{ "schema_version": "ocme-reviewed-question-reader-v1", "question_id": "q-20261015-advance-20261117-r06-path-connected-space-0083", "pilot_number": "R0052-26658", "number": 26658, "family_id": "qf-mod48-path-connected-boundary", "title": { "zh-Hant": "第 26658 題：道路連通空間", "en": "Question 26658: A Disconnected Gap, Discrete Pair and Endpoint Samples Have Different Obstructions" }, "original_question": { "schema_version": "ocme-question-v0.1", "id": "q-20261015-advance-20261117-r06-path-connected-space-0083", "batch_id": "batch-20261015-advance-20261117-r06-path-connected-space-foundations", "language": "zh-Hant", "source_mko_ids": [ "mko-path-connected-space" ], "title_zh": "道路連通空間", "stem_zh": "unit-interval path的continuity、兩端點與全range containment責任。操作=path-connected-boundary；資料={\"mode\":\"connected_not_path\",\"scale\":8}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。", "answer": { "kind": "expression", "value": "(connected_not_path, 8, topologists_sine_curve_scaled, connected_but_not_path_connected, 否)", "explanation_zh": "Wave6第十一層核對=(connected_not_path, 8, topologists_sine_curve_scaled, connected_but_not_path_connected, 否)；依完整明示資料獨立重算；linear／box／concatenated paths逐段exact核對；有限samples、graph walk或單一端點對不足；connected一般不推出path connected。" }, "difficulty": { "band": "undergraduate_core", "level": 1, "skills": [ "道路連通空間" ] }, "variant": { "family_id": "qf-mod48-path-connected-boundary", "seed": 202611176083, "parameters": { "mode": "connected_not_path", "scale": 8, "domain": "Exact_explicit_path_connectedness", "operation": "path-connected-boundary", "semantic_template": "path-connected-boundary|{mode:\"connected_not_path\",scale:[8,1]}" } }, "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；不構成一般series、uniform-limit或topology定理證明、人工審定、Lean或Evidence。" }, "provenance": { "generator_role": "question_producer", "generator_model": "model_unknown", "generated_at": "2026-10-15", "contract_version": "ocme-question-factory-v0.1" } }, "original_english_edition": { "schema_version": "ocme-question-localization-v0.1", "question_id": "q-20261015-advance-20261117-r06-path-connected-space-0083", "batch_id": "batch-20261015-advance-20261117-r06-path-connected-space-foundations", "locale": "en", "translation_state": "ai_candidate", "source": { "question_sha256": "365bab14fb002be818e2a27cd200552b57a12db208721733bef41d82194333a3", "family_id": "qf-mod48-path-connected-boundary", "seed": 202611176083, "semantic_template": "path-connected-boundary|{mode:\"connected_not_path\",scale:[8,1]}" }, "fields": { "title": "A Disconnected Gap, Discrete Pair and Endpoint Samples Have Different Obstructions", "stem": "Use mode=connected_not_path, positive exact scale=8, and the declared example description in the result. Give (mode, scale, example_description, scope_or_obstruction, path_connectedness_inference_claim).", "answer": { "kind": "expression", "value": "(connected_not_path, 8, topologists_sine_curve_scaled, connected_but_not_path_connected, No)", "explanation": "A continuous image of the connected unit interval cannot cross the disconnected gap or meet both isolated points. Three endpoint/interior samples do not define a full continuous path. connected_not_path records a named topologist-sine-curve scope, not a supplied full curve construction/proof in this finite family. A single pair or graph walk does not prove the universal path-connectedness claim. The exact result, retaining the requested order, is (connected_not_path, 8, topologists_sine_curve_scaled, connected_but_not_path_connected, No)." }, "skills": [ "A Disconnected Gap, Discrete Pair and Endpoint Samples Have Different Obstructions" ], "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": "unit-interval path的continuity、兩端點與全range containment責任。操作=path-connected-boundary；資料={\"mode\":\"connected_not_path\",\"scale\":8}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。", "en": "Use mode=connected_not_path, positive exact scale=8, and the declared example description in the result. Give (mode, scale, example_description, scope_or_obstruction, path_connectedness_inference_claim)." } } ], "steps": [ { "id": "S001", "uses": [ "G001" ], "before": "source roles = [path-connected-boundary]", "after": "derived = [[mode, scale, space_or_samples, scope, path_claim]]", "relation": "implies", "rule_id": "source_ordered_fields_without_JS", "conditions": [], "explanation": { "zh-Hant": "直接列出此操作及mode的完整來源欄序，不需JavaScript；布林、字串與null角色保持區別，不補欄或以答案形狀猜介面。", "en": "List this operation/mode exact source field order without JavaScript.Keep Boolean,string and null roles distinct;do not pad fields or infer the interface from answer shape." