{ "schema_version": "ocme-reviewed-question-reader-v1", "question_id": "q-20261014-advance-20261104-r03-absolute-convergence-of-series-0030", "pilot_number": "R0034-17930", "number": 17930, "family_id": "qf-mod35-absseries-conditional-alternating", "title": { "zh-Hant": "第 17930 題：絕對收斂", "en": "Question 17930: Conditional Convergence Needs Both Convergence and Absolute Divergence" }, "original_question": { "schema_version": "ocme-question-v0.1", "id": "q-20261014-advance-20261104-r03-absolute-convergence-of-series-0030", "batch_id": "batch-20261014-advance-20261104-r03-absolute-convergence-of-series-foundations", "language": "zh-Hant", "source_mko_ids": [ "mko-absolute-convergence-of-series" ], "title_zh": "絕對收斂", "stem_zh": "partial sums與absolute-series exact convergence certificate。操作=absseries-conditional-alternating；資料={\"shift\":5,\"n\":5}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。", "answer": { "kind": "expression", "value": "(5, 5, [1/5, -1/6, 1/7, -1/8, 1/9], 是, 否, alternating_remainder_and_harmonic_absolute_divergence)", "explanation_zh": "Wave5第四層核對=(5, 5, [1/5, -1/6, 1/7, -1/8, 1/9], 是, 否, alternating_remainder_and_harmonic_absolute_divergence)；依完整明示資料重算；absolute convergence核sum absolute values並推出原級數收斂；term趨零 bounded或alternation不足；conditional需雙證書。" }, "difficulty": { "band": "undergraduate_core", "level": 1, "skills": [ "絕對收斂" ] }, "variant": { "family_id": "qf-mod35-absseries-conditional-alternating", "seed": 202611043030, "parameters": { "shift": 5, "n": 5, "domain": "Exact_absolute_or_conditional_series", "operation": "absseries-conditional-alternating", "semantic_template": "qf-mod35-absseries-conditional-alternating/{\"n\":5,\"shift\":5}" } }, "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；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或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-20261104-r03-absolute-convergence-of-series-0030", "batch_id": "batch-20261014-advance-20261104-r03-absolute-convergence-of-series-foundations", "locale": "en", "translation_state": "ai_candidate", "source": { "question_sha256": "769174f583cb40adab34fe55845df3c9e0eb103ddbb5113007b0079cfe02c04a", "family_id": "qf-mod35-absseries-conditional-alternating", "seed": 202611043030, "semantic_template": "qf-mod35-absseries-conditional-alternating/{\"n\":5,\"shift\":5}" }, "fields": { "title": "Conditional Convergence Needs Both Convergence and Absolute Divergence", "stem": "Use terms (−1)^k/(k+shift), k=0,1,..., positive shift=5, and display n=5 terms. Give (shift, n, terms, series_converges, absolutely_converges, certificate).", "answer": { "kind": "expression", "value": "(5, 5, [1/5, -1/6, 1/7, -1/8, 1/9], Yes, No, alternating_remainder_and_harmonic_absolute_divergence)", "explanation": "The alternating remainder argument certifies convergence of this declared whole series, while divergence of the shifted harmonic absolute series certifies failure of absolute convergence. The displayed finite list alone is neither proof. The exact result, retaining the requested order, is (5, 5, [1/5, -1/6, 1/7, -1/8, 1/9], Yes, No, alternating_remainder_and_harmonic_absolute_divergence)." }, "skills": [ "Conditional Convergence Needs Both Convergence and Absolute Divergence" ], "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": "partial sums與absolute-series exact convergence certificate。