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{"schema_version":"ocme-question-v0.1","id":"q-20261010-advance-20261014-r01-angle-0003","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","language":"zh-Hant","source_mko_ids":["mko-angle"],"title_zh":"拆角候選資格與算術餘量","stem_zh":"精確度數協議；非定向0到180度；total=180，候選first=30。依序答 (first是否在[0,total], total−first)。超界候選仍計算有號算術餘量，不當作已構造的角。","answer":{"kind":"expression","value":"(是, 150)","explanation_zh":"拆角資格與餘量=(是, 150)。先檢候選範圍，再精確相減。不由示意圖猜角，有限量值核對非射線度量證明。"},"difficulty":{"band":"primary_foundation","level":1,"skills":["拆角候選資格與算術餘量"]},"variant":{"family_id":"qf-density14-angle-split-candidate","seed":202610141003,"parameters":{"total":180,"first":30,"angle_unit":"degrees","domain":"finite_nondirected_degree_protocol","operation":"density14_angle_split_candidate","semantic_template":"qf-density14-angle-split-candidate/[\"150\",true]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-10","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261010-advance-20261014-r01-angle-0004","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","language":"zh-Hant","source_mko_ids":["mko-angle"],"title_zh":"拆角候選資格與算術餘量","stem_zh":"精確度數協議；非定向0到180度；total=90，候選first=-1。依序答 (first是否在[0,total], total−first)。超界候選仍計算有號算術餘量，不當作已構造的角。","answer":{"kind":"expression","value":"(否, 91)","explanation_zh":"拆角資格與餘量=(否, 91)。先檢候選範圍，再精確相減。不由示意圖猜角，有限量值核對非射線度量證明。"},"difficulty":{"band":"primary_foundation","level":1,"skills":["拆角候選資格與算術餘量"]},"variant":{"family_id":"qf-density14-angle-split-candidate","seed":202610141004,"parameters":{"total":90,"first":-1,"angle_unit":"degrees","domain":"finite_nondirected_degree_protocol","operation":"density14_angle_split_candidate","semantic_template":"qf-density14-angle-split-candidate/[\"91\",false]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-10","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261010-advance-20261014-r01-angle-0005","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","language":"zh-Hant","source_mko_ids":["mko-angle"],"title_zh":"拆角候選資格與算術餘量","stem_zh":"精確度數協議；非定向0到180度；total=90，候選first=100。依序答 (first是否在[0,total], total−first)。超界候選仍計算有號算術餘量，不當作已構造的角。","answer":{"kind":"expression","value":"(否, -10)","explanation_zh":"拆角資格與餘量=(否, -10)。先檢候選範圍，再精確相減。不由示意圖猜角，有限量值核對非射線度量證明。"},"difficulty":{"band":"primary_foundation","level":1,"skills":["拆角候選資格與算術餘量"]},"variant":{"family_id":"qf-density14-angle-split-candidate","seed":202610141005,"parameters":{"total":90,"first":100,"angle_unit":"degrees","domain":"finite_nondirected_degree_protocol","operation":"density14_angle_split_candidate","semantic_template":"qf-density14-angle-split-candidate/[\"-10\",false]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-10","contract_version":"ocme-question-factory-v0.1"}}
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{"schema_version":"ocme-question-v0.1","id":"q-20261010-advance-20261014-r01-angle-0007","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","language":"zh-Hant","source_mko_ids":["mko-angle"],"title_zh":"拆角候選資格與算術餘量","stem_zh":"精確度數協議；非定向0到180度；total=90，候選first=83。依序答 (first是否在[0,total], total−first)。超界候選仍計算有號算術餘量，不當作已構造的角。","answer":{"kind":"expression","value":"(是, 7)","explanation_zh":"拆角資格與餘量=(是, 7)。先檢候選範圍，再精確相減。不由示意圖猜角，有限量值核對非射線度量證明。"},"difficulty":{"band":"primary_foundation","level":1,"skills":["拆角候選資格與算術餘量"]},"variant":{"family_id":"qf-density14-angle-split-candidate","seed":202610141007,"parameters":{"total":90,"first":83,"angle_unit":"degrees","domain":"finite_nondirected_degree_protocol","operation":"density14_angle_split_candidate","semantic_template":"qf-density14-angle-split-candidate/[\"7\",true]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-10","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261010-advance-20261014-r01-angle-0008","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","language":"zh-Hant","source_mko_ids":["mko-angle"],"title_zh":"拆角候選資格與算術餘量","stem_zh":"精確度數協議；非定向0到180度；total=90，候選first=82。依序答 (first是否在[0,total], total−first)。超界候選仍計算有號算術餘量，不當作已構造的角。","answer":{"kind":"expression","value":"(是, 8)","explanation_zh":"拆角資格與餘量=(是, 8)。先檢候選範圍，再精確相減。不由示意圖猜角，有限量值核對非射線度量證明。"},"difficulty":{"band":"primary_foundation","level":1,"skills":["拆角候選資格與算術餘量"]},"variant":{"family_id":"qf-density14-angle-split-candidate","seed":202610141008,"parameters":{"total":90,"first":82,"angle_unit":"degrees","domain":"finite_nondirected_degree_protocol","operation":"density14_angle_split_candidate","semantic_template":"qf-density14-angle-split-candidate/[\"8\",true]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-10","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261010-advance-20261014-r01-angle-0009","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","language":"zh-Hant","source_mko_ids":["mko-angle"],"title_zh":"拆角候選資格與算術餘量","stem_zh":"精確度數協議；非定向0到180度；total=90，候選first=81。