{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r01-harmonic-oscillator-model-0001","batch_id":"batch-20261013-advance-20261022-r01-harmonic-oscillator-model-foundations","language":"zh-Hant","source_mko_ids":["mko-harmonic-oscillator-model"],"title_zh":"簡諧振子精確切片","stem_zh":"無阻尼線性振子模型m x_second+k x=0。操作=oscillator-model-qualification；資料={\"mass\":[-1,1],\"spring\":[-8,1]}。請依 [mass,spring,mass_positive,spring_positive,qualified] 欄序回答。","answer":{"kind":"expression","value":"(-1, -8, 否, 否, 否)","explanation_zh":"結構基礎核對=(-1, -8, 否, 否, 否)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；不宣稱sin/cos閉式解；單點能量不證沿軌道守恆。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["簡諧振子精確切片"]},"variant":{"family_id":"qf-str22-oscillator-model-qualification","seed":202610221001,"parameters":{"mass":[-1,1],"spring":[-8,1],"domain":"Exact_harmonic_oscillator_model","operation":"oscillator-model-qualification","semantic_template":"qf-str22-oscillator-model-qualification/{\"mass\":[-1,1],\"spring\":[-8,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r01-harmonic-oscillator-model-0002","batch_id":"batch-20261013-advance-20261022-r01-harmonic-oscillator-model-foundations","language":"zh-Hant","source_mko_ids":["mko-harmonic-oscillator-model"],"title_zh":"簡諧振子精確切片","stem_zh":"無阻尼線性振子模型m x_second+k x=0。操作=oscillator-model-qualification；資料={\"mass\":[0,1],\"spring\":[-7,1]}。請依 [mass,spring,mass_positive,spring_positive,qualified] 欄序回答。","answer":{"kind":"expression","value":"(0, -7, 否, 否, 否)","explanation_zh":"結構基礎核對=(0, -7, 否, 否, 否)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；不宣稱sin/cos閉式解；單點能量不證沿軌道守恆。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["簡諧振子精確切片"]},"variant":{"family_id":"qf-str22-oscillator-model-qualification","seed":202610221002,"parameters":{"mass":[0,1],"spring":[-7,1],"domain":"Exact_harmonic_oscillator_model","operation":"oscillator-model-qualification","semantic_template":"qf-str22-oscillator-model-qualification/{\"mass\":[0,1],\"spring\":[-7,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r01-harmonic-oscillator-model-0003","batch_id":"batch-20261013-advance-20261022-r01-harmonic-oscillator-model-foundations","language":"zh-Hant","source_mko_ids":["mko-harmonic-oscillator-model"],"title_zh":"簡諧振子精確切片","stem_zh":"無阻尼線性振子模型m x_second+k x=0。操作=oscillator-model-qualification；資料={\"mass\":[1,1],\"spring\":[-6,1]}。請依 [mass,spring,mass_positive,spring_positive,qualified] 欄序回答。","answer":{"kind":"expression","value":"(1, -6, 是, 否, 否)","explanation_zh":"結構基礎核對=(1, -6, 是, 否, 否)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；不宣稱sin/cos閉式解；單點能量不證沿軌道守恆。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["簡諧振子精確切片"]},"variant":{"family_id":"qf-str22-oscillator-model-qualification","seed":202610221003,"parameters":{"mass":[1,1],"spring":[-6,1],"domain":"Exact_harmonic_oscillator_model","operation":"oscillator-model-qualification","semantic_template":"qf-str22-oscillator-model-qualification/{\"mass\":[1,1],\"spring\":[-6,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r01-harmonic-oscillator-model-0004","batch_id":"batch-20261013-advance-20261022-r01-harmonic-oscillator-model-foundations","language":"zh-Hant","source_mko_ids":["mko-harmonic-oscillator-model"],"title_zh":"簡諧振子精確切片","stem_zh":"無阻尼線性振子模型m x_second+k x=0。操作=oscillator-model-qualification；資料={\"mass\":[2,1],\"spring\":[-5,1]}。請依 [mass,spring,mass_positive,spring_positive,qualified] 欄序回答。","answer":{"kind":"expression","value":"(2, -5, 是, 否, 否)","explanation_zh":"結構基礎核對=(2, -5, 是, 否, 否)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；不宣稱sin/cos閉式解；單點能量不證沿軌道守恆。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["簡諧振子精確切片"]},"variant":{"family_id":"qf-str22-oscillator-model-qualification","seed":202610221004,"parameters":{"mass":[2,1],"spring":[-5,1],"domain":"Exact_harmonic_oscillator_model","operation":"oscillator-model-qualification","semantic_template":"qf-str22-oscillator-model-qualification/{\"mass\":[2,1],\"spring\":[-5,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r01-harmonic-oscillator-model-0005","batch_id":"batch-20261013-advance-20261022-r01-harmonic-oscillator-model-foundations","language":"zh-Hant","source_mko_ids":["mko-harmonic-oscillator-model"],"title_zh":"簡諧振子精確切片","stem_zh":"無阻尼線性振子模型m x_second+k x=0。操作=oscillator-model-qualification；資料={\"mass\":[3,1],\"spring\":[-4,1]}。請依 [mass,spring,mass_positive,spring_positive,qualified] 欄序回答。","answer":{"kind":"expression","value":"(3, -4, 是, 否, 否)","explanation_zh":"結構基礎核對=(3, -4, 是, 否, 否)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；不宣稱sin/cos閉式解；單點能量不證沿軌道守恆。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["簡諧振子精確切片"]},"variant":{"family_id":"qf-str22-oscillator-model-qualification","seed":202610221005,"parameters":{"mass":[3,1],"spring":[-4,1],"domain":"Exact_harmonic_oscillator_model","operation":"oscillator-model-qualification","semantic_template":"qf-str22-oscillator-model-qualification/{\"mass\":[3,1],\"spring\":[-4,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r01-harmonic-oscillator-model-0006","batch_id":"batch-20261013-advance-20261022-r01-harmonic-oscillator-model-foundations","language":"zh-Hant","source_mko_ids":["mko-harmonic-oscillator-model"],"title_zh":"簡諧振子精確切片","stem_zh":"無阻尼線性振子模型m x_second+k x=0。操作=oscillator-model-qualification；資料={\"mass\":[-1,1],\"spring\":[-3,1]}。請依 [mass,spring,mass_positive,spring_positive,qualified] 欄序回答。","answer":{"kind":"expression","value":"(-1, -3, 否, 否, 否)","explanation_zh":"結構基礎核對=(-1, -3, 否, 否, 否)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；不宣稱sin/cos閉式解；單點能量不證沿軌道守恆。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["簡諧振子精確切片"]},"variant":{"family_id":"qf-str22-oscillator-model-qualification","seed":202610221006,"parameters":{"mass":[-1,1],"spring":[-3,1],"domain":"Exact_harmonic_oscillator_model","operation":"oscillator-model-qualification","semantic_template":"qf-str22-oscillator-model-qualification/{\"mass\":[-1,1],\"spring\":[-3,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r01-harmonic-oscillator-model-0007","batch_id":"batch-20261013-advance-20261022-r01-harmonic-oscillator-model-foundations","language":"zh-Hant","source_mko_ids":["mko-harmonic-oscillator-model"],"title_zh":"簡諧振子精確切片","stem_zh":"無阻尼線性振子模型m x_second+k x=0。操作=oscillator-model-qualification；資料={\"mass\":[0,1],\"spring\":[-2,1]}。請依 [mass,spring,mass_positive,spring_positive,qualified] 欄序回答。","answer":{"kind":"expression","value":"(0, -2, 否, 否, 否)","explanation_zh":"結構基礎核對=(0, -2, 否, 否, 否)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；不宣稱sin/cos閉式解；單點能量不證沿軌道守恆。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["簡諧振子精確切片"]},"variant":{"family_id":"qf-str22-oscillator-model-qualification","seed":202610221007,"parameters":{"mass":[0,1],"spring":[-2,1],"domain":"Exact_harmonic_oscillator_model","operation":"oscillator-model-qualification","semantic_template":"qf-str22-oscillator-model-qualification/{\"mass\":[0,1],\"spring\":[-2,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r01-harmonic-oscillator-model-0008","batch_id":"batch-20261013-advance-20261022-r01-harmonic-oscillator-model-foundations","language":"zh-Hant","source_mko_ids":["mko-harmonic-oscillator-model"],"title_zh":"簡諧振子精確切片","stem_zh":"無阻尼線性振子模型m x_second+k x=0。操作=oscillator-model-qualification；資料={\"mass\":[1,1],\"spring\":[-1,1]}。請依 [mass,spring,mass_positive,spring_positive,qualified] 欄序回答。","answer":{"kind":"expression","value":"(1, -1, 是, 否, 否)","explanation_zh":"結構基礎核對=(1, -1, 是, 否, 否)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；不宣稱sin/cos閉式解；單點能量不證沿軌道守恆。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["簡諧振子精確切片"]},"variant":{"family_id":"qf-str22-oscillator-model-qualification","seed":202610221008,"parameters":{"mass":[1,1],"spring":[-1,1],"domain":"Exact_harmonic_oscillator_model","operation":"oscillator-model-qualification","semantic_template":"qf-str22-oscillator-model-qualification/{\"mass\":[1,1],\"spring\":[-1,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r01-harmonic-oscillator-model-0009","batch_id":"batch-20261013-advance-20261022-r01-harmonic-oscillator-model-foundations","language":"zh-Hant","source_mko_ids":["mko-harmonic-oscillator-model"],"title_zh":"簡諧振子精確切片","stem_zh":"無阻尼線性振子模型m x_second+k x=0。操作=oscillator-model-qualification；資料={\"mass\":[2,1],\"spring\":[0,1]}。請依 [mass,spring,mass_positive,spring_positive,qualified] 欄序回答。","answer":{"kind":"expression","value":"(2, 0, 是, 否, 否)","explanation_zh":"結構基礎核對=(2, 0, 是, 否, 否)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；不宣稱sin/cos閉式解；單點能量不證沿軌道守恆。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["簡諧振子精確切片"]},"variant":{"family_id":"qf-str22-oscillator-model-qualification","seed":202610221009,"parameters":{"mass":[2,1],"spring":[0,1],"domain":"Exact_harmonic_oscillator_model","operation":"oscillator-model-qualification","semantic_template":"qf-str22-oscillator-model-qualification/{\"mass\":[2,1],\"spring\":[0,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r01-harmonic-oscillator-model-0010","batch_id":"batch-20261013-advance-20261022-r01-harmonic-oscillator-model-foundations","language":"zh-Hant","source_mko_ids":["mko-harmonic-oscillator-model"],"title_zh":"簡諧振子精確切片","stem_zh":"無阻尼線性振子模型m x_second+k x=0。操作=oscillator-model-qualification；資料={\"mass\":[3,1],\"spring\":[1,1]}。請依 [mass,spring,mass_positive,spring_positive,qualified] 欄序回答。","answer":{"kind":"expression","value":"(3, 1, 是, 是, 是)","explanation_zh":"結構基礎核對=(3, 1, 是, 是, 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；不宣稱sin/cos閉式解；單點能量不證沿軌道守恆。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["簡諧振子精確切片"]},"variant":{"family_id":"qf-str22-oscillator-model-qualification","seed":202610221010,"parameters":{"mass":[3,1],"spring":[1,1],"domain":"Exact_harmonic_oscillator_model","operation":"oscillator-model-qualification","semantic_template":"qf-str22-oscillator-model-qualification/{\"mass\":[3,1],\"spring\":[1,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r01-harmonic-oscillator-model-0011","batch_id":"batch-20261013-advance-20261022-r01-harmonic-oscillator-model-foundations","language":"zh-Hant","source_mko_ids":["mko-harmonic-oscillator-model"],"title_zh":"簡諧振子精確切片","stem_zh":"無阻尼線性振子模型m x_second+k x=0。操作=oscillator-model-qualification；資料={\"mass\":[-1,1],\"spring\":[2,1]}。請依 [mass,spring,mass_positive,spring_positive,qualified] 欄序回答。","answer":{"kind":"expression","value":"(-1, 2, 否, 是, 否)","explanation_zh":"結構基礎核對=(-1, 2, 否, 是, 否)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；不宣稱sin/cos閉式解；單點能量不證沿軌道守恆。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["簡諧振子精確切片"]},"variant":{"family_id":"qf-str22-oscillator-model-qualification","seed":202610221011,"parameters":{"mass":[-1,1],"spring":[2,1],"domain":"Exact_harmonic_oscillator_model","operation":"oscillator-model-qualification","semantic_template":"qf-str22-oscillator-model-qualification/{\"mass\":[-1,1],\"spring\":[2,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r01-harmonic-oscillator-model-0012","batch_id":"batch-20261013-advance-20261022-r01-harmonic-oscillator-model-foundations","language":"zh-Hant","source_mko_ids":["mko-harmonic-oscillator-model"],"title_zh":"簡諧振子精確切片","stem_zh":"無阻尼線性振子模型m x_second+k x=0。操作=oscillator-model-qualification；資料={\"mass\":[0,1],\"spring\":[3,1]}。請依 [mass,spring,mass_positive,spring_positive,qualified] 欄序回答。","answer":{"kind":"expression","value":"(0, 3, 否, 是, 否)","explanation_zh":"結構基礎核對=(0, 3, 否, 是, 否)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；不宣稱sin/cos閉式解；單點能量不證沿軌道守恆。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["簡諧振子精確切片"]},"variant":{"family_id":"qf-str22-oscillator-model-qualification","seed":202610221012,"parameters":{"mass":[0,1],"spring":[3,1],"domain":"Exact_harmonic_oscillator_model","operation":"oscillator-model-qualification","semantic_template":"qf-str22-oscillator-model-qualification/{\"mass\":[0,1],\"spring\":[3,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r01-harmonic-oscillator-model-0013","batch_id":"batch-20261013-advance-20261022-r01-harmonic-oscillator-model-foundations","language":"zh-Hant","source_mko_ids":["mko-harmonic-oscillator-model"],"title_zh":"簡諧振子精確切片","stem_zh":"無阻尼線性振子模型m x_second+k x=0。操作=oscillator-model-qualification；資料={\"mass\":[1,1],\"spring\":[4,1]}。請依 [mass,spring,mass_positive,spring_positive,qualified] 欄序回答。","answer":{"kind":"expression","value":"(1, 4, 是, 是, 是)","explanation_zh":"結構基礎核對=(1, 4, 是, 是, 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；不宣稱sin/cos閉式解；單點能量不證沿軌道守恆。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["簡諧振子精確切片"]},"variant":{"family_id":"qf-str22-oscillator-model-qualification","seed":202610221013,"parameters":{"mass":[1,1],"spring":[4,1],"domain":"Exact_harmonic_oscillator_model","operation":"oscillator-model-qualification","semantic_template":"qf-str22-oscillator-model-qualification/{\"mass\":[1,1],\"spring\":[4,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r01-harmonic-oscillator-model-0014","batch_id":"batch-20261013-advance-20261022-r01-harmonic-oscillator-model-foundations","language":"zh-Hant","source_mko_ids":["mko-harmonic-oscillator-model"],"title_zh":"簡諧振子精確切片","stem_zh":"無阻尼線性振子模型m x_second+k x=0。