916333e-16,
            -0.0003115606276778,
            -2.0525881170773434e-16
          ],
          [
            -2.0517288472569348e-16,
            -0.00038989867240718745,
            -8.352395043395276e-17
          ],
          [
            -2.0134042992924078e-16,
            -0.0004683309287352631,
            -1.5808152865936688e-16
          ],
          [
            -2.6976987391424707e-16,
            -0.0005468556525770657,
            -1.3615080051353776e-16
          ],
          [
            -2.507390402935112e-16,
            -0.00062547095811236,
            -1.6646231795204464e-16
          ]
        ],
        "raw_reduced_polarization": [
          [
            -1.2415194498779648e-14,
            7.093311258228217e-05,
            -6.802094438439428e-15
          ],
          [
            -1.23811238138614e-14,
            -0.006673134425583738,
            -6.9157961345816245e-15
          ],
          [
            -8.962525729761587e-15,
            -0.013426324429558836,
            -4.211133112647973e-15
          ],
          [
            -1.808391951696241e-14,
            -0.02018854074139526,
            -9.401129655846254e-15
          ],
          [
            -2.56460612227469e-14,
            -0.02695967375578749,
            -1.5685382674229737e-14
          ],
          [
            -1.675093275638351e-14,
            -0.033739599777255186,
            -6.342512834974778e-15
          ],
          [
            -1.9370532371626184e-14,
            -0.04052818153826744,
            -1.2075199638851987e-14
          ],
          [
            -2.310080208683059e-14,
            -0.04732526903965395,
            -1.041236516878438e-14
          ],
          [
            -2.3035943160884004e-14,
            -0.05413069999359585,
            -1.2765989168221723e-14
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -1.2415194498779648e-14,
            7.093311258228217e-05,
            -6.802094438439428e-15
          ],
          [
            -1.23811238138614e-14,
            -0.006673134425583738,
            -6.9157961345816245e-15
          ],
          [
            -8.962525729761587e-15,
            -0.013426324429558836,
            -4.211133112647973e-15
          ],
          [
            -1.808391951696241e-14,
            -0.02018854074139526,
            -9.401129655846254e-15
          ],
          [
            -2.56460612227469e-14,
            -0.02695967375578749,
            -1.5685382674229737e-14
          ],
          [
            -1.675093275638351e-14,
            -0.033739599777255186,
            -6.342512834974778e-15
          ],
          [
            -1.9370532371626184e-14,
            -0.04052818153826744,
            -1.2075199638851987e-14
          ],
          [
            -2.310080208683059e-14,
            -0.04732526903965395,
            -1.041236516878438e-14
          ],
          [
            -2.3035943160884004e-14,
            -0.05413069999359585,
            -1.2765989168221723e-14
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          -1.961705250178933e-14,
          -0.060640993502861895,
          -1.0133299705581316e-14
        ],
        "actual_opposite_endpoint_branch_residual": 0.006510293509266046
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            -5.945848364139635e-16,
            0.060782901828622185,
            -2.568842896651032e-15
          ],
          [
            8.327687960789668e-16,
            0.053199990426686924,
            -7.690470338924945e-17
          ],
          [
            -3.2971421111257284e-15,
            0.045615118475695604,
            -3.2660569952984346e-15
          ],
          [
            -5.817708027268081e-15,
            0.03802839990193341,
            -7.381169792590788e-15
          ],
          [
            -3.0346745493603384e-15,
            0.0304399461729962,
            -4.70371968423438e-15
          ],
          [
            -7.874845429807519e-15,
            0.022849866610015212,
            -1.158969558101285e-15
          ],
          [
            -7.426419278231565e-15,
            0.015258268368141455,
            -4.811699702402312e-15
          ],
          [
            -9.56813722150961e-15,
            0.007665256313175714,
            -2.566144066752262e-15
          ],
          [
            -1.0127558462115183e-14,
            7.093311259205674e-05,
            -6.3647803599723985e-15
          ],
          [
            -1.23811238138614e-14,
            -0.006673134425583738,
            -6.9157961345816245e-15
          ],
          [
            -8.962525729761587e-15,
            -0.013426324429558836,
            -4.211133112647973e-15
          ],
          [
            -1.808391951696241e-14,
            -0.02018854074139526,
            -9.401129655846254e-15
          ],
          [
            -2.56460612227469e-14,
            -0.02695967375578749,
            -1.5685382674229737e-14
          ],
          [
            -1.675093275638351e-14,
            -0.033739599777255186,
            -6.342512834974778e-15
