{
  "schema_version": "ocme-reviewed-question-reader-v1",
  "question_id": "q-20261008-advance-20261011-r06-sample-space-0013",
  "pilot_number": "R0008-04938",
  "number": 4938,
  "family_id": "qf-density11-sample-ordered-product",
  "title": {
    "zh-Hant": "第 4938 題：兩階段全部有序基本結果",
    "en": "Question 4938: All Ordered Elementary Outcomes"
  },
  "original_question": {
    "schema_version": "ocme-question-v0.1",
    "id": "q-20261008-advance-20261011-r06-sample-space-0013",
    "batch_id": "batch-20261008-advance-20261011-r06-sample-space-foundations",
    "language": "zh-Hant",
    "source_mko_ids": [
      "mko-sample-space"
    ],
    "title_zh": "兩階段全部有序基本結果",
    "stem_zh": "基本可能結果協定：第一階段A=[-12, 12]、第二階段B=[-1, 0, 13]，所有兩階段組合均允許。列全部有序對，各軸先去重排序，再按A外層、B內層逐行列舉。",
    "answer": {
      "kind": "expression",
      "value": "[[-12, -1], [-12, 0], [-12, 13], [12, -1], [12, 0], [12, 13]]",
      "explanation_zh": "全部有序基本結果=[[-12, -1], [-12, 0], [-12, 13], [12, -1], [12, 0], [12, 13]]。逐個第一階段搭配每個第二階段值；次序有別，不指定概率，也不推論兩階段獨立或等可能。"
    },
    "difficulty": {
      "band": "lower_secondary",
      "level": 2,
      "skills": [
        "兩階段全部有序基本結果"
      ]
    },
    "variant": {
      "family_id": "qf-density11-sample-ordered-product",
      "seed": 202610116013,
      "parameters": {
        "A": [
          -12,
          12
        ],
        "B": [
          -1,
          0,
          13
        ],
        "operation": "density11_sample_ordered_product",
        "domain": "finite_possible_outcome_protocol",
        "semantic_template": "qf-density11-sample-ordered-product/[[-12,12],[-1,0,13]]"
      }
    },
    "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-0013",
    "batch_id": "batch-20261008-advance-20261011-r06-sample-space-foundations",
    "locale": "en",
    "translation_state": "ai_candidate",
    "source": {
      "question_sha256": "34e173942ce5577ae4b12b4b07d6e81663feec4fbdd31efa728aac543989ee35",
      "family_id": "qf-density11-sample-ordered-product",
      "seed": 202610116013,
      "semantic_template": "qf-density11-sample-ordered-product/[[-12,12],[-1,0,13]]"
    },
    "fields": {
      "title": "All Ordered Elementary Outcomes",
      "stem": "First-stage outcomes A=[-12, 12], second-stage outcomes B=[-1, 0, 13]; every pair is allowed. Normalize and sort each axis, then list all ordered pairs with A as the outer loop and B as the inner loop.",
      "answer": {
        "kind": "expression",
        "value": "[[-12, -1], [-12, 0], [-12, 13], [12, -1], [12, 0], [12, 13]]",
        "explanation": "Pair every first-stage value with every second-stage value. Order matters; no probabilities, equiprobability, or stochastic independence are asserted. The exact result, retaining the requested order, is [[-12, -1], [-12, 0], [-12, 13], [12, -1], [12, 0], [12, 13]]."
      },
      "skills": [
        "All Ordered Elementary Outcomes"
      ],
      "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": "基本可能結果協定：第一階段A=[-12, 12]、第二階段B=[-1, 0, 13]，所有兩階段組合均允許。列全部有序對，各軸先去重排序，再按A外層、B內層逐行列舉。",
        "en": "First-stage outcomes A=[-12, 12], second-stage outcomes B=[-1, 0, 13]; every pair is allowed. Normalize and sort each axis, then list all ordered pairs with A as the outer loop and B as the inner loop."
      }
    }
  ],
  "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": "first-stage outcome=-12;second-stage outcome=-1",
      "after": "[-12, -1]",
      "relation": "implies",
      "rule_id": "ordered_outcome_pair",
      "conditions": [],
      "explanation": {
        "zh-Hant": "按A外層、B內層列舉，兩個階段的順序不可交換。",
        "en": "Enumerate with A as the outer loop and B as the inner loop;stage order matters."
