{
  "schema": "ferrofinder.endpoint_parent_recovery.v4_variable_cell",
  "status": "complete",
  "input_atom_count": 40,
  "input_formula": "Bi8O24Sc8",
  "input_spacegroup": "Cc",
  "input_pointgroup": "m",
  "input_is_polar_point_group": true,
  "input_energy_eV": -288.6374199237597,
  "input_cartesian_polarization_e_A2": [
    -0.003075870362494527,
    -2.5333371047458425e-17,
    0.0010426712631271154
  ],
  "input_reduced_polarization": [
    -0.18435904333002018,
    -2.432116384118153e-15,
    -0.0006406512196815895
  ],
  "input_formal_targets": [
    {
      "orbit_id": 0,
      "representative_formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ]
    },
    {
      "orbit_id": 1,
      "representative_formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        -0.5,
        0.0,
        0.0
      ]
    },
    {
      "orbit_id": 2,
      "representative_formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        -0.5
      ]
    },
    {
      "orbit_id": 3,
      "representative_formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        -0.5,
        0.0
      ]
    },
    {
      "orbit_id": 4,
      "representative_formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        -0.5,
        0.0,
        -0.5
      ]
    },
    {
      "orbit_id": 5,
      "representative_formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        -0.5,
        -0.5,
        0.0
      ]
    },
    {
      "orbit_id": 6,
      "representative_formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        -0.5,
        -0.5
      ]
    },
    {
      "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": "C2/c",
      "spacegroup_number": 15,
      "pointgroup": "2/m",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 4.988984946909493e-15,
      "parent_symmetrization_rmsd_A": 0.0489790159189006,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -288.75563534176797,
      "reduced_polarization": [
        2.142408626445406e-15,
        -1.7594033417024937e-15,
        4.147837503932371e-15
      ],
      "cartesian_polarization_e_A2": [
        3.574602355729385e-17,
        -1.832626841731035e-17,
        6.213903512487083e-17
      ],
      "ranking_score": 0.04897901591891058
    },
    {
      "candidate_id": "symmetry_projection_00",
      "source": "spglib_refine_cell_from_polar_endpoint",
      "spacegroup": "C2/c",
      "spacegroup_number": 15,
      "pointgroup": "2/m",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 3.4771942361590726e-15,
      "parent_symmetrization_rmsd_A": 2.924586427400265,
      "parent_cell_rmsd_A": 1.0968297477096934e-15,
      "energy_eV": -288.4260394828332,
      "reduced_polarization": [
        3.0748971709844456e-15,
        -1.5488864980094805e-15,
        4.866597991756206e-16
      ],
      "cartesian_polarization_e_A2": [
        5.140175286031698e-17,
        -1.6133486300533238e-17,
        8.256620931328324e-18
      ],
      "ranking_score": 2.9245864274002726
    },
    {
      "candidate_id": "bec_projection_00",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cc",
      "spacegroup_number": 9,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 0.0003288613630209254,
      "parent_symmetrization_rmsd_A": 0.016828283651934253,
      "parent_cell_rmsd_A": 0.0049084347530361245,
      "energy_eV": -288.6280838116027,
      "reduced_polarization": [
        8.12929071699254e-05,
        1.2775256195597054e-14,
        -0.00031865539275499914
      ],
      "cartesian_polarization_e_A2": [
        1.3535262033970845e-06,
        1.3297138207432182e-16,
        -6.173125827716617e-06
      ],
      "ranking_score": 0.5187131150662352
    },
    {
      "candidate_id": "inversion_parent_bec_00_00",
      "source": "same_species_inversion_center_projection_after_BEC",
      "spacegroup": "C2/c",
      "spacegroup_number": 15,
      "pointgroup": "2/m",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 2.6407775794034057e-15,
      "parent_symmetrization_rmsd_A": 0.04898167153662738,
      "parent_cell_rmsd_A": 0.0049084347530361245,
      "energy_eV": -288.75569192745024,
      "reduced_polarization": [
        -2.013756220411126e-15,
        -1.6975533689158353e-15,
        -1.9184542819078428e-16
      ],
      "cartesian_polarization_e_A2": [
        -3.3585555266194684e-17,
        -1.7674031269819653e-17,
        8.053679068934439e-18
      ],
      "ranking_score": 0.05020878022489169
    },
    {
      "candidate_id": "symmetry_parent_00_00",
      "source": "spglib_refine_cell_after_MACEField_BEC_backprojection",
      "spacegroup": "C2/c",
      "spacegroup_number": 15,
      "pointgroup": "2/m",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 4.415756200163518e-15,
      "parent_symmetrization_rmsd_A": 2.924094584898886,
      "parent_cell_rmsd_A": 0.004908434753035958,
      "energy_eV": -288.4410262344361,
      "reduced_polarization": [
        -1.887214734845845e-15,
        3.939405359582353e-15,
        6.468452494662943e-16
      ],
      "cartesian_polarization_e_A2": [
        -3.7012652742337016e-17,
        4.101501300911751e-17,
        1.0966711923655412e-17
      ],
      "ranking_score": 2.9253216935871538
    },
    {
      "candidate_id": "bec_projection_01",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cc",
      "spacegroup_number": 9,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        -0.5,
        0.0,
        0.0
      ],
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_residual": 3.158415678042164e-06,
      "parent_symmetrization_rmsd_A": 0.029013241026602646,
      "parent_cell_rmsd_A": 0.00846556879036409,
      "energy_eV": -288.53846039270127,
      "reduced_polarization": [
        -0.5000027300428505,
        1.5408563970969648e-14,
        -1.5882240490559927e-06
      ],
      "cartesian_polarization_e_A2": [
        -0.0083479537669563,
        8.985331372034331e-17,
        0.0028691644277686014
      ],
      "ranking_score": 0.5311359500555497
    },
    {
      "candidate_id": "symmetry_parent_01_00",
      "source": "spglib_refine_cell_after_MACEField_BEC_backprojection",
      "spacegroup": "C2/c",
      "spacegroup_number": 15,
      "pointgroup": "2/m",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        -0.5,
        0.0,
        0.0
      ],
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_residual": 0.4999999999999998,
      "parent_symmetrization_rmsd_A": 2.925734020521314,
      "parent_cell_rmsd_A": 0.008465568790362707,
      "energy_eV": -288.0047111583989,
      "reduced_polarization": [
        2.0546844765533443e-16,
        2.9069510895782803e-15,
        -8.667118592652498e-17
      ],
      "cartesian_polarization_e_A2": [
        4.134430191665172e-18,
        3.03027969537477e-17,
        -1.4722006617205357e-18
      ],
      "ranking_score": 3.9278504127189042
    },
    {
      "candidate_id": "bec_projection_02",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cc",
      "spacegroup_number": 9,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        -0.5
      ],
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_residual": 4.234198376702693e-06,
      "parent_symmetrization_rmsd_A": 0.05656802282386164,
      "parent_cell_rmsd_A": 0.01978428731681375,
      "energy_eV": -288.37588494918145,
      "reduced_polarization": [
        8.097386029746469e-07,
        9.225289939010148e-15,
        -0.5000041560509246
      ],
      "cartesian_polarization_e_A2": [
        -1.565501299479601e-05,
        -2.5313927023574307e-17,
        -0.00895459607264982
      ],
      "ranking_score": 0.5615225630498185
    },
    {
      "candidate_id": "symmetry_parent_02_00",
      "source": "spglib_refine_cell_after_MACEField_BEC_backprojection",
      "spacegroup": "C2/c",
      "spacegroup_number": 15,
      "pointgroup": "2/m",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        -0.5
      ],
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_residual": 0.4999999999999998,
      "parent_symmetrization_rmsd_A": 2.928796852206491,
      "parent_cell_rmsd_A": 0.019784287316814458,
      "energy_eV": -288.21225748379254,
      "reduced_polarization": [
        1.5097711348010545e-17,
        2.0789805981852444e-15,
        2.5464854899200864e-16
      ],
      "cartesian_polarization_e_A2": [
        -1.1990163597439744e-18,
        2.165570364027382e-17,
        4.31890586724105e-18
      ],
      "ranking_score": 3.9337429240356943
    },
    {
      "candidate_id": "bec_projection_03",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        -0.5,
        0.0
      ],
      "formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_residual": 2.346718099422835e-06,
      "parent_symmetrization_rmsd_A": 0.040675378618872576,
      "parent_cell_rmsd_A": 0.013540361390512843,
      "energy_eV": -288.5376111325575,
      "reduced_polarization": [
        -1.26367380955385e-06,
        -0.4999981009602885,
        -5.512372587317485e-07
      ],
      "cartesian_polarization_e_A2": [
        7.228807679778224e-06,
        -0.0052057236645737595,
        -5.779481997677282e-06
      ],
      "ranking_score": 0.5440651624026996
    },
    {
      "candidate_id": "symmetry_parent_03_00",
      "source": "spglib_refine_cell_after_MACEField_BEC_backprojection",
      "spacegroup": "C2/c",
      "spacegroup_number": 15,
      "pointgroup": "2/m",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        -0.5,
        0.0
      ],
      "formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_residual": 0.49999999999999134,
      "parent_symmetrization_rmsd_A": 2.9199388336242085,
