{ "schema_version": "ocme-reviewed-question-reader-v1", "question_id": "q-20260914-basic-counting-principle-0011", "pilot_number": "R0070-35531", "number": 35531, "family_id": "qf-basic-counting-principle", "title": { "zh-Hant": "第 35531 題：基本計數原理邊界", "en": "Question 35531: Boundary of the Basic Counting Principles" }, "original_question": { "schema_version": "ocme-question-v0.1", "id": "q-20260914-basic-counting-principle-0011", "batch_id": "batch-20260914-domain-foundations", "language": "zh-Hant", "source_mko_ids": [ "mko-counting-principle" ], "title_zh": "基本計數原理邊界", "stem_zh": "兩個選擇分支各報稱有 12 與 7 種結果，但都包含「共用結果11」。是否可無條件直接相加？", "answer": { "kind": "choice", "value": "不可無條件相加", "choices": [ "不可無條件相加", "不可無條件相乘" ], "explanation_zh": "「共用結果11」同時屬於兩分支，直接相加會重複計數。" }, "difficulty": { "band": "upper_secondary", "level": 2, "skills": [ "基本計數原理", "條件辨識" ] }, "variant": { "family_id": "qf-basic-counting-principle", "seed": 20261004, "parameters": { "mode": "addition_overlap", "branch_counts": [ 12, 7 ], "stages": [ 4, 3 ], "overlap_witness": "共用結果11", "conditional_stage_witness": null, "semantic_template": "qf-basic-counting-principle/{\"branch_counts\":[12,7],\"mode\":\"addition_overlap\",\"overlap_witness\":\"共用結果11\"}" } }, "verification": { "status": "candidate", "checks": [ "schema_pending", "independent_recomputation_pending" ], "warning_zh": "本題僅依明示的有限參數重算或分類；不構成普遍證明、形式 Evidence、人工審查或發布。" }, "provenance": { "generator_role": "question_producer", "generator_model": "GPT-5.6 Terra", "generated_at": "2026-09-14", "contract_version": "ocme-question-factory-v0.1" } }, "original_english_edition": { "schema_version": "ocme-question-localization-v0.1", "question_id": "q-20260914-basic-counting-principle-0011", "batch_id": "batch-20260914-domain-foundations", "locale": "en", "translation_state": "ai_candidate", "source": { "question_sha256": "48079f58f5629b73a288d9b029d356308e6c97c2693a16d6b20939201fe08cb7", "family_id": "qf-basic-counting-principle", "seed": 20261004, "semantic_template": "qf-basic-counting-principle/{\"branch_counts\":[12,7],\"mode\":\"addition_overlap\",\"overlap_witness\":\"共用結果11\"}" }, "fields": { "title": "Boundary of the Basic Counting Principles", "stem": "Two branches report 12 and 7 outcomes, but both include shared outcome 11. May their counts be added unconditionally?", "answer": { "kind": "choice", "value": "Cannot add unconditionally", "choices": [ "Cannot add unconditionally", "Cannot multiply unconditionally" ], "explanation": "The shared outcome belongs to both branches, so direct addition would count it twice." }, "skills": [ "basic counting principles", "condition recognition" ], "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": "兩個選擇分支各報稱有 12 與 7 種結果，但都包含「共用結果11」。是否可無條件直接相加？", "en": "Two branches report 12 and 7 outcomes, but both include shared outcome 11. May their counts be added unconditionally?" } } ], "steps": [ { "id": "S001", "uses": [ "G001" ], "before": "source roles = [qf-basic-counting-principle, [branch_counts, conditional_stage_witness, mode, overlap_witness, stages]]", "after": "derived = [counting, null, null]", "relation": "implies", "rule_id": "R70_SOURCE_bank_specific_interface", "conditions": [], "explanation": { "zh-Hant": "只使用此bank真正明示的欄位、operation/domain與型別；BASE容許保留額外metadata，不把LDL SAFE/集合上限或其他bank的去重規則搬來。", "en": "Use THIS bank’s actual fields,operation/domain and types.BASE retains permissible extra metadata.Do not import LDL SAFE/set limits or a different bank’s deduplication rules." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "反查本題原始操作數、角色與必要條件；重建下一步，不把單向推論倒當等價。數值/有限表核對不是任意命題的形式證明。