{
  "schema": "ferrofinder.endpoint_parent_recovery.v4_variable_cell",
  "status": "complete",
  "input_atom_count": 24,
  "input_formula": "Br4F20",
  "input_spacegroup": "Cmc2_1",
  "input_pointgroup": "mm2",
  "input_is_polar_point_group": true,
  "input_energy_eV": -68.02840828370863,
  "input_cartesian_polarization_e_A2": [
    -1.8014426727716847e-18,
    -1.510692491469113e-17,
    0.0014668900919889098
  ],
  "input_reduced_polarization": [
    -1.087473635468381e-16,
    -8.179657707072981e-16,
    0.07466112154638371
  ],
  "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": [
        0.0,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        -0.5,
        0.0
      ]
    },
    {
      "orbit_id": 3,
      "representative_formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        -0.5,
        0.0,
        0.0
      ]
    },
    {
      "orbit_id": 4,
      "representative_formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        -0.5,
        0.5
      ]
    },
    {
      "orbit_id": 5,
      "representative_formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        -0.5,
        0.0,
        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": 7.090393213236037e-16,
      "parent_symmetrization_rmsd_A": 0.23164031138782606,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -67.45266324600402,
      "reduced_polarization": [
        2.523700715781286e-16,
        -7.737514047231197e-17,
        6.580723317322927e-16
      ],
      "cartesian_polarization_e_A2": [
        4.180609087368573e-18,
        -1.4290334378761879e-18,
        1.2929350152213129e-17
      ],
      "ranking_score": 0.23164031138782748
    },
    {
      "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": 4.3011022397168104e-07,
      "parent_symmetrization_rmsd_A": 0.03742954289714333,
      "parent_cell_rmsd_A": 0.007490143854708299,
      "energy_eV": -67.9819750121143,
      "reduced_polarization": [
        5.404353491321977e-16,
        -3.315023952620479e-16,
        4.3011022397168104e-07
      ],
      "cartesian_polarization_e_A2": [
        8.960717969886222e-18,
        -6.127023231363649e-18,
        8.443721354137704e-09
      ],
      "ranking_score": 0.5393029390812684
    },
    {
      "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": 1.2936549827976097e-15,
      "parent_symmetrization_rmsd_A": 0.2316757417601184,
      "parent_cell_rmsd_A": 0.007490143854708299,
      "energy_eV": -67.42847959692548,
      "reduced_polarization": [
        -7.237088664591397e-16,
        9.760951295922129e-16,
        -4.438772230154103e-16
      ],
      "cartesian_polarization_e_A2": [
        -1.1999484220348274e-17,
        1.8040679514570745e-17,
        -8.71398859571719e-18
      ],
      "ranking_score": 0.23354827772379805
    },
    {
      "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": 0.00040267291454776366,
      "parent_symmetrization_rmsd_A": 0.2149188597349735,
      "parent_cell_rmsd_A": 0.044074621350755974,
      "energy_eV": -64.09717627389719,
      "reduced_polarization": [
        9.245582042766768e-18,
        6.46739511264865e-17,
        0.49959732708545224
      ],
      "cartesian_polarization_e_A2": [
        -5.2046968939774055e-17,
        2.0924330993210316e-16,
        0.00986193013436937
      ],
      "ranking_score": 0.726742860901758
    },
    {
      "candidate_id": "bec_projection_02",
      "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": 0.0007664288730431059,
      "parent_symmetrization_rmsd_A": 0.2869790094187273,
      "parent_cell_rmsd_A": 0.12087886862637778,
      "energy_eV": -60.2668591678035,
      "reduced_polarization": [
        -1.594645247278084e-15,
        -0.4997108818411334,
        -0.0007098055421365078
      ],
      "cartesian_polarization_e_A2": [
        -4.559465916310672e-17,
        -0.009233492788190675,
        0.0001321775322455087
      ],
      "ranking_score": 0.8187315843214079
    },
    {
      "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,
        0.0,
        0.0
      ],
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_residual": 0.00010304092894740208,
      "parent_symmetrization_rmsd_A": 0.24499539289454275,
      "parent_cell_rmsd_A": 0.10636574933583673,
      "energy_eV": -62.53677000197118,
      "reduced_polarization": [
        -0.49989951267587834,
        1.2206955072261258e-15,
        -2.279760358486687e-05
      ],
      "cartesian_polarization_e_A2": [
        -0.008296299294832011,
        8.737690185259076e-17,
        0.0001273073672016465
      ],
      "ranking_score": 0.7717929120863967
    },
    {
      "candidate_id": "bec_projection_04",
      "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": 0.13400569834070455,
      "parent_symmetrization_rmsd_A": 0.3921335516096298,
      "parent_cell_rmsd_A": 0.12496776102299606,
      "energy_eV": -53.91745916929407,
      "reduced_polarization": [
        9.155936598139012e-15,
        -0.3984575339954832,
        0.41255484698680284
      ],
      "cartesian_polarization_e_A2": [
        6.464260198278881e-16,
        -0.007334857557508168,
        0.008202347636234886
      ],
      "ranking_score": 1.191386888546788
    },
    {
      "candidate_id": "bec_projection_05",
      "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": 3.589019891847793e-06,
      "parent_symmetrization_rmsd_A": 0.3182367498011632,
      "parent_cell_rmsd_A": 0.1145254115668073,
      "energy_eV": -58.813111965196384,
      "reduced_polarization": [
        -0.4999969874381506,
        1.043226445296449e-15,
        0.49999804922197894
      ],
      "cartesian_polarization_e_A2": [
        -0.008390838785448784,
        3.1172589231920475e-16,
        0.01000063736099165
      ],
      "ranking_score": 0.8468752807326487
    },
    {
      "candidate_id": "bec_projection_06",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        -0.5,
        -0.5,
        0.0
      ],
      "formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_residual": 0.0009337555248542265,
      "parent_symmetrization_rmsd_A": 0.41981785404175437,
      "parent_cell_rmsd_A": 0.18369424761738842,
      "energy_eV": -53.38483367992916,
      "reduced_polarization": [
        -0.49981223852537426,
        -0.4992961748114811,
        -0.000584187566495964
      ],
      "cartesian_polarization_e_A2": [
        -0.008293753354435331,
        -0.009250005600005657,
        0.0003007712566503133
      ],
      "ranking_score": 0.9676089269958099
    },
    {
      "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": 0.18182923872559842,
      "parent_symmetrization_rmsd_A": 0.40701888176660117,
      "parent_cell_rmsd_A": 0.11511294680926974,
      "energy_eV": -51.81803808676067,
      "reduced_polarization": [
        -0.4228927717581633,
        -0.3742399443344589,
        0.39369498691316596
      ],
      "cartesian_polarization_e_A2": [
        -0.00705521606667396,
        -0.0069843051095126564,
        0.008002587600900403
      ],
      "ranking_score": 1.2994555959201155
    }
  ],
  "formal_branches": [
    {
      "orbit_id": 0,
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.0,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -1.087473635468381e-16,
              -8.179657707072981e-16,
              0.07466112154638371
            ],
            "branch_aligned_reduced_polarization": [
              -1.087473635468381e-16,
              -8.179657707072981e-16,
              0.07466112154638371
            ],
            "target_residual": 0.07466112154638371,
            "energy_eV": -68.02840828370863,
            "max_atomic_step_A": 0.034140747612632555,
            "max_log_strain_component": 0.0012020097415935814,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.0754574970846853,
            "cell_principal_stretches": [
              1.000480718206906,
              1.0003065697656282,
              0.9987987123827532
            ],
            "cell_volume_ratio": 0.9995852017926249,
            "cell_rmsd_from_input_A": 0.007338011246634004
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -5.275565357321799e-16,
              1.9168326935445543e-15,
              0.0014233807515345559
            ],
            "branch_aligned_reduced_polarization": [
              -5.275565357321799e-16,
              1.9168326935445543e-15,
              0.0014233807515345559
            ],
            "target_residual": 0.0014233807515345559,
            "energy_eV": -67.98479245789753,
            "max_atomic_step_A": 0.0006792774761725796,
            "max_log_strain_component": 2.4946022777536257e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.0754574970846853,
            "cell_principal_stretches": [
              1.0004906972850036,
              1.000312933185638,
              0.9987737966380995
            ],
            "cell_volume_ratio": 0.999576595061531,
            "cell_rmsd_from_input_A": 0.007490143854708299
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              5.404353491321977e-16,
              -3.315023952620479e-16,
              4.3011022397168104e-07
            ],
            "branch_aligned_reduced_polarization": [
              5.404353491321977e-16,
              -3.315023952620479e-16,
              4.3011022397168104e-07
            ],
            "target_residual": 4.3011022397168104e-07,
            "energy_eV": -67.9819750121143
          }
        ],
        "iterations": 2
      },
      "parent": {
        "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": 7.090393213236037e-16,
        "parent_symmetrization_rmsd_A": 0.23164031138782606,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -67.45266324600402,
        "reduced_polarization": [
          2.523700715781286e-16,
          -7.737514047231197e-17,
          6.580723317322927e-16
        ],
        "cartesian_polarization_e_A2": [
          4.180609087368573e-18,
          -1.4290334378761879e-18,
          1.2929350152213129e-17
        ],
        "ranking_score": 0.23164031138782748
      },
      "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": [
          -68.02840828370863,
          -67.94181381785822,
          -67.78048937433361,
          -67.6084463848847,
          -67.47484639861814,
          -67.4067153852171,
          -67.40270948466281,
          -67.4336300366563,
          -67.45266324600406
        ],
        "cartesian_polarizations_e_A2": [
          [
            -7.355859984746336e-18,
            -1.3337645420177753e-17,
            0.0014668900919889147