      "parent_cell_rmsd_A": 0.00489597136043167,
      "energy_eV": -288.10160014651433,
      "reduced_polarization": [
        -6.374810669624152e-18,
        8.634692365244785e-15,
        1.8206961926370027e-15
      ],
      "cartesian_polarization_e_A2": [
        -1.0660655645354059e-17,
        8.989955880037378e-17,
        3.086816709251772e-17
      ],
      "ranking_score": 3.921162826464299
    },
    {
      "candidate_id": "bec_projection_04",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Cc",
      "spacegroup_number": 9,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        -0.5,
        0.0,
        -0.5
      ],
      "formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_residual": 3.893990845460535e-06,
      "parent_symmetrization_rmsd_A": 0.04642086393153353,
      "parent_cell_rmsd_A": 0.014525363466553141,
      "energy_eV": -288.4775693743296,
      "reduced_polarization": [
        -0.5000020455850978,
        -1.8096422595391696e-14,
        -0.5000033134191272
      ],
      "cartesian_polarization_e_A2": [
        -0.00834380890621873,
        -3.3620147390436243e-16,
        -0.0061221024055053775
      ],
      "ranking_score": 0.5500599927798627
    },
    {
      "candidate_id": "symmetry_parent_04_00",
      "source": "spglib_refine_cell_after_MACEField_BEC_backprojection",
      "spacegroup": "C2/c",
      "spacegroup_number": 15,
      "pointgroup": "2/m",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        -0.5,
        0.0,
        -0.5
      ],
      "formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_residual": 0.7071067811865447,
      "parent_symmetrization_rmsd_A": 2.93013483121836,
      "parent_cell_rmsd_A": 0.014525363466553254,
      "energy_eV": -288.17166903979967,
      "reduced_polarization": [
        2.976001612879618e-15,
        -2.0930487570662502e-16,
        9.613238843772597e-16
      ],
      "cartesian_polarization_e_A2": [
        4.687076539348798e-17,
        -2.1828875562639615e-18,
        1.6334866432267398e-17
      ],
      "ranking_score": 4.347979734458088
    },
    {
      "candidate_id": "bec_projection_05",
      "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": 8.03674150031818e-06,
      "parent_symmetrization_rmsd_A": 0.04720082137492832,
      "parent_cell_rmsd_A": 0.015196617059942824,
      "energy_eV": -288.4441399858881,
      "reduced_polarization": [
        -0.5000047570217425,
        -0.5000059256037348,
        -2.6167113830610628e-06
      ],
      "cartesian_polarization_e_A2": [
        -0.008340758404172836,
        -0.005197406399010073,
        0.002863400576720747
      ],
      "ranking_score": 0.5510160491229147
    },
    {
      "candidate_id": "symmetry_parent_05_00",
      "source": "spglib_refine_cell_after_MACEField_BEC_backprojection",
      "spacegroup": "C2/c",
      "spacegroup_number": 15,
      "pointgroup": "2/m",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        -0.5,
        -0.5,
        0.0
      ],
      "formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_residual": 0.7071067811865454,
      "parent_symmetrization_rmsd_A": 2.921554054032477,
      "parent_cell_rmsd_A": 0.008491013723704477,
      "energy_eV": -287.5203236685428,
      "reduced_polarization": [
        -2.592225510664329e-17,
        3.0163980664586944e-15,
        1.0689451351312107e-15
      ],
      "cartesian_polarization_e_A2": [
        -6.710754909445348e-18,
        3.144362857935727e-17,
        1.8157069956086134e-17
      ],
      "ranking_score": 4.337890369836494
    },
    {
      "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": [
        0.0,
        -0.5,
        -0.5
      ],
      "formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_residual": 1.8349616344448643e-05,
      "parent_symmetrization_rmsd_A": 0.06778835144005872,
      "parent_cell_rmsd_A": 0.02352805049788686,
      "energy_eV": -288.2845364387547,
      "reduced_polarization": [
        -4.0420374071303654e-06,
        -0.4999828555202016,
        -0.5000051417084739
      ],
      "cartesian_polarization_e_A2": [
        -8.425831277399585e-06,
        -0.005218112750588098,
        -0.008960388395456579
      ],
      "ranking_score": 0.5737070632972193
    },
    {
      "candidate_id": "symmetry_parent_06_00",
      "source": "spglib_refine_cell_after_MACEField_BEC_backprojection",
      "spacegroup": "C2/c",
      "spacegroup_number": 15,
      "pointgroup": "2/m",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        -0.5,
        -0.5
      ],
      "formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_residual": 0.7071067811865352,
      "parent_symmetrization_rmsd_A": 2.9246193139589653,
      "parent_cell_rmsd_A": 0.019776914233225276,
      "energy_eV": -287.85329392218307,
      "reduced_polarization": [
        2.9839922673625956e-15,
        1.5182353985495906e-14,
        2.2420586191235186e-15
      ],
      "cartesian_polarization_e_A2": [
        3.961608743354177e-17,
        1.5814624649967911e-16,
        3.802557126110186e-17
      ],
      "ranking_score": 4.343777104890342
    },
    {
      "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": 7.521432482924923e-06,
      "parent_symmetrization_rmsd_A": 0.059571403133755134,
      "parent_cell_rmsd_A": 0.01926854848647025,
      "energy_eV": -288.38149693440494,
      "reduced_polarization": [
        -0.5000056574977041,
        -0.5000011845559623,
        -0.5000048126389326
      ],
      "cartesian_polarization_e_A2": [
        -0.008336564518186521,
        -0.005209761833230026,
        -0.006127930080231902
      ],
      "ranking_score": 0.5644035831203386
    },
    {
      "candidate_id": "symmetry_parent_07_00",
      "source": "spglib_refine_cell_after_MACEField_BEC_backprojection",
      "spacegroup": "C2/c",
      "spacegroup_number": 15,
      "pointgroup": "2/m",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        -0.5,
        -0.5,
        -0.5
      ],
      "formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "target_residual": 0.8660254037844355,
      "parent_symmetrization_rmsd_A": 2.9259348049664347,
      "parent_cell_rmsd_A": 0.014494156797174126,
      "energy_eV": -287.67608999823494,
      "reduced_polarization": [
        -3.716686283303575e-16,
        2.385832574753054e-15,
        2.7995302658220513e-15
      ],
      "cartesian_polarization_e_A2": [
        -2.2809788796317348e-17,
        2.4882291111681666e-17,
        4.7569446634900535e-17
      ],
      "ranking_score": 4.6616091517345986
    }
  ],
  "formal_branches": [
    {
      "orbit_id": 0,
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.0,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -0.18435904333002018,
              -2.432116384118153e-15,
              -0.0006406512196815895
            ],
            "branch_aligned_reduced_polarization": [
              -0.18435904333002018,
              -2.432116384118153e-15,
              -0.0006406512196815895
            ],
            "target_residual": 0.18436015646431184,
            "energy_eV": -288.6374199237597,
            "max_atomic_step_A": 0.01756731876278661,
            "max_log_strain_component": 0.0005829828705183671,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.3450781842320736,
            "cell_principal_stretches": [
              1.0007374984094881,
              1.0004089660276305,
              0.9997151533689153
            ],
            "cell_volume_ratio": 1.0008615927653832,
            "cell_rmsd_from_input_A": 0.0049084347530361245
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              8.12929071699254e-05,
              1.2775256195597054e-14,
              -0.00031865539275499914
            ],
            "branch_aligned_reduced_polarization": [
              8.12929071699254e-05,
              1.2775256195597054e-14,
              -0.00031865539275499914
            ],
            "target_residual": 0.0003288613630209254,
            "energy_eV": -288.6280838116027
          }
        ],
        "iterations": 1
      },
      "parent": {
        "candidate_id": "inversion_parent_endpoint_00",
        "source": "same_species_inversion_center_projection_from_endpoint",
        "spacegroup": "C2/c",
        "spacegroup_number": 15,
        "pointgroup": "2/m",
        "has_inversion": true,
        "is_polar_point_group": false,
        "nonpolar_parent_hypothesis": true,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.0
        ],
        "formal_class": [
          0.0,
          0.0,
          0.0
        ],
        "target_residual": 4.988984946909493e-15,
        "parent_symmetrization_rmsd_A": 0.0489790159189006,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -288.75563534176797,
        "reduced_polarization": [
          2.142408626445406e-15,
          -1.7594033417024937e-15,
          4.147837503932371e-15
        ],
        "cartesian_polarization_e_A2": [
          3.574602355729385e-17,
          -1.832626841731035e-17,
          6.213903512487083e-17
        ],
        "ranking_score": 0.04897901591891058
      },
      "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": [
          -288.6374199237597,
          -288.6644696365106,
          -288.68823349949264,
          -288.7085775454263,
          -288.7253856980062,
          -288.73856139827365,
          -288.74802832090074,
          -288.7537308959688,
          -288.75563534176797
        ],
        "cartesian_polarizations_e_A2": [
          [
            -0.0030758703624945154,
            5.5150307763857746e-17,
            0.0010426712631272427
          ],
          [
