{ "schema_version": "ocme-reviewed-question-reader-v1", "question_id": "q-20261014-advance-20261109-r07-context-free-grammar-0043", "pilot_number": "R0042-21543", "number": 21543, "family_id": "qf-mod40-cfg-derivation-audit", "title": { "zh-Hant": "第 21543 題：上下文無關文法", "en": "Question 21543: Each Derivation Step Replaces One Nonterminal by One Declared Right Side" }, "original_question": { "schema_version": "ocme-question-v0.1", "id": "q-20261014-advance-20261109-r07-context-free-grammar-0043", "batch_id": "batch-20261014-advance-20261109-r07-context-free-grammar-foundations", "language": "zh-Hant", "source_mko_ids": [ "mko-context-free-grammar" ], "title_zh": "上下文無關文法", "stem_zh": "finite disjoint nonterminals/terminals、start與complete production set。操作=cfg-derivation-audit；資料={\"nonterminals\":[\"S17\",\"A17\"],\"terminals\":[\"a17\",\"b17\"],\"start\":\"S17\",\"productions\":[[\"S17\",[\"a17\",\"A17\"]],[\"A17\",[\"b17\",\"A17\"]],[\"A17\",[]]],\"allow_epsilon\":true,\"forms\":[[\"S17\"],[\"a17\",\"A17\"],[\"a17\",\"b17\",\"A17\"],[\"a17\",\"b17\",\"b17\",\"A17\"],[\"a17\",\"b17\",\"b17\"]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。", "answer": { "kind": "expression", "value": "([[S17], [a17, A17], [a17, b17, A17], [a17, b17, b17, A17], [a17, b17, b17]], [[0, 0, S17, [a17, A17]], [1, 1, A17, [b17, A17]], [2, 1, A17, [b17, A17]], [3, 2, A17, []]], 是, 是, finite_production_sequence)", "explanation_zh": "Wave6第三層核對=([[S17], [a17, A17], [a17, b17, A17], [a17, b17, b17, A17], [a17, b17, b17]], [[0, 0, S17, [a17, A17]], [1, 1, A17, [b17, A17]], [2, 1, A17, [b17, A17]], [3, 2, A17, []]], 是, 是, finite_production_sequence)；依完整明示資料獨立重算；lhs單一nonterminal，rhs有限symbol string且epsilon convention明示；finite derivation proves membership；bounded search failure不證nonmembership，也不推unambiguous regular或PDA equivalence。" }, "difficulty": { "band": "undergraduate_core", "level": 3, "skills": [ "上下文無關文法" ] }, "variant": { "family_id": "qf-mod40-cfg-derivation-audit", "seed": 202611097043, "parameters": { "nonterminals": [ "S17", "A17" ], "terminals": [ "a17", "b17" ], "start": "S17", "productions": [ [ "S17", [ "a17", "A17" ] ], [ "A17", [ "b17", "A17" ] ], [ "A17", [] ] ], "allow_epsilon": true, "forms": [ [ "S17" ], [ "a17", "A17" ], [ "a17", "b17", "A17" ], [ "a17", "b17", "b17", "A17" ], [ "a17", "b17", "b17" ] ], "domain": "Complete_finite_context_free_grammar", "operation": "cfg-derivation-audit", "semantic_template": "qf-mod40-cfg-derivation-audit/{\"allow_epsilon\":true,\"forms\":[[\"S17\"],[\"a17\",\"A17\"],[\"a17\",\"b17\",\"A17\"],[\"a17\",\"b17\",\"b17\",\"A17\"],[\"a17\",\"b17\",\"b17\"]],\"nonterminals\":[\"A17\",\"S17\"],\"productions\":[[\"A17\",[\"b17\",\"A17\"]],[\"A17\",[]],[\"S17\",[\"a17\",\"A17\"]]],\"start\":\"S17\",\"terminals\":[\"a17\",\"b17\"]}" } }, "verification": { "status": "candidate", "checks": [ "producer_exact_finite_or_symbolic_model", "producer_source_snapshot_check", "producer_substantive_template_deduplication", "producer_json_schema" ], "warning_zh": "候選須主端重算；不構成人工審定、single-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、Lean或Evidence。" }, "provenance": { "generator_role": "question_producer", "generator_model": "model_unknown", "generated_at": "2026-10-14", "contract_version": "ocme-question-factory-v0.1" } }, "original_english_edition": { "schema_version": "ocme-question-localization-v0.1", "question_id": "q-20261014-advance-20261109-r07-context-free-grammar-0043", "batch_id": "batch-20261014-advance-20261109-r07-context-free-grammar-foundations", "locale": "en", "translation_state": "ai_candidate", "source": { "question_sha256": "ddbf92a1f6af6bb8f3514dd7785d6678bc04e426fdb02d4dc752de54cc4d37ad", "family_id": "qf-mod40-cfg-derivation-audit", "seed": 