          ],
          [
            -1.9370532371626184e-14,
            -0.04052818153826744,
            -1.2075199638851987e-14
          ],
          [
            -2.310080208683059e-14,
            -0.04732526903965395,
            -1.041236516878438e-14
          ],
          [
            -2.3035943160884004e-14,
            -0.05413069999359585,
            -1.2765989168221723e-14
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -5.945848364139635e-16,
            0.060782901828622185,
            -2.568842896651032e-15
          ],
          [
            8.327687960789667e-16,
            0.053199990426686924,
            -7.690470338924944e-17
          ],
          [
            -3.2971421111257284e-15,
            0.045615118475695604,
            -3.2660569952984346e-15
          ],
          [
            -5.817708027268081e-15,
            0.03802839990193341,
            -7.381169792590788e-15
          ],
          [
            -3.0346745493603384e-15,
            0.0304399461729962,
            -4.70371968423438e-15
          ],
          [
            -7.874845429807519e-15,
            0.022849866610015212,
            -1.1589695581012852e-15
          ],
          [
            -7.426419278231565e-15,
            0.015258268368141455,
            -4.811699702402312e-15
          ],
          [
            -9.56813722150961e-15,
            0.007665256313175714,
            -2.566144066752262e-15
          ],
          [
            -1.0127558462115183e-14,
            7.093311259205679e-05,
            -6.364780359972398e-15
          ],
          [
            -1.23811238138614e-14,
            -0.006673134425583738,
            -6.9157961345816245e-15
          ],
          [
            -8.962525729761587e-15,
            -0.013426324429558836,
            -4.211133112647973e-15
          ],
          [
            -1.808391951696241e-14,
            -0.02018854074139526,
            -9.401129655846254e-15
          ],
          [
            -2.56460612227469e-14,
            -0.02695967375578749,
            -1.5685382674229737e-14
          ],
          [
            -1.675093275638351e-14,
            -0.033739599777255186,
            -6.342512834974778e-15
          ],
          [
            -1.9370532371626184e-14,
            -0.04052818153826744,
            -1.2075199638851987e-14
          ],
          [
            -2.310080208683059e-14,
            -0.04732526903965395,
            -1.041236516878438e-14
          ],
          [
            -2.3035943160884004e-14,
            -0.05413069999359585,
            -1.2765989168221723e-14
          ]
        ],
        "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": [
          [
            -6.106226635438361e-16,
            0.06078290182862223,
            -2.55351295663786e-15
          ],
          [
            8.881784197001252e-16,
            0.05319999042668688,
            -5.551115123125783e-17
          ],
          [
            -3.2751579226442118e-15,
            0.04561511847569566,
            -3.2751579226442118e-15
          ],
          [
            -5.828670879282072e-15,
            0.03802839990193341,
            -7.382983113757291e-15
          ],
          [
            -3.0531133177191805e-15,
            0.03043994617299617,
            -4.718447854656915e-15
          ],
          [
            -7.882583474838611e-15,
            0.0228498666100152,
            -1.1657341758564144e-15
          ],
          [
            -7.438494264988549e-15,
            0.015258268368141481,
            -4.829470157119431e-15
          ],
          [
            -9.547918011776346e-15,
            0.007665256313175717,
            -2.55351295663786e-15
          ],
          [
            -1.0103029524088925e-14,
            7.093311259209756e-05,
            -6.38378239159465e-15
          ],
          [
            -1.2378986724570495e-14,
            -0.00667313442558376,
            -6.938893903907228e-15
          ],
          [
            -8.93729534823251e-15,
            -0.013426324429558822,
            -4.218847493575595e-15
          ],
          [
            -1.8096635301390052e-14,
            -0.020188540741395256,
            -9.381384558082573e-15
          ],
          [
            -2.5646151868841116e-14,
            -0.026959673755787505,
            -1.5709655798445965e-14
          ],
          [
            -1.6764367671839864e-14,
            -0.03373959977725516,
            -6.328271240363392e-15
          ],
          [
            -1.9373391779708982e-14,
            -0.04052818153826743,
            -1.2101430968414206e-14
          ],
          [
            -2.3092638912203256e-14,
            -0.04732526903965395,
            -1.0436096431476471e-14
          ],
          [
            -2.3037127760971998e-14,
            -0.05413069999359588,
            -1.27675647831893e-14
          ]
        ]
      },
      "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,
        0.5,
        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": [