      },
      "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": "first-stage outcome=-12;second-stage outcome=0",
      "after": "[-12, 0]",
      "relation": "implies",
      "rule_id": "ordered_outcome_pair",
      "conditions": [],
      "explanation": {
        "zh-Hant": "按A外層、B內層列舉，兩個階段的順序不可交換。",
        "en": "Enumerate with A as the outer loop and B as the inner loop;stage order matters."
      },
      "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": "S004",
      "uses": [
        "G001",
        "S003"
      ],
      "before": "first-stage outcome=-12;second-stage outcome=13",
      "after": "[-12, 13]",
      "relation": "implies",
      "rule_id": "ordered_outcome_pair",
      "conditions": [],
      "explanation": {
        "zh-Hant": "按A外層、B內層列舉，兩個階段的順序不可交換。",
        "en": "Enumerate with A as the outer loop and B as the inner loop;stage order matters."
      },
      "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": "S005",
      "uses": [
        "G001",
        "S004"
      ],
      "before": "first-stage outcome=12;second-stage outcome=-1",
      "after": "[12, -1]",
      "relation": "implies",
      "rule_id": "ordered_outcome_pair",
      "conditions": [],
      "explanation": {
        "zh-Hant": "按A外層、B內層列舉，兩個階段的順序不可交換。",
        "en": "Enumerate with A as the outer loop and B as the inner loop;stage order matters."
      },
      "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": "S006",
      "uses": [
        "G001",
        "S005"
      ],
      "before": "first-stage outcome=12;second-stage outcome=0",
      "after": "[12, 0]",
      "relation": "implies",
      "rule_id": "ordered_outcome_pair",
      "conditions": [],
      "explanation": {
        "zh-Hant": "按A外層、B內層列舉，兩個階段的順序不可交換。",
        "en": "Enumerate with A as the outer loop and B as the inner loop;stage order matters."
      },
      "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": "S007",
      "uses": [
        "G001",
        "S006"
      ],
      "before": "first-stage outcome=12;second-stage outcome=13",
      "after": "[12, 13]",
      "relation": "implies",
      "rule_id": "ordered_outcome_pair",
      "conditions": [],
      "explanation": {
        "zh-Hant": "按A外層、B內層列舉，兩個階段的順序不可交換。",
        "en": "Enumerate with A as the outer loop and B as the inner loop;stage order matters."
      },
      "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": "S008",
      "uses": [
        "G001",
        "S007"
      ],
      "before": "A=[-12, 12];B=[-1, 0, 13]",
      "after": "[[-12, -1], [-12, 0], [-12, 13], [12, -1], [12, 0], [12, 13]]",
      "relation": "implies",
      "rule_id": "complete_cartesian_outcome_protocol",
      "conditions": [],
      "explanation": {
        "zh-Hant": "去重後每個A值與每個B值各配一次，完整列出協定允許的笛卡兒積。",
        "en": "After deduplication,pair each A-value with each B-value exactly once to list the protocol's full Cartesian product."
      },
      "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": [
      [
        -12,
        -1
      ],
      [
        -12,
        0
      ],
      [
        -12,
        13
      ],
      [
        12,
        -1
      ],
      [
        12,
        0
      ],
      [
        12,
        13
      ]
    ]
  },
  "conclusion": {
    "canonical_value": "[[-12, -1], [-12, 0], [-12, 13], [12, -1], [12, 0], [12, 13]]",
    "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": 13,
      "original_line_sha256": "32bbef8c54d7fc33ed92389defd62e8850d315690e4c291fd60c7a0dbfe1648d",
      "question_compact_sha256": "34e173942ce5577ae4b12b4b07d6e81663feec4fbdd31efa728aac543989ee35",
      "english_row_compact_sha256": "85cb88c46d23d4f75289a760c46cf0b62e5cf7d8870cc5bdc2c19ced6b2ac853",
      "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": "d10119c1a1ece865116d4231f4624eed4cf307cd2a33927684555d505150e4be",
    "original_candidate_line_sha256": "d10119c1a1ece865116d4231f4624eed4cf307cd2a33927684555d505150e4be"
  },
  "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": 8,
    "method": "family_template_semantic_review_plus_independent_per_instance_reconstruction",
    "exact_question_first_check": {
      "model_sha256": "1c56588bbe11462036f517d7bc997771d9994a159881a8e7f45033cc4b47dd30",
      "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."
  }
}