          ],
          [
            4.699698998810713e-18,
            1.0207381699115627e-18,
            0.0022955536226163652
          ],
          [
            -1.5784550002100618e-17,
            -1.1296169080354627e-17,
            0.0030919384475410756
          ],
          [
            -4.2247090963014235e-18,
            -9.458840374513815e-18,
            0.003748550505697295
          ],
          [
            -1.861406681975096e-18,
            2.1027206300178192e-17,
            0.0041121609455093255
          ],
          [
            -1.44166837890609e-17,
            -2.2660387372036693e-17,
            0.003976458331865336
          ],
          [
            -1.6972683547143234e-18,
            8.165905359292502e-19,
            0.003178501497640019
          ],
          [
            -5.908459388643886e-18,
            -1.701230283185938e-17,
            0.0017595887931391113
          ],
          [
            -1.5108999936814893e-17,
            -1.2180808827611315e-17,
            -1.565131860531063e-18
          ]
        ],
        "raw_reduced_polarization": [
          [
            -4.440498673932725e-16,
            -7.221679777415783e-16,
            0.07466112154638396
          ],
          [
            2.837058782437059e-16,
            5.526795748022283e-17,
            0.1168380705346653
          ],
          [
            -9.52863071052183e-16,
            -6.116320627811327e-16,
            0.15737211227107156
          ],
          [
            -2.550322488299091e-16,
            -5.121497393167316e-16,
            0.190792061693699
          ],
          [
            -1.123672000296368e-16,
            1.1385199240925903e-15,
            0.20929894465009793
          ],
          [
            -8.702893391198764e-16,
            -1.226948656060947e-15,
            0.20239201318552003
          ],
          [
            -1.024586913568996e-16,
            4.4214365984178266e-17,
            0.16177796001669242
          ],
          [
            -3.5667489776402104e-16,
            -9.211326246703807e-16,
            0.08955877026757302
          ],
          [
            -9.1208226261786e-16,
            -6.595309592639926e-16,
            -7.966138752548806e-17
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -4.440498673932725e-16,
            -7.221679777415783e-16,
            0.07466112154638396
          ],
          [
            2.8370587824370585e-16,
            5.5267957480222845e-17,
            0.1168380705346653
          ],
          [
            -9.52863071052183e-16,
            -6.116320627811327e-16,
            0.15737211227107156
          ],
          [
            -2.5503224882990916e-16,
            -5.121497393167316e-16,
            0.190792061693699
          ],
          [
            -1.123672000296368e-16,
            1.1385199240925903e-15,
            0.20929894465009793
          ],
          [
            -8.702893391198764e-16,
            -1.226948656060947e-15,
            0.20239201318552003
          ],
          [
            -1.0245869135689956e-16,
            4.4214365984178315e-17,
            0.16177796001669242
          ],
          [
            -3.5667489776402104e-16,
            -9.211326246703807e-16,
            0.08955877026757302
          ],
          [
            -9.1208226261786e-16,
            -6.595309592639926e-16,
            -8.326672684688674e-17
          ]
        ],
        "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": [
          [
            -4.440892098500626e-16,
            -7.216449660063518e-16,
            0.07466112154638394
          ],
          [
            3.3306690738754696e-16,
            0.0,
            0.11683807053466533
          ],
          [
            -9.43689570931383e-16,
            -6.106226635438361e-16,
            0.15737211227107162
          ],
          [
            -2.7755575615628914e-16,
            -4.996003610813204e-16,
            0.190792061693699
          ],
          [
            -1.1102230246251565e-16,
            1.1102230246251565e-15,
            0.2092989446500979
          ],
          [
            -8.881784197001252e-16,
            -1.2212453270876722e-15,
            0.20239201318552003
          ],
          [
            -1.1102230246251565e-16,
            0.0,
            0.16177796001669242
          ],
          [
            -3.3306690738754696e-16,
            -9.43689570931383e-16,
            0.08955877026757297
          ],
          [
            -8.881784197001252e-16,
            -6.661338147750939e-16,
            -1.1102230246251565e-16
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -67.45266324600408,
          -67.43363003665633,
          -67.40270948466281,
          -67.40671538521713,
          -67.47484639861818,
          -67.60844638488472,
          -67.7804893743336,
          -67.94181381785819,
          -68.02840828370864
        ],
        "cartesian_polarizations_e_A2": [
          [
            -1.4446271435639335e-17,
            -1.3745940688142378e-17,
            -2.1775747624780006e-18
          ],
          [
            -2.0919659087162833e-18,
            -1.6808155197877067e-17,
            -0.0017595887931391345
          ],
          [
            7.624788279388022e-19,
            8.370052993274814e-18,
            -0.0031785014976400293
          ],
          [
            -7.775058256792093e-18,
            2.381722396460313e-18,
            -0.00397645833186531
          ],
          [
            -1.516721626104276e-17,
            -2.6743340051682944e-17,
            -0.004112160945509373
          ],
          [
            -1.7315384021949913e-18,
            1.966622207362944e-17,
            -0.003748550505697297
          ],
          [
            -9.567610395749915e-18,
            -1.1568365925664377e-18,
            -0.0030919384475411055
          ],
          [
            -3.7346251091197046e-19,
            -2.1299403145487943e-17,
            -0.0022955536226163557
          ],
          [
            -3.590132551779231e-18,
            -2.715163531964757e-17,
            -0.0014668900919889
          ]
        ],
        "raw_reduced_polarization": [
          [
            -8.720754512219119e-16,
            -7.442751607336675e-16,
            -1.1083323481807035e-16
          ],
          [
            -1.2628532711104158e-16,
            -9.10079033174336e-16,
            -0.0895587702675742
          ],
          [
            4.602842130471555e-17,
            4.531972513378272e-16,
            -0.16177796001669295
          ],
          [
            -4.693555335559525e-16,
            1.2895856745385328e-16,
            -0.2023920131855187
          ],
          [
            -9.155965969182837e-16,
            -1.4480204859818383e-15,
            -0.20929894465010035
          ],
          [
            -1.045274651061156e-16,
            1.06482931411896e-15,
            -0.1907920616936991
          ],
          [
            -5.775662038583177e-16,
            -6.263701847758588e-17,
            -0.1573721122710731
          ],
          [
            -2.2544743754055813e-17,
            -1.1532580460873167e-15,
            -0.11683807053466481
          ],
          [
            -2.1672488150232422e-16,
            -1.4701276689739275e-15,
            -0.07466112154638321
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -8.720754512219119e-16,
            -7.442751607336675e-16,
            -1.1083323481807035e-16
          ],
          [
            -1.2628532711104156e-16,
            -9.10079033174336e-16,
            -0.0895587702675742
          ],
          [
            4.602842130471556e-17,
            4.531972513378271e-16,
            -0.16177796001669295
          ],
          [
            -4.693555335559525e-16,
            1.289585674538533e-16,
            -0.2023920131855187
          ],
          [
            -9.155965969182837e-16,
            -1.4480204859818383e-15,
            -0.20929894465010035
          ],
          [
            -1.045274651061156e-16,
            1.0648293141189598e-15,
            -0.1907920616936991
          ],
          [
            -5.775662038583177e-16,
            -6.263701847758593e-17,
            -0.1573721122710731
          ],
          [
            -2.254474375405583e-17,
            -1.1532580460873167e-15,
            -0.11683807053466481
          ],
          [
            -2.1672488150232422e-16,
            -1.4701276689739275e-15,
            -0.07466112154638321
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          -1.3801146578424475e-15,
          -5.968939407864067e-16,
          -0.07466112154638412
        ],
        "actual_opposite_endpoint_branch_residual": 1.7116419944721518e-15
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            -4.440498673932725e-16,
            -7.221679777415783e-16,
            0.07466112154638396
          ],
          [
            2.837058782437059e-16,
            5.526795748022283e-17,
            0.1168380705346653
          ],
          [
            -9.52863071052183e-16,
            -6.116320627811327e-16,
            0.15737211227107156
          ],
          [
            -2.550322488299091e-16,
            -5.121497393167316e-16,
            0.190792061693699
          ],
          [
            -1.123672000296368e-16,
            1.1385199240925903e-15,
            0.20929894465009793
          ],
          [
            -8.702893391198764e-16,
            -1.226948656060947e-15,
            0.20239201318552003
          ],
          [
            -1.024586913568996e-16,
            4.4214365984178266e-17,
            0.16177796001669242
          ],
          [
            -3.5667489776402104e-16,
            -9.211326246703807e-16,
            0.08955877026757302
          ],
          [
            -9.1208226261786e-16,
            -6.595309592639926e-16,
            -7.966138752548806e-17
          ],
          [
            -1.2628532711104158e-16,
            -9.10079033174336e-16,
            -0.0895587702675742
          ],
          [
            4.602842130471555e-17,
            4.531972513378272e-16,
            -0.16177796001669295
          ],
          [
            -4.693555335559525e-16,
            1.2895856745385328e-16,
            -0.2023920131855187
          ],
          [
            -9.155965969182837e-16,
            -1.4480204859818383e-15,
            -0.20929894465010035
          ],
          [
            -1.045274651061156e-16,
            1.06482931411896e-15,
            -0.1907920616936991