              3.5437628776493192e-15,
              0.06078290182861926,
              5.725468948456793e-16
            ],
            "branch_aligned_reduced_polarization": [
              3.5437628776493192e-15,
              0.06078290182861923,
              5.725468948456793e-16
            ],
            "target_residual": 0.43921709817138077,
            "energy_eV": -91.03895516074655,
            "max_atomic_step_A": 0.09847077897213855,
            "max_log_strain_component": 0.016238406587876633,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.5906290845812385,
            "cell_principal_stretches": [
              1.0010726441209985,
              1.0010725925583053,
              0.9838927255844196
            ],
            "cell_volume_ratio": 0.9860045403263634,
            "cell_rmsd_from_input_A": 0.0685940511806855
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              1.1610741962677757e-13,
              0.49928981333777483,
              8.507795794633917e-14
            ],
            "branch_aligned_reduced_polarization": [
              1.1610741962677757e-13,
              0.49928981333777483,
              8.507795794633917e-14
            ],
            "target_residual": 0.0007101866622251651,
            "energy_eV": -90.77569363700849
          }
        ],
        "iterations": 1
      },
      "parent": {
        "candidate_id": "bec_projection_01",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P6_3mc",
        "spacegroup_number": 186,
        "pointgroup": "6mm",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.5,
          0.0
        ],
        "formal_class": [
          0.0,
          0.5,
          0.0
        ],
        "target_residual": 0.0007101866622251651,
        "parent_symmetrization_rmsd_A": 0.11545411755726663,
        "parent_cell_rmsd_A": 0.0685940511806855,
        "energy_eV": -90.77569363700849,
        "reduced_polarization": [
          1.1610741962677757e-13,
          0.49928981333777483,
          8.507795794633917e-14
        ],
        "cartesian_polarization_e_A2": [
          8.743775996906336e-16,
          0.005756851760651353,
          8.828615602958381e-16
        ],
        "ranking_score": 0.6340230036768884
      },
      "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
        ],
        [
          0.0,
          0.0,
          0.5
        ],
        [
          0.5,
          0.0,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              3.5437628776493192e-15,
              0.06078290182861926,
              5.725468948456793e-16
            ],
            "branch_aligned_reduced_polarization": [
              3.552713678800501e-15,
              0.06078290182861926,
              5.725468948456793e-16
            ],
            "target_residual": 0.5036810113104364,
            "energy_eV": -91.03895516074655,
            "max_atomic_step_A": 0.11999999999999998,
            "max_log_strain_component": 0.0016599781734245843,
            "step_scale": 0.7386807386117273,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.5906290845812385,
            "cell_principal_stretches": [
              1.0024212643065593,
              0.9998904150969723,
              0.9991324276461636
            ],
            "cell_volume_ratio": 1.0014418363967361,
            "cell_rmsd_from_input_A": 0.014024670565634853
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.3660081215568035,
              0.019150056922679282,
              -1.3732084941944773e-08
            ],
            "branch_aligned_reduced_polarization": [
              0.3660081215568035,
              0.019150056922679282,
              -1.3732084941944773e-08
            ],
            "target_residual": 0.13535341949458976,
            "energy_eV": -90.74374847969754,
            "max_atomic_step_A": 0.04389595897886777,
            "max_log_strain_component": 0.0009900324122873619,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.5906290845812385,
            "cell_principal_stretches": [
              1.0036189500530472,
              0.9998250629631122,
              0.9988632899210285
            ],
            "cell_volume_ratio": 1.0023027557241198,
            "cell_rmsd_from_input_A": 0.02019320659425592
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.49874914502358086,
              0.0005641814046939107,
              -1.1384340682704776e-08
            ],
            "branch_aligned_reduced_polarization": [
              0.49874914502358086,
              0.0005641814046939107,
              -1.1384340682704776e-08
            ],
            "target_residual": 0.001372202182466022,
            "energy_eV": -90.4492040172914,
            "max_atomic_step_A": 0.0004366373758488387,
            "max_log_strain_component": 2.552882054468716e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.5906290845812385,
            "cell_principal_stretches": [
              1.00364319777646,
              0.9998233778597272,
              0.9988629737295956
            ],
            "cell_volume_ratio": 1.0023249650404689,
