{
  "schema": "ferrofinder.endpoint_parent_recovery.v4_variable_cell",
  "status": "complete",
  "input_atom_count": 28,
  "input_formula": "Ba8Cr4O16",
  "input_spacegroup": "Pna2_1",
  "input_pointgroup": "mm2",
  "input_is_polar_point_group": true,
  "input_energy_eV": -187.75016339874318,
  "input_cartesian_polarization_e_A2": [
    3.3725100566955783e-17,
    -2.172313694250925e-17,
    0.0016693033662869463
  ],
  "input_reduced_polarization": [
    2.1761861735961544e-15,
    -1.0106605621611383e-15,
    0.1384226535008205
  ],
  "input_formal_targets": [
    {
      "orbit_id": 0,
      "representative_formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ]
    },
    {
      "orbit_id": 1,
      "representative_formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.5
      ]
    },
    {
      "orbit_id": 2,
      "representative_formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.0
      ]
    },
    {
      "orbit_id": 3,
      "representative_formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        0.0,
        -0.5,
        0.0
      ]
    },
    {
      "orbit_id": 4,
      "representative_formal_class": [
        0.5,
        0.0,
        0.5
      ],
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.5
      ]
    },
    {
      "orbit_id": 5,
      "representative_formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_reduced_polarization": [
        0.0,
        -0.5,
        0.5
      ]
    },
    {
      "orbit_id": 6,
      "representative_formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_reduced_polarization": [
        0.5,
        -0.5,
        0.0
      ]
    },
    {
      "orbit_id": 7,
      "representative_formal_class": [
        0.5,
        0.5,
        0.5
      ],
      "target_reduced_polarization": [
        0.5,
        -0.5,
        0.5
      ]
    }
  ],
  "parent_candidates": [
    {
      "candidate_id": "inversion_parent_endpoint_00",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "Pnma",
      "spacegroup_number": 62,
      "pointgroup": "mmm",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 9.384984824305606e-16,
      "parent_symmetrization_rmsd_A": 0.05185828432656478,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -187.77527892723657,
      "reduced_polarization": [
        -5.972172777436044e-16,
        -4.975659233687037e-16,
        5.25869828561435e-16
      ],
      "cartesian_polarization_e_A2": [
        -9.255280176209927e-18,
        -1.0694681375665565e-17,
        6.341709632384263e-18
      ],
      "ranking_score": 0.05185828432656666
    },
    {
      "candidate_id": "inversion_parent_endpoint_01",
      "source": "same_species_inversion_center_projection_from_endpoint",
      "spacegroup": "Pbcn",
      "spacegroup_number": 60,
      "pointgroup": "mmm",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 3.638715663418842e-15,
      "parent_symmetrization_rmsd_A": 0.7455325854694288,
      "parent_cell_rmsd_A": 0.0,
      "energy_eV": -174.31769922523824,
      "reduced_polarization": [
        1.2085685481610805e-15,
        3.6233669322038244e-16,
        -3.4129643807622074e-15
      ],
      "cartesian_polarization_e_A2": [
        1.8729599665380494e-17,
        7.788064460822778e-18,
        -4.115852994965181e-17
      ],
      "ranking_score": 0.7455325854694361
    },
    {
      "candidate_id": "symmetry_projection_00",
      "source": "spglib_refine_cell_from_polar_endpoint",
      "spacegroup": "Pnma",
      "spacegroup_number": 62,
      "pointgroup": "mmm",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 2.7779728479477566e-15,
      "parent_symmetrization_rmsd_A": 1.626863208119497,
      "parent_cell_rmsd_A": 4.429634238884639,
      "energy_eV": -187.71148166591968,
      "reduced_polarization": [
        2.506428034166622e-15,
        -1.9374151578579183e-16,
        1.182123461631498e-15
      ],
      "cartesian_polarization_e_A2": [
        3.884297149835361e-17,
        -2.3364193382468338e-18,
        2.5408560303434318e-17
      ],
      "ranking_score": 2.7342717678406623
    },
    {
      "candidate_id": "bec_projection_00",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Pna2_1",
      "spacegroup_number": 33,
      "pointgroup": "mm2",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 1.3869042749710358e-05,
      "parent_symmetrization_rmsd_A": 0.012965452868438258,
      "parent_cell_rmsd_A": 0.0031446331217333244,
      "energy_eV": -187.73135137921153,
      "reduced_polarization": [
        -2.8822206769929683e-15,
        1.9098460986447196e-15,
        -1.3869042749710358e-05
      ],
      "cartesian_polarization_e_A2": [
        -4.4641544380914246e-17,
        4.1054091195966146e-17,
        -1.6727503812592648e-07
      ],
      "ranking_score": 0.513779349234371
    },
    {
      "candidate_id": "inversion_parent_bec_00_00",
      "source": "same_species_inversion_center_projection_after_BEC",
      "spacegroup": "Pnma",
      "spacegroup_number": 62,
      "pointgroup": "mmm",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 2.669554223588849e-15,
      "parent_symmetrization_rmsd_A": 0.05185910399551354,
      "parent_cell_rmsd_A": 0.0031446331217333244,
      "energy_eV": -187.77799946787934,
      "reduced_polarization": [
        1.4543504219063743e-15,
        1.7918055084496085e-15,
        -1.3419454619586652e-15
      ],
      "cartesian_polarization_e_A2": [
        2.2525868835720628e-17,
        3.851645473762108e-17,
        -1.6185253904184453e-17
      ],
      "ranking_score": 0.05264526227595221
    },
    {
      "candidate_id": "symmetry_parent_00_00",
      "source": "spglib_refine_cell_after_MACEField_BEC_backprojection",
      "spacegroup": "Pnma",
      "spacegroup_number": 62,
      "pointgroup": "mmm",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.0
      ],
      "formal_class": [
        0.0,
        0.0,
        0.0
      ],
      "target_residual": 1.893114137311412e-15,
      "parent_symmetrization_rmsd_A": 1.6278475514075246,
      "parent_cell_rmsd_A": 4.430704072560644,
      "energy_eV": -187.81042595571185,
      "reduced_polarization": [
        1.7667664384640452e-15,
        6.133290255687389e-16,
        2.9367498225130794e-16
      ],
      "cartesian_polarization_e_A2": [
        2.736475917820876e-17,
        7.397384086792206e-18,
        6.3128052169241756e-18
      ],
      "ranking_score": 2.7355235695476896
    },
    {
      "candidate_id": "bec_projection_01",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Pna2_1",
      "spacegroup_number": 33,
      "pointgroup": "mm2",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.5
      ],
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_residual": 4.5355685163173126e-07,
      "parent_symmetrization_rmsd_A": 0.03405179578813717,
      "parent_cell_rmsd_A": 0.008249283221771422,
      "energy_eV": -187.52555833583054,
      "reduced_polarization": [
        5.396585910732196e-15,
        2.6402643123397524e-15,
        0.5000004535568516
      ],
      "cartesian_polarization_e_A2": [
        8.879632965288874e-17,
        8.000296074962556e-17,
        0.0060276791369971855
      ],
      "ranking_score": 0.5361150237072833
    },
    {
      "candidate_id": "symmetry_parent_01_00",
      "source": "spglib_refine_cell_after_MACEField_BEC_backprojection",
      "spacegroup": "Pnma",
      "spacegroup_number": 62,
      "pointgroup": "mmm",
      "has_inversion": true,
      "is_polar_point_group": false,
      "nonpolar_parent_hypothesis": true,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.5
      ],
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "target_residual": 0.49999999999999845,
      "parent_symmetrization_rmsd_A": 1.6258492974658785,
      "parent_cell_rmsd_A": 4.426839174631933,
      "energy_eV": -187.01198542405348,
      "reduced_polarization": [
        -3.9131203784493985e-16,
        6.463183913631494e-17,
        -1.5293298143215376e-15
      ],
      "cartesian_polarization_e_A2": [
        -6.073268237775923e-18,
        7.791592699093967e-19,
        -3.286382492010705e-17
      ],
      "ranking_score": 3.7325590911238584
    },
    {
      "candidate_id": "bec_projection_02",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Pc",
      "spacegroup_number": 7,
      "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": 5.66222233832365e-06,
      "parent_symmetrization_rmsd_A": 0.05852839834084723,
      "parent_cell_rmsd_A": 0.01479904311219431,
      "energy_eV": -187.1075501886498,
      "reduced_polarization": [
        0.49999437346686354,
        2.3289894541916393e-15,
        -6.34733544825258e-07
      ],
      "cartesian_polarization_e_A2": [
        0.007744355964796416,
        1.7057161086996849e-16,
        2.144263663280243e-05
      ],
      "ranking_score": 0.5622394835635725
    },
    {
      "candidate_id": "symmetry_parent_02_00",
      "source": "spglib_refine_cell_after_MACEField_BEC_backprojection",
      "spacegroup": "Pnma",
      "spacegroup_number": 62,
      "pointgroup": "mmm",
      "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": 0.49999999999999906,
      "parent_symmetrization_rmsd_A": 1.632893129132572,
      "parent_cell_rmsd_A": 4.430662044189345,
