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      "perfect_pitchfork_nonzero_modes_supported": true,
      "imperfect_positive_and_negative_roots": true,
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      ]
    },
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      "scope": "Independent curved TET10 diagnostic, not one of the 1000 dataset IDs",
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      "original_mode_row_removed": true,
      "scope": "Signed numerical mode-plane validation; physical endpoint has only original constraints; no new sample count"
    },
    "remaining_dispatch_compatibility": {
      "error": "Legacy provenance record lacked solver_module",
      "classification": "orchestration_metadata_compatibility_not_numerical_failure",
      "fix": "Unknown provenance conservatively excluded instead of causing KeyError; only baseline modules eligible",
      "no_original_solver_interrupted": true,
      "old_status_preserved": true,
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      "state": "validated",
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      "profile": "mode_tail_v3",
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      "source_policy": "Original CCX constant Cauchy958.2434MPa tail, original four points unchanged; not damage/fracture calibration",
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        "ccx_constant_tail_investigation/ufl_quadrature_review.json": "6d9fbc0dc36fdc6befa972490e80842b7945ba383530a2552a16131844bc4190",
        "ccx_constant_tail_investigation/curved_tet10_assembly_review.json": "b1457f696fe895d42726b2334854f96d01ea23401527134259a208ef78cf9d95",
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      },
      "allowed_source_edits": [
        "from geobc.rod_r05_mode_plane import continue_target",
        "if p.max()>PLASTIC_P[-1]+1e-12:",
        "Plastic strain exceeds frozen material data range",
        "trial_plastic.max()>.00951460622563769",
        "pp.max()<=.00951460622563769",
        "material_data_range_passed=True,max_yield_consistency_residual_MPa=",
        "with frozen piecewise Cauchy hardening;"
      ],
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    },
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      "legacy_0095_full_field_reverified": true,
      "legacy_manifest_unchanged": true,
      "arc_v2_policy_witness_compatible": true,
      "arc_v2_manifest_unchanged": true,
      "new_profile_metadata_unit_checks": [
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        "tail_validation_manifest_sha256",
        "tail_solver_sha256",
        "tail_profile",
        "wrong_provenance_module"
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      "scope": "Synthetic policy witnesses are not dataset results; no new sample count",
      "created_unix": 1792926303.1936202
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      "scope": "Independent curved TET10 diagnostic, not one of the 1000 dataset IDs",
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      "numerical_mode_roots": 9,
      "original_mode_row_removed": true,
      "scope": "Bounded-tail signed numerical-mode regression; original physical constraints restored; no new dataset count"
    },
    "mode_tail_main_capability_loaded": true,
    "mode_tail_isolated_pending_count": 0,
    "mode_tail_reference_checks": [
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      {
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      {
        "passed": true,
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      "largest_singular_value_N_per_mm": 23218376.6427143,
      "estimated_reduced_condition_number": 12705347384349.385,
      "right_singular_mode_xyz_squared_fractions": [
        0.006206904609814247,
        7.20991671817865e-07,
        0.993792374398508
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      "interpretation": "A small singular value measures conditioning of this frozen-history numerical operator. It does not establish a physical limit load, a negative energy direction, or nonexistence at the original target."