            "cell_rmsd_from_input_A": 0.02029289783189068
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.49999597124007966,
              -1.4122652263625666e-06,
              3.011840992408741e-11
            ],
            "branch_aligned_reduced_polarization": [
              0.49999597124007966,
              -1.4122652263625666e-06,
              3.011840992408741e-11
            ],
            "target_residual": 4.26912163872417e-06,
            "energy_eV": -90.44573506474107
          }
        ],
        "iterations": 3
      },
      "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": 4.26912163872417e-06,
        "parent_symmetrization_rmsd_A": 0.19232695657284257,
        "parent_cell_rmsd_A": 0.02029289783189068,
        "energy_eV": -90.44573506474107,
        "reduced_polarization": [
          0.49999597124007966,
          -1.4122652263625666e-06,
          3.011840992408741e-11
        ],
        "cartesian_polarization_e_A2": [
          0.007509531765608518,
          1.4382011255318628e-05,
          -2.984243711855167e-11
        ],
        "ranking_score": 0.6974087192740928
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 3,
      "formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.5,
          0.0
        ],
        [
          0.0,
          0.5,
          0.5
        ],
        [
          0.5,
          0.5,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.5,
        0.5,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              3.5437628776493192e-15,
              0.06078290182861926,
              5.725468948456793e-16
            ],
            "branch_aligned_reduced_polarization": [
              3.552713678800501e-15,
              0.06078290182861923,
              5.725468948456793e-16
            ],
            "target_residual": 0.6655160849491805,
            "energy_eV": -91.03895516074655,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.010596413338808747,
            "step_scale": 0.6525525322642832,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.5906290845812385,
            "cell_principal_stretches": [
              1.0008308314204968,
              1.0006998145305377,
              0.9893299925326133
            ],
            "cell_volume_ratio": 0.9908448817039806,
            "cell_rmsd_from_input_A": 0.046219321062115334
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.3275414070955282,
              0.3476456449255566,
              -5.156611731540365e-08
            ],
            "branch_aligned_reduced_polarization": [
              0.3275414070955282,
              0.3476456449255566,
              -5.156611731540365e-08
            ],
            "target_residual": 0.23011696108010501,
            "energy_eV": -90.68892899674567,
            "max_atomic_step_A": 0.06540691582255247,
            "max_log_strain_component": 0.005863475099830798,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.5906290845812385,
            "cell_principal_stretches": [
              1.0012839775144209,
              1.0010872640370245,
              0.9834815658581333
            ],
            "cell_volume_ratio": 0.9858150111746449,
            "cell_rmsd_from_input_A": 0.07132482293263068
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.49931227639695197,
              0.4988768098623908,
              -5.481448452904252e-08
            ],
            "branch_aligned_reduced_polarization": [
              0.49931227639695197,
              0.4988768098623908,
              -5.481448452904252e-08
            ],
            "target_residual": 0.001317011709293642,
            "energy_eV": -90.0788817981903,
            "max_atomic_step_A": 0.00033923596480801545,
            "max_log_strain_component": 4.5971102593949006e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.5906290845812385,
            "cell_principal_stretches": [
              1.001287030804236,
              1.0010903023300732,
              0.9834363409790503
            ],
            "cell_volume_ratio": 0.9857756767876291,
            "cell_rmsd_from_input_A": 0.07151593446653497
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              0.5000046735125949,
              0.5000111897955601,
              -1.644454352957916e-10
            ],
            "branch_aligned_reduced_polarization": [
              0.5000046735125949,
              0.5000111897955601,
              -1.644454352957916e-10
            ],
            "target_residual": 1.2126551227767472e-05,
            "energy_eV": -90.07458722942775
          }
        ],
        "iterations": 3
      },
      "parent": {
        "candidate_id": "bec_projection_03",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cc",
        "spacegroup_number": 9,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.5,
          0.5,
          0.0
        ],
        "formal_class": [
          0.5,
          0.5,
          0.0
        ],
        "target_residual": 1.2126551227767472e-05,
        "parent_symmetrization_rmsd_A": 0.22031948421804376,
        "parent_cell_rmsd_A": 0.07151593446653497,