      "energy_eV": -187.0724138617543,
      "reduced_polarization": [
        9.668569695762147e-16,
        -6.871128355221212e-16,
        4.916176680925127e-17
      ],
      "cartesian_polarization_e_A2": [
        1.4975365459079035e-17,
        -8.287203169555344e-18,
        1.0567574511513525e-18
      ],
      "ranking_score": 3.7405586401799065
    },
    {
      "candidate_id": "bec_projection_03",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Pc",
      "spacegroup_number": 7,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        -0.5,
        0.0
      ],
      "formal_class": [
        0.0,
        0.5,
        0.0
      ],
      "target_residual": 8.28606379602279e-05,
      "parent_symmetrization_rmsd_A": 0.09288330446758523,
      "parent_cell_rmsd_A": 0.03362147602297462,
      "energy_eV": -186.4266030487654,
      "reduced_polarization": [
        1.877203591064159e-15,
        -0.49996643917282807,
        7.575985878228522e-05
      ],
      "cartesian_polarization_e_A2": [
        -7.6364844649619e-17,
        -0.01074737893365376,
        -4.860436269031938e-05
      ],
      "ranking_score": 0.6014543947492493
    },
    {
      "candidate_id": "bec_projection_04",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Pc",
      "spacegroup_number": 7,
      "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": 1.64174938680212e-05,
      "parent_symmetrization_rmsd_A": 0.06682406493073668,
      "parent_cell_rmsd_A": 0.016824639247175446,
      "energy_eV": -186.91443253710744,
      "reduced_polarization": [
        0.4999835889060163,
        4.0780023837339706e-16,
        0.49999954163424587
      ],
      "cartesian_polarization_e_A2": [
        0.007776882799531179,
        1.105855592201143e-16,
        0.0060493014984753695
      ],
      "ranking_score": 0.5710630597302666
    },
    {
      "candidate_id": "bec_projection_05",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "Pc",
      "spacegroup_number": 7,
      "pointgroup": "m",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.0,
        -0.5,
        0.5
      ],
      "formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "target_residual": 5.616516037132824e-05,
      "parent_symmetrization_rmsd_A": 0.09791703849600215,
      "parent_cell_rmsd_A": 0.03416102508705402,
      "energy_eV": -186.16029162760242,
      "reduced_polarization": [
        1.0653896649500488e-16,
        -0.4999995553337752,
        0.5000561634001062
      ],
      "cartesian_polarization_e_A2": [
        -6.823165994378281e-17,
        -0.01071701034163845,
        0.005979173614857845
      ],
      "ranking_score": 0.6065696250885083
    },
    {
      "candidate_id": "bec_projection_06",
      "source": "MACEField_BEC_backprojection",
      "spacegroup": "P1",
      "spacegroup_number": 1,
      "pointgroup": "1",
      "has_inversion": false,
      "is_polar_point_group": true,
      "nonpolar_parent_hypothesis": false,
      "symmetry_tolerance_A": null,
      "target_reduced_polarization": [
        0.5,
        -0.5,
        0.0
      ],
      "formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "target_residual": 9.402570154835737e-05,
      "parent_symmetrization_rmsd_A": 0.10926475212992116,
      "parent_cell_rmsd_A": 0.0366916606799628,
      "energy_eV": -185.77476998640702,
      "reduced_polarization": [
        0.5000082641975823,
        -0.4999664465576687,
        8.744542353778186e-05
      ],
      "cartesian_polarization_e_A2": [
        0.007744294532605345,
        -0.010747305539689951,
        -2.711352560258345e-05
      ],
      "ranking_score": 0.6186257187030086
    },
    {
      "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": 6.545328901684375e-05,
      "parent_symmetrization_rmsd_A": 0.11380624389370289,
      "parent_cell_rmsd_A": 0.03725689135167763,
      "energy_eV": -185.51833603828857,
      "reduced_polarization": [
        0.49998689560610254,
        -0.5000047761012144,
        0.5000639499551282
      ],
      "cartesian_polarization_e_A2": [
        0.0077767766029409,
        -0.01071698358901584,
        0.006000873929630802
      ],
      "ranking_score": 0.623251373309656
    }
  ],
  "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": [
              2.1761861735961544e-15,
              -1.0106605621611383e-15,
              0.1384226535008205
            ],
            "branch_aligned_reduced_polarization": [
              2.1761861735961544e-15,
              -1.0106605621611383e-15,
              0.1384226535008205
            ],
            "target_residual": 0.1384226535008205,
            "energy_eV": -187.75016339874318,
            "max_atomic_step_A": 0.01346968577631058,
            "max_log_strain_component": 0.00039084760434740393,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.1491838861024513,
            "cell_principal_stretches": [
              1.0003028952028301,
              1.0002606663337257,
              0.9996092287666274
            ],
            "cell_volume_ratio": 1.0001726490032758,
            "cell_rmsd_from_input_A": 0.0031446331217333244
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -2.8822206769929683e-15,
              1.9098460986447196e-15,
              -1.3869042749710358e-05
            ],
            "branch_aligned_reduced_polarization": [
              -2.8822206769929683e-15,
              1.9098460986447196e-15,
              -1.3869042749710358e-05
            ],
            "target_residual": 1.3869042749710358e-05,
            "energy_eV": -187.73135137921153
          }
        ],
        "iterations": 1
      },
      "parent": {
        "candidate_id": "inversion_parent_endpoint_00",
        "source": "same_species_inversion_center_projection_from_endpoint",
        "spacegroup": "Pnma",
        "spacegroup_number": 62,
        "pointgroup": "mmm",
        "has_inversion": true,
        "is_polar_point_group": false,
        "nonpolar_parent_hypothesis": true,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.0
        ],
        "formal_class": [
          0.0,
          0.0,
          0.0
        ],
        "target_residual": 9.384984824305606e-16,
        "parent_symmetrization_rmsd_A": 0.05185828432656478,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -187.77527892723657,
        "reduced_polarization": [
          -5.972172777436044e-16,
          -4.975659233687037e-16,
          5.25869828561435e-16
        ],
        "cartesian_polarization_e_A2": [
          -9.255280176209927e-18,
          -1.0694681375665565e-17,
          6.341709632384263e-18
        ],
        "ranking_score": 0.05185828432656666
      },
      "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": [
          -187.75016339874315,
          -187.75611499052184,
          -187.76124096110442,
          -187.76555483211772,
          -187.7690682523527,
          -187.77179091851625,
          -187.77373042683644,
          -187.77489208821225,
          -187.77527892723657
        ],
        "cartesian_polarizations_e_A2": [
          [
            4.440587468465559e-17,
            -1.6855596654495013e-17,
            0.001669303366286952
          ],
          [
            -4.5935673060888636e-17,
            -5.562903186301984e-18,
            0.0014619779191645278
          ],
          [
            4.9593281905882194e-17,
            -2.983106833654439e-17,
            0.0012541251391043763
          ],
          [
            9.929782187549043e-18,
            -1.3350967647124764e-18,
            0.0010458147417201867
          ],
          [
            -1.4254939414898836e-17,
            -1.5576128921645557e-18,
            0.0008371194036220939
          ],
          [
            1.244699587935069e-17,
            -1.6104604724344247e-17,
            0.0006281138333409447
          ],
          [
            6.605947533733607e-18,
            -2.232114903503671e-17,
            0.00041887405250040063
          ],
          [
            1.2606929345956873e-17,
            2.503306433835893e-19,
            0.00020947687815255956
          ],
          [
            -9.498657190610639e-18,
            -1.0388721700418956e-17,
            8.066209620137877e-18
          ]
        ],
        "raw_reduced_polarization": [
          [
            2.8653865782649565e-15,
            -7.842001288983991e-16,
            0.13842265350082097
          ],
          [
            -2.964100177891998e-15,
            -2.588119237288446e-16,
            0.12123072834897483
          ],
          [
            3.2001154206366538e-15,
            -1.3878789409959294e-15,
            0.10399507548052976
          ],
          [
            6.407410012155274e-16,
            -6.211486169492272e-17,
            0.08672147588199322
          ],
          [
            -9.198312692519827e-16,
            -7.24673386440765e-17,
            0.06941595607282564
          ],
          [
            8.031697424200238e-16,
            -7.492605191950052e-16,
            0.052084711064244144
          ],
          [
            4.2626327111677244e-16,
            -1.038482843961989e-15,
            0.034734044752283
          ],
          [
            8.134898005628509e-16,
            1.1646536567798007e-17,