            -0.0027014118272807915,
            2.0009443070076686e-16,
            0.0009126510192966756
          ],
          [
            -0.0023230013477598278,
            1.156416937562899e-17,
            0.0007825555482979891
          ],
          [
            -0.0019411581822383701,
            6.845400261760043e-17,
            0.0006523620899679597
          ],
          [
            -0.0015564258941323072,
            -1.180672292821104e-16,
            0.0005220622334401273
          ],
          [
            -0.001169365810760615,
            -9.07248288092249e-17,
            0.0003916593341670557
          ],
          [
            -0.0007805521553415604,
            -4.390464305323549e-17,
            0.00026116628350304104
          ],
          [
            -0.000390567931346258,
            2.3520344492804726e-17,
            0.00013060359160211435
          ],
          [
            5.958487271510531e-17,
            -1.5655729303023145e-17,
            3.7461048676560863e-17
          ]
        ],
        "raw_reduced_polarization": [
          [
            -0.18435904333001946,
            5.29467502964213e-15,
            -0.0006406512196742747
          ],
          [
            -0.1619150444112298,
            1.9209956004925486e-14,
            -0.0007346570754282826
          ],
          [
            -0.13923417886898531,
            1.1102117343363327e-15,
            -0.0007573382250751122
          ],
          [
            -0.1163475693014331,
            6.571888952829903e-15,
            -0.0007198864387694982
          ],
          [
            -0.09328779509566769,
            -1.1334979550353364e-14,
            -0.0006331578532136949
          ],
          [
            -0.07008850036565416,
            -8.709987398829323e-15,
            -0.0005076919950930945
          ],
          [
            -0.04678410217689055,
            -4.215041160870145e-15,
            -0.00035374312028755347
          ],
          [
            -0.02340954386534471,
            2.2580577647518633e-15,
            -0.00018130846031197658
          ],
          [
            3.571266478659395e-15,
            -1.503019699662959e-15,
            3.2273862603422477e-15
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -0.18435904333001946,
            5.29467502964213e-15,
            -0.0006406512196742747
          ],
          [
            -0.1619150444112298,
            1.9209956004925486e-14,
            -0.0007346570754282826
          ],
          [
            -0.13923417886898531,
            1.110211734336333e-15,
            -0.0007573382250751122
          ],
          [
            -0.1163475693014331,
            6.571888952829903e-15,
            -0.0007198864387694982
          ],
          [
            -0.09328779509566769,
            -1.1334979550353364e-14,
            -0.0006331578532136949
          ],
          [
            -0.07008850036565416,
            -8.709987398829323e-15,
            -0.0005076919950930945
          ],
          [
            -0.04678410217689055,
            -4.215041160870145e-15,
            -0.00035374312028755347
          ],
          [
            -0.02340954386534471,
            2.2580577647518637e-15,
            -0.00018130846031197658
          ],
          [
            3.570060913560269e-15,
            -1.503019699662959e-15,
            3.2273988169462253e-15
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            -0.18435904333001946,
            5.329070518200751e-15,
            -0.0006406512196742709
          ],
          [
            -0.16191504441122984,
            1.9206858326015208e-14,
            -0.0007346570754283022
          ],
          [
            -0.13923417886898531,
            1.1102230246251565e-15,
            -0.0007573382250751215
          ],
          [
            -0.11634756930143308,
            6.5503158452884236e-15,
            -0.0007198864387695236
          ],
          [
            -0.0932877950956677,
            -1.1324274851176597e-14,
            -0.0006331578532137172
          ],
          [
            -0.07008850036565417,
            -8.715250743307479e-15,
            -0.0005076919950930958
          ],
          [
            -0.04678410217689055,
            -4.218847493575595e-15,
            -0.00035374312028757515
          ],
          [
            -0.023409543865344717,
            2.220446049250313e-15,
            -0.00018130846031200187
          ],
          [
            3.552713678800501e-15,
            -1.4988010832439613e-15,
            3.219646771412954e-15
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -288.75563534176797,
          -288.75373089596883,
          -288.74802832090074,
          -288.7385613982738,
          -288.7253856980063,
          -288.7085775454261,
          -288.6882334994925,
          -288.66446963651066,
          -288.6374199237597
        ],
        "cartesian_polarizations_e_A2": [
          [
            6.129989783437231e-17,
            -7.889115548628252e-18,
            5.443979735730427e-17
          ],
          [
            0.0003905679313463292,
            -6.262291721209258e-17,
            -0.00013060359160192687
          ],
          [
            0.0007805521553416404,
            3.66525368346207e-17,
            -0.0002611662835028677
          ],
          [
            0.001169365810760664,
            5.1646756448783713e-17,
            -0.0003916593341668514
          ],
          [
            0.0015564258941323553,
            2.6068381812858572e-17,
            -0.000522062233439909
          ],
          [
            0.0019411581822384393,
            1.494521889646967e-18,
            -0.0006523620899677358
          ],
          [
            0.0023230013477599748,
            -6.188790644669243e-17,
            -0.0007825555482977656
          ],
          [
            0.0027014118272809693,
            -2.3133238823027316e-16,
            -0.000912651019296487
          ],
          [
            0.0030758703624946065,
            8.621676278143732e-17,
            -0.001042671263127026
          ]
        ],
        "raw_reduced_polarization": [
          [
            3.674034787555128e-15,
            -7.573902085938542e-16,
            4.2068616711748896e-15
          ],
          [
            0.023409543865348974,
            -6.012078798651836e-15,
            0.00018130846032379065
          ],
          [
            0.04678410217689535,
            3.5188066834049874e-15,
            0.0003537431202987494
          ],
          [
            0.07008850036565709,
            4.9583185084343e-15,
            0.000507691995105424
          ],
          [
            0.09328779509567056,
            2.5026806892666486e-15,
            0.000633157853226783
          ],
          [
            0.11634756930143723,
            1.4348075380194132e-16,
            0.0007198864387833056
          ],
          [
            0.1392341788689941,
            -5.9415144935033405e-15,
            0.0007573382250903887
          ],
          [
            0.16191504441124044,
            -2.2208938973736557e-14,
            0.0007346570754421931
          ],
          [
            0.1843590433300249,
            8.277192993918549e-15,
            0.0006406512196880942
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            3.674034787555128e-15,
            -7.573902085938542e-16,
            4.2068616711748896e-15
          ],
          [
            0.023409543865348974,
            -6.012078798651836e-15,
            0.00018130846032379065
          ],
          [
            0.04678410217689535,
            3.518806683404988e-15,
            0.0003537431202987494
          ],
          [
            0.07008850036565709,
            4.9583185084343e-15,
            0.000507691995105424
          ],
          [
            0.09328779509567056,
            2.5026806892666486e-15,
            0.000633157853226783
          ],
          [
            0.11634756930143723,
            1.4348075380194114e-16,
            0.0007198864387833056
          ],
          [
            0.1392341788689941,
            -5.9415144935033405e-15,
            0.0007573382250903887
          ],
          [
            0.16191504441124044,
            -2.2208938973736557e-14,
            0.0007346570754421931
          ],
          [
            0.1843590433300249,
            8.277192993918549e-15,
            0.0006406512196880942
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          0.18435904333002662,
          -8.300714428968046e-15,
          0.0006406512196807311
        ],
        "actual_opposite_endpoint_branch_residual": 1.8220982071992964e-14
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            -0.18435904333001946,
            5.29467502964213e-15,
            -0.0006406512196742747
          ],
          [
            -0.1619150444112298,
            1.9209956004925486e-14,
            -0.0007346570754282826
          ],
          [
            -0.13923417886898531,
            1.1102117343363327e-15,
            -0.0007573382250751122
          ],
          [
            -0.1163475693014331,
            6.571888952829903e-15,
            -0.0007198864387694982
          ],
          [
            -0.09328779509566769,
            -1.1334979550353364e-14,
            -0.0006331578532136949
          ],
          [
            -0.07008850036565416,
            -8.709987398829323e-15,
            -0.0005076919950930945
          ],
          [
            -0.04678410217689055,
            -4.215041160870145e-15,
            -0.00035374312028755347
