{ "schema_version": "ocme-reviewed-question-reader-v1", "question_id": "q-20261013-advance-20261018-r07-lean-formal-statement-0086", "pilot_number": "R0016-08936", "number": 8936, "family_id": "qf-ext18-formal-receipt-completeness", "title": { "zh-Hant": "第 8936 題：形式陳述pipeline狀態", "en": "Question 8936: Synthetic Receipt Metadata Completeness, Not Proof Acceptance" }, "original_question": { "schema_version": "ocme-question-v0.1", "id": "q-20261013-advance-20261018-r07-lean-formal-statement-0086", "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-receipt-completeness；資料={\"lean_version\":\"\",\"imports\":[\"Mathlib\",\"Module10\"],\"imports_declared\":true,\"environment_id\":\"env-10\",\"context_id\":\"ctx-10\",\"source_sha256\":\"000000000000000000000000000000000000000000000000000000000000000a\",\"core_type\":\"Type\",\"elaboration_status\":\"success\"}。請依 [version,imports,declared,environment,context,source_hash_valid,core_type,status,missing,complete] 的欄序回答。", "answer": { "kind": "expression", "value": "(缺, [Mathlib, Module10], 是, env-10, ctx-10, 是, Type, success, [lean_version, core_type_Prop], 否)", "explanation_zh": "擴展基礎核對=(缺, [Mathlib, Module10], 是, env-10, ctx-10, 是, Type, success, [lean_version, core_type_Prop], 否)；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": 2, "skills": [ "形式陳述pipeline狀態" ] }, "variant": { "family_id": "qf-ext18-formal-receipt-completeness", "seed": 202610187086, "parameters": { "lean_version": "", "imports": [ "Mathlib", "Module10" ], "imports_declared": true, "environment_id": "env-10", "context_id": "ctx-10", "source_sha256": "000000000000000000000000000000000000000000000000000000000000000a", "core_type": "Type", "elaboration_status": "success", "domain": "Synthetic_formal_statement_receipt", "operation": "formal-receipt-completeness", "semantic_template": "qf-ext18-formal-receipt-completeness/{\"context_id\":\"ctx-10\",\"core_type\":\"Type\",\"elaboration_status\":\"success\",\"environment_id\":\"env-10\",\"imports\":[\"Mathlib\",\"Module10\"],\"imports_declared\":true,\"lean_version\":\"\",\"source_sha256\":\"000000000000000000000000000000000000000000000000000000000000000a\"}" } }, "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-0086", "batch_id": "batch-20261013-advance-20261018-r07-lean-formal-statement-foundations", "locale": "en", "translation_state": "ai_candidate", "source": { "question_sha256": "b354fd3f788c3301f3af80e75b30aa55687adb4b83bbb73b927425f00fc669e2", "family_id": "qf-ext18-formal-receipt-completeness", "seed": 202610187086, "semantic_template": "qf-ext18-formal-receipt-completeness/{\"context_id\":\"ctx-10\",\"core_type\":\"Type\",\"elaboration_status\":\"success\",\"environment_id\":\"env-10\",\"imports\":[\"Mathlib\",\"Module10\"],\"imports_declared\":true,\"lean_version\":\"\",\"source_sha256\":\"000000000000000000000000000000000000000000000000000000000000000a\"}" }, "fields": { "title": "Synthetic Receipt Metadata Completeness, Not Proof Acceptance", "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. Supplied metadata={\"lean_version\":\"\",\"imports\":[\"Mathlib\",\"Module10\"],\"imports_declared\":true,\"environment_id\":\"env-10\",\"context_id\":\"ctx-10\",\"source_sha256\":\"000000000000000000000000000000000000000000000000000000000000000a\",\"core_type\":\"Type\",\"elaboration_status\":\"success\"}. Give (version or missing, sorted distinct imports, imports declared?, environment or missing, context or missing, lexical lowercase 64-hex source-hash shape?, core type or missing, status or missing, missing-field reasons in protocol order, metadata complete?). Imports may be explicitly empty. Hash shape is not a verified source digest.", "answer": { "kind": "expression", "value": "(missing, [Mathlib, Module10], Yes, env-10, ctx-10, Yes, Type, success, [lean_version, core_type_Prop], No)", "explanation": "Check