202611097043, "semantic_template": "qf-mod40-cfg-derivation-audit/{\"allow_epsilon\":true,\"forms\":[[\"S17\"],[\"a17\",\"A17\"],[\"a17\",\"b17\",\"A17\"],[\"a17\",\"b17\",\"b17\",\"A17\"],[\"a17\",\"b17\",\"b17\"]],\"nonterminals\":[\"A17\",\"S17\"],\"productions\":[[\"A17\",[\"b17\",\"A17\"]],[\"A17\",[]],[\"S17\",[\"a17\",\"A17\"]]],\"start\":\"S17\",\"terminals\":[\"a17\",\"b17\"]}" }, "fields": { "title": "Each Derivation Step Replaces One Nonterminal by One Declared Right Side", "stem": "Use the complete finite grammar: nonterminals=[S17, A17], terminals=[a17, b17], start=S17, productions=[[S17, [a17, A17]], [A17, [b17, A17]], [A17, []]] and allow_epsilon=true. Alphabets must be unique and disjoint, the start belongs to nonterminals, and each production [lhs,rhs] has exactly one nonterminal lhs and a finite legal-symbol rhs. Empty rhs is permitted only under the explicit epsilon convention. Keep original symbol and production order. Supplied forms=[[S17], [a17, A17], [a17, b17, A17], [a17, b17, b17, A17], [a17, b17, b17]]. Give (forms, step_witnesses, valid_derivation, final_form_terminal_only, certificate).", "answer": { "kind": "expression", "value": "([[S17], [a17, A17], [a17, b17, A17], [a17, b17, b17, A17], [a17, b17, b17]], [[0, 0, S17, [a17, A17]], [1, 1, A17, [b17, A17]], [2, 1, A17, [b17, A17]], [3, 2, A17, []]], Yes, Yes, finite_production_sequence)", "explanation": "A derivation must begin with [start]; each successive form replaces exactly one matching lhs occurrence. Each step witness is [position,production index,lhs,rhs], using the first matching witness in source order. Keep validity separate from whether the last form is terminal-only. The exact result, retaining the requested order, is ([[S17], [a17, A17], [a17, b17, A17], [a17, b17, b17, A17], [a17, b17, b17]], [[0, 0, S17, [a17, A17]], [1, 1, A17, [b17, A17]], [2, 1, A17, [b17, A17]], [3, 2, A17, []]], Yes, Yes, finite_production_sequence)." }, "skills": [ "Each Derivation Step Replaces One Nonterminal by One Declared Right Side" ], "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": "finite disjoint nonterminals/terminals、start與complete production set。操作=cfg-derivation-audit；資料={\"nonterminals\":[\"S17\",\"A17\"],\"terminals\":[\"a17\",\"b17\"],\"start\":\"S17\",\"productions\":[[\"S17\",[\"a17\",\"A17\"]],[\"A17\",[\"b17\",\"A17\"]],[\"A17\",[]]],\"allow_epsilon\":true,\"forms\":[[\"S17\"],[\"a17\",\"A17\"],[\"a17\",\"b17\",\"A17\"],[\"a17\",\"b17\",\"b17\",\"A17\"],[\"a17\",\"b17\",\"b17\"]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。", "en": "Use the complete finite grammar: nonterminals=[S17, A17], terminals=[a17, b17], start=S17, productions=[[S17, [a17, A17]], [A17, [b17, A17]], [A17, []]] and allow_epsilon=true. Alphabets must be unique and disjoint, the start belongs to nonterminals, and each production [lhs,rhs] has exactly one nonterminal lhs and a finite legal-symbol rhs. Empty rhs is permitted only under the explicit epsilon convention. Keep original symbol and production order. Supplied forms=[[S17], [a17, A17], [a17, b17, A17], [a17, b17, b17, A17], [a17, b17, b17]]. Give (forms, step_witnesses, valid_derivation, final_form_terminal_only, certificate)." } } ], "steps": [ { "id": "S001", "uses": [ "G001" ], "before": "source operation=cfg-derivation-audit;original snapshot and mathematics retained", "after": "explicit ordered source output fields=[forms, step_witnesses, valid_derivation, final_form_terminal_only, certificate]", "relation": "implies", "rule_id": "source_ordered_interface_explicit_without_javascript", "conditions": [], "explanation": { "zh-Hant": "原題歷史介面標記保留，本頁直接列來源有序欄位，不需JavaScript。