依序答 (first是否在[0,total], total−first)。超界候選仍計算有號算術餘量，不當作已構造的角。","answer":{"kind":"expression","value":"(是, 9)","explanation_zh":"拆角資格與餘量=(是, 9)。先檢候選範圍，再精確相減。不由示意圖猜角，有限量值核對非射線度量證明。"},"difficulty":{"band":"primary_foundation","level":2,"skills":["拆角候選資格與算術餘量"]},"variant":{"family_id":"qf-density14-angle-split-candidate","seed":202610141009,"parameters":{"total":90,"first":81,"angle_unit":"degrees","domain":"finite_nondirected_degree_protocol","operation":"density14_angle_split_candidate","semantic_template":"qf-density14-angle-split-candidate/[\"9\",true]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-10","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261010-advance-20261014-r01-angle-0010","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","language":"zh-Hant","source_mko_ids":["mko-angle"],"title_zh":"拆角候選資格與算術餘量","stem_zh":"精確度數協議；非定向0到180度；total=90，候選first=80。依序答 (first是否在[0,total], total−first)。超界候選仍計算有號算術餘量，不當作已構造的角。","answer":{"kind":"expression","value":"(是, 10)","explanation_zh":"拆角資格與餘量=(是, 10)。先檢候選範圍，再精確相減。不由示意圖猜角，有限量值核對非射線度量證明。"},"difficulty":{"band":"primary_foundation","level":2,"skills":["拆角候選資格與算術餘量"]},"variant":{"family_id":"qf-density14-angle-split-candidate","seed":202610141010,"parameters":{"total":90,"first":80,"angle_unit":"degrees","domain":"finite_nondirected_degree_protocol","operation":"density14_angle_split_candidate","semantic_template":"qf-density14-angle-split-candidate/[\"10\",true]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-10","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261010-advance-20261014-r01-angle-0011","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","language":"zh-Hant","source_mko_ids":["mko-angle"],"title_zh":"拆角候選資格與算術餘量","stem_zh":"精確度數協議；非定向0到180度；total=90，候選first=79。依序答 (first是否在[0,total], total−first)。超界候選仍計算有號算術餘量，不當作已構造的角。","answer":{"kind":"expression","value":"(是, 11)","explanation_zh":"拆角資格與餘量=(是, 11)。先檢候選範圍，再精確相減。不由示意圖猜角，有限量值核對非射線度量證明。"},"difficulty":{"band":"primary_foundation","level":2,"skills":["拆角候選資格與算術餘量"]},"variant":{"family_id":"qf-density14-angle-split-candidate","seed":202610141011,"parameters":{"total":90,"first":79,"angle_unit":"degrees","domain":"finite_nondirected_degree_protocol","operation":"density14_angle_split_candidate","semantic_template":"qf-density14-angle-split-candidate/[\"11\",true]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-10","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261010-advance-20261014-r01-angle-0012","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","language":"zh-Hant","source_mko_ids":["mko-angle"],"title_zh":"拆角候選資格與算術餘量","stem_zh":"精確度數協議；非定向0到180度；total=90，候選first=78。依序答 (first是否在[0,total], total−first)。超界候選仍計算有號算術餘量，不當作已構造的角。","answer":{"kind":"expression","value":"(是, 12)","explanation_zh":"拆角資格與餘量=(是, 12)。先檢候選範圍，再精確相減。不由示意圖猜角，有限量值核對非射線度量證明。"},"difficulty":{"band":"primary_foundation","level":2,"skills":["拆角候選資格與算術餘量"]},"variant":{"family_id":"qf-density14-angle-split-candidate","seed":202610141012,"parameters":{"total":90,"first":78,"angle_unit":"degrees","domain":"finite_nondirected_degree_protocol","operation":"density14_angle_split_candidate","semantic_template":"qf-density14-angle-split-candidate/[\"12\",true]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-10","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261010-advance-20261014-r01-angle-0013","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","language":"zh-Hant","source_mko_ids":["mko-angle"],"title_zh":"拆角候選資格與算術餘量","stem_zh":"精確度數協議；非定向0到180度；total=90，候選first=77。依序答 (first是否在[0,total], total−first)。超界候選仍計算有號算術餘量，不當作已構造的角。","answer":{"kind":"expression","value":"(是, 13)","explanation_zh":"拆角資格與餘量=(是, 13)。先檢候選範圍，再精確相減。不由示意圖猜角，有限量值核對非射線度量證明。"},"difficulty":{"band":"primary_foundation","level":2,"skills":["拆角候選資格與算術餘量"]},"variant":{"family_id":"qf-density14-angle-split-candidate","seed":202610141013,"parameters":{"total":90,"first":77,"angle_unit":"degrees","domain":"finite_nondirected_degree_protocol","operation":"density14_angle_split_candidate","semantic_template":"qf-density14-angle-split-candidate/[\"13\",true]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-10","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261010-advance-20261014-r01-angle-0014","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","language":"zh-Hant","source_mko_ids":["mko-angle"],"title_zh":"拆角候選資格與算術餘量","stem_zh":"精確度數協議；非定向0到180度；total=90，候選first=76。依序答 (first是否在[0,total], total−first)。超界候選仍計算有號算術餘量，不當作已構造的角。","answer":{"kind":"expression","value":"(是, 14)","explanation_zh":"拆角資格與餘量=(是, 14)。先檢候選範圍，再精確相減。不由示意圖猜角，有限量值核對非射線度量證明。"