          ],
          [
            -0.02340954386534471,
            2.2580577647518633e-15,
            -0.00018130846031197658
          ],
          [
            3.571266478659395e-15,
            -1.503019699662959e-15,
            3.2273862603422477e-15
          ],
          [
            0.023409543865348974,
            -6.012078798651836e-15,
            0.00018130846032379065
          ],
          [
            0.04678410217689535,
            3.5188066834049874e-15,
            0.0003537431202987494
          ],
          [
            0.07008850036565709,
            4.9583185084343e-15,
            0.000507691995105424
          ],
          [
            0.09328779509567056,
            2.5026806892666486e-15,
            0.000633157853226783
          ],
          [
            0.11634756930143723,
            1.4348075380194132e-16,
            0.0007198864387833056
          ],
          [
            0.1392341788689941,
            -5.9415144935033405e-15,
            0.0007573382250903887
          ],
          [
            0.16191504441124044,
            -2.2208938973736557e-14,
            0.0007346570754421931
          ],
          [
            0.1843590433300249,
            8.277192993918549e-15,
            0.0006406512196880942
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -0.18435904333001946,
            5.29467502964213e-15,
            -0.0006406512196742747
          ],
          [
            -0.1619150444112298,
            1.9209956004925486e-14,
            -0.0007346570754282826
          ],
          [
            -0.13923417886898531,
            1.110211734336333e-15,
            -0.0007573382250751122
          ],
          [
            -0.1163475693014331,
            6.571888952829903e-15,
            -0.0007198864387694982
          ],
          [
            -0.09328779509566769,
            -1.1334979550353364e-14,
            -0.0006331578532136949
          ],
          [
            -0.07008850036565416,
            -8.709987398829323e-15,
            -0.0005076919950930945
          ],
          [
            -0.04678410217689055,
            -4.215041160870145e-15,
            -0.00035374312028755347
          ],
          [
            -0.02340954386534471,
            2.2580577647518637e-15,
            -0.00018130846031197658
          ],
          [
            3.570060913560269e-15,
            -1.503019699662959e-15,
            3.2273988169462253e-15
          ],
          [
            0.023409543865348974,
            -6.012078798651836e-15,
            0.00018130846032379065
          ],
          [
            0.04678410217689535,
            3.518806683404988e-15,
            0.0003537431202987494
          ],
          [
            0.07008850036565709,
            4.9583185084343e-15,
            0.000507691995105424
          ],
          [
            0.09328779509567056,
            2.5026806892666486e-15,
            0.000633157853226783
          ],
          [
            0.11634756930143723,
            1.4348075380194114e-16,
            0.0007198864387833056
          ],
          [
            0.1392341788689941,
            -5.9415144935033405e-15,
            0.0007573382250903887
          ],
          [
            0.16191504441124044,
            -2.2208938973736557e-14,
            0.0007346570754421931
          ],
          [
            0.1843590433300249,
            8.277192993918549e-15,
            0.0006406512196880942
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            -0.18435904333001946,
            5.329070518200751e-15,
            -0.0006406512196742709
          ],
          [
            -0.16191504441122984,
            1.9206858326015208e-14,
            -0.0007346570754283022
          ],
          [
            -0.13923417886898531,
            1.1102230246251565e-15,
            -0.0007573382250751215
          ],
          [
            -0.11634756930143308,
            6.5503158452884236e-15,
            -0.0007198864387695236
          ],
          [
            -0.0932877950956677,
            -1.1324274851176597e-14,
            -0.0006331578532137172
          ],
          [
            -0.07008850036565417,
            -8.715250743307479e-15,
            -0.0005076919950930958
          ],
          [
            -0.04678410217689055,
            -4.218847493575595e-15,
            -0.00035374312028757515
          ],
          [
            -0.023409543865344717,
            2.220446049250313e-15,
            -0.00018130846031200187
          ],
          [
            3.552713678800501e-15,
            -1.4988010832439613e-15,
            3.219646771412954e-15
          ],
          [
            0.023409543865348992,
            -5.995204332975845e-15,
            0.00018130846032382575
          ],
          [
            0.046784102176895326,
            3.552713678800501e-15,
            0.0003537431202987884
          ],
          [
            0.07008850036565706,
            4.9960036108132044e-15,
            0.0005076919951054748
          ],
          [
            0.09328779509567053,
            2.55351295663786e-15,
            0.0006331578532268178
          ],
          [
            0.11634756930143719,
            1.1102230246251565e-16,
            0.0007198864387832904
          ],
          [
            0.13923417886899414,
            -5.9396931817445875e-15,
            0.0007573382250903871
          ],
          [
            0.1619150444112405,
            -2.220446049250313e-14,
            0.00073465707544218
          ],
          [
            0.18435904333002484,
            8.326672684688674e-15,
            0.0006406512196881486
          ]
        ]
      },
      "incoming_structure_ids": [
        "incoming_00_000",
        "incoming_00_001",
        "incoming_00_002",
        "incoming_00_003",
        "incoming_00_004",
        "incoming_00_005",
        "incoming_00_006",
        "incoming_00_007",
        "incoming_00_008"
      ],
      "reflected_structure_ids": [
        "reflected_00_001",
        "reflected_00_002",
        "reflected_00_003",
        "reflected_00_004",
        "reflected_00_005",
        "reflected_00_006",
        "reflected_00_007",
        "reflected_00_008"
      ]
    },
    {
      "orbit_id": 1,
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.0,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        -0.5,
        0.0,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -0.18435904333002018,
              -2.432116384118153e-15,
              -0.0006406512196815895
            ],
            "branch_aligned_reduced_polarization": [
              -0.18435904333002018,
              -2.432116384118153e-15,
              -0.0006406512196815895
            ],
            "target_residual": 0.3156416068288928,
            "energy_eV": -288.6374199237597,
            "max_atomic_step_A": 0.030119908515410045,
            "max_log_strain_component": 0.000996624284679842,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.3450781842320736,
            "cell_principal_stretches": [
              1.0004916149265946,
              0.999297155400864,
              0.9987364981631639
            ],
            "cell_volume_ratio": 0.998525190287382,
            "cell_rmsd_from_input_A": 0.008424458435611338
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.49902159650846756,
              -6.850674429443571e-15,
              -0.0008226668889403374
            ],
            "branch_aligned_reduced_polarization": [
              -0.49902159650846756,
              -6.850674429443571e-15,
              -0.0008226668889403374
            ],
            "target_residual": 0.0012783012956269924,
            "energy_eV": -288.53920320134006,
            "max_atomic_step_A": 0.00013647083643590106,
            "max_log_strain_component": 4.259568575534235e-06,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.3450781842320736,
            "cell_principal_stretches": [
              1.0004949674190105,
              0.9992934655926732,
              0.9987314617996151
            ],
            "cell_volume_ratio": 0.9985198139242155,
            "cell_rmsd_from_input_A": 0.00846556879036409
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.5000027300428505,
              1.5408563970969648e-14,
              -1.5882240490559927e-06
            ],
            "branch_aligned_reduced_polarization": [
              -0.5000027300428505,
              1.5408563970969648e-14,
              -1.5882240490559927e-06
            ],
            "target_residual": 3.158415678042164e-06,
            "energy_eV": -288.53846039270127
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_01",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cc",
        "spacegroup_number": 9,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          -0.5,
          0.0,
          0.0
        ],
        "formal_class": [
          0.5,
          0.0,
          0.0
        ],
        "target_residual": 3.158415678042164e-06,
        "parent_symmetrization_rmsd_A": 0.029013241026602646,
        "parent_cell_rmsd_A": 0.00846556879036409,
        "energy_eV": -288.53846039270127,
        "reduced_polarization": [
          -0.5000027300428505,
          1.5408563970969648e-14,
          -1.5882240490559927e-06
        ],
        "cartesian_polarization_e_A2": [
          -0.0083479537669563,
          8.985331372034331e-17,
          0.0028691644277686014
        ],
        "ranking_score": 0.5311359500555497
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 2,
