{ "schema_version": "ocme-reviewed-question-reader-v1", "question_id": "q-20261014-advance-20261110-r07-pushdown-automaton-0013", "pilot_number": "R0043-22463", "number": 22463, "family_id": "qf-mod41-pda-qualification", "title": { "zh-Hant": "第 22463 題：下推自動機", "en": "Question 22463: A Complete PDA Definition Retains Its Final-State Acceptance Convention" }, "original_question": { "schema_version": "ocme-question-v0.1", "id": "q-20261014-advance-20261110-r07-pushdown-automaton-0013", "batch_id": "batch-20261014-advance-20261110-r07-pushdown-automaton-foundations", "language": "zh-Hant", "source_mko_ids": [ "mko-pushdown-automaton" ], "title_zh": "下推自動機", "stem_zh": "transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-qualification；資料={\"states\":[\"push12\",\"pop12\",\"accept12\"],\"input_alphabet\":[\"a12\",\"b12\"],\"stack_alphabet\":[\"Z12\",\"A12\"],\"start_state\":\"push12\",\"bottom_symbol\":\"Z12\",\"final_states\":[\"accept12\"],\"transitions\":[[\"push12\",\"a12\",\"Z12\",\"push12\",[\"Z12\",\"A12\"]],[\"push12\",\"a12\",\"A12\",\"push12\",[\"A12\",\"A12\"]],[\"push12\",\"b12\",\"A12\",\"pop12\",[]],[\"pop12\",\"b12\",\"A12\",\"pop12\",[]],[\"push12\",null,\"Z12\",\"accept12\",[\"Z12\"]],[\"pop12\",null,\"Z12\",\"accept12\",[\"Z12\"]]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。", "answer": { "kind": "expression", "value": "([push12, pop12, accept12], [a12, b12], [Z12, A12], push12, Z12, [accept12], 6, 是, accept_only_after_full_input_in_final_state_bottom_marker_preserved)", "explanation_zh": "Wave6第四層核對=([push12, pop12, accept12], [a12, b12], [Z12, A12], push12, Z12, [accept12], 6, 是, accept_only_after_full_input_in_final_state_bottom_marker_preserved)；依完整明示資料獨立重算；stack為bottom-first/top-last且null是epsilon；epsilon不消耗input、bottom marker不可underflow、接受witness必須讀完整input到final state；不混用empty-stack acceptance；bounded search failure不證rejection，也不自動宣稱CFG equivalence或determinism。" }, "difficulty": { "band": "undergraduate_core", "level": 2, "skills": [ "下推自動機" ] }, "variant": { "family_id": "qf-mod41-pda-qualification", "seed": 202611107013, "parameters": { "states": [ "push12", "pop12", "accept12" ], "input_alphabet": [ "a12", "b12" ], "stack_alphabet": [ "Z12", "A12" ], "start_state": "push12", "bottom_symbol": "Z12", "final_states": [ "accept12" ], "transitions": [ [ "push12", "a12", "Z12", "push12", [ "Z12", "A12" ] ], [ "push12", "a12", "A12", "push12", [ "A12", "A12" ] ], [ "push12", "b12", "A12", "pop12", [] ], [ "pop12", "b12", "A12", "pop12", [] ], [ "push12", null, "Z12", "accept12", [ "Z12" ] ], [ "pop12", null, "Z12", "accept12", [ "Z12" ] ] ], "domain": "Finite_nondeterministic_PDA_final_state_acceptance", "operation": "pda-qualification", "semantic_template": "qf-mod41-pda-qualification/{\"bottom_symbol\":\"Z12\",\"final_states\":[\"accept12\"],\"input_alphabet\":[\"a12\",\"b12\"],\"stack_alphabet\":[\"A12\",\"Z12\"],\"start_state\":\"push12\",\"states\":[\"accept12\",\"pop12\",\"push12\"],\"transitions\":[[\"pop12\",\"b12\",\"A12\",\"pop12\",[]],[\"pop12\",null,\"Z12\",\"accept12\",[\"Z12\"]],[\"push12\",\"a12\",\"A12\",\"push12\",[\"A12\",\"A12\"]],[\"push12\",\"a12\",\"Z12\",\"push12\",[\"Z12\",\"A12\"]],[\"push12\",\"b12\",\"A12\",\"pop12\",[]],[\"push12\",null,\"Z12\",\"accept12\",[\"Z12\"]]]}" } }, "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、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、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-20261110-r07-pushdown-automaton-0013", "batch_id": "batch-20261014-advance-20261110-r07-pushdown-automaton-foundations", "locale": "en", "translation_state": "ai_candidate", "source": { "question_sha256": "7de5cd716f8ea05e991899cfa9e2f8590355993e37de257d65f6bd9f6697a4a0", "family_id": "qf-mod41-pda-qualification", "seed": 