{
  "schema_version": "ocme-reviewed-question-reader-v1",
  "question_id": "q-20261015-advance-20261117-r01-series-comparison-test-0083",
  "pilot_number": "R0052-26908",
  "number": 26908,
  "family_id": "qf-mod48-series-comparison-boundary",
  "title": {
    "zh-Hant": "第 26908 題：級數比較判別法",
    "en": "Question 26908: Comparison Direction, Nonnegativity and Reference Status Cannot Be Omitted"
  },
  "original_question": {
    "schema_version": "ocme-question-v0.1",
    "id": "q-20261015-advance-20261117-r01-series-comparison-test-0083",
    "batch_id": "batch-20261015-advance-20261117-r01-series-comparison-test-foundations",
    "language": "zh-Hant",
    "source_mko_ids": [
      "mko-series-comparison-test"
    ],
    "title_zh": "級數比較判別法",
    "stem_zh": "非負項、eventual forall比較方向與reference series狀態責任。操作=series-comparison-boundary；資料={\"mode\":\"unknown_reference\",\"scale\":8}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。",
    "answer": {
      "kind": "expression",
      "value": "(unknown_reference, 8, comparison_holds_reference_status_not_proved, 否)",
      "explanation_zh": "Wave6第十一層核對=(unknown_reference, 8, comparison_holds_reference_status_not_proved, 否)；依完整明示資料獨立重算；有限前綴不改變收斂性，但有限samples不證明eventual comparison；上界收斂與下界發散方向不得反轉；exact families不取代一般定理。"
    },
    "difficulty": {
      "band": "undergraduate_core",
      "level": 1,
      "skills": [
        "級數比較判別法"
      ]
    },
    "variant": {
      "family_id": "qf-mod48-series-comparison-boundary",
      "seed": 202611171083,
      "parameters": {
        "mode": "unknown_reference",
        "scale": 8,
        "domain": "Exact_nonnegative_series_comparison",
        "operation": "series-comparison-boundary",
        "semantic_template": "series-comparison-boundary|{mode:\"unknown_reference\",scale:[8,1]}"
      }
    },
    "verification": {
      "status": "candidate",
      "checks": [
        "producer_exact_finite_or_symbolic_model",
        "producer_source_snapshot_check",
        "producer_substantive_template_deduplication",
        "producer_json_schema"
      ],
      "warning_zh": "候選須主端重算；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。"
    },
    "provenance": {
      "generator_role": "question_producer",
      "generator_model": "model_unknown",
      "generated_at": "2026-10-15",
      "contract_version": "ocme-question-factory-v0.1"
    }
  },
  "original_english_edition": {
    "schema_version": "ocme-question-localization-v0.1",
    "question_id": "q-20261015-advance-20261117-r01-series-comparison-test-0083",
    "batch_id": "batch-20261015-advance-20261117-r01-series-comparison-test-foundations",
    "locale": "en",
    "translation_state": "ai_candidate",
    "source": {
      "question_sha256": "b1893ffa62bec72ffc0b0503f8c72e48c828d9eb3d0015b8d1e85d7f6f9cf431",
      "family_id": "qf-mod48-series-comparison-boundary",
      "seed": 202611171083,
      "semantic_template": "series-comparison-boundary|{mode:\"unknown_reference\",scale:[8,1]}"
    },
    "fields": {
      "title": "Comparison Direction, Nonnegativity and Reference Status Cannot Be Omitted",
      "stem": "Boundary mode=unknown_reference, positive scale=8. Give (mode, scale, reference_status_scope, comparison_test_claim).",
      "answer": {
        "kind": "expression",
        "value": "(unknown_reference, 8, comparison_holds_reference_status_not_proved, No)",
        "explanation": "finite_sample records insufficient eventual-forall evidence. A scaled1/n^2 series can converge below divergent scaled1/n; signed terms violate the nonnegative premise; an unproved reference status supplies no convergence certificate. Keep the distinct branch field roles, not one padded tuple. The exact result, retaining the requested order, is (unknown_reference, 8, comparison_holds_reference_status_not_proved, No)."
      },
      "skills": [
        "Comparison Direction, Nonnegativity and Reference Status Cannot Be Omitted"
      ],
      "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": "非負項、eventual forall比較方向與reference series狀態責任。操作=series-comparison-boundary；資料={\"mode\":\"unknown_reference\",\"scale\":8}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。",
        "en": "Boundary mode=unknown_reference, positive scale=8. Give (mode, scale, reference_status_scope, comparison_test_claim)."