操作=oscillator-model-qualification；資料={\"mass\":[2,1],\"spring\":[5,1]}。請依 [mass,spring,mass_positive,spring_positive,qualified] 欄序回答。","answer":{"kind":"expression","value":"(2, 5, 是, 是, 是)","explanation_zh":"結構基礎核對=(2, 5, 是, 是, 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；不宣稱sin/cos閉式解；單點能量不證沿軌道守恆。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["簡諧振子精確切片"]},"variant":{"family_id":"qf-str22-oscillator-model-qualification","seed":202610221014,"parameters":{"mass":[2,1],"spring":[5,1],"domain":"Exact_harmonic_oscillator_model","operation":"oscillator-model-qualification","semantic_template":"qf-str22-oscillator-model-qualification/{\"mass\":[2,1],\"spring\":[5,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r01-harmonic-oscillator-model-0015","batch_id":"batch-20261013-advance-20261022-r01-harmonic-oscillator-model-foundations","language":"zh-Hant","source_mko_ids":["mko-harmonic-oscillator-model"],"title_zh":"簡諧振子精確切片","stem_zh":"無阻尼線性振子模型m x_second+k x=0。操作=oscillator-model-qualification；資料={\"mass\":[3,1],\"spring\":[6,1]}。請依 [mass,spring,mass_positive,spring_positive,qualified] 欄序回答。","answer":{"kind":"expression","value":"(3, 6, 是, 是, 是)","explanation_zh":"結構基礎核對=(3, 6, 是, 是, 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；不宣稱sin/cos閉式解；單點能量不證沿軌道守恆。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["簡諧振子精確切片"]},"variant":{"family_id":"qf-str22-oscillator-model-qualification","seed":202610221015,"parameters":{"mass":[3,1],"spring":[6,1],"domain":"Exact_harmonic_oscillator_model","operation":"oscillator-model-qualification","semantic_template":"qf-str22-oscillator-model-qualification/{\"mass\":[3,1],\"spring\":[6,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r01-harmonic-oscillator-model-0016","batch_id":"batch-20261013-advance-20261022-r01-harmonic-oscillator-model-foundations","language":"zh-Hant","source_mko_ids":["mko-harmonic-oscillator-model"],"title_zh":"簡諧振子精確切片","stem_zh":"無阻尼線性振子模型m x_second+k x=0。操作=oscillator-model-qualification；資料={\"mass\":[-1,1],\"spring\":[7,1]}。請依 [mass,spring,mass_positive,spring_positive,qualified] 欄序回答。","answer":{"kind":"expression","value":"(-1, 7, 否, 是, 否)","explanation_zh":"結構基礎核對=(-1, 7, 否, 是, 否)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；不宣稱sin/cos閉式解；單點能量不證沿軌道守恆。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["簡諧振子精確切片"]},"variant":{"family_id":"qf-str22-oscillator-model-qualification","seed":202610221016,"parameters":{"mass":[-1,1],"spring":[7,1],"domain":"Exact_harmonic_oscillator_model","operation":"oscillator-model-qualification","semantic_template":"qf-str22-oscillator-model-qualification/{\"mass\":[-1,1],\"spring\":[7,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r01-harmonic-oscillator-model-0017","batch_id":"batch-20261013-advance-20261022-r01-harmonic-oscillator-model-foundations","language":"zh-Hant","source_mko_ids":["mko-harmonic-oscillator-model"],"title_zh":"簡諧振子精確切片","stem_zh":"無阻尼線性振子模型m x_second+k x=0。操作=oscillator-model-qualification；資料={\"mass\":[0,1],\"spring\":[8,1]}。請依 [mass,spring,mass_positive,spring_positive,qualified] 欄序回答。","answer":{"kind":"expression","value":"(0, 8, 否, 是, 否)","explanation_zh":"結構基礎核對=(0, 8, 否, 是, 否)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；不宣稱sin/cos閉式解；單點能量不證沿軌道守恆。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["簡諧振子精確切片"]},"variant":{"family_id":"qf-str22-oscillator-model-qualification","seed":202610221017,"parameters":{"mass":[0,1],"spring":[8,1],"domain":"Exact_harmonic_oscillator_model","operation":"oscillator-model-qualification","semantic_template":"qf-str22-oscillator-model-qualification/{\"mass\":[0,1],\"spring\":[8,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r01-harmonic-oscillator-model-0018","batch_id":"batch-20261013-advance-20261022-r01-harmonic-oscillator-model-foundations","language":"zh-Hant","source_mko_ids":["mko-harmonic-oscillator-model"],"title_zh":"簡諧振子精確切片","stem_zh":"無阻尼線性振子模型m x_second+k x=0。操作=oscillator-model-qualification；資料={\"mass\":[1,1],\"spring\":[9,1]}。請依 [mass,spring,mass_positive,spring_positive,qualified] 欄序回答。","answer":{"kind":"expression","value":"(1, 9, 是, 是, 是)","explanation_zh":"結構基礎核對=(1, 9, 是, 是, 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；不宣稱sin/cos閉式解；單點能量不證沿軌道守恆。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["簡諧振子精確切片"]},"variant":{"family_id":"qf-str22-oscillator-model-qualification","seed":202610221018,"parameters":{"mass":[1,1],"spring":[9,1],"domain":"Exact_harmonic_oscillator_model","operation":"oscillator-model-qualification","semantic_template":"qf-str22-oscillator-model-qualification/{\"mass\":[1,1],\"spring\":[9,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r01-harmonic-oscillator-model-0019","batch_id":"batch-20261013-advance-20261022-r01-harmonic-oscillator-model-foundations","language":"zh-Hant","source_mko_ids":["mko-harmonic-oscillator-model"],"title_zh":"簡諧振子精確切片","stem_zh":"無阻尼線性振子模型m x_second+k x=0。操作=oscillator-model-qualification；資料={\"mass\":[2,1],\"spring\":[10,1]}。請依 [mass,spring,mass_positive,spring_positive,qualified] 欄序回答。","answer":{"kind":"expression","value":"(2, 10, 是, 是, 是)","explanation_zh":"結構基礎核對=(2, 10, 是, 是, 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；不宣稱sin/cos閉式解；單點能量不證沿軌道守恆。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["簡諧振子精確切片"]},"variant":{"family_id":"qf-str22-oscillator-model-qualification","seed":202610221019,"parameters":{"mass":[2,1],"spring":[10,1],"domain":"Exact_harmonic_oscillator_model","operation":"oscillator-model-qualification","semantic_template":"qf-str22-oscillator-model-qualification/{\"mass\":[2,1],\"spring\":[10,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r01-harmonic-oscillator-model-0020","batch_id":"batch-20261013-advance-20261022-r01-harmonic-oscillator-model-foundations","language":"zh-Hant","source_mko_ids":["mko-harmonic-oscillator-model"],"title_zh":"簡諧振子精確切片","stem_zh":"無阻尼線性振子模型m x_second+k x=0。操作=oscillator-model-qualification；資料={\"mass\":[3,1],\"spring\":[11,1]}。請依 [mass,spring,mass_positive,spring_positive,qualified] 欄序回答。","answer":{"kind":"expression","value":"(3, 11, 是, 是, 是)","explanation_zh":"結構基礎核對=(3, 11, 是, 是, 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；不宣稱sin/cos閉式解；單點能量不證沿軌道守恆。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["簡諧振子精確切片"]},"variant":{"family_id":"qf-str22-oscillator-model-qualification","seed":202610221020,"parameters":{"mass":[3,1],"spring":[11,1],"domain":"Exact_harmonic_oscillator_model","operation":"oscillator-model-qualification","semantic_template":"qf-str22-oscillator-model-qualification/{\"mass\":[3,1],\"spring\":[11,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r01-harmonic-oscillator-model-0021","batch_id":"batch-20261013-advance-20261022-r01-harmonic-oscillator-model-foundations","language":"zh-Hant","source_mko_ids":["mko-harmonic-oscillator-model"],"title_zh":"簡諧振子精確切片","stem_zh":"無阻尼線性振子模型m x_second+k x=0。操作=oscillator-model-qualification；資料={\"mass\":[-1,1],\"spring\":[12,1]}。請依 [mass,spring,mass_positive,spring_positive,qualified] 欄序回答。","answer":{"kind":"expression","value":"(-1, 12, 否, 是, 否)","explanation_zh":"結構基礎核對=(-1, 12, 否, 是, 否)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；不宣稱sin/cos閉式解；單點能量不證沿軌道守恆。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["簡諧振子精確切片"]},"variant":{"family_id":"qf-str22-oscillator-model-qualification","seed":202610221021,"parameters":{"mass":[-1,1],"spring":[12,1],"domain":"Exact_harmonic_oscillator_model","operation":"oscillator-model-qualification","semantic_template":"qf-str22-oscillator-model-qualification/{\"mass\":[-1,1],\"spring\":[12,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r01-harmonic-oscillator-model-0022","batch_id":"batch-20261013-advance-20261022-r01-harmonic-oscillator-model-foundations","language":"zh-Hant","source_mko_ids":["mko-harmonic-oscillator-model"],"title_zh":"簡諧振子精確切片","stem_zh":"無阻尼線性振子模型m x_second+k x=0。操作=oscillator-model-qualification；資料={\"mass\":[0,1],\"spring\":[13,1]}。請依 [mass,spring,mass_positive,spring_positive,qualified] 欄序回答。","answer":{"kind":"expression","value":"(0, 13, 否, 是, 否)","explanation_zh":"結構基礎核對=(0, 13, 否, 是, 否)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；不宣稱sin/cos閉式解；單點能量不證沿軌道守恆。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["簡諧振子精確切片"]},"variant":{"family_id":"qf-str22-oscillator-model-qualification","seed":202610221022,"parameters":{"mass":[0,1],"spring":[13,1],"domain":"Exact_harmonic_oscillator_model","operation":"oscillator-model-qualification","semantic_template":"qf-str22-oscillator-model-qualification/{\"mass\":[0,1],\"spring\":[13,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r01-harmonic-oscillator-model-0023","batch_id":"batch-20261013-advance-20261022-r01-harmonic-oscillator-model-foundations","language":"zh-Hant","source_mko_ids":["mko-harmonic-oscillator-model"],"title_zh":"簡諧振子精確切片","stem_zh":"無阻尼線性振子模型m x_second+k x=0。操作=oscillator-model-qualification；資料={\"mass\":[1,1],\"spring\":[14,1]}。請依 [mass,spring,mass_positive,spring_positive,qualified] 欄序回答。","answer":{"kind":"expression","value":"(1, 14, 是, 是, 是)","explanation_zh":"結構基礎核對=(1, 14, 是, 是, 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；不宣稱sin/cos閉式解；單點能量不證沿軌道守恆。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["簡諧振子精確切片"]},"variant":{"family_id":"qf-str22-oscillator-model-qualification","seed":202610221023,"parameters":{"mass":[1,1],"spring":[14,1],"domain":"Exact_harmonic_oscillator_model","operation":"oscillator-model-qualification","semantic_template":"qf-str22-oscillator-model-qualification/{\"mass\":[1,1],\"spring\":[14,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r01-harmonic-oscillator-model-0024","batch_id":"batch-20261013-advance-20261022-r01-harmonic-oscillator-model-foundations","language":"zh-Hant","source_mko_ids":["mko-harmonic-oscillator-model"],"title_zh":"簡諧振子精確切片","stem_zh":"無阻尼線性振子模型m x_second+k x=0。操作=oscillator-model-qualification；資料={\"mass\":[2,1],\"spring\":[15,1]}。請依 [mass,spring,mass_positive,spring_positive,qualified] 欄序回答。","answer":{"kind":"expression","value":"(2, 15, 是, 是, 是)","explanation_zh":"結構基礎核對=(2, 15, 是, 是, 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；不宣稱sin/cos閉式解；單點能量不證沿軌道守恆。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["簡諧振子精確切片"]},"variant":{"family_id":"qf-str22-oscillator-model-qualification","seed":202610221024,"parameters":{"mass":[2,1],"spring":[15,1],"domain":"Exact_harmonic_oscillator_model","operation":"oscillator-model-qualification","semantic_template":"qf-str22-oscillator-model-qualification/{\"mass\":[2,1],\"spring\":[15,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r01-harmonic-oscillator-model-0025","batch_id":"batch-20261013-advance-20261022-r01-harmonic-oscillator-model-foundations","language":"zh-Hant","source_mko_ids":["mko-harmonic-oscillator-model"],"title_zh":"簡諧振子精確切片","stem_zh":"無阻尼線性振子模型m x_second+k x=0。操作=oscillator-model-qualification；資料={\"mass\":[3,1],\"spring\":[16,1]}。請依 [mass,spring,mass_positive,spring_positive,qualified] 欄序回答。","answer":{"kind":"expression","value":"(3, 16, 是, 是, 是)","explanation_zh":"結構基礎核對=(3, 16, 是, 是, 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；不宣稱sin/cos閉式解；單點能量不證沿軌道守恆。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["簡諧振子精確切片"]},"variant":{"family_id":"qf-str22-oscillator-model-qualification","seed":202610221025,"parameters":{"mass":[3,1],"spring":[16,1],"domain":"Exact_harmonic_oscillator_model","operation":"oscillator-model-qualification","semantic_template":"qf-str22-oscillator-model-qualification/{\"mass\":[3,1],\"spring\":[16,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r01-harmonic-oscillator-model-0026","batch_id":"batch-20261013-advance-20261022-r01-harmonic-oscillator-model-foundations","language":"zh-Hant","source_mko_ids":["mko-harmonic-oscillator-model"],"title_zh":"簡諧振子精確切片","stem_zh":"無阻尼線性振子模型m x_second+k x=0。操作=oscillator-omega-square；資料={\"mass\":[1,1],\"spring\":[2,1]}。請依 [mass,spring,omega_square] 欄序回答。","answer":{"kind":"expression","value":"(1, 2, 2)","explanation_zh":"結構基礎核對=(1, 2, 2)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；不宣稱sin/cos閉式解；單點能量不證沿軌道守恆。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["簡諧振子精確切片"]},"variant":{"family_id":"qf-str22-oscillator-omega-square","seed":202610221026,"parameters":{"mass":[1,1],"spring":[2,1],"domain":"Exact_harmonic_oscillator_model","operation":"oscillator-omega-square","semantic_template":"qf-str22-oscillator-omega-square/{\"mass\":[1,1],\"spring\":[2,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r01-harmonic-oscillator-model-0027","batch_id":"batch-20261013-advance-20261022-r01-harmonic-oscillator-model-foundations","language":"zh-Hant","source_mko_ids":["mko-harmonic-oscillator-model"],"title_zh":"簡諧振子精確切片","stem_zh":"無阻尼線性振子模型m x_second+k x=0。操作=oscillator-omega-square；資料={\"mass\":[2,1],\"spring\":[3,1]}。請依 [mass,spring,omega_square] 欄序回答。","answer":{"kind":"expression","value":"(2, 3, 3/2)","explanation_zh":"結構基礎核對=(2, 3, 3/2)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；不宣稱sin/cos閉式解；單點能量不證沿軌道守恆。