原題、中英來源、MKO、AST、狀態與歷史均保留。", "en": "Reverse-audit THIS question’s original operands,roles and necessary premises;reconstruct the next step,without reversing a one-way implication.Numerical/finite-table checking is not formal proof of an arbitrary theorem.Original Q,bilingual sources,MKO,AST,status and history remain preserved." } }, "arithmetic": null }, { "id": "S002", "uses": [ "G001", "S001" ], "before": "source roles = [12, 7, addition_overlap]", "after": "derived = [12, 7]", "relation": "implies", "rule_id": "Counting_TWO_GIVEN_branch_cardinalities", "conditions": [], "explanation": { "zh-Hant": "兩分支個數均為明示正整數；能否相加還要查互斥/重疊前提，不單憑看到兩個數字就相加。", "en": "Both branch counts are GIVEN positive integers.Addition still requires the disjointness/overlap premise,not merely two numbers." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "反查本題原始操作數、角色與必要條件；重建下一步，不把單向推論倒當等價。數值/有限表核對不是任意命題的形式證明。原題、中英來源、MKO、AST、狀態與歷史均保留。", "en": "Reverse-audit THIS question’s original operands,roles and necessary premises;reconstruct the next step,without reversing a one-way implication.Numerical/finite-table checking is not formal proof of an arbitrary theorem.Original Q,bilingual sources,MKO,AST,status and history remain preserved." } }, "arithmetic": null }, { "id": "S003", "uses": [ "G001", "S002" ], "before": "source roles = [12, 7, 共用結果11]", "after": "derived = [不可無條件相加]", "relation": "implies", "rule_id": "Counting_OVERLAP_given_witness_blocks_unconditional_sum", "conditions": [], "explanation": { "zh-Hant": "已給共同結果w，簡單加總把w至少算兩次。正確聯集須減交集大小；本題未給完整交集個數，所以只判定不可無條件相加，不捏造聯集總數。", "en": "A GIVEN shared outcome w would be counted at least twice by simple addition.A union count requires subtracting intersection size;the full intersection count is not given,so do not invent a union total." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "反查本題原始操作數、角色與必要條件；重建下一步，不把單向推論倒當等價。數值/有限表核對不是任意命題的形式證明。原題、中英來源、MKO、AST、狀態與歷史均保留。", "en": "Reverse-audit THIS question’s original operands,roles and necessary premises;reconstruct the next step,without reversing a one-way implication.Numerical/finite-table checking is not formal proof of an arbitrary theorem.Original Q,bilingual sources,MKO,AST,status and history remain preserved." } }, "arithmetic": null } ], "math_model": { "result": "不可無條件相加" }, "conclusion": { "canonical_value": "不可無條件相加", "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-20260914-domain-foundations", "batch_path": "public/data/questions/batches/batch-20260914-domain-foundations/questions.jsonl", "batch_sha256": "726b3f94ccd05d8c91cc7e306b42fd71b6d9040e194db91739a250d488fd1de7", "original_line": 91, "original_line_sha256": "39856fedacf66bd8c1a0aa540bce41c39b7934024e57238eb4b5f76d71a7cbc7", "question_compact_sha256": "48079f58f5629b73a288d9b029d356308e6c97c2693a16d6b20939201fe08cb7", "english_row_compact_sha256": "93e8c718624b944c350f28e0f0bcc029489adaf8e0600872c6bb02e7e1463ebb", "english_manifest_path": "public/data/i18n/editions/batch-20260914-domain-foundations.en.json", "english_rows_path": "public/data/i18n/questions/batch-20260914-domain-foundations.en.jsonl" }, "mko_bindings": { "mko-counting-principle": { "sha256": "0a0619ebbab98b96543b42abc4e66d927aeea705c65ee85b3a9badb6d3b3cf57", "english_sha256": "122425d1403554c17fc2a0e18e7b67e807bc50d412bad0250aa17710f6a34102", "original_path": "public/data/mko/counting-principle.json", "english_path": "public/data/i18n/editions/mko-counting-principle.en.json" } }, "selected_manifest_sha256": "5233edba9654a6cffd8b6b2d83c932f82ded15f9c0b7c733bd049943e672acff", "selected_part_sha256": "20c37a7e64ee5969e7606c5cc3a00e575002ebebdfe82873521cc3d7c608caff", "original_candidate_sha256": "06400bfe85e766917b527b074bfc320445379ab62019d523d5f1a317099dc013", "original_candidate_line_sha256": "06400bfe85e766917b527b074bfc320445379ab62019d523d5f1a317099dc013" }, "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-20261026-012-p71", "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": "9820ac6529139bd53d516c8bfdfdd41184b0cd52dad69fa433344010db37af80", "question_first_witness_sha256": "c9c939762bbd4d3ea3403084c8e95541dc2c7e56eb82fc74eaba8c80a4517dab" }, "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": "90663dcb5ead49442be54eb7f6037a98439c47cf2ce7a11a9aa9bfc7a6225fad", "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." } }