{ "schema_version": "ocme-reviewed-question-reader-v1", "question_id": "q-20261014-advance-20261031-r01-at-most-countable-set-0076", "pilot_number": "R0030-15826", "number": 15826, "family_id": "qf-mod31-countable-classification", "title": { "zh-Hant": "第 15826 題：至多可數集", "en": "Question 15826: A Failed Encoding Does Not Prove Uncountability" }, "original_question": { "schema_version": "ocme-question-v0.1", "id": "q-20261014-advance-20261031-r01-at-most-countable-set-0076", "batch_id": "batch-20261014-advance-20261031-r01-at-most-countable-set-foundations", "language": "zh-Hant", "source_mko_ids": [ "mko-at-most-countable-set" ], "title_zh": "至多可數集", "stem_zh": "有限完整清單或明示全稱注入證書。操作=countable-classification；資料={\"evidence_mode\":\"complete_finite_list\",\"certificate_parameter\":1}。請依 [evidence_mode,certificate_parameter,proved,classification] 欄序回答。", "answer": { "kind": "expression", "value": "(complete_finite_list, 1, 是, at_most_countable)", "explanation_zh": "Wave4收束核對=(complete_finite_list, 1, 是, at_most_countable)；依完整明示資料重算；有限與可數無限不可混同；單一失敗encoding不證不可數。" }, "difficulty": { "band": "undergraduate_core", "level": 1, "skills": [ "至多可數集" ] }, "variant": { "family_id": "qf-mod31-countable-classification", "seed": 202610311076, "parameters": { "evidence_mode": "complete_finite_list", "certificate_parameter": 1, "domain": "Explicit_at_most_countable_certificate", "operation": "countable-classification", "semantic_template": "qf-mod31-countable-classification/{\"certificate_parameter\":1,\"evidence_mode\":\"complete_finite_list\"}" } }, "verification": { "status": "candidate", "checks": [ "producer_exact_finite_model", "producer_source_snapshot_check", "producer_substantive_template_deduplication", "producer_json_schema" ], "warning_zh": "候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式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-20261031-r01-at-most-countable-set-0076", "batch_id": "batch-20261014-advance-20261031-r01-at-most-countable-set-foundations", "locale": "en", "translation_state": "ai_candidate", "source": { "question_sha256": "774e32691c1b969ce0c570c47cb658547376413e0f0b2b8da59e416af5e3700f", "family_id": "qf-mod31-countable-classification", "seed": 202610311076, "semantic_template": "qf-mod31-countable-classification/{\"certificate_parameter\":1,\"evidence_mode\":\"complete_finite_list\"}" }, "fields": { "title": "A Failed Encoding Does Not Prove Uncountability", "stem": "Declared evidence_mode=complete_finite_list, certificate_parameter=1. The registered modes complete_finite_list and universal_affine_injection refer to their supplied complete or universal certificates; failed_candidate_encoding records only a failed witness. Give (evidence_mode,certificate_parameter,proved?,classification).", "answer": { "kind": "expression", "value": "(complete_finite_list, 1, Yes, at_most_countable)", "explanation": "This mode audit reports at_most_countable for a declared qualifying certificate and no_classification_from_failed_witness for the failed mode. A numeric certificate parameter alone is not a new construction or verification of an unspecified set. Failure of one encoding does not establish uncountability. The exact result, retaining the requested order, is (complete_finite_list, 1, Yes, at_most_countable)." }, "skills": [ "A Failed Encoding Does Not Prove Uncountability" ], "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": "有限完整清單或明示全稱注入證書。操作=countable-classification；資料={\"evidence_mode\":\"complete_finite_list\",\"certificate_parameter\":1}。請依 [evidence_mode,certificate_parameter,proved,classification] 欄序回答。", "en": "Declared evidence_mode=complete_finite_list, certificate_parameter=1. The registered modes complete_finite_list and universal_affine_injection refer to their supplied complete or universal certificates; failed_candidate_encoding records only a failed witness. Give (evidence_mode,certificate_parameter,proved?,classification)." } } ], "steps": [ { "id": "S001", "uses": [ "G001" ], "before": "registered DECLARED evidence mode=complete_finite_list;numeric certificate parameter=1", "after": "qualifying declared certificate flag=是;classification=at_most_countable", "relation": "implies", "rule_id": "countability_declared_evidence_mode_not_unspecified_set_construction", "conditions": [], "explanation": { "zh-Hant": "這是對宣告已供應的完整／全稱證書作mode核對，數字參數本身不構造或證明一個未知集合。某個encoding失敗只否定那個見證，不能由此斷言不可數；at most countable亦不等於可數無限。", "en": "This audits the declared complete or universal certificate mode;the numeric parameter does not construct or verify an unspecified set.A failed encoding refutes that witness,not countability itself.At most countable does not mean countably infinite." }, "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": [ "complete_finite_list", 1, true, "at_most_countable" ] }, "conclusion": { "canonical_value": "(complete_finite_list, 1, 是, at_most_countable)", "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-20261031-r01-at-most-countable-set-foundations", "batch_path": "public/data/questions/batches/batch-20261014-advance-20261031-r01-at-most-countable-set-foundations/questions.jsonl", "batch_sha256": "7b382f15a68b0f6e0c1e44dc793ede056d8bd39aff2ca4e878a95654740ee01a", "original_line": 76, "original_line_sha256": "da9a195e864cfa3812d45693e3381ba828f8d837b702a992b4ae4e4968869bef", "question_compact_sha256": "774e32691c1b969ce0c570c47cb658547376413e0f0b2b8da59e416af5e3700f", "english_row_compact_sha256": "5fe5898829b4fc278f54e429c0c8fcba894aa6add125d835ce083c5d8b4a1d7a", "english_manifest_path": "public/data/i18n/editions/batch-20261014-advance-20261031-r01-at-most-countable-set-foundations.en.json", "english_rows_path": "public/data/i18n/questions/batch-20261014-advance-20261031-r01-at-most-countable-set-foundations.en.jsonl" }, "mko_bindings": { "mko-at-most-countable-set": { "sha256": "9c7748686b7974341920a59d07628f20017ef6d65476d751b2feb7424f7b3b57", "english_sha256": "a73faf7f1c04553efad774692eab18a2de59165f0fedaac3ba03ee75c7276def", "original_path": "public/data/mko/at-most-countable-set.json", "english_path": "public/data/i18n/editions/mko-at-most-countable-set.en.json" } }, "selected_manifest_sha256": "5233edba9654a6cffd8b6b2d83c932f82ded15f9c0b7c733bd049943e672acff", "selected_part_sha256": "d85118d74859ec7e59736714f767732c6ec092eaa0bf5279abeb28e4a628e3c3", "original_candidate_sha256": "f5867832b7a1eb7a302a9bb8e9f20d537f635990f2a35a1f279ee4735bca460b", "original_candidate_line_sha256": "f5867832b7a1eb7a302a9bb8e9f20d537f635990f2a35a1f279ee4735bca460b" }, "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-20261026-007-p31", "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": "73bc08066ffb1a81eacb2d4e288d03f522aeefd3949fa0d97da41b484ed737bc", "question_first_witness_sha256": "ac120452a208b257b8270f38351a09dcd832cdbc8d9db6b69933f83e43cc9336" }, "status": "second_context_reviewed", "mathematical_semantics": true, "bilingual_semantics": true, "steps_reviewed": 1, "method": "family_template_semantic_review_plus_independent_per_instance_reconstruction", "exact_question_first_check": { "model_sha256": "f0ca09e3e958a8ed1c72fe9709703afcd329f4479ddcc51d2016d8ff0930ab23", "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." } }