tag不是額外證據，固定No保留其原聲稱範圍。", "en": "Keep the original historical interface marker while listing ordered source fields without JavaScript.Tags are not additional evidence;fixed No markers retain their source claim scope." }, "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 production index=0;lhs=S17,rhs=[a17, A17];N=[S17, A17],T=[a17, b17],allow_epsilon=是", "after": "lhs is ONE declared nonterminal;every rhs symbol legal;empty rhs accepted ONLY under the explicit epsilon convention;original production position retained", "relation": "implies", "rule_id": "cfg_each_original_production_single_nonterminal_legal_rhs", "conditions": [], "explanation": { "zh-Hant": "每條production左邊只有一個非終結符；右邊逐symbol核合法，空右邊依明示epsilon慣例。重複production位置可存在，不能排序改變首witness索引。", "en": "Each production has one nonterminal on the left.Check every right-hand symbol and the explicit epsilon convention.Duplicate production positions may exist;sorting them would change first-witness indices." }, "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 production index=1;lhs=A17,rhs=[b17, A17];N=[S17, A17],T=[a17, b17],allow_epsilon=是", "after": "lhs is ONE declared nonterminal;every rhs symbol legal;empty rhs accepted ONLY under the explicit epsilon convention;original production position retained", "relation": "implies", "rule_id": "cfg_each_original_production_single_nonterminal_legal_rhs", "conditions": [], "explanation": { "zh-Hant": "每條production左邊只有一個非終結符；右邊逐symbol核合法，空右邊依明示epsilon慣例。重複production位置可存在，不能排序改變首witness索引。", "en": "Each production has one nonterminal on the left.Check every right-hand symbol and the explicit epsilon convention.Duplicate production positions may exist;sorting them would change first-witness indices." }, "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": "ORIGINAL production index=2;lhs=A17,rhs=[];N=[S17, A17],T=[a17, b17],allow_epsilon=是", "after": "lhs is ONE declared nonterminal;every rhs symbol legal;empty rhs accepted ONLY under the explicit epsilon convention;original production position retained", "relation": "implies", "rule_id": "cfg_each_original_production_single_nonterminal_legal_rhs", "conditions": [], "explanation": { "zh-Hant": "每條production左邊只有一個非終結符；右邊逐symbol核合法，空右邊依明示epsilon慣例。重複production位置可存在，不能排序改變首witness索引。", "en": "Each production has one nonterminal on the left.Check every right-hand symbol and the explicit epsilon convention.Duplicate production positions may exist;sorting them would change first-witness indices." }, "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": "ORIGINAL unique disjoint N=[S17, A17],T=[a17, b17];start=S17;complete productions=[[S17, [a17, A17]], [A17, [b17, A17]], [A17, []]];allow_epsilon=是", "after": "start belongs to nonterminals;finite grammar qualified;NO derivation,membership,regularity,unambiguity or PDA equivalence inferred", "relation": "implies", "rule_id": "cfg_qualified_alphabets_start_not_language_property", "conditions": [], "explanation": { "zh-Hant": "定義合格只是文法的資格，不自動有某個word的推導，也不推regular、unambiguous等額外性質。非終結符／終結符順序保原輸入。", "en": "Grammar qualification alone supplies no derivation for a word and no regularity or unambiguity claim.Retain both alphabet orders." }, "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": "ORIGINAL forms=[[S17], [a17, A17], [a17, b17, A17], [a17, b17, b17, A17], [a17, b17, b17]];actual grammar start=S17", "after": "first form exactly [start]=是;empty forms or wrong start fail even if the last form is terminal", "relation": "implies", "rule_id": "cfg_derivation_actual_start_required", "conditions": [], "explanation": { "zh-Hant": "推導必須真從[start]開始；單看末項是終結字串不足。