},"difficulty":{"band":"primary_foundation","level":2,"skills":["拆角候選資格與算術餘量"]},"variant":{"family_id":"qf-density14-angle-split-candidate","seed":202610141014,"parameters":{"total":90,"first":76,"angle_unit":"degrees","domain":"finite_nondirected_degree_protocol","operation":"density14_angle_split_candidate","semantic_template":"qf-density14-angle-split-candidate/[\"14\",true]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-10","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261010-advance-20261014-r01-angle-0015","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","language":"zh-Hant","source_mko_ids":["mko-angle"],"title_zh":"拆角候選資格與算術餘量","stem_zh":"精確度數協議；非定向0到180度；total=90，候選first=75。依序答 (first是否在[0,total], total−first)。超界候選仍計算有號算術餘量，不當作已構造的角。","answer":{"kind":"expression","value":"(是, 15)","explanation_zh":"拆角資格與餘量=(是, 15)。先檢候選範圍，再精確相減。不由示意圖猜角，有限量值核對非射線度量證明。"},"difficulty":{"band":"primary_foundation","level":2,"skills":["拆角候選資格與算術餘量"]},"variant":{"family_id":"qf-density14-angle-split-candidate","seed":202610141015,"parameters":{"total":90,"first":75,"angle_unit":"degrees","domain":"finite_nondirected_degree_protocol","operation":"density14_angle_split_candidate","semantic_template":"qf-density14-angle-split-candidate/[\"15\",true]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-10","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261010-advance-20261014-r01-angle-0016","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","language":"zh-Hant","source_mko_ids":["mko-angle"],"title_zh":"拆角候選資格與算術餘量","stem_zh":"精確度數協議；非定向0到180度；total=90，候選first=74。依序答 (first是否在[0,total], total−first)。超界候選仍計算有號算術餘量，不當作已構造的角。","answer":{"kind":"expression","value":"(是, 16)","explanation_zh":"拆角資格與餘量=(是, 16)。先檢候選範圍，再精確相減。不由示意圖猜角，有限量值核對非射線度量證明。"},"difficulty":{"band":"primary_foundation","level":2,"skills":["拆角候選資格與算術餘量"]},"variant":{"family_id":"qf-density14-angle-split-candidate","seed":202610141016,"parameters":{"total":90,"first":74,"angle_unit":"degrees","domain":"finite_nondirected_degree_protocol","operation":"density14_angle_split_candidate","semantic_template":"qf-density14-angle-split-candidate/[\"16\",true]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-10","contract_version":"ocme-question-factory-v0.1"}}
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{"schema_version":"ocme-question-v0.1","id":"q-20261010-advance-20261014-r01-angle-0018","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","language":"zh-Hant","source_mko_ids":["mko-angle"],"title_zh":"拆角候選資格與算術餘量","stem_zh":"精確度數協議；非定向0到180度；total=90，候選first=72。依序答 (first是否在[0,total], total−first)。超界候選仍計算有號算術餘量，不當作已構造的角。","answer":{"kind":"expression","value":"(是, 18)","explanation_zh":"拆角資格與餘量=(是, 18)。先檢候選範圍，再精確相減。不由示意圖猜角，有限量值核對非射線度量證明。"},"difficulty":{"band":"primary_foundation","level":3,"skills":["拆角候選資格與算術餘量"]},"variant":{"family_id":"qf-density14-angle-split-candidate","seed":202610141018,"parameters":{"total":90,"first":72,"angle_unit":"degrees","domain":"finite_nondirected_degree_protocol","operation":"density14_angle_split_candidate","semantic_template":"qf-density14-angle-split-candidate/[\"18\",true]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-10","contract_version":"ocme-question-factory-v0.1"}}
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{"schema_version":"ocme-question-v0.1","id":"q-20261010-advance-20261014-r01-angle-0022","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","language":"zh-Hant","source_mko_ids":["mko-angle"],"title_zh":"拆角候選資格與算術餘量","stem_zh":"精確度數協議；非定向0到180度；total=90，候選first=68。依序答 (first是否在[0,total], total−first)。超界候選仍計算有號算術餘量，不當作已構造的角。","answer":{"kind":"expression","value":"(是, 22)","explanation_zh":"拆角資格與餘量=(是, 22)。先檢候選範圍，再精確相減。不由示意圖猜角，有限量值核對非射線度量證明。"},"difficulty":{"band":"primary_foundation","level":3,"skills":["拆角候選資格與算術餘量"]},"variant":{"family_id":"qf-density14-angle-split-candidate","seed":202610141022,"parameters":{"total":90,"first":68,"angle_unit":"degrees","domain":"finite_nondirected_degree_protocol","operation":"density14_angle_split_candidate","semantic_template":"qf-density14-angle-split-candidate/[\"22\",true]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-10","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261010-advance-20261014-r01-angle-0023","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","language":"zh-Hant","source_mko_ids":["mko-angle"],"title_zh":"拆角候選資格與算術餘量","stem_zh":"精確度數協議；非定向0到180度；total=90，候選first=67。依序答 (first是否在[0,total], total−first)。超界候選仍計算有號算術餘量，不當作已構造的角。","answer":{"kind":"expression","value":"(是, 23)","explanation_zh":"拆角資格與餘量=(是, 23)。先檢候選範圍，再精確相減。不由示意圖猜角，有限量值核對非射線度量證明。"