{
  "schema_version": "3.0",
  "episode_id": "dev_sample_8_smith_cyclic_four",
  "problem_id": "sample_8",
  "milestone_id": "m2",
  "split": "dev",
  "episode_type": "exact_benchmark",
  "reward_mode": "exact_machine",
  "verifier_id": "smith_root_group",
  "prompt": "Compute the Smith invariants and character count for a cyclic order-four root-choice group.",
  "input": {
    "matching_matrix": [
      [
        4
      ]
    ]
  },
  "candidate_required_fields": [
    "torsion_invariant_factors",
    "free_rank",
    "finite_torsion_cokernel",
    "torsion_order",
    "regular_character_count",
    "every_character_multiplicity_one"
  ],
  "submission_schema_ref": "schemas/submission.schema.json",
  "policy_visibility": "public"
}