{ "schema_version": "ocme-reviewed-question-reader-v1", "question_id": "q-20261013-advance-20261018-r07-lean-formal-statement-0049", "pilot_number": "R0016-08899", "number": 8899, "family_id": "qf-ext18-formal-context-inventory", "title": { "zh-Hant": "第 8899 題：形式陳述pipeline狀態", "en": "Question 8899: Synthetic Required and Available Context Names" }, "original_question": { "schema_version": "ocme-question-v0.1", "id": "q-20261013-advance-20261018-r07-lean-formal-statement-0049", "batch_id": "batch-20261013-advance-20261018-r07-lean-formal-statement-foundations", "language": "zh-Hant", "source_mko_ids": [ "mko-lean-formal-statement" ], "title_zh": "形式陳述pipeline狀態", "stem_zh": "合成pipeline receipt。操作=formal-context-inventory；資料={\"environment_id\":\"env-23\",\"required_names\":[\"Nat\",\"x23\"],\"available_names\":[\"Nat\",\"x23\",\"h\"]}。請依 [environment,required,available,missing,complete] 的欄序回答。", "answer": { "kind": "expression", "value": "(env-23, [Nat, x23], [h, Nat, x23], [], 是)", "explanation_zh": "擴展基礎核對=(env-23, [Nat, x23], [h, Nat, x23], [], 是)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；合成receipt不是Lean執行；陳述與證明分離；本輪未跑Lean build。" }, "difficulty": { "band": "undergraduate_core", "level": 3, "skills": [ "形式陳述pipeline狀態" ] }, "variant": { "family_id": "qf-ext18-formal-context-inventory", "seed": 202610187049, "parameters": { "environment_id": "env-23", "required_names": [ "Nat", "x23" ], "available_names": [ "Nat", "x23", "h" ], "domain": "Synthetic_formal_statement_receipt", "operation": "formal-context-inventory", "semantic_template": "qf-ext18-formal-context-inventory/{\"available_names\":[\"h\",\"Nat\",\"x23\"],\"environment_id\":\"env-23\",\"required_names\":[\"Nat\",\"x23\"]}" } }, "verification": { "status": "candidate", "checks": [ "producer_exact_finite_arithmetic", "producer_source_snapshot_check", "producer_substantive_template_deduplication", "producer_json_schema" ], "warning_zh": "僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。" }, "provenance": { "generator_role": "question_producer", "generator_model": "model_unknown", "generated_at": "2026-10-13", "contract_version": "ocme-question-factory-v0.1" } }, "original_english_edition": { "schema_version": "ocme-question-localization-v0.1", "question_id": "q-20261013-advance-20261018-r07-lean-formal-statement-0049", "batch_id": "batch-20261013-advance-20261018-r07-lean-formal-statement-foundations", "locale": "en", "translation_state": "ai_candidate", "source": { "question_sha256": "cf17b62deb9026bda55d077b2c6c0ee946a15f9901a984592e5d2e7a3b8219d8", "family_id": "qf-ext18-formal-context-inventory", "seed": 202610187049, "semantic_template": "qf-ext18-formal-context-inventory/{\"available_names\":[\"h\",\"Nat\",\"x23\"],\"environment_id\":\"env-23\",\"required_names\":[\"Nat\",\"x23\"]}" }, "fields": { "title": "Synthetic Required and Available Context Names", "stem": "These are synthetic pipeline receipts, not actual Lean elaboration or kernel checks. The Chinese source pulse did not run Lean builds for these records. A formal statement and a checked proof are distinct states. environment_id=\"env-23\", required_names=[\"Nat\",\"x23\"], available_names=[\"Nat\",\"x23\",\"h\"]. Give (environment ID, sorted distinct required names, sorted distinct available names, missing required names, complete?). Use the specified English-locale name order and retain opaque names exactly.", "answer": { "kind": "expression", "value": "(env-23, [Nat, x23], [h, Nat, x23], [], Yes)", "explanation": "Compare explicit name inventories only; this is not an actual Lean name-resolution or elaboration run. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (env-23, [Nat, x23], [h, Nat, x23], [], Yes)." }, "skills": [ "Synthetic Required and Available Context Names" ], "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": "合成pipeline receipt。操作=formal-context-inventory；資料={\"environment_id\":\"env-23\",\"required_names\":[\"Nat\",\"x23\"],\"available_names\":[\"Nat\",\"x23\",\"h\"]}。請依 [environment,required,available,missing,complete] 的欄序回答。", "en": "These are synthetic pipeline receipts, not actual Lean elaboration or kernel checks. The Chinese source pulse did not run Lean builds for these records. A formal statement and a checked proof are distinct states. environment_id=\"env-23\", required_names=[\"Nat\",\"x23\"], available_names=[\"Nat\",\"x23\",\"h\"]. Give (environment ID, sorted distinct required names, sorted distinct available names, missing required names, complete?). Use the specified English-locale name order and retain opaque names exactly." } } ], "steps": [ { "id": "S001", "uses": [ "G001" ], "before": "all pipeline flags,names and receipt fields are synthetic input data", "after": "no actual Lean run,digest verification,name resolution or kernel acceptance is claimed", "relation": "implies", "rule_id": "synthetic_formal_receipt_not_execution", "conditions": [], "explanation": { "zh-Hant": "這些是題目給定的合成receipt，不是本輪執行Lean。