        "energy_eV": -90.07458722942775,
        "reduced_polarization": [
          0.5000046735125949,
          0.5000111897955601,
          -1.644454352957916e-10
        ],
        "cartesian_polarization_e_A2": [
          0.007656286321234583,
          0.005779144965244842,
          3.0279745585854644e-10
        ],
        "ranking_score": 0.738222720937133
      },
      "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
        ],
        "endpoint_rmsd_A": 0.015685487650349144,
        "minimum_distance_A_by_image": [
          2.395194389999999,
          2.3926129444305446,
          2.390029859339483,
          2.3874451340093406,
          2.3848587677223705,
          2.3822707597605612,
          2.379681109405612,
          2.3770898159389606,
          2.3744968786417675
        ],
        "minimum_distance_A": 2.3744968786417675,
        "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": [
          663.9297123241824,
          664.0916065535095,
          664.2535402595174,
          664.4155134518331,
          664.5775261400844,
          664.7395783339002,
          664.901670042918,
          665.0638012767689,
          665.2259720450944
        ],
        "cell_deformation_log_strain_norm": 0.0022569933370668294
      },
      "parent_reduced_polarization": [
        -1.0127558462115183e-14,
        7.093311259205674e-05,
        -6.3647803599723985e-15
      ],
      "incoming": {
        "reached": true,
        "construction": "variable_cell_linear_interpolation",
        "continuation_fractions": [
          0.0,
          0.125,
          0.25,
          0.375,
          0.5,
          0.625,
          0.75,
          0.875,
          1.0
        ],
        "energies_eV": [
          -91.03895516074655,
          -91.0382049247404,
          -91.03728341703923,
          -91.03619089093682,
          -91.03492762603854,
          -91.03349392865105,
          -91.03189013086846,
          -91.03011658907984,
          -91.02817368283576
        ],
        "cartesian_polarizations_e_A2": [
          [
            1.0386687329998324e-17,
            0.0007023360098446114,
            -3.34964676372776e-17
          ],
          [
            1.3570706255093951e-17,
            0.0006147395687809545,
            -5.369020025873565e-19
          ],
          [
            -2.4260401242888213e-17,
            0.0005271139732711738,
            -4.176705490901607e-17
          ],
          [
            -3.102381902826615e-17,
            0.0004394605369779431,
            -9.51728464502952e-17
          ],
          [
            -9.225956256439333e-18,
            0.0003517805453451088,
            -6.020454763174789e-17
          ],
          [
            -1.087206169504159e-16,
            0.00026407525920080975,
            -1.4093068873243666e-17
          ],
          [
            -7.468952477157193e-17,
            0.00017634591452734194,
            -6.184270592678719e-17
          ],
          [
            -1.2405713898731077e-16,
            8.859372103065043e-05,
            -3.2930564405533635e-17
          ],
          [
            -1.0434743763451508e-16,
            8.198631875065126e-07,
            -8.281489482179892e-17
          ]
        ],
        "raw_reduced_polarization": [
          [
            -5.945848364139635e-16,
            0.060782901828622185,
            -2.568842896651032e-15
          ],
          [
            8.327687960789668e-16,
            0.053199990426686924,
            -7.690470338924945e-17
          ],
          [
            -3.2971421111257284e-15,
            0.045615118475695604,
            -3.2660569952984346e-15
          ],
          [
            -5.817708027268081e-15,
            0.03802839990193341,
            -7.381169792590788e-15
          ],
          [
            -3.0346745493603384e-15,
            0.0304399461729962,
            -4.70371968423438e-15
          ],
          [
            -7.874845429807519e-15,
            0.022849866610015212,
            -1.158969558101285e-15
          ],
          [
            -7.426419278231565e-15,
            0.015258268368141455,
            -4.811699702402312e-15
          ],
          [
            -9.56813722150961e-15,
            0.007665256313175714,
            -2.566144066752262e-15
          ],
          [
            -1.0127558462115183e-14,
            7.093311259205674e-05,
            -6.3647803599723985e-15
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -5.945848364139635e-16,
            0.060782901828622185,
            -2.568842896651032e-15
          ],
          [
            8.327687960789667e-16,
            0.053199990426686924,
            -7.690470338924944e-17
          ],
          [
            -3.2971421111257284e-15,
            0.045615118475695604,
            -3.2660569952984346e-15
          ],
          [
            -5.817708027268081e-15,
            0.03802839990193341,
            -7.381169792590788e-15
          ],
          [
            -3.0346745493603384e-15,
            0.0304399461729962,
            -4.70371968423438e-15