            0.017370326991817137
          ],
          [
            -6.129217140479065e-16,
            -4.833312675636173e-16,
            6.688695187842812e-16
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            2.8653865782649565e-15,
            -7.842001288983991e-16,
            0.13842265350082097
          ],
          [
            -2.9641001778919985e-15,
            -2.5881192372884453e-16,
            0.12123072834897483
          ],
          [
            3.2001154206366534e-15,
            -1.3878789409959294e-15,
            0.10399507548052976
          ],
          [
            6.407410012155274e-16,
            -6.211486169492273e-17,
            0.08672147588199322
          ],
          [
            -9.198312692519827e-16,
            -7.24673386440765e-17,
            0.06941595607282564
          ],
          [
            8.031697424200237e-16,
            -7.492605191950053e-16,
            0.052084711064244144
          ],
          [
            4.2626327111677244e-16,
            -1.038482843961989e-15,
            0.034734044752283
          ],
          [
            8.134898005628509e-16,
            1.1646536567798073e-17,
            0.017370326991817137
          ],
          [
            -6.129217140479065e-16,
            -4.833312675636173e-16,
            6.696032617270475e-16
          ]
        ],
        "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": [
          [
            2.886579864025407e-15,
            -7.771561172376096e-16,
            0.13842265350082095
          ],
          [
            -2.942091015256665e-15,
            -2.7755575615628914e-16,
            0.12123072834897486
          ],
          [
            3.219646771412954e-15,
            -1.3877787807814457e-15,
            0.10399507548052978
          ],
          [
            6.661338147750939e-16,
            -5.551115123125783e-17,
            0.08672147588199319
          ],
          [
            -9.43689570931383e-16,
            -5.551115123125783e-17,
            0.06941595607282558
          ],
          [
            7.771561172376096e-16,
            -7.216449660063518e-16,
            0.05208471106424417
          ],
          [
            4.440892098500626e-16,
            -1.0547118733938987e-15,
            0.03473404475228303
          ],
          [
            7.771561172376096e-16,
            0.0,
            0.017370326991817175
          ],
          [
            -6.106226635438361e-16,
            -4.996003610813204e-16,
            6.661338147750939e-16
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -187.77527892723657,
          -187.77489208821225,
          -187.7737304268364,
          -187.77179091851625,
          -187.76906825235264,
          -187.76555483211774,
          -187.76124096110442,
          -187.7561149905218,
          -187.75016339874318
        ],
        "cartesian_polarizations_e_A2": [
          [
            -9.498657190610639e-18,
            -1.0388721700418956e-17,
            8.066209620137877e-18
          ],
          [
            -7.224820513209703e-18,
            1.12092499203985e-17,
            -0.00020947687815255382
          ],
          [
            -4.5546269837847495e-18,
            -3.596416909944233e-17,
            -0.00041887405250039825
          ],
          [
            3.134000582582881e-17,
            -5.8271410876513286e-18,
            -0.0006281138333409369
          ],
          [
            4.145058236693266e-17,
            -1.5297983762330456e-17,
            -0.0008371194036220855
          ],
          [
            5.622356714105587e-17,
            -5.295883833359489e-17,
            -0.0010458147417201536
          ],
          [
            4.752805409796758e-17,
            2.6562862714591976e-18,
            -0.0012541251391043663
          ],
          [
            -1.3893350707789208e-17,
            -4.199991905657998e-18,
            -0.0014619779191645324
          ],
          [
            6.038531408730805e-17,
            -2.2515850646557284e-17,
            -0.0016693033662869374
          ]
        ],
        "raw_reduced_polarization": [
          [
            -6.129217140479065e-16,
            -4.833312675636173e-16,
            6.688695187842812e-16
          ],
          [
            -4.661974091477121e-16,
            5.215060263136219e-16,
            -0.01737032699181666
          ],
          [
            -2.938973079805115e-16,
            -1.6732190869069803e-15,
            -0.034734044752282804
          ],
          [
            2.022282697813993e-15,
            -2.7110549010596473e-16,
            -0.0520847110642435
          ],
          [
            2.6746898517127165e-15,
            -7.117327902543227e-16,
            -0.06941595607282494
          ],
          [
            3.627949135383856e-15,
            -2.4638895138986007e-15,
            -0.08672147588199047
          ],
          [
            3.0668520611401467e-15,
            1.235826935805233e-16,
            -0.10399507548052894
          ],
          [
            -8.964989638855909e-16,
            -1.9540300241527768e-16,
            -0.12123072834897522
          ],
          [
            3.896494996187424e-15,
            -1.0475412612924985e-15,
            -0.13842265350081978
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -6.129217140479065e-16,
            -4.833312675636173e-16,
            6.688695187842812e-16
          ],
          [
            -4.661974091477121e-16,
            5.215060263136219e-16,
            -0.01737032699181666
          ],
          [
            -2.938973079805115e-16,
            -1.6732190869069803e-15,
            -0.034734044752282804
          ],
          [
            2.022282697813993e-15,
            -2.7110549010596473e-16,
            -0.0520847110642435
          ],
          [
            2.6746898517127165e-15,
            -7.117327902543227e-16,
            -0.06941595607282494
          ],
          [
            3.627949135383856e-15,
            -2.4638895138986007e-15,
            -0.08672147588199047
          ],
          [
            3.0668520611401467e-15,
            1.2358269358052313e-16,
            -0.10399507548052894
          ],
          [
            -8.964989638855905e-16,
            -1.9540300241527765e-16,
            -0.12123072834897522
          ],
          [
            3.896494996187424e-15,
            -1.0475412612924985e-15,
            -0.13842265350081978
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          -4.0912300063607685e-15,
          -1.824624062288354e-16,
          -0.13842265350081964
        ],
        "actual_opposite_endpoint_branch_residual": 8.03563136544078e-15
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            2.8653865782649565e-15,
            -7.842001288983991e-16,
            0.13842265350082097
          ],
          [
            -2.964100177891998e-15,
            -2.588119237288446e-16,
            0.12123072834897483
          ],
          [
            3.2001154206366538e-15,
            -1.3878789409959294e-15,
            0.10399507548052976
          ],
          [
            6.407410012155274e-16,
            -6.211486169492272e-17,
            0.08672147588199322
          ],
          [
            -9.198312692519827e-16,
            -7.24673386440765e-17,
            0.06941595607282564
          ],
          [
            8.031697424200238e-16,
            -7.492605191950052e-16,
            0.052084711064244144
          ],
          [
            4.2626327111677244e-16,
            -1.038482843961989e-15,
            0.034734044752283
          ],
          [
            8.134898005628509e-16,
            1.1646536567798007e-17,
            0.017370326991817137
          ],
          [
            -6.129217140479065e-16,
            -4.833312675636173e-16,
            6.688695187842812e-16
          ],
          [
            -4.661974091477121e-16,
            5.215060263136219e-16,
            -0.01737032699181666
          ],
          [
            -2.938973079805115e-16,
            -1.6732190869069803e-15,
            -0.034734044752282804
          ],
          [
            2.022282697813993e-15,
            -2.7110549010596473e-16,
            -0.0520847110642435
          ],
          [
            2.6746898517127165e-15,
            -7.117327902543227e-16,
            -0.06941595607282494
          ],
          [
            3.627949135383856e-15,
            -2.4638895138986007e-15,
            -0.08672147588199047
          ],
          [
            3.0668520611401467e-15,
            1.235826935805233e-16,
            -0.10399507548052894
          ],
          [
            -8.964989638855909e-16,
            -1.9540300241527768e-16,
            -0.12123072834897522
          ],
          [
            3.896494996187424e-15,
            -1.0475412612924985e-15,
            -0.13842265350081978
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            2.8653865782649565e-15,
            -7.842001288983991e-16,
            0.13842265350082097
          ],
          [
            -2.9641001778919985e-15,
            -2.5881192372884453e-16,
            0.12123072834897483