          ],
          [
            -5.775662038583177e-16,
            -6.263701847758588e-17,
            -0.1573721122710731
          ],
          [
            -2.2544743754055813e-17,
            -1.1532580460873167e-15,
            -0.11683807053466481
          ],
          [
            -2.1672488150232422e-16,
            -1.4701276689739275e-15,
            -0.07466112154638321
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -4.440498673932725e-16,
            -7.221679777415783e-16,
            0.07466112154638396
          ],
          [
            2.8370587824370585e-16,
            5.5267957480222845e-17,
            0.1168380705346653
          ],
          [
            -9.52863071052183e-16,
            -6.116320627811327e-16,
            0.15737211227107156
          ],
          [
            -2.5503224882990916e-16,
            -5.121497393167316e-16,
            0.190792061693699
          ],
          [
            -1.123672000296368e-16,
            1.1385199240925903e-15,
            0.20929894465009793
          ],
          [
            -8.702893391198764e-16,
            -1.226948656060947e-15,
            0.20239201318552003
          ],
          [
            -1.0245869135689956e-16,
            4.4214365984178315e-17,
            0.16177796001669242
          ],
          [
            -3.5667489776402104e-16,
            -9.211326246703807e-16,
            0.08955877026757302
          ],
          [
            -9.1208226261786e-16,
            -6.595309592639926e-16,
            -8.326672684688674e-17
          ],
          [
            -1.2628532711104156e-16,
            -9.10079033174336e-16,
            -0.0895587702675742
          ],
          [
            4.602842130471556e-17,
            4.531972513378271e-16,
            -0.16177796001669295
          ],
          [
            -4.693555335559525e-16,
            1.289585674538533e-16,
            -0.2023920131855187
          ],
          [
            -9.155965969182837e-16,
            -1.4480204859818383e-15,
            -0.20929894465010035
          ],
          [
            -1.045274651061156e-16,
            1.0648293141189598e-15,
            -0.1907920616936991
          ],
          [
            -5.775662038583177e-16,
            -6.263701847758593e-17,
            -0.1573721122710731
          ],
          [
            -2.254474375405583e-17,
            -1.1532580460873167e-15,
            -0.11683807053466481
          ],
          [
            -2.1672488150232422e-16,
            -1.4701276689739275e-15,
            -0.07466112154638321
          ]
        ],
        "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": [
          [
            -4.440892098500626e-16,
            -7.216449660063518e-16,
            0.07466112154638394
          ],
          [
            3.3306690738754696e-16,
            0.0,
            0.11683807053466533
          ],
          [
            -9.43689570931383e-16,
            -6.106226635438361e-16,
            0.15737211227107162
          ],
          [
            -2.7755575615628914e-16,
            -4.996003610813204e-16,
            0.190792061693699
          ],
          [
            -1.1102230246251565e-16,
            1.1102230246251565e-15,
            0.2092989446500979
          ],
          [
            -8.881784197001252e-16,
            -1.2212453270876722e-15,
            0.20239201318552003
          ],
          [
            -1.1102230246251565e-16,
            0.0,
            0.16177796001669242
          ],
          [
            -3.3306690738754696e-16,
            -9.43689570931383e-16,
            0.08955877026757297
          ],
          [
            -8.881784197001252e-16,
            -6.661338147750939e-16,
            -1.1102230246251565e-16
          ],
          [
            -1.1102230246251565e-16,
            -8.881784197001252e-16,
            -0.0895587702675742
          ],
          [
            0.0,
            4.440892098500626e-16,
            -0.16177796001669298
          ],
          [
            -4.440892098500626e-16,
            1.1102230246251565e-16,
            -0.2023920131855187
          ],
          [
            -8.881784197001252e-16,
            -1.4432899320127035e-15,
            -0.20929894465010035
          ],
          [
            -1.1102230246251565e-16,
            1.1102230246251565e-15,
            -0.1907920616936991
          ],
          [
            -5.551115123125783e-16,
            -5.551115123125783e-17,
            -0.15737211227107306
          ],
          [
            0.0,
            -1.1657341758564144e-15,
            -0.11683807053466483
          ],
          [
            -2.220446049250313e-16,
            -1.4432899320127035e-15,
            -0.07466112154638321
          ]
        ]
      },
      "incoming_structure_ids": [
        "incoming_00_000",
        "incoming_00_001",
        "incoming_00_002",
        "incoming_00_003",
        "incoming_00_004",
        "incoming_00_005",
        "incoming_00_006",
        "incoming_00_007",
        "incoming_00_008"
      ],
      "reflected_structure_ids": [
        "reflected_00_001",
        "reflected_00_002",
        "reflected_00_003",
        "reflected_00_004",
        "reflected_00_005",
        "reflected_00_006",
        "reflected_00_007",
        "reflected_00_008"
      ]
    },
    {
      "orbit_id": 1,
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.0,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -1.087473635468381e-16,
              -8.179657707072981e-16,
              0.07466112154638371
            ],
            "branch_aligned_reduced_polarization": [
              -1.087473635468381e-16,
              -8.179657707072981e-16,
              0.07466112154638371
            ],
            "target_residual": 0.4253388784536163,
            "energy_eV": -68.02840828370863,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.004224897785713964,
            "step_scale": 0.6169751140860958,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.0754574970846853,
            "cell_principal_stretches": [
              1.0042338352485531,
              0.9989231950374313,
              0.9983121740507946
            ],
            "cell_volume_ratio": 1.0014593244991572,
            "cell_rmsd_from_input_A": 0.025910606475076935
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              2.667270034846875e-15,
              -5.776713698785989e-15,
              0.34015639158671906
            ],
            "branch_aligned_reduced_polarization": [
              2.667270034846875e-15,
              -5.776713698785989e-15,
              0.34015639158671906
            ],
            "target_residual": 0.15984360841328094,
            "energy_eV": -66.66309480477246,
            "max_atomic_step_A": 0.07407290584659533,
            "max_log_strain_component": 0.0026448140656540296,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.0754574970846853,
            "cell_principal_stretches": [
              1.006893362448406,
              0.9982496981873371,
              0.9972570339669823
            ],
            "cell_volume_ratio": 1.0023739549924673,
            "cell_rmsd_from_input_A": 0.04222535502355774
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -1.868994924919139e-15,
              -4.675712268441228e-15,
              0.48711289489507914
            ],
            "branch_aligned_reduced_polarization": [
              -1.868994924919139e-15,
              -4.675712268441228e-15,
              0.48711289489507914
            ],
            "target_residual": 0.01288710510492086,
            "energy_eV": -64.39284420216117,
            "max_atomic_step_A": 0.007035753597211728,
            "max_log_strain_component": 0.0002990410695954069,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.0754574970846853,
            "cell_principal_stretches": [
              1.0071945099419715,
              0.9981735765295159,
              0.9971378026886301
            ],
            "cell_volume_ratio": 1.0024774220255415,
            "cell_rmsd_from_input_A": 0.044074621350755974
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              9.245582042766768e-18,
              6.46739511264865e-17,
              0.49959732708545224
            ],
            "branch_aligned_reduced_polarization": [
              9.245582042766768e-18,
              6.46739511264865e-17,
              0.49959732708545224
            ],
            "target_residual": 0.00040267291454776366,
            "energy_eV": -64.09717627389719
          }
        ],
        "iterations": 3
      },
      "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": 0.00040267291454776366,
        "parent_symmetrization_rmsd_A": 0.2149188597349735,
        "parent_cell_rmsd_A": 0.044074621350755974,
        "energy_eV": -64.09717627389719,
        "reduced_polarization": [
          9.245582042766768e-18,
          6.46739511264865e-17,
          0.49959732708545224
        ],
        "cartesian_polarization_e_A2": [
          -5.2046968939774055e-17,
          2.0924330993210316e-16,
          0.00986193013436937
        ],
        "ranking_score": 0.726742860901758
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 2,
      "formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.5,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        -0.5,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -1.087473635468381e-16,
              -8.179657707072981e-16,
              0.07466112154638371
            ],
            "branch_aligned_reduced_polarization": [
              -1.087473635468381e-16,
              -8.326672684688674e-16,
              0.07466112154638371
            ],
            "target_residual": 0.5055435521006703,
            "energy_eV": -68.02840828370863,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.006485091799675228,
            "step_scale": 0.45730483326667615,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.0754574970846853,
            "cell_principal_stretches": [
              1.0063093235931657,
              1.0002198060909189,
              0.993323374719806
            ],
            "cell_volume_ratio": 0.9998102894200102,
            "cell_rmsd_from_input_A": 0.04961033964366224
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              5.507144930689648e-16,
              -0.22937325505618822,
              0.04523145744579796
            ],
            "branch_aligned_reduced_polarization": [
              5.507144930689648e-16,