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.0,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        -0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -0.18435904333002018,
              -2.432116384118153e-15,
              -0.0006406512196815895
            ],
            "branch_aligned_reduced_polarization": [
              -0.18435904333002018,
              -2.432116384118153e-15,
              -0.0006406512196815983
            ],
            "target_residual": 0.5323044392749923,
            "energy_eV": -288.6374199237597,
            "max_atomic_step_A": 0.05330098123421528,
            "max_log_strain_component": 0.001725678406898377,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.3450781842320736,
            "cell_principal_stretches": [
              1.0017244397091905,
              1.0012858101052664,
              0.9982580264692229
            ],
            "cell_volume_ratio": 1.0012652459477007,
            "cell_rmsd_from_input_A": 0.019769736669751646
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.003183313284033568,
              2.1231474779605624e-14,
              -0.49786073296776895
            ],
            "branch_aligned_reduced_polarization": [
              0.003183313284033568,
              2.1231474779605624e-14,
              -0.49786073296776895
            ],
            "target_residual": 0.003835354859657087,
            "energy_eV": -288.37603534382976,
            "max_atomic_step_A": 0.0003154932463961198,
            "max_log_strain_component": 1.2018405253698777e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.3450781842320736,
            "cell_principal_stretches": [
              1.0017184407253124,
              1.0012825534291703,
              0.9982540912516177
            ],
            "cell_volume_ratio": 1.0012520460882242,
            "cell_rmsd_from_input_A": 0.01978428731681375
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              8.097386029746469e-07,
              9.225289939010148e-15,
              -0.5000041560509246
            ],
            "branch_aligned_reduced_polarization": [
              8.097386029746469e-07,
              9.225289939010148e-15,
              -0.5000041560509246
            ],
            "target_residual": 4.234198376702693e-06,
            "energy_eV": -288.37588494918145
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_02",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cc",
        "spacegroup_number": 9,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          -0.5
        ],
        "formal_class": [
          0.0,
          0.0,
          0.5
        ],
        "target_residual": 4.234198376702693e-06,
        "parent_symmetrization_rmsd_A": 0.05656802282386164,
        "parent_cell_rmsd_A": 0.01978428731681375,
        "energy_eV": -288.37588494918145,
        "reduced_polarization": [
          8.097386029746469e-07,
          9.225289939010148e-15,
          -0.5000041560509246
        ],
        "cartesian_polarization_e_A2": [
          -1.565501299479601e-05,
          -2.5313927023574307e-17,
          -0.00895459607264982
        ],
        "ranking_score": 0.5615225630498185
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 3,
      "formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.5,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        -0.5,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -0.18435904333002018,
              -2.432116384118153e-15,
              -0.0006406512196815895
            ],
            "branch_aligned_reduced_polarization": [
              -0.18435904333002018,
              -2.4424906541753444e-15,
              -0.0006406512196815895
            ],
            "target_residual": 0.5329058709486536,
            "energy_eV": -288.6374199237597,
            "max_atomic_step_A": 0.03756124407238529,
            "max_log_strain_component": 0.0013869826640035188,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.3450781842320736,
            "cell_principal_stretches": [
              1.002023525112438,
              1.000498128269155,
              0.9983431111781484
            ],
            "cell_volume_ratio": 1.0008615927654003,
            "cell_rmsd_from_input_A": 0.013493215364589365
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -2.8560837111566515e-06,
              -0.49794675391056975,
              -0.0002727714784945288
            ],
            "branch_aligned_reduced_polarization": [
              -2.8560837111566515e-06,
              -0.49794675391056975,
              -0.0002727714784945288
            ],
            "target_residual": 0.002071287507917447,
            "energy_eV": -288.5383282123601,
            "max_atomic_step_A": 0.0001348045531478631,
            "max_log_strain_component": 5.7744667682379986e-06,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.3450781842320736,
            "cell_principal_stretches": [
              1.0020307316832544,
              1.0004975750905156,
              0.998336276296688
            ],
            "cell_volume_ratio": 1.000861385426955,
            "cell_rmsd_from_input_A": 0.013540361390512843
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -1.26367380955385e-06,
              -0.4999981009602885,
              -5.512372587317485e-07
            ],
            "branch_aligned_reduced_polarization": [
              -1.26367380955385e-06,
              -0.4999981009602885,
              -5.512372587317485e-07
            ],
            "target_residual": 2.346718099422835e-06,
            "energy_eV": -288.5376111325575
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_03",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "P1",
        "spacegroup_number": 1,
        "pointgroup": "1",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          -0.5,
          0.0
        ],
        "formal_class": [
          0.0,
          0.5,
          0.0
        ],
        "target_residual": 2.346718099422835e-06,
        "parent_symmetrization_rmsd_A": 0.040675378618872576,
        "parent_cell_rmsd_A": 0.013540361390512843,
        "energy_eV": -288.5376111325575,
        "reduced_polarization": [
          -1.26367380955385e-06,
          -0.4999981009602885,
          -5.512372587317485e-07
        ],
        "cartesian_polarization_e_A2": [
          7.228807679778224e-06,
          -0.0052057236645737595,
          -5.779481997677282e-06
        ],
        "ranking_score": 0.5440651624026996
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 4,
      "formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.0,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        -0.5,
        0.0,
        -0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -0.18435904333002018,
              -2.432116384118153e-15,
              -0.0006406512196815895
            ],
            "branch_aligned_reduced_polarization": [
              -0.18435904333002018,
              -2.432116384118153e-15,
              -0.0006406512196815983
            ],
            "target_residual": 0.5907528863592998,
            "energy_eV": -288.6374199237597,
            "max_atomic_step_A": 0.04752761116930283,
            "max_log_strain_component": 0.0014283276532061672,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.3450781842320736,
            "cell_principal_stretches": [
              1.0004634345787853,
              1.0001730249924679,
              0.9982924483527622
            ],
            "cell_volume_ratio": 0.9989279011852692,
            "cell_rmsd_from_input_A": 0.014486909020422037
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.49828430765873766,
              2.318678378363599e-14,
              -0.4986853779430937
            ],
            "branch_aligned_reduced_polarization": [
              -0.49828430765873766,
              2.318678378363599e-14,
              -0.4986853779430937
            ],
            "target_residual": 0.0021614419636832288,
            "energy_eV": -288.47857072727834,
            "max_atomic_step_A": 0.00018075013055485157,
            "max_log_strain_component": 6.63674901976129e-06,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.3450781842320736,
            "cell_principal_stretches": [
              1.0004636684048989,
              1.0001715021391222,
              0.9982867085510049
            ],
            "cell_volume_ratio": 0.9989208702466461,
            "cell_rmsd_from_input_A": 0.014525363466553141
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.5000020455850978,
              -1.8096422595391696e-14,
              -0.5000033134191272
            ],
            "branch_aligned_reduced_polarization": [
              -0.5000020455850978,
              -1.8096422595391696e-14,
              -0.5000033134191272
            ],
            "target_residual": 3.893990845460535e-06,
            "energy_eV": -288.4775693743296
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_04",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Cc",
        "spacegroup_number": 9,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          -0.5,
          0.0,
          -0.5
        ],
        "formal_class": [
          0.5,
          0.0,
          0.5
        ],
        "target_residual": 3.893990845460535e-06,
        "parent_symmetrization_rmsd_A": 0.04642086393153353,
        "parent_cell_rmsd_A": 0.014525363466553141,
        "energy_eV": -288.4775693743296,
        "reduced_polarization": [
          -0.5000020455850978,
          -1.8096422595391696e-14,
          -0.5000033134191272
        ],
        "cartesian_polarization_e_A2": [
          -0.00834380890621873,