          ],
          [
            3.2001154206366534e-15,
            -1.3878789409959294e-15,
            0.10399507548052976
          ],
          [
            6.407410012155274e-16,
            -6.211486169492273e-17,
            0.08672147588199322
          ],
          [
            -9.198312692519827e-16,
            -7.24673386440765e-17,
            0.06941595607282564
          ],
          [
            8.031697424200237e-16,
            -7.492605191950053e-16,
            0.052084711064244144
          ],
          [
            4.2626327111677244e-16,
            -1.038482843961989e-15,
            0.034734044752283
          ],
          [
            8.134898005628509e-16,
            1.1646536567798073e-17,
            0.017370326991817137
          ],
          [
            -6.129217140479065e-16,
            -4.833312675636173e-16,
            6.696032617270475e-16
          ],
          [
            -4.661974091477121e-16,
            5.215060263136219e-16,
            -0.01737032699181666
          ],
          [
            -2.938973079805115e-16,
            -1.6732190869069803e-15,
            -0.034734044752282804
          ],
          [
            2.022282697813993e-15,
            -2.7110549010596473e-16,
            -0.0520847110642435
          ],
          [
            2.6746898517127165e-15,
            -7.117327902543227e-16,
            -0.06941595607282494
          ],
          [
            3.627949135383856e-15,
            -2.4638895138986007e-15,
            -0.08672147588199047
          ],
          [
            3.0668520611401467e-15,
            1.2358269358052313e-16,
            -0.10399507548052894
          ],
          [
            -8.964989638855905e-16,
            -1.9540300241527765e-16,
            -0.12123072834897522
          ],
          [
            3.896494996187424e-15,
            -1.0475412612924985e-15,
            -0.13842265350081978
          ]
        ],
        "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": [
          [
            2.886579864025407e-15,
            -7.771561172376096e-16,
            0.13842265350082095
          ],
          [
            -2.942091015256665e-15,
            -2.7755575615628914e-16,
            0.12123072834897486
          ],
          [
            3.219646771412954e-15,
            -1.3877787807814457e-15,
            0.10399507548052978
          ],
          [
            6.661338147750939e-16,
            -5.551115123125783e-17,
            0.08672147588199319
          ],
          [
            -9.43689570931383e-16,
            -5.551115123125783e-17,
            0.06941595607282558
          ],
          [
            7.771561172376096e-16,
            -7.216449660063518e-16,
            0.05208471106424417
          ],
          [
            4.440892098500626e-16,
            -1.0547118733938987e-15,
            0.03473404475228303
          ],
          [
            7.771561172376096e-16,
            0.0,
            0.017370326991817175
          ],
          [
            -6.106226635438361e-16,
            -4.996003610813204e-16,
            6.661338147750939e-16
          ],
          [
            -4.440892098500626e-16,
            5.551115123125783e-16,
            -0.017370326991816676
          ],
          [
            -2.7755575615628914e-16,
            -1.6653345369377348e-15,
            -0.03473404475228281
          ],
          [
            1.9984014443252818e-15,
            -2.7755575615628914e-16,
            -0.052084711064243505
          ],
          [
            2.6645352591003757e-15,
            -7.216449660063518e-16,
            -0.06941595607282491
          ],
          [
            3.6637359812630166e-15,
            -2.4424906541753444e-15,
            -0.08672147588199047
          ],
          [
            3.1086244689504383e-15,
            1.1102230246251565e-16,
            -0.10399507548052894
          ],
          [
            -8.881784197001252e-16,
            -2.220446049250313e-16,
            -0.12123072834897519
          ],
          [
            3.885780586188048e-15,
            -1.0547118733938987e-15,
            -0.13842265350081978
          ]
        ]
      },
      "incoming_structure_ids": [
        "incoming_00_000",
        "incoming_00_001",
        "incoming_00_002",
        "incoming_00_003",
        "incoming_00_004",
        "incoming_00_005",
        "incoming_00_006",
        "incoming_00_007",
        "incoming_00_008"
      ],
      "reflected_structure_ids": [
        "reflected_00_001",
        "reflected_00_002",
        "reflected_00_003",
        "reflected_00_004",
        "reflected_00_005",
        "reflected_00_006",
        "reflected_00_007",
        "reflected_00_008"
      ]
    },
    {
      "orbit_id": 1,
      "formal_class": [
        0.0,
        0.0,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.0,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        0.0,
        0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              2.1761861735961544e-15,
              -1.0106605621611383e-15,
              0.1384226535008205
            ],
            "branch_aligned_reduced_polarization": [
              2.1761861735961544e-15,
              -1.0106605621611383e-15,
              0.1384226535008205
            ],
            "target_residual": 0.3615773464991795,
            "energy_eV": -187.75016339874318,
            "max_atomic_step_A": 0.03518451003503734,
            "max_log_strain_component": 0.0010209430038462441,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.1491838861024513,
            "cell_principal_stretches": [
              1.001021464343559,
              0.9993194272383873,
              0.9992092323320454
            ],
            "cell_volume_ratio": 0.9995491597168678,
            "cell_rmsd_from_input_A": 0.008213098132753918
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -1.0578636963973836e-14,
              -1.2239981080288302e-15,
              0.4984451993725671
            ],
            "branch_aligned_reduced_polarization": [
              -1.0578636963973836e-14,
              -1.2239981080288302e-15,
              0.4984451993725671
            ],
            "target_residual": 0.0015548006274329063,
            "energy_eV": -187.52743398274873,
            "max_atomic_step_A": 0.00015176725075749403,
            "max_log_strain_component": 4.498472522542933e-06,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.1491838861024513,
            "cell_principal_stretches": [
              1.0010259674212394,
              0.9993164295282015,
              0.9992057494406725
            ],
            "cell_volume_ratio": 0.9995471736771355,
            "cell_rmsd_from_input_A": 0.008249283221771422
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              5.396585910732196e-15,
              2.6402643123397524e-15,
              0.5000004535568516
            ],
            "branch_aligned_reduced_polarization": [
              5.396585910732196e-15,
              2.6402643123397524e-15,
              0.5000004535568516
            ],
            "target_residual": 4.5355685163173126e-07,
            "energy_eV": -187.52555833583054
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_01",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Pna2_1",
        "spacegroup_number": 33,
        "pointgroup": "mm2",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.5
        ],
        "formal_class": [
          0.0,
          0.0,
          0.5
        ],
        "target_residual": 4.5355685163173126e-07,
        "parent_symmetrization_rmsd_A": 0.03405179578813717,
        "parent_cell_rmsd_A": 0.008249283221771422,
        "energy_eV": -187.52555833583054,
        "reduced_polarization": [
          5.396585910732196e-15,
          2.6402643123397524e-15,
          0.5000004535568516
        ],
        "cartesian_polarization_e_A2": [
          8.879632965288874e-17,
          8.000296074962556e-17,
          0.0060276791369971855
        ],
        "ranking_score": 0.5361150237072833
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 2,
      "formal_class": [
        0.5,
        0.0,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.0,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.5,
        0.0,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              2.1761861735961544e-15,
              -1.0106605621611383e-15,
              0.1384226535008205
            ],
            "branch_aligned_reduced_polarization": [
              2.1649348980190553e-15,
              -1.0106605621611383e-15,
              0.1384226535008205
            ],
            "target_residual": 0.5188071231220771,
            "energy_eV": -187.75016339874318,
            "max_atomic_step_A": 0.057551939754551994,
            "max_log_strain_component": 0.0027633033054598275,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.1491838861024513,
            "cell_principal_stretches": [
              1.0027447471666193,
              1.0002606663336977,
              0.9971750123170477
            ],
            "cell_volume_ratio": 1.0001726490032505,
            "cell_rmsd_from_input_A": 0.014786644016104158
