{ "schema_version": "ocme-reviewed-question-reader-v1", "question_id": "q-20261006-advance-20261007-r01-matrix-0020", "pilot_number": "R0065-33170", "number": 33170, "family_id": "qf-matrix-shape", "title": { "zh-Hant": "第 33170 題：非空矩陣尺寸", "en": "Question 33170: Dimensions of a Nonempty Matrix" }, "original_question": { "schema_version": "ocme-question-v0.1", "id": "q-20261006-advance-20261007-r01-matrix-0020", "batch_id": "batch-20261006-advance-20261007-r01-matrix-foundations", "language": "zh-Hant", "source_mko_ids": [ "mko-matrix" ], "title_zh": "非空矩陣尺寸", "stem_zh": "實矩陣，橫列／直行次序固定，M=[[7, 6, 5, 4, 3], [9, 8, 7, 6, 5], [11, 10, 9, 8, 7], [13, 12, 11, 10, 9]]。求 (橫列數, 直行數)，每邊為1至5。", "answer": { "kind": "short_text", "value": "(4, 5)", "explanation_zh": "尺寸=(4, 5)。先驗矩形等長橫列，再計兩個維度，不把元素個數當其中一個邊長。" }, "difficulty": { "band": "undergraduate_core", "level": 3, "skills": [ "非空矩陣尺寸" ] }, "variant": { "family_id": "qf-matrix-shape", "seed": 202610071020, "parameters": { "M": [ [ 7, 6, 5, 4, 3 ], [ 9, 8, 7, 6, 5 ], [ 11, 10, 9, 8, 7 ], [ 13, 12, 11, 10, 9 ] ], "operation": "matrix_shape", "domain": "reals", "semantic_template": "qf-matrix-shape/{\"inputs\":[4,5],\"operation\":\"matrix_shape\"}" } }, "verification": { "status": "candidate", "checks": [ "producer_exact_integer_rational_arithmetic", "producer_finite_enumeration", "producer_source_snapshot_check", "producer_substantive_template_deduplication", "producer_json_schema" ], "warning_zh": "僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。" }, "provenance": { "generator_role": "question_producer", "generator_model": "model_unknown", "generated_at": "2026-10-06", "contract_version": "ocme-question-factory-v0.1" } }, "original_english_edition": { "schema_version": "ocme-question-localization-v0.1", "question_id": "q-20261006-advance-20261007-r01-matrix-0020", "batch_id": "batch-20261006-advance-20261007-r01-matrix-foundations", "locale": "en", "translation_state": "ai_candidate", "source": { "question_sha256": "5a403d66cf77e34af7657792a70b2b2f88b8dc33134f7d193ee3c28ddffc79c6", "family_id": "qf-matrix-shape", "seed": 202610071020, "semantic_template": "qf-matrix-shape/{\"inputs\":[4,5],\"operation\":\"matrix_shape\"}" }, "fields": { "title": "Dimensions of a Nonempty Matrix", "stem": "The real matrix M=[[7, 6, 5, 4, 3], [9, 8, 7, 6, 5], [11, 10, 9, 8, 7], [13, 12, 11, 10, 9]] is displayed as nested rows. Each dimension is from one through five. Give (number of rows, number of columns).", "answer": { "kind": "short_text", "value": "(4, 5)", "explanation": "Count the nonempty equal-length rows and entries per row to obtain dimensions (4, 5). The total number of entries is not either dimension by itself." }, "skills": [ "Dimensions of a Nonempty Matrix" ], "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": "實矩陣，橫列／直行次序固定，M=[[7, 6, 5, 4, 3], [9, 8, 7, 6, 5], [11, 10, 9, 8, 7], [13, 12, 11, 10, 9]]。求 (橫列數, 直行數)，每邊為1至5。", "en": "The real matrix M=[[7, 6, 5, 4, 3], [9, 8, 7, 6, 5], [11, 10, 9, 8, 7], [13, 12, 11, 10, 9]] is displayed as nested rows. Each dimension is from one through five. Give (number of rows, number of columns)." } } ], "steps": [ { "id": "S001", "uses": [ "G001" ], "before": "source roles = [qf-matrix-shape, matrix_shape, reals, []]", "after": "derived = [[rows_columns_NUMBER_pair]]", "relation": "implies", "rule_id": "R65_SOURCE_bank_keys_operation_domain_ordered_output_roles", "conditions": [], "explanation": { "zh-Hant": "MOD25用LOCAL hyphen及具名domain，矩陣legacy用underscore/reals，BASElogic不補domain/op。輸出tuple/矩陣/數字欄與fraction文字各依來源，不一律保/1；原中英/AST/status不變。", "en": "MOD25 uses LOCAL hyphens/named domains,legacy matrices underscores/reals;BASE logic acquires no domain/op.Output tuples,matrices,numeric fields and fraction texts follow THIS source,not a universal/1 rule.Retain originals/English/AST/status." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "以原始資料、型別、欄序、論域與明示前提反向核對；不表示結論唯一還原前提。