字串欄位、旗標一致或metadata完整，均不等於真實elaboration、雜湊對檔案驗證或kernel接受；教學候選的正式狀態仍未形式化。", "en": "These are supplied synthetic receipts,not a Lean run.String fields,coherent flags or complete metadata do not establish actual elaboration,file-digest verification or kernel acceptance.The teaching candidate remains not formalized." }, "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": "environment=env-23;raw required=[Nat, x23];raw available=[Nat, x23, h]", "after": "English-locale distinct required=[Nat, x23];available=[h, Nat, x23]", "relation": "implies", "rule_id": "formal_opaque_context_name_normalization", "conditions": [], "explanation": { "zh-Hant": "只按指定English排序去重，保留每個不透明名稱的字元與大小寫；不翻譯名稱、不解析其含義。", "en": "Deduplicate and sort in the specified English locale while preserving every opaque name's characters and case.Names are neither translated nor semantically resolved." }, "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": "required opaque name=Nat;available names=[h, Nat, x23]", "after": "present=是", "relation": "implies", "rule_id": "formal_declared_name_membership", "conditions": [], "explanation": { "zh-Hant": "只比完整名稱是否出現在明示清單；相似拼字、前綴或某套件可能存在都不代替此成員測試。", "en": "Test complete-name membership in the declared inventory.Similar spelling,prefixes or a package's possible availability do not replace this membership test." }, "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": "required opaque name=x23;available names=[h, Nat, x23]", "after": "present=是", "relation": "implies", "rule_id": "formal_declared_name_membership", "conditions": [], "explanation": { "zh-Hant": "只比完整名稱是否出現在明示清單；相似拼字、前綴或某套件可能存在都不代替此成員測試。", "en": "Test complete-name membership in the declared inventory.Similar spelling,prefixes or a package's possible availability do not replace this membership test." }, "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": "missing required names=[]", "after": "declared inventory complete=是", "relation": "implies", "rule_id": "formal_context_inventory_not_resolution", "conditions": [], "explanation": { "zh-Hant": "缺名為空只表示這兩份合成清單涵蓋，不表示真實Lean環境可解析或證明該名稱。", "en": "An empty missing-name list means only that these synthetic inventories cover the requirements.It does not establish real Lean resolution or a proof." }, "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": [ "env-23", [ "Nat", "x23" ], [ "h", "Nat", "x23" ], [], true ] }, "conclusion": { "canonical_value": "(env-23, [Nat, x23], [h, Nat, x23], [], 是)", "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-20261013-advance-20261018-r07-lean-formal-statement-foundations", "batch_path": "public/data/questions/batches/batch-20261013-advance-20261018-r07-lean-formal-statement-foundations/questions.jsonl", "batch_sha256": "84956b176bb31e86c2f2d49615d81b8e7836b4a3e5cf77ee78e49ec0ad3c7475", "original_line": 49, "original_line_sha256": "1322bbe617d4827a8217b8c194c8d7ec37d423c14b67cbc59f84bb49121e685f", "question_compact_sha256": "cf17b62deb9026bda55d077b2c6c0ee946a15f9901a984592e5d2e7a3b8219d8", "english_row_compact_sha256": "52160653ae3df408ad9a42641dd16fcbffea9def1e4de1af598153b471c78555", "english_manifest_path": "public/data/i18n/editions/batch-20261013-advance-20261018-r07-lean-formal-statement-foundations.en.json", "english_rows_path": "public/data/i18n/questions/batch-20261013-advance-20261018-r07-lean-formal-statement-foundations.en.jsonl" }, "mko_bindings": { "mko-lean-formal-statement": { "sha256": "b60e51a622407c4c4ee426df9c55830652f67ff5e0a8344c040c14f26dd49128", "english_sha256": "6789411a1961a61e6cf08b736a42a177d218afda0346550c73cd38cbc89b71df", "original_path": "public/data/mko/lean-formal-statement.json", "english_path": "public/data/i18n/editions/mko-lean-formal-statement.en.json" } }, "selected_manifest_sha256": "5233edba9654a6cffd8b6b2d83c932f82ded15f9c0b7c733bd049943e672acff", "selected_part_sha256": "8e8954cf690c44da1ec1efa08994a485c73ca8706b7865d854e3f2cdfd4ca89f", "original_candidate_sha256": "fcf32e252eac7903d4f71b20377402f55adb38f95c276c1dd1b554193e762574", "original_candidate_line_sha256": "fcf32e252eac7903d4f71b20377402f55adb38f95c276c1dd1b554193e762574" }, "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-p17", "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": "00fcddb10a9fb0f56697308976a52e68e2537472bd8e68ecbe96d3c4553f4ad2", "question_first_witness_sha256": "198e04380b2d32aef2375b07ca0df1f8afa454d1184993173fad8a3c9187a3d1" }, "status": "second_context_reviewed", "mathematical_semantics": true, "bilingual_semantics": true, "steps_reviewed": 5, "method": "family_template_semantic_review_plus_independent_per_instance_reconstruction", "exact_question_first_check": { "model_sha256": "71066f065cc08d790ed01c037c2577ca49e1e3caf8ad6f74c6b5ef9c73273d44", "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." } }