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["簡諧振子精確切片"]},"variant":{"family_id":"qf-str22-oscillator-omega-square","seed":202610221027,"parameters":{"mass":[2,1],"spring":[3,1],"domain":"Exact_harmonic_oscillator_model","operation":"oscillator-omega-square","semantic_template":"qf-str22-oscillator-omega-square/{\"mass\":[2,1],\"spring\":[3,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r01-harmonic-oscillator-model-0028","batch_id":"batch-20261013-advance-20261022-r01-harmonic-oscillator-model-foundations","language":"zh-Hant","source_mko_ids":["mko-harmonic-oscillator-model"],"title_zh":"簡諧振子精確切片","stem_zh":"無阻尼線性振子模型m x_second+k x=0。操作=oscillator-omega-square；資料={\"mass\":[3,1],\"spring\":[4,1]}。請依 [mass,spring,omega_square] 欄序回答。","answer":{"kind":"expression","value":"(3, 4, 4/3)","explanation_zh":"結構基礎核對=(3, 4, 4/3)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；不宣稱sin/cos閉式解；單點能量不證沿軌道守恆。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["簡諧振子精確切片"]},"variant":{"family_id":"qf-str22-oscillator-omega-square","seed":202610221028,"parameters":{"mass":[3,1],"spring":[4,1],"domain":"Exact_harmonic_oscillator_model","operation":"oscillator-omega-square","semantic_template":"qf-str22-oscillator-omega-square/{\"mass\":[3,1],\"spring\":[4,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r01-harmonic-oscillator-model-0029","batch_id":"batch-20261013-advance-20261022-r01-harmonic-oscillator-model-foundations","language":"zh-Hant","source_mko_ids":["mko-harmonic-oscillator-model"],"title_zh":"簡諧振子精確切片","stem_zh":"無阻尼線性振子模型m x_second+k x=0。操作=oscillator-omega-square；資料={\"mass\":[4,1],\"spring\":[5,1]}。請依 [mass,spring,omega_square] 欄序回答。","answer":{"kind":"expression","value":"(4, 5, 5/4)","explanation_zh":"結構基礎核對=(4, 5, 5/4)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；不宣稱sin/cos閉式解；單點能量不證沿軌道守恆。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["簡諧振子精確切片"]},"variant":{"family_id":"qf-str22-oscillator-omega-square","seed":202610221029,"parameters":{"mass":[4,1],"spring":[5,1],"domain":"Exact_harmonic_oscillator_model","operation":"oscillator-omega-square","semantic_template":"qf-str22-oscillator-omega-square/{\"mass\":[4,1],\"spring\":[5,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r01-harmonic-oscillator-model-0030","batch_id":"batch-20261013-advance-20261022-r01-harmonic-oscillator-model-foundations","language":"zh-Hant","source_mko_ids":["mko-harmonic-oscillator-model"],"title_zh":"簡諧振子精確切片","stem_zh":"無阻尼線性振子模型m x_second+k x=0。操作=oscillator-omega-square；資料={\"mass\":[5,1],\"spring\":[6,1]}。請依 [mass,spring,omega_square] 欄序回答。","answer":{"kind":"expression","value":"(5, 6, 6/5)","explanation_zh":"結構基礎核對=(5, 6, 6/5)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；不宣稱sin/cos閉式解；單點能量不證沿軌道守恆。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["簡諧振子精確切片"]},"variant":{"family_id":"qf-str22-oscillator-omega-square","seed":202610221030,"parameters":{"mass":[5,1],"spring":[6,1],"domain":"Exact_harmonic_oscillator_model","operation":"oscillator-omega-square","semantic_template":"qf-str22-oscillator-omega-square/{\"mass\":[5,1],\"spring\":[6,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r01-harmonic-oscillator-model-0031","batch_id":"batch-20261013-advance-20261022-r01-harmonic-oscillator-model-foundations","language":"zh-Hant","source_mko_ids":["mko-harmonic-oscillator-model"],"title_zh":"簡諧振子精確切片","stem_zh":"無阻尼線性振子模型m x_second+k x=0。操作=oscillator-omega-square；資料={\"mass\":[1,1],\"spring\":[7,1]}。請依 [mass,spring,omega_square] 欄序回答。","answer":{"kind":"expression","value":"(1, 7, 7)","explanation_zh":"結構基礎核對=(1, 7, 7)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；不宣稱sin/cos閉式解；單點能量不證沿軌道守恆。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["簡諧振子精確切片"]},"variant":{"family_id":"qf-str22-oscillator-omega-square","seed":202610221031,"parameters":{"mass":[1,1],"spring":[7,1],"domain":"Exact_harmonic_oscillator_model","operation":"oscillator-omega-square","semantic_template":"qf-str22-oscillator-omega-square/{\"mass\":[1,1],\"spring\":[7,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r01-harmonic-oscillator-model-0032","batch_id":"batch-20261013-advance-20261022-r01-harmonic-oscillator-model-foundations","language":"zh-Hant","source_mko_ids":["mko-harmonic-oscillator-model"],"title_zh":"簡諧振子精確切片","stem_zh":"無阻尼線性振子模型m x_second+k x=0。操作=oscillator-omega-square；資料={\"mass\":[2,1],\"spring\":[8,1]}。請依 [mass,spring,omega_square] 欄序回答。","answer":{"kind":"expression","value":"(2, 8, 4)","explanation_zh":"結構基礎核對=(2, 8, 4)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；不宣稱sin/cos閉式解；單點能量不證沿軌道守恆。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["簡諧振子精確切片"]},"variant":{"family_id":"qf-str22-oscillator-omega-square","seed":202610221032,"parameters":{"mass":[2,1],"spring":[8,1],"domain":"Exact_harmonic_oscillator_model","operation":"oscillator-omega-square","semantic_template":"qf-str22-oscillator-omega-square/{\"mass\":[2,1],\"spring\":[8,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r01-harmonic-oscillator-model-0033","batch_id":"batch-20261013-advance-20261022-r01-harmonic-oscillator-model-foundations","language":"zh-Hant","source_mko_ids":["mko-harmonic-oscillator-model"],"title_zh":"簡諧振子精確切片","stem_zh":"無阻尼線性振子模型m x_second+k x=0。操作=oscillator-omega-square；資料={\"mass\":[3,1],\"spring\":[9,1]}。請依 [mass,spring,omega_square] 欄序回答。","answer":{"kind":"expression","value":"(3, 9, 3)","explanation_zh":"結構基礎核對=(3, 9, 3)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；不宣稱sin/cos閉式解；單點能量不證沿軌道守恆。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["簡諧振子精確切片"]},"variant":{"family_id":"qf-str22-oscillator-omega-square","seed":202610221033,"parameters":{"mass":[3,1],"spring":[9,1],"domain":"Exact_harmonic_oscillator_model","operation":"oscillator-omega-square","semantic_template":"qf-str22-oscillator-omega-square/{\"mass\":[3,1],\"spring\":[9,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r01-harmonic-oscillator-model-0034","batch_id":"batch-20261013-advance-20261022-r01-harmonic-oscillator-model-foundations","language":"zh-Hant","source_mko_ids":["mko-harmonic-oscillator-model"],"title_zh":"簡諧振子精確切片","stem_zh":"無阻尼線性振子模型m x_second+k x=0。操作=oscillator-omega-square；資料={\"mass\":[4,1],\"spring\":[10,1]}。請依 [mass,spring,omega_square] 欄序回答。","answer":{"kind":"expression","value":"(4, 10, 5/2)","explanation_zh":"結構基礎核對=(4, 10, 5/2)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；不宣稱sin/cos閉式解；單點能量不證沿軌道守恆。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["簡諧振子精確切片"]},"variant":{"family_id":"qf-str22-oscillator-omega-square","seed":202610221034,"parameters":{"mass":[4,1],"spring":[10,1],"domain":"Exact_harmonic_oscillator_model","operation":"oscillator-omega-square","semantic_template":"qf-str22-oscillator-omega-square/{\"mass\":[4,1],\"spring\":[10,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r01-harmonic-oscillator-model-0035","batch_id":"batch-20261013-advance-20261022-r01-harmonic-oscillator-model-foundations","language":"zh-Hant","source_mko_ids":["mko-harmonic-oscillator-model"],"title_zh":"簡諧振子精確切片","stem_zh":"無阻尼線性振子模型m x_second+k x=0。操作=oscillator-omega-square；資料={\"mass\":[5,1],\"spring\":[11,1]}。請依 [mass,spring,omega_square] 欄序回答。","answer":{"kind":"expression","value":"(5, 11, 11/5)","explanation_zh":"結構基礎核對=(5, 11, 11/5)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；不宣稱sin/cos閉式解；單點能量不證沿軌道守恆。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["簡諧振子精確切片"]},"variant":{"family_id":"qf-str22-oscillator-omega-square","seed":202610221035,"parameters":{"mass":[5,1],"spring":[11,1],"domain":"Exact_harmonic_oscillator_model","operation":"oscillator-omega-square","semantic_template":"qf-str22-oscillator-omega-square/{\"mass\":[5,1],\"spring\":[11,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r01-harmonic-oscillator-model-0036","batch_id":"batch-20261013-advance-20261022-r01-harmonic-oscillator-model-foundations","language":"zh-Hant","source_mko_ids":["mko-harmonic-oscillator-model"],"title_zh":"簡諧振子精確切片","stem_zh":"無阻尼線性振子模型m x_second+k x=0。操作=oscillator-omega-square；資料={\"mass\":[1,1],\"spring\":[12,1]}。請依 [mass,spring,omega_square] 欄序回答。","answer":{"kind":"expression","value":"(1, 12, 12)","explanation_zh":"結構基礎核對=(1, 12, 12)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；不宣稱sin/cos閉式解；單點能量不證沿軌道守恆。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["簡諧振子精確切片"]},"variant":{"family_id":"qf-str22-oscillator-omega-square","seed":202610221036,"parameters":{"mass":[1,1],"spring":[12,1],"domain":"Exact_harmonic_oscillator_model","operation":"oscillator-omega-square","semantic_template":"qf-str22-oscillator-omega-square/{\"mass\":[1,1],\"spring\":[12,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r01-harmonic-oscillator-model-0037","batch_id":"batch-20261013-advance-20261022-r01-harmonic-oscillator-model-foundations","language":"zh-Hant","source_mko_ids":["mko-harmonic-oscillator-model"],"title_zh":"簡諧振子精確切片","stem_zh":"無阻尼線性振子模型m x_second+k x=0。操作=oscillator-omega-square；資料={\"mass\":[2,1],\"spring\":[13,1]}。請依 [mass,spring,omega_square] 欄序回答。","answer":{"kind":"expression","value":"(2, 13, 13/2)","explanation_zh":"結構基礎核對=(2, 13, 13/2)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；不宣稱sin/cos閉式解；單點能量不證沿軌道守恆。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["簡諧振子精確切片"]},"variant":{"family_id":"qf-str22-oscillator-omega-square","seed":202610221037,"parameters":{"mass":[2,1],"spring":[13,1],"domain":"Exact_harmonic_oscillator_model","operation":"oscillator-omega-square","semantic_template":"qf-str22-oscillator-omega-square/{\"mass\":[2,1],\"spring\":[13,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r01-harmonic-oscillator-model-0038","batch_id":"batch-20261013-advance-20261022-r01-harmonic-oscillator-model-foundations","language":"zh-Hant","source_mko_ids":["mko-harmonic-oscillator-model"],"title_zh":"簡諧振子精確切片","stem_zh":"無阻尼線性振子模型m x_second+k x=0。操作=oscillator-omega-square；資料={\"mass\":[3,1],\"spring\":[14,1]}。請依 [mass,spring,omega_square] 欄序回答。","answer":{"kind":"expression","value":"(3, 14, 14/3)","explanation_zh":"結構基礎核對=(3, 14, 14/3)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；不宣稱sin/cos閉式解；單點能量不證沿軌道守恆。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["簡諧振子精確切片"]},"variant":{"family_id":"qf-str22-oscillator-omega-square","seed":202610221038,"parameters":{"mass":[3,1],"spring":[14,1],"domain":"Exact_harmonic_oscillator_model","operation":"oscillator-omega-square","semantic_template":"qf-str22-oscillator-omega-square/{\"mass\":[3,1],\"spring\":[14,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r01-harmonic-oscillator-model-0039","batch_id":"batch-20261013-advance-20261022-r01-harmonic-oscillator-model-foundations","language":"zh-Hant","source_mko_ids":["mko-harmonic-oscillator-model"],"title_zh":"簡諧振子精確切片","stem_zh":"無阻尼線性振子模型m x_second+k x=0。操作=oscillator-omega-square；資料={\"mass\":[4,1],\"spring\":[15,1]}。請依 [mass,spring,omega_square] 欄序回答。","answer":{"kind":"expression","value":"(4, 15, 15/4)","explanation_zh":"結構基礎核對=(4, 15, 15/4)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；不宣稱sin/cos閉式解；單點能量不證沿軌道守恆。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["簡諧振子精確切片"]},"variant":{"family_id":"qf-str22-oscillator-omega-square","seed":202610221039,"parameters":{"mass":[4,1],"spring":[15,1],"domain":"Exact_harmonic_oscillator_model","operation":"oscillator-omega-square","semantic_template":"qf-str22-oscillator-omega-square/{\"mass\":[4,1],\"spring\":[15,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r01-harmonic-oscillator-model-0040","batch_id":"batch-20261013-advance-20261022-r01-harmonic-oscillator-model-foundations","language":"zh-Hant","source_mko_ids":["mko-harmonic-oscillator-model"],"title_zh":"簡諧振子精確切片","stem_zh":"無阻尼線性振子模型m x_second+k x=0。操作=oscillator-omega-square；資料={\"mass\":[5,1],\"spring\":[16,1]}。請依 [mass,spring,omega_square] 欄序回答。","answer":{"kind":"expression","value":"(5, 16, 16/5)","explanation_zh":"結構基礎核對=(5, 16, 16/5)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；不宣稱sin/cos閉式解；單點能量不證沿軌道守恆。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["簡諧振子精確切片"]},"variant":{"family_id":"qf-str22-oscillator-omega-square","seed":202610221040,"parameters":{"mass":[5,1],"spring":[16,1],"domain":"Exact_harmonic_oscillator_model","operation":"oscillator-omega-square","semantic_template":"qf-str22-oscillator-omega-square/{\"mass\":[5,1],\"spring\":[16,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r01-harmonic-oscillator-model-0041","batch_id":"batch-20261013-advance-20261022-r01-harmonic-oscillator-model-foundations","language":"zh-Hant","source_mko_ids":["mko-harmonic-oscillator-model"],"title_zh":"簡諧振子精確切片","stem_zh":"無阻尼線性振子模型m x_second+k x=0。操作=oscillator-omega-square；資料={\"mass\":[1,1],\"spring\":[17,1]}。請依 [mass,spring,omega_square] 欄序回答。","answer":{"kind":"expression","value":"(1, 17, 17)","explanation_zh":"結構基礎核對=(1, 17, 17)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；不宣稱sin/cos閉式解；單點能量不證沿軌道守恆。