有限來源候選、獨立審查、形式證明及發布各自分開。", "en": "Reverse-check ORIGINAL data,types,ordered roles,domain and premises;the conclusion need not uniquely recover its premises.Keep finite source candidates,independent review,formal proof and publication separate." } }, "arithmetic": null }, { "id": "S002", "uses": [ "G001", "S001" ], "before": "source roles = [M ORIGINAL, [[7, 6, 5, 4, 3], [9, 8, 7, 6, 5], [11, 10, 9, 8, 7], [13, 12, 11, 10, 9]]]", "after": "derived = [4, 5]", "relation": "implies", "rule_id": "Matrix_RAW_rectangular_1to5_ALL_SAFE_entries_even_unused", "conditions": [], "explanation": { "zh-Hant": "本bank允許1..5乘1..5矩陣，不搬R64的2×2界。每個raw cell先驗SAFE，包括shape/entry未選到的欄位；不改原row順序。", "en": "THIS bank allows1..5 by1..5 matrices,not the R64 2×2 restriction.Type EVERY raw SAFE cell,including unused shape/entry cells.Keep original row order." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "以原始資料、型別、欄序、論域與明示前提反向核對；不表示結論唯一還原前提。有限來源候選、獨立審查、形式證明及發布各自分開。", "en": "Reverse-check ORIGINAL data,types,ordered roles,domain and premises;the conclusion need not uniquely recover its premises.Keep finite source candidates,independent review,formal proof and publication separate." } }, "arithmetic": null }, { "id": "S003", "uses": [ "G001", "S002" ], "before": "source roles = [[[7, 6, 5, 4, 3], [9, 8, 7, 6, 5], [11, 10, 9, 8, 7], [13, 12, 11, 10, 9]]]", "after": "derived = [4, 5, 20]", "relation": "implies", "rule_id": "Matrix_SHAPE_rows_THEN_columns_NOT_total_entries", "conditions": [], "explanation": { "zh-Hant": "先數row再數每row欄數，shape為(m,n)，不是(n,m)或總entries。", "en": "Count rows FIRST,then columns per row.Shape is(m,n),not(n,m)or total entries." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "以原始資料、型別、欄序、論域與明示前提反向核對；不表示結論唯一還原前提。有限來源候選、獨立審查、形式證明及發布各自分開。", "en": "Reverse-check ORIGINAL data,types,ordered roles,domain and premises;the conclusion need not uniquely recover its premises.Keep finite source candidates,independent review,formal proof and publication separate." } }, "arithmetic": null } ], "math_model": { "result": [ 4, 5 ] }, "conclusion": { "canonical_value": "(4, 5)", "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-20261006-advance-20261007-r01-matrix-foundations", "batch_path": "public/data/questions/batches/batch-20261006-advance-20261007-r01-matrix-foundations/questions.jsonl", "batch_sha256": "7a870e76f1679781814f6ee29550fd91d2940bcdc5c617ba275d633c187947c5", "original_line": 20, "original_line_sha256": "aba59a68946cd1ca5ed30c70d14cb7aa7c7d1a9680a1f41e6e0f58514d7b23a4", "question_compact_sha256": "5a403d66cf77e34af7657792a70b2b2f88b8dc33134f7d193ee3c28ddffc79c6", "english_row_compact_sha256": "32822868e2c4b59e0729061133f401916a39c568764d5dbf03ca7293c78a7aa8", "english_manifest_path": "public/data/i18n/editions/batch-20261006-advance-20261007-r01-matrix-foundations.en.json", "english_rows_path": "public/data/i18n/questions/batch-20261006-advance-20261007-r01-matrix-foundations.en.jsonl" }, "mko_bindings": { "mko-matrix": { "sha256": "c0233ecc6ee07427af1589feb16108500eb2e48b0b2fb84b5b39f0f38b02f109", "english_sha256": "18504021d52173d8f2f8aa663d83dc058f5205bea2c677a9722daba770776432", "original_path": "public/data/mko/matrix.json", "english_path": "public/data/i18n/editions/mko-matrix.en.json" } }, "selected_manifest_sha256": "5233edba9654a6cffd8b6b2d83c932f82ded15f9c0b7c733bd049943e672acff", "selected_part_sha256": "871e2c05026567a1deae741d6b90b0588100c6482ee167c7f9f45af5b72d8606", "original_candidate_sha256": "79cee74f3d0af854a15765d2cdc29ec7285c80e2e2552618df0c4f845ab92c52", "original_candidate_line_sha256": "79cee74f3d0af854a15765d2cdc29ec7285c80e2e2552618df0c4f845ab92c52" }, "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-p66", "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": "92bb5fa69818f30cd2806d74a26bd5ede6c48c80d2ecc3d31a5130d4ad7666b6", "question_first_witness_sha256": "012b5aa905280d616be49aa9462daaa73bf7f6247d0a796e78bc5bcd24e6bd00" }, "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": "dc84b677b47b26dbad67d3d20d7e44783b550761660ece06d174e054ed301ecd", "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." } }