{
  "schema_version": "ocme-reviewed-question-reader-v1",
  "question_id": "q-20261008-advance-20261011-r06-sample-space-0026",
  "pilot_number": "R0008-04976",
  "number": 4976,
  "family_id": "qf-density11-sample-recording-image",
  "title": {
    "zh-Hant": "第 4976 題：記錄像與對齊的原結果纖維",
    "en": "Question 4976: Recording Codes and Outcome Fibers"
  },
  "original_question": {
    "schema_version": "ocme-question-v0.1",
    "id": "q-20261008-advance-20261011-r06-sample-space-0026",
    "batch_id": "batch-20261008-advance-20261011-r06-sample-space-foundations",
    "language": "zh-Hant",
    "source_mko_ids": [
      "mko-sample-space"
    ],
    "title_zh": "記錄像與對齊的原結果纖維",
    "stem_zh": "基本可能結果S={0,…,0}，記錄表=[0]按原索引排列。依序答 (遞增記錄碼, 對齊各碼的原結果索引纖維列表)，纖維內索引遞增。",
    "answer": {
      "kind": "expression",
      "value": "([0], [[0]])",
      "explanation_zh": "記錄像與原結果纖維=([0], [[0]])。按相同記錄碼分組原索引，允許多對一；記錄尺度不改原結果資格，不指定概率。"
    },
    "difficulty": {
      "band": "lower_secondary",
      "level": 1,
      "skills": [
        "記錄像與對齊的原結果纖維"
      ]
    },
    "variant": {
      "family_id": "qf-density11-sample-recording-image",
      "seed": 202610116026,
      "parameters": {
        "n": 1,
        "recording": [
          0
        ],
        "operation": "density11_sample_recording_image",
        "domain": "finite_possible_outcome_protocol",
        "semantic_template": "qf-density11-sample-recording-image/[0]"
      }
    },
    "verification": {
      "status": "candidate",
      "checks": [
        "producer_exact_integer_rational_arithmetic",
        "producer_finite_enumeration",
        "producer_source_snapshot_check",
        "producer_substantive_template_deduplication",
        "producer_json_schema"
      ],
      "warning_zh": "僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"
    },
    "provenance": {
      "generator_role": "question_producer",
      "generator_model": "model_unknown",
      "generated_at": "2026-10-08",
      "contract_version": "ocme-question-factory-v0.1"
    }
  },
  "original_english_edition": {
    "schema_version": "ocme-question-localization-v0.1",
    "question_id": "q-20261008-advance-20261011-r06-sample-space-0026",
    "batch_id": "batch-20261008-advance-20261011-r06-sample-space-foundations",
    "locale": "en",
    "translation_state": "ai_candidate",
    "source": {
      "question_sha256": "91b9f50d18907ca1b59db11ee8a4c074fd23fc94d58b8abd914d19213fe79663",
      "family_id": "qf-density11-sample-recording-image",
      "seed": 202610116026,
      "semantic_template": "qf-density11-sample-recording-image/[0]"
    },
    "fields": {
      "title": "Recording Codes and Outcome Fibers",
      "stem": "Elementary outcomes are Fin(1)={0,…,0}, with recording=[0] in original index order. Give (increasing distinct recording codes, aligned original-index fiber lists), sorting each fiber increasingly.",
      "answer": {
        "kind": "expression",
        "value": "([0], [[0]])",
        "explanation": "Group original indices by their recorded code; many-to-one recording is allowed and does not change elementary-outcome eligibility or assign probabilities. The exact result, retaining the requested order, is ([0], [[0]])."
      },
      "skills": [
        "Recording Codes and Outcome Fibers"
      ],
      "verification_warning": "This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."
    }
  },
  "givens": [
    {
      "id": "G001",
      "text": {
        "zh-Hant": "基本可能結果S={0,…,0}，記錄表=[0]按原索引排列。依序答 (遞增記錄碼, 對齊各碼的原結果索引纖維列表)，纖維內索引遞增。",
        "en": "Elementary outcomes are Fin(1)={0,…,0}, with recording=[0] in original index order. Give (increasing distinct recording codes, aligned original-index fiber lists), sorting each fiber increasingly."