202611107013, "semantic_template": "qf-mod41-pda-qualification/{\"bottom_symbol\":\"Z12\",\"final_states\":[\"accept12\"],\"input_alphabet\":[\"a12\",\"b12\"],\"stack_alphabet\":[\"A12\",\"Z12\"],\"start_state\":\"push12\",\"states\":[\"accept12\",\"pop12\",\"push12\"],\"transitions\":[[\"pop12\",\"b12\",\"A12\",\"pop12\",[]],[\"pop12\",null,\"Z12\",\"accept12\",[\"Z12\"]],[\"push12\",\"a12\",\"A12\",\"push12\",[\"A12\",\"A12\"]],[\"push12\",\"a12\",\"Z12\",\"push12\",[\"Z12\",\"A12\"]],[\"push12\",\"b12\",\"A12\",\"pop12\",[]],[\"push12\",null,\"Z12\",\"accept12\",[\"Z12\"]]]}" }, "fields": { "title": "A Complete PDA Definition Retains Its Final-State Acceptance Convention", "stem": "Use the complete finite nondeterministic PDA: states=[push12, pop12, accept12], input_alphabet=[a12, b12], stack_alphabet=[Z12, A12], start_state=push12, bottom_symbol=Z12, final_states=[accept12], transitions=[[push12, a12, Z12, push12, [Z12, A12]], [push12, a12, A12, push12, [A12, A12]], [push12, b12, A12, pop12, []], [pop12, b12, A12, pop12, []], [push12, null, Z12, accept12, [Z12]], [pop12, null, Z12, accept12, [Z12]]]. Alphabets are unique and pairwise disjoint. Each transition is [from,input symbol or null,required top,to,replacement bottom-to-top]. null is epsilon and consumes no input. Configurations are [state,input position,stack] with bottom first and top last. Preserve the bottom marker and accept only after consuming the entire input in a final state, not by empty stack. Give (states, input_alphabet, stack_alphabet, start_state, bottom_symbol, final_states, transition_count, qualified, convention).", "answer": { "kind": "expression", "value": "([push12, pop12, accept12], [a12, b12], [Z12, A12], push12, Z12, [accept12], 6, Yes, accept_only_after_full_input_in_final_state_bottom_marker_preserved)", "explanation": "Validate all finite states, alphabets, transitions, start, bottom and final states. Qualification alone is not an accepting run, determinism proof or CFG-equivalence claim. The exact result, retaining the requested order, is ([push12, pop12, accept12], [a12, b12], [Z12, A12], push12, Z12, [accept12], 6, Yes, accept_only_after_full_input_in_final_state_bottom_marker_preserved)." }, "skills": [ "A Complete PDA Definition Retains Its Final-State Acceptance Convention" ], "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": "transition=[from,input-or-null,required-top,to,replacement-bottom-to-top]的finite nondeterministic PDA。操作=pda-qualification；資料={\"states\":[\"push12\",\"pop12\",\"accept12\"],\"input_alphabet\":[\"a12\",\"b12\"],\"stack_alphabet\":[\"Z12\",\"A12\"],\"start_state\":\"push12\",\"bottom_symbol\":\"Z12\",\"final_states\":[\"accept12\"],\"transitions\":[[\"push12\",\"a12\",\"Z12\",\"push12\",[\"Z12\",\"A12\"]],[\"push12\",\"a12\",\"A12\",\"push12\",[\"A12\",\"A12\"]],[\"push12\",\"b12\",\"A12\",\"pop12\",[]],[\"pop12\",\"b12\",\"A12\",\"pop12\",[]],[\"push12\",null,\"Z12\",\"accept12\",[\"Z12\"]],[\"pop12\",null,\"Z12\",\"accept12\",[\"Z12\"]]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。", "en": "Use the complete finite nondeterministic PDA: states=[push12, pop12, accept12], input_alphabet=[a12, b12], stack_alphabet=[Z12, A12], start_state=push12, bottom_symbol=Z12, final_states=[accept12], transitions=[[push12, a12, Z12, push12, [Z12, A12]], [push12, a12, A12, push12, [A12, A12]], [push12, b12, A12, pop12, []], [pop12, b12, A12, pop12, []], [push12, null, Z12, accept12, [Z12]], [pop12, null, Z12, accept12, [Z12]]]. Alphabets are unique and pairwise disjoint. Each transition is [from,input symbol or null,required top,to,replacement bottom-to-top]. null is epsilon and consumes no input. Configurations are [state,input position,stack] with