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        -0.375,
        -0.5,
        -0.625,
        -0.75,
        -0.875,
        -1.0,
        -1.0875,
        -1.175,
        -1.2625,
        -1.35
      ],
      "parent": {
        "candidate_id": "bec_projection_00",
        "source": "MACEField_BEC_backprojection",
        "spacegroup": "R3m",
        "spacegroup_number": 160,
        "pointgroup": "3m",
        "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": [
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          0.0,
          0.0
        ],
        "target_residual": 0.00021926631435708244,
        "parent_symmetrization_rmsd_A": 0.04565664240846051,
        "parent_cell_rmsd_A": 0.09828083543039326,
        "energy_eV": -51.5454372618261,
        "reduced_polarization": [
          -1.75035065000348e-08,
          -2.5191877128302647e-08,
          0.00021926631221128222
        ],
        "cartesian_polarization_e_A2": [
          -7.923544536003077e-11,
          -3.5328405056697476e-10,
          2.16417553347424e-05
        ],
        "ranking_score": 0.570665383894773
      }
    }
  ],
  "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": 115,
      "full_response": 33,
      "energy_polarization": 82
    },
    "model_evaluations_for_recovery_and_path_properties": {
      "total": 140,
      "full_response": 58,
      "energy_polarization": 82
    },
    "elapsed_seconds": 165.32414553599665
  }
}