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["簡諧振子精確切片"]},"variant":{"family_id":"qf-str22-oscillator-omega-square","seed":202610221041,"parameters":{"mass":[1,1],"spring":[17,1],"domain":"Exact_harmonic_oscillator_model","operation":"oscillator-omega-square","semantic_template":"qf-str22-oscillator-omega-square/{\"mass\":[1,1],\"spring\":[17,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r01-harmonic-oscillator-model-0042","batch_id":"batch-20261013-advance-20261022-r01-harmonic-oscillator-model-foundations","language":"zh-Hant","source_mko_ids":["mko-harmonic-oscillator-model"],"title_zh":"簡諧振子精確切片","stem_zh":"無阻尼線性振子模型m x_second+k x=0。操作=oscillator-omega-square；資料={\"mass\":[2,1],\"spring\":[18,1]}。請依 [mass,spring,omega_square] 欄序回答。","answer":{"kind":"expression","value":"(2, 18, 9)","explanation_zh":"結構基礎核對=(2, 18, 9)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；不宣稱sin/cos閉式解；單點能量不證沿軌道守恆。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["簡諧振子精確切片"]},"variant":{"family_id":"qf-str22-oscillator-omega-square","seed":202610221042,"parameters":{"mass":[2,1],"spring":[18,1],"domain":"Exact_harmonic_oscillator_model","operation":"oscillator-omega-square","semantic_template":"qf-str22-oscillator-omega-square/{\"mass\":[2,1],\"spring\":[18,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r01-harmonic-oscillator-model-0043","batch_id":"batch-20261013-advance-20261022-r01-harmonic-oscillator-model-foundations","language":"zh-Hant","source_mko_ids":["mko-harmonic-oscillator-model"],"title_zh":"簡諧振子精確切片","stem_zh":"無阻尼線性振子模型m x_second+k x=0。操作=oscillator-omega-square；資料={\"mass\":[3,1],\"spring\":[19,1]}。請依 [mass,spring,omega_square] 欄序回答。","answer":{"kind":"expression","value":"(3, 19, 19/3)","explanation_zh":"結構基礎核對=(3, 19, 19/3)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；不宣稱sin/cos閉式解；單點能量不證沿軌道守恆。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["簡諧振子精確切片"]},"variant":{"family_id":"qf-str22-oscillator-omega-square","seed":202610221043,"parameters":{"mass":[3,1],"spring":[19,1],"domain":"Exact_harmonic_oscillator_model","operation":"oscillator-omega-square","semantic_template":"qf-str22-oscillator-omega-square/{\"mass\":[3,1],\"spring\":[19,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r01-harmonic-oscillator-model-0044","batch_id":"batch-20261013-advance-20261022-r01-harmonic-oscillator-model-foundations","language":"zh-Hant","source_mko_ids":["mko-harmonic-oscillator-model"],"title_zh":"簡諧振子精確切片","stem_zh":"無阻尼線性振子模型m x_second+k x=0。操作=oscillator-omega-square；資料={\"mass\":[4,1],\"spring\":[20,1]}。請依 [mass,spring,omega_square] 欄序回答。","answer":{"kind":"expression","value":"(4, 20, 5)","explanation_zh":"結構基礎核對=(4, 20, 5)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；不宣稱sin/cos閉式解；單點能量不證沿軌道守恆。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["簡諧振子精確切片"]},"variant":{"family_id":"qf-str22-oscillator-omega-square","seed":202610221044,"parameters":{"mass":[4,1],"spring":[20,1],"domain":"Exact_harmonic_oscillator_model","operation":"oscillator-omega-square","semantic_template":"qf-str22-oscillator-omega-square/{\"mass\":[4,1],\"spring\":[20,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r01-harmonic-oscillator-model-0045","batch_id":"batch-20261013-advance-20261022-r01-harmonic-oscillator-model-foundations","language":"zh-Hant","source_mko_ids":["mko-harmonic-oscillator-model"],"title_zh":"簡諧振子精確切片","stem_zh":"無阻尼線性振子模型m x_second+k x=0。操作=oscillator-omega-square；資料={\"mass\":[5,1],\"spring\":[21,1]}。請依 [mass,spring,omega_square] 欄序回答。","answer":{"kind":"expression","value":"(5, 21, 21/5)","explanation_zh":"結構基礎核對=(5, 21, 21/5)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；不宣稱sin/cos閉式解；單點能量不證沿軌道守恆。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["簡諧振子精確切片"]},"variant":{"family_id":"qf-str22-oscillator-omega-square","seed":202610221045,"parameters":{"mass":[5,1],"spring":[21,1],"domain":"Exact_harmonic_oscillator_model","operation":"oscillator-omega-square","semantic_template":"qf-str22-oscillator-omega-square/{\"mass\":[5,1],\"spring\":[21,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r01-harmonic-oscillator-model-0046","batch_id":"batch-20261013-advance-20261022-r01-harmonic-oscillator-model-foundations","language":"zh-Hant","source_mko_ids":["mko-harmonic-oscillator-model"],"title_zh":"簡諧振子精確切片","stem_zh":"無阻尼線性振子模型m x_second+k x=0。操作=oscillator-omega-square；資料={\"mass\":[1,1],\"spring\":[22,1]}。請依 [mass,spring,omega_square] 欄序回答。","answer":{"kind":"expression","value":"(1, 22, 22)","explanation_zh":"結構基礎核對=(1, 22, 22)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；不宣稱sin/cos閉式解；單點能量不證沿軌道守恆。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["簡諧振子精確切片"]},"variant":{"family_id":"qf-str22-oscillator-omega-square","seed":202610221046,"parameters":{"mass":[1,1],"spring":[22,1],"domain":"Exact_harmonic_oscillator_model","operation":"oscillator-omega-square","semantic_template":"qf-str22-oscillator-omega-square/{\"mass\":[1,1],\"spring\":[22,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r01-harmonic-oscillator-model-0047","batch_id":"batch-20261013-advance-20261022-r01-harmonic-oscillator-model-foundations","language":"zh-Hant","source_mko_ids":["mko-harmonic-oscillator-model"],"title_zh":"簡諧振子精確切片","stem_zh":"無阻尼線性振子模型m x_second+k x=0。操作=oscillator-omega-square；資料={\"mass\":[2,1],\"spring\":[23,1]}。請依 [mass,spring,omega_square] 欄序回答。","answer":{"kind":"expression","value":"(2, 23, 23/2)","explanation_zh":"結構基礎核對=(2, 23, 23/2)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；不宣稱sin/cos閉式解；單點能量不證沿軌道守恆。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["簡諧振子精確切片"]},"variant":{"family_id":"qf-str22-oscillator-omega-square","seed":202610221047,"parameters":{"mass":[2,1],"spring":[23,1],"domain":"Exact_harmonic_oscillator_model","operation":"oscillator-omega-square","semantic_template":"qf-str22-oscillator-omega-square/{\"mass\":[2,1],\"spring\":[23,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r01-harmonic-oscillator-model-0048","batch_id":"batch-20261013-advance-20261022-r01-harmonic-oscillator-model-foundations","language":"zh-Hant","source_mko_ids":["mko-harmonic-oscillator-model"],"title_zh":"簡諧振子精確切片","stem_zh":"無阻尼線性振子模型m x_second+k x=0。操作=oscillator-omega-square；資料={\"mass\":[3,1],\"spring\":[24,1]}。請依 [mass,spring,omega_square] 欄序回答。","answer":{"kind":"expression","value":"(3, 24, 8)","explanation_zh":"結構基礎核對=(3, 24, 8)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；不宣稱sin/cos閉式解；單點能量不證沿軌道守恆。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["簡諧振子精確切片"]},"variant":{"family_id":"qf-str22-oscillator-omega-square","seed":202610221048,"parameters":{"mass":[3,1],"spring":[24,1],"domain":"Exact_harmonic_oscillator_model","operation":"oscillator-omega-square","semantic_template":"qf-str22-oscillator-omega-square/{\"mass\":[3,1],\"spring\":[24,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r01-harmonic-oscillator-model-0049","batch_id":"batch-20261013-advance-20261022-r01-harmonic-oscillator-model-foundations","language":"zh-Hant","source_mko_ids":["mko-harmonic-oscillator-model"],"title_zh":"簡諧振子精確切片","stem_zh":"無阻尼線性振子模型m x_second+k x=0。操作=oscillator-omega-square；資料={\"mass\":[4,1],\"spring\":[25,1]}。請依 [mass,spring,omega_square] 欄序回答。","answer":{"kind":"expression","value":"(4, 25, 25/4)","explanation_zh":"結構基礎核對=(4, 25, 25/4)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；不宣稱sin/cos閉式解；單點能量不證沿軌道守恆。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["簡諧振子精確切片"]},"variant":{"family_id":"qf-str22-oscillator-omega-square","seed":202610221049,"parameters":{"mass":[4,1],"spring":[25,1],"domain":"Exact_harmonic_oscillator_model","operation":"oscillator-omega-square","semantic_template":"qf-str22-oscillator-omega-square/{\"mass\":[4,1],\"spring\":[25,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r01-harmonic-oscillator-model-0050","batch_id":"batch-20261013-advance-20261022-r01-harmonic-oscillator-model-foundations","language":"zh-Hant","source_mko_ids":["mko-harmonic-oscillator-model"],"title_zh":"簡諧振子精確切片","stem_zh":"無阻尼線性振子模型m x_second+k x=0。操作=oscillator-omega-square；資料={\"mass\":[5,1],\"spring\":[26,1]}。請依 [mass,spring,omega_square] 欄序回答。","answer":{"kind":"expression","value":"(5, 26, 26/5)","explanation_zh":"結構基礎核對=(5, 26, 26/5)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；不宣稱sin/cos閉式解；單點能量不證沿軌道守恆。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["簡諧振子精確切片"]},"variant":{"family_id":"qf-str22-oscillator-omega-square","seed":202610221050,"parameters":{"mass":[5,1],"spring":[26,1],"domain":"Exact_harmonic_oscillator_model","operation":"oscillator-omega-square","semantic_template":"qf-str22-oscillator-omega-square/{\"mass\":[5,1],\"spring\":[26,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r01-harmonic-oscillator-model-0051","batch_id":"batch-20261013-advance-20261022-r01-harmonic-oscillator-model-foundations","language":"zh-Hant","source_mko_ids":["mko-harmonic-oscillator-model"],"title_zh":"簡諧振子精確切片","stem_zh":"無阻尼線性振子模型m x_second+k x=0。操作=oscillator-polynomial-residual；資料={\"coefficients\":[-12,-2,-3],\"mass\":[1,1],\"spring\":[1,1],\"x\":-2}。請依 [coefficients,x,position,acceleration,mass,spring,residual,zero_at_x] 欄序回答。","answer":{"kind":"expression","value":"([-12, -2, -3], -2, -20, -6, 1, 1, -26, 否)","explanation_zh":"結構基礎核對=([-12, -2, -3], -2, -20, -6, 1, 1, -26, 否)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；不宣稱sin/cos閉式解；單點能量不證沿軌道守恆。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["簡諧振子精確切片"]},"variant":{"family_id":"qf-str22-oscillator-polynomial-residual","seed":202610221051,"parameters":{"coefficients":[-12,-2,-3],"mass":[1,1],"spring":[1,1],"x":-2,"domain":"Exact_harmonic_oscillator_model","operation":"oscillator-polynomial-residual","semantic_template":"qf-str22-oscillator-polynomial-residual/{\"coefficients\":[-12,-2,-3],\"mass\":[1,1],\"spring\":[1,1],\"x\":-2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r01-harmonic-oscillator-model-0052","batch_id":"batch-20261013-advance-20261022-r01-harmonic-oscillator-model-foundations","language":"zh-Hant","source_mko_ids":["mko-harmonic-oscillator-model"],"title_zh":"簡諧振子精確切片","stem_zh":"無阻尼線性振子模型m x_second+k x=0。操作=oscillator-polynomial-residual；資料={\"coefficients\":[-11,-1,-1],\"mass\":[2,1],\"spring\":[2,1],\"x\":-1}。請依 [coefficients,x,position,acceleration,mass,spring,residual,zero_at_x] 欄序回答。","answer":{"kind":"expression","value":"([-11, -1, -1], -1, -11, -2, 2, 2, -26, 否)","explanation_zh":"結構基礎核對=([-11, -1, -1], -1, -11, -2, 2, 2, -26, 否)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；不宣稱sin/cos閉式解；單點能量不證沿軌道守恆。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["簡諧振子精確切片"]},"variant":{"family_id":"qf-str22-oscillator-polynomial-residual","seed":202610221052,"parameters":{"coefficients":[-11,-1,-1],"mass":[2,1],"spring":[2,1],"x":-1,"domain":"Exact_harmonic_oscillator_model","operation":"oscillator-polynomial-residual","semantic_template":"qf-str22-oscillator-polynomial-residual/{\"coefficients\":[-11,-1,-1],\"mass\":[2,1],\"spring\":[2,1],\"x\":-1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r01-harmonic-oscillator-model-0053","batch_id":"batch-20261013-advance-20261022-r01-harmonic-oscillator-model-foundations","language":"zh-Hant","source_mko_ids":["mko-harmonic-oscillator-model"],"title_zh":"簡諧振子精確切片","stem_zh":"無阻尼線性振子模型m x_second+k x=0。操作=oscillator-polynomial-residual；資料={\"coefficients\":[-10,0,1],\"mass\":[3,1],\"spring\":[3,1],\"x\":0}。請依 [coefficients,x,position,acceleration,mass,spring,residual,zero_at_x] 欄序回答。","answer":{"kind":"expression","value":"([-10, 0, 1], 0, -10, 2, 3, 3, -24, 否)","explanation_zh":"結構基礎核對=([-10, 0, 1], 0, -10, 2, 3, 3, -24, 否)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；不宣稱sin/cos閉式解；單點能量不證沿軌道守恆。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["簡諧振子精確切片"]},"variant":{"family_id":"qf-str22-oscillator-polynomial-residual","seed":202610221053,"parameters":{"coefficients":[-10,0,1],"mass":[3,1],"spring":[3,1],"x":0,"domain":"Exact_harmonic_oscillator_model","operation":"oscillator-polynomial-residual","semantic_template":"qf-str22-oscillator-polynomial-residual/{\"coefficients\":[-10,0,1],\"mass\":[3,1],\"spring\":[3,1],\"x\":0}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r01-harmonic-oscillator-model-0054","batch_id":"batch-20261013-advance-20261022-r01-harmonic-oscillator-model-foundations","language":"zh-Hant","source_mko_ids":["mko-harmonic-oscillator-model"],"title_zh":"簡諧振子精確切片","stem_zh":"無阻尼線性振子模型m x_second+k x=0。操作=oscillator-polynomial-residual；資料={\"coefficients\":[-9,1,3],\"mass\":[4,1],\"spring\":[4,1],\"x\":1}。請依 [coefficients,x,position,acceleration,mass,spring,residual,zero_at_x] 欄序回答。","answer":{"kind":"expression","value":"([-9, 1, 3], 1, -5, 6, 4, 4, 4, 否)","explanation_zh":"結構基礎核對=([-9, 1, 3], 1, -5, 6, 4, 4, 4, 否)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；不宣稱sin/cos閉式解；單點能量不證沿軌道守恆。