          ],
          [
            -7.874845429807519e-15,
            0.022849866610015212,
            -1.1589695581012852e-15
          ],
          [
            -7.426419278231565e-15,
            0.015258268368141455,
            -4.811699702402312e-15
          ],
          [
            -9.56813722150961e-15,
            0.007665256313175714,
            -2.566144066752262e-15
          ],
          [
            -1.0127558462115183e-14,
            7.093311259205679e-05,
            -6.364780359972398e-15
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            -6.106226635438361e-16,
            0.06078290182862223,
            -2.55351295663786e-15
          ],
          [
            8.881784197001252e-16,
            0.05319999042668688,
            -5.551115123125783e-17
          ],
          [
            -3.2751579226442118e-15,
            0.04561511847569566,
            -3.2751579226442118e-15
          ],
          [
            -5.828670879282072e-15,
            0.03802839990193341,
            -7.382983113757291e-15
          ],
          [
            -3.0531133177191805e-15,
            0.03043994617299617,
            -4.718447854656915e-15
          ],
          [
            -7.882583474838611e-15,
            0.0228498666100152,
            -1.1657341758564144e-15
          ],
          [
            -7.438494264988549e-15,
            0.015258268368141481,
            -4.829470157119431e-15
          ],
          [
            -9.547918011776346e-15,
            0.007665256313175717,
            -2.55351295663786e-15
          ],
          [
            -1.0103029524088925e-14,
            7.093311259209756e-05,
            -6.38378239159465e-15
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -91.02817368283574,
          -91.02777941819993,
          -91.02722238926648,
          -91.02649997591345,
          -91.02560952574055,
          -91.02454835726124,
          -91.02331376010238,
          -91.02190299460932,
          -91.020313292766
        ],
        "cartesian_polarizations_e_A2": [
          [
            -1.3543419166328213e-16,
            8.198631873935357e-07,
            -8.850530264580776e-17
          ],
          [
            -1.3450860211448799e-16,
            -7.71269459944859e-05,
            -9.042174337603423e-17
          ],
          [
            -1.0377174260046159e-16,
            -0.000155173405208611,
            -5.552945625272852e-17
          ],
          [
            -2.0211105982691297e-16,
            -0.00023331839175084405,
            -1.233085840498106e-16
          ],
          [
            -2.687042981916333e-16,
            -0.0003115606276778,
            -2.0525881170773434e-16
          ],
          [
            -2.0517288472569348e-16,
            -0.00038989867240718745,
            -8.352395043395276e-17
          ],
          [
            -2.0134042992924078e-16,
            -0.0004683309287352631,
            -1.5808152865936688e-16
          ],
          [
            -2.6976987391424707e-16,
            -0.0005468556525770657,
            -1.3615080051353776e-16
          ],
          [
            -2.507390402935112e-16,
            -0.00062547095811236,
            -1.6646231795204464e-16
          ]
        ],
        "raw_reduced_polarization": [
          [
            -1.2415194498779648e-14,
            7.093311258228217e-05,
            -6.802094438439428e-15
          ],
          [
            -1.23811238138614e-14,
            -0.006673134425583738,
            -6.9157961345816245e-15
          ],
          [
            -8.962525729761587e-15,
            -0.013426324429558836,
            -4.211133112647973e-15
          ],
          [
            -1.808391951696241e-14,
            -0.02018854074139526,
            -9.401129655846254e-15
          ],
          [
            -2.56460612227469e-14,
            -0.02695967375578749,
            -1.5685382674229737e-14
          ],
          [
            -1.675093275638351e-14,
            -0.033739599777255186,
            -6.342512834974778e-15
          ],
          [
            -1.9370532371626184e-14,
            -0.04052818153826744,
            -1.2075199638851987e-14
          ],
          [
            -2.310080208683059e-14,
            -0.04732526903965395,
            -1.041236516878438e-14
          ],
          [
            -2.3035943160884004e-14,
            -0.05413069999359585,
            -1.2765989168221723e-14
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -1.2415194498779648e-14,
            7.093311258228217e-05,
            -6.802094438439428e-15
          ],
          [
            -1.23811238138614e-14,
            -0.006673134425583738,
            -6.9157961345816245e-15
          ],
          [
            -8.962525729761587e-15,
            -0.013426324429558836,
            -4.211133112647973e-15
          ],
          [
            -1.808391951696241e-14,
            -0.02018854074139526,
            -9.401129655846254e-15
          ],
          [
            -2.56460612227469e-14,
            -0.02695967375578749,