空forms不是epsilon推導；epsilon是實際空字串形式[]，仍需要合法production鏈。", "en": "A derivation must actually start at[start];a terminal final form alone is insufficient.Empty forms are not an epsilon derivation:epsilon is an actual empty-string form[] requiring a legal chain." }, "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": "ORIGINAL transition index=0;from=[S17];to=[a17, A17];original productions=[[S17, [a17, A17]], [A17, [b17, A17]], [A17, []]]", "after": "FIRST matching [position,production_index,lhs,rhs]=[0, 0, S17, [a17, A17]];replace EXACTLY ONE occurrence,retaining both surrounding substrings", "relation": "implies", "rule_id": "cfg_each_transition_first_position_then_original_production", "conditions": [], "explanation": { "zh-Hant": "按原位置、再原production順序找第一個真替換witness；只換一個lhs occurrence，兩側字串保持。不把一次換全部同名symbol當一步；找不到就保先前partial witnesses並停止。", "en": "Scan original positions and then original production indices for the first actual replacement.Replace one occurrence and preserve both surrounding strings,not every matching symbol.On failure retain prior partial witnesses and stop." }, "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": "ORIGINAL transition index=1;from=[a17, A17];to=[a17, b17, A17];original productions=[[S17, [a17, A17]], [A17, [b17, A17]], [A17, []]]", "after": "FIRST matching [position,production_index,lhs,rhs]=[1, 1, A17, [b17, A17]];replace EXACTLY ONE occurrence,retaining both surrounding substrings", "relation": "implies", "rule_id": "cfg_each_transition_first_position_then_original_production", "conditions": [], "explanation": { "zh-Hant": "按原位置、再原production順序找第一個真替換witness；只換一個lhs occurrence，兩側字串保持。不把一次換全部同名symbol當一步；找不到就保先前partial witnesses並停止。", "en": "Scan original positions and then original production indices for the first actual replacement.Replace one occurrence and preserve both surrounding strings,not every matching symbol.On failure retain prior partial witnesses and stop." }, "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": "ORIGINAL transition index=2;from=[a17, b17, A17];to=[a17, b17, b17, A17];original productions=[[S17, [a17, A17]], [A17, [b17, A17]], [A17, []]]", "after": "FIRST matching [position,production_index,lhs,rhs]=[2, 1, A17, [b17, A17]];replace EXACTLY ONE occurrence,retaining both surrounding substrings", "relation": "implies", "rule_id": "cfg_each_transition_first_position_then_original_production", "conditions": [], "explanation": { "zh-Hant": "按原位置、再原production順序找第一個真替換witness；只換一個lhs occurrence，兩側字串保持。不把一次換全部同名symbol當一步；找不到就保先前partial witnesses並停止。", "en": "Scan original positions and then original production indices for the first actual replacement.Replace one occurrence and preserve both surrounding strings,not every matching symbol.On failure retain prior partial witnesses and stop." }, "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": "ORIGINAL transition index=3;from=[a17, b17, b17, A17];to=[a17, b17, b17];original productions=[[S17, [a17, A17]], [A17, [b17, A17]], [A17, []]]", "after": "FIRST matching [position,production_index,lhs,rhs]=[3, 2, A17, []];replace EXACTLY ONE occurrence,retaining both surrounding substrings", "relation": "implies", "rule_id": "cfg_each_transition_first_position_then_original_production", "conditions": [], "explanation": { "zh-Hant": "按原位置、再原production順序找第一個真替換witness；只換一個lhs occurrence，兩側字串保持。不把一次換全部同名symbol當一步；找不到就保先前partial witnesses並停止。", "en": "Scan original positions and then original production indices for the first actual replacement.Replace one occurrence and preserve both surrounding strings,not every matching symbol.On failure retain prior partial witnesses and stop." }, "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": "S011", "uses": [ "G001", "S010" ], "before": "ORIGINAL actual forms=[[S17], [a17, A17], [a17, b17, A17], [a17, b17, b17, A17], [a17, b17, b17]];accepted prior witnesses=[[0, 0, S17, [a17, A17]], [1, 1, A17, [b17, A17]], [2, 1, A17, [b17, A17]], [3, 2, A17, []]]", "after": "valid_derivation=是;this is separate from whether the actual final form contains only terminals", "relation": "implies", "rule_id": "cfg_partial_trace_validity_not_final_terminal_flag", "conditions": [], "explanation": { "zh-Hant": "合法性核完整從start的鏈；錯誤處後面出現terminal字串不能修補前面的錯誤。