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "反查原題的完整資料、型別、欄序與本步條件；有限核對不升格為無限定理的形式證明。", "en": "Reverse-check the complete original data,types,field order and premises;finite audits are not formal proofs of infinite theorems." } }, "arithmetic": null }, { "id": "S002", "uses": [ "G001", "S001" ], "before": "source roles = [connected_not_path, 8]", "after": "derived = [connected_not_path, 8, topologists_sine_curve_scaled, connected_but_not_path_connected, 否]", "relation": "implies", "rule_id": "Path_original_boundary_scope_NO_invented_full_infinite_witness", "conditions": [], "explanation": { "zh-Hant": "gap中跨兩側的連續實值path會依IVT取缺口值，矛盾；discrete兩點的連通image不能跨兩點。三個samples沒有定義完整path，不能據此否定某插值的可能；sine-curve僅保來源命名與範圍，不冒稱本頁已構造、形式驗證整個無限反例。", "en": "A real path crossing the gap must hit a missing value by IVT;a connected image cannot meet both points of a discrete two-point space.Three samples do not define a full path or rule out interpolation.The sine-curve branch retains the named source scope,not a newly constructed or formally verified infinite witness." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "反查原題的完整資料、型別、欄序與本步條件；有限核對不升格為無限定理的形式證明。", "en": "Reverse-check the complete original data,types,field order and premises;finite audits are not formal proofs of infinite theorems." } }, "arithmetic": null } ], "math_model": { "result": [ "connected_not_path", "8", "topologists_sine_curve_scaled", "connected_but_not_path_connected", false ] }, "conclusion": { "canonical_value": "(connected_not_path, 8, topologists_sine_curve_scaled, connected_but_not_path_connected, 否)", "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-20261015-advance-20261117-r06-path-connected-space-foundations", "batch_path": "public/data/questions/batches/batch-20261015-advance-20261117-r06-path-connected-space-foundations/questions.jsonl", "batch_sha256": "2455669d9f59c769c41b1462899255c75387a7fdce752cd36e1fad7467bb3f32", "original_line": 83, "original_line_sha256": "282963d1a4b3de90437492acc7badc25fd2245a7c44022e9141d4a9e50e6cb1b", "question_compact_sha256": "365bab14fb002be818e2a27cd200552b57a12db208721733bef41d82194333a3", "english_row_compact_sha256": "40898438cde657859f78f0d3b20d2cbd357fa396759bcc0d6aca9033265bf295", "english_manifest_path": "public/data/i18n/editions/batch-20261015-advance-20261117-r06-path-connected-space-foundations.en.json", "english_rows_path": "public/data/i18n/questions/batch-20261015-advance-20261117-r06-path-connected-space-foundations.en.jsonl" }, "mko_bindings": { "mko-path-connected-space": { "sha256": "6df47a43396e20219abd3fe5ab3d088f1aaf4a1022bc9628ef0fe164b6a45e17", "english_sha256": "bb59736c31f281af474355507a3b5172c4fd2b948847c2332ec737e88490c538", "original_path": "public/data/mko/path-connected-space.json", "english_path": "public/data/i18n/editions/mko-path-connected-space.en.json" } }, "selected_manifest_sha256": "5233edba9654a6cffd8b6b2d83c932f82ded15f9c0b7c733bd049943e672acff", "selected_part_sha256": "a3def7368821a4d3dc7757fefd3c4a099713f8de8fb8e6f3434025e9d7b5a6d0", "original_candidate_sha256": "0efb51e3eb83c913e5cf79032fe6f75bdd8d82ee5633749f90bb20bc33be1353", "original_candidate_line_sha256": "0efb51e3eb83c913e5cf79032fe6f75bdd8d82ee5633749f90bb20bc33be1353", "mko_binding_revision": { "id": "edition-symbol-bindings-20261101", "path": "content/edition-symbol-bindings-20261101/revision.json", "sha256": "e9b4c69f2c4732074c37abb624c8ab8a70afc3645c12bf9df2268ef650ad7b6c", "previous_english_sha256": { "mko-path-connected-space": "b17c14e650f00c01de1e7a49d95f7fbc2a4d9dcdac715c039f9e61fb4f9de607" } } }, "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-20261026-010-p53", "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": "729b25cbf6bf5cb1d07a21a511ae216ec5fdd54a4a7aa2f7c21156b81ff37252", "question_first_witness_sha256": "d1ab788770eaad04f986986e65afb0d55791e8a8c0d747e9a2b499f79fe78df2" }, "status": "second_context_reviewed", "mathematical_semantics": true, "bilingual_semantics": true, "steps_reviewed": 2, "method": "family_template_semantic_review_plus_independent_per_instance_reconstruction", "exact_question_first_check": { "model_sha256": "b65f4531fc37f8d256f8601f9c9c38ccc22166b9fb8f2ab57d12e31eb6bbfe44", "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." } }