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.4990381888920712,
              -8.739994913520937e-15,
              -0.003394470620274527
            ],
            "branch_aligned_reduced_polarization": [
              0.4990381888920712,
              -8.739994913520937e-15,
              -0.003394470620274527
            ],
            "target_residual": 0.0035281030879556483,
            "energy_eV": -187.1086249367039,
            "max_atomic_step_A": 0.0003582138493698671,
            "max_log_strain_component": 9.64027547781206e-06,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.1491838861024513,
            "cell_principal_stretches": [
              1.0027503431002476,
              1.000254236168477,
              0.9971716118372698
            ],
            "cell_volume_ratio": 1.0001683902485363,
            "cell_rmsd_from_input_A": 0.01479904311219431
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.49999437346686354,
              2.3289894541916393e-15,
              -6.34733544825258e-07
            ],
            "branch_aligned_reduced_polarization": [
              0.49999437346686354,
              2.3289894541916393e-15,
              -6.34733544825258e-07
            ],
            "target_residual": 5.66222233832365e-06,
            "energy_eV": -187.1075501886498
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_02",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Pc",
        "spacegroup_number": 7,
        "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": 5.66222233832365e-06,
        "parent_symmetrization_rmsd_A": 0.05852839834084723,
        "parent_cell_rmsd_A": 0.01479904311219431,
        "energy_eV": -187.1075501886498,
        "reduced_polarization": [
          0.49999437346686354,
          2.3289894541916393e-15,
          -6.34733544825258e-07
        ],
        "cartesian_polarization_e_A2": [
          0.007744355964796416,
          1.7057161086996849e-16,
          2.144263663280243e-05
        ],
        "ranking_score": 0.5622394835635725
      },
      "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": [
              2.1761861735961544e-15,
              -1.0106605621611383e-15,
              0.1384226535008205
            ],
            "branch_aligned_reduced_polarization": [
              2.1761861735961544e-15,
              -9.992007221626409e-16,
              0.1384226535008205
            ],
            "target_residual": 0.5188071231220782,
            "energy_eV": -187.75016339874318,
            "max_atomic_step_A": 0.09110304106560213,
            "max_log_strain_component": 0.004480999021019192,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.1491838861024513,
            "cell_principal_stretches": [
              1.0047741497014515,
              0.999609228766617,
              0.9958094968789014
            ],
            "cell_volume_ratio": 1.0001726490032556,
            "cell_rmsd_from_input_A": 0.03269168316748959
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              7.803952935651419e-15,
              -0.4875904708494446,
              0.006015139887530672
            ],
            "branch_aligned_reduced_polarization": [
              7.803952935651419e-15,
              -0.4875904708494446,
              0.006015139887530672
            ],
            "target_residual": 0.013790515639563523,
            "energy_eV": -186.49764590099528,
            "max_atomic_step_A": 0.0026444027786449906,
            "max_log_strain_component": 0.00012638818350349147,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.1491838861024513,
            "cell_principal_stretches": [
              1.0049147185814227,
              0.9995905087843242,
              0.9956970843560723
            ],
            "cell_volume_ratio": 1.0001809222341855,
            "cell_rmsd_from_input_A": 0.03362147602297462
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              1.877203591064159e-15,
              -0.49996643917282807,
              7.575985878228522e-05
            ],
            "branch_aligned_reduced_polarization": [
              1.877203591064159e-15,
              -0.49996643917282807,
              7.575985878228522e-05
            ],
            "target_residual": 8.28606379602279e-05,
            "energy_eV": -186.4266030487654
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_03",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Pc",
        "spacegroup_number": 7,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          -0.5,
          0.0
        ],
        "formal_class": [
          0.0,
          0.5,
          0.0
        ],
        "target_residual": 8.28606379602279e-05,
        "parent_symmetrization_rmsd_A": 0.09288330446758523,
        "parent_cell_rmsd_A": 0.03362147602297462,
        "energy_eV": -186.4266030487654,
        "reduced_polarization": [
          1.877203591064159e-15,
          -0.49996643917282807,
          7.575985878228522e-05
        ],
        "cartesian_polarization_e_A2": [
          -7.6364844649619e-17,
          -0.01074737893365376,
          -4.860436269031938e-05
        ],
        "ranking_score": 0.6014543947492493
      },
      "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": [
              2.1761861735961544e-15,
              -1.0106605621611383e-15,
              0.1384226535008205
            ],
            "branch_aligned_reduced_polarization": [
              2.1649348980190553e-15,
              -1.0106605621611383e-15,
              0.1384226535008205
            ],
            "target_residual": 0.6170398508211488,
            "energy_eV": -187.75016339874318,
            "max_atomic_step_A": 0.06651879938671001,
            "max_log_strain_component": 0.002763303305460913,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.1491838861024513,
            "cell_principal_stretches": [
              1.0030275460428948,
              0.999319427238359,
              0.9972107873614224
            ],
            "cell_volume_ratio": 0.9995491597168426,
            "cell_rmsd_from_input_A": 0.016634103927835896
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.4953027191496479,
              -5.621885591011145e-15,
              0.4943437087521124
            ],
            "branch_aligned_reduced_polarization": [
              0.4953027191496479,
              -5.621885591011145e-15,
              0.4943437087521124
            ],
            "target_residual": 0.007352419878381138,
            "energy_eV": -186.93286209406074,
            "max_atomic_step_A": 0.0007971798306015888,
            "max_log_strain_component": 2.7212484045838926e-05,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.1491838861024513,
            "cell_principal_stretches": [
              1.0030600143886057,
              0.9993082830078319,
              0.9971822629855872
            ],
            "cell_volume_ratio": 0.9995417764430432,
            "cell_rmsd_from_input_A": 0.016824639247175446
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.4999835889060163,
              4.0780023837339706e-16,
              0.49999954163424587
            ],
            "branch_aligned_reduced_polarization": [
              0.4999835889060163,
              4.0780023837339706e-16,
              0.49999954163424587
            ],
            "target_residual": 1.64174938680212e-05,
            "energy_eV": -186.91443253710744
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_04",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Pc",
        "spacegroup_number": 7,
        "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": 1.64174938680212e-05,
        "parent_symmetrization_rmsd_A": 0.06682406493073668,
        "parent_cell_rmsd_A": 0.016824639247175446,
        "energy_eV": -186.91443253710744,
        "reduced_polarization": [
          0.4999835889060163,
          4.0780023837339706e-16,
          0.49999954163424587
        ],
        "cartesian_polarization_e_A2": [
          0.007776882799531179,
          1.105855592201143e-16,
          0.0060493014984753695
        ],
        "ranking_score": 0.5710630597302666
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 5,
      "formal_class": [
        0.0,
        0.5,
        0.5
      ],
      "formal_classes_in_orbit": [
        [
          0.0,
          0.5,
          0.5
        ]
      ],
      "target_reduced_polarization": [
        0.0,
        -0.5,
        0.5
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              2.1761861735961544e-15,
              -1.0106605621611383e-15,
              0.1384226535008205
            ],
            "branch_aligned_reduced_polarization": [
              2.1761861735961544e-15,
              -9.992007221626409e-16,
              0.1384226535008205
            ],
            "target_residual": 0.6170398508211498,
            "energy_eV": -187.75016339874318,
            "max_atomic_step_A": 0.09772511894604449,
            "max_log_strain_component": 0.004480999021024533,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.1491838861024513,
            "cell_principal_stretches": [
              1.003752418527321,
              1.0010214643435487,
              0.9947963056570998
            ],