            -1.5685382674229737e-14
          ],
          [
            -1.675093275638351e-14,
            -0.033739599777255186,
            -6.342512834974778e-15
          ],
          [
            -1.9370532371626184e-14,
            -0.04052818153826744,
            -1.2075199638851987e-14
          ],
          [
            -2.310080208683059e-14,
            -0.04732526903965395,
            -1.041236516878438e-14
          ],
          [
            -2.3035943160884004e-14,
            -0.05413069999359585,
            -1.2765989168221723e-14
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          -1.961705250178933e-14,
          -0.060640993502861895,
          -1.0133299705581316e-14
        ],
        "actual_opposite_endpoint_branch_residual": 0.006510293509266046
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            -5.945848364139635e-16,
            0.060782901828622185,
            -2.568842896651032e-15
          ],
          [
            8.327687960789668e-16,
            0.053199990426686924,
            -7.690470338924945e-17
          ],
          [
            -3.2971421111257284e-15,
            0.045615118475695604,
            -3.2660569952984346e-15
          ],
          [
            -5.817708027268081e-15,
            0.03802839990193341,
            -7.381169792590788e-15
          ],
          [
            -3.0346745493603384e-15,
            0.0304399461729962,
            -4.70371968423438e-15
          ],
          [
            -7.874845429807519e-15,
            0.022849866610015212,
            -1.158969558101285e-15
          ],
          [
            -7.426419278231565e-15,
            0.015258268368141455,
            -4.811699702402312e-15
          ],
          [
            -9.56813722150961e-15,
            0.007665256313175714,
            -2.566144066752262e-15
          ],
          [
            -1.0127558462115183e-14,
            7.093311259205674e-05,
            -6.3647803599723985e-15
          ],
          [
            -1.23811238138614e-14,
            -0.006673134425583738,
            -6.9157961345816245e-15
          ],
          [
            -8.962525729761587e-15,
            -0.013426324429558836,
            -4.211133112647973e-15
          ],
          [
            -1.808391951696241e-14,
            -0.02018854074139526,
            -9.401129655846254e-15
          ],
          [
            -2.56460612227469e-14,
            -0.02695967375578749,
            -1.5685382674229737e-14
          ],
          [
            -1.675093275638351e-14,
            -0.033739599777255186,
            -6.342512834974778e-15
          ],
          [
            -1.9370532371626184e-14,
            -0.04052818153826744,
            -1.2075199638851987e-14
          ],
          [
            -2.310080208683059e-14,
            -0.04732526903965395,
            -1.041236516878438e-14
          ],
          [
            -2.3035943160884004e-14,
            -0.05413069999359585,
            -1.2765989168221723e-14
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -5.945848364139635e-16,
            0.060782901828622185,
            -2.568842896651032e-15
          ],
          [
            8.327687960789667e-16,
            0.053199990426686924,
            -7.690470338924944e-17
          ],
          [
            -3.2971421111257284e-15,
            0.045615118475695604,
            -3.2660569952984346e-15
          ],
          [
            -5.817708027268081e-15,
            0.03802839990193341,
            -7.381169792590788e-15
          ],
          [
            -3.0346745493603384e-15,
            0.0304399461729962,
            -4.70371968423438e-15
          ],
          [
            -7.874845429807519e-15,
            0.022849866610015212,
            -1.1589695581012852e-15
          ],
          [
            -7.426419278231565e-15,
            0.015258268368141455,
            -4.811699702402312e-15
          ],
          [
            -9.56813722150961e-15,
            0.007665256313175714,
            -2.566144066752262e-15
          ],
          [
            -1.0127558462115183e-14,
            7.093311259205679e-05,
            -6.364780359972398e-15
          ],
          [
            -1.23811238138614e-14,
            -0.006673134425583738,
            -6.9157961345816245e-15
          ],
          [
            -8.962525729761587e-15,
            -0.013426324429558836,
            -4.211133112647973e-15
          ],
          [
            -1.808391951696241e-14,
            -0.02018854074139526,
            -9.401129655846254e-15
          ],
          [
            -2.56460612227469e-14,
            -0.02695967375578749,
            -1.5685382674229737e-14
          ],
          [
            -1.675093275638351e-14,
            -0.033739599777255186,
            -6.342512834974778e-15
          ],
          [
            -1.9370532371626184e-14,
            -0.04052818153826744,
            -1.2075199638851987e-14
          ],
          [
            -2.310080208683059e-14,
            -0.04732526903965395,