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["簡諧振子精確切片"]},"variant":{"family_id":"qf-str22-oscillator-polynomial-residual","seed":202610221054,"parameters":{"coefficients":[-9,1,3],"mass":[4,1],"spring":[4,1],"x":1,"domain":"Exact_harmonic_oscillator_model","operation":"oscillator-polynomial-residual","semantic_template":"qf-str22-oscillator-polynomial-residual/{\"coefficients\":[-9,1,3],\"mass\":[4,1],\"spring\":[4,1],\"x\":1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r01-harmonic-oscillator-model-0055","batch_id":"batch-20261013-advance-20261022-r01-harmonic-oscillator-model-foundations","language":"zh-Hant","source_mko_ids":["mko-harmonic-oscillator-model"],"title_zh":"簡諧振子精確切片","stem_zh":"無阻尼線性振子模型m x_second+k x=0。操作=oscillator-polynomial-residual；資料={\"coefficients\":[-8,2,-2],\"mass\":[1,1],\"spring\":[5,1],\"x\":2}。請依 [coefficients,x,position,acceleration,mass,spring,residual,zero_at_x] 欄序回答。","answer":{"kind":"expression","value":"([-8, 2, -2], 2, -12, -4, 1, 5, -64, 否)","explanation_zh":"結構基礎核對=([-8, 2, -2], 2, -12, -4, 1, 5, -64, 否)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；不宣稱sin/cos閉式解；單點能量不證沿軌道守恆。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["簡諧振子精確切片"]},"variant":{"family_id":"qf-str22-oscillator-polynomial-residual","seed":202610221055,"parameters":{"coefficients":[-8,2,-2],"mass":[1,1],"spring":[5,1],"x":2,"domain":"Exact_harmonic_oscillator_model","operation":"oscillator-polynomial-residual","semantic_template":"qf-str22-oscillator-polynomial-residual/{\"coefficients\":[-8,2,-2],\"mass\":[1,1],\"spring\":[5,1],\"x\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r01-harmonic-oscillator-model-0056","batch_id":"batch-20261013-advance-20261022-r01-harmonic-oscillator-model-foundations","language":"zh-Hant","source_mko_ids":["mko-harmonic-oscillator-model"],"title_zh":"簡諧振子精確切片","stem_zh":"無阻尼線性振子模型m x_second+k x=0。操作=oscillator-polynomial-residual；資料={\"coefficients\":[-7,-2,0],\"mass\":[2,1],\"spring\":[6,1],\"x\":-2}。請依 [coefficients,x,position,acceleration,mass,spring,residual,zero_at_x] 欄序回答。","answer":{"kind":"expression","value":"([-7, -2, 0], -2, -3, 0, 2, 6, -18, 否)","explanation_zh":"結構基礎核對=([-7, -2, 0], -2, -3, 0, 2, 6, -18, 否)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；不宣稱sin/cos閉式解；單點能量不證沿軌道守恆。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["簡諧振子精確切片"]},"variant":{"family_id":"qf-str22-oscillator-polynomial-residual","seed":202610221056,"parameters":{"coefficients":[-7,-2,0],"mass":[2,1],"spring":[6,1],"x":-2,"domain":"Exact_harmonic_oscillator_model","operation":"oscillator-polynomial-residual","semantic_template":"qf-str22-oscillator-polynomial-residual/{\"coefficients\":[-7,-2,0],\"mass\":[2,1],\"spring\":[6,1],\"x\":-2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r01-harmonic-oscillator-model-0057","batch_id":"batch-20261013-advance-20261022-r01-harmonic-oscillator-model-foundations","language":"zh-Hant","source_mko_ids":["mko-harmonic-oscillator-model"],"title_zh":"簡諧振子精確切片","stem_zh":"無阻尼線性振子模型m x_second+k x=0。操作=oscillator-polynomial-residual；資料={\"coefficients\":[-6,-1,2],\"mass\":[3,1],\"spring\":[1,1],\"x\":-1}。請依 [coefficients,x,position,acceleration,mass,spring,residual,zero_at_x] 欄序回答。","answer":{"kind":"expression","value":"([-6, -1, 2], -1, -3, 4, 3, 1, 9, 否)","explanation_zh":"結構基礎核對=([-6, -1, 2], -1, -3, 4, 3, 1, 9, 否)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；不宣稱sin/cos閉式解；單點能量不證沿軌道守恆。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["簡諧振子精確切片"]},"variant":{"family_id":"qf-str22-oscillator-polynomial-residual","seed":202610221057,"parameters":{"coefficients":[-6,-1,2],"mass":[3,1],"spring":[1,1],"x":-1,"domain":"Exact_harmonic_oscillator_model","operation":"oscillator-polynomial-residual","semantic_template":"qf-str22-oscillator-polynomial-residual/{\"coefficients\":[-6,-1,2],\"mass\":[3,1],\"spring\":[1,1],\"x\":-1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r01-harmonic-oscillator-model-0058","batch_id":"batch-20261013-advance-20261022-r01-harmonic-oscillator-model-foundations","language":"zh-Hant","source_mko_ids":["mko-harmonic-oscillator-model"],"title_zh":"簡諧振子精確切片","stem_zh":"無阻尼線性振子模型m x_second+k x=0。操作=oscillator-polynomial-residual；資料={\"coefficients\":[-5,0,-3],\"mass\":[4,1],\"spring\":[2,1],\"x\":0}。請依 [coefficients,x,position,acceleration,mass,spring,residual,zero_at_x] 欄序回答。","answer":{"kind":"expression","value":"([-5, 0, -3], 0, -5, -6, 4, 2, -34, 否)","explanation_zh":"結構基礎核對=([-5, 0, -3], 0, -5, -6, 4, 2, -34, 否)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；不宣稱sin/cos閉式解；單點能量不證沿軌道守恆。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["簡諧振子精確切片"]},"variant":{"family_id":"qf-str22-oscillator-polynomial-residual","seed":202610221058,"parameters":{"coefficients":[-5,0,-3],"mass":[4,1],"spring":[2,1],"x":0,"domain":"Exact_harmonic_oscillator_model","operation":"oscillator-polynomial-residual","semantic_template":"qf-str22-oscillator-polynomial-residual/{\"coefficients\":[-5,0,-3],\"mass\":[4,1],\"spring\":[2,1],\"x\":0}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r01-harmonic-oscillator-model-0059","batch_id":"batch-20261013-advance-20261022-r01-harmonic-oscillator-model-foundations","language":"zh-Hant","source_mko_ids":["mko-harmonic-oscillator-model"],"title_zh":"簡諧振子精確切片","stem_zh":"無阻尼線性振子模型m x_second+k x=0。操作=oscillator-polynomial-residual；資料={\"coefficients\":[-4,1,-1],\"mass\":[1,1],\"spring\":[3,1],\"x\":1}。請依 [coefficients,x,position,acceleration,mass,spring,residual,zero_at_x] 欄序回答。","answer":{"kind":"expression","value":"([-4, 1, -1], 1, -4, -2, 1, 3, -14, 否)","explanation_zh":"結構基礎核對=([-4, 1, -1], 1, -4, -2, 1, 3, -14, 否)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；不宣稱sin/cos閉式解；單點能量不證沿軌道守恆。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["簡諧振子精確切片"]},"variant":{"family_id":"qf-str22-oscillator-polynomial-residual","seed":202610221059,"parameters":{"coefficients":[-4,1,-1],"mass":[1,1],"spring":[3,1],"x":1,"domain":"Exact_harmonic_oscillator_model","operation":"oscillator-polynomial-residual","semantic_template":"qf-str22-oscillator-polynomial-residual/{\"coefficients\":[-4,1,-1],\"mass\":[1,1],\"spring\":[3,1],\"x\":1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r01-harmonic-oscillator-model-0060","batch_id":"batch-20261013-advance-20261022-r01-harmonic-oscillator-model-foundations","language":"zh-Hant","source_mko_ids":["mko-harmonic-oscillator-model"],"title_zh":"簡諧振子精確切片","stem_zh":"無阻尼線性振子模型m x_second+k x=0。操作=oscillator-polynomial-residual；資料={\"coefficients\":[-3,2,1],\"mass\":[2,1],\"spring\":[4,1],\"x\":2}。請依 [coefficients,x,position,acceleration,mass,spring,residual,zero_at_x] 欄序回答。","answer":{"kind":"expression","value":"([-3, 2, 1], 2, 5, 2, 2, 4, 24, 否)","explanation_zh":"結構基礎核對=([-3, 2, 1], 2, 5, 2, 2, 4, 24, 否)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；不宣稱sin/cos閉式解；單點能量不證沿軌道守恆。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["簡諧振子精確切片"]},"variant":{"family_id":"qf-str22-oscillator-polynomial-residual","seed":202610221060,"parameters":{"coefficients":[-3,2,1],"mass":[2,1],"spring":[4,1],"x":2,"domain":"Exact_harmonic_oscillator_model","operation":"oscillator-polynomial-residual","semantic_template":"qf-str22-oscillator-polynomial-residual/{\"coefficients\":[-3,2,1],\"mass\":[2,1],\"spring\":[4,1],\"x\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r01-harmonic-oscillator-model-0061","batch_id":"batch-20261013-advance-20261022-r01-harmonic-oscillator-model-foundations","language":"zh-Hant","source_mko_ids":["mko-harmonic-oscillator-model"],"title_zh":"簡諧振子精確切片","stem_zh":"無阻尼線性振子模型m x_second+k x=0。操作=oscillator-polynomial-residual；資料={\"coefficients\":[-2,-2,3],\"mass\":[3,1],\"spring\":[5,1],\"x\":-2}。請依 [coefficients,x,position,acceleration,mass,spring,residual,zero_at_x] 欄序回答。","answer":{"kind":"expression","value":"([-2, -2, 3], -2, 14, 6, 3, 5, 88, 否)","explanation_zh":"結構基礎核對=([-2, -2, 3], -2, 14, 6, 3, 5, 88, 否)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；不宣稱sin/cos閉式解；單點能量不證沿軌道守恆。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["簡諧振子精確切片"]},"variant":{"family_id":"qf-str22-oscillator-polynomial-residual","seed":202610221061,"parameters":{"coefficients":[-2,-2,3],"mass":[3,1],"spring":[5,1],"x":-2,"domain":"Exact_harmonic_oscillator_model","operation":"oscillator-polynomial-residual","semantic_template":"qf-str22-oscillator-polynomial-residual/{\"coefficients\":[-2,-2,3],\"mass\":[3,1],\"spring\":[5,1],\"x\":-2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r01-harmonic-oscillator-model-0062","batch_id":"batch-20261013-advance-20261022-r01-harmonic-oscillator-model-foundations","language":"zh-Hant","source_mko_ids":["mko-harmonic-oscillator-model"],"title_zh":"簡諧振子精確切片","stem_zh":"無阻尼線性振子模型m x_second+k x=0。操作=oscillator-polynomial-residual；資料={\"coefficients\":[-1,-1,-2],\"mass\":[4,1],\"spring\":[6,1],\"x\":-1}。請依 [coefficients,x,position,acceleration,mass,spring,residual,zero_at_x] 欄序回答。","answer":{"kind":"expression","value":"([-1, -1, -2], -1, -2, -4, 4, 6, -28, 否)","explanation_zh":"結構基礎核對=([-1, -1, -2], -1, -2, -4, 4, 6, -28, 否)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；不宣稱sin/cos閉式解；單點能量不證沿軌道守恆。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["簡諧振子精確切片"]},"variant":{"family_id":"qf-str22-oscillator-polynomial-residual","seed":202610221062,"parameters":{"coefficients":[-1,-1,-2],"mass":[4,1],"spring":[6,1],"x":-1,"domain":"Exact_harmonic_oscillator_model","operation":"oscillator-polynomial-residual","semantic_template":"qf-str22-oscillator-polynomial-residual/{\"coefficients\":[-1,-1,-2],\"mass\":[4,1],\"spring\":[6,1],\"x\":-1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r01-harmonic-oscillator-model-0063","batch_id":"batch-20261013-advance-20261022-r01-harmonic-oscillator-model-foundations","language":"zh-Hant","source_mko_ids":["mko-harmonic-oscillator-model"],"title_zh":"簡諧振子精確切片","stem_zh":"無阻尼線性振子模型m x_second+k x=0。操作=oscillator-polynomial-residual；資料={\"coefficients\":[0,0,0],\"mass\":[1,1],\"spring\":[1,1],\"x\":0}。請依 [coefficients,x,position,acceleration,mass,spring,residual,zero_at_x] 欄序回答。","answer":{"kind":"expression","value":"([0, 0, 0], 0, 0, 0, 1, 1, 0, 是)","explanation_zh":"結構基礎核對=([0, 0, 0], 0, 0, 0, 1, 1, 0, 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；不宣稱sin/cos閉式解；單點能量不證沿軌道守恆。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["簡諧振子精確切片"]},"variant":{"family_id":"qf-str22-oscillator-polynomial-residual","seed":202610221063,"parameters":{"coefficients":[0,0,0],"mass":[1,1],"spring":[1,1],"x":0,"domain":"Exact_harmonic_oscillator_model","operation":"oscillator-polynomial-residual","semantic_template":"qf-str22-oscillator-polynomial-residual/{\"coefficients\":[0,0,0],\"mass\":[1,1],\"spring\":[1,1],\"x\":0}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r01-harmonic-oscillator-model-0064","batch_id":"batch-20261013-advance-20261022-r01-harmonic-oscillator-model-foundations","language":"zh-Hant","source_mko_ids":["mko-harmonic-oscillator-model"],"title_zh":"簡諧振子精確切片","stem_zh":"無阻尼線性振子模型m x_second+k x=0。操作=oscillator-polynomial-residual；資料={\"coefficients\":[1,1,2],\"mass\":[2,1],\"spring\":[2,1],\"x\":1}。請依 [coefficients,x,position,acceleration,mass,spring,residual,zero_at_x] 欄序回答。","answer":{"kind":"expression","value":"([1, 1, 2], 1, 4, 4, 2, 2, 16, 否)","explanation_zh":"結構基礎核對=([1, 1, 2], 1, 4, 4, 2, 2, 16, 否)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；不宣稱sin/cos閉式解；單點能量不證沿軌道守恆。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["簡諧振子精確切片"]},"variant":{"family_id":"qf-str22-oscillator-polynomial-residual","seed":202610221064,"parameters":{"coefficients":[1,1,2],"mass":[2,1],"spring":[2,1],"x":1,"domain":"Exact_harmonic_oscillator_model","operation":"oscillator-polynomial-residual","semantic_template":"qf-str22-oscillator-polynomial-residual/{\"coefficients\":[1,1,2],\"mass\":[2,1],\"spring\":[2,1],\"x\":1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r01-harmonic-oscillator-model-0065","batch_id":"batch-20261013-advance-20261022-r01-harmonic-oscillator-model-foundations","language":"zh-Hant","source_mko_ids":["mko-harmonic-oscillator-model"],"title_zh":"簡諧振子精確切片","stem_zh":"無阻尼線性振子模型m x_second+k x=0。操作=oscillator-polynomial-residual；資料={\"coefficients\":[2,2,-3],\"mass\":[3,1],\"spring\":[3,1],\"x\":2}。請依 [coefficients,x,position,acceleration,mass,spring,residual,zero_at_x] 欄序回答。","answer":{"kind":"expression","value":"([2, 2, -3], 2, -6, -6, 3, 3, -36, 否)","explanation_zh":"結構基礎核對=([2, 2, -3], 2, -6, -6, 3, 3, -36, 否)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；不宣稱sin/cos閉式解；單點能量不證沿軌道守恆。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["簡諧振子精確切片"]},"variant":{"family_id":"qf-str22-oscillator-polynomial-residual","seed":202610221065,"parameters":{"coefficients":[2,2,-3],"mass":[3,1],"spring":[3,1],"x":2,"domain":"Exact_harmonic_oscillator_model","operation":"oscillator-polynomial-residual","semantic_template":"qf-str22-oscillator-polynomial-residual/{\"coefficients\":[2,2,-3],\"mass\":[3,1],\"spring\":[3,1],\"x\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r01-harmonic-oscillator-model-0066","batch_id":"batch-20261013-advance-20261022-r01-harmonic-oscillator-model-foundations","language":"zh-Hant","source_mko_ids":["mko-harmonic-oscillator-model"],"title_zh":"簡諧振子精確切片","stem_zh":"無阻尼線性振子模型m x_second+k x=0。