{ "schema_version": "ocme-reviewed-question-reader-v1", "question_id": "q-20261013-advance-20261025-r04-linear-independence-basis-0029", "pilot_number": "R0065-33279", "number": 33279, "family_id": "qf-mod25-basisdeep-zero-vector-dependence-certificate", "title": { "zh-Hant": "第 33279 題：基底密度", "en": "Question 33279: A Selected Zero Vector Gives a Nontrivial Zero Relation" }, "original_question": { "schema_version": "ocme-question-v0.1", "id": "q-20261013-advance-20261025-r04-linear-independence-basis-0029", "batch_id": "batch-20261013-advance-20261025-r04-linear-independence-basis-foundations", "language": "zh-Hant", "source_mko_ids": [ "mko-linear-independence-basis" ], "title_zh": "基底密度", "stem_zh": "只深化既有有限R2基底語義。操作=basisdeep-zero-vector-dependence-certificate；資料={\"vectors\":[[0,0],[1,1],[1,1]],\"zero_index\":0}。請依 [vectors,zero_index,selected_vector,is_zero,coefficients,dependence_certificate] 欄序回答。", "answer": { "kind": "expression", "value": "([[0, 0], [1, 1], [1, 1]], 0, [0, 0], 是, [1, 0, 0], 是)", "explanation_zh": "收束波核對=([[0, 0], [1, 1], [1, 1]], 0, [0, 0], 是, [1, 0, 0], 是)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；不新增維度或換基底定理；座標唯一性只在非零行列式有序R2基底後使用。" }, "difficulty": { "band": "undergraduate_core", "level": 1, "skills": [ "基底密度" ] }, "variant": { "family_id": "qf-mod25-basisdeep-zero-vector-dependence-certificate", "seed": 202610254029, "parameters": { "vectors": [ [ 0, 0 ], [ 1, 1 ], [ 1, 1 ] ], "zero_index": 0, "domain": "R2_basis_density_without_dimension_extension", "operation": "basisdeep-zero-vector-dependence-certificate", "semantic_template": "qf-mod25-basisdeep-zero-vector-dependence-certificate/{\"vectors\":[[0,0],[1,1],[1,1]],\"zero_index\":0}" } }, "verification": { "status": "candidate", "checks": [ "producer_exact_finite_model", "producer_source_snapshot_check", "producer_substantive_template_deduplication", "producer_json_schema" ], "warning_zh": "產生端候選須由主端重算；不構成人工審定、一般無限定理、BVP適定性、全域最佳解、Markov長期性、Lean執行或形式Evidence。" }, "provenance": { "generator_role": "question_producer", "generator_model": "model_unknown", "generated_at": "2026-10-13", "contract_version": "ocme-question-factory-v0.1" } }, "original_english_edition": { "schema_version": "ocme-question-localization-v0.1", "question_id": "q-20261013-advance-20261025-r04-linear-independence-basis-0029", "batch_id": "batch-20261013-advance-20261025-r04-linear-independence-basis-foundations", "locale": "en", "translation_state": "ai_candidate", "source": { "question_sha256": "a3d6e48f45f1067f92d2bbc431b33f4f2e475bc2c0473292e680c388141f1df6", "family_id": "qf-mod25-basisdeep-zero-vector-dependence-certificate", "seed": 202610254029, "semantic_template": "qf-mod25-basisdeep-zero-vector-dependence-certificate/{\"vectors\":[[0,0],[1,1],[1,1]],\"zero_index\":0}" }, "fields": { "title": "A Selected Zero Vector Gives a Nontrivial Zero Relation", "stem": "Deepen only the existing explicit finite-coordinate basis semantics, preserving vector and coefficient order. No new dimension or change-of-basis theorem is inferred. Coordinate uniqueness is used only after qualifying a nonzero-determinant ordered R² basis. vectors=[[0, 0], [1, 1], [1, 1]], selected zero-based index=0. Give (vectors,index,selected vector,is it zero?,coefficient list with 1 at this index and 0 elsewhere,valid dependence certificate?). If the selected vector is not zero, retain the proposed list but report No.", "answer": { "kind": "expression", "value": "([[0, 0], [1, 1], [1, 1]], 0, [0, 0], Yes, [1, 0, 0], Yes)", "explanation": "The proposed coefficients are nontrivial by construction. They give a zero sum exactly when the selected vector is zero. This exact finite slice does not automatically establish a general infinite conclusion. The exact result, retaining the requested order, is ([[0, 0], [1, 1], [1, 1]], 0, [0, 0], Yes, [1, 0, 0], Yes)." }, "skills": [ "A Selected Zero Vector Gives a Nontrivial Zero Relation" ], "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": "只深化既有有限R2基底語義。