only the supplied lexical/presence/status conditions; complete synthetic metadata is not an actual Lean elaboration or kernel-proof receipt. Exact finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (missing, [Mathlib, Module10], Yes, env-10, ctx-10, Yes, Type, success, [lean_version, core_type_Prop], No)." }, "skills": [ "Synthetic Receipt Metadata Completeness, Not Proof Acceptance" ], "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-receipt-completeness；資料={\"lean_version\":\"\",\"imports\":[\"Mathlib\",\"Module10\"],\"imports_declared\":true,\"environment_id\":\"env-10\",\"context_id\":\"ctx-10\",\"source_sha256\":\"000000000000000000000000000000000000000000000000000000000000000a\",\"core_type\":\"Type\",\"elaboration_status\":\"success\"}。請依 [version,imports,declared,environment,context,source_hash_valid,core_type,status,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. Supplied metadata={\"lean_version\":\"\",\"imports\":[\"Mathlib\",\"Module10\"],\"imports_declared\":true,\"environment_id\":\"env-10\",\"context_id\":\"ctx-10\",\"source_sha256\":\"000000000000000000000000000000000000000000000000000000000000000a\",\"core_type\":\"Type\",\"elaboration_status\":\"success\"}. Give (version or missing, sorted distinct imports, imports declared?, environment or missing, context or missing, lexical lowercase 64-hex source-hash shape?, core type or missing, status or missing, missing-field reasons in protocol order, metadata complete?). Imports may be explicitly empty. Hash shape is not a verified source digest." } } ], "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": "raw imports=[Mathlib, Module10];imports declared=是", "after": "English-locale distinct imports=[Mathlib, Module10]", "relation": "implies", "rule_id": "synthetic_import_inventory_not_actual_imports", "conditions": [], "explanation": { "zh-Hant": "imports清單按English排序去重；明示空清單可合法，是否宣告由獨立旗標決定，不啟動任何import。", "en": "Sort and deduplicate imports in the English locale.An explicitly empty list is allowed;declaration is a separate flag.No imports are actually executed." }, "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": "synthetic field=lean_version;supplied value=", "after": "lexical/presence condition=否", "relation": "implies", "rule_id": "synthetic_receipt_each_field_condition", "conditions": [], "explanation": { "zh-Hant": "依固定協定核非空、旗標、64位小寫十六進位外形、Prop及success精確字串；不是對檔案計算雜湊，也不是重新執行型別檢查。", "en": "Apply the protocol's presence,flag,64-lowercase-hex-shape and exact Prop/success tests.This does not hash a source file or rerun type checking." }, "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": "synthetic field=imports_declaration;supplied value=是", "after": "lexical/presence condition=是", "relation": "implies", "rule_id": "synthetic_receipt_each_field_condition", "conditions": [], "explanation": { "zh-Hant": "依固定協定核非空、旗標、64位小寫十六進位外形、Prop及success精確字串；不是對檔案計算雜湊，也不是重新執行型別檢查。", "en": "Apply the protocol's presence,flag,64-lowercase-hex-shape and exact Prop/success tests.This does not hash a source file or rerun type checking." }, "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": "synthetic field=environment_id;supplied value=env-10", "after": "lexical/presence condition=是", "relation": "implies", "rule_id": "synthetic_receipt_each_field_condition", "conditions": [], "explanation": { "zh-Hant": "依固定協定核非空、旗標、64位小寫十六進位外形、Prop及success精確字串；不是對檔案計算雜湊，也不是重新執行型別檢查。", "en": "Apply the protocol's presence,flag,64-lowercase-hex-shape and exact Prop/success tests.This does not hash a source file or rerun type checking." }, "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": "S006", "uses": [ "G001", "S005" ], "before": "synthetic field=context_id;supplied value=ctx-10", "after": "lexical/presence