{ "schema_version": "ocme-reviewed-question-reader-v1", "question_id": "q-20261013-advance-20261019-r07-lean-proof-term-0061", "pilot_number": "R0018-09986", "number": 9986, "family_id": "qf-ext19-proofterm-tactic-vs-term", "title": { "zh-Hant": "第 9986 題：合成證明項判定", "en": "Question 9986: Synthetic Tactic Completion Is Not a Kernel Receipt" }, "original_question": { "schema_version": "ocme-question-v0.1", "id": "q-20261013-advance-20261019-r07-lean-proof-term-0061", "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-tactic-vs-term；資料={\"statement_ready\":false,\"tactic_finished\":true,\"term_present\":true,\"unresolved_goals\":10}。請依 [statement,tactic_finished,term_present,goals,tactic_complete,term_candidate,kernel_checked,boundary] 欄序回答。", "answer": { "kind": "expression", "value": "(否, 是, 是, 10, 否, 否, 否, 尚無kernel receipt)", "explanation_zh": "第二批擴展核對=(否, 是, 是, 10, 否, 否, 否, 尚無kernel receipt)；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": 2, "skills": [ "合成證明項判定" ] }, "variant": { "family_id": "qf-ext19-proofterm-tactic-vs-term", "seed": 202610197061, "parameters": { "statement_ready": false, "tactic_finished": true, "term_present": true, "unresolved_goals": 10, "domain": "Synthetic_typed_proof_calculus", "operation": "proofterm-tactic-vs-term", "semantic_template": "qf-ext19-proofterm-tactic-vs-term/{\"statement_ready\":false,\"tactic_finished\":true,\"term_present\":true,\"unresolved_goals\":10}" } }, "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-0061", "batch_id": "batch-20261013-advance-20261019-r07-lean-proof-term-foundations", "locale": "en", "translation_state": "ai_candidate", "source": { "question_sha256": "63269c4c5abbc5842fb67fe9255d399e7e973ac198e2e5f38ae045da0b42c3c0", "family_id": "qf-ext19-proofterm-tactic-vs-term", "seed": 202610197061, "semantic_template": "qf-ext19-proofterm-tactic-vs-term/{\"statement_ready\":false,\"tactic_finished\":true,\"term_present\":true,\"unresolved_goals\":10}" }, "fields": { "title": "Synthetic Tactic Completion Is Not a Kernel Receipt", "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. statement_ready=false, tactic_finished=true, term_present=true, unresolved_goals=10. Give (those three flags, goal count, tactic finished with zero goals?, term candidate?, kernel checked?, no-kernel receipt boundary). The kernel flag remains false in this protocol.", "answer": { "kind": "expression", "value": "(No, Yes, Yes, 10, No, No, No, no-kernel receipt)", "explanation": "A tactic candidate needs a ready statement, a finished zero-goal tactic and a term. These supplied flags are not actual Lean execution. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (No, Yes, Yes, 10, No, No, No, no-kernel receipt)." }, "skills": [ "Synthetic Tactic Completion Is Not a Kernel Receipt" ], "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-tactic-vs-term；資料={\"statement_ready\":false,\"tactic_finished\":true,\"term_present\":true,\"unresolved_goals\":10}。請依 [statement,tactic_finished,term_present,goals,tactic_complete,term_candidate,kernel_checked,boundary] 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. statement_ready=false, tactic_finished=true, term_present=true, unresolved_goals=10. Give (those three flags, goal count, tactic finished with zero goals?, term candidate?, kernel checked?, no-kernel receipt boundary). The kernel flag remains false in this protocol." } } ], "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": "statement ready=否;tactic finished=是;term present=是;unresolved goals=10", "after": "tactic complete=否;term candidate=否;kernel checked=否", "relation": "implies", "rule_id": "tactic_candidate_is_not_kernel_receipt", "conditions": [], "explanation": { "zh-Hant": "tactic須finished且零goals才算完成；再加陳述已備與term存在才是候選。協定kernel欄仍為假，沒有真實kernel回執。", "en": "A tactic is complete only if finished with zero goals.A candidate additionally needs a ready statement and a term.The protocol's kernel flag remains false;there is no real kernel receipt." }, "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": [ false, true, true, 10, false, false, false, "尚無kernel receipt" ] }, "conclusion": { "canonical_value": "(否, 是, 是, 10, 否, 否, 否, 尚無kernel receipt)", "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": 61, "original_line_sha256": "bb16eeaa1f19d1a5b177be9a8ce6e2f9d08d6a3ecd14c172c883cdf9695ee94d", "question_compact_sha256": "63269c4c5abbc5842fb67fe9255d399e7e973ac198e2e5f38ae045da0b42c3c0", "english_row_compact_sha256": "c412815371c9bdeab28538a5069d83d75a4b23401b2081b0bc63a56e2436e391", "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": "e8babc9b6f91ec002687181a67d60606339612b9cd621a3c2fbf7f61e940f2a6", "original_candidate_line_sha256": "e8babc9b6f91ec002687181a67d60606339612b9cd621a3c2fbf7f61e940f2a6" }, "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": 2, "method": "family_template_semantic_review_plus_independent_per_instance_reconstruction", "exact_question_first_check": { "model_sha256": "9b3f120a20dd79530fc9f00b5d6e296acd1d1f58b1aea836f106c52e3f56b227", "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." } }