{
  "schema_version": "ocme-reviewed-question-reader-v1",
  "question_id": "q-20261009-advance-20261013-r02-integer-0047",
  "pilot_number": "R0011-06197",
  "number": 6197,
  "family_id": "qf-density13-integer-two-step-displacement",
  "title": {
    "zh-Hant": "第 6197 題：兩步的終點、淨移與步量",
    "en": "Question 6197: Endpoint, Net Displacement, and Step Magnitude"
  },
  "original_question": {
    "schema_version": "ocme-question-v0.1",
    "id": "q-20261009-advance-20261013-r02-integer-0047",
    "batch_id": "batch-20261009-advance-20261013-r02-integer-foundations",
    "language": "zh-Hant",
    "source_mko_ids": [
      "mko-integer"
    ],
    "title_zh": "兩步的終點、淨移與步量",
    "stem_zh": "有限整數協議；start=9，有號步s1=22、s2=-2。依序求 (終點, 淨移s1+s2, |s1|+|s2|)。",
    "answer": {
      "kind": "expression",
      "value": "(29, 20, 24)",
      "explanation_zh": "終點淨移與步量=(29, 20, 24)。終點累加有號步，步量另加絕對值；返回原點也可能有正步量，有限運算非整數環公理證明。"
    },
    "difficulty": {
      "band": "lower_secondary",
      "level": 3,
      "skills": [
        "兩步的終點、淨移與步量"
      ]
    },
    "variant": {
      "family_id": "qf-density13-integer-two-step-displacement",
      "seed": 202610132047,
      "parameters": {
        "start": 9,
        "s1": 22,
        "s2": -2,
        "operation": "density13_integer_two_step_displacement",
        "domain": "finite_integer_arithmetic_protocol",
        "semantic_template": "qf-density13-integer-two-step-displacement/[9,\"20\",\"24\"]"
      }
    },
    "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": "2026-10-09",
      "contract_version": "ocme-question-factory-v0.1"
    }
  },
  "original_english_edition": {
    "schema_version": "ocme-question-localization-v0.1",
    "question_id": "q-20261009-advance-20261013-r02-integer-0047",
    "batch_id": "batch-20261009-advance-20261013-r02-integer-foundations",
    "locale": "en",
    "translation_state": "ai_candidate",
    "source": {
      "question_sha256": "21344a05f04e0e9b588550f31745b412a3bdea935e81327c5bda20cbd7d87e2c",
      "family_id": "qf-density13-integer-two-step-displacement",
      "seed": 202610132047,
      "semantic_template": "qf-density13-integer-two-step-displacement/[9,\"20\",\"24\"]"
    },
    "fields": {
      "title": "Endpoint, Net Displacement, and Step Magnitude",
      "stem": "Integer start=9, signed steps s1=22, s2=-2. Give (endpoint, s1+s2, |s1|+|s2|).",
      "answer": {
        "kind": "expression",
        "value": "(29, 20, 24)",
        "explanation": "Add signed steps for displacement and endpoint, but add their absolute values for step magnitude; returning to the start can still have positive step magnitude. The exact result, retaining the requested order, is (29, 20, 24)."
      },
      "skills": [
        "Endpoint, Net Displacement, and Step Magnitude"
      ],
      "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": "有限整數協議；start=9，有號步s1=22、s2=-2。依序求 (終點, 淨移s1+s2, |s1|+|s2|)。",
        "en": "Integer start=9, signed steps s1=22, s2=-2. Give (endpoint, s1+s2, |s1|+|s2|)."
      }
    }
  ],
  "steps": [
    {
      "id": "S001",
      "uses": [
        "G001"
      ],
      "before": "declared exact integer or rational-representation protocol",
      "after": "retain signs,ordered operands and original index order",
      "relation": "implies",
      "rule_id": "integer_arithmetic_scope",
      "conditions": [],
      "explanation": {
        "zh-Hant": "用精確整數運算核對此有限資料，不取浮點近似，也不把有限計算升為全部整數環公理證明。",
        "en": "Check these finite data with exact integer arithmetic,without floating approximations or a claim to prove all integer-ring axioms."