操作=oscillator-polynomial-residual；資料={\"coefficients\":[3,-2,-1],\"mass\":[4,1],\"spring\":[4,1],\"x\":-2}。請依 [coefficients,x,position,acceleration,mass,spring,residual,zero_at_x] 欄序回答。","answer":{"kind":"expression","value":"([3, -2, -1], -2, 3, -2, 4, 4, 4, 否)","explanation_zh":"結構基礎核對=([3, -2, -1], -2, 3, -2, 4, 4, 4, 否)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；不宣稱sin/cos閉式解；單點能量不證沿軌道守恆。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["簡諧振子精確切片"]},"variant":{"family_id":"qf-str22-oscillator-polynomial-residual","seed":202610221066,"parameters":{"coefficients":[3,-2,-1],"mass":[4,1],"spring":[4,1],"x":-2,"domain":"Exact_harmonic_oscillator_model","operation":"oscillator-polynomial-residual","semantic_template":"qf-str22-oscillator-polynomial-residual/{\"coefficients\":[3,-2,-1],\"mass\":[4,1],\"spring\":[4,1],\"x\":-2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r01-harmonic-oscillator-model-0067","batch_id":"batch-20261013-advance-20261022-r01-harmonic-oscillator-model-foundations","language":"zh-Hant","source_mko_ids":["mko-harmonic-oscillator-model"],"title_zh":"簡諧振子精確切片","stem_zh":"無阻尼線性振子模型m x_second+k x=0。操作=oscillator-polynomial-residual；資料={\"coefficients\":[4,-1,1],\"mass\":[1,1],\"spring\":[5,1],\"x\":-1}。請依 [coefficients,x,position,acceleration,mass,spring,residual,zero_at_x] 欄序回答。","answer":{"kind":"expression","value":"([4, -1, 1], -1, 6, 2, 1, 5, 32, 否)","explanation_zh":"結構基礎核對=([4, -1, 1], -1, 6, 2, 1, 5, 32, 否)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；不宣稱sin/cos閉式解；單點能量不證沿軌道守恆。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["簡諧振子精確切片"]},"variant":{"family_id":"qf-str22-oscillator-polynomial-residual","seed":202610221067,"parameters":{"coefficients":[4,-1,1],"mass":[1,1],"spring":[5,1],"x":-1,"domain":"Exact_harmonic_oscillator_model","operation":"oscillator-polynomial-residual","semantic_template":"qf-str22-oscillator-polynomial-residual/{\"coefficients\":[4,-1,1],\"mass\":[1,1],\"spring\":[5,1],\"x\":-1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r01-harmonic-oscillator-model-0068","batch_id":"batch-20261013-advance-20261022-r01-harmonic-oscillator-model-foundations","language":"zh-Hant","source_mko_ids":["mko-harmonic-oscillator-model"],"title_zh":"簡諧振子精確切片","stem_zh":"無阻尼線性振子模型m x_second+k x=0。操作=oscillator-polynomial-residual；資料={\"coefficients\":[5,0,3],\"mass\":[2,1],\"spring\":[6,1],\"x\":0}。請依 [coefficients,x,position,acceleration,mass,spring,residual,zero_at_x] 欄序回答。","answer":{"kind":"expression","value":"([5, 0, 3], 0, 5, 6, 2, 6, 42, 否)","explanation_zh":"結構基礎核對=([5, 0, 3], 0, 5, 6, 2, 6, 42, 否)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；不宣稱sin/cos閉式解；單點能量不證沿軌道守恆。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["簡諧振子精確切片"]},"variant":{"family_id":"qf-str22-oscillator-polynomial-residual","seed":202610221068,"parameters":{"coefficients":[5,0,3],"mass":[2,1],"spring":[6,1],"x":0,"domain":"Exact_harmonic_oscillator_model","operation":"oscillator-polynomial-residual","semantic_template":"qf-str22-oscillator-polynomial-residual/{\"coefficients\":[5,0,3],\"mass\":[2,1],\"spring\":[6,1],\"x\":0}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r01-harmonic-oscillator-model-0069","batch_id":"batch-20261013-advance-20261022-r01-harmonic-oscillator-model-foundations","language":"zh-Hant","source_mko_ids":["mko-harmonic-oscillator-model"],"title_zh":"簡諧振子精確切片","stem_zh":"無阻尼線性振子模型m x_second+k x=0。操作=oscillator-polynomial-residual；資料={\"coefficients\":[6,1,-2],\"mass\":[3,1],\"spring\":[1,1],\"x\":1}。請依 [coefficients,x,position,acceleration,mass,spring,residual,zero_at_x] 欄序回答。","answer":{"kind":"expression","value":"([6, 1, -2], 1, 5, -4, 3, 1, -7, 否)","explanation_zh":"結構基礎核對=([6, 1, -2], 1, 5, -4, 3, 1, -7, 否)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；不宣稱sin/cos閉式解；單點能量不證沿軌道守恆。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["簡諧振子精確切片"]},"variant":{"family_id":"qf-str22-oscillator-polynomial-residual","seed":202610221069,"parameters":{"coefficients":[6,1,-2],"mass":[3,1],"spring":[1,1],"x":1,"domain":"Exact_harmonic_oscillator_model","operation":"oscillator-polynomial-residual","semantic_template":"qf-str22-oscillator-polynomial-residual/{\"coefficients\":[6,1,-2],\"mass\":[3,1],\"spring\":[1,1],\"x\":1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r01-harmonic-oscillator-model-0070","batch_id":"batch-20261013-advance-20261022-r01-harmonic-oscillator-model-foundations","language":"zh-Hant","source_mko_ids":["mko-harmonic-oscillator-model"],"title_zh":"簡諧振子精確切片","stem_zh":"無阻尼線性振子模型m x_second+k x=0。操作=oscillator-polynomial-residual；資料={\"coefficients\":[7,2,0],\"mass\":[4,1],\"spring\":[2,1],\"x\":2}。請依 [coefficients,x,position,acceleration,mass,spring,residual,zero_at_x] 欄序回答。","answer":{"kind":"expression","value":"([7, 2, 0], 2, 11, 0, 4, 2, 22, 否)","explanation_zh":"結構基礎核對=([7, 2, 0], 2, 11, 0, 4, 2, 22, 否)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；不宣稱sin/cos閉式解；單點能量不證沿軌道守恆。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["簡諧振子精確切片"]},"variant":{"family_id":"qf-str22-oscillator-polynomial-residual","seed":202610221070,"parameters":{"coefficients":[7,2,0],"mass":[4,1],"spring":[2,1],"x":2,"domain":"Exact_harmonic_oscillator_model","operation":"oscillator-polynomial-residual","semantic_template":"qf-str22-oscillator-polynomial-residual/{\"coefficients\":[7,2,0],\"mass\":[4,1],\"spring\":[2,1],\"x\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r01-harmonic-oscillator-model-0071","batch_id":"batch-20261013-advance-20261022-r01-harmonic-oscillator-model-foundations","language":"zh-Hant","source_mko_ids":["mko-harmonic-oscillator-model"],"title_zh":"簡諧振子精確切片","stem_zh":"無阻尼線性振子模型m x_second+k x=0。操作=oscillator-polynomial-residual；資料={\"coefficients\":[8,-2,2],\"mass\":[1,1],\"spring\":[3,1],\"x\":-2}。請依 [coefficients,x,position,acceleration,mass,spring,residual,zero_at_x] 欄序回答。","answer":{"kind":"expression","value":"([8, -2, 2], -2, 20, 4, 1, 3, 64, 否)","explanation_zh":"結構基礎核對=([8, -2, 2], -2, 20, 4, 1, 3, 64, 否)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；不宣稱sin/cos閉式解；單點能量不證沿軌道守恆。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["簡諧振子精確切片"]},"variant":{"family_id":"qf-str22-oscillator-polynomial-residual","seed":202610221071,"parameters":{"coefficients":[8,-2,2],"mass":[1,1],"spring":[3,1],"x":-2,"domain":"Exact_harmonic_oscillator_model","operation":"oscillator-polynomial-residual","semantic_template":"qf-str22-oscillator-polynomial-residual/{\"coefficients\":[8,-2,2],\"mass\":[1,1],\"spring\":[3,1],\"x\":-2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r01-harmonic-oscillator-model-0072","batch_id":"batch-20261013-advance-20261022-r01-harmonic-oscillator-model-foundations","language":"zh-Hant","source_mko_ids":["mko-harmonic-oscillator-model"],"title_zh":"簡諧振子精確切片","stem_zh":"無阻尼線性振子模型m x_second+k x=0。操作=oscillator-polynomial-residual；資料={\"coefficients\":[9,-1,-3],\"mass\":[2,1],\"spring\":[4,1],\"x\":-1}。請依 [coefficients,x,position,acceleration,mass,spring,residual,zero_at_x] 欄序回答。","answer":{"kind":"expression","value":"([9, -1, -3], -1, 7, -6, 2, 4, 16, 否)","explanation_zh":"結構基礎核對=([9, -1, -3], -1, 7, -6, 2, 4, 16, 否)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；不宣稱sin/cos閉式解；單點能量不證沿軌道守恆。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["簡諧振子精確切片"]},"variant":{"family_id":"qf-str22-oscillator-polynomial-residual","seed":202610221072,"parameters":{"coefficients":[9,-1,-3],"mass":[2,1],"spring":[4,1],"x":-1,"domain":"Exact_harmonic_oscillator_model","operation":"oscillator-polynomial-residual","semantic_template":"qf-str22-oscillator-polynomial-residual/{\"coefficients\":[9,-1,-3],\"mass\":[2,1],\"spring\":[4,1],\"x\":-1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r01-harmonic-oscillator-model-0073","batch_id":"batch-20261013-advance-20261022-r01-harmonic-oscillator-model-foundations","language":"zh-Hant","source_mko_ids":["mko-harmonic-oscillator-model"],"title_zh":"簡諧振子精確切片","stem_zh":"無阻尼線性振子模型m x_second+k x=0。操作=oscillator-polynomial-residual；資料={\"coefficients\":[10,0,-1],\"mass\":[3,1],\"spring\":[5,1],\"x\":0}。請依 [coefficients,x,position,acceleration,mass,spring,residual,zero_at_x] 欄序回答。","answer":{"kind":"expression","value":"([10, 0, -1], 0, 10, -2, 3, 5, 44, 否)","explanation_zh":"結構基礎核對=([10, 0, -1], 0, 10, -2, 3, 5, 44, 否)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；不宣稱sin/cos閉式解；單點能量不證沿軌道守恆。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["簡諧振子精確切片"]},"variant":{"family_id":"qf-str22-oscillator-polynomial-residual","seed":202610221073,"parameters":{"coefficients":[10,0,-1],"mass":[3,1],"spring":[5,1],"x":0,"domain":"Exact_harmonic_oscillator_model","operation":"oscillator-polynomial-residual","semantic_template":"qf-str22-oscillator-polynomial-residual/{\"coefficients\":[10,0,-1],\"mass\":[3,1],\"spring\":[5,1],\"x\":0}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r01-harmonic-oscillator-model-0074","batch_id":"batch-20261013-advance-20261022-r01-harmonic-oscillator-model-foundations","language":"zh-Hant","source_mko_ids":["mko-harmonic-oscillator-model"],"title_zh":"簡諧振子精確切片","stem_zh":"無阻尼線性振子模型m x_second+k x=0。操作=oscillator-polynomial-residual；資料={\"coefficients\":[11,1,1],\"mass\":[4,1],\"spring\":[6,1],\"x\":1}。請依 [coefficients,x,position,acceleration,mass,spring,residual,zero_at_x] 欄序回答。","answer":{"kind":"expression","value":"([11, 1, 1], 1, 13, 2, 4, 6, 86, 否)","explanation_zh":"結構基礎核對=([11, 1, 1], 1, 13, 2, 4, 6, 86, 否)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；不宣稱sin/cos閉式解；單點能量不證沿軌道守恆。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["簡諧振子精確切片"]},"variant":{"family_id":"qf-str22-oscillator-polynomial-residual","seed":202610221074,"parameters":{"coefficients":[11,1,1],"mass":[4,1],"spring":[6,1],"x":1,"domain":"Exact_harmonic_oscillator_model","operation":"oscillator-polynomial-residual","semantic_template":"qf-str22-oscillator-polynomial-residual/{\"coefficients\":[11,1,1],\"mass\":[4,1],\"spring\":[6,1],\"x\":1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r01-harmonic-oscillator-model-0075","batch_id":"batch-20261013-advance-20261022-r01-harmonic-oscillator-model-foundations","language":"zh-Hant","source_mko_ids":["mko-harmonic-oscillator-model"],"title_zh":"簡諧振子精確切片","stem_zh":"無阻尼線性振子模型m x_second+k x=0。操作=oscillator-polynomial-residual；資料={\"coefficients\":[12,2,3],\"mass\":[1,1],\"spring\":[1,1],\"x\":2}。請依 [coefficients,x,position,acceleration,mass,spring,residual,zero_at_x] 欄序回答。","answer":{"kind":"expression","value":"([12, 2, 3], 2, 28, 6, 1, 1, 34, 否)","explanation_zh":"結構基礎核對=([12, 2, 3], 2, 28, 6, 1, 1, 34, 否)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；不宣稱sin/cos閉式解；單點能量不證沿軌道守恆。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["簡諧振子精確切片"]},"variant":{"family_id":"qf-str22-oscillator-polynomial-residual","seed":202610221075,"parameters":{"coefficients":[12,2,3],"mass":[1,1],"spring":[1,1],"x":2,"domain":"Exact_harmonic_oscillator_model","operation":"oscillator-polynomial-residual","semantic_template":"qf-str22-oscillator-polynomial-residual/{\"coefficients\":[12,2,3],\"mass\":[1,1],\"spring\":[1,1],\"x\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r01-harmonic-oscillator-model-0076","batch_id":"batch-20261013-advance-20261022-r01-harmonic-oscillator-model-foundations","language":"zh-Hant","source_mko_ids":["mko-harmonic-oscillator-model"],"title_zh":"簡諧振子精確切片","stem_zh":"無阻尼線性振子模型m x_second+k x=0。操作=oscillator-energy-snapshot；資料={\"mass\":[1,1],\"spring\":[1,1],\"position\":[-10,1],\"velocity\":[-3,1]}。請依 [mass,spring,position,velocity,kinetic,potential,total] 欄序回答。","answer":{"kind":"expression","value":"(1, 1, -10, -3, 9/2, 50, 109/2)","explanation_zh":"結構基礎核對=(1, 1, -10, -3, 9/2, 50, 109/2)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；不宣稱sin/cos閉式解；單點能量不證沿軌道守恆。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["簡諧振子精確切片"]},"variant":{"family_id":"qf-str22-oscillator-energy-snapshot","seed":202610221076,"parameters":{"mass":[1,1],"spring":[1,1],"position":[-10,1],"velocity":[-3,1],"domain":"Exact_harmonic_oscillator_model","operation":"oscillator-energy-snapshot","semantic_template":"qf-str22-oscillator-energy-snapshot/{\"mass\":[1,1],\"position\":[-10,1],\"spring\":[1,1],\"velocity\":[-3,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r01-harmonic-oscillator-model-0077","batch_id":"batch-20261013-advance-20261022-r01-harmonic-oscillator-model-foundations","language":"zh-Hant","source_mko_ids":["mko-harmonic-oscillator-model"],"title_zh":"簡諧振子精確切片","stem_zh":"無阻尼線性振子模型m x_second+k x=0。操作=oscillator-energy-snapshot；資料={\"mass\":[2,1],\"spring\":[2,1],\"position\":[-9,2],\"velocity\":[-2,2]}。請依 [mass,spring,position,velocity,kinetic,potential,total] 欄序回答。","answer":{"kind":"expression","value":"(2, 2, -9/2, -1, 1, 81/4, 85/4)","explanation_zh":"結構基礎核對=(2, 2, -9/2, -1, 1, 81/4, 85/4)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；不宣稱sin/cos閉式解；單點能量不證沿軌道守恆。