      }
    }
  ],
  "steps": [
    {
      "id": "S001",
      "uses": [
        "G001"
      ],
      "before": "explicit finite possible-outcome protocol",
      "after": "no probability law,equiprobability or independence inferred",
      "relation": "implies",
      "rule_id": "possible_outcomes_not_probabilities",
      "conditions": [],
      "explanation": {
        "zh-Hant": "這裡列可能基本結果、記錄或事件資格，不指定概率；所有組合可發生不等於等可能或兩階段獨立。",
        "en": "These tasks list possible outcomes,recordings or event membership without assigning probabilities.All combinations being possible does not imply equiprobability or independence."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "回到原始資料與本步條件核對，不把單向推論誤稱等價。",
          "en": "Check against the original data and this step's premises; a one-way implication is not an equivalence."
        }
      },
      "arithmetic": null
    },
    {
      "id": "S002",
      "uses": [
        "G001",
        "S001"
      ],
      "before": "original outcome index=0∈[0]",
      "after": "recorded code=0",
      "relation": "implies",
      "rule_id": "recording_total_mapping_row",
      "conditions": [],
      "explanation": {
        "zh-Hant": "每個原始結果有一個記錄碼，允許不同結果共用同碼；記錄碼不重新定義原索引。",
        "en": "Each original outcome has one code;different outcomes may share a code.Codes do not redefine original indices."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "回到原始資料與本步條件核對，不把單向推論誤稱等價。",
          "en": "Check against the original data and this step's premises; a one-way implication is not an equivalence."
        }
      },
      "arithmetic": null
    },
    {
      "id": "S003",
      "uses": [
        "G001",
        "S002"
      ],
      "before": "recorded code=0",
      "after": "[0]",
      "relation": "implies",
      "rule_id": "recording_preimage_fiber",
      "conditions": [],
      "explanation": {
        "zh-Hant": "按原索引列全部映到此碼的結果，纖維依記錄碼排序對齊。",
        "en": "List all original indices mapping to this code and align fibers with the sorted code list."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "回到原始資料與本步條件核對，不把單向推論誤稱等價。",
          "en": "Check against the original data and this step's premises; a one-way implication is not an equivalence."
        }
      },
      "arithmetic": null
    }
  ],
  "math_model": {
    "result": [
      [
        0
      ],
      [
        [
          0
        ]
      ]
    ]
  },
  "conclusion": {
    "canonical_value": "([0], [[0]])",
    "explanation": {
      "zh-Hant": "依上列完整代值及條件核對得到原題答案；原題編號、格式與狀態保持不變。",
      "en": "The full substitutions and premise checks give the original answer; source identity,format and status are unchanged."
    }
  },
  "definition_note": {
    "zh-Hant": "沿用原題明示的論域、假設與來源 MKO 定義。本題已完成第二對話數理與中英語義覆核，並由原始參數逐題獨立重算模型、答案與每個算術步驟；原題仍為 candidate。",
    "en": "Use the original question domain, assumptions and cited MKO definitions. This item has second-context mathematical and bilingual review, with the model, answer and every arithmetic step independently recomputed from the original parameters; the source question remains a candidate."