              -0.22937325505618822,
              0.04523145744579796
            ],
            "target_residual": 0.2743806112347481,
            "energy_eV": -66.8119347513792,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.0061245175704577135,
            "step_scale": 0.7849000551749507,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.0754574970846853,
            "cell_principal_stretches": [
              1.0123826818068513,
              1.000337165315738,
              0.9871485308895285
            ],
            "cell_volume_ratio": 0.9997090306455304,
            "cell_rmsd_from_input_A": 0.09635817103284278
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              1.0173885038458393e-15,
              -0.43036792304430915,
              0.013100138153393092
            ],
            "branch_aligned_reduced_polarization": [
              1.0173885038458393e-15,
              -0.43036792304430915,
              0.013100138153393092
            ],
            "target_residual": 0.07085365029976393,
            "energy_eV": -62.93958895736989,
            "max_atomic_step_A": 0.04377000762168163,
            "max_log_strain_component": 0.0028612726748903357,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.0754574970846853,
            "cell_principal_stretches": [
              1.0152912629977624,
              1.0003261655983384,
              0.9843407397760606
            ],
            "cell_volume_ratio": 0.9997185203773822,
            "cell_rmsd_from_input_A": 0.11817412706558028
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -7.012435121612612e-16,
              -0.49493122999239625,
              -0.003369692959437038
            ],
            "branch_aligned_reduced_polarization": [
              -7.012435121612612e-16,
              -0.49493122999239625,
              -0.003369692959437038
            ],
            "target_residual": 0.006086646041200595,
            "energy_eV": -60.48717995871077,
            "max_atomic_step_A": 0.00486991173561921,
            "max_log_strain_component": 0.0003564647492076235,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.0754574970846853,
            "cell_principal_stretches": [
              1.0157225847988107,
              1.000248952755525,
              0.9840642680857284
            ],
            "cell_volume_ratio": 0.9997851393048129,
            "cell_rmsd_from_input_A": 0.12087886862637778
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              -1.594645247278084e-15,
              -0.4997108818411334,
              -0.0007098055421365078
            ],
            "branch_aligned_reduced_polarization": [
              -1.594645247278084e-15,
              -0.4997108818411334,
              -0.0007098055421365078
            ],
            "target_residual": 0.0007664288730431059,
            "energy_eV": -60.2668591678035
          }
        ],
        "iterations": 4
      },
      "parent": {
        "candidate_id": "bec_projection_02",
        "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": 0.0007664288730431059,
        "parent_symmetrization_rmsd_A": 0.2869790094187273,
        "parent_cell_rmsd_A": 0.12087886862637778,
        "energy_eV": -60.2668591678035,
        "reduced_polarization": [
          -1.594645247278084e-15,
          -0.4997108818411334,
          -0.0007098055421365078
        ],
        "cartesian_polarization_e_A2": [
          -4.559465916310672e-17,
          -0.009233492788190675,
          0.0001321775322455087
        ],
        "ranking_score": 0.8187315843214079
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 3,
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.0,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        -0.5,
        0.0,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -1.087473635468381e-16,
              -8.179657707072981e-16,
              0.07466112154638371
            ],
            "branch_aligned_reduced_polarization": [
              -1.1102230246251565e-16,
              -8.179657707072981e-16,
              0.07466112154638371
            ],
            "target_residual": 0.5055435521006709,
            "energy_eV": -68.02840828370863,
            "max_atomic_step_A": 0.12000000000000001,
            "max_log_strain_component": 0.007257129294857857,
            "step_scale": 0.6719144279467878,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.0754574970846853,
            "cell_principal_stretches": [
              1.0070615663462155,
              1.0002059782908188,
              0.9925067414553648
            ],
            "cell_volume_ratio": 0.9997212721316513,
            "cell_rmsd_from_input_A": 0.049911482611399674
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.3164375673519857,
              -4.438655802527514e-15,
              0.04123737673157723
            ],
            "branch_aligned_reduced_polarization": [
              -0.3164375673519857,
              -4.438655802527514e-15,
              0.04123737673157723
            ],
            "target_residual": 0.18813741764826797,
            "energy_eV": -66.6000024667177,
            "max_atomic_step_A": 0.08250897435440219,
            "max_log_strain_component": 0.005909512445203857,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.0754574970846853,
            "cell_principal_stretches": [
              1.012725809211204,
              1.0005046967229476,
              0.9862622067031536
            ],
            "cell_volume_ratio": 0.9993172891224038,
            "cell_rmsd_from_input_A": 0.09080809784240032
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.4704622229976086,
              -1.155372246595844e-15,
              0.00678415596301758
            ],
            "branch_aligned_reduced_polarization": [
              -0.4704622229976086,
              -1.155372246595844e-15,
              0.00678415596301758
            ],
            "target_residual": 0.030306848110180473,
            "energy_eV": -63.616583119461694,
            "max_atomic_step_A": 0.018802510991766837,
            "max_log_strain_component": 0.0020512048607964155,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.0754574970846853,
            "cell_principal_stretches": [
              1.0147207225947663,
              1.000585722086517,
              0.9841356569299871
            ],
            "cell_volume_ratio": 0.9992077603876486,
            "cell_rmsd_from_input_A": 0.10493127387432036
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -0.49747524982256747,
              -6.775534716243801e-16,
              -1.7856166033379912e-05
            ],
            "branch_aligned_reduced_polarization": [
              -0.49747524982256747,
              -6.775534716243801e-16,
              -1.7856166033379912e-05
            ],
            "target_residual": 0.0025248133200518053,
            "energy_eV": -62.633365377832256,
            "max_atomic_step_A": 0.0016474623051058483,
            "max_log_strain_component": 0.00020985614307635127,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.0754574970846853,
            "cell_principal_stretches": [
              1.0149283925389576,
              1.0005902967187537,
              0.9839237004245912
            ],
            "cell_volume_ratio": 0.9992015770986462,
            "cell_rmsd_from_input_A": 0.10636574933583673
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              -0.49989951267587834,
              1.2206955072261258e-15,
              -2.279760358486687e-05
            ],
            "branch_aligned_reduced_polarization": [
              -0.49989951267587834,
              1.2206955072261258e-15,
              -2.279760358486687e-05
            ],
            "target_residual": 0.00010304092894740208,
            "energy_eV": -62.53677000197118
          }
        ],
        "iterations": 4
      },
      "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,
          0.0,
          0.0
        ],
        "formal_class": [
          0.5,
          0.0,
          0.0
        ],
        "target_residual": 0.00010304092894740208,
        "parent_symmetrization_rmsd_A": 0.24499539289454275,
        "parent_cell_rmsd_A": 0.10636574933583673,
        "energy_eV": -62.53677000197118,
        "reduced_polarization": [
          -0.49989951267587834,
          1.2206955072261258e-15,
          -2.279760358486687e-05
        ],
        "cartesian_polarization_e_A2": [
          -0.008296299294832011,
          8.737690185259076e-17,
          0.0001273073672016465
        ],
        "ranking_score": 0.7717929120863967
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 4,
      "formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.5,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        -0.5,
        0.5
      ],
      "bec_backprojection": {
        "converged_to_target": false,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -1.087473635468381e-16,
              -8.179657707072981e-16,
              0.07466112154638371
            ],
            "branch_aligned_reduced_polarization": [
              -1.087473635468381e-16,
              -8.326672684688674e-16,
              0.07466112154638371
            ],
            "target_residual": 0.6564397622967238,
            "energy_eV": -68.02840828370863,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.004567828562616104,
            "step_scale": 0.32210647801869335,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.0754574970846853,
            "cell_principal_stretches": [
              1.005610215527649,
              0.9991184747725037,
              0.9960564928085646
            ],
            "cell_volume_ratio": 1.0007616094407914,
            "cell_rmsd_from_input_A": 0.03749416615209475
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -1.228078258864402e-15,
              -0.1430316025942103,
              0.20635315087912745
            ],
            "branch_aligned_reduced_polarization": [
              -1.228078258864402e-15,
              -0.14303160259421033,
              0.20635315087912742
            ],
            "target_residual": 0.4622281998591976,
            "energy_eV": -67.09382751039658,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.006403266355780653,
            "step_scale": 0.40878751556901627,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.0754574970846853,
            "cell_principal_stretches": [
              1.0134652040860843,
              0.9979285912193864,
              0.99053331247754
            ],