操作=basisdeep-zero-vector-dependence-certificate；資料={\"vectors\":[[0,0],[1,1],[1,1]],\"zero_index\":0}。請依 [vectors,zero_index,selected_vector,is_zero,coefficients,dependence_certificate] 欄序回答。", "en": "Deepen only the existing explicit finite-coordinate basis semantics, preserving vector and coefficient order. No new dimension or change-of-basis theorem is inferred. Coordinate uniqueness is used only after qualifying a nonzero-determinant ordered R² basis. vectors=[[0, 0], [1, 1], [1, 1]], selected zero-based index=0. Give (vectors,index,selected vector,is it zero?,coefficient list with 1 at this index and 0 elsewhere,valid dependence certificate?). If the selected vector is not zero, retain the proposed list but report No." } } ], "steps": [ { "id": "S001", "uses": [ "G001" ], "before": "source roles = [qf-mod25-basisdeep-zero-vector-dependence-certificate, basisdeep-zero-vector-dependence-certificate, R2_basis_density_without_dimension_extension, []]", "after": "derived = [[vectors, index, selected, is_zero, nontrivial_coefficients, THIS_certificate]]", "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 = [zero certificate ORIGINAL vector0, [0, 0]]", "after": "derived = [[0, 0]]", "relation": "implies", "rule_id": "Basis_RAW_vector_1to6_components_bound1000", "conditions": [], "explanation": { "zh-Hant": "raw vector非空、1..6分量且每值±1000；只有R²座標題另驗2維，不對其他families憑domain名字強加2維。", "en": "RAW vectors are nonempty with1..6 components bounded±1000.ONLY the R² coordinate task adds dimension2;do not infer an extra2D gate elsewhere from a domain label." }, "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 = [zero certificate ORIGINAL vector1, [1, 1]]", "after": "derived = [[1, 1]]", "relation": "implies", "rule_id": "Basis_RAW_vector_1to6_components_bound1000", "conditions": [], "explanation": { "zh-Hant": "raw vector非空、1..6分量且每值±1000；只有R²座標題另驗2維，不對其他families憑domain名字強加2維。", "en": "RAW vectors are nonempty with1..6 components bounded±1000.ONLY the R² coordinate task adds dimension2;do not infer an extra2D gate elsewhere from a domain label." }, "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": "S004", "uses": [ "G001", "S003" ], "before": "source roles = [zero certificate ORIGINAL vector2, [1, 1]]", "after": "derived = [[1, 1]]", "relation": "implies", "rule_id": "Basis_RAW_vector_1to6_components_bound1000", "conditions": [], "explanation": { "zh-Hant": "raw vector非空、1..6分量且每值±1000；只有R²座標題另驗2維，不對其他families憑domain名字強加2維。", "en": "RAW vectors are nonempty with1..6 components bounded±1000.ONLY the R² coordinate task adds dimension2;do not infer an extra2D gate elsewhere from a domain label." }, "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": "S005", "uses": [ "G001", "S004" ], "before": "zero proposed nontrivial relation ORIGINAL vector0 coordinate0 weighted term := mul(1, 0)", "after": "zero proposed nontrivial relation ORIGINAL vector0 coordinate0 weighted term = 0", "relation": "calculation", "rule_id": "exact_rational_arithmetic", "conditions": [], "explanation": { "zh-Hant": "保原操作數與次序作精確運算；有理計算另驗此MOD25來源的pre-reduction界。不是把所有衍生整數都截成100萬，也不用浮點近似。", "en": "Use ORIGINAL operands/order for exact arithmetic.Rational operations separately enforce this MOD25 SOURCE pre-reduction envelope.Do not globally cap every derived integer at one million or use floating approximations." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "以精確有理數重算 zero proposed nontrivial relation ORIGINAL vector0 coordinate0 weighted term，不以小數近似替代。", "en": "Recompute zero proposed nontrivial relation ORIGINAL vector0 coordinate0 weighted term with exact rational arithmetic, not rounded decimals." } }, "arithmetic": { "operation": "mul", "inputs": [ "1", "0" ], "output": "0", "label": "zero proposed nontrivial relation ORIGINAL vector0 coordinate0 weighted term" } }, { "id": "S006", "uses": [ "G001", "S005" ], "before": "zero proposed nontrivial relation ORIGINAL vector1 coordinate0 weighted term := mul(0, 1)", "after": "zero proposed nontrivial relation ORIGINAL vector1 coordinate0 weighted term = 0", "relation": "calculation", "rule_id": "exact_rational_arithmetic", "conditions": [], "explanation": { "zh-Hant": "保原操作數與次序作精確運算；有理計算另驗此MOD25來源的pre-reduction界。