          -3.3620147390436243e-16,
          -0.0061221024055053775
        ],
        "ranking_score": 0.5500599927798627
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 5,
      "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": [
              -0.18435904333002018,
              -2.432116384118153e-15,
              -0.0006406512196815895
            ],
            "branch_aligned_reduced_polarization": [
              -0.18435904333002018,
              -2.4424906541753444e-15,
              -0.0006406512196815895
            ],
            "target_residual": 0.5912948705692642,
            "energy_eV": -288.6374199237597,
            "max_atomic_step_A": 0.04270415302082836,
            "max_log_strain_component": 0.0013869826639952303,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.3450781842320736,
            "cell_principal_stretches": [
              1.0016483069913462,
              0.9991594169386395,
              0.9977206897916762
            ],
            "cell_volume_ratio": 0.998525190287399,
            "cell_rmsd_from_input_A": 0.015129804874016094
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.4985815374855928,
              -0.49840898345366375,
              -0.0010861133564718944
            ],
            "branch_aligned_reduced_polarization": [
              -0.4985815374855928,
              -0.49840898345366375,
              -0.0010861133564718944
            ],
            "target_residual": 0.0023922817097074426,
            "energy_eV": -288.4458196804817,
            "max_atomic_step_A": 0.00021631616370526368,
            "max_log_strain_component": 5.910683779115353e-06,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.3450781842320736,
            "cell_principal_stretches": [
              1.001655195878058,
              0.9991531929299613,
              0.9977122825716317
            ],
            "cell_volume_ratio": 0.9985174235894513,
            "cell_rmsd_from_input_A": 0.015196617059942824
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.5000047570217425,
              -0.5000059256037348,
              -2.6167113830610628e-06
            ],
            "branch_aligned_reduced_polarization": [
              -0.5000047570217425,
              -0.5000059256037348,
              -2.6167113830610628e-06
            ],
            "target_residual": 8.03674150031818e-06,
            "energy_eV": -288.4441399858881
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_05",
        "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": 8.03674150031818e-06,
        "parent_symmetrization_rmsd_A": 0.04720082137492832,
        "parent_cell_rmsd_A": 0.015196617059942824,
        "energy_eV": -288.4441399858881,
        "reduced_polarization": [
          -0.5000047570217425,
          -0.5000059256037348,
          -2.6167113830610628e-06
        ],
        "cartesian_polarization_e_A2": [
          -0.008340758404172836,
          -0.005197406399010073,
          0.002863400576720747
        ],
        "ranking_score": 0.5510160491229147
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 6,
      "formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.5,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        -0.5,
        -0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -0.18435904333002018,
              -2.432116384118153e-15,
              -0.0006406512196815895
            ],
            "branch_aligned_reduced_polarization": [
              -0.18435904333002018,
              -2.4424906541753444e-15,
              -0.0006406512196815983
            ],
            "target_residual": 0.7303067958549074,
            "energy_eV": -288.6374199237597,
            "max_atomic_step_A": 0.06171716539875846,
            "max_log_strain_component": 0.0017256784069065267,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.3450781842320736,
            "cell_principal_stretches": [
              1.0022209189090439,
              1.0015949279675447,
              0.9974555750144581
            ],
            "cell_volume_ratio": 1.0012652459477174,
            "cell_rmsd_from_input_A": 0.023402565501357643
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.0024872414061251364,
              -0.4929234549934025,
              -0.4977260093349732
            ],
            "branch_aligned_reduced_polarization": [
              0.0024872414061251364,
              -0.4929234549934025,
              -0.4977260093349732
            ],
            "target_residual": 0.007838041374436111,
            "energy_eV": -288.2878108842203,
            "max_atomic_step_A": 0.00054183441534848,
            "max_log_strain_component": 2.0191798776929e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.3450781842320736,
            "cell_principal_stretches": [
              1.00223477371624,
              1.0015955733796738,
              0.9974314003118339
            ],
            "cell_volume_ratio": 1.00125546536587,
            "cell_rmsd_from_input_A": 0.02352805049788686
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -4.0420374071303654e-06,
              -0.4999828555202016,
              -0.5000051417084739
            ],
            "branch_aligned_reduced_polarization": [
              -4.0420374071303654e-06,
              -0.4999828555202016,
              -0.5000051417084739
            ],
            "target_residual": 1.8349616344448643e-05,
            "energy_eV": -288.2845364387547
          }
        ],
        "iterations": 2
      },
      "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": [
          0.0,
          -0.5,
          -0.5
        ],
        "formal_class": [
          0.0,
          0.5,
          0.5
        ],
        "target_residual": 1.8349616344448643e-05,
        "parent_symmetrization_rmsd_A": 0.06778835144005872,
        "parent_cell_rmsd_A": 0.02352805049788686,
        "energy_eV": -288.2845364387547,
        "reduced_polarization": [
          -4.0420374071303654e-06,
          -0.4999828555202016,
          -0.5000051417084739
        ],
        "cartesian_polarization_e_A2": [
          -8.425831277399585e-06,
          -0.005218112750588098,
          -0.008960388395456579
        ],
        "ranking_score": 0.5737070632972193
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 7,
      "formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.5,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        -0.5,
        -0.5,
        -0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              -0.18435904333002018,
              -2.432116384118153e-15,
              -0.0006406512196815895
            ],
            "branch_aligned_reduced_polarization": [
              -0.18435904333002018,
              -2.4424906541753444e-15,
              -0.0006406512196815983
            ],
            "target_residual": 0.7739437787991071,
            "energy_eV": -288.6374199237597,
            "max_atomic_step_A": 0.05411426841865891,
            "max_log_strain_component": 0.0014283276531853208,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.3450781842320736,
            "cell_principal_stretches": [
              1.0013991542045337,
              1.0002562939734758,
              0.9972766038303088
            ],
            "cell_volume_ratio": 0.9989279011852864,
            "cell_rmsd_from_input_A": 0.019148699774229467
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -0.498453135949497,
              -0.4944595203779471,
              -0.49885404800114236
            ],
            "branch_aligned_reduced_polarization": [
              -0.498453135949497,
              -0.4944595203779471,
              -0.49885404800114236
            ],
            "target_residual": 0.005865399288778886,
            "energy_eV": -288.3845720670287,
            "max_atomic_step_A": 0.0004088192709367588,
            "max_log_strain_component": 1.5899288408272878e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.3450781842320736,
            "cell_principal_stretches": [
              1.0014155967981226,
              1.0002547777021946,
              0.997255289542216
            ],
            "cell_volume_ratio": 0.9989214390207591,
            "cell_rmsd_from_input_A": 0.01926854848647025
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              -0.5000056574977041,
              -0.5000011845559623,
              -0.5000048126389326
            ],
            "branch_aligned_reduced_polarization": [
              -0.5000056574977041,
              -0.5000011845559623,
              -0.5000048126389326
            ],
            "target_residual": 7.521432482924923e-06,
            "energy_eV": -288.38149693440494
          }
        ],
        "iterations": 2
      },
      "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": 7.521432482924923e-06,
        "parent_symmetrization_rmsd_A": 0.059571403133755134,
        "parent_cell_rmsd_A": 0.01926854848647025,
        "energy_eV": -288.38149693440494,
        "reduced_polarization": [
          -0.5000056574977041,
          -0.5000011845559623,
          -0.5000048126389326
        ],
        "cartesian_polarization_e_A2": [
          -0.008336564518186521,
          -0.005209761833230026,
          -0.006127930080231902
        ],
        "ranking_score": 0.5644035831203386
      },
      "branch_status": "awaiting_branch_sampling"
    }
  ],
  "sampled_polarization_branches": [
    {
      "orbit_id": 0,
      "candidate_id": "inversion_parent_endpoint_00",
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "construction": "MACEField-BEC-parent plus variable-cell P-N-P path and symmetric log-strain continuation beyond both polar endpoints",