},"difficulty":{"band":"primary_foundation","level":3,"skills":["拆角候選資格與算術餘量"]},"variant":{"family_id":"qf-density14-angle-split-candidate","seed":202610141023,"parameters":{"total":90,"first":67,"angle_unit":"degrees","domain":"finite_nondirected_degree_protocol","operation":"density14_angle_split_candidate","semantic_template":"qf-density14-angle-split-candidate/[\"23\",true]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-10","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261010-advance-20261014-r01-angle-0024","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","language":"zh-Hant","source_mko_ids":["mko-angle"],"title_zh":"拆角候選資格與算術餘量","stem_zh":"精確度數協議；非定向0到180度；total=90，候選first=66。依序答 (first是否在[0,total], total−first)。超界候選仍計算有號算術餘量，不當作已構造的角。","answer":{"kind":"expression","value":"(是, 24)","explanation_zh":"拆角資格與餘量=(是, 24)。先檢候選範圍，再精確相減。不由示意圖猜角，有限量值核對非射線度量證明。"},"difficulty":{"band":"primary_foundation","level":3,"skills":["拆角候選資格與算術餘量"]},"variant":{"family_id":"qf-density14-angle-split-candidate","seed":202610141024,"parameters":{"total":90,"first":66,"angle_unit":"degrees","domain":"finite_nondirected_degree_protocol","operation":"density14_angle_split_candidate","semantic_template":"qf-density14-angle-split-candidate/[\"24\",true]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-10","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261010-advance-20261014-r01-angle-0025","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","language":"zh-Hant","source_mko_ids":["mko-angle"],"title_zh":"拆角候選資格與算術餘量","stem_zh":"精確度數協議；非定向0到180度；total=90，候選first=65。依序答 (first是否在[0,total], total−first)。超界候選仍計算有號算術餘量，不當作已構造的角。","answer":{"kind":"expression","value":"(是, 25)","explanation_zh":"拆角資格與餘量=(是, 25)。先檢候選範圍，再精確相減。不由示意圖猜角，有限量值核對非射線度量證明。"},"difficulty":{"band":"primary_foundation","level":3,"skills":["拆角候選資格與算術餘量"]},"variant":{"family_id":"qf-density14-angle-split-candidate","seed":202610141025,"parameters":{"total":90,"first":65,"angle_unit":"degrees","domain":"finite_nondirected_degree_protocol","operation":"density14_angle_split_candidate","semantic_template":"qf-density14-angle-split-candidate/[\"25\",true]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-10","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261010-advance-20261014-r01-angle-0026","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","language":"zh-Hant","source_mko_ids":["mko-angle"],"title_zh":"互餘資格與互補量","stem_zh":"精確度數協議；非定向0到180度；a=0。依序答 (a≤90是否, 合法互餘量90−a或無, 互補量180−a)。","answer":{"kind":"expression","value":"(是, 90, 180)","explanation_zh":"互餘資格與互補量=(是, 90, 180)。互餘須先核90門檻，互補量另從180扣除。不由示意圖猜角，有限量值核對非射線度量證明。"},"difficulty":{"band":"primary_foundation","level":1,"skills":["互餘資格與互補量"]},"variant":{"family_id":"qf-density14-angle-complement-supplement-pair","seed":202610141026,"parameters":{"a":0,"angle_unit":"degrees","domain":"finite_nondirected_degree_protocol","operation":"density14_angle_complement_supplement_pair","semantic_template":"qf-density14-angle-complement-supplement-pair/0"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-10","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261010-advance-20261014-r01-angle-0027","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","language":"zh-Hant","source_mko_ids":["mko-angle"],"title_zh":"互餘資格與互補量","stem_zh":"精確度數協議；非定向0到180度；a=90。依序答 (a≤90是否, 合法互餘量90−a或無, 互補量180−a)。","answer":{"kind":"expression","value":"(是, 0, 90)","explanation_zh":"互餘資格與互補量=(是, 0, 90)。互餘須先核90門檻，互補量另從180扣除。不由示意圖猜角，有限量值核對非射線度量證明。"},"difficulty":{"band":"primary_foundation","level":1,"skills":["互餘資格與互補量"]},"variant":{"family_id":"qf-density14-angle-complement-supplement-pair","seed":202610141027,"parameters":{"a":90,"angle_unit":"degrees","domain":"finite_nondirected_degree_protocol","operation":"density14_angle_complement_supplement_pair","semantic_template":"qf-density14-angle-complement-supplement-pair/90"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-10","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261010-advance-20261014-r01-angle-0028","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","language":"zh-Hant","source_mko_ids":["mko-angle"],"title_zh":"互餘資格與互補量","stem_zh":"精確度數協議；非定向0到180度；a=180。依序答 (a≤90是否, 合法互餘量90−a或無, 互補量180−a)。","answer":{"kind":"expression","value":"(否, 無, 0)","explanation_zh":"互餘資格與互補量=(否, 無, 0)。互餘須先核90門檻，互補量另從180扣除。不由示意圖猜角，有限量值核對非射線度量證明。"},"difficulty":{"band":"primary_foundation","level":1,"skills":["互餘資格與互補量"]},"variant":{"family_id":"qf-density14-angle-complement-supplement-pair","seed":202610141028,"parameters":{"a":180,"angle_unit":"degrees","domain":"finite_nondirected_degree_protocol","operation":"density14_angle_complement_supplement_pair","semantic_template":"qf-density14-angle-complement-supplement-pair/180"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-10","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261010-advance-20261014-r01-angle-0029","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","language":"zh-Hant","source_mko_ids":["mko-angle"],"title_zh":"互餘資格與互補量","stem_zh":"精確度數協議；非定向0到180度；a=4。