            "cell_volume_ratio": 1.0017916183854816,
            "cell_rmsd_from_input_A": 0.09012991293048866
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -4.50082023389081e-16,
              -0.24365240265071758,
              0.27846067294151905
            ],
            "branch_aligned_reduced_polarization": [
              -4.50082023389081e-16,
              -0.24365240265071758,
              0.27846067294151905
            ],
            "target_residual": 0.33881228445892336,
            "energy_eV": -63.87683560983496,
            "max_atomic_step_A": 0.11999999999999998,
            "max_log_strain_component": 0.0156465583258605,
            "step_scale": 0.37617578277639524,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.0754574970846853,
            "cell_principal_stretches": [
              1.0338022267699651,
              0.9944189453194592,
              0.9774428889822894
            ],
            "cell_volume_ratio": 1.0048430763297358,
            "cell_rmsd_from_input_A": 0.22428770542168358
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -1.7353024109626818e-16,
              -0.2799462520744981,
              0.3025337339360352
            ],
            "branch_aligned_reduced_polarization": [
              -1.7353024109626818e-16,
              -0.2799462520744981,
              0.3025337339360352
            ],
            "target_residual": 0.29566294696715867,
            "energy_eV": -59.30115203061226,
            "max_atomic_step_A": 0.12000000000000001,
            "max_log_strain_component": 0.00631053372606477,
            "step_scale": 0.5392784421592264,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.0754574970846853,
            "cell_principal_stretches": [
              1.0424024181682463,
              0.9928208697716993,
              0.9722879771186806
            ],
            "cell_volume_ratio": 1.0062391799009216,
            "cell_rmsd_from_input_A": 0.28057756705173137
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              -3.956358300650422e-15,
              -0.3151592575061449,
              0.34060499610752126
            ],
            "branch_aligned_reduced_polarization": [
              -3.956358300650422e-15,
              -0.3151592575061449,
              0.34060499610752126
            ],
            "target_residual": 0.24407553615953193,
            "energy_eV": -59.8470557773954,
            "max_atomic_step_A": 0.11409656872556946,
            "max_log_strain_component": 0.02,
            "step_scale": 0.5751847405463952,
            "strain_jacobian_refreshed": true,
            "strain_jacobian_frobenius_norm": 1.8864793539702467,
            "cell_principal_stretches": [
              1.0171581343946086,
              1.0073292165855208,
              0.9858742864679559
            ],
            "cell_volume_ratio": 1.0101397154374079,
            "cell_rmsd_from_input_A": 0.12496776102299606
          },
          {
            "iteration": 5,
            "reduced_polarization": [
              9.155936598139012e-15,
              -0.3984575339954832,
              0.41255484698680284
            ],
            "branch_aligned_reduced_polarization": [
              9.155936598139012e-15,
              -0.3984575339954832,
              0.41255484698680284
            ],
            "target_residual": 0.13400569834070455,
            "energy_eV": -53.91745916929407
          }
        ],
        "iterations": 5
      },
      "parent": {
        "candidate_id": "bec_projection_04",
        "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": 0.13400569834070455,
        "parent_symmetrization_rmsd_A": 0.3921335516096298,
        "parent_cell_rmsd_A": 0.12496776102299606,
        "energy_eV": -53.91745916929407,
        "reduced_polarization": [
          9.155936598139012e-15,
          -0.3984575339954832,
          0.41255484698680284
        ],
        "cartesian_polarization_e_A2": [
          6.464260198278881e-16,
          -0.007334857557508168,
          0.008202347636234886
        ],
        "ranking_score": 1.191386888546788
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 5,
      "formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.0,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        -0.5,
        0.0,
        0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -1.087473635468381e-16,
              -8.179657707072981e-16,
              0.07466112154638371
            ],
            "branch_aligned_reduced_polarization": [
              -1.1102230246251565e-16,
              -8.179657707072981e-16,
              0.07466112154638371
            ],
            "target_residual": 0.6564397622967244,
            "energy_eV": -68.02840828370863,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.004949921921021639,
            "step_scale": 0.4582974645772576,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.0754574970846853,
            "cell_principal_stretches": [
              1.0063774079286105,
              0.9992000238936384,
              0.9955363455955718
            ],
            "cell_volume_ratio": 1.0010838026882944,
            "cell_rmsd_from_input_A": 0.039088421644731426
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.22534599820651435,
              -5.112288600955918e-15,
              0.27903885051856614
            ],
            "branch_aligned_reduced_polarization": [
              -0.22534599820651435,
              -5.112288600955918e-15,
              0.27903885051856614
            ],
            "target_residual": 0.3525034046379305,
            "energy_eV": -66.59696981438546,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.0054830028779673575,
            "step_scale": 0.8648220747609647,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.0754574970846853,
            "cell_principal_stretches": [
              1.0131057947088766,
              0.9984830437712869,
              0.990596728249496
            ],
            "cell_volume_ratio": 1.0020568997609056,
            "cell_rmsd_from_input_A": 0.0807267810426119
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.42480157421634285,
              -1.2303102854682636e-14,
              0.4578619024549028
            ],
            "branch_aligned_reduced_polarization": [
              -0.42480157421634285,
              -1.2303102854682636e-14,
              0.4578619024549028
            ],
            "target_residual": 0.08619989852117181,
            "energy_eV": -62.24022520934861,
            "max_atomic_step_A": 0.04575094611764356,
            "max_log_strain_component": 0.003719727849832823,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.0754574970846853,
            "cell_principal_stretches": [
              1.0171929031164735,
              0.99823124187879,
              0.987202309055581
            ],
            "cell_volume_ratio": 1.0023990397019944,
            "cell_rmsd_from_input_A": 0.10666465176845145
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -0.4866120919899204,
              -6.817369905208315e-15,
              0.4945490600326565
            ],
            "branch_aligned_reduced_polarization": [
              -0.4866120919899204,
              -6.817369905208315e-15,
              0.4945490600326565
            ],
            "target_residual": 0.014455062345556893,
            "energy_eV": -59.58082224372151,
            "max_atomic_step_A": 0.009995430185377952,
            "max_log_strain_component": 0.0012243301614712897,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.0754574970846853,
            "cell_principal_stretches": [
              1.0185001757950367,
              0.9981711152565211,
              0.9860749881918011
            ],
            "cell_volume_ratio": 1.0024807677777923,
            "cell_rmsd_from_input_A": 0.11504919786870609
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              -0.4983569944323146,
              -1.9619514463469303e-15,
              0.4991858867066849
            ],
            "branch_aligned_reduced_polarization": [
              -0.4983569944323146,
              -1.9619514463469303e-15,
              0.4991858867066849
            ],
            "target_residual": 0.001833643299498977,
            "energy_eV": -58.894209804107156,
            "max_atomic_step_A": 0.001096862706664801,
            "max_log_strain_component": 0.0002783940371801503,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": true,
            "strain_jacobian_frobenius_norm": 2.0819753459899646,
            "cell_principal_stretches": [
              1.0182798995409645,
              0.9981603041847097,
              0.9859224269111015
            ],
            "cell_volume_ratio": 1.0020980364336483,
            "cell_rmsd_from_input_A": 0.1145254115668073
          },
          {
            "iteration": 5,
            "reduced_polarization": [
              -0.4999969874381506,
              1.043226445296449e-15,
              0.49999804922197894
            ],
            "branch_aligned_reduced_polarization": [
              -0.4999969874381506,
              1.043226445296449e-15,
              0.49999804922197894
            ],
            "target_residual": 3.589019891847793e-06,
            "energy_eV": -58.813111965196384
          }
        ],
        "iterations": 5
      },
      "parent": {
        "candidate_id": "bec_projection_05",
        "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": 3.589019891847793e-06,
        "parent_symmetrization_rmsd_A": 0.3182367498011632,
        "parent_cell_rmsd_A": 0.1145254115668073,
        "energy_eV": -58.813111965196384,
        "reduced_polarization": [
          -0.4999969874381506,
          1.043226445296449e-15,
          0.49999804922197894
        ],
        "cartesian_polarization_e_A2": [
          -0.008390838785448784,
          3.1172589231920475e-16,
          0.01000063736099165
        ],
        "ranking_score": 0.8468752807326487
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 6,
      "formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.5,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        -0.5,
        -0.5,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -1.087473635468381e-16,
              -8.179657707072981e-16,
              0.07466112154638371
            ],
            "branch_aligned_reduced_polarization": [
              -1.1102230246251565e-16,
              -8.326672684688674e-16,
              0.07466112154638371
            ],
            "target_residual": 0.7110374695264399,