      "geometry_diagnostics": {
        "collision_aware": false,
        "permutations_tested": 1,
        "selected_order": [
          0,
          1,
          2,
          3,
          4,
          5,
          6,
          7,
          8,
          9,
          10,
          11,
          12,
          13,
          14,
          15,
          16,
          17,
          18,
          19,
          20,
          21,
          22,
          23,
          24,
          25,
          26,
          27,
          28,
          29,
          30,
          31,
          32,
          33,
          34,
          35,
          36,
          37,
          38,
          39
        ],
        "endpoint_rmsd_A": 0.0489790159189006,
        "minimum_distance_A_by_image": [
          2.0809819066698485,
          2.08200949898493,
          2.083061254851491,
          2.0841371376872635,
          2.0852371101471494,
          2.086361134129521,
          2.087509170782584,
          2.08868118051089,
          2.089877122981906
        ],
        "minimum_distance_A": 2.0809819066698485,
        "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": [
          566.4320222681055,
          566.4320222681055,
          566.4320222681055,
          566.4320222681055,
          566.4320222681055,
          566.4320222681055,
          566.4320222681055,
          566.4320222681055,
          566.4320222681055
        ],
        "cell_deformation_log_strain_norm": 0.0
      },
      "parent_reduced_polarization": [
        3.571266478659395e-15,
        -1.503019699662959e-15,
        3.2273862603422477e-15
      ],
      "incoming": {
        "reached": true,
        "construction": "variable_cell_linear_interpolation",
        "continuation_fractions": [
          0.0,
          0.125,
          0.25,
          0.375,
          0.5,
          0.625,
          0.75,
          0.875,
          1.0
        ],
        "energies_eV": [
          -288.6374199237597,
          -288.6644696365106,
          -288.68823349949264,
          -288.7085775454263,
          -288.7253856980062,
          -288.73856139827365,
          -288.74802832090074,
          -288.7537308959688,
          -288.75563534176797
        ],
        "cartesian_polarizations_e_A2": [
          [
            -0.0030758703624945154,
            5.5150307763857746e-17,
            0.0010426712631272427
          ],
          [
            -0.0027014118272807915,
            2.0009443070076686e-16,
            0.0009126510192966756
          ],
          [
            -0.0023230013477598278,
            1.156416937562899e-17,
            0.0007825555482979891
          ],
          [
            -0.0019411581822383701,
            6.845400261760043e-17,
            0.0006523620899679597
          ],
          [
            -0.0015564258941323072,
            -1.180672292821104e-16,
            0.0005220622334401273
          ],
          [
            -0.001169365810760615,
            -9.07248288092249e-17,
            0.0003916593341670557
          ],
          [
            -0.0007805521553415604,
            -4.390464305323549e-17,
            0.00026116628350304104
          ],
          [
            -0.000390567931346258,
            2.3520344492804726e-17,
            0.00013060359160211435
          ],
          [
            5.958487271510531e-17,
            -1.5655729303023145e-17,
            3.7461048676560863e-17
          ]
        ],
        "raw_reduced_polarization": [
          [
            -0.18435904333001946,
            5.29467502964213e-15,
            -0.0006406512196742747
          ],
          [
            -0.1619150444112298,
            1.9209956004925486e-14,
            -0.0007346570754282826
          ],
          [
            -0.13923417886898531,
            1.1102117343363327e-15,
            -0.0007573382250751122
          ],
          [
            -0.1163475693014331,
            6.571888952829903e-15,
            -0.0007198864387694982
          ],
          [
            -0.09328779509566769,
            -1.1334979550353364e-14,
            -0.0006331578532136949
          ],
          [
            -0.07008850036565416,
            -8.709987398829323e-15,
            -0.0005076919950930945
          ],
          [
            -0.04678410217689055,
            -4.215041160870145e-15,
            -0.00035374312028755347
          ],
          [
            -0.02340954386534471,
            2.2580577647518633e-15,
            -0.00018130846031197658
          ],
          [
            3.571266478659395e-15,
            -1.503019699662959e-15,
            3.2273862603422477e-15
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -0.18435904333001946,
            5.29467502964213e-15,
            -0.0006406512196742747
          ],
          [
            -0.1619150444112298,
            1.9209956004925486e-14,
            -0.0007346570754282826
          ],
          [
            -0.13923417886898531,
            1.110211734336333e-15,
            -0.0007573382250751122
          ],
          [
            -0.1163475693014331,
            6.571888952829903e-15,
            -0.0007198864387694982
          ],
          [
            -0.09328779509566769,
            -1.1334979550353364e-14,
            -0.0006331578532136949
          ],
          [
            -0.07008850036565416,
            -8.709987398829323e-15,
            -0.0005076919950930945
          ],
          [
            -0.04678410217689055,
            -4.215041160870145e-15,
            -0.00035374312028755347
          ],
          [
            -0.02340954386534471,
            2.2580577647518637e-15,
            -0.00018130846031197658
          ],
          [
            3.570060913560269e-15,
            -1.503019699662959e-15,
            3.2273988169462253e-15
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            -0.18435904333001946,
            5.329070518200751e-15,
            -0.0006406512196742709
          ],
          [
            -0.16191504441122984,
            1.9206858326015208e-14,
            -0.0007346570754283022
          ],
          [
            -0.13923417886898531,
            1.1102230246251565e-15,
            -0.0007573382250751215
          ],
          [
            -0.11634756930143308,
            6.5503158452884236e-15,
            -0.0007198864387695236
          ],
          [
            -0.0932877950956677,
            -1.1324274851176597e-14,
            -0.0006331578532137172
          ],
          [
            -0.07008850036565417,
            -8.715250743307479e-15,
            -0.0005076919950930958
          ],
          [
            -0.04678410217689055,
            -4.218847493575595e-15,
            -0.00035374312028757515
          ],
          [
            -0.023409543865344717,
            2.220446049250313e-15,
            -0.00018130846031200187
          ],
          [
            3.552713678800501e-15,
            -1.4988010832439613e-15,
            3.219646771412954e-15
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -288.75563534176797,
          -288.75373089596883,
          -288.74802832090074,
          -288.7385613982738,
          -288.7253856980063,
          -288.7085775454261,
          -288.6882334994925,
          -288.66446963651066,
          -288.6374199237597
        ],
        "cartesian_polarizations_e_A2": [
          [
            6.129989783437231e-17,
            -7.889115548628252e-18,
            5.443979735730427e-17
          ],
          [
            0.0003905679313463292,
            -6.262291721209258e-17,
            -0.00013060359160192687
          ],
          [
            0.0007805521553416404,
            3.66525368346207e-17,
            -0.0002611662835028677
          ],
          [
            0.001169365810760664,
            5.1646756448783713e-17,
            -0.0003916593341668514
          ],
          [
            0.0015564258941323553,
            2.6068381812858572e-17,
            -0.000522062233439909
          ],
          [
            0.0019411581822384393,
            1.494521889646967e-18,
            -0.0006523620899677358
          ],
          [
            0.0023230013477599748,
            -6.188790644669243e-17,
            -0.0007825555482977656
          ],
          [
            0.0027014118272809693,
            -2.3133238823027316e-16,
            -0.000912651019296487
          ],
          [
            0.0030758703624946065,
            8.621676278143732e-17,
            -0.001042671263127026
          ]
        ],
        "raw_reduced_polarization": [
          [
            3.674034787555128e-15,
            -7.573902085938542e-16,
            4.2068616711748896e-15
          ],
          [
            0.023409543865348974,
            -6.012078798651836e-15,
            0.00018130846032379065
          ],
          [
            0.04678410217689535,
            3.5188066834049874e-15,
            0.0003537431202987494
          ],
          [
            0.07008850036565709,
            4.9583185084343e-15,
            0.000507691995105424
          ],
          [
            0.09328779509567056,
            2.5026806892666486e-15,
            0.000633157853226783
          ],
          [
            0.11634756930143723,
            1.4348075380194132e-16,
            0.0007198864387833056
          ],
          [
            0.1392341788689941,
            -5.9415144935033405e-15,
            0.0007573382250903887
          ],
          [
            0.16191504441124044,
            -2.2208938973736557e-14,