依序答 (a≤90是否, 合法互餘量90−a或無, 互補量180−a)。","answer":{"kind":"expression","value":"(是, 86, 176)","explanation_zh":"互餘資格與互補量=(是, 86, 176)。互餘須先核90門檻，互補量另從180扣除。不由示意圖猜角，有限量值核對非射線度量證明。"},"difficulty":{"band":"primary_foundation","level":1,"skills":["互餘資格與互補量"]},"variant":{"family_id":"qf-density14-angle-complement-supplement-pair","seed":202610141029,"parameters":{"a":4,"angle_unit":"degrees","domain":"finite_nondirected_degree_protocol","operation":"density14_angle_complement_supplement_pair","semantic_template":"qf-density14-angle-complement-supplement-pair/4"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-10","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261010-advance-20261014-r01-angle-0030","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","language":"zh-Hant","source_mko_ids":["mko-angle"],"title_zh":"互餘資格與互補量","stem_zh":"精確度數協議；非定向0到180度；a=5。依序答 (a≤90是否, 合法互餘量90−a或無, 互補量180−a)。","answer":{"kind":"expression","value":"(是, 85, 175)","explanation_zh":"互餘資格與互補量=(是, 85, 175)。互餘須先核90門檻，互補量另從180扣除。不由示意圖猜角，有限量值核對非射線度量證明。"},"difficulty":{"band":"primary_foundation","level":1,"skills":["互餘資格與互補量"]},"variant":{"family_id":"qf-density14-angle-complement-supplement-pair","seed":202610141030,"parameters":{"a":5,"angle_unit":"degrees","domain":"finite_nondirected_degree_protocol","operation":"density14_angle_complement_supplement_pair","semantic_template":"qf-density14-angle-complement-supplement-pair/5"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-10","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261010-advance-20261014-r01-angle-0031","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","language":"zh-Hant","source_mko_ids":["mko-angle"],"title_zh":"互餘資格與互補量","stem_zh":"精確度數協議；非定向0到180度；a=6。依序答 (a≤90是否, 合法互餘量90−a或無, 互補量180−a)。","answer":{"kind":"expression","value":"(是, 84, 174)","explanation_zh":"互餘資格與互補量=(是, 84, 174)。互餘須先核90門檻，互補量另從180扣除。不由示意圖猜角，有限量值核對非射線度量證明。"},"difficulty":{"band":"primary_foundation","level":1,"skills":["互餘資格與互補量"]},"variant":{"family_id":"qf-density14-angle-complement-supplement-pair","seed":202610141031,"parameters":{"a":6,"angle_unit":"degrees","domain":"finite_nondirected_degree_protocol","operation":"density14_angle_complement_supplement_pair","semantic_template":"qf-density14-angle-complement-supplement-pair/6"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-10","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261010-advance-20261014-r01-angle-0032","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","language":"zh-Hant","source_mko_ids":["mko-angle"],"title_zh":"互餘資格與互補量","stem_zh":"精確度數協議；非定向0到180度；a=7。依序答 (a≤90是否, 合法互餘量90−a或無, 互補量180−a)。","answer":{"kind":"expression","value":"(是, 83, 173)","explanation_zh":"互餘資格與互補量=(是, 83, 173)。互餘須先核90門檻，互補量另從180扣除。不由示意圖猜角，有限量值核對非射線度量證明。"},"difficulty":{"band":"primary_foundation","level":1,"skills":["互餘資格與互補量"]},"variant":{"family_id":"qf-density14-angle-complement-supplement-pair","seed":202610141032,"parameters":{"a":7,"angle_unit":"degrees","domain":"finite_nondirected_degree_protocol","operation":"density14_angle_complement_supplement_pair","semantic_template":"qf-density14-angle-complement-supplement-pair/7"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-10","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261010-advance-20261014-r01-angle-0033","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","language":"zh-Hant","source_mko_ids":["mko-angle"],"title_zh":"互餘資格與互補量","stem_zh":"精確度數協議；非定向0到180度；a=8。依序答 (a≤90是否, 合法互餘量90−a或無, 互補量180−a)。","answer":{"kind":"expression","value":"(是, 82, 172)","explanation_zh":"互餘資格與互補量=(是, 82, 172)。互餘須先核90門檻，互補量另從180扣除。不由示意圖猜角，有限量值核對非射線度量證明。"},"difficulty":{"band":"primary_foundation","level":1,"skills":["互餘資格與互補量"]},"variant":{"family_id":"qf-density14-angle-complement-supplement-pair","seed":202610141033,"parameters":{"a":8,"angle_unit":"degrees","domain":"finite_nondirected_degree_protocol","operation":"density14_angle_complement_supplement_pair","semantic_template":"qf-density14-angle-complement-supplement-pair/8"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-10","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261010-advance-20261014-r01-angle-0034","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","language":"zh-Hant","source_mko_ids":["mko-angle"],"title_zh":"互餘資格與互補量","stem_zh":"精確度數協議；非定向0到180度；a=9。依序答 (a≤90是否, 合法互餘量90−a或無, 互補量180−a)。","answer":{"kind":"expression","value":"(是, 81, 171)","explanation_zh":"互餘資格與互補量=(是, 81, 171)。互餘須先核90門檻，互補量另從180扣除。不由示意圖猜角，有限量值核對非射線度量證明。"