{ "schema_version": "ocme-reviewed-question-reader-v1", "question_id": "q-20261011-advance-20261015-r05-sequence-0075", "pilot_number": "R0013-07175", "number": 7175, "family_id": "qf-density15-sequence-two-finite-extensions", "title": { "zh-Hant": "第 7175 題：同前綴的兩個候選延伸", "en": "Question 7175: Two Fifth-Term Extensions of a Given Four-Term Prefix" }, "original_question": { "schema_version": "ocme-question-v0.1", "id": "q-20261011-advance-20261015-r05-sequence-0075", "batch_id": "batch-20261011-advance-20261015-r05-sequence-foundations", "language": "zh-Hant", "source_mko_ids": [ "mko-sequence" ], "title_zh": "同前綴的兩個候選延伸", "stem_zh": "N從0起，明示有限索引。已給原序四項prefix=[12, 0, 12, 1]，兩個候選nexts=[24, -23]。只附加各自第五項，求 (第一五項列, 第二五項列, 前四項相同資格, 第五項相同資格)。未指定通項。", "answer": { "kind": "expression", "value": "([12, 0, 12, 1, 24], [12, 0, 12, 1, -23], 是, 否)", "explanation_zh": "兩個有限延伸與同前綴=([12, 0, 12, 1, 24], [12, 0, 12, 1, -23], 是, 否)。各附加一個候選後核對，不從前四項補出唯一規則。相同候選不當不同延伸。數列次序與重複保留，有限前綴不推定唯一無限規則。" }, "difficulty": { "band": "upper_secondary", "level": 3, "skills": [ "同前綴的兩個候選延伸" ] }, "variant": { "family_id": "qf-density15-sequence-two-finite-extensions", "seed": 202610155075, "parameters": { "prefix": [ 12, 0, 12, 1 ], "nexts": [ 24, -23 ], "domain": "finite_zero_based_sequence_protocol", "operation": "density15_sequence_two_finite_extensions", "semantic_template": "qf-density15-sequence-two-finite-extensions/[[12,0,12,1],[24,-23]]" } }, "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": "2026-10-11", "contract_version": "ocme-question-factory-v0.1" } }, "original_english_edition": { "schema_version": "ocme-question-localization-v0.1", "question_id": "q-20261011-advance-20261015-r05-sequence-0075", "batch_id": "batch-20261011-advance-20261015-r05-sequence-foundations", "locale": "en", "translation_state": "ai_candidate", "source": { "question_sha256": "facf912f5f3f645e89af4e06d3e568e5e0c62fa3f2695c06831684c34d34de91", "family_id": "qf-density15-sequence-two-finite-extensions", "seed": 202610155075, "semantic_template": "qf-density15-sequence-two-finite-extensions/[[12,0,12,1],[24,-23]]" }, "fields": { "title": "Two Fifth-Term Extensions of a Given Four-Term Prefix", "stem": "N begins at 0; retain sequence order and repeated values. A finite prefix does not determine a unique infinite rule, convergence, or infinite series. Given ordered prefix=[12, 0, 12, 1] and candidate nexts=[24, -23]. Append each candidate separately and give (first five-term list, second five-term list, are the first four terms equal?, are the fifth terms equal?). No general rule is specified.", "answer": { "kind": "expression", "value": "([12, 0, 12, 1, 24], [12, 0, 12, 1, -23], Yes, No)", "explanation": "Append the declared candidate values without inventing a unique continuation rule; equal candidates are not different extensions. The exact result, retaining the requested order, is ([12, 0, 12, 1, 24], [12, 0, 12, 1, -23], Yes, No)." }, "skills": [ "Two Fifth-Term Extensions of a Given Four-Term Prefix" ], "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": "N從0起，明示有限索引。已給原序四項prefix=[12, 0, 12, 1]，兩個候選nexts=[24, -23]。只附加各自第五項，求 (第一五項列, 第二五項列, 前四項相同資格, 第五項相同資格)。未指定通項。", "en": "N begins at 0; retain sequence order and repeated values. A finite prefix does not determine a unique infinite rule, convergence, or infinite series. Given ordered prefix=[12, 0, 12, 1] and candidate nexts=[24, -23]. Append each candidate separately and give (first five-term list, second five-term list, are the first four terms equal?, are the fifth terms equal?). No general rule is specified." } } ], "steps": [ { "id": "S001", "uses": [ "G001" ], "before": "N starts at0;ordered finite indices and repeated values retained", "after": "given recurrences differ from guessing an infinite rule from observations", "relation": "implies", "rule_id": "finite_ordered_sequence_scope", "conditions": [], "explanation": { "zh-Hant": "數列有序且可重複，有限前綴本身不能決定唯一無限規則；若題目另明示遞推，則只依該規則推導，不擅自補規則。", "en": "Sequences are ordered and may repeat.A finite observed prefix alone does not determine a unique