{ "schema_version": "ocme-reviewed-question-reader-v1", "question_id": "q-20261013-advance-20261019-r07-lean-proof-term-0078", "pilot_number": "R0018-09928", "number": 9928, "family_id": "qf-ext19-proofterm-kernel-receipt", "title": { "zh-Hant": "第 9928 題：合成證明項判定", "en": "Question 9928: Synthetic Kernel Metadata Qualification and Axiom Inventory Flag" }, "original_question": { "schema_version": "ocme-question-v0.1", "id": "q-20261013-advance-20261019-r07-lean-proof-term-0078", "batch_id": "batch-20261013-advance-20261019-r07-lean-proof-term-foundations", "language": "zh-Hant", "source_mko_ids": [ "mko-lean-proof-term" ], "title_zh": "合成證明項判定", "stem_zh": "合成proof-term receipt。操作=proofterm-kernel-receipt；資料={\"environment_id\":\"env-2\",\"statement_id\":\"thm-2\",\"term_sha256\":\"0000000000000000000000000000000000000000000000000000000000000002\",\"type_sha256\":\"0000000000000000000000000000000000000000000000000000000000000066\",\"kernel_checked\":true,\"axioms_recorded\":true}。請依 [environment,statement,term_hash_valid,type_hash_valid,kernel,axioms_recorded,qualified,status] 欄序回答。", "answer": { "kind": "expression", "value": "(env-2, thm-2, 是, 是, 是, 是, 是, 合成receipt欄位完整)", "explanation_zh": "第二批擴展核對=(env-2, thm-2, 是, 是, 是, 是, 是, 合成receipt欄位完整)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；本輪未跑Lean build；statement不等於已驗證proof；tactic log不等於kernel receipt。" }, "difficulty": { "band": "undergraduate_core", "level": 1, "skills": [ "合成證明項判定" ] }, "variant": { "family_id": "qf-ext19-proofterm-kernel-receipt", "seed": 202610197078, "parameters": { "environment_id": "env-2", "statement_id": "thm-2", "term_sha256": "0000000000000000000000000000000000000000000000000000000000000002", "type_sha256": "0000000000000000000000000000000000000000000000000000000000000066", "kernel_checked": true, "axioms_recorded": true, "domain": "Synthetic_typed_proof_calculus", "operation": "proofterm-kernel-receipt", "semantic_template": "qf-ext19-proofterm-kernel-receipt/{\"axioms_recorded\":true,\"environment_id\":\"env-2\",\"kernel_checked\":true,\"statement_id\":\"thm-2\",\"term_sha256\":\"0000000000000000000000000000000000000000000000000000000000000002\",\"type_sha256\":\"0000000000000000000000000000000000000000000000000000000000000066\"}" } }, "verification": { "status": "candidate", "checks": [ "producer_exact_finite_model", "producer_source_snapshot_check", "producer_substantive_template_deduplication", "producer_json_schema" ], "warning_zh": "僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、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-20261019-r07-lean-proof-term-0078", "batch_id": "batch-20261013-advance-20261019-r07-lean-proof-term-foundations", "locale": "en", "translation_state": "ai_candidate", "source": { "question_sha256": "3fc0888494048392cf6d7a4576c61d4eda84442520c86869b30b96b58d2067dc", "family_id": "qf-ext19-proofterm-kernel-receipt", "seed": 202610197078, "semantic_template": "qf-ext19-proofterm-kernel-receipt/{\"axioms_recorded\":true,\"environment_id\":\"env-2\",\"kernel_checked\":true,\"statement_id\":\"thm-2\",\"term_sha256\":\"0000000000000000000000000000000000000000000000000000000000000002\",\"type_sha256\":\"0000000000000000000000000000000000000000000000000000000000000066\"}" }, "fields": { "title": "Synthetic Kernel Metadata Qualification and Axiom Inventory Flag", "stem": "Use the synthetic small propositional calculus or synthetic receipt specified here, not actual Lean execution. The original source pulse did not run Lean builds for these questions. A statement, tactic