},"difficulty":{"band":"primary_foundation","level":2,"skills":["互餘資格與互補量"]},"variant":{"family_id":"qf-density14-angle-complement-supplement-pair","seed":202610141034,"parameters":{"a":9,"angle_unit":"degrees","domain":"finite_nondirected_degree_protocol","operation":"density14_angle_complement_supplement_pair","semantic_template":"qf-density14-angle-complement-supplement-pair/9"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-10","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261010-advance-20261014-r01-angle-0035","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","language":"zh-Hant","source_mko_ids":["mko-angle"],"title_zh":"互餘資格與互補量","stem_zh":"精確度數協議；非定向0到180度；a=10。依序答 (a≤90是否, 合法互餘量90−a或無, 互補量180−a)。","answer":{"kind":"expression","value":"(是, 80, 170)","explanation_zh":"互餘資格與互補量=(是, 80, 170)。互餘須先核90門檻，互補量另從180扣除。不由示意圖猜角，有限量值核對非射線度量證明。"},"difficulty":{"band":"primary_foundation","level":2,"skills":["互餘資格與互補量"]},"variant":{"family_id":"qf-density14-angle-complement-supplement-pair","seed":202610141035,"parameters":{"a":10,"angle_unit":"degrees","domain":"finite_nondirected_degree_protocol","operation":"density14_angle_complement_supplement_pair","semantic_template":"qf-density14-angle-complement-supplement-pair/10"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-10","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261010-advance-20261014-r01-angle-0036","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","language":"zh-Hant","source_mko_ids":["mko-angle"],"title_zh":"互餘資格與互補量","stem_zh":"精確度數協議；非定向0到180度；a=11。依序答 (a≤90是否, 合法互餘量90−a或無, 互補量180−a)。","answer":{"kind":"expression","value":"(是, 79, 169)","explanation_zh":"互餘資格與互補量=(是, 79, 169)。互餘須先核90門檻，互補量另從180扣除。不由示意圖猜角，有限量值核對非射線度量證明。"},"difficulty":{"band":"primary_foundation","level":2,"skills":["互餘資格與互補量"]},"variant":{"family_id":"qf-density14-angle-complement-supplement-pair","seed":202610141036,"parameters":{"a":11,"angle_unit":"degrees","domain":"finite_nondirected_degree_protocol","operation":"density14_angle_complement_supplement_pair","semantic_template":"qf-density14-angle-complement-supplement-pair/11"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-10","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261010-advance-20261014-r01-angle-0037","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","language":"zh-Hant","source_mko_ids":["mko-angle"],"title_zh":"互餘資格與互補量","stem_zh":"精確度數協議；非定向0到180度；a=12。依序答 (a≤90是否, 合法互餘量90−a或無, 互補量180−a)。","answer":{"kind":"expression","value":"(是, 78, 168)","explanation_zh":"互餘資格與互補量=(是, 78, 168)。互餘須先核90門檻，互補量另從180扣除。不由示意圖猜角，有限量值核對非射線度量證明。"},"difficulty":{"band":"primary_foundation","level":2,"skills":["互餘資格與互補量"]},"variant":{"family_id":"qf-density14-angle-complement-supplement-pair","seed":202610141037,"parameters":{"a":12,"angle_unit":"degrees","domain":"finite_nondirected_degree_protocol","operation":"density14_angle_complement_supplement_pair","semantic_template":"qf-density14-angle-complement-supplement-pair/12"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-10","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261010-advance-20261014-r01-angle-0038","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","language":"zh-Hant","source_mko_ids":["mko-angle"],"title_zh":"互餘資格與互補量","stem_zh":"精確度數協議；非定向0到180度；a=13。依序答 (a≤90是否, 合法互餘量90−a或無, 互補量180−a)。","answer":{"kind":"expression","value":"(是, 77, 167)","explanation_zh":"互餘資格與互補量=(是, 77, 167)。互餘須先核90門檻，互補量另從180扣除。不由示意圖猜角，有限量值核對非射線度量證明。"},"difficulty":{"band":"primary_foundation","level":2,"skills":["互餘資格與互補量"]},"variant":{"family_id":"qf-density14-angle-complement-supplement-pair","seed":202610141038,"parameters":{"a":13,"angle_unit":"degrees","domain":"finite_nondirected_degree_protocol","operation":"density14_angle_complement_supplement_pair","semantic_template":"qf-density14-angle-complement-supplement-pair/13"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-10","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261010-advance-20261014-r01-angle-0039","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","language":"zh-Hant","source_mko_ids":["mko-angle"],"title_zh":"互餘資格與互補量","stem_zh":"精確度數協議；非定向0到180度；a=14。依序答 (a≤90是否, 合法互餘量90−a或無, 互補量180−a)。","answer":{"kind":"expression","value":"(是, 76, 166)","explanation_zh":"互餘資格與互補量=(是, 76, 166)。互餘須先核90門檻，互補量另從180扣除。不由示意圖猜角，有限量值核對非射線度量證明。"},"difficulty":{"band":"primary_foundation","level":2,"skills":["互餘資格與互補量"]},"variant":{"family_id":"qf-density14-angle-complement-supplement-pair","seed":202610141039,"parameters":{"a":14,"angle_unit":"degrees","domain":"finite_nondirected_degree_protocol","operation":"density14_angle_complement_supplement_pair","semantic_template":"qf-density14-angle-complement-supplement-pair/14"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-10","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261010-advance-20261014-r01-angle-0040","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","language":"zh-Hant","source_mko_ids":["mko-angle"],"title_zh":"互餘資格與互補量","stem_zh":"精確度數協議；非定向0到180度；a=15。