  },
  "source": {
    "input_commit": "0f7be61e2c22317a4075561dc822c87d881a50db",
    "question_binding": {
      "batch_id": "batch-20261008-advance-20261011-r06-sample-space-foundations",
      "batch_path": "public/data/questions/batches/batch-20261008-advance-20261011-r06-sample-space-foundations/questions.jsonl",
      "batch_sha256": "a3c5671d763c26ec164aeff524d6308ad28eb3415359ccb057a20ba767acdcc9",
      "original_line": 26,
      "original_line_sha256": "7de7bd431c674e8adaaf1075dbbd58fdc433d72cdb6009533952af096a346c65",
      "question_compact_sha256": "91b9f50d18907ca1b59db11ee8a4c074fd23fc94d58b8abd914d19213fe79663",
      "english_row_compact_sha256": "5fb21b1f9c64bdee0951ad2960b36cae4d5355011103c5e63dfac0e3e34967ce",
      "english_manifest_path": "public/data/i18n/editions/batch-20261008-advance-20261011-r06-sample-space-foundations.en.json",
      "english_rows_path": "public/data/i18n/questions/batch-20261008-advance-20261011-r06-sample-space-foundations.en.jsonl"
    },
    "mko_bindings": {
      "mko-sample-space": {
        "sha256": "c58b0d07252ece257a4143fd10f0f25b249023f4ed50bc6d393f4752a91267f7",
        "english_sha256": "ba452c266ef8c6ab4b549a3ccb6bc04a19fc7fafef1934d17f821c9ef4c04756",
        "original_path": "public/data/mko/sample-space.json",
        "english_path": "public/data/i18n/editions/mko-sample-space.en.json"
      }
    },
    "selected_manifest_sha256": "5233edba9654a6cffd8b6b2d83c932f82ded15f9c0b7c733bd049943e672acff",
    "selected_part_sha256": "6dc34e24b0f43c50e49365ca1a1153175f8661d5290c9236df5527bb047157eb",
    "original_candidate_sha256": "d47bc6a280e15607d6cb398c3288100c3db9eac97754276a3d68485ff8bb6591",
    "original_candidate_line_sha256": "d47bc6a280e15607d6cb398c3288100c3db9eac97754276a3d68485ff8bb6591"
  },
  "historical_source_state": {
    "review_state": {
      "derivation": "candidate_authored_and_locally_checked",
      "source_question_state": "candidate",
      "independent_AI_or_human_review": "NOT_PERFORMED",
      "formalization": "not_formalized",
      "Lean": "NOT_RUN"
    },
    "scope_note": {
      "zh-Hant": "來源綁定教學推導候選；精確核對不等於獨立AI／人工審查或一般形式證明。原題、答案、MKO、公式、AST與歷史不變。",
      "en": "Source-bound pedagogical derivation candidate.Exact checking is not independent AI/human review or general formal proof.Original questions,answers,MKOs,formulas,ASTs and history remain unchanged."
    },
    "label": "Frozen producer metadata; current per-question review is separate below."
  },
  "revision": {
    "id": "review-20261026-004-p9",
    "review_date": "2026-10-26",
    "owner_authorized_reader_publication": true,
    "scope": "One hundred sixty family prototypes and their mathematical/bilingual reasoning variants, stems, boundary statements and every distinct explanation shape were reviewed in a context independent of the producer; parameter substitutions, source bindings, full math models, both answer strings and every arithmetic step were independently reconstructed per question from the original parameters only, with negative controls. This grouped method does not claim a separate literal AI reading of every repeated sentence or an extra AI voter.",
    "review_receipts": {
      "semantic_review_sha256": "b6e05a3e8193a93db505dbf337528fca72e2e41528b1e92b698a3f0683d74289",
      "question_first_witness_sha256": "caa8693baf0b91acd09a20215d1aa6954ae513fc0b0814f26ac1c8c834b60d67"
    },
    "status": "second_context_reviewed",
    "mathematical_semantics": true,
    "bilingual_semantics": true,
    "steps_reviewed": 3,
    "method": "family_template_semantic_review_plus_independent_per_instance_reconstruction",
    "exact_question_first_check": {
      "model_sha256": "a9c68c2ec88c6e16417344794cb4ea043098c577e29008fba2383e6502f28080",
      "arithmetic_steps": 0
    },
    "uses_answer_as_premise": false,
    "human_review": "NOT_PERFORMED",
    "formalization": "not_formalized",
    "Lean": "NOT_RUN",
    "Canonical_truth_promotion": false,
    "authority": "Owner-authorized reviewed reader publication; original question/candidate states remain historical and unchanged."
  }
}