    },
    "trial_conditioning_driver": {
      "pid": 41168,
      "stage": "complete",
      "updated_unix": 1792902376.5571547
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    "plastic_trial_conditioning": {
      "sample_id": "normal_rodv2_0053__compression_skew",
      "scope": "Algorithmic derivative of an uncommitted endpoint residual with old history frozen; not an accepted physical state or a structural stability certificate.",
      "snapshot_sha256": "77f486d059fd9a7cb23c5249b59d735f196f5bfae88e3e9e03d2181ac7060115",
      "solver_source_sha256": "6f6fe8946b2d11bad960e5cb5000320080075bc1609c3d4e5e3eb5347e24716a",
      "load_factor": 0.7336552721210643,
      "history_base_factor": 0.7,
      "original_target_factor": 0.8,
      "reassembled_free_residual_relative": 4.49172807760776e-10,
      "old_PEEQ_max": 0.0,
      "trial_PEEQ_max": 0.0002630373294990779,
      "trial_material_range_passed": true,
      "does_not_change_effective_count": true,
      "created_unix": 1792900893.1609929,
      "state": "complete",
      "seconds": 3.9905905723571777,
      "relative_Frobenius_asymmetry": 8.695209717428828e-06,
      "reduced_dofs": 107245,
      "smallest_singular_value_N_per_mm": 0.0006200829984740852,
      "singular_triplet_relative_residual": 4.7432142272392714e-07,
      "inverse_eigen_relative_residual": 2.8996577061518764e-15,
      "directional_Rayleigh_N_per_mm": 0.0006200830007524182,
      "singular_mode_quality": "passed",
      "largest_singular_value_N_per_mm": 27262178.194579497,
      "estimated_reduced_condition_number": 43965369574.181046,
      "right_singular_mode_xyz_squared_fractions": [
        0.019312910289224435,
        3.4468223487892235e-07,
        0.9806867450285381
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      "interpretation": "A small singular value measures conditioning of this frozen-history numerical operator. It does not establish a physical limit load, a negative energy direction, or nonexistence at the original target."
    },
    "conditional_branch_diagnostic": {
      "pid": 25660,
      "stage": "complete",
      "updated_unix": 1792898330.0869353,
      "report": "C:\\Users\\ASUS\\Desktop\\GeoBC Neural Operator\\publication\\GeoBC-Neural-Operator\\results\\rod_r05_yield_branch_20261025\\normal_rodv2_0053__compression_skew\\tangent_inertia.json"
    },
    "preyield_branch_check": {
      "sample_id": "normal_rodv2_0053__compression_skew",
      "load_factor": 0.7,
      "backend": "cpu",
      "constitutive_scope": "Virgin hyperelastic tangent; PEEQ=0 verified.",
      "fields_sha256": null,
      "snapshot_sha256": "6d611773825201615b89d18bdf4358427ed3fe42c1aabe0c52f3a138bfed5ab8",
      "partial_diagnostic_only": true,
      "reassembled_free_residual_relative": 3.8520305266074707e-10,
      "bordered_inertia_negative_zero_positive": [
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        0,
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      "mean_constraint_rank": 2,
      "negative_admissible_directions": 0,
      "zero_pivots": 0,
      "label": "no_negative_direction_detected_at_checkpoint",
      "branch_applicability": "This is an equilibrated branch at the specified frozen constraints. A negative tangent direction precludes a stable local potential minimum. Direct convergence is not a stability certificate; no critical load or post-buckled branch is inferred.",
      "seconds": 5.301937103271484,
      "created_unix": 1792898327.727844,
      "does_not_change_effective_count": true,
      "modes_state": "complete",
      "near_zero_eigenvalues_N_per_mm": [
        0.0007631026425848069,
        0.03339596478082396,
        0.05670108025273578,
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        1.5921929008437188,
        1.682938669236383
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      "relative_eigen_residuals": [
        3.955855023107275e-07,
        1.6292763612624996e-08,
        6.445972923852007e-09,
        1.6659228349572886e-09,
        2.8155397550477053e-10,
        2.7146915591044224e-10
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      "mode_xyz_squared_fractions": [
        [
          0.014372493477849895,
          3.4971320485273735e-07,
          0.9856271568089452
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        [
          0.005879530840676233,
          0.845061729339972,
          0.14905873981935
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          0.5824305951651615
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          0.06349176276747123,
          2.0856143904243527e-05,
          0.936487381088627
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          0.11319627256588709,
          0.7804589645910367,
          0.10634476284307232
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        [
          0.07005223047622242,
          0.0024151459347413165,
          0.9275326235890422
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      "eigenvalue_scope": "Constrained tangent, reduced Euclidean displacement norm; eigenvalues nearest zero, not a critical load or vibration frequency."