      }
    }
  ],
  "steps": [
    {
      "id": "S001",
      "uses": [
        "G001"
      ],
      "before": "source roles = [series-comparison-boundary]",
      "after": "derived = [[mode, scale, reference_status, inference]]",
      "relation": "implies",
      "rule_id": "source_ordered_fields_without_JS",
      "conditions": [],
      "explanation": {
        "zh-Hant": "直接列出此操作及mode的完整來源欄序，不需JavaScript；布林、字串與null角色保持區別，不補欄或以答案形狀猜介面。",
        "en": "List this operation/mode exact source field order without JavaScript.Keep Boolean,string and null roles distinct;do not pad fields or infer the interface from answer shape."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "反查原題的完整資料、型別、欄序與本步條件；有限核對不升格為無限定理的形式證明。",
          "en": "Reverse-check the complete original data,types,field order and premises;finite audits are not formal proofs of infinite theorems."
        }
      },
      "arithmetic": null
    },
    {
      "id": "S002",
      "uses": [
        "G001",
        "S001"
      ],
      "before": "source roles = [unknown_reference, 8]",
      "after": "derived = [unknown_reference, 8, comparison_holds_reference_status_not_proved, 否]",
      "relation": "implies",
      "rule_id": "Series_original_comparison_boundary_scope_and_direction",
      "conditions": [],
      "explanation": {
        "zh-Hant": "finite_sample僅敘述範圍，不給完整無限見證；divergent upper無法迫小級數diverge，例如1/n²≤1/n；signed失非負前提，unknown未證reference狀態。No指此推理無效，不是任意實際收斂主張都假。",
        "en": "finite_sample is a scope statement,not a complete infinite witness.A divergent upper series cannot force a smaller one to diverge,e.g.1/n²<=1/n.Signed terms fail nonnegativity and unknown_reference lacks the reference status.No rejects this inference,not every underlying convergence claim."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "反查原題的完整資料、型別、欄序與本步條件；有限核對不升格為無限定理的形式證明。",
          "en": "Reverse-check the complete original data,types,field order and premises;finite audits are not formal proofs of infinite theorems."
        }
      },
      "arithmetic": null
    }
  ],
  "math_model": {
    "result": [
      "unknown_reference",
      "8",
      "comparison_holds_reference_status_not_proved",
      false
    ]
  },
  "conclusion": {
    "canonical_value": "(unknown_reference, 8, comparison_holds_reference_status_not_proved, 否)",
    "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-20261015-advance-20261117-r01-series-comparison-test-foundations",
      "batch_path": "public/data/questions/batches/batch-20261015-advance-20261117-r01-series-comparison-test-foundations/questions.jsonl",
      "batch_sha256": "c62071690ae3f92dd63f88f17bae18ae63a3b9197857ad9735879ab85b1a2824",
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      "original_line_sha256": "f85e6b5b19100192b8fe733a02aaef45fbae17a9982f2226dd71a390199af1bd",
      "question_compact_sha256": "b1893ffa62bec72ffc0b0503f8c72e48c828d9eb3d0015b8d1e85d7f6f9cf431",
      "english_row_compact_sha256": "6957011d2bb3b87817fbfaa1bb19c53fdd05024601edc52c2ebebd286e5449e7",
      "english_manifest_path": "public/data/i18n/editions/batch-20261015-advance-20261117-r01-series-comparison-test-foundations.en.json",
      "english_rows_path": "public/data/i18n/questions/batch-20261015-advance-20261117-r01-series-comparison-test-foundations.en.jsonl"
    },
    "mko_bindings": {
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        "original_path": "public/data/mko/series-comparison-test.json",
        "english_path": "public/data/i18n/editions/mko-series-comparison-test.en.json"
      }
    },
    "selected_manifest_sha256": "5233edba9654a6cffd8b6b2d83c932f82ded15f9c0b7c733bd049943e672acff",
    "selected_part_sha256": "a3def7368821a4d3dc7757fefd3c4a099713f8de8fb8e6f3434025e9d7b5a6d0",
    "original_candidate_sha256": "c787c51bad6e63ba2ad8be046b29afa502254e2fac814b1866c87efd36ac4352",
    "original_candidate_line_sha256": "c787c51bad6e63ba2ad8be046b29afa502254e2fac814b1866c87efd36ac4352"
  },
  "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-20261026-010-p53",
    "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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      "question_first_witness_sha256": "d1ab788770eaad04f986986e65afb0d55791e8a8c0d747e9a2b499f79fe78df2"
    },
    "status": "second_context_reviewed",
    "mathematical_semantics": true,
    "bilingual_semantics": true,
    "steps_reviewed": 2,
    "method": "family_template_semantic_review_plus_independent_per_instance_reconstruction",
    "exact_question_first_check": {
      "model_sha256": "2425907e0633eb3c736957f77255d3b9411728e3d253bed847dde1bd87b01b6d",
      "arithmetic_steps": 0
    },
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    "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."
  }
}