            -1.041236516878438e-14
          ],
          [
            -2.3035943160884004e-14,
            -0.05413069999359585,
            -1.2765989168221723e-14
          ]
        ],
        "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": [
          [
            -6.106226635438361e-16,
            0.06078290182862223,
            -2.55351295663786e-15
          ],
          [
            8.881784197001252e-16,
            0.05319999042668688,
            -5.551115123125783e-17
          ],
          [
            -3.2751579226442118e-15,
            0.04561511847569566,
            -3.2751579226442118e-15
          ],
          [
            -5.828670879282072e-15,
            0.03802839990193341,
            -7.382983113757291e-15
          ],
          [
            -3.0531133177191805e-15,
            0.03043994617299617,
            -4.718447854656915e-15
          ],
          [
            -7.882583474838611e-15,
            0.0228498666100152,
            -1.1657341758564144e-15
          ],
          [
            -7.438494264988549e-15,
            0.015258268368141481,
            -4.829470157119431e-15
          ],
          [
            -9.547918011776346e-15,
            0.007665256313175717,
            -2.55351295663786e-15
          ],
          [
            -1.0103029524088925e-14,
            7.093311259209756e-05,
            -6.38378239159465e-15
          ],
          [
            -1.2378986724570495e-14,
            -0.00667313442558376,
            -6.938893903907228e-15
          ],
          [
            -8.93729534823251e-15,
            -0.013426324429558822,
            -4.218847493575595e-15
          ],
          [
            -1.8096635301390052e-14,
            -0.020188540741395256,
            -9.381384558082573e-15
          ],
          [
            -2.5646151868841116e-14,
            -0.026959673755787505,
            -1.5709655798445965e-14
          ],
          [
            -1.6764367671839864e-14,
            -0.03373959977725516,
            -6.328271240363392e-15
          ],
          [
            -1.9373391779708982e-14,
            -0.04052818153826743,
            -1.2101430968414206e-14
          ],
          [
            -2.3092638912203256e-14,
            -0.04732526903965395,
            -1.0436096431476471e-14
          ],
          [
            -2.3037127760971998e-14,
            -0.05413069999359588,
            -1.27675647831893e-14
          ]
        ]
      },
      "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": "P6_3mc",
        "spacegroup_number": 186,
        "pointgroup": "6mm",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.0
        ],
        "formal_class": [
          0.0,
          0.0,
          0.0
        ],
        "target_residual": 7.093311259182705e-05,
        "parent_symmetrization_rmsd_A": 0.015685487650349144,
        "parent_cell_rmsd_A": 0.009663495351995682,
        "energy_eV": -91.02817368283577,
        "reduced_polarization": [
          -1.7585236705943975e-14,
          7.093311259182705e-05,
          -1.2973109318405298e-14
        ],
        "cartesian_polarization_e_A2": [
          -1.6675467347455967e-16,
          8.198631875038579e-07,
          -1.688036367020376e-16
        ],
        "ranking_score": 0.5182432277135317
      }
    }
  ],
  "path_sampling": {
    "num_images": 17,
    "images_per_leg_including_parent": 9,
    "extension_fraction_beyond_polar_endpoint": 0.35,
    "extension_images_per_side": 4,
    "total_images_per_sampled_branch": 25,
    "construction": "linear polar-to-parent interpolation plus parent-reflected second leg and symmetric log-strain continuation beyond both polar endpoints"
  },
  "branch_folding": "componentwise integer unwrap with per-image shifts, then reduced-coordinate fold [-0.5, 0.5)",
  "bec_backprojection_settings": {
    "variable_cell": true,
    "max_strain_step_log_component": 0.02,
    "strain_response_refresh_iterations": 4,
    "cell_principal_stretch_bounds": [
      0.85,
      1.15
    ],
    "cell_volume_ratio_bounds": [
      0.7,
      1.3
    ],
    "strain_jacobian": "branch-matched finite differences of reduced polarization in six symmetric log-strain coordinates at fixed fractional positions"
  },
  "model_input_contract": "one polar endpoint structure; no reference parent or path frame",
  "run": {
    "model_file": "MACEField-MH-0-omat-dielectric.model",
    "model_sha256": "f92e043aaf2cd8879919db8452503553fe7b608cb749d8d169dd96d4aa094aa2",
    "model_head": "mp-ferroelectric",
    "device": "cpu",
    "dtype": "float64",
    "num_images": 17,
    "compute_becs_for_every_image": true,
    "compute_polarizability_for_every_image": true,
    "initial_structure_relaxation": {
      "enabled": false
    },
    "model_evaluations_for_recovery": {
      "total": 43,
      "full_response": 9,
      "energy_polarization": 34
    },
    "model_evaluations_for_recovery_and_path_properties": {
      "total": 68,
      "full_response": 34,
      "energy_polarization": 34
    },
    "elapsed_seconds": 151.08577046002029
  }
}