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["簡諧振子精確切片"]},"variant":{"family_id":"qf-str22-oscillator-energy-snapshot","seed":202610221077,"parameters":{"mass":[2,1],"spring":[2,1],"position":[-9,2],"velocity":[-2,2],"domain":"Exact_harmonic_oscillator_model","operation":"oscillator-energy-snapshot","semantic_template":"qf-str22-oscillator-energy-snapshot/{\"mass\":[2,1],\"position\":[-9,2],\"spring\":[2,1],\"velocity\":[-2,2]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r01-harmonic-oscillator-model-0078","batch_id":"batch-20261013-advance-20261022-r01-harmonic-oscillator-model-foundations","language":"zh-Hant","source_mko_ids":["mko-harmonic-oscillator-model"],"title_zh":"簡諧振子精確切片","stem_zh":"無阻尼線性振子模型m x_second+k x=0。操作=oscillator-energy-snapshot；資料={\"mass\":[3,1],\"spring\":[3,1],\"position\":[-8,3],\"velocity\":[-1,3]}。請依 [mass,spring,position,velocity,kinetic,potential,total] 欄序回答。","answer":{"kind":"expression","value":"(3, 3, -8/3, -1/3, 1/6, 32/3, 65/6)","explanation_zh":"結構基礎核對=(3, 3, -8/3, -1/3, 1/6, 32/3, 65/6)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；不宣稱sin/cos閉式解；單點能量不證沿軌道守恆。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["簡諧振子精確切片"]},"variant":{"family_id":"qf-str22-oscillator-energy-snapshot","seed":202610221078,"parameters":{"mass":[3,1],"spring":[3,1],"position":[-8,3],"velocity":[-1,3],"domain":"Exact_harmonic_oscillator_model","operation":"oscillator-energy-snapshot","semantic_template":"qf-str22-oscillator-energy-snapshot/{\"mass\":[3,1],\"position\":[-8,3],\"spring\":[3,1],\"velocity\":[-1,3]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r01-harmonic-oscillator-model-0079","batch_id":"batch-20261013-advance-20261022-r01-harmonic-oscillator-model-foundations","language":"zh-Hant","source_mko_ids":["mko-harmonic-oscillator-model"],"title_zh":"簡諧振子精確切片","stem_zh":"無阻尼線性振子模型m x_second+k x=0。操作=oscillator-energy-snapshot；資料={\"mass\":[4,1],\"spring\":[4,1],\"position\":[-7,1],\"velocity\":[0,4]}。請依 [mass,spring,position,velocity,kinetic,potential,total] 欄序回答。","answer":{"kind":"expression","value":"(4, 4, -7, 0, 0, 98, 98)","explanation_zh":"結構基礎核對=(4, 4, -7, 0, 0, 98, 98)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；不宣稱sin/cos閉式解；單點能量不證沿軌道守恆。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["簡諧振子精確切片"]},"variant":{"family_id":"qf-str22-oscillator-energy-snapshot","seed":202610221079,"parameters":{"mass":[4,1],"spring":[4,1],"position":[-7,1],"velocity":[0,4],"domain":"Exact_harmonic_oscillator_model","operation":"oscillator-energy-snapshot","semantic_template":"qf-str22-oscillator-energy-snapshot/{\"mass\":[4,1],\"position\":[-7,1],\"spring\":[4,1],\"velocity\":[0,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r01-harmonic-oscillator-model-0080","batch_id":"batch-20261013-advance-20261022-r01-harmonic-oscillator-model-foundations","language":"zh-Hant","source_mko_ids":["mko-harmonic-oscillator-model"],"title_zh":"簡諧振子精確切片","stem_zh":"無阻尼線性振子模型m x_second+k x=0。操作=oscillator-energy-snapshot；資料={\"mass\":[1,1],\"spring\":[5,1],\"position\":[-6,2],\"velocity\":[1,1]}。請依 [mass,spring,position,velocity,kinetic,potential,total] 欄序回答。","answer":{"kind":"expression","value":"(1, 5, -3, 1, 1/2, 45/2, 23)","explanation_zh":"結構基礎核對=(1, 5, -3, 1, 1/2, 45/2, 23)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；不宣稱sin/cos閉式解；單點能量不證沿軌道守恆。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["簡諧振子精確切片"]},"variant":{"family_id":"qf-str22-oscillator-energy-snapshot","seed":202610221080,"parameters":{"mass":[1,1],"spring":[5,1],"position":[-6,2],"velocity":[1,1],"domain":"Exact_harmonic_oscillator_model","operation":"oscillator-energy-snapshot","semantic_template":"qf-str22-oscillator-energy-snapshot/{\"mass\":[1,1],\"position\":[-6,2],\"spring\":[5,1],\"velocity\":[1,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r01-harmonic-oscillator-model-0081","batch_id":"batch-20261013-advance-20261022-r01-harmonic-oscillator-model-foundations","language":"zh-Hant","source_mko_ids":["mko-harmonic-oscillator-model"],"title_zh":"簡諧振子精確切片","stem_zh":"無阻尼線性振子模型m x_second+k x=0。操作=oscillator-energy-snapshot；資料={\"mass\":[2,1],\"spring\":[6,1],\"position\":[-5,3],\"velocity\":[2,2]}。請依 [mass,spring,position,velocity,kinetic,potential,total] 欄序回答。","answer":{"kind":"expression","value":"(2, 6, -5/3, 1, 1, 25/3, 28/3)","explanation_zh":"結構基礎核對=(2, 6, -5/3, 1, 1, 25/3, 28/3)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；不宣稱sin/cos閉式解；單點能量不證沿軌道守恆。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["簡諧振子精確切片"]},"variant":{"family_id":"qf-str22-oscillator-energy-snapshot","seed":202610221081,"parameters":{"mass":[2,1],"spring":[6,1],"position":[-5,3],"velocity":[2,2],"domain":"Exact_harmonic_oscillator_model","operation":"oscillator-energy-snapshot","semantic_template":"qf-str22-oscillator-energy-snapshot/{\"mass\":[2,1],\"position\":[-5,3],\"spring\":[6,1],\"velocity\":[2,2]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r01-harmonic-oscillator-model-0082","batch_id":"batch-20261013-advance-20261022-r01-harmonic-oscillator-model-foundations","language":"zh-Hant","source_mko_ids":["mko-harmonic-oscillator-model"],"title_zh":"簡諧振子精確切片","stem_zh":"無阻尼線性振子模型m x_second+k x=0。操作=oscillator-energy-snapshot；資料={\"mass\":[3,1],\"spring\":[1,1],\"position\":[-4,1],\"velocity\":[3,3]}。請依 [mass,spring,position,velocity,kinetic,potential,total] 欄序回答。","answer":{"kind":"expression","value":"(3, 1, -4, 1, 3/2, 8, 19/2)","explanation_zh":"結構基礎核對=(3, 1, -4, 1, 3/2, 8, 19/2)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；不宣稱sin/cos閉式解；單點能量不證沿軌道守恆。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["簡諧振子精確切片"]},"variant":{"family_id":"qf-str22-oscillator-energy-snapshot","seed":202610221082,"parameters":{"mass":[3,1],"spring":[1,1],"position":[-4,1],"velocity":[3,3],"domain":"Exact_harmonic_oscillator_model","operation":"oscillator-energy-snapshot","semantic_template":"qf-str22-oscillator-energy-snapshot/{\"mass\":[3,1],\"position\":[-4,1],\"spring\":[1,1],\"velocity\":[3,3]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r01-harmonic-oscillator-model-0083","batch_id":"batch-20261013-advance-20261022-r01-harmonic-oscillator-model-foundations","language":"zh-Hant","source_mko_ids":["mko-harmonic-oscillator-model"],"title_zh":"簡諧振子精確切片","stem_zh":"無阻尼線性振子模型m x_second+k x=0。操作=oscillator-energy-snapshot；資料={\"mass\":[4,1],\"spring\":[2,1],\"position\":[-3,2],\"velocity\":[-3,4]}。請依 [mass,spring,position,velocity,kinetic,potential,total] 欄序回答。","answer":{"kind":"expression","value":"(4, 2, -3/2, -3/4, 9/8, 9/4, 27/8)","explanation_zh":"結構基礎核對=(4, 2, -3/2, -3/4, 9/8, 9/4, 27/8)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；不宣稱sin/cos閉式解；單點能量不證沿軌道守恆。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["簡諧振子精確切片"]},"variant":{"family_id":"qf-str22-oscillator-energy-snapshot","seed":202610221083,"parameters":{"mass":[4,1],"spring":[2,1],"position":[-3,2],"velocity":[-3,4],"domain":"Exact_harmonic_oscillator_model","operation":"oscillator-energy-snapshot","semantic_template":"qf-str22-oscillator-energy-snapshot/{\"mass\":[4,1],\"position\":[-3,2],\"spring\":[2,1],\"velocity\":[-3,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r01-harmonic-oscillator-model-0084","batch_id":"batch-20261013-advance-20261022-r01-harmonic-oscillator-model-foundations","language":"zh-Hant","source_mko_ids":["mko-harmonic-oscillator-model"],"title_zh":"簡諧振子精確切片","stem_zh":"無阻尼線性振子模型m x_second+k x=0。操作=oscillator-energy-snapshot；資料={\"mass\":[1,1],\"spring\":[3,1],\"position\":[-2,3],\"velocity\":[-2,1]}。請依 [mass,spring,position,velocity,kinetic,potential,total] 欄序回答。","answer":{"kind":"expression","value":"(1, 3, -2/3, -2, 2, 2/3, 8/3)","explanation_zh":"結構基礎核對=(1, 3, -2/3, -2, 2, 2/3, 8/3)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；不宣稱sin/cos閉式解；單點能量不證沿軌道守恆。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["簡諧振子精確切片"]},"variant":{"family_id":"qf-str22-oscillator-energy-snapshot","seed":202610221084,"parameters":{"mass":[1,1],"spring":[3,1],"position":[-2,3],"velocity":[-2,1],"domain":"Exact_harmonic_oscillator_model","operation":"oscillator-energy-snapshot","semantic_template":"qf-str22-oscillator-energy-snapshot/{\"mass\":[1,1],\"position\":[-2,3],\"spring\":[3,1],\"velocity\":[-2,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r01-harmonic-oscillator-model-0085","batch_id":"batch-20261013-advance-20261022-r01-harmonic-oscillator-model-foundations","language":"zh-Hant","source_mko_ids":["mko-harmonic-oscillator-model"],"title_zh":"簡諧振子精確切片","stem_zh":"無阻尼線性振子模型m x_second+k x=0。操作=oscillator-energy-snapshot；資料={\"mass\":[2,1],\"spring\":[4,1],\"position\":[-1,1],\"velocity\":[-1,2]}。請依 [mass,spring,position,velocity,kinetic,potential,total] 欄序回答。","answer":{"kind":"expression","value":"(2, 4, -1, -1/2, 1/4, 2, 9/4)","explanation_zh":"結構基礎核對=(2, 4, -1, -1/2, 1/4, 2, 9/4)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；不宣稱sin/cos閉式解；單點能量不證沿軌道守恆。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["簡諧振子精確切片"]},"variant":{"family_id":"qf-str22-oscillator-energy-snapshot","seed":202610221085,"parameters":{"mass":[2,1],"spring":[4,1],"position":[-1,1],"velocity":[-1,2],"domain":"Exact_harmonic_oscillator_model","operation":"oscillator-energy-snapshot","semantic_template":"qf-str22-oscillator-energy-snapshot/{\"mass\":[2,1],\"position\":[-1,1],\"spring\":[4,1],\"velocity\":[-1,2]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r01-harmonic-oscillator-model-0086","batch_id":"batch-20261013-advance-20261022-r01-harmonic-oscillator-model-foundations","language":"zh-Hant","source_mko_ids":["mko-harmonic-oscillator-model"],"title_zh":"簡諧振子精確切片","stem_zh":"無阻尼線性振子模型m x_second+k x=0。操作=oscillator-energy-snapshot；資料={\"mass\":[3,1],\"spring\":[5,1],\"position\":[0,2],\"velocity\":[0,3]}。請依 [mass,spring,position,velocity,kinetic,potential,total] 欄序回答。","answer":{"kind":"expression","value":"(3, 5, 0, 0, 0, 0, 0)","explanation_zh":"結構基礎核對=(3, 5, 0, 0, 0, 0, 0)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；不宣稱sin/cos閉式解；單點能量不證沿軌道守恆。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["簡諧振子精確切片"]},"variant":{"family_id":"qf-str22-oscillator-energy-snapshot","seed":202610221086,"parameters":{"mass":[3,1],"spring":[5,1],"position":[0,2],"velocity":[0,3],"domain":"Exact_harmonic_oscillator_model","operation":"oscillator-energy-snapshot","semantic_template":"qf-str22-oscillator-energy-snapshot/{\"mass\":[3,1],\"position\":[0,2],\"spring\":[5,1],\"velocity\":[0,3]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r01-harmonic-oscillator-model-0087","batch_id":"batch-20261013-advance-20261022-r01-harmonic-oscillator-model-foundations","language":"zh-Hant","source_mko_ids":["mko-harmonic-oscillator-model"],"title_zh":"簡諧振子精確切片","stem_zh":"無阻尼線性振子模型m x_second+k x=0。操作=oscillator-energy-snapshot；資料={\"mass\":[4,1],\"spring\":[6,1],\"position\":[1,3],\"velocity\":[1,4]}。請依 [mass,spring,position,velocity,kinetic,potential,total] 欄序回答。","answer":{"kind":"expression","value":"(4, 6, 1/3, 1/4, 1/8, 1/3, 11/24)","explanation_zh":"結構基礎核對=(4, 6, 1/3, 1/4, 1/8, 1/3, 11/24)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；不宣稱sin/cos閉式解；單點能量不證沿軌道守恆。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["簡諧振子精確切片"]},"variant":{"family_id":"qf-str22-oscillator-energy-snapshot","seed":202610221087,"parameters":{"mass":[4,1],"spring":[6,1],"position":[1,3],"velocity":[1,4],"domain":"Exact_harmonic_oscillator_model","operation":"oscillator-energy-snapshot","semantic_template":"qf-str22-oscillator-energy-snapshot/{\"mass\":[4,1],\"position\":[1,3],\"spring\":[6,1],\"velocity\":[1,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r01-harmonic-oscillator-model-0088","batch_id":"batch-20261013-advance-20261022-r01-harmonic-oscillator-model-foundations","language":"zh-Hant","source_mko_ids":["mko-harmonic-oscillator-model"],"title_zh":"簡諧振子精確切片","stem_zh":"無阻尼線性振子模型m x_second+k x=0。操作=oscillator-energy-snapshot；資料={\"mass\":[1,1],\"spring\":[1,1],\"position\":[2,1],\"velocity\":[2,1]}。請依 [mass,spring,position,velocity,kinetic,potential,total] 欄序回答。","answer":{"kind":"expression","value":"(1, 1, 2, 2, 2, 2, 4)","explanation_zh":"結構基礎核對=(1, 1, 2, 2, 2, 2, 4)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；不宣稱sin/cos閉式解；單點能量不證沿軌道守恆。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["簡諧振子精確切片"]},"variant":{"family_id":"qf-str22-oscillator-energy-snapshot","seed":202610221088,"parameters":{"mass":[1,1],"spring":[1,1],"position":[2,1],"velocity":[2,1],"domain":"Exact_harmonic_oscillator_model","operation":"oscillator-energy-snapshot","semantic_template":"qf-str22-oscillator-energy-snapshot/{\"mass\":[1,1],\"position\":[2,1],\"spring\":[1,1],\"velocity\":[2,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r01-harmonic-oscillator-model-0089","batch_id":"batch-20261013-advance-20261022-r01-harmonic-oscillator-model-foundations","language":"zh-Hant","source_mko_ids":["mko-harmonic-oscillator-model"],"title_zh":"簡諧振子精確切片","stem_zh":"無阻尼線性振子模型m x_second+k x=0。操作=oscillator-energy-snapshot；資料={\"mass\":[2,1],\"spring\":[2,1],\"position\":[3,2],\"velocity\":[3,2]}。