    },
    "elastic_path_comparison_0053": {
      "sample_id": "normal_rodv2_0053__compression_skew",
      "scope": "Scalar maxima and equilibrium history only; not a complete raw-field comparison",
      "common_accepted_states": 7,
      "last_common_load_factor": 0.7,
      "maximum_VM_history_absolute_difference_MPa": 2.11125137639101e-06,
      "maximum_min_J_history_absolute_difference": 8.921197114375445e-12,
      "elastic_CPU_failure": {
        "error": "RuntimeError('Yield detected: full J2 return map required; elastic-branch comparison invalid')",
        "time_unix": 1792892551.7271135,
        "no_accepted_full_case": true
      },
      "GPU_failure": {
        "error": "RuntimeError('Yield detected: full J2 return map required; elastic-branch comparison invalid')",
        "time_unix": 1792893206.4102037,
        "no_accepted_full_case": true
      },
      "interpretation": "The two original virgin-elastic methods match through 70% load, and neither exports an accepted full-load case. CPU detects yield at the next target; full-J2 recovery is required. This comparison does not establish stability.",
      "created_unix": 1792893348.99383
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      "scope": "Material-point prototype only, not a production FE recovery solver",
      "reference": "Unmodified CalculiX incplas.f compiled as an independent static-isotropic oracle",
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        {
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          "passed": true
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        {
          "history": "plastic_tension_unload",
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          "stress_relative_error": 4.0835690262886305e-13,
          "PEEQ_absolute_error": 9.367506770274758e-17,
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          "passed": true
        },
        {
          "history": "plastic_shear_unload",
          "states": 42,
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          "PEEQ_absolute_error": 2.168404344971009e-18,
          "metric_absolute_error": 2.220446049250313e-16,
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          "passed": true
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        {
          "history": "nonproportional",
          "states": 30,
          "stress_relative_error": 9.217801438188697e-13,
          "PEEQ_absolute_error": 9.150666335777657e-17,
          "metric_absolute_error": 2.220446049250313e-16,
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          "passed": true
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        {
          "history": "superposed_rotation",
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          "PEEQ_absolute_error": 7.45931094670027e-17,
          "metric_absolute_error": 1.1102230246251565e-16,
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          "passed": true
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      "all_passed": true
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      "scope": "One native TET10/P2 quadrature integration and automatic material tangent; not a full structural solve",
      "cases": [
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          "history_absolute_error": 3.252606517456513e-17,
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          "state": 2,
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          "history_absolute_error": 2.0599841277224584e-18,
          "tangent_relative_error": 3.111454034379703e-10,
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          "passed": true
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          "state": 3,
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          "history_absolute_error": 0.0,
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          "PEEQ": 0.0026610207766471702,
          "passed": true
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      "scope": "Independent curved TET10 diagnostic, not one of the 1000 dataset IDs",
      "U_relative_L2": 2.140992925197314e-07,
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      "unload_displacement_norm_mm": 0.0013880615084031973,
      "passed": true
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      "scope": "Independent curved TET10 diagnostic, not one of the 1000 dataset IDs",
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      "globalization": "Backtracking at original target loads, no trial history commit, positive determinant and residual descent"
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      "scope": "Independent curved TET10 diagnostic, not one of the 1000 dataset IDs",
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      "passed": true
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    "hybrid_full_rod_regression": {
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      "relative_L2": {
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      "scope": "Independent curved TET10 diagnostic, not one of the 1000 dataset IDs",
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      "GP_match_mm": 2.0032143250599133e-15,
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      "unload_displacement_norm_mm": 0.0013880615083843794,
      "passed": true
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    "plastic_merit_full_rod_regression": {
      "sample_id": "normal_rodv2_0028__compression",
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      "relative_L2": {
        "U_peak_mm": 2.7302352305649335e-12,
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      "sample_id": "normal_rodv2_0028__compression",
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      "scope": "Independent curved TET10 diagnostic, not one of the 1000 dataset IDs",
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      "unload_displacement_norm_mm": 0.0013880615186398339,
      "passed": true
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    "adaptive_homotopy_full_rod_regression": {