            "cell_volume_ratio": 0.9995491597168475,
            "cell_rmsd_from_input_A": 0.03344391654973022
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              -4.407408097040568e-15,
              -0.48960153878232954,
              0.5033311036907618
            ],
            "branch_aligned_reduced_polarization": [
              -4.407408097040568e-15,
              -0.48960153878232954,
              0.5033311036907618
            ],
            "target_residual": 0.010918985644005758,
            "energy_eV": -186.21448886839494,
            "max_atomic_step_A": 0.0021655240002850414,
            "max_log_strain_component": 0.00010473559897676572,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.1491838861024513,
            "cell_principal_stretches": [
              1.0038646177774502,
              1.001011671406645,
              0.9946991491424826
            ],
            "cell_volume_ratio": 0.9995534788433174,
            "cell_rmsd_from_input_A": 0.03416102508705402
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              1.0653896649500488e-16,
              -0.4999995553337752,
              0.5000561634001062
            ],
            "branch_aligned_reduced_polarization": [
              1.0653896649500488e-16,
              -0.4999995553337752,
              0.5000561634001062
            ],
            "target_residual": 5.616516037132824e-05,
            "energy_eV": -186.16029162760242
          }
        ],
        "iterations": 2
      },
      "parent": {
        "candidate_id": "bec_projection_05",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "Pc",
        "spacegroup_number": 7,
        "pointgroup": "m",
        "has_inversion": false,
        "is_polar_point_group": true,
        "nonpolar_parent_hypothesis": false,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          -0.5,
          0.5
        ],
        "formal_class": [
          0.0,
          0.5,
          0.5
        ],
        "target_residual": 5.616516037132824e-05,
        "parent_symmetrization_rmsd_A": 0.09791703849600215,
        "parent_cell_rmsd_A": 0.03416102508705402,
        "energy_eV": -186.16029162760242,
        "reduced_polarization": [
          1.0653896649500488e-16,
          -0.4999995553337752,
          0.5000561634001062
        ],
        "cartesian_polarization_e_A2": [
          -6.823165994378281e-17,
          -0.01071701034163845,
          0.005979173614857845
        ],
        "ranking_score": 0.6065696250885083
      },
      "branch_status": "awaiting_branch_sampling"
    },
    {
      "orbit_id": 6,
      "formal_class": [
        0.5,
        0.5,
        0.0
      ],
      "formal_classes_in_orbit": [
        [
          0.5,
          0.5,
          0.0
        ]
      ],
      "target_reduced_polarization": [
        0.5,
        -0.5,
        0.0
      ],
      "bec_backprojection": {
        "converged_to_target": true,
        "history": [
          {
            "iteration": 0,
            "reduced_polarization": [
              2.1761861735961544e-15,
              -1.0106605621611383e-15,
              0.1384226535008205
            ],
            "branch_aligned_reduced_polarization": [
              2.1649348980190553e-15,
              -9.992007221626409e-16,
              0.1384226535008205
            ],
            "target_residual": 0.7205281611444517,
            "energy_eV": -187.75016339874318,
            "max_atomic_step_A": 0.10910166172954595,
            "max_log_strain_component": 0.004480999021022226,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.1491838861024513,
            "cell_principal_stretches": [
              1.0054799561939929,
              0.9997902398229783,
              0.9949303148697372
            ],
            "cell_volume_ratio": 1.0001726490032303,
            "cell_rmsd_from_input_A": 0.03574261466426161
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.4983486938869558,
              -0.48631835375912696,
              0.00266358663237368
            ],
            "branch_aligned_reduced_polarization": [
              0.4983486938869558,
              -0.48631835375912696,
              0.00266358663237368
            ],
            "target_residual": 0.014035987656290246,
            "energy_eV": -185.85721464070286,
            "max_atomic_step_A": 0.00292728184228644,
            "max_log_strain_component": 0.00013896790636584957,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.1491838861024513,
            "cell_principal_stretches": [
              1.005612696135848,
              0.9997780920171724,
              0.9948152036460642
            ],
            "cell_volume_ratio": 1.0001768026159208,
            "cell_rmsd_from_input_A": 0.0366916606799628
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.5000082641975823,
              -0.4999664465576687,
              8.744542353778186e-05
            ],
            "branch_aligned_reduced_polarization": [
              0.5000082641975823,
              -0.4999664465576687,
              8.744542353778186e-05
            ],
            "target_residual": 9.402570154835737e-05,
            "energy_eV": -185.77476998640702
          }
        ],
        "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": [
          0.5,
          -0.5,
          0.0
        ],
        "formal_class": [
          0.5,
          0.5,
          0.0
        ],
        "target_residual": 9.402570154835737e-05,
        "parent_symmetrization_rmsd_A": 0.10926475212992116,
        "parent_cell_rmsd_A": 0.0366916606799628,
        "energy_eV": -185.77476998640702,
        "reduced_polarization": [
          0.5000082641975823,
          -0.4999664465576687,
          8.744542353778186e-05
        ],
        "cartesian_polarization_e_A2": [
          0.007744294532605345,
          -0.010747305539689951,
          -2.711352560258345e-05
        ],
        "ranking_score": 0.6186257187030086
      },
      "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": [
              2.1761861735961544e-15,
              -1.0106605621611383e-15,
              0.1384226535008205
            ],
            "branch_aligned_reduced_polarization": [
              2.1649348980190553e-15,
              -9.992007221626409e-16,
              0.1384226535008205
            ],
            "target_residual": 0.7941902653025813,
            "energy_eV": -187.75016339874318,
            "max_atomic_step_A": 0.11493308907625652,
            "max_log_strain_component": 0.004480999021027567,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.1491838861024513,
            "cell_principal_stretches": [
              1.0048542000808802,
              1.0005238168608679,
              0.9941998083404521
            ],
            "cell_volume_ratio": 0.9995491597168222,
            "cell_rmsd_from_input_A": 0.03643852575529768
          },
          {
            "iteration": 1,
            "reduced_polarization": [
              0.4936415605663,
              -0.4886829607116982,
              0.4989811452313285
            ],
            "branch_aligned_reduced_polarization": [
              0.4936415605663,
              -0.4886829607116982,
              0.4989811452313285
            ],
            "target_residual": 0.01302087536706509,
            "energy_eV": -185.60178136027812,
            "max_atomic_step_A": 0.002539457376597041,
            "max_log_strain_component": 0.00011418054056357088,
            "step_scale": 1.0,
            "strain_jacobian_refreshed": false,
            "strain_jacobian_frobenius_norm": 1.1491838861024513,
            "cell_principal_stretches": [
              1.004963390928666,
              1.0005347123305433,
              0.9940795152988734
            ],
            "cell_volume_ratio": 0.999547705395297,
            "cell_rmsd_from_input_A": 0.03725689135167763
          },
          {
            "iteration": 2,
            "reduced_polarization": [
              0.49998689560610254,
              -0.5000047761012144,
              0.5000639499551282
            ],
            "branch_aligned_reduced_polarization": [
              0.49998689560610254,
              -0.5000047761012144,
              0.5000639499551282
            ],
            "target_residual": 6.545328901684375e-05,
            "energy_eV": -185.51833603828857
          }
        ],
        "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": 6.545328901684375e-05,
        "parent_symmetrization_rmsd_A": 0.11380624389370289,
        "parent_cell_rmsd_A": 0.03725689135167763,
        "energy_eV": -185.51833603828857,
        "reduced_polarization": [
          0.49998689560610254,
          -0.5000047761012144,
          0.5000639499551282
        ],
        "cartesian_polarization_e_A2": [
          0.0077767766029409,
          -0.01071698358901584,
          0.006000873929630802
        ],
        "ranking_score": 0.623251373309656
      },
      "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
        ],
        "endpoint_rmsd_A": 0.05185828432656478,
        "minimum_distance_A_by_image": [
          1.779766263178609,
          1.779169334506479,
          1.7786518342762985,
          1.7782138318344594,
          1.7778553859375281,