log and kernel-checked proof are different obligations. Supplied metadata={\"environment_id\":\"env-2\",\"statement_id\":\"thm-2\",\"term_sha256\":\"0000000000000000000000000000000000000000000000000000000000000002\",\"type_sha256\":\"0000000000000000000000000000000000000000000000000000000000000066\",\"kernel_checked\":true,\"axioms_recorded\":true}. Give (environment or missing, statement or missing, term-hash lexical shape?, type-hash lexical shape?, kernel flag, axioms-recorded flag, nonempty IDs plus both shapes plus kernel flag qualify?, synthetic receipt fields complete/still incomplete). Completeness additionally requires the axiom-recorded flag; no digest or kernel run is independently verified here.", "answer": { "kind": "expression", "value": "(env-2, thm-2, Yes, Yes, Yes, Yes, Yes, synthetic-receipt-fields-complete)", "explanation": "Keep qualification and recorded axioms separate. Synthetic metadata completeness is not an actual Lean kernel acceptance or semantic-trust certificate. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (env-2, thm-2, Yes, Yes, Yes, Yes, Yes, synthetic-receipt-fields-complete)." }, "skills": [ "Synthetic Kernel Metadata Qualification and Axiom Inventory Flag" ], "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proof-term receipt。操作=proofterm-kernel-receipt；資料={\"environment_id\":\"env-2\",\"statement_id\":\"thm-2\",\"term_sha256\":\"0000000000000000000000000000000000000000000000000000000000000002\",\"type_sha256\":\"0000000000000000000000000000000000000000000000000000000000000066\",\"kernel_checked\":true,\"axioms_recorded\":true}。請依 [environment,statement,term_hash_valid,type_hash_valid,kernel,axioms_recorded,qualified,status] 欄序回答。", "en": "Use the synthetic small propositional calculus or synthetic receipt specified here, not actual Lean execution. The original source pulse did not run Lean builds for these questions. A statement, tactic log and kernel-checked proof are different obligations. Supplied metadata={\"environment_id\":\"env-2\",\"statement_id\":\"thm-2\",\"term_sha256\":\"0000000000000000000000000000000000000000000000000000000000000002\",\"type_sha256\":\"0000000000000000000000000000000000000000000000000000000000000066\",\"kernel_checked\":true,\"axioms_recorded\":true}. Give (environment or missing, statement or missing, term-hash lexical shape?, type-hash lexical shape?, kernel flag, axioms-recorded flag, nonempty IDs plus both shapes plus kernel flag qualify?, synthetic receipt fields complete/still incomplete). Completeness additionally requires the axiom-recorded flag; no digest or kernel run is independently verified here." } } ], "steps": [ { "id": "S001", "uses": [ "G001" ], "before": "synthetic proposition/term calculus or supplied synthetic receipt", "after": "no actual Lean build,source-digest check or kernel acceptance", "relation": "implies", "rule_id": "synthetic_proofterm_not_actual_kernel", "conditions": [], "explanation": { "zh-Hant": "本題只套明定的小演算或合成receipt規格。陳述、tactic完成、term存在與kernel接受分開；本輪不執行Lean或把教學稿標成形式證明。", "en": "Apply only the specified small calculus or synthetic receipt protocol.Statement,tactic completion,term presence and kernel acceptance are separate.No Lean is run and the teaching guide is not promoted to a formal 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 }, { "id": "S002", "uses": [ "G001", "S001" ], "before": "environment ID=\"env-2\";statement ID=\"thm-2\";term hash text=\"0000000000000000000000000000000000000000000000000000000000000002\";type hash