bottom first and top last. Preserve the bottom marker and accept only after consuming the entire input in a final state, not by empty stack. Give (states, input_alphabet, stack_alphabet, start_state, bottom_symbol, final_states, transition_count, qualified, convention)." } } ], "steps": [ { "id": "S001", "uses": [ "G001" ], "before": "source operation=pda-qualification;original snapshot and mathematics retained", "after": "explicit ordered source output fields=[states, input_alphabet, stack_alphabet, start_state, bottom_symbol, final_states, transition_count, qualified, convention]", "relation": "implies", "rule_id": "source_ordered_interface_explicit_without_javascript", "conditions": [], "explanation": { "zh-Hant": "原題歷史介面標記保留，直接列來源有序欄位，不需JavaScript；MVT由原mode選欄序，不補空欄或看答案形狀猜。tag與固定No保原聲稱範圍。", "en": "Retain the historical interface marker and list ordered source fields without JavaScript.MVT fields come from the original mode,without padding or answer-shape inference.Tags and fixed No markers retain their 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 transition index=0;[from,input_or_null,required_top,to,replacement_bottom_to_top]=[push12, a12, Z12, push12, [Z12, A12]];bottom=Z12", "after": "states/input/stack symbols legal;null input consumes0;top=bottom requires replacement first bottom,otherwise replacement contains NO bottom;ORIGINAL transition position retained", "relation": "implies", "rule_id": "pda_EVERY_original_transition_roles_epsilon_bottom_guard", "conditions": [], "explanation": { "zh-Hant": "逐原transition核state、input與stack角色，不把字母表混用；null是epsilon而不是一個字母。stack bottom-first/top-last，pop一個top再按原replacement順序append；只施來源明示bottom guard，不另加更強慣例。", "en": "Check each original transition's state,input and stack roles without mixing alphabets.Null is epsilon,not an input symbol.The stack is bottom-first/top-last:pop one top then append the replacement in its original order.Apply the declared bottom guard,not an invented stronger convention." }, "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 transition index=1;[from,input_or_null,required_top,to,replacement_bottom_to_top]=[push12, a12, A12, push12, [A12, A12]];bottom=Z12", "after": "states/input/stack symbols legal;null input consumes0;top=bottom requires replacement first bottom,otherwise replacement contains NO bottom;ORIGINAL transition position retained", "relation": "implies", "rule_id": "pda_EVERY_original_transition_roles_epsilon_bottom_guard", "conditions": [], "explanation": { "zh-Hant": "逐原transition核state、input與stack角色，不把字母表混用；null是epsilon而不是一個字母。stack bottom-first/top-last，pop一個top再按原replacement順序append；只施來源明示bottom guard，不另加更強慣例。", "en": "Check each original transition's state,input and stack roles without mixing alphabets.Null is epsilon,not an input symbol.The stack is bottom-first/top-last:pop one top then append the replacement in its original order.Apply the declared bottom guard,not an invented stronger convention." }, "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 transition index=2;[from,input_or_null,required_top,to,replacement_bottom_to_top]=[push12, b12, A12, pop12, []];bottom=Z12", "after": "states/input/stack symbols legal;null input consumes0;top=bottom requires replacement first bottom,otherwise replacement contains NO bottom;ORIGINAL transition position retained", "relation": "implies", "rule_id": "pda_EVERY_original_transition_roles_epsilon_bottom_guard", "conditions": [], "explanation": { "zh-Hant": "逐原transition核state、input與stack角色，不把字母表混用；null是epsilon而不是一個字母。