          1.7775765447129133,
          1.7773773456266002,
          1.7772578154580032,
          1.777217970281976
        ],
        "minimum_distance_A": 1.777217970281976,
        "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": [
          498.9404756130552,
          498.9404756130552,
          498.9404756130552,
          498.9404756130552,
          498.9404756130552,
          498.9404756130552,
          498.9404756130552,
          498.9404756130552,
          498.9404756130552
        ],
        "cell_deformation_log_strain_norm": 0.0
      },
      "parent_reduced_polarization": [
        -6.129217140479065e-16,
        -4.833312675636173e-16,
        6.688695187842812e-16
      ],
      "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": [
          -187.75016339874315,
          -187.75611499052184,
          -187.76124096110442,
          -187.76555483211772,
          -187.7690682523527,
          -187.77179091851625,
          -187.77373042683644,
          -187.77489208821225,
          -187.77527892723657
        ],
        "cartesian_polarizations_e_A2": [
          [
            4.440587468465559e-17,
            -1.6855596654495013e-17,
            0.001669303366286952
          ],
          [
            -4.5935673060888636e-17,
            -5.562903186301984e-18,
            0.0014619779191645278
          ],
          [
            4.9593281905882194e-17,
            -2.983106833654439e-17,
            0.0012541251391043763
          ],
          [
            9.929782187549043e-18,
            -1.3350967647124764e-18,
            0.0010458147417201867
          ],
          [
            -1.4254939414898836e-17,
            -1.5576128921645557e-18,
            0.0008371194036220939
          ],
          [
            1.244699587935069e-17,
            -1.6104604724344247e-17,
            0.0006281138333409447
          ],
          [
            6.605947533733607e-18,
            -2.232114903503671e-17,
            0.00041887405250040063
          ],
          [
            1.2606929345956873e-17,
            2.503306433835893e-19,
            0.00020947687815255956
          ],
          [
            -9.498657190610639e-18,
            -1.0388721700418956e-17,
            8.066209620137877e-18
          ]
        ],
        "raw_reduced_polarization": [
          [
            2.8653865782649565e-15,
            -7.842001288983991e-16,
            0.13842265350082097
          ],
          [
            -2.964100177891998e-15,
            -2.588119237288446e-16,
            0.12123072834897483
          ],
          [
            3.2001154206366538e-15,
            -1.3878789409959294e-15,
            0.10399507548052976
          ],
          [
            6.407410012155274e-16,
            -6.211486169492272e-17,
            0.08672147588199322
          ],
          [
            -9.198312692519827e-16,
            -7.24673386440765e-17,
            0.06941595607282564
          ],
          [
            8.031697424200238e-16,
            -7.492605191950052e-16,
            0.052084711064244144
          ],
          [
            4.2626327111677244e-16,
            -1.038482843961989e-15,
            0.034734044752283
          ],
          [
            8.134898005628509e-16,
            1.1646536567798007e-17,
            0.017370326991817137
          ],
          [
            -6.129217140479065e-16,
            -4.833312675636173e-16,
            6.688695187842812e-16
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            2.8653865782649565e-15,
            -7.842001288983991e-16,
            0.13842265350082097
          ],
          [
            -2.9641001778919985e-15,
            -2.5881192372884453e-16,
            0.12123072834897483
          ],
          [
            3.2001154206366534e-15,
            -1.3878789409959294e-15,
            0.10399507548052976
          ],
          [
            6.407410012155274e-16,
            -6.211486169492273e-17,
            0.08672147588199322
          ],
          [
            -9.198312692519827e-16,
            -7.24673386440765e-17,
            0.06941595607282564
          ],
          [
            8.031697424200237e-16,
            -7.492605191950053e-16,
            0.052084711064244144
          ],
          [
            4.2626327111677244e-16,
            -1.038482843961989e-15,
            0.034734044752283
          ],
          [
            8.134898005628509e-16,
            1.1646536567798073e-17,
            0.017370326991817137
          ],
          [
            -6.129217140479065e-16,
            -4.833312675636173e-16,
            6.696032617270475e-16
          ]
        ],
        "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": [
          [
            2.886579864025407e-15,
            -7.771561172376096e-16,
            0.13842265350082095
          ],
          [
            -2.942091015256665e-15,
            -2.7755575615628914e-16,
            0.12123072834897486
          ],
          [
            3.219646771412954e-15,
            -1.3877787807814457e-15,
            0.10399507548052978
          ],
          [
            6.661338147750939e-16,
            -5.551115123125783e-17,
            0.08672147588199319
          ],
          [
            -9.43689570931383e-16,
            -5.551115123125783e-17,
            0.06941595607282558
          ],
          [
            7.771561172376096e-16,
            -7.216449660063518e-16,
            0.05208471106424417
          ],
          [
            4.440892098500626e-16,
            -1.0547118733938987e-15,
            0.03473404475228303
          ],
          [
            7.771561172376096e-16,
            0.0,
            0.017370326991817175
          ],
          [
            -6.106226635438361e-16,
            -4.996003610813204e-16,
            6.661338147750939e-16
          ]
        ]
      },
      "reflected": {
        "reached": true,
        "construction": "reflect_displacements_about_reconstructed_parent",
        "energies_eV": [
          -187.77527892723657,
          -187.77489208821225,
          -187.7737304268364,
          -187.77179091851625,
          -187.76906825235264,
          -187.76555483211774,
          -187.76124096110442,
          -187.7561149905218,
          -187.75016339874318
        ],
        "cartesian_polarizations_e_A2": [
          [
            -9.498657190610639e-18,
            -1.0388721700418956e-17,
            8.066209620137877e-18
          ],
          [
            -7.224820513209703e-18,
            1.12092499203985e-17,
            -0.00020947687815255382
          ],
          [
            -4.5546269837847495e-18,
            -3.596416909944233e-17,
            -0.00041887405250039825
          ],
          [
            3.134000582582881e-17,
            -5.8271410876513286e-18,
            -0.0006281138333409369
          ],
          [
            4.145058236693266e-17,
            -1.5297983762330456e-17,
            -0.0008371194036220855
          ],
          [
            5.622356714105587e-17,
            -5.295883833359489e-17,
            -0.0010458147417201536
          ],
          [
            4.752805409796758e-17,
            2.6562862714591976e-18,
            -0.0012541251391043663
          ],
          [
            -1.3893350707789208e-17,
            -4.199991905657998e-18,
            -0.0014619779191645324
          ],
          [
            6.038531408730805e-17,
            -2.2515850646557284e-17,
            -0.0016693033662869374
          ]
        ],
        "raw_reduced_polarization": [
          [
            -6.129217140479065e-16,
            -4.833312675636173e-16,
            6.688695187842812e-16
          ],
          [
            -4.661974091477121e-16,
            5.215060263136219e-16,
            -0.01737032699181666
          ],
          [
            -2.938973079805115e-16,
            -1.6732190869069803e-15,
            -0.034734044752282804
          ],
          [
            2.022282697813993e-15,
            -2.7110549010596473e-16,
            -0.0520847110642435
          ],
          [
            2.6746898517127165e-15,
            -7.117327902543227e-16,
            -0.06941595607282494
          ],
          [
            3.627949135383856e-15,
            -2.4638895138986007e-15,
            -0.08672147588199047
          ],
          [
            3.0668520611401467e-15,
            1.235826935805233e-16,
            -0.10399507548052894
          ],
          [
            -8.964989638855909e-16,
            -1.9540300241527768e-16,
            -0.12123072834897522
          ],
          [
            3.896494996187424e-15,
            -1.0475412612924985e-15,
            -0.13842265350081978
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            -6.129217140479065e-16,
            -4.833312675636173e-16,
            6.688695187842812e-16
          ],
          [
            -4.661974091477121e-16,
            5.215060263136219e-16,
            -0.01737032699181666
          ],
          [
            -2.938973079805115e-16,
            -1.6732190869069803e-15,
            -0.034734044752282804
          ],
          [
            2.022282697813993e-15,