操作=absseries-conditional-alternating；資料={\"shift\":5,\"n\":5}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。", "en": "Use terms (−1)^k/(k+shift), k=0,1,..., positive shift=5, and display n=5 terms. Give (shift, n, terms, series_converges, absolutely_converges, certificate)." } } ], "steps": [ { "id": "S001", "uses": [ "G001" ], "before": "source operation=absseries-conditional-alternating;original question snapshot retained;source presentation interface resolved in this page", "after": "EXPLICIT ordered output fields=[shift, n, terms, series_converges, absolutely_converges, certificate]", "relation": "implies", "rule_id": "absseries_explicit_source_interface_fields_without_javascript", "conditions": [], "explanation": { "zh-Hant": "原題快照保留歷史介面標記，這裡直接列完整欄位，不需瀏覽器JavaScript或外部查表。欄位名只是presentation metadata，不是數學運算；term-zero的第四個否是『條件是否充分』，不是誤標成另一個converges旗標。", "en": "Preserve the original snapshot's historical interface marker while listing the full ordered fields here,without browser JavaScript or an external lookup.Field labels are presentation metadata,not mathematical evaluation.The fourth term-zero No marks insufficiency,not a mislabeled second convergence flag." }, "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 }, { "id": "S002", "uses": [ "G001", "S001" ], "before": "alternating displayed term0 denominator := sum(0, 5)", "after": "alternating displayed term0 denominator = 5", "relation": "calculation", "rule_id": "exact_rational_arithmetic", "conditions": [], "explanation": { "zh-Hant": "依原始角色及已核中間量精確計算，保留分母、正負號、索引與嚴格條件。", "en": "Compute exactly from original roles and established intermediates,retaining denominators,signs,indices and strict conditions." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "以精確有理數重算 alternating displayed term0 denominator，不以小數近似替代。", "en": "Recompute alternating displayed term0 denominator with exact rational arithmetic, not rounded decimals." } }, "arithmetic": { "operation": "sum", "inputs": [ "0", "5" ], "output": "5", "label": "alternating displayed term0 denominator" } }, { "id": "S003", "uses": [ "G001", "S002" ], "before": "alternating displayed term0 signed value := div(1, 5)", "after": "alternating displayed term0 signed value = 1/5", "relation": "calculation", "rule_id": "exact_rational_arithmetic", "conditions": [], "explanation": { "zh-Hant": "依原始角色及已核中間量精確計算，保留分母、正負號、索引與嚴格條件。", "en": "Compute exactly from original roles and established intermediates,retaining denominators,signs,indices and strict conditions." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "以精確有理數重算 alternating displayed term0 signed value，不以小數近似替代。", "en": "Recompute alternating displayed term0 signed value with exact rational arithmetic, not rounded decimals." } }, "arithmetic": { "operation": "div", "inputs": [ "1", "5" ], "output": "1/5", "label": "alternating displayed term0 signed value" } }, { "id": "S004", "uses": [ "G001", "S003" ], "before": "alternating displayed term1 denominator := sum(1, 5)", "after": "alternating displayed term1 denominator = 6", "relation": "calculation", "rule_id": "exact_rational_arithmetic", "conditions": [], "explanation": { "zh-Hant": "依原始角色及已核中間量精確計算，保留分母、正負號、索引與嚴格條件。", "en": "Compute exactly from original roles and established intermediates,retaining denominators,signs,indices and strict conditions." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "以精確有理數重算 alternating displayed term1 denominator，不以小數近似替代。", "en": "Recompute alternating displayed term1 denominator with exact rational arithmetic, not rounded decimals." } }, "arithmetic": { "operation": "sum", "inputs": [ "1", "5" ], "output": "6", "label": "alternating displayed term1 denominator" } }, { "id": "S005", "uses": [ "G001", "S004" ], "before": "alternating displayed term1 signed value := div(-1, 6)", "after": "alternating displayed term1 signed value = -1/6", "relation": "calculation", "rule_id": "exact_rational_arithmetic", "conditions": [], "explanation": { "zh-Hant": "依原始角色及已核中間量精確計算，保留分母、正負號、索引與嚴格條件。", "en": "Compute exactly from original roles and established intermediates,retaining denominators,signs,indices and strict conditions." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "以精確有理數重算 alternating displayed term1 signed value，不以小數近似替代。", "en": "Recompute alternating displayed term1 signed value with exact rational arithmetic, not rounded decimals." } }, "arithmetic": { "operation": "div", "inputs": [ "-1", "6" ], "output": "-1/6", "label": "alternating displayed term1 signed value" } }, { "id": "S006", "uses": [ "G001", "S005" ], "before": "alternating displayed term2 denominator := sum(2, 5)", "after": "alternating displayed term2 denominator = 7", "relation": "calculation", "rule_id": "exact_rational_arithmetic", "conditions": [], "explanation": { "zh-Hant": "依原始角色及已核中間量精確計算，保留分母、正負號、索引與嚴格條件。", "en": "Compute exactly from original roles and established intermediates,retaining denominators,signs,indices and strict conditions." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "以精確有理數重算 alternating displayed term2 denominator，不以小數近似替代。", "en": "Recompute alternating displayed term2 denominator with exact rational arithmetic, not rounded decimals." } }, "arithmetic": { "operation": "sum", "inputs": [ "2", "5" ], "output": "7", "label": "alternating displayed term2 denominator" } }, { "id": "S007", "uses": [ "G001", "S006" ], "before": "alternating displayed term2 signed value := div(1, 7)", "after": "alternating displayed term2 signed value = 1/7", "relation": "calculation", "rule_id": "exact_rational_arithmetic", "conditions": [], "explanation": { "zh-Hant": "依原始角色及已核中間量精確計算，保留分母、正負號、索引與嚴格條件。", "en": "Compute exactly from original roles and established intermediates,retaining denominators,signs,indices and strict conditions." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "以精確有理數重算 alternating displayed term2 signed value，不以小數近似替代。", "en": "Recompute alternating displayed term2 signed value with exact rational arithmetic, not rounded decimals." } }, "arithmetic": { "operation": "div", "inputs": [ "1", "7" ], "output": "1/7", "label": "alternating displayed term2 signed value" } }, { "id": "S008", "uses": [ "G001", "S007" ], "before": "alternating displayed term3 denominator := sum(3, 5)", "after": "alternating displayed term3 denominator = 8", "relation": "calculation", "rule_id": "exact_rational_arithmetic", "conditions": [], "explanation": { "zh-Hant": "依原始角色及已核中間量精確計算，保留分母、正負號、索引與嚴格條件。", "en": "Compute exactly from original roles and established intermediates,retaining denominators,signs,indices and strict conditions." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "以精確有理數重算 alternating displayed term3 denominator，不以小數近似替代。", "en": "Recompute alternating displayed term3 denominator with exact rational arithmetic, not rounded decimals." } }, "arithmetic": { "operation": "sum", "inputs": [ "3", "5" ], "output": "8", "label": "alternating displayed term3 denominator" } }, { "id": "S009", "uses": [ "G001", "S008" ], "before": "alternating displayed term3 signed value := div(-1, 8)", "after": "alternating displayed term3 signed value = -1/8", "relation": "calculation", "rule_id": "exact_rational_arithmetic", "conditions": [], "explanation": { "zh-Hant": "依原始角色及已核中間量精確計算，保留分母、正負號、索引與嚴格條件。", "en": "Compute exactly from original roles and established intermediates,retaining denominators,signs,indices and strict conditions." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "以精確有理數重算 alternating displayed term3 signed value，不以小數近似替代。", "en": "Recompute alternating displayed term3 signed value with exact rational arithmetic, not rounded decimals." } }, "arithmetic": { "operation": "div", "inputs": [ "-1", "8" ], "output": "-1/8", "label": "alternating displayed term3 signed value" } }, { "id": "S010", "uses": [ "G001", "S009" ], "before": "alternating displayed term4 denominator := sum(4, 5)", "after": "alternating displayed term4 denominator = 9", "relation": "calculation", "rule_id": "exact_rational_arithmetic", "conditions": [], "explanation": { "zh-Hant": "依原始角色及已核中間量精確計算，保留分母、正負號、索引與嚴格條件。", "en": "Compute exactly from original roles and established intermediates,retaining denominators,signs,indices and strict conditions." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "以精確有理數重算 alternating displayed term4 denominator，不以小數近似替代。", "en": "Recompute alternating displayed term4 denominator with exact rational arithmetic, not rounded decimals." } }, "arithmetic": { "operation": "sum", "inputs": [ "4", "5" ], "output": "9", "label": "alternating displayed term4 denominator" } }, { "id": "S011", "uses": [ "G001", "S010" ], "before": "alternating displayed term4 signed value := div(1, 9)", "after": "alternating displayed term4 signed value = 1/9", "relation": "calculation", "rule_id": "exact_rational_arithmetic", "conditions": [], "explanation": { "zh-Hant": "依原始角色及已核中間量精確計算，保留分母、正負號、索引與嚴格條件。", "en": "Compute exactly from original roles and established intermediates,retaining denominators,signs,indices and strict conditions." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "以精確有理數重算 alternating displayed term4 signed value，不以小數近似替代。", "en": "Recompute alternating displayed term4 signed value with exact rational arithmetic, not rounded decimals." } }, "arithmetic": { "operation": "div", "inputs": [ "1", "9" ], "output": "1/9", "label": "alternating displayed term4 signed value" } }, { "id": "S012", "uses": [ "G001", "S011" ], "before": "absolute series of declared alternating tail:DECLARED whole positive tail b_k=1/(k+5),k>=0;shift>0", "after": "b_k decreases to0:for ANY epsilon>0 choose N with N+shift>1/epsilon,then every k>=N has b_k=0 large enough that2^j>=shift-1,the block m=2^j+1..2^(j+1) has2^j terms each>=1/2^(j+1);each block sum>=1/2;infinitely many disjoint blocks make partial sums unbounded", "relation": "implies", "rule_id": "harmonic_shifted_dyadic_blocks_diverge_not_term_limit", "conditions": [], "explanation": { "zh-Hant": "整個尾和只少有限開頭；每個充分晚的dyadic區塊至少1/2，任取多個不交塊總和無界，才證級數發散。項趨零沒有給partial sums的有限極限。", "en": "Removing finitely many initial terms leaves the dyadic-block argument.Each sufficiently late block contributes at least1/2,so arbitrarily many disjoint blocks force unbounded partial sums.Terms tending to zero do not give a finite limit of partial sums." }, "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 }, { "id": "S014", "uses": [ "G001", "S013" ], "before": "WHOLE declared terms=(-1)^k/(k+5),k starts0 positive;displayed first5 terms=[1/5, -1/6, 1/7, -1/8, 1/9]", "after": "b_k positive decreasing to0;even S_2m increases by b_2m-b_(2m+1)>=0;odd S_(2m+1) decreases;0<=S_2m<=S_(2m+1)<=b_0=1/5;gap b_2m tends0", "relation": "implies", "rule_id": "absseries_alternating_monotone_subsequences_not_alternation_alone", "conditions": [], "explanation": { "zh-Hant": "正遞減幅值才給偶partial sums遞增、奇partial sums遞減且互相夾住；實數完備性給兩子列極限，差趨零使極限相同，整個partial-sum sequence收斂。單有交錯或項趨零不足以一般推出。", "en": "Positive decreasing magnitudes make even partial sums increase and odd partial sums decrease while bounding one another.Real completeness gives both limits,and their vanishing gap makes them equal,so the whole partial-sum sequence converges.Alternation or a term-zero condition alone is not a general criterion." }, "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 }, { "id": "S015", "uses": [ "G001", "S014" ], "before": "alternating displayed exact partial sum := sum(1/5, -1/6, 1/7, -1/8, 1/9)", "after": "alternating displayed exact partial sum = 409/2520", "relation": "calculation", "rule_id": "exact_rational_arithmetic", "conditions": [], "explanation": { "zh-Hant": "依原始角色及已核中間量精確計算，保留分母、正負號、索引與嚴格條件。", "en": "Compute exactly from original roles and established intermediates,retaining denominators,signs,indices and strict conditions." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "以精確有理數重算 alternating displayed exact partial sum，不以小數近似替代。", "en": "Recompute alternating displayed exact partial sum with exact rational arithmetic, not rounded decimals." } }, "arithmetic": { "operation": "sum", "inputs": [ "1/5", "-1/6", "1/7", "-1/8", "1/9" ], "output": "409/2520", "label": "alternating displayed exact partial sum" } }, { "id": "S016", "uses": [ "G001", "S015" ], "before": "alternating next-term remainder denominator := sum(5, 5)", "after": "alternating next-term remainder denominator = 10", "relation": "calculation", "rule_id": "exact_rational_arithmetic", "conditions": [], "explanation": { "zh-Hant": "依原始角色及已核中間量精確計算，保留分母、正負號、索引與嚴格條件。", "en": "Compute exactly from original roles and established intermediates,retaining denominators,signs,indices and strict conditions." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "以精確有理數重算 alternating next-term remainder denominator，不以小數近似替代。", "en": "Recompute alternating next-term remainder denominator with exact rational arithmetic, not rounded decimals." } }, "arithmetic": { "operation": "sum", "inputs": [ "5", "5" ], "output": "10", "label": "alternating next-term remainder denominator" } }, { "id": "S017", "uses": [ "G001", "S016" ], "before": "alternating next-term absolute remainder bound := div(1, 10)", "after": "alternating next-term absolute remainder bound = 1/10", "relation": "calculation", "rule_id": "exact_rational_arithmetic", "conditions": [], "explanation": { "zh-Hant": "依原始角色及已核中間量精確計算，保留分母、正負號、索引與嚴格條件。", "en": "Compute exactly from original roles and established intermediates,retaining denominators,signs,indices and strict conditions." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "以精確有理數重算 alternating next-term absolute remainder bound，不以小數近似替代。", "en": "Recompute alternating next-term absolute remainder bound with exact rational arithmetic, not rounded decimals." } }, "arithmetic": { "operation": "div", "inputs": [ "1", "10" ], "output": "1/10", "label": "alternating next-term absolute remainder bound" } }, { "id": "S018", "uses": [ "G001", "S017" ], "before": "alternating next signed term := mul(-1, 1/10)", "after": "alternating next signed term = -1/10", "relation": "calculation", "rule_id": "exact_rational_arithmetic", "conditions": [], "explanation": { "zh-Hant": "依原始角色及已核中間量精確計算，保留分母、正負號、索引與嚴格條件。", "en": "Compute exactly from original roles and established intermediates,retaining denominators,signs,indices and strict conditions." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "以精確有理數重算 alternating next signed term，不以小數近似替代。", "en": "Recompute alternating next signed term with exact rational arithmetic, not rounded decimals." } }, "arithmetic": { "operation": "mul", "inputs": [ "-1", "1/10" ], "output": "-1/10", "label": "alternating next signed term" } }, { "id": "S019", "uses": [ "G001", "S018" ], "before": "alternating next exact partial sum := sum(409/2520, -1/10)", "after": "alternating next exact partial sum = 157/2520", "relation": "calculation", "rule_id": "exact_rational_arithmetic", "conditions": [], "explanation": { "zh-Hant": "依原始角色及已核中間量精確計算，保留分母、正負號、索引與嚴格條件。", "en": "Compute exactly from original roles and established intermediates,retaining denominators,signs,indices and strict conditions." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "以精確有理數重算 alternating next exact partial sum，不以小數近似替代。", "en": "Recompute alternating next exact partial sum with exact rational arithmetic, not rounded decimals." } }, "arithmetic": { "operation": "sum", "inputs": [ "409/2520", "-1/10" ], "output": "157/2520", "label": "alternating next exact partial sum" } }, { "id": "S020", "uses": [ "G001", "S019" ], "before": "displayed S_n=409/2520;adjacent S_(n+1)=157/2520;n=5;positive shift=5", "after": "common limit L lies between these two endpoints;abs(L-S_n)<=1/10;original series converges=是;absolute harmonic series converges=否", "relation": "implies", "rule_id": "absseries_conditional_requires_convergence_and_absolute_divergence", "conditions": [], "explanation": { "zh-Hant": "全尾交錯證書給相鄰partial sums夾住同一極限與下一項餘界；前面的dyadic論證另證絕對值和發散。兩份證書兼具才叫conditional，顯示清單本身不證任何無限結論。", "en": "The whole-tail alternating certificate traps the common limit between adjacent partial sums and gives the next-term error bound.The separate dyadic argument proves divergence of the absolute series.Both certificates establish conditional convergence;the displayed finite list alone proves neither infinite claim." }, "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": [ 5, 5, [ "1/5", "-1/6", "1/7", "-1/8", "1/9" ], true, false, "alternating_remainder_and_harmonic_absolute_divergence" ] }, "conclusion": { "canonical_value": "(5, 5, [1/5, -1/6, 1/7, -1/8, 1/9], 是, 否, alternating_remainder_and_harmonic_absolute_divergence)", "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-20261104-r03-absolute-convergence-of-series-foundations", "batch_path": "public/data/questions/batches/batch-20261014-advance-20261104-r03-absolute-convergence-of-series-foundations/questions.jsonl", "batch_sha256": "80786ddf5c8f2dd129df5ad6a139679d6f762f4ad7b6c20caa9920af15a19506", "original_line": 30, "original_line_sha256": "41ef048f1b08a1c0b77f9eb30272c24f9086acfa8247a2f023cba555354266ef", "question_compact_sha256": "769174f583cb40adab34fe55845df3c9e0eb103ddbb5113007b0079cfe02c04a", "english_row_compact_sha256": "39488e7baea7bda108e76c396f1d0b753b2bd6fa4c488720ab74e148dde9e3a2", "english_manifest_path": "public/data/i18n/editions/batch-20261014-advance-20261104-r03-absolute-convergence-of-series-foundations.en.json", "english_rows_path": "public/data/i18n/questions/batch-20261014-advance-20261104-r03-absolute-convergence-of-series-foundations.en.jsonl" }, "mko_bindings": { "mko-absolute-convergence-of-series": { "sha256": "4419bd0abbb51b07728caad18022eaace6aec3c8243880972704e8b1413cc1f8", "english_sha256": "faeb3d8b3f3ed278c06df7c7a387e9df82810c62c55a1d90becc7eaa1efaee1c", "original_path": "public/data/mko/absolute-convergence-of-series.json", "english_path": "public/data/i18n/editions/mko-absolute-convergence-of-series.en.json" } }, "selected_manifest_sha256": "5233edba9654a6cffd8b6b2d83c932f82ded15f9c0b7c733bd049943e672acff", "selected_part_sha256": "d5b0037cbaeef26e3828d04bf29e0e0f6e466926098b6b09e3237d1fdbdbd0e2", "original_candidate_sha256": "940c0f996ebbcfa2931d985c7845cb5d4ff62b2921342e4e87f6a41409d3c219", "original_candidate_line_sha256": "940c0f996ebbcfa2931d985c7845cb5d4ff62b2921342e4e87f6a41409d3c219" }, "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-20261026-008-p35", "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": "f73d099ebe3ff1c69a5d96f08c75b11b9e5b05120af40cf3ef388fce3b5c5336", "question_first_witness_sha256": "22675ffb6209b4fea076032b29b96e3dc19aad4244c54493f5f65f5e5d875699" }, "status": "second_context_reviewed", "mathematical_semantics": true, "bilingual_semantics": true, "steps_reviewed": 20, "method": "family_template_semantic_review_plus_independent_per_instance_reconstruction", "exact_question_first_check": { "model_sha256": "1fdd7a06e089349e43b64e1c61a888551538c8e51bf8c4467ed5f248bce9d6e2", "arithmetic_steps": 15 }, "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." } }