不是把所有衍生整數都截成100萬，也不用浮點近似。", "en": "Use ORIGINAL operands/order for exact arithmetic.Rational operations separately enforce this MOD25 SOURCE pre-reduction envelope.Do not globally cap every derived integer at one million or use floating approximations." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "以精確有理數重算 zero proposed nontrivial relation ORIGINAL vector1 coordinate0 weighted term，不以小數近似替代。", "en": "Recompute zero proposed nontrivial relation ORIGINAL vector1 coordinate0 weighted term with exact rational arithmetic, not rounded decimals." } }, "arithmetic": { "operation": "mul", "inputs": [ "0", "1" ], "output": "0", "label": "zero proposed nontrivial relation ORIGINAL vector1 coordinate0 weighted term" } }, { "id": "S007", "uses": [ "G001", "S006" ], "before": "zero proposed nontrivial relation ORIGINAL vector2 coordinate0 weighted term := mul(0, 1)", "after": "zero proposed nontrivial relation ORIGINAL vector2 coordinate0 weighted term = 0", "relation": "calculation", "rule_id": "exact_rational_arithmetic", "conditions": [], "explanation": { "zh-Hant": "保原操作數與次序作精確運算；有理計算另驗此MOD25來源的pre-reduction界。不是把所有衍生整數都截成100萬，也不用浮點近似。", "en": "Use ORIGINAL operands/order for exact arithmetic.Rational operations separately enforce this MOD25 SOURCE pre-reduction envelope.Do not globally cap every derived integer at one million or use floating approximations." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "以精確有理數重算 zero proposed nontrivial relation ORIGINAL vector2 coordinate0 weighted term，不以小數近似替代。", "en": "Recompute zero proposed nontrivial relation ORIGINAL vector2 coordinate0 weighted term with exact rational arithmetic, not rounded decimals." } }, "arithmetic": { "operation": "mul", "inputs": [ "0", "1" ], "output": "0", "label": "zero proposed nontrivial relation ORIGINAL vector2 coordinate0 weighted term" } }, { "id": "S008", "uses": [ "G001", "S007" ], "before": "zero proposed nontrivial relation ORIGINAL coordinate0 all terms sum := sum(0, 0, 0)", "after": "zero proposed nontrivial relation ORIGINAL coordinate0 all terms sum = 0", "relation": "calculation", "rule_id": "exact_rational_arithmetic", "conditions": [], "explanation": { "zh-Hant": "保原操作數與次序作精確運算；有理計算另驗此MOD25來源的pre-reduction界。不是把所有衍生整數都截成100萬，也不用浮點近似。", "en": "Use ORIGINAL operands/order for exact arithmetic.Rational operations separately enforce this MOD25 SOURCE pre-reduction envelope.Do not globally cap every derived integer at one million or use floating approximations." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "以精確有理數重算 zero proposed nontrivial relation ORIGINAL coordinate0 all terms sum，不以小數近似替代。", "en": "Recompute zero proposed nontrivial relation ORIGINAL coordinate0 all terms sum with exact rational arithmetic, not rounded decimals." } }, "arithmetic": { "operation": "sum", "inputs": [ "0", "0", "0" ], "output": "0", "label": "zero proposed nontrivial relation ORIGINAL coordinate0 all terms sum" } }, { "id": "S009", "uses": [ "G001", "S008" ], "before": "source roles = [zero proposed nontrivial relation, 0, [[0, 0], [1, 1], [1, 1]], [1, 0, 0]]", "after": "derived = [[0, 0, 0], 0]", "relation": "implies", "rule_id": "Basis_EACH_coordinate_complete_linear_combination_no_derived_raw_cap", "conditions": [], "explanation": { "zh-Hant": "每個coordinate保全部coeff*vector分量，再加總；不對衍生重構值重套raw vector/係數界。", "en": "For EACH coordinate retain EVERY coefficient*vector component before summing.Do not recap derived reconstructions as RAW vector/coefficient inputs." }, "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": "S010", "uses": [ "G001", "S009" ], "before": "zero proposed nontrivial relation ORIGINAL vector0 coordinate1 weighted term := mul(1, 0)", "after": "zero proposed nontrivial relation ORIGINAL vector0 coordinate1 weighted term = 0", "relation": "calculation", "rule_id": "exact_rational_arithmetic", "conditions": [], "explanation": { "zh-Hant": "保原操作數與次序作精確運算；有理計算另驗此MOD25來源的pre-reduction界。