            -2.7110549010596473e-16,
            -0.0520847110642435
          ],
          [
            2.6746898517127165e-15,
            -7.117327902543227e-16,
            -0.06941595607282494
          ],
          [
            3.627949135383856e-15,
            -2.4638895138986007e-15,
            -0.08672147588199047
          ],
          [
            3.0668520611401467e-15,
            1.2358269358052313e-16,
            -0.10399507548052894
          ],
          [
            -8.964989638855905e-16,
            -1.9540300241527765e-16,
            -0.12123072834897522
          ],
          [
            3.896494996187424e-15,
            -1.0475412612924985e-15,
            -0.13842265350081978
          ]
        ],
        "gauge_integer_shift": [
          0,
          0,
          0
        ],
        "expected_opposite_endpoint_reduced_polarization": [
          -4.0912300063607685e-15,
          -1.824624062288354e-16,
          -0.13842265350081964
        ],
        "actual_opposite_endpoint_branch_residual": 8.03563136544078e-15
      },
      "pnp_branch": {
        "construction": "incoming_path_concatenated_with_parent_reflection",
        "reduced_polarization": [
          [
            2.8653865782649565e-15,
            -7.842001288983991e-16,
            0.13842265350082097
          ],
          [
            -2.964100177891998e-15,
            -2.588119237288446e-16,
            0.12123072834897483
          ],
          [
            3.2001154206366538e-15,
            -1.3878789409959294e-15,
            0.10399507548052976
          ],
          [
            6.407410012155274e-16,
            -6.211486169492272e-17,
            0.08672147588199322
          ],
          [
            -9.198312692519827e-16,
            -7.24673386440765e-17,
            0.06941595607282564
          ],
          [
            8.031697424200238e-16,
            -7.492605191950052e-16,
            0.052084711064244144
          ],
          [
            4.2626327111677244e-16,
            -1.038482843961989e-15,
            0.034734044752283
          ],
          [
            8.134898005628509e-16,
            1.1646536567798007e-17,
            0.017370326991817137
          ],
          [
            -6.129217140479065e-16,
            -4.833312675636173e-16,
            6.688695187842812e-16
          ],
          [
            -4.661974091477121e-16,
            5.215060263136219e-16,
            -0.01737032699181666
          ],
          [
            -2.938973079805115e-16,
            -1.6732190869069803e-15,
            -0.034734044752282804
          ],
          [
            2.022282697813993e-15,
            -2.7110549010596473e-16,
            -0.0520847110642435
          ],
          [
            2.6746898517127165e-15,
            -7.117327902543227e-16,
            -0.06941595607282494
          ],
          [
            3.627949135383856e-15,
            -2.4638895138986007e-15,
            -0.08672147588199047
          ],
          [
            3.0668520611401467e-15,
            1.235826935805233e-16,
            -0.10399507548052894
          ],
          [
            -8.964989638855909e-16,
            -1.9540300241527768e-16,
            -0.12123072834897522
          ],
          [
            3.896494996187424e-15,
            -1.0475412612924985e-15,
            -0.13842265350081978
          ]
        ],
        "unwrapped_reduced_polarization": [
          [
            2.8653865782649565e-15,
            -7.842001288983991e-16,
            0.13842265350082097
          ],
          [
            -2.9641001778919985e-15,
            -2.5881192372884453e-16,
            0.12123072834897483
          ],
          [
            3.2001154206366534e-15,
            -1.3878789409959294e-15,
            0.10399507548052976
          ],
          [
            6.407410012155274e-16,
            -6.211486169492273e-17,
            0.08672147588199322
          ],
          [
            -9.198312692519827e-16,
            -7.24673386440765e-17,
            0.06941595607282564
          ],
          [
            8.031697424200237e-16,
            -7.492605191950053e-16,
            0.052084711064244144
          ],
          [
            4.2626327111677244e-16,
            -1.038482843961989e-15,
            0.034734044752283
          ],
          [
            8.134898005628509e-16,
            1.1646536567798073e-17,
            0.017370326991817137
          ],
          [
            -6.129217140479065e-16,
            -4.833312675636173e-16,
            6.696032617270475e-16
          ],
          [
            -4.661974091477121e-16,
            5.215060263136219e-16,
            -0.01737032699181666
          ],
          [
            -2.938973079805115e-16,
            -1.6732190869069803e-15,
            -0.034734044752282804
          ],
          [
            2.022282697813993e-15,
            -2.7110549010596473e-16,
            -0.0520847110642435
          ],
          [
            2.6746898517127165e-15,
            -7.117327902543227e-16,
            -0.06941595607282494
          ],
          [
            3.627949135383856e-15,
            -2.4638895138986007e-15,
            -0.08672147588199047
          ],
          [
            3.0668520611401467e-15,
            1.2358269358052313e-16,
            -0.10399507548052894
          ],
          [
            -8.964989638855905e-16,
            -1.9540300241527765e-16,
            -0.12123072834897522
          ],
          [
            3.896494996187424e-15,
            -1.0475412612924985e-15,
            -0.13842265350081978
          ]
        ],
        "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": [
          [
            2.886579864025407e-15,
            -7.771561172376096e-16,
            0.13842265350082095
          ],
          [
            -2.942091015256665e-15,
            -2.7755575615628914e-16,
            0.12123072834897486
          ],
          [
            3.219646771412954e-15,
            -1.3877787807814457e-15,
            0.10399507548052978
          ],
          [
            6.661338147750939e-16,
            -5.551115123125783e-17,
            0.08672147588199319
          ],
          [
            -9.43689570931383e-16,
            -5.551115123125783e-17,
            0.06941595607282558
          ],
          [
            7.771561172376096e-16,
            -7.216449660063518e-16,
            0.05208471106424417
          ],
          [
            4.440892098500626e-16,
            -1.0547118733938987e-15,
            0.03473404475228303
          ],
          [
            7.771561172376096e-16,
            0.0,
            0.017370326991817175
          ],
          [
            -6.106226635438361e-16,
            -4.996003610813204e-16,
            6.661338147750939e-16
          ],
          [
            -4.440892098500626e-16,
            5.551115123125783e-16,
            -0.017370326991816676
          ],
          [
            -2.7755575615628914e-16,
            -1.6653345369377348e-15,
            -0.03473404475228281
          ],
          [
            1.9984014443252818e-15,
            -2.7755575615628914e-16,
            -0.052084711064243505
          ],
          [
            2.6645352591003757e-15,
            -7.216449660063518e-16,
            -0.06941595607282491
          ],
          [
            3.6637359812630166e-15,
            -2.4424906541753444e-15,
            -0.08672147588199047
          ],
          [
            3.1086244689504383e-15,
            1.1102230246251565e-16,
            -0.10399507548052894
          ],
          [
            -8.881784197001252e-16,
            -2.220446049250313e-16,
            -0.12123072834897519
          ],
          [
            3.885780586188048e-15,
            -1.0547118733938987e-15,
            -0.13842265350081978
          ]
        ]
      },
      "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": "Pnma",
        "spacegroup_number": 62,
        "pointgroup": "mmm",
        "has_inversion": true,
        "is_polar_point_group": false,
        "nonpolar_parent_hypothesis": true,
        "symmetry_tolerance_A": null,
        "target_reduced_polarization": [
          0.0,
          0.0,
          0.0
        ],
        "formal_class": [
          0.0,
          0.0,
          0.0
        ],
        "target_residual": 9.384984824305606e-16,
        "parent_symmetrization_rmsd_A": 0.05185828432656478,
        "parent_cell_rmsd_A": 0.0,
        "energy_eV": -187.77527892723657,
        "reduced_polarization": [
          -5.972172777436044e-16,
          -4.975659233687037e-16,
          5.25869828561435e-16
        ],
        "cartesian_polarization_e_A2": [
          -9.255280176209927e-18,
          -1.0694681375665565e-17,
          6.341709632384263e-18
        ],
        "ranking_score": 0.05185828432656666
      }
    }
  ],
  "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": 53,
      "full_response": 16,
      "energy_polarization": 37
    },
    "model_evaluations_for_recovery_and_path_properties": {
      "total": 78,
      "full_response": 41,
      "energy_polarization": 37
    },
    "elapsed_seconds": 307.98864595399937
  }
}