零步[start]可以合法，但通常尚非terminal word。", "en": "Validity concerns the complete start-to-form chain.A terminal string after a failed step cannot repair it.A zero-step[start] derivation can be valid without being a terminal word." }, "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": "S012", "uses": [ "G001", "S011" ], "before": "ORIGINAL actual final form=[a17, b17, b17];terminals=[a17, b17]", "after": "final_form_terminal_only=是;valid_derivation remains=是", "relation": "implies", "rule_id": "cfg_final_terminal_only_audited_separately", "conditions": [], "explanation": { "zh-Hant": "末形式空字串時逐symbol條件vacuous True，但仍須另核整段推導；forms全空則沒有末形式而是False。", "en": "An empty final string vacuously contains only terminals,but still needs a valid derivation.An empty forms list has no final form and gives false." }, "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": [ [ [ "S17" ], [ "a17", "A17" ], [ "a17", "b17", "A17" ], [ "a17", "b17", "b17", "A17" ], [ "a17", "b17", "b17" ] ], [ [ 0, 0, "S17", [ "a17", "A17" ] ], [ 1, 1, "A17", [ "b17", "A17" ] ], [ 2, 1, "A17", [ "b17", "A17" ] ], [ 3, 2, "A17", [] ] ], true, true, "finite_production_sequence" ] }, "conclusion": { "canonical_value": "([[S17], [a17, A17], [a17, b17, A17], [a17, b17, b17, A17], [a17, b17, b17]], [[0, 0, S17, [a17, A17]], [1, 1, A17, [b17, A17]], [2, 1, A17, [b17, A17]], [3, 2, A17, []]], 是, 是, finite_production_sequence)", "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-20261014-advance-20261109-r07-context-free-grammar-foundations", "batch_path": "public/data/questions/batches/batch-20261014-advance-20261109-r07-context-free-grammar-foundations/questions.jsonl", "batch_sha256": "39b1ee6da8a53fac842295ae98c60a416b9e3823e9624674682652d96474f427", "original_line": 43, "original_line_sha256": "9429cc23006c8ad363a1b149529c6c1eb242bab5d1d92b3a21f04da57d7f720f", "question_compact_sha256": "ddbf92a1f6af6bb8f3514dd7785d6678bc04e426fdb02d4dc752de54cc4d37ad", "english_row_compact_sha256": "9528911cc740ca9b194685d978dc2da0791f07f37515894c1454f39dcca4b0d7", "english_manifest_path": "public/data/i18n/editions/batch-20261014-advance-20261109-r07-context-free-grammar-foundations.en.json", "english_rows_path": "public/data/i18n/questions/batch-20261014-advance-20261109-r07-context-free-grammar-foundations.en.jsonl" }, "mko_bindings": { "mko-context-free-grammar": { "sha256": "0cffcd9eae42c9318c21e6233a518469b8747f149bd785b0f4c94ecbe19ea685", "english_sha256": "a115d11c0e542ef86b3dc7c6f96803d1f34c21848831700815c78d4215ea10a4", "original_path": "public/data/mko/context-free-grammar.json", "english_path": "public/data/i18n/editions/mko-context-free-grammar.en.json" } }, "selected_manifest_sha256": "5233edba9654a6cffd8b6b2d83c932f82ded15f9c0b7c733bd049943e672acff", "selected_part_sha256": "a84fbe07a4e46e8e47a8ad331f35fd3f81b821aef6cb27e7852de854aaa96b9a", "original_candidate_sha256": "fa73aff90acdc1740a64fdf854cb998d0785e4ae522b6c4b13d826c26d666332", "original_candidate_line_sha256": "fa73aff90acdc1740a64fdf854cb998d0785e4ae522b6c4b13d826c26d666332" }, "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-20261026-009-p43", "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": "dd44555041dfbb6fe9936aa00b9a5f8c5982c2784ef61dd0cbd5d1a303a49c1a", "question_first_witness_sha256": "9a6011263f6ac53b9a1fd57addf2f3e2f6088b54802c539f332d689480dc2d17" }, "status": "second_context_reviewed", "mathematical_semantics": true, "bilingual_semantics": true, "steps_reviewed": 12, "method": "family_template_semantic_review_plus_independent_per_instance_reconstruction", "exact_question_first_check": { "model_sha256": "d47025f65088f8d8a3dbd3f5378cd44cd20dc046778b07d1a6f14bd812f8b8ec", "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." } }