            0.0007346570754421931
          ],
          [
            0.1843590433300249,
            8.277192993918549e-15,
            0.0006406512196880942
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            3.674034787555128e-15,
            -7.573902085938542e-16,
            4.2068616711748896e-15
          ],
          [
            0.023409543865348974,
            -6.012078798651836e-15,
            0.00018130846032379065
          ],
          [
            0.04678410217689535,
            3.518806683404988e-15,
            0.0003537431202987494
          ],
          [
            0.07008850036565709,
            4.9583185084343e-15,
            0.000507691995105424
          ],
          [
            0.09328779509567056,
            2.5026806892666486e-15,
            0.000633157853226783
          ],
          [
            0.11634756930143723,
            1.4348075380194114e-16,
            0.0007198864387833056
          ],
          [
            0.1392341788689941,
            -5.9415144935033405e-15,
            0.0007573382250903887
          ],
          [
            0.16191504441124044,
            -2.2208938973736557e-14,
            0.0007346570754421931
          ],
          [
            0.1843590433300249,
            8.277192993918549e-15,
            0.0006406512196880942
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          0.18435904333002662,
          -8.300714428968046e-15,
          0.0006406512196807311
        ],
        "actual_opposite_endpoint_branch_residual": 1.8220982071992964e-14
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            -0.18435904333001946,
            5.29467502964213e-15,
            -0.0006406512196742747
          ],
          [
            -0.1619150444112298,
            1.9209956004925486e-14,
            -0.0007346570754282826
          ],
          [
            -0.13923417886898531,
            1.1102117343363327e-15,
            -0.0007573382250751122
          ],
          [
            -0.1163475693014331,
            6.571888952829903e-15,
            -0.0007198864387694982
          ],
          [
            -0.09328779509566769,
            -1.1334979550353364e-14,
            -0.0006331578532136949
          ],
          [
            -0.07008850036565416,
            -8.709987398829323e-15,
            -0.0005076919950930945
          ],
          [
            -0.04678410217689055,
            -4.215041160870145e-15,
            -0.00035374312028755347
          ],
          [
            -0.02340954386534471,
            2.2580577647518633e-15,
            -0.00018130846031197658
          ],
          [
            3.571266478659395e-15,
            -1.503019699662959e-15,
            3.2273862603422477e-15
          ],
          [
            0.023409543865348974,
            -6.012078798651836e-15,
            0.00018130846032379065
          ],
          [
            0.04678410217689535,
            3.5188066834049874e-15,
            0.0003537431202987494
          ],
          [
            0.07008850036565709,
            4.9583185084343e-15,
            0.000507691995105424
          ],
          [
            0.09328779509567056,
            2.5026806892666486e-15,
            0.000633157853226783
          ],
          [
            0.11634756930143723,
            1.4348075380194132e-16,
            0.0007198864387833056
          ],
          [
            0.1392341788689941,
            -5.9415144935033405e-15,
            0.0007573382250903887
          ],
          [
            0.16191504441124044,
            -2.2208938973736557e-14,
            0.0007346570754421931
          ],
          [
            0.1843590433300249,
            8.277192993918549e-15,
            0.0006406512196880942
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -0.18435904333001946,
            5.29467502964213e-15,
            -0.0006406512196742747
          ],
          [
            -0.1619150444112298,
            1.9209956004925486e-14,
            -0.0007346570754282826
          ],
          [
            -0.13923417886898531,
            1.110211734336333e-15,
            -0.0007573382250751122
          ],
          [
            -0.1163475693014331,
            6.571888952829903e-15,
            -0.0007198864387694982
          ],
          [
            -0.09328779509566769,
            -1.1334979550353364e-14,
            -0.0006331578532136949
          ],
          [
            -0.07008850036565416,
            -8.709987398829323e-15,
            -0.0005076919950930945
          ],
          [
            -0.04678410217689055,
            -4.215041160870145e-15,
            -0.00035374312028755347
          ],
          [
            -0.02340954386534471,
            2.2580577647518637e-15,
            -0.00018130846031197658
          ],
          [
            3.570060913560269e-15,
            -1.503019699662959e-15,
            3.2273988169462253e-15
          ],
          [
            0.023409543865348974,
            -6.012078798651836e-15,
            0.00018130846032379065
          ],
          [
            0.04678410217689535,
            3.518806683404988e-15,
            0.0003537431202987494
          ],
          [
            0.07008850036565709,
            4.9583185084343e-15,
            0.000507691995105424
          ],
          [
            0.09328779509567056,
            2.5026806892666486e-15,
            0.000633157853226783
          ],
          [
            0.11634756930143723,
            1.4348075380194114e-16,
            0.0007198864387833056
          ],
          [
            0.1392341788689941,
            -5.9415144935033405e-15,
            0.0007573382250903887
          ],
          [
            0.16191504441124044,
            -2.2208938973736557e-14,
            0.0007346570754421931
          ],
          [
            0.1843590433300249,
            8.277192993918549e-15,
            0.0006406512196880942
          ]
        ],
        "berry_integer_shifts": [
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ],
          [
            0,
            0,
            0
          ]
        ],
        "folded_reduced_polarization": [
          [
            -0.18435904333001946,
            5.329070518200751e-15,
            -0.0006406512196742709
          ],
          [
            -0.16191504441122984,
            1.9206858326015208e-14,
            -0.0007346570754283022
          ],
          [
            -0.13923417886898531,
            1.1102230246251565e-15,
            -0.0007573382250751215
          ],
          [
            -0.11634756930143308,
            6.5503158452884236e-15,
            -0.0007198864387695236
          ],
          [
            -0.0932877950956677,
            -1.1324274851176597e-14,
            -0.0006331578532137172
          ],
          [
            -0.07008850036565417,
            -8.715250743307479e-15,
            -0.0005076919950930958
          ],
          [
            -0.04678410217689055,
            -4.218847493575595e-15,
            -0.00035374312028757515
          ],
          [
            -0.023409543865344717,
            2.220446049250313e-15,
            -0.00018130846031200187
          ],
          [
            3.552713678800501e-15,
            -1.4988010832439613e-15,
            3.219646771412954e-15
          ],
          [
            0.023409543865348992,
            -5.995204332975845e-15,
            0.00018130846032382575
          ],
          [
            0.046784102176895326,
            3.552713678800501e-15,
            0.0003537431202987884
          ],
          [
            0.07008850036565706,
            4.9960036108132044e-15,
            0.0005076919951054748
          ],
          [
            0.09328779509567053,
            2.55351295663786e-15,
            0.0006331578532268178
          ],
          [
            0.11634756930143719,
            1.1102230246251565e-16,
            0.0007198864387832904
          ],
          [
            0.13923417886899414,
            -5.9396931817445875e-15,
            0.0007573382250903871
          ],
          [
            0.1619150444112405,
            -2.220446049250313e-14,
            0.00073465707544218
          ],
          [
            0.18435904333002484,
            8.326672684688674e-15,
            0.0006406512196881486
          ]
        ]
      },
      "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": "C2/c",
        "spacegroup_number": 15,
        "pointgroup": "2/m",
        "has_inversion": true,
        "is_polar_point_group": false,
        "nonpolar_parent_hypothesis": true,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.0
        ],
        "formal_class": [
          0.0,
          0.0,
          0.0
        ],
        "target_residual": 4.988984946909493e-15,
        "parent_symmetrization_rmsd_A": 0.0489790159189006,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -288.75563534176797,
        "reduced_polarization": [
          2.142408626445406e-15,
          -1.7594033417024937e-15,
          4.147837503932371e-15
        ],
        "cartesian_polarization_e_A2": [
          3.574602355729385e-17,
          -1.832626841731035e-17,
          6.213903512487083e-17
        ],
        "ranking_score": 0.04897901591891058
      }
    }
  ],
  "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": 57,
      "full_response": 16,
      "energy_polarization": 41
    },
    "model_evaluations_for_recovery_and_path_properties": {
      "total": 82,
      "full_response": 41,
      "energy_polarization": 41
    },
    "elapsed_seconds": 1023.0838201599545
  }
}