            "energy_eV": -68.02840828370863,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.005392481447513593,
            "step_scale": 0.3802579678783505,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.0754574970846853,
            "cell_principal_stretches": [
              1.006648967863087,
              1.0001584505033951,
              0.9930808860921665
            ],
            "cell_volume_ratio": 0.9998422493983482,
            "cell_rmsd_from_input_A": 0.049928166967514134
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.1843716786657816,
              -0.1905200498800853,
              0.05444549039404774
            ],
            "branch_aligned_reduced_polarization": [
              -0.18437167866578164,
              -0.1905200498800853,
              0.05444549039404774
            ],
            "target_residual": 0.44538004914761264,
            "energy_eV": -66.77805250100093,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.004756147940236863,
            "step_scale": 0.5377874315168373,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.0754574970846853,
            "cell_principal_stretches": [
              1.0129630617864984,
              1.000332379537943,
              0.9865425123768196
            ],
            "cell_volume_ratio": 0.9996632811369887,
            "cell_rmsd_from_input_A": 0.09677780862350113
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.3348428393218745,
              -0.3522395280603055,
              0.030513172270684657
            ],
            "branch_aligned_reduced_polarization": [
              -0.3348428393218745,
              -0.3522395280603055,
              0.030513172270684657
            ],
            "target_residual": 0.2236986778528695,
            "energy_eV": -63.29921399756576,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.00640480177387889,
            "step_scale": 0.9245877559961868,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.0754574970846853,
            "cell_principal_stretches": [
              1.021046085406732,
              1.0005550039954605,
              0.9782763817284955
            ],
            "cell_volume_ratio": 0.9994196442255247,
            "cell_rmsd_from_input_A": 0.15539811340286644
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -0.44763431390610864,
              -0.4607184174656055,
              -0.009602873109570309
            ],
            "branch_aligned_reduced_polarization": [
              -0.44763431390610864,
              -0.4607184174656055,
              -0.009602873109570309
            ],
            "target_residual": 0.06616209623681012,
            "energy_eV": -57.281874159082825,
            "max_atomic_step_A": 0.06308276784409723,
            "max_log_strain_component": 0.006974797800960515,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.0754574970846853,
            "cell_principal_stretches": [
              1.0304293285468413,
              1.000144045384025,
              0.9701805614918951
            ],
            "cell_volume_ratio": 0.9998465070784681,
            "cell_rmsd_from_input_A": 0.21806802061741687
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              -0.4868066333301978,
              -0.4882439011420668,
              -0.02594091966837662
            ],
            "branch_aligned_reduced_polarization": [
              -0.4868066333301978,
              -0.4882439011420668,
              -0.02594091966837662
            ],
            "target_residual": 0.03138792917161811,
            "energy_eV": -53.38690407014888,
            "max_atomic_step_A": 0.007922844551363262,
            "max_log_strain_component": 0.005844707714090731,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": true,
            "strain_jacobian_frobenius_norm": 3.939146357014749,
            "cell_principal_stretches": [
              1.0207139804519596,
              1.0005528233207033,
              0.9695634340353619
            ],
            "cell_volume_ratio": 0.9901940519692638,
            "cell_rmsd_from_input_A": 0.18369424761738842
          },
          {
            "iteration": 5,
            "reduced_polarization": [
              -0.49981223852537426,
              -0.4992961748114811,
              -0.000584187566495964
            ],
            "branch_aligned_reduced_polarization": [
              -0.49981223852537426,
              -0.4992961748114811,
              -0.000584187566495964
            ],
            "target_residual": 0.0009337555248542265,
            "energy_eV": -53.38483367992916
          }
        ],
        "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": 0.0009337555248542265,
        "parent_symmetrization_rmsd_A": 0.41981785404175437,
        "parent_cell_rmsd_A": 0.18369424761738842,
        "energy_eV": -53.38483367992916,
        "reduced_polarization": [
          -0.49981223852537426,
          -0.4992961748114811,
          -0.000584187566495964
        ],
        "cartesian_polarization_e_A2": [
          -0.008293753354435331,
          -0.009250005600005657,
          0.0003007712566503133
        ],
        "ranking_score": 0.9676089269958099
      },
      "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": false,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -1.087473635468381e-16,
              -8.179657707072981e-16,
              0.07466112154638371
            ],
            "branch_aligned_reduced_polarization": [
              -1.1102230246251565e-16,
              -8.326672684688674e-16,
              0.07466112154638371
            ],
            "target_residual": 0.8251746248668698,
            "energy_eV": -68.02840828370863,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.004133124935869561,
            "step_scale": 0.29145277631475375,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.0754574970846853,
            "cell_principal_stretches": [
              1.0060666579442488,
              0.9993103097647975,
              0.9953413511916165
            ],
            "cell_volume_ratio": 1.000689104874029,
            "cell_rmsd_from_input_A": 0.04021906746774138
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.14434922663900254,
              -0.13142869159182707,
              0.197865710905412
            ],
            "branch_aligned_reduced_polarization": [
              -0.14434922663900251,
              -0.13142869159182707,
              0.197865710905412
            ],
            "target_residual": 0.594657389276111,
            "energy_eV": -66.99920442137781,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.0058646261742518035,
            "step_scale": 0.39507880112801336,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.0754574970846853,
            "cell_principal_stretches": [
              1.013830820062612,
              0.9983458001933271,
              0.9895650548568782
            ],
            "cell_volume_ratio": 1.0015919725490268,
            "cell_rmsd_from_input_A": 0.09212819081717145
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.27332325176619127,
              -0.24064837467384328,
              0.27936339713156016
            ],
            "branch_aligned_reduced_polarization": [
              -0.27332325176619127,
              -0.24064837467384326,
              0.27936339713156016
            ],
            "target_residual": 0.40905516043010426,
            "energy_eV": -63.55114943021736,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.010707256201822087,
            "step_scale": 0.3266239078533432,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.0754574970846853,
            "cell_principal_stretches": [
              1.0272994605249768,
              0.9959784803505791,
              0.9809259897093253
            ],
            "cell_volume_ratio": 1.0036522356304194,
            "cell_rmsd_from_input_A": 0.1810264763802972
          },
          {
            "iteration": 3,
            "reduced_polarization": [
              -0.31973489884728323,
              -0.27840464742164095,
              0.3076413342782024
            ],
            "branch_aligned_reduced_polarization": [
              -0.31973489884728323,
              -0.27840464742164095,
              0.3076413342782024
            ],
            "target_residual": 0.34438621234915423,
            "energy_eV": -58.925717760253484,
            "max_atomic_step_A": 0.12,
            "max_log_strain_component": 0.008675489465050184,
            "step_scale": 0.4819693980974082,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.0754574970846853,
            "cell_principal_stretches": [
              1.0395070846981187,
              0.9940922881090614,
              0.9729370604249096
            ],
            "cell_volume_ratio": 1.0054000553566749,
            "cell_rmsd_from_input_A": 0.2611267937400619
          },
          {
            "iteration": 4,
            "reduced_polarization": [
              -0.37720696818500526,
              -0.31545501576403767,
              0.3358903055470137
            ],
            "branch_aligned_reduced_polarization": [
              -0.37720696818500526,
              -0.31545501576403767,
              0.3358903055470137
            ],
            "target_residual": 0.2758024142070232,
            "energy_eV": -57.517609961714825,
            "max_atomic_step_A": 0.0961416705733964,
            "max_log_strain_component": 0.02,
            "step_scale": 0.41286676092352137,
            "strain_jacobian_refreshed": true,
            "strain_jacobian_frobenius_norm": 2.521705628590165,
            "cell_principal_stretches": [
              1.0122146408472705,
              0.9947362905481555,
              0.9810123646925658
            ],
            "cell_volume_ratio": 0.987768240814239,
            "cell_rmsd_from_input_A": 0.11511294680926974
          },
          {
            "iteration": 5,
            "reduced_polarization": [
              -0.4228927717581633,
              -0.3742399443344589,
              0.39369498691316596
            ],
            "branch_aligned_reduced_polarization": [
              -0.4228927717581633,
              -0.3742399443344589,
              0.39369498691316596
            ],
            "target_residual": 0.18182923872559842,
            "energy_eV": -51.81803808676067
          }
        ],
        "iterations": 5
      },
      "parent": {
        "candidate_id": "bec_projection_07",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          -0.5,
          -0.5,
          0.5
        ],