infinite rule;when a recurrence is explicitly supplied,use that rule rather than inventing one." }, "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 prefix=[12, 0, 12, 1];candidate next=24", "after": "[12, 0, 12, 1, 24]", "relation": "implies", "rule_id": "first_given_sequence_extension", "conditions": [], "explanation": { "zh-Hant": "第一候選只附加自己的第五項，原前綴不變。", "en": "The first candidate appends only its own fifth term,leaving the original prefix unchanged." }, "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": "original prefix=[12, 0, 12, 1];candidate next=-23", "after": "[12, 0, 12, 1, -23]", "relation": "implies", "rule_id": "second_given_sequence_extension", "conditions": [], "explanation": { "zh-Hant": "第二候選重新從原前綴附加，不在第一候選之後繼續加。", "en": "The second candidate appends afresh to the original prefix,not to the first candidate." }, "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": "same prefix=是;nexts=(24,-23)", "after": "same fifth term=否", "relation": "implies", "rule_id": "finite_extensions_not_unique_rule", "conditions": [], "explanation": { "zh-Hant": "同前綴可有不同候選後項，不能由前四項選出唯一；兩個候選相同時，也不能稱為兩個不同延伸。", "en": "The same prefix may have different proposed next terms,so the first four do not select a unique one.If the candidates coincide,do not call them distinct extensions." }, "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, 0, 12, 1, 24 ], [ 12, 0, 12, 1, -23 ], true, false ] }, "conclusion": { "canonical_value": "([12, 0, 12, 1, 24], [12, 0, 12, 1, -23], 是, 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-20261011-advance-20261015-r05-sequence-foundations", "batch_path": "public/data/questions/batches/batch-20261011-advance-20261015-r05-sequence-foundations/questions.jsonl", "batch_sha256": "e8a28d58ec052ac711318299c789c1b43033dbf1739c5b39fa88b9544e87f61b", "original_line": 75, "original_line_sha256": "b98846b0d7069bc217d8c31a542de65445faa421c9821f4fa026a223f0432559", "question_compact_sha256": "facf912f5f3f645e89af4e06d3e568e5e0c62fa3f2695c06831684c34d34de91", "english_row_compact_sha256": "0aa24e8810fb31ad94c3a6ec976810289db180680566ba2828ea3c901a81842e", "english_manifest_path": "public/data/i18n/editions/batch-20261011-advance-20261015-r05-sequence-foundations.en.json", "english_rows_path": "public/data/i18n/questions/batch-20261011-advance-20261015-r05-sequence-foundations.en.jsonl" }, "mko_bindings": { "mko-sequence": { "sha256": "61e652778c86fb6151fba32a0e61c914e4f99a1c496dd1c3d933c1f9297782f7", "english_sha256": "24722e5fa3e44eb82dbc3fccbd220761d9b4aa84bdf79ad9d04bad0d83621dde", "original_path": "public/data/mko/sequence.json", "english_path": "public/data/i18n/editions/mko-sequence.en.json" } }, "selected_manifest_sha256": "5233edba9654a6cffd8b6b2d83c932f82ded15f9c0b7c733bd049943e672acff", "selected_part_sha256": "944e5a6e7ddc77eb28f9280c1b90da6c7083069b4790cbeb7488d009328efce8", "original_candidate_sha256": "9b94be75b9c94819fdff180d9832f64bc3ca9ddb61dea597b2303a4e6f551105", "original_candidate_line_sha256": "9b94be75b9c94819fdff180d9832f64bc3ca9ddb61dea597b2303a4e6f551105", "mko_binding_revision": { "id": "edition-symbol-bindings-20261101", "path": "content/edition-symbol-bindings-20261101/revision.json", "sha256": "e9b4c69f2c4732074c37abb624c8ab8a70afc3645c12bf9df2268ef650ad7b6c", "previous_english_sha256": { "mko-sequence": "73ebcb30e2878e2fcb357eb7ed8f9eb08672f5b078965a636df48b982cf49fa3" } } }, "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-20261026-005-p14", "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": "e89fc6d4a50a4a7fc942c6c8939a92f835e30105a9a5850e37dd198f31c1ed59", "question_first_witness_sha256": "0e1039f4cf022bf35af4e5531651c9a2b7ca7a5fdacac34fb1e4bcd9a81f6299" }, "status": "second_context_reviewed", "mathematical_semantics": true, "bilingual_semantics": true, "steps_reviewed": 4, "method": "family_template_semantic_review_plus_independent_per_instance_reconstruction", "exact_question_first_check": { "model_sha256": "a0c9e5162196e7047aea99f842860afec0138b87c2586222edc04ebbef04285d", "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." } }