{
  "schema_version": "ocme-reviewed-question-reader-v1",
  "question_id": "q-20261014-advance-20261107-r07-subsequence-0011",
  "pilot_number": "R0039-20486",
  "number": 20486,
  "family_id": "qf-mod38-subseq-index-certificate",
  "title": {
    "zh-Hant": "第 20486 題：子數列",
    "en": "Question 20486: A Positive Affine Index Step Gives Strict Increase for Every Natural Index"
  },
  "original_question": {
    "schema_version": "ocme-question-v0.1",
    "id": "q-20261014-advance-20261107-r07-subsequence-0011",
    "batch_id": "batch-20261014-advance-20261107-r07-subsequence-foundations",
    "language": "zh-Hant",
    "source_mko_ids": [
      "mko-subsequence"
    ],
    "title_zh": "子數列",
    "stem_zh": "自然數索引與symbolic嚴格遞增證書。操作=subseq-index-certificate；資料={\"index_start\":10,\"index_step\":1}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。",
    "answer": {
      "kind": "expression",
      "value": "(10, 1, k(j)=10+1j, 是, strictly_increasing_for_all_natural_j)",
      "explanation_zh": "Wave6根層核對=(10, 1, k(j)=10+1j, 是, strictly_increasing_for_all_natural_j)；依完整明示資料獨立重算；subsequence索引必須嚴格遞增並保留原數列次序，不是重排或任意子集合；有限索引列表只證finite prefix；無限subsequence需要通用increasing-index certificate。"
    },
    "difficulty": {
      "band": "undergraduate_core",
      "level": 2,
      "skills": [
        "子數列"
      ]
    },
    "variant": {
      "family_id": "qf-mod38-subseq-index-certificate",
      "seed": 202611077011,
      "parameters": {
        "index_start": 10,
        "index_step": 1,
        "domain": "Symbolic_affine_subsequence_index",
        "operation": "subseq-index-certificate",
        "semantic_template": "qf-mod38-subseq-index-certificate/{\"index_start\":10,\"index_step\":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；不構成人工審定、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、Lean或Evidence。"
    },
    "provenance": {
      "generator_role": "question_producer",
      "generator_model": "model_unknown",
      "generated_at": "2026-10-14",
      "contract_version": "ocme-question-factory-v0.1"
    }
  },
  "original_english_edition": {
    "schema_version": "ocme-question-localization-v0.1",
    "question_id": "q-20261014-advance-20261107-r07-subsequence-0011",
    "batch_id": "batch-20261014-advance-20261107-r07-subsequence-foundations",
    "locale": "en",
    "translation_state": "ai_candidate",
    "source": {
      "question_sha256": "bf5b3a3577ba7a36be43471917771ca9b3aa9628e585991972e5a3e41d481b20",
      "family_id": "qf-mod38-subseq-index-certificate",
      "seed": 202611077011,
      "semantic_template": "qf-mod38-subseq-index-certificate/{\"index_start\":10,\"index_step\":1}"
    },
    "fields": {
      "title": "A Positive Affine Index Step Gives Strict Increase for Every Natural Index",
      "stem": "Use k(j)=index_start+index_step*j on natural j starting at0, with index_start=10≥0 and positive integer index_step=1. Give (index_start, index_step, index_formula, strictly_increasing, certificate).",
      "answer": {
        "kind": "expression",
        "value": "(10, 1, k(j)=10+1j, Yes, strictly_increasing_for_all_natural_j)",
        "explanation": "The consecutive index difference is the positive step for every j, supplying a symbolic all-j certificate. Strict increase preserves source order and is stronger than arbitrary injectivity. Retain the source literal index formula. The exact result, retaining the requested order, is (10, 1, k(j)=10+1j, Yes, strictly_increasing_for_all_natural_j)."
      },
      "skills": [
        "A Positive Affine Index Step Gives Strict Increase for Every Natural Index"
      ],
      "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": "自然數索引與symbolic嚴格遞增證書。操作=subseq-index-certificate；資料={\"index_start\":10,\"index_step\":1}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。",
        "en": "Use k(j)=index_start+index_step*j on natural j starting at0, with index_start=10≥0 and positive integer index_step=1. Give (index_start, index_step, index_formula, strictly_increasing, certificate)."