        "formal_class": [
          0.5,
          0.5,
          0.5
        ],
        "target_residual": 0.18182923872559842,
        "parent_symmetrization_rmsd_A": 0.40701888176660117,
        "parent_cell_rmsd_A": 0.11511294680926974,
        "energy_eV": -51.81803808676067,
        "reduced_polarization": [
          -0.4228927717581633,
          -0.3742399443344589,
          0.39369498691316596
        ],
        "cartesian_polarization_e_A2": [
          -0.00705521606667396,
          -0.0069843051095126564,
          0.008002587600900403
        ],
        "ranking_score": 1.2994555959201155
      },
      "branch_status": "awaiting_branch_sampling"
    }
  ],
  "sampled_polarization_branches": [
    {
      "orbit_id": 0,
      "candidate_id": "inversion_parent_endpoint_00",
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "construction": "MACEField-BEC-parent plus variable-cell P-N-P path and symmetric log-strain continuation beyond both polar endpoints",
      "geometry_diagnostics": {
        "collision_aware": false,
        "permutations_tested": 1,
        "selected_order": [
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          10,
          11,
          12,
          13,
          14,
          15,
          16,
          17,
          18,
          19,
          20,
          21,
          22,
          23
        ],
        "endpoint_rmsd_A": 0.23164031138782606,
        "minimum_distance_A_by_image": [
          1.751956303856395,
          1.7553215878566475,
          1.7587136024911805,
          1.7621321933946743,
          1.7655772061925914,
          1.7690484865243947,
          1.7725458800663432,
          1.7760692325538934,
          1.779618389803691
        ],
        "minimum_distance_A": 1.751956303856395,
        "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": [
          407.87505210126994,
          407.87505210126994,
          407.87505210126994,
          407.87505210126994,
          407.87505210126994,
          407.87505210126994,
          407.87505210126994,
          407.87505210126994,
          407.87505210126994
        ],
        "cell_deformation_log_strain_norm": 0.0
      },
      "parent_reduced_polarization": [
        -9.1208226261786e-16,
        -6.595309592639926e-16,
        -7.966138752548806e-17
      ],
      "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": [
          -68.02840828370863,
          -67.94181381785822,
          -67.78048937433361,
          -67.6084463848847,
          -67.47484639861814,
          -67.4067153852171,
          -67.40270948466281,
          -67.4336300366563,
          -67.45266324600406
        ],
        "cartesian_polarizations_e_A2": [
          [
            -7.355859984746336e-18,
            -1.3337645420177753e-17,
            0.0014668900919889147
          ],
          [
            4.699698998810713e-18,
            1.0207381699115627e-18,
            0.0022955536226163652
          ],
          [
            -1.5784550002100618e-17,
            -1.1296169080354627e-17,
            0.0030919384475410756
          ],
          [
            -4.2247090963014235e-18,
            -9.458840374513815e-18,
            0.003748550505697295
          ],
          [
            -1.861406681975096e-18,
            2.1027206300178192e-17,
            0.0041121609455093255
          ],
          [
            -1.44166837890609e-17,
            -2.2660387372036693e-17,
            0.003976458331865336
          ],
          [
            -1.6972683547143234e-18,
            8.165905359292502e-19,
            0.003178501497640019
          ],
          [
            -5.908459388643886e-18,
            -1.701230283185938e-17,
            0.0017595887931391113
          ],
          [
            -1.5108999936814893e-17,
            -1.2180808827611315e-17,
            -1.565131860531063e-18
          ]
        ],
        "raw_reduced_polarization": [
          [
            -4.440498673932725e-16,
            -7.221679777415783e-16,
            0.07466112154638396
          ],
          [
            2.837058782437059e-16,
            5.526795748022283e-17,
            0.1168380705346653
          ],
          [
            -9.52863071052183e-16,
            -6.116320627811327e-16,
            0.15737211227107156
          ],
          [
            -2.550322488299091e-16,
            -5.121497393167316e-16,
            0.190792061693699
          ],
          [
            -1.123672000296368e-16,
            1.1385199240925903e-15,
            0.20929894465009793
          ],
          [
            -8.702893391198764e-16,
            -1.226948656060947e-15,
            0.20239201318552003
          ],
          [
            -1.024586913568996e-16,
            4.4214365984178266e-17,
            0.16177796001669242
          ],
          [
            -3.5667489776402104e-16,
            -9.211326246703807e-16,
            0.08955877026757302
          ],
          [
            -9.1208226261786e-16,
            -6.595309592639926e-16,
            -7.966138752548806e-17
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -4.440498673932725e-16,
            -7.221679777415783e-16,
            0.07466112154638396
          ],
          [
            2.8370587824370585e-16,
            5.5267957480222845e-17,
            0.1168380705346653
          ],
          [
            -9.52863071052183e-16,
            -6.116320627811327e-16,
            0.15737211227107156
          ],
          [
            -2.5503224882990916e-16,
            -5.121497393167316e-16,
            0.190792061693699
          ],
          [
            -1.123672000296368e-16,
            1.1385199240925903e-15,
            0.20929894465009793
          ],
          [
            -8.702893391198764e-16,
            -1.226948656060947e-15,
            0.20239201318552003
          ],
          [
            -1.0245869135689956e-16,
            4.4214365984178315e-17,
            0.16177796001669242
          ],
          [
            -3.5667489776402104e-16,
            -9.211326246703807e-16,
            0.08955877026757302
          ],
          [
            -9.1208226261786e-16,
            -6.595309592639926e-16,
            -8.326672684688674e-17
          ]
        ],
        "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": [
          [
            -4.440892098500626e-16,
            -7.216449660063518e-16,
            0.07466112154638394
          ],
          [
            3.3306690738754696e-16,
            0.0,
            0.11683807053466533
          ],
          [
            -9.43689570931383e-16,
            -6.106226635438361e-16,
            0.15737211227107162
          ],
          [
            -2.7755575615628914e-16,
            -4.996003610813204e-16,
            0.190792061693699
          ],
          [
            -1.1102230246251565e-16,
            1.1102230246251565e-15,
            0.2092989446500979
          ],
          [
            -8.881784197001252e-16,
            -1.2212453270876722e-15,
            0.20239201318552003
          ],
          [
            -1.1102230246251565e-16,
            0.0,
            0.16177796001669242
          ],
          [
            -3.3306690738754696e-16,
            -9.43689570931383e-16,
            0.08955877026757297
          ],
          [
            -8.881784197001252e-16,
            -6.661338147750939e-16,
            -1.1102230246251565e-16
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -67.45266324600408,
          -67.43363003665633,
          -67.40270948466281,
          -67.40671538521713,
          -67.47484639861818,
          -67.60844638488472,
          -67.7804893743336,
          -67.94181381785819,
          -68.02840828370864
        ],
        "cartesian_polarizations_e_A2": [
          [
            -1.4446271435639335e-17,
            -1.3745940688142378e-17,
            -2.1775747624780006e-18
          ],
          [
            -2.0919659087162833e-18,
            -1.6808155197877067e-17,
            -0.0017595887931391345
          ],
          [
            7.624788279388022e-19,
            8.370052993274814e-18,
            -0.0031785014976400293
          ],
          [
            -7.775058256792093e-18,
            2.381722396460313e-18,
            -0.00397645833186531
          ],
          [
            -1.516721626104276e-17,
            -2.6743340051682944e-17,
            -0.004112160945509373
          ],
          [
            -1.7315384021949913e-18,
            1.966622207362944e-17,
            -0.003748550505697297
          ],
          [
            -9.567610395749915e-18,
            -1.1568365925664377e-18,
            -0.0030919384475411055
          ],
          [
            -3.7346251091197046e-19,
            -2.1299403145487943e-17,
            -0.0022955536226163557
          ],
          [
            -3.590132551779231e-18,
            -2.715163531964757e-17,
            -0.0014668900919889
          ]
        ],
        "raw_reduced_polarization": [
          [
            -8.720754512219119e-16,
            -7.442751607336675e-16,
            -1.1083323481807035e-16
          ],
          [
            -1.2628532711104158e-16,
            -9.10079033174336e-16,
            -0.0895587702675742
          ],
          [
            4.602842130471555e-17,
            4.531972513378272e-16,
            -0.16177796001669295
          ],
          [
            -4.693555335559525e-16,
            1.2895856745385328e-16,
            -0.2023920131855187
          ],
          [
            -9.155965969182837e-16,
            -1.4480204859818383e-15,
            -0.20929894465010035
          ],
          [
            -1.045274651061156e-16,
            1.06482931411896e-15,
            -0.1907920616936991
          ],
          [
            -5.775662038583177e-16,
            -6.263701847758588e-17,
            -0.1573721122710731
          ],
          [
            -2.2544743754055813e-17,
            -1.1532580460873167e-15,
            -0.11683807053466481
          ],
          [
            -2.1672488150232422e-16,
            -1.4701276689739275e-15,
            -0.07466112154638321
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -8.720754512219119e-16,
            -7.442751607336675e-16,
            -1.1083323481807035e-16
          ],
          [
            -1.2628532711104156e-16,
            -9.10079033174336e-16,
            -0.0895587702675742
          ],
          [
            4.602842130471556e-17,
            4.531972513378271e-16,
            -0.16177796001669295