依序答 (a≤90是否, 合法互餘量90−a或無, 互補量180−a)。","answer":{"kind":"expression","value":"(是, 75, 165)","explanation_zh":"互餘資格與互補量=(是, 75, 165)。互餘須先核90門檻，互補量另從180扣除。不由示意圖猜角，有限量值核對非射線度量證明。"},"difficulty":{"band":"primary_foundation","level":2,"skills":["互餘資格與互補量"]},"variant":{"family_id":"qf-density14-angle-complement-supplement-pair","seed":202610141040,"parameters":{"a":15,"angle_unit":"degrees","domain":"finite_nondirected_degree_protocol","operation":"density14_angle_complement_supplement_pair","semantic_template":"qf-density14-angle-complement-supplement-pair/15"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-10","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261010-advance-20261014-r01-angle-0041","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","language":"zh-Hant","source_mko_ids":["mko-angle"],"title_zh":"互餘資格與互補量","stem_zh":"精確度數協議；非定向0到180度；a=16。依序答 (a≤90是否, 合法互餘量90−a或無, 互補量180−a)。","answer":{"kind":"expression","value":"(是, 74, 164)","explanation_zh":"互餘資格與互補量=(是, 74, 164)。互餘須先核90門檻，互補量另從180扣除。不由示意圖猜角，有限量值核對非射線度量證明。"},"difficulty":{"band":"primary_foundation","level":2,"skills":["互餘資格與互補量"]},"variant":{"family_id":"qf-density14-angle-complement-supplement-pair","seed":202610141041,"parameters":{"a":16,"angle_unit":"degrees","domain":"finite_nondirected_degree_protocol","operation":"density14_angle_complement_supplement_pair","semantic_template":"qf-density14-angle-complement-supplement-pair/16"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-10","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261010-advance-20261014-r01-angle-0042","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","language":"zh-Hant","source_mko_ids":["mko-angle"],"title_zh":"互餘資格與互補量","stem_zh":"精確度數協議；非定向0到180度；a=17。依序答 (a≤90是否, 合法互餘量90−a或無, 互補量180−a)。","answer":{"kind":"expression","value":"(是, 73, 163)","explanation_zh":"互餘資格與互補量=(是, 73, 163)。互餘須先核90門檻，互補量另從180扣除。不由示意圖猜角，有限量值核對非射線度量證明。"},"difficulty":{"band":"primary_foundation","level":2,"skills":["互餘資格與互補量"]},"variant":{"family_id":"qf-density14-angle-complement-supplement-pair","seed":202610141042,"parameters":{"a":17,"angle_unit":"degrees","domain":"finite_nondirected_degree_protocol","operation":"density14_angle_complement_supplement_pair","semantic_template":"qf-density14-angle-complement-supplement-pair/17"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-10","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261010-advance-20261014-r01-angle-0043","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","language":"zh-Hant","source_mko_ids":["mko-angle"],"title_zh":"互餘資格與互補量","stem_zh":"精確度數協議；非定向0到180度；a=18。依序答 (a≤90是否, 合法互餘量90−a或無, 互補量180−a)。","answer":{"kind":"expression","value":"(是, 72, 162)","explanation_zh":"互餘資格與互補量=(是, 72, 162)。互餘須先核90門檻，互補量另從180扣除。不由示意圖猜角，有限量值核對非射線度量證明。"},"difficulty":{"band":"primary_foundation","level":3,"skills":["互餘資格與互補量"]},"variant":{"family_id":"qf-density14-angle-complement-supplement-pair","seed":202610141043,"parameters":{"a":18,"angle_unit":"degrees","domain":"finite_nondirected_degree_protocol","operation":"density14_angle_complement_supplement_pair","semantic_template":"qf-density14-angle-complement-supplement-pair/18"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-10","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261010-advance-20261014-r01-angle-0044","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","language":"zh-Hant","source_mko_ids":["mko-angle"],"title_zh":"互餘資格與互補量","stem_zh":"精確度數協議；非定向0到180度；a=19。依序答 (a≤90是否, 合法互餘量90−a或無, 互補量180−a)。","answer":{"kind":"expression","value":"(是, 71, 161)","explanation_zh":"互餘資格與互補量=(是, 71, 161)。互餘須先核90門檻，互補量另從180扣除。不由示意圖猜角，有限量值核對非射線度量證明。"},"difficulty":{"band":"primary_foundation","level":3,"skills":["互餘資格與互補量"]},"variant":{"family_id":"qf-density14-angle-complement-supplement-pair","seed":202610141044,"parameters":{"a":19,"angle_unit":"degrees","domain":"finite_nondirected_degree_protocol","operation":"density14_angle_complement_supplement_pair","semantic_template":"qf-density14-angle-complement-supplement-pair/19"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-10","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261010-advance-20261014-r01-angle-0045","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","language":"zh-Hant","source_mko_ids":["mko-angle"],"title_zh":"互餘資格與互補量","stem_zh":"精確度數協議；非定向0到180度；a=20。依序答 (a≤90是否, 合法互餘量90−a或無, 互補量180−a)。","answer":{"kind":"expression","value":"(是, 70, 160)","explanation_zh":"互餘資格與互補量=(是, 70, 160)。互餘須先核90門檻，互補量另從180扣除。不由示意圖猜角，有限量值核對非射線度量證明。"