請依 [mass,spring,position,velocity,kinetic,potential,total] 欄序回答。","answer":{"kind":"expression","value":"(2, 2, 3/2, 3/2, 9/4, 9/4, 9/2)","explanation_zh":"結構基礎核對=(2, 2, 3/2, 3/2, 9/4, 9/4, 9/2)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；不宣稱sin/cos閉式解；單點能量不證沿軌道守恆。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["簡諧振子精確切片"]},"variant":{"family_id":"qf-str22-oscillator-energy-snapshot","seed":202610221089,"parameters":{"mass":[2,1],"spring":[2,1],"position":[3,2],"velocity":[3,2],"domain":"Exact_harmonic_oscillator_model","operation":"oscillator-energy-snapshot","semantic_template":"qf-str22-oscillator-energy-snapshot/{\"mass\":[2,1],\"position\":[3,2],\"spring\":[2,1],\"velocity\":[3,2]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r01-harmonic-oscillator-model-0090","batch_id":"batch-20261013-advance-20261022-r01-harmonic-oscillator-model-foundations","language":"zh-Hant","source_mko_ids":["mko-harmonic-oscillator-model"],"title_zh":"簡諧振子精確切片","stem_zh":"無阻尼線性振子模型m x_second+k x=0。操作=oscillator-energy-snapshot；資料={\"mass\":[3,1],\"spring\":[3,1],\"position\":[4,3],\"velocity\":[-3,3]}。請依 [mass,spring,position,velocity,kinetic,potential,total] 欄序回答。","answer":{"kind":"expression","value":"(3, 3, 4/3, -1, 3/2, 8/3, 25/6)","explanation_zh":"結構基礎核對=(3, 3, 4/3, -1, 3/2, 8/3, 25/6)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；不宣稱sin/cos閉式解；單點能量不證沿軌道守恆。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["簡諧振子精確切片"]},"variant":{"family_id":"qf-str22-oscillator-energy-snapshot","seed":202610221090,"parameters":{"mass":[3,1],"spring":[3,1],"position":[4,3],"velocity":[-3,3],"domain":"Exact_harmonic_oscillator_model","operation":"oscillator-energy-snapshot","semantic_template":"qf-str22-oscillator-energy-snapshot/{\"mass\":[3,1],\"position\":[4,3],\"spring\":[3,1],\"velocity\":[-3,3]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r01-harmonic-oscillator-model-0091","batch_id":"batch-20261013-advance-20261022-r01-harmonic-oscillator-model-foundations","language":"zh-Hant","source_mko_ids":["mko-harmonic-oscillator-model"],"title_zh":"簡諧振子精確切片","stem_zh":"無阻尼線性振子模型m x_second+k x=0。操作=oscillator-energy-snapshot；資料={\"mass\":[4,1],\"spring\":[4,1],\"position\":[5,1],\"velocity\":[-2,4]}。請依 [mass,spring,position,velocity,kinetic,potential,total] 欄序回答。","answer":{"kind":"expression","value":"(4, 4, 5, -1/2, 1/2, 50, 101/2)","explanation_zh":"結構基礎核對=(4, 4, 5, -1/2, 1/2, 50, 101/2)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；不宣稱sin/cos閉式解；單點能量不證沿軌道守恆。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["簡諧振子精確切片"]},"variant":{"family_id":"qf-str22-oscillator-energy-snapshot","seed":202610221091,"parameters":{"mass":[4,1],"spring":[4,1],"position":[5,1],"velocity":[-2,4],"domain":"Exact_harmonic_oscillator_model","operation":"oscillator-energy-snapshot","semantic_template":"qf-str22-oscillator-energy-snapshot/{\"mass\":[4,1],\"position\":[5,1],\"spring\":[4,1],\"velocity\":[-2,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r01-harmonic-oscillator-model-0092","batch_id":"batch-20261013-advance-20261022-r01-harmonic-oscillator-model-foundations","language":"zh-Hant","source_mko_ids":["mko-harmonic-oscillator-model"],"title_zh":"簡諧振子精確切片","stem_zh":"無阻尼線性振子模型m x_second+k x=0。操作=oscillator-energy-snapshot；資料={\"mass\":[1,1],\"spring\":[5,1],\"position\":[6,2],\"velocity\":[-1,1]}。請依 [mass,spring,position,velocity,kinetic,potential,total] 欄序回答。","answer":{"kind":"expression","value":"(1, 5, 3, -1, 1/2, 45/2, 23)","explanation_zh":"結構基礎核對=(1, 5, 3, -1, 1/2, 45/2, 23)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；不宣稱sin/cos閉式解；單點能量不證沿軌道守恆。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["簡諧振子精確切片"]},"variant":{"family_id":"qf-str22-oscillator-energy-snapshot","seed":202610221092,"parameters":{"mass":[1,1],"spring":[5,1],"position":[6,2],"velocity":[-1,1],"domain":"Exact_harmonic_oscillator_model","operation":"oscillator-energy-snapshot","semantic_template":"qf-str22-oscillator-energy-snapshot/{\"mass\":[1,1],\"position\":[6,2],\"spring\":[5,1],\"velocity\":[-1,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r01-harmonic-oscillator-model-0093","batch_id":"batch-20261013-advance-20261022-r01-harmonic-oscillator-model-foundations","language":"zh-Hant","source_mko_ids":["mko-harmonic-oscillator-model"],"title_zh":"簡諧振子精確切片","stem_zh":"無阻尼線性振子模型m x_second+k x=0。操作=oscillator-energy-snapshot；資料={\"mass\":[2,1],\"spring\":[6,1],\"position\":[7,3],\"velocity\":[0,2]}。請依 [mass,spring,position,velocity,kinetic,potential,total] 欄序回答。","answer":{"kind":"expression","value":"(2, 6, 7/3, 0, 0, 49/3, 49/3)","explanation_zh":"結構基礎核對=(2, 6, 7/3, 0, 0, 49/3, 49/3)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；不宣稱sin/cos閉式解；單點能量不證沿軌道守恆。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["簡諧振子精確切片"]},"variant":{"family_id":"qf-str22-oscillator-energy-snapshot","seed":202610221093,"parameters":{"mass":[2,1],"spring":[6,1],"position":[7,3],"velocity":[0,2],"domain":"Exact_harmonic_oscillator_model","operation":"oscillator-energy-snapshot","semantic_template":"qf-str22-oscillator-energy-snapshot/{\"mass\":[2,1],\"position\":[7,3],\"spring\":[6,1],\"velocity\":[0,2]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r01-harmonic-oscillator-model-0094","batch_id":"batch-20261013-advance-20261022-r01-harmonic-oscillator-model-foundations","language":"zh-Hant","source_mko_ids":["mko-harmonic-oscillator-model"],"title_zh":"簡諧振子精確切片","stem_zh":"無阻尼線性振子模型m x_second+k x=0。操作=oscillator-energy-snapshot；資料={\"mass\":[3,1],\"spring\":[1,1],\"position\":[8,1],\"velocity\":[1,3]}。請依 [mass,spring,position,velocity,kinetic,potential,total] 欄序回答。","answer":{"kind":"expression","value":"(3, 1, 8, 1/3, 1/6, 32, 193/6)","explanation_zh":"結構基礎核對=(3, 1, 8, 1/3, 1/6, 32, 193/6)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；不宣稱sin/cos閉式解；單點能量不證沿軌道守恆。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["簡諧振子精確切片"]},"variant":{"family_id":"qf-str22-oscillator-energy-snapshot","seed":202610221094,"parameters":{"mass":[3,1],"spring":[1,1],"position":[8,1],"velocity":[1,3],"domain":"Exact_harmonic_oscillator_model","operation":"oscillator-energy-snapshot","semantic_template":"qf-str22-oscillator-energy-snapshot/{\"mass\":[3,1],\"position\":[8,1],\"spring\":[1,1],\"velocity\":[1,3]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r01-harmonic-oscillator-model-0095","batch_id":"batch-20261013-advance-20261022-r01-harmonic-oscillator-model-foundations","language":"zh-Hant","source_mko_ids":["mko-harmonic-oscillator-model"],"title_zh":"簡諧振子精確切片","stem_zh":"無阻尼線性振子模型m x_second+k x=0。操作=oscillator-energy-snapshot；資料={\"mass\":[4,1],\"spring\":[2,1],\"position\":[9,2],\"velocity\":[2,4]}。請依 [mass,spring,position,velocity,kinetic,potential,total] 欄序回答。","answer":{"kind":"expression","value":"(4, 2, 9/2, 1/2, 1/2, 81/4, 83/4)","explanation_zh":"結構基礎核對=(4, 2, 9/2, 1/2, 1/2, 81/4, 83/4)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；不宣稱sin/cos閉式解；單點能量不證沿軌道守恆。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["簡諧振子精確切片"]},"variant":{"family_id":"qf-str22-oscillator-energy-snapshot","seed":202610221095,"parameters":{"mass":[4,1],"spring":[2,1],"position":[9,2],"velocity":[2,4],"domain":"Exact_harmonic_oscillator_model","operation":"oscillator-energy-snapshot","semantic_template":"qf-str22-oscillator-energy-snapshot/{\"mass\":[4,1],\"position\":[9,2],\"spring\":[2,1],\"velocity\":[2,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r01-harmonic-oscillator-model-0096","batch_id":"batch-20261013-advance-20261022-r01-harmonic-oscillator-model-foundations","language":"zh-Hant","source_mko_ids":["mko-harmonic-oscillator-model"],"title_zh":"簡諧振子精確切片","stem_zh":"無阻尼線性振子模型m x_second+k x=0。操作=oscillator-energy-snapshot；資料={\"mass\":[1,1],\"spring\":[3,1],\"position\":[10,3],\"velocity\":[3,1]}。請依 [mass,spring,position,velocity,kinetic,potential,total] 欄序回答。","answer":{"kind":"expression","value":"(1, 3, 10/3, 3, 9/2, 50/3, 127/6)","explanation_zh":"結構基礎核對=(1, 3, 10/3, 3, 9/2, 50/3, 127/6)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；不宣稱sin/cos閉式解；單點能量不證沿軌道守恆。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["簡諧振子精確切片"]},"variant":{"family_id":"qf-str22-oscillator-energy-snapshot","seed":202610221096,"parameters":{"mass":[1,1],"spring":[3,1],"position":[10,3],"velocity":[3,1],"domain":"Exact_harmonic_oscillator_model","operation":"oscillator-energy-snapshot","semantic_template":"qf-str22-oscillator-energy-snapshot/{\"mass\":[1,1],\"position\":[10,3],\"spring\":[3,1],\"velocity\":[3,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r01-harmonic-oscillator-model-0097","batch_id":"batch-20261013-advance-20261022-r01-harmonic-oscillator-model-foundations","language":"zh-Hant","source_mko_ids":["mko-harmonic-oscillator-model"],"title_zh":"簡諧振子精確切片","stem_zh":"無阻尼線性振子模型m x_second+k x=0。操作=oscillator-energy-snapshot；資料={\"mass\":[2,1],\"spring\":[4,1],\"position\":[11,1],\"velocity\":[-3,2]}。請依 [mass,spring,position,velocity,kinetic,potential,total] 欄序回答。","answer":{"kind":"expression","value":"(2, 4, 11, -3/2, 9/4, 242, 977/4)","explanation_zh":"結構基礎核對=(2, 4, 11, -3/2, 9/4, 242, 977/4)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；不宣稱sin/cos閉式解；單點能量不證沿軌道守恆。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["簡諧振子精確切片"]},"variant":{"family_id":"qf-str22-oscillator-energy-snapshot","seed":202610221097,"parameters":{"mass":[2,1],"spring":[4,1],"position":[11,1],"velocity":[-3,2],"domain":"Exact_harmonic_oscillator_model","operation":"oscillator-energy-snapshot","semantic_template":"qf-str22-oscillator-energy-snapshot/{\"mass\":[2,1],\"position\":[11,1],\"spring\":[4,1],\"velocity\":[-3,2]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r01-harmonic-oscillator-model-0098","batch_id":"batch-20261013-advance-20261022-r01-harmonic-oscillator-model-foundations","language":"zh-Hant","source_mko_ids":["mko-harmonic-oscillator-model"],"title_zh":"簡諧振子精確切片","stem_zh":"無阻尼線性振子模型m x_second+k x=0。操作=oscillator-energy-snapshot；資料={\"mass\":[3,1],\"spring\":[5,1],\"position\":[12,2],\"velocity\":[-2,3]}。請依 [mass,spring,position,velocity,kinetic,potential,total] 欄序回答。","answer":{"kind":"expression","value":"(3, 5, 6, -2/3, 2/3, 90, 272/3)","explanation_zh":"結構基礎核對=(3, 5, 6, -2/3, 2/3, 90, 272/3)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；不宣稱sin/cos閉式解；單點能量不證沿軌道守恆。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["簡諧振子精確切片"]},"variant":{"family_id":"qf-str22-oscillator-energy-snapshot","seed":202610221098,"parameters":{"mass":[3,1],"spring":[5,1],"position":[12,2],"velocity":[-2,3],"domain":"Exact_harmonic_oscillator_model","operation":"oscillator-energy-snapshot","semantic_template":"qf-str22-oscillator-energy-snapshot/{\"mass\":[3,1],\"position\":[12,2],\"spring\":[5,1],\"velocity\":[-2,3]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r01-harmonic-oscillator-model-0099","batch_id":"batch-20261013-advance-20261022-r01-harmonic-oscillator-model-foundations","language":"zh-Hant","source_mko_ids":["mko-harmonic-oscillator-model"],"title_zh":"簡諧振子精確切片","stem_zh":"無阻尼線性振子模型m x_second+k x=0。操作=oscillator-energy-snapshot；資料={\"mass\":[4,1],\"spring\":[6,1],\"position\":[13,3],\"velocity\":[-1,4]}。請依 [mass,spring,position,velocity,kinetic,potential,total] 欄序回答。","answer":{"kind":"expression","value":"(4, 6, 13/3, -1/4, 1/8, 169/3, 1355/24)","explanation_zh":"結構基礎核對=(4, 6, 13/3, -1/4, 1/8, 169/3, 1355/24)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；不宣稱sin/cos閉式解；單點能量不證沿軌道守恆。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["簡諧振子精確切片"]},"variant":{"family_id":"qf-str22-oscillator-energy-snapshot","seed":202610221099,"parameters":{"mass":[4,1],"spring":[6,1],"position":[13,3],"velocity":[-1,4],"domain":"Exact_harmonic_oscillator_model","operation":"oscillator-energy-snapshot","semantic_template":"qf-str22-oscillator-energy-snapshot/{\"mass\":[4,1],\"position\":[13,3],\"spring\":[6,1],\"velocity\":[-1,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r01-harmonic-oscillator-model-0100","batch_id":"batch-20261013-advance-20261022-r01-harmonic-oscillator-model-foundations","language":"zh-Hant","source_mko_ids":["mko-harmonic-oscillator-model"],"title_zh":"簡諧振子精確切片","stem_zh":"無阻尼線性振子模型m x_second+k x=0。操作=oscillator-energy-snapshot；資料={\"mass\":[1,1],\"spring\":[1,1],\"position\":[14,1],\"velocity\":[0,1]}。請依 [mass,spring,position,velocity,kinetic,potential,total] 欄序回答。","answer":{"kind":"expression","value":"(1, 1, 14, 0, 0, 98, 98)","explanation_zh":"結構基礎核對=(1, 1, 14, 0, 0, 98, 98)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；不宣稱sin/cos閉式解；單點能量不證沿軌道守恆。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["簡諧振子精確切片"]},"variant":{"family_id":"qf-str22-oscillator-energy-snapshot","seed":202610221100,"parameters":{"mass":[1,1],"spring":[1,1],"position":[14,1],"velocity":[0,1],"domain":"Exact_harmonic_oscillator_model","operation":"oscillator-energy-snapshot","semantic_template":"qf-str22-oscillator-energy-snapshot/{\"mass\":[1,1],\"position\":[14,1],\"spring\":[1,1],\"velocity\":[0,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、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"}}