condition=是", "relation": "implies", "rule_id": "synthetic_receipt_each_field_condition", "conditions": [], "explanation": { "zh-Hant": "依固定協定核非空、旗標、64位小寫十六進位外形、Prop及success精確字串；不是對檔案計算雜湊，也不是重新執行型別檢查。", "en": "Apply the protocol's presence,flag,64-lowercase-hex-shape and exact Prop/success tests.This does not hash a source file or rerun type checking." }, "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": "S007", "uses": [ "G001", "S006" ], "before": "synthetic field=source_sha256;supplied value=000000000000000000000000000000000000000000000000000000000000000a", "after": "lexical/presence condition=是", "relation": "implies", "rule_id": "synthetic_receipt_each_field_condition", "conditions": [], "explanation": { "zh-Hant": "依固定協定核非空、旗標、64位小寫十六進位外形、Prop及success精確字串；不是對檔案計算雜湊，也不是重新執行型別檢查。", "en": "Apply the protocol's presence,flag,64-lowercase-hex-shape and exact Prop/success tests.This does not hash a source file or rerun type checking." }, "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": "S008", "uses": [ "G001", "S007" ], "before": "synthetic field=core_type_Prop;supplied value=Type", "after": "lexical/presence condition=否", "relation": "implies", "rule_id": "synthetic_receipt_each_field_condition", "conditions": [], "explanation": { "zh-Hant": "依固定協定核非空、旗標、64位小寫十六進位外形、Prop及success精確字串；不是對檔案計算雜湊，也不是重新執行型別檢查。", "en": "Apply the protocol's presence,flag,64-lowercase-hex-shape and exact Prop/success tests.This does not hash a source file or rerun type checking." }, "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": "S009", "uses": [ "G001", "S008" ], "before": "synthetic field=elaboration_success;supplied value=success", "after": "lexical/presence condition=是", "relation": "implies", "rule_id": "synthetic_receipt_each_field_condition", "conditions": [], "explanation": { "zh-Hant": "依固定協定核非空、旗標、64位小寫十六進位外形、Prop及success精確字串；不是對檔案計算雜湊，也不是重新執行型別檢查。", "en": "Apply the protocol's presence,flag,64-lowercase-hex-shape and exact Prop/success tests.This does not hash a source file or rerun type checking." }, "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": "S010", "uses": [ "G001", "S009" ], "before": "missing reasons in protocol order=[lean_version, core_type_Prop]", "after": "synthetic metadata complete=否", "relation": "implies", "rule_id": "synthetic_metadata_complete_not_proof", "conditions": [], "explanation": { "zh-Hant": "缺欄理由維持協定順序。完整metadata不保證其內容真實、環境存在、陳述已證或kernel執行成功。", "en": "Keep missing reasons in protocol order.Complete metadata guarantees neither truthful contents,an existing environment,a proved statement nor a successful kernel execution." }, "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": [ "缺", [ "Mathlib", "Module10" ], true, "env-10", "ctx-10", true, "Type", "success", [ "lean_version", "core_type_Prop" ], false ] }, "conclusion": { "canonical_value": "(缺, [Mathlib, Module10], 是, env-10, ctx-10, 是, Type, success, [lean_version, core_type_Prop], 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-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": 86, "original_line_sha256": "b68f0de73f6247af9cdc2512eb077fd748d69f081b4fa278971932a194bd053b", "question_compact_sha256": "b354fd3f788c3301f3af80e75b30aa55687adb4b83bbb73b927425f00fc669e2", "english_row_compact_sha256": "3b9c138d45041f6ac6f344288f8c901345738ecd8db72e8581d796e4d52d5f17", "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": "61ac2b72802cc87229cd5d3971a142b7fce173e0fbd6df5b022140d1e0221210", "original_candidate_line_sha256": "61ac2b72802cc87229cd5d3971a142b7fce173e0fbd6df5b022140d1e0221210" }, "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": 10, "method": "family_template_semantic_review_plus_independent_per_instance_reconstruction", "exact_question_first_check": { "model_sha256": "1c3071603b771608137ecc6f9c29928e138a3af9c4dcdfd0f95a932a67cf6fcf", "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." } }