      },
      "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": "signed net displacement := sum(22, -2)",
      "after": "signed net displacement = 20",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "先把兩個有號步相加得淨移。",
        "en": "Add the two signed steps to obtain net displacement."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 signed net displacement，不以小數近似替代。",
          "en": "Recompute signed net displacement with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "sum",
        "inputs": [
          "22",
          "-2"
        ],
        "output": "20",
        "label": "signed net displacement"
      }
    },
    {
      "id": "S003",
      "uses": [
        "G001",
        "S002"
      ],
      "before": "final position := sum(9, 20)",
      "after": "final position = 29",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "起點加淨移才是終點，淨移本身不是絕對位置。",
        "en": "Add net displacement to the start to obtain the endpoint;net displacement alone is not an absolute position."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 final position，不以小數近似替代。",
          "en": "Recompute final position with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "sum",
        "inputs": [
          "9",
          "20"
        ],
        "output": "29",
        "label": "final position"
      }
    },
    {
      "id": "S004",
      "uses": [
        "G001",
        "S003"
      ],
      "before": "steps=(22,-2)",
      "after": "absolute step lengths=(22,2)",
      "relation": "implies",
      "rule_id": "signed_step_vs_length",
      "conditions": [],
      "explanation": {
        "zh-Hant": "方向由步的符號表達，步量另用各自絕對值，不能先相消再取絕對值。",
        "en": "Step signs encode direction;path length uses each step's absolute value.Do not cancel first and then take an absolute value."
      },
      "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": "sum of step lengths := sum(22, 2)",
      "after": "sum of step lengths = 24",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "兩步步量相加；返回起點仍可能有正步量。",
        "en": "Add both step lengths;returning to the start may still involve positive travel."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 sum of step lengths，不以小數近似替代。",
          "en": "Recompute sum of step lengths with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "sum",
        "inputs": [
          "22",
          "2"
        ],
        "output": "24",
        "label": "sum of step lengths"
      }
    }
  ],
  "math_model": {
    "result": [
      "29",
      "20",
      "24"
    ]
  },
  "conclusion": {
    "canonical_value": "(29, 20, 24)",
    "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": {
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      "batch_sha256": "fe7ab53bd896704506979e7b4bde27359c6a58a2382c94c9e728ab4500a3982d",
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      "question_compact_sha256": "21344a05f04e0e9b588550f31745b412a3bdea935e81327c5bda20cbd7d87e2c",
      "english_row_compact_sha256": "b74747842aa85d62ae72e77aa880d5eecc220e29125bdc8f9031f29185b46a30",
      "english_manifest_path": "public/data/i18n/editions/batch-20261009-advance-20261013-r02-integer-foundations.en.json",
      "english_rows_path": "public/data/i18n/questions/batch-20261009-advance-20261013-r02-integer-foundations.en.jsonl"
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        "original_path": "public/data/mko/integer.json",
        "english_path": "public/data/i18n/editions/mko-integer.en.json"
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    },
    "selected_manifest_sha256": "5233edba9654a6cffd8b6b2d83c932f82ded15f9c0b7c733bd049943e672acff",
    "selected_part_sha256": "5b2ce631281eb24b279908f47c6de66fa60d326520852879d324c4f3ac653970",
    "original_candidate_sha256": "cfc3fefea73d9c2651caf6a4cec803601224d0f2d3084d064bd9e11c3f407b44",
    "original_candidate_line_sha256": "cfc3fefea73d9c2651caf6a4cec803601224d0f2d3084d064bd9e11c3f407b44"
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  "historical_source_state": {
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      "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-20261026-005-p12",
    "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": {
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    "bilingual_semantics": true,
    "steps_reviewed": 5,
    "method": "family_template_semantic_review_plus_independent_per_instance_reconstruction",
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    "formalization": "not_formalized",
    "Lean": "NOT_RUN",
    "Canonical_truth_promotion": false,
    "authority": "Owner-authorized reviewed reader publication; original question/candidate states remain historical and unchanged."
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}