      }
    }
  ],
  "steps": [
    {
      "id": "S001",
      "uses": [
        "G001"
      ],
      "before": "source operation=subseq-index-certificate;original snapshot and mathematics retained",
      "after": "explicit ordered source output fields=[index_start, index_step, index_formula, strictly_increasing, certificate]",
      "relation": "implies",
      "rule_id": "source_ordered_interface_explicit_without_javascript",
      "conditions": [],
      "explanation": {
        "zh-Hant": "原題快照保留歷史介面標記；本頁直接列來源欄位順序，不需JavaScript或外部表。欄位標籤不是額外數學證據，No保持原題的聲稱範圍。",
        "en": "Retain the historical interface marker in the original snapshot while listing ordered source fields here,without JavaScript or external lookup.Field labels are not additional mathematical evidence,and No retains the source claim scope."
      },
      "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 subsequence index k:ORIGINAL nonnegative start=10;positive integer step=1;F(q)=start+step*q for EVERY natural q>=0",
      "after": "F(q)>=start>=0 and for ANY q<r,F(r)-F(q)=(1)*(r-q)>0;strictly increasing on ALL naturals,not just the evaluated prefix",
      "relation": "implies",
      "rule_id": "subseq_affine_all_natural_index_order_not_value_monotonicity",
      "conditions": [],
      "explanation": {
        "zh-Hant": "正整數step讓任意兩個自然索引的差都保持正，故保原順序，不只是單射或任意重排。此全稱數學law不以某個數值輸出安全範圍截斷，也不宣稱原數列的值遞增。",
        "en": "A positive integer step preserves the order of every pair of natural indices,not merely injectivity or an arbitrary reordering.This universal mathematical law is not truncated by an evaluated-output safety range and says nothing about monotonicity of source values."
      },
      "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": [
      10,
      1,
      "k(j)=10+1j",
      true,
      "strictly_increasing_for_all_natural_j"
    ]
  },
  "conclusion": {
    "canonical_value": "(10, 1, k(j)=10+1j, 是, strictly_increasing_for_all_natural_j)",
    "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-20261014-advance-20261107-r07-subsequence-foundations",
      "batch_path": "public/data/questions/batches/batch-20261014-advance-20261107-r07-subsequence-foundations/questions.jsonl",
      "batch_sha256": "9ba8fa0ce8414b0f93d4e18a0af4fe49e8c59529895aa0a7d8920db4ef56b98f",
      "original_line": 11,
      "original_line_sha256": "2b5e544ca8f1169a33b7475933f7458da54e6acd3654fa229edecfb4ded6f211",
      "question_compact_sha256": "bf5b3a3577ba7a36be43471917771ca9b3aa9628e585991972e5a3e41d481b20",
      "english_row_compact_sha256": "ebdb109147f3b54579bba913204410f8b6f9951766fbe2f7fee0969a303e265c",
      "english_manifest_path": "public/data/i18n/editions/batch-20261014-advance-20261107-r07-subsequence-foundations.en.json",
      "english_rows_path": "public/data/i18n/questions/batch-20261014-advance-20261107-r07-subsequence-foundations.en.jsonl"
    },
    "mko_bindings": {
      "mko-subsequence": {
        "sha256": "f4791c70590c6e099961027b14a591894bd691565f6e1bc8cd191792d0e2a44f",
        "english_sha256": "e54379f1fd9f6ccb9ef4be2d69a165c97d4e793ec8b2ecf051c61d8e2163b155",
        "original_path": "public/data/mko/source13-20261018-subsequence.json",
        "english_path": "public/data/i18n/editions/mko-subsequence.en.json"
      }
    },
    "selected_manifest_sha256": "5233edba9654a6cffd8b6b2d83c932f82ded15f9c0b7c733bd049943e672acff",
    "selected_part_sha256": "521929dfe9b0919224c38312ad78e5fa56457fc886faaa12b137edd83962251e",
    "original_candidate_sha256": "6ee827b1b06178b47cd8b7c694f1d92faeb3af78ae71e7c0d502d187c4b140ab",
    "original_candidate_line_sha256": "6ee827b1b06178b47cd8b7c694f1d92faeb3af78ae71e7c0d502d187c4b140ab"
  },
  "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-20261026-008-p40",
    "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": "6e11e35fafe32f16900ce9b522d01acb7b2ee6b463ab179392076cfbe1af8034",
      "question_first_witness_sha256": "cc0fa361fc25151729e70264340d2eae94f179f6f2a2edfe80ba5704fbbd0682"
    },
    "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": "3015970529686e24b8aa0aa1f63ceb02b5f6c6c3ca7213703a9ee55d2698ecd5",
      "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."
  }
}