      "sample_id": "normal_rodv2_0028__compression",
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      "relative_L2": {
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      "scope": "Independent curved TET10 diagnostic, not one of the 1000 dataset IDs",
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      "GP_match_mm": 2.0032143250599133e-15,
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      "unload_displacement_norm_mm": 0.0013880616038298031,
      "passed": true
    },
    "predictor_full_rod_regression": {
      "sample_id": "normal_rodv2_0028__compression",
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      "relative_L2": {
        "U_peak_mm": 1.4483702962470963e-07,
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    },
    "pc_plastic_regression": {
      "scope": "Independent curved TET10 diagnostic, not one of the 1000 dataset IDs",
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      "GP_tensor_relative_L2": 1.0476593010471696e-07,
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      "GP_match_mm": 2.0032143250599133e-15,
      "material_range_passed": true,
      "unload_displacement_norm_mm": 0.0013880615186388557,
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      "solver_sha256": "167a25beec8a763e6deea9619c6ef692787805e5c3d541c2fd2a06cc5840084b"
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    "pc_full_rod_regression": {
      "sample_id": "normal_rodv2_0028__compression",
      "scope": "Existing accepted ID used only for full nonlinear elastic-rod regression; no new effective count",
      "relative_L2": {
        "U_peak_mm": 6.676505727732906e-12,
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    },
    "target_cases": [
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        "sample_id": "extreme_rodv2_0040__combined_bending",
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        "last_failure": {
          "error": "RuntimeError('Numerical signed-mode attempt budget or amplitude list exhausted; no original target accepted')",
          "time_unix": 1792952450.7323568,
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        "solver_module": "tools.rod_fenicsx_solver_r05_j2_mode_bracket_tail",
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          "time_unix": 1792946580.0227807,
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        "sample_id": "extreme_rodv2_0154__combined_bending",
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          "time_unix": 1792946827.553202,
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      {
        "sample_id": "extreme_rodv2_0158__combined_bending",
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          "time_unix": 1792947459.8502707,
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          "time_unix": 1792947797.2202744,
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          "time_unix": 1792948983.5402486,
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      {
        "sample_id": "normal_rodv2_0135__compression",
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          "time_unix": 1792947999.0202034,
          "no_accepted_full_case": true
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        "archived": false
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      {
        "sample_id": "normal_rodv2_0135__compression_skew",
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          "time_unix": 1792948277.5936005,
          "no_accepted_full_case": true
        },
        "archived": false
      },
      {
        "sample_id": "extreme_rodv2_0040__combined_bending",
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        "last_relative_residual": 0.23731466458994296,
        "failure": {
          "error": "RuntimeError('Newton stagnation; cut numerical homotopy interval')",
          "time_unix": 1792950468.2987425,
          "no_accepted_full_case": true
        },
        "archived": true
      },
      {
        "sample_id": "extreme_rodv2_0040__combined_bending",
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        "method": "初始完整J2牛顿（历史版本）",
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          "time_unix": 1792952450.7323568,
          "no_accepted_full_case": true
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        "archived": false
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    ]
  },
  "stability_note": "Effective count follows frozen identity/equilibrium/yield gates; structural stability is not yet assessed sample by sample. R04 negative-mode result shows direct-solve convergence alone is not a stability certificate.",
  "user_authorized_condition_supplement": true,
  "retained_original_valid": 985,
  "new_conditions_required": 15,
  "new_conditions_verified": 15,
  "supplement_elapsed_seconds": 1163.2157871723175,
  "supplement_phase": "completed_pending_website_summary",
  "revised_selection_finalized": true,
  "original_1000_all_converged": false,
  "excluded_original_sample_ids": [
    "normal_rodv2_0053__compression_skew",
    "normal_rodv2_0079__compression_skew",
    "normal_rodv2_0096__gas_inertia_30deg",
    "normal_rodv2_0154__compression_skew",
    "normal_rodv2_0159__compression_skew",
    "normal_rodv2_0135__compression",
    "normal_rodv2_0135__compression_skew",
    "normal_rodv2_0051__compression_skew",
    "extreme_rodv2_0054__combined_bending",
    "extreme_rodv2_0040__combined_bending",
    "extreme_rodv2_0154__combined_bending",
    "extreme_rodv2_0061__combined_bending",
    "extreme_rodv2_0053__combined_bending",
    "extreme_rodv2_0135__combined_bending",
    "extreme_rodv2_0158__combined_bending"
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  "supplement_protocol_sha256": "781fe8952a1d6d4c62ce13e8067a037eea145e12ce99c698508e92d4051bb88d",
  "selection_bias_notice": "Final data are a user-authorized revised population, not a claim that all original 1000 cases converged. Original 15 failures remain excluded and preserved."
}