stack bottom-first/top-last，pop一個top再按原replacement順序append；只施來源明示bottom guard，不另加更強慣例。", "en": "Check each original transition's state,input and stack roles without mixing alphabets.Null is epsilon,not an input symbol.The stack is bottom-first/top-last:pop one top then append the replacement in its original order.Apply the declared bottom guard,not an invented stronger convention." }, "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 transition index=3;[from,input_or_null,required_top,to,replacement_bottom_to_top]=[pop12, b12, A12, pop12, []];bottom=Z12", "after": "states/input/stack symbols legal;null input consumes0;top=bottom requires replacement first bottom,otherwise replacement contains NO bottom;ORIGINAL transition position retained", "relation": "implies", "rule_id": "pda_EVERY_original_transition_roles_epsilon_bottom_guard", "conditions": [], "explanation": { "zh-Hant": "逐原transition核state、input與stack角色，不把字母表混用；null是epsilon而不是一個字母。stack bottom-first/top-last，pop一個top再按原replacement順序append；只施來源明示bottom guard，不另加更強慣例。", "en": "Check each original transition's state,input and stack roles without mixing alphabets.Null is epsilon,not an input symbol.The stack is bottom-first/top-last:pop one top then append the replacement in its original order.Apply the declared bottom guard,not an invented stronger convention." }, "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 transition index=4;[from,input_or_null,required_top,to,replacement_bottom_to_top]=[push12, null, Z12, accept12, [Z12]];bottom=Z12", "after": "states/input/stack symbols legal;null input consumes0;top=bottom requires replacement first bottom,otherwise replacement contains NO bottom;ORIGINAL transition position retained", "relation": "implies", "rule_id": "pda_EVERY_original_transition_roles_epsilon_bottom_guard", "conditions": [], "explanation": { "zh-Hant": "逐原transition核state、input與stack角色，不把字母表混用；null是epsilon而不是一個字母。stack bottom-first/top-last，pop一個top再按原replacement順序append；只施來源明示bottom guard，不另加更強慣例。", "en": "Check each original transition's state,input and stack roles without mixing alphabets.Null is epsilon,not an input symbol.The stack is bottom-first/top-last:pop one top then append the replacement in its original order.Apply the declared bottom guard,not an invented stronger convention." }, "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=5;[from,input_or_null,required_top,to,replacement_bottom_to_top]=[pop12, null, Z12, accept12, [Z12]];bottom=Z12", "after": "states/input/stack symbols legal;null input consumes0;top=bottom requires replacement first bottom,otherwise replacement contains NO bottom;ORIGINAL transition position retained", "relation": "implies", "rule_id": "pda_EVERY_original_transition_roles_epsilon_bottom_guard", "conditions": [], "explanation": { "zh-Hant": "逐原transition核state、input與stack角色，不把字母表混用；null是epsilon而不是一個字母。stack bottom-first/top-last，pop一個top再按原replacement順序append；只施來源明示bottom guard，不另加更強慣例。", "en": "Check each original transition's state,input and stack roles without mixing alphabets.Null is epsilon,not an input symbol.The stack is bottom-first/top-last:pop one top then append the replacement in its original order.Apply the declared bottom guard,not an invented stronger convention." }, "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": "PDA complete ORIGINAL transition count := sum(1, 1, 1, 1, 1, 1)", "after": "PDA complete ORIGINAL transition count = 6", "relation": "calculation", "rule_id": "exact_rational_arithmetic", "conditions": [], "explanation": { "zh-Hant": "依原始角色、次序與已核中間量精確代值；不改source binding或用浮點近似。", "en": "Substitute original roles,order and established intermediates exactly,without changing source bindings or using floating-point approximations." