{ "schema_version": "ocme-reviewed-question-reader-v1", "question_id": "q-20260914-basic-counting-principle-0017", "pilot_number": "R0070-35537", "number": 35537, "family_id": "qf-basic-counting-principle", "title": { "zh-Hant": "第 35537 題：基本計數原理邊界", "en": "Question 35537: Boundary of the Basic Counting Principles" }, "original_question": { "schema_version": "ocme-question-v0.1", "id": "q-20260914-basic-counting-principle-0017", "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": "一件工作可由兩個明示互斥分支完成，分支數分別為 18 與 7。總數是多少？", "answer": { "kind": "numeric", "value": 25, "explanation_zh": "分支已明示互斥，所以 18+7=25。" }, "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": 20261010, "parameters": { "mode": "addition_disjoint", "branch_counts": [ 18, 7 ], "stages": [ 2, 5 ], "overlap_witness": null, "conditional_stage_witness": null, "semantic_template": "qf-basic-counting-principle/{\"branch_counts\":[18,7],\"mode\":\"addition_disjoint\"}" } }, "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-0017", "batch_id": "batch-20260914-domain-foundations", "locale": "en", "translation_state": "ai_candidate", "source": { "question_sha256": "e65abe078567781b55ab8e60f7e23a013b3100a42ba73d181fbbe0cd4c533111", "family_id": "qf-basic-counting-principle", "seed": 20261010, "semantic_template": "qf-basic-counting-principle/{\"branch_counts\":[18,7],\"mode\":\"addition_disjoint\"}" }, "fields": { "title": "Boundary of the Basic Counting Principles", "stem": "A task can be completed through two explicitly disjoint branches with 18 and 7 outcomes. What is the total?", "answer": { "kind": "numeric", "value": 25, "explanation": "The branches are explicitly disjoint, so 18+7=25." }, "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": "一件工作可由兩個明示互斥分支完成，分支數分別為 18 與 7。總數是多少？", "en": "A task can be completed through two explicitly disjoint branches with 18 and 7 outcomes. What is the total?" } } ], "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 = [18, 7, addition_disjoint]", "after": "derived = [18, 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": "Counting disjoint union cardinality := sum(18, 7)", "after": "Counting disjoint union cardinality = 25", "relation": "calculation", "rule_id": "exact_rational_arithmetic", "conditions": [], "explanation": { "zh-Hant": "本步精確列出原操作數與運算；乘、減、除恰兩項。分數保持精確，衍生BigInt不重套raw SAFE，不用近似值湊答案。", "en": "This step displays the exact original operands and operation.Mul/sub/div have EXACTLY TWO inputs.Keep rational values exact and derived BigInts unbounded;do not force an answer by approximation." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "以精確有理數重算 Counting disjoint union cardinality，不以小數近似替代。", "en": "Recompute Counting disjoint union cardinality with exact rational arithmetic, not rounded decimals." } }, "arithmetic": { "operation": "sum", "inputs": [ "18", "7" ], "output": "25", "label": "Counting disjoint union cardinality" } }, { "id": "S004", "uses": [ "G001", "S003" ], "before": "source roles = [18, 7]", "after": "derived = [25]", "relation": "implies", "rule_id": "Counting_DISJOINT_no_double_count", "conditions": [], "explanation": { "zh-Hant": "題目已給兩分支互斥，聯集每個結果恰被計一次，故|A∪B|=|A|+|B|。這不是未證明互斥時的通則。", "en": "The branches are GIVEN disjoint,so every union outcome is counted once:|A∪B|=|A|+|B|.This is not a rule without the disjointness premise." }, "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": 25 }, "conclusion": { "canonical_value": "25", "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": 97, "original_line_sha256": "cf6de9498bd665728a0fed58abc30a6b66ffbbed47e99cbc0b6e2b83636f8402", "question_compact_sha256": "e65abe078567781b55ab8e60f7e23a013b3100a42ba73d181fbbe0cd4c533111", "english_row_compact_sha256": "16facaede29ebd34dcf07e8b21f12dcb13a29df64bd40792c4132a655a8062c9", "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": "fcc15dc4bbd5d66fc8238c13ae32f286a93ea4e9565531280bae73c2242ed5c9", "original_candidate_line_sha256": "fcc15dc4bbd5d66fc8238c13ae32f286a93ea4e9565531280bae73c2242ed5c9" }, "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": 4, "method": "family_template_semantic_review_plus_independent_per_instance_reconstruction", "exact_question_first_check": { "model_sha256": "763dcd26441eddc858a86433623e602ba31bc5666ff234994531c2cbebf5b37b", "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." } }