不是把所有衍生整數都截成100萬，也不用浮點近似。", "en": "Use ORIGINAL operands/order for exact arithmetic.Rational operations separately enforce this MOD25 SOURCE pre-reduction envelope.Do not globally cap every derived integer at one million or use floating approximations." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "以精確有理數重算 zero proposed nontrivial relation ORIGINAL vector0 coordinate1 weighted term，不以小數近似替代。", "en": "Recompute zero proposed nontrivial relation ORIGINAL vector0 coordinate1 weighted term with exact rational arithmetic, not rounded decimals." } }, "arithmetic": { "operation": "mul", "inputs": [ "1", "0" ], "output": "0", "label": "zero proposed nontrivial relation ORIGINAL vector0 coordinate1 weighted term" } }, { "id": "S011", "uses": [ "G001", "S010" ], "before": "zero proposed nontrivial relation ORIGINAL vector1 coordinate1 weighted term := mul(0, 1)", "after": "zero proposed nontrivial relation ORIGINAL vector1 coordinate1 weighted term = 0", "relation": "calculation", "rule_id": "exact_rational_arithmetic", "conditions": [], "explanation": { "zh-Hant": "保原操作數與次序作精確運算；有理計算另驗此MOD25來源的pre-reduction界。不是把所有衍生整數都截成100萬，也不用浮點近似。", "en": "Use ORIGINAL operands/order for exact arithmetic.Rational operations separately enforce this MOD25 SOURCE pre-reduction envelope.Do not globally cap every derived integer at one million or use floating approximations." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "以精確有理數重算 zero proposed nontrivial relation ORIGINAL vector1 coordinate1 weighted term，不以小數近似替代。", "en": "Recompute zero proposed nontrivial relation ORIGINAL vector1 coordinate1 weighted term with exact rational arithmetic, not rounded decimals." } }, "arithmetic": { "operation": "mul", "inputs": [ "0", "1" ], "output": "0", "label": "zero proposed nontrivial relation ORIGINAL vector1 coordinate1 weighted term" } }, { "id": "S012", "uses": [ "G001", "S011" ], "before": "zero proposed nontrivial relation ORIGINAL vector2 coordinate1 weighted term := mul(0, 1)", "after": "zero proposed nontrivial relation ORIGINAL vector2 coordinate1 weighted term = 0", "relation": "calculation", "rule_id": "exact_rational_arithmetic", "conditions": [], "explanation": { "zh-Hant": "保原操作數與次序作精確運算；有理計算另驗此MOD25來源的pre-reduction界。不是把所有衍生整數都截成100萬，也不用浮點近似。", "en": "Use ORIGINAL operands/order for exact arithmetic.Rational operations separately enforce this MOD25 SOURCE pre-reduction envelope.Do not globally cap every derived integer at one million or use floating approximations." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "以精確有理數重算 zero proposed nontrivial relation ORIGINAL vector2 coordinate1 weighted term，不以小數近似替代。", "en": "Recompute zero proposed nontrivial relation ORIGINAL vector2 coordinate1 weighted term with exact rational arithmetic, not rounded decimals." } }, "arithmetic": { "operation": "mul", "inputs": [ "0", "1" ], "output": "0", "label": "zero proposed nontrivial relation ORIGINAL vector2 coordinate1 weighted term" } }, { "id": "S013", "uses": [ "G001", "S012" ], "before": "zero proposed nontrivial relation ORIGINAL coordinate1 all terms sum := sum(0, 0, 0)", "after": "zero proposed nontrivial relation ORIGINAL coordinate1 all terms sum = 0", "relation": "calculation", "rule_id": "exact_rational_arithmetic", "conditions": [], "explanation": { "zh-Hant": "保原操作數與次序作精確運算；有理計算另驗此MOD25來源的pre-reduction界。不是把所有衍生整數都截成100萬，也不用浮點近似。", "en": "Use ORIGINAL operands/order for exact arithmetic.Rational operations separately enforce this MOD25 SOURCE pre-reduction envelope.Do not globally cap every derived integer at one million or use floating approximations." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "以精確有理數重算 zero proposed nontrivial relation ORIGINAL coordinate1 all terms sum，不以小數近似替代。", "en": "Recompute zero proposed nontrivial relation ORIGINAL coordinate1 all terms sum with exact rational arithmetic, not rounded decimals." } }, "arithmetic": { "operation": "sum", "inputs": [ "0", "0", "0" ], "output": "0", "label": "zero proposed nontrivial relation ORIGINAL coordinate1 all terms sum" } }, { "id": "S014", "uses": [ "G001", "S013" ], "before": "source roles = [zero proposed nontrivial relation, 1, [[0, 0], [1, 1], [1, 1]], [1, 0, 0]]", "after": "derived = [[0, 0, 0], 0]", "relation": "implies", "rule_id": "Basis_EACH_coordinate_complete_linear_combination_no_derived_raw_cap", "conditions": [], "explanation": { "zh-Hant": "每個coordinate保全部coeff*vector分量，再加總；不對衍生重構值重套raw vector/係數界。", "en": "For EACH coordinate retain EVERY coefficient*vector component before summing.Do not recap derived reconstructions as RAW vector/coefficient inputs." }, "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": "S015", "uses": [ "G001", "S014" ], "before": "source roles = [[[0, 0], [1, 1], [1, 1]], 0, [0, 0]]", "after": "derived = [[1, 0, 0], [0, 0], 是]", "relation": "implies", "rule_id": "Basis_ZERO_selected_vector_nontrivial_e_index_relation_ONLY_THIS_certificate", "conditions": [], "explanation": { "zh-Hant": "coeff在此index為1，其餘0，所以非全0且組合恰等selected。selected零才給依賴證書；No不證整個family獨立，其他依賴可能仍存在。", "en": "The coefficient is1 at THIS index and0 elsewhere,so the list is nontrivial and its combination equals the selected vector.ONLY a zero selection certifies dependence.No does not establish whole-family independence." }, "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": [ [ [ 0, 0 ], [ 1, 1 ], [ 1, 1 ] ], 0, [ 0, 0 ], true, [ 1, 0, 0 ], true ] }, "conclusion": { "canonical_value": "([[0, 0], [1, 1], [1, 1]], 0, [0, 0], 是, [1, 0, 0], 是)", "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-20261013-advance-20261025-r04-linear-independence-basis-foundations", "batch_path": "public/data/questions/batches/batch-20261013-advance-20261025-r04-linear-independence-basis-foundations/questions.jsonl", "batch_sha256": "27f05761dc76f45a861163c0fea8c42129f9765370396ea0909c413aa85b68e4", "original_line": 29, "original_line_sha256": "eb702cc7f10217fe507ab47d95bd6bca9306c694be4c7a5398cacbc0815e857d", "question_compact_sha256": "a3d6e48f45f1067f92d2bbc431b33f4f2e475bc2c0473292e680c388141f1df6", "english_row_compact_sha256": "2d1debebb61023442750a4cd7dbc7b15dd98bdc1d25b3d522d963547c06d1b58", "english_manifest_path": "public/data/i18n/editions/batch-20261013-advance-20261025-r04-linear-independence-basis-foundations.en.json", "english_rows_path": "public/data/i18n/questions/batch-20261013-advance-20261025-r04-linear-independence-basis-foundations.en.jsonl" }, "mko_bindings": { "mko-linear-independence-basis": { "sha256": "78c45988a718f6a7ca4acf2aba00ea4df794c8f141cefe822bf72206fa2b2f62", "english_sha256": "48c43771b8f6734ece79626851e05a5dca9bb984732eb3f69cffe2c6e364a912", "original_path": "public/data/mko/linear-independence-basis.json", "english_path": "public/data/i18n/editions/mko-linear-independence-basis.en.json" } }, "selected_manifest_sha256": "5233edba9654a6cffd8b6b2d83c932f82ded15f9c0b7c733bd049943e672acff", "selected_part_sha256": "871e2c05026567a1deae741d6b90b0588100c6482ee167c7f9f45af5b72d8606", "original_candidate_sha256": "f2003aeb25ccd071fe5e621dfe0621884d64e1f9423602baf6b8e8e590248f29", "original_candidate_line_sha256": "f2003aeb25ccd071fe5e621dfe0621884d64e1f9423602baf6b8e8e590248f29" }, "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": 15, "method": "family_template_semantic_review_plus_independent_per_instance_reconstruction", "exact_question_first_check": { "model_sha256": "dc9f9ef8d9ef41047e45554e36a5a8ed964536ed304959caa549790ad0db6c42", "arithmetic_steps": 8 }, "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." } }