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "以精確有理數重算 PDA complete ORIGINAL transition count，不以小數近似替代。", "en": "Recompute PDA complete ORIGINAL transition count with exact rational arithmetic, not rounded decimals." } }, "arithmetic": { "operation": "sum", "inputs": [ "1", "1", "1", "1", "1", "1" ], "output": "6", "label": "PDA complete ORIGINAL transition count" } }, { "id": "S009", "uses": [ "G001", "S008" ], "before": "ORIGINAL states=[push12, pop12, accept12],input alphabet=[a12, b12],stack alphabet=[Z12, A12];start=push12,bottom=Z12,final states=[accept12]", "after": "finite unique pairwise-disjoint alphabets qualified;transition count=6;acceptance convention FULL input in final state,NOT empty stack;qualification alone proves NO run,determinism or CFG equivalence", "relation": "implies", "rule_id": "pda_complete_definition_not_determinism_or_accepting_run", "conditions": [], "explanation": { "zh-Hant": "有限完整定義的資格不等於存在接受run，也不推deterministic或CFG等價。接受時可保非空stack（至少bottom），但必須讀完整input到final。", "en": "A qualified complete definition gives no accepting run,determinism or CFG-equivalence proof.Acceptance may retain a nonempty stack,including its bottom,but requires full input consumption in a final state." }, "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": [ [ "push12", "pop12", "accept12" ], [ "a12", "b12" ], [ "Z12", "A12" ], "push12", "Z12", [ "accept12" ], 6, true, "accept_only_after_full_input_in_final_state_bottom_marker_preserved" ] }, "conclusion": { "canonical_value": "([push12, pop12, accept12], [a12, b12], [Z12, A12], push12, Z12, [accept12], 6, 是, accept_only_after_full_input_in_final_state_bottom_marker_preserved)", "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-20261110-r07-pushdown-automaton-foundations", "batch_path": "public/data/questions/batches/batch-20261014-advance-20261110-r07-pushdown-automaton-foundations/questions.jsonl", "batch_sha256": "236ebf7fa3a2cca5c2cd5e8058cd576a90d0637db9efc8d95dcea38f63a1055e", "original_line": 13, "original_line_sha256": "f58195528a2f0e211e8cb844300f75193e3c8ad03aca85492b43d90b52f634c6", "question_compact_sha256": "7de5cd716f8ea05e991899cfa9e2f8590355993e37de257d65f6bd9f6697a4a0", "english_row_compact_sha256": "564c9a2edc699069766dad295912c9108c1dcd3355b1cb158e20752706ae722a", "english_manifest_path": "public/data/i18n/editions/batch-20261014-advance-20261110-r07-pushdown-automaton-foundations.en.json", "english_rows_path": "public/data/i18n/questions/batch-20261014-advance-20261110-r07-pushdown-automaton-foundations.en.jsonl" }, "mko_bindings": { "mko-pushdown-automaton": { "sha256": "95321a6ccc573a74997a3ea1c00f5b63623fbe7f09a34e305b5357dfd4ce1ba7", "english_sha256": "6af04c57849b9bb696bff49fd70aea9cd365c9b7249350fce67f10053d0a967f", "original_path": "public/data/mko/pushdown-automaton.json", "english_path": "public/data/i18n/editions/mko-pushdown-automaton.en.json" } }, "selected_manifest_sha256": "5233edba9654a6cffd8b6b2d83c932f82ded15f9c0b7c733bd049943e672acff", "selected_part_sha256": "747b98e75085a6b55251b2d7e04bbf7c60cb5500e5047439b2798fb5f45538fa", "original_candidate_sha256": "3989b69fc022adc364818047fedd7d17ed2bb757ae65a8af48e058101d571251", "original_candidate_line_sha256": "3989b69fc022adc364818047fedd7d17ed2bb757ae65a8af48e058101d571251" }, "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-p44", "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": "49cf6ec60211c92d1c0c302663af4d44479635dc8181fb61a20c3374288e21c5", "question_first_witness_sha256": "10fd25b4643e5ff12753daceaa61f9f2499bf381f65ef96e9d21185c7c0d0c5e" }, "status": "second_context_reviewed", "mathematical_semantics": true, "bilingual_semantics": true, "steps_reviewed": 9, "method": "family_template_semantic_review_plus_independent_per_instance_reconstruction", "exact_question_first_check": { "model_sha256": "8f98c36a869242af7e7e75976ca15a748791a6165c88f5e3561686add45caf22", "arithmetic_steps": 1 }, "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." } }