},"difficulty":{"band":"primary_foundation","level":3,"skills":["互餘資格與互補量"]},"variant":{"family_id":"qf-density14-angle-complement-supplement-pair","seed":202610141045,"parameters":{"a":20,"angle_unit":"degrees","domain":"finite_nondirected_degree_protocol","operation":"density14_angle_complement_supplement_pair","semantic_template":"qf-density14-angle-complement-supplement-pair/20"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-10","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261010-advance-20261014-r01-angle-0046","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","language":"zh-Hant","source_mko_ids":["mko-angle"],"title_zh":"互餘資格與互補量","stem_zh":"精確度數協議；非定向0到180度；a=21。依序答 (a≤90是否, 合法互餘量90−a或無, 互補量180−a)。","answer":{"kind":"expression","value":"(是, 69, 159)","explanation_zh":"互餘資格與互補量=(是, 69, 159)。互餘須先核90門檻，互補量另從180扣除。不由示意圖猜角，有限量值核對非射線度量證明。"},"difficulty":{"band":"primary_foundation","level":3,"skills":["互餘資格與互補量"]},"variant":{"family_id":"qf-density14-angle-complement-supplement-pair","seed":202610141046,"parameters":{"a":21,"angle_unit":"degrees","domain":"finite_nondirected_degree_protocol","operation":"density14_angle_complement_supplement_pair","semantic_template":"qf-density14-angle-complement-supplement-pair/21"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-10","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261010-advance-20261014-r01-angle-0047","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","language":"zh-Hant","source_mko_ids":["mko-angle"],"title_zh":"互餘資格與互補量","stem_zh":"精確度數協議；非定向0到180度；a=22。依序答 (a≤90是否, 合法互餘量90−a或無, 互補量180−a)。","answer":{"kind":"expression","value":"(是, 68, 158)","explanation_zh":"互餘資格與互補量=(是, 68, 158)。互餘須先核90門檻，互補量另從180扣除。不由示意圖猜角，有限量值核對非射線度量證明。"},"difficulty":{"band":"primary_foundation","level":3,"skills":["互餘資格與互補量"]},"variant":{"family_id":"qf-density14-angle-complement-supplement-pair","seed":202610141047,"parameters":{"a":22,"angle_unit":"degrees","domain":"finite_nondirected_degree_protocol","operation":"density14_angle_complement_supplement_pair","semantic_template":"qf-density14-angle-complement-supplement-pair/22"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-10","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261010-advance-20261014-r01-angle-0048","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","language":"zh-Hant","source_mko_ids":["mko-angle"],"title_zh":"互餘資格與互補量","stem_zh":"精確度數協議；非定向0到180度；a=23。依序答 (a≤90是否, 合法互餘量90−a或無, 互補量180−a)。","answer":{"kind":"expression","value":"(是, 67, 157)","explanation_zh":"互餘資格與互補量=(是, 67, 157)。互餘須先核90門檻，互補量另從180扣除。不由示意圖猜角，有限量值核對非射線度量證明。"},"difficulty":{"band":"primary_foundation","level":3,"skills":["互餘資格與互補量"]},"variant":{"family_id":"qf-density14-angle-complement-supplement-pair","seed":202610141048,"parameters":{"a":23,"angle_unit":"degrees","domain":"finite_nondirected_degree_protocol","operation":"density14_angle_complement_supplement_pair","semantic_template":"qf-density14-angle-complement-supplement-pair/23"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-10","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261010-advance-20261014-r01-angle-0049","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","language":"zh-Hant","source_mko_ids":["mko-angle"],"title_zh":"互餘資格與互補量","stem_zh":"精確度數協議；非定向0到180度；a=24。依序答 (a≤90是否, 合法互餘量90−a或無, 互補量180−a)。","answer":{"kind":"expression","value":"(是, 66, 156)","explanation_zh":"互餘資格與互補量=(是, 66, 156)。互餘須先核90門檻，互補量另從180扣除。不由示意圖猜角，有限量值核對非射線度量證明。"},"difficulty":{"band":"primary_foundation","level":3,"skills":["互餘資格與互補量"]},"variant":{"family_id":"qf-density14-angle-complement-supplement-pair","seed":202610141049,"parameters":{"a":24,"angle_unit":"degrees","domain":"finite_nondirected_degree_protocol","operation":"density14_angle_complement_supplement_pair","semantic_template":"qf-density14-angle-complement-supplement-pair/24"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-10","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261010-advance-20261014-r01-angle-0050","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","language":"zh-Hant","source_mko_ids":["mko-angle"],"title_zh":"互餘資格與互補量","stem_zh":"精確度數協議；非定向0到180度；a=25。依序答 (a≤90是否, 合法互餘量90−a或無, 互補量180−a)。","answer":{"kind":"expression","value":"(是, 65, 155)","explanation_zh":"互餘資格與互補量=(是, 65, 155)。互餘須先核90門檻，互補量另從180扣除。不由示意圖猜角，有限量值核對非射線度量證明。"},"difficulty":{"band":"primary_foundation","level":3,"skills":["互餘資格與互補量"]},"variant":{"family_id":"qf-density14-angle-complement-supplement-pair","seed":202610141050,"parameters":{"a":25,"angle_unit":"degrees","domain":"finite_nondirected_degree_protocol","operation":"density14_angle_complement_supplement_pair","semantic_template":"qf-density14-angle-complement-supplement-pair/25"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-10","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261010-advance-20261014-r01-angle-0051","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","language":"zh-Hant","source