          ],
          [
            -4.693555335559525e-16,
            1.289585674538533e-16,
            -0.2023920131855187
          ],
          [
            -9.155965969182837e-16,
            -1.4480204859818383e-15,
            -0.20929894465010035
          ],
          [
            -1.045274651061156e-16,
            1.0648293141189598e-15,
            -0.1907920616936991
          ],
          [
            -5.775662038583177e-16,
            -6.263701847758593e-17,
            -0.1573721122710731
          ],
          [
            -2.254474375405583e-17,
            -1.1532580460873167e-15,
            -0.11683807053466481
          ],
          [
            -2.1672488150232422e-16,
            -1.4701276689739275e-15,
            -0.07466112154638321
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          -1.3801146578424475e-15,
          -5.968939407864067e-16,
          -0.07466112154638412
        ],
        "actual_opposite_endpoint_branch_residual": 1.7116419944721518e-15
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            -4.440498673932725e-16,
            -7.221679777415783e-16,
            0.07466112154638396
          ],
          [
            2.837058782437059e-16,
            5.526795748022283e-17,
            0.1168380705346653
          ],
          [
            -9.52863071052183e-16,
            -6.116320627811327e-16,
            0.15737211227107156
          ],
          [
            -2.550322488299091e-16,
            -5.121497393167316e-16,
            0.190792061693699
          ],
          [
            -1.123672000296368e-16,
            1.1385199240925903e-15,
            0.20929894465009793
          ],
          [
            -8.702893391198764e-16,
            -1.226948656060947e-15,
            0.20239201318552003
          ],
          [
            -1.024586913568996e-16,
            4.4214365984178266e-17,
            0.16177796001669242
          ],
          [
            -3.5667489776402104e-16,
            -9.211326246703807e-16,
            0.08955877026757302
          ],
          [
            -9.1208226261786e-16,
            -6.595309592639926e-16,
            -7.966138752548806e-17
          ],
          [
            -1.2628532711104158e-16,
            -9.10079033174336e-16,
            -0.0895587702675742
          ],
          [
            4.602842130471555e-17,
            4.531972513378272e-16,
            -0.16177796001669295
          ],
          [
            -4.693555335559525e-16,
            1.2895856745385328e-16,
            -0.2023920131855187
          ],
          [
            -9.155965969182837e-16,
            -1.4480204859818383e-15,
            -0.20929894465010035
          ],
          [
            -1.045274651061156e-16,
            1.06482931411896e-15,
            -0.1907920616936991
          ],
          [
            -5.775662038583177e-16,
            -6.263701847758588e-17,
            -0.1573721122710731
          ],
          [
            -2.2544743754055813e-17,
            -1.1532580460873167e-15,
            -0.11683807053466481
          ],
          [
            -2.1672488150232422e-16,
            -1.4701276689739275e-15,
            -0.07466112154638321
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -4.440498673932725e-16,
            -7.221679777415783e-16,
            0.07466112154638396
          ],
          [
            2.8370587824370585e-16,
            5.5267957480222845e-17,
            0.1168380705346653
          ],
          [
            -9.52863071052183e-16,
            -6.116320627811327e-16,
            0.15737211227107156
          ],
          [
            -2.5503224882990916e-16,
            -5.121497393167316e-16,
            0.190792061693699
          ],
          [
            -1.123672000296368e-16,
            1.1385199240925903e-15,
            0.20929894465009793
          ],
          [
            -8.702893391198764e-16,
            -1.226948656060947e-15,
            0.20239201318552003
          ],
          [
            -1.0245869135689956e-16,
            4.4214365984178315e-17,
            0.16177796001669242
          ],
          [
            -3.5667489776402104e-16,
            -9.211326246703807e-16,
            0.08955877026757302
          ],
          [
            -9.1208226261786e-16,
            -6.595309592639926e-16,
            -8.326672684688674e-17
          ],
          [
            -1.2628532711104156e-16,
            -9.10079033174336e-16,
            -0.0895587702675742
          ],
          [
            4.602842130471556e-17,
            4.531972513378271e-16,
            -0.16177796001669295
          ],
          [
            -4.693555335559525e-16,
            1.289585674538533e-16,
            -0.2023920131855187
          ],
          [
            -9.155965969182837e-16,
            -1.4480204859818383e-15,
            -0.20929894465010035
          ],
          [
            -1.045274651061156e-16,
            1.0648293141189598e-15,
            -0.1907920616936991
          ],
          [
            -5.775662038583177e-16,
            -6.263701847758593e-17,
            -0.1573721122710731
          ],
          [
            -2.254474375405583e-17,
            -1.1532580460873167e-15,
            -0.11683807053466481
          ],
          [
            -2.1672488150232422e-16,
            -1.4701276689739275e-15,
            -0.07466112154638321
          ]
        ],
        "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": [
          [
            -4.440892098500626e-16,
            -7.216449660063518e-16,
            0.07466112154638394
          ],
          [
            3.3306690738754696e-16,
            0.0,
            0.11683807053466533
          ],
          [
            -9.43689570931383e-16,
            -6.106226635438361e-16,
            0.15737211227107162
          ],
          [
            -2.7755575615628914e-16,
            -4.996003610813204e-16,
            0.190792061693699
          ],
          [
            -1.1102230246251565e-16,
            1.1102230246251565e-15,
            0.2092989446500979
          ],
          [
            -8.881784197001252e-16,
            -1.2212453270876722e-15,
            0.20239201318552003
          ],
          [
            -1.1102230246251565e-16,
            0.0,
            0.16177796001669242
          ],
          [
            -3.3306690738754696e-16,
            -9.43689570931383e-16,
            0.08955877026757297
          ],
          [
            -8.881784197001252e-16,
            -6.661338147750939e-16,
            -1.1102230246251565e-16
          ],
          [
            -1.1102230246251565e-16,
            -8.881784197001252e-16,
            -0.0895587702675742
          ],
          [
            0.0,
            4.440892098500626e-16,
            -0.16177796001669298
          ],
          [
            -4.440892098500626e-16,
            1.1102230246251565e-16,
            -0.2023920131855187
          ],
          [
            -8.881784197001252e-16,
            -1.4432899320127035e-15,
            -0.20929894465010035
          ],
          [
            -1.1102230246251565e-16,
            1.1102230246251565e-15,
            -0.1907920616936991
          ],
          [
            -5.551115123125783e-16,
            -5.551115123125783e-17,
            -0.15737211227107306
          ],
          [
            0.0,
            -1.1657341758564144e-15,
            -0.11683807053466483
          ],
          [
            -2.220446049250313e-16,
            -1.4432899320127035e-15,
            -0.07466112154638321
          ]
        ]
      },
      "incoming_structure_ids": [
        "incoming_00_000",
        "incoming_00_001",
        "incoming_00_002",
        "incoming_00_003",
        "incoming_00_004",
        "incoming_00_005",
        "incoming_00_006",
        "incoming_00_007",
        "incoming_00_008"
      ],
      "reflected_structure_ids": [
        "reflected_00_001",
        "reflected_00_002",
        "reflected_00_003",
        "reflected_00_004",
        "reflected_00_005",
        "reflected_00_006",
        "reflected_00_007",
        "reflected_00_008"
      ],
      "positive_extension_structure_ids": [
        "extension_plus_00_000",
        "extension_plus_00_001",
        "extension_plus_00_002",
        "extension_plus_00_003"
      ],
      "negative_extension_structure_ids": [
        "extension_minus_00_000",
        "extension_minus_00_001",
        "extension_minus_00_002",
        "extension_minus_00_003"
      ],
      "extension": {
        "enabled": true,
        "fraction_beyond_polar_endpoint": 0.35,
        "images_per_side": 4,
        "construction": "continue fractional atomic displacements and symmetric log strain beyond +P; reflect these structures about N for the -P side",
        "positive_path_coordinates": [
          1.35,
          1.2625,
          1.175,
          1.0875
        ],
        "negative_path_coordinates": [
          -1.0875,
          -1.175,
          -1.2625,
          -1.35
        ]
      },
      "branch_coordinates": [
        1.35,
        1.2625,
        1.175,
        1.0875,
        1.0,
        0.875,
        0.75,
        0.625,
        0.5,
        0.375,
        0.25,
        0.125,
        0.0,
        -0.125,
        -0.25,
        -0.375,
        -0.5,
        -0.625,
        -0.75,
        -0.875,
        -1.0,
        -1.0875,
        -1.175,
        -1.2625,
        -1.35
      ],
      "parent": {
        "candidate_id": "inversion_parent_endpoint_00",
        "source": "same_species_inversion_center_projection_from_endpoint",
        "spacegroup": "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": 7.090393213236037e-16,
        "parent_symmetrization_rmsd_A": 0.23164031138782606,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -67.45266324600402,
        "reduced_polarization": [
          2.523700715781286e-16,
          -7.737514047231197e-17,
          6.580723317322927e-16
        ],
        "cartesian_polarization_e_A2": [
          4.180609087368573e-18,
          -1.4290334378761879e-18,
          1.2929350152213129e-17
        ],
        "ranking_score": 0.23164031138782748
      }
    }
  ],
  "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": 114,
      "full_response": 34,
      "energy_polarization": 80
    },
    "model_evaluations_for_recovery_and_path_properties": {
      "total": 139,
      "full_response": 59,
      "energy_polarization": 80
    },
    "elapsed_seconds": 609.9561929639895
  }
}