text=\"0000000000000000000000000000000000000000000000000000000000000066\"", "after": "IDs nonempty=是;term lexical shape=是;type lexical shape=是", "relation": "implies", "rule_id": "synthetic_receipt_lexical_shape_only", "conditions": [], "explanation": { "zh-Hant": "只查非空ID與64位小寫hex外形，不讀取檔案重算digest，也不把名字視為已存在的實際環境。", "en": "Check only nonempty IDs and64-lowercase-hex shape.Do not read files to recompute digests or treat a name as an existing real environment." }, "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": "IDs and shapes qualified=是;supplied kernel flag=是;axioms recorded=是", "after": "synthetic qualified=是;status=合成receipt欄位完整", "relation": "implies", "rule_id": "synthetic_qualification_and_axiom_inventory_separate", "conditions": [], "explanation": { "zh-Hant": "合格旗標另要求題內kernel旗標；欄位完整再要求axioms已記錄。兩者都只是合成資料分類，不是實際kernel接受或語意信任證書。", "en": "Qualification additionally requires the supplied kernel flag;field completeness also requires the axioms-recorded flag.Both merely classify synthetic data,not real kernel acceptance or a semantic trust certificate." }, "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-2", "thm-2", true, true, true, true, true, "合成receipt欄位完整" ] }, "conclusion": { "canonical_value": "(env-2, thm-2, 是, 是, 是, 是, 是, 合成receipt欄位完整)", "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-20261019-r07-lean-proof-term-foundations", "batch_path": "public/data/questions/batches/batch-20261013-advance-20261019-r07-lean-proof-term-foundations/questions.jsonl", "batch_sha256": "f4cf6c211d2edd61cb9e5b827c3869edb45d363ecd7d8f63108f53d848e14557", "original_line": 78, "original_line_sha256": "849f972f866ca834124914b2d1c93b4a357b22c1be1e4abe474d7519ac128319", "question_compact_sha256": "3fc0888494048392cf6d7a4576c61d4eda84442520c86869b30b96b58d2067dc", "english_row_compact_sha256": "5f1e150bb7fce94d1b2f16b63a31dc1bff5179a7b78c5bb24fe6fdac6500d684", "english_manifest_path": "public/data/i18n/editions/batch-20261013-advance-20261019-r07-lean-proof-term-foundations.en.json", "english_rows_path": "public/data/i18n/questions/batch-20261013-advance-20261019-r07-lean-proof-term-foundations.en.jsonl" }, "mko_bindings": { "mko-lean-proof-term": { "sha256": "a11c7813a596785a48d1af6603780643970769d714b6a167fec2a29245c6e1b2", "english_sha256": "d42bc57cd7682e13350bb803d8c13f2fcb0aa358ca7532f8aed5e5715b020506", "original_path": "public/data/mko/lean-proof-term.json", "english_path": "public/data/i18n/editions/mko-lean-proof-term.en.json" } }, "selected_manifest_sha256": "5233edba9654a6cffd8b6b2d83c932f82ded15f9c0b7c733bd049943e672acff", "selected_part_sha256": "2cf5df7bf9c3d48dfd41d968723b60d910c4ecfec9c2089d22ac1cda059a6086", "original_candidate_sha256": "27413d7982ba10f8c885ff953f98a61360702592c84633a10ab137374ad18b1a", "original_candidate_line_sha256": "27413d7982ba10f8c885ff953f98a61360702592c84633a10ab137374ad18b1a" }, "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-20261026-006-p19", "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": "bd35da62087a15d6b89b45585dc46e89b9efbe097cba7b3c707b5030496f013c", "question_first_witness_sha256": "fab45a10d8ac95c7d61d32e47d1bdd3ca862c17c3289a6bf4b01d4dc9492fbb6" }, "status": "second_context_reviewed", "mathematical_semantics": true, "bilingual_semantics": true, "steps_reviewed": 3, "method": "family_template_semantic_review_plus_independent_per_instance_reconstruction", "exact_question_first_check": { "model_sha256": "9b80c4e3eb4ac4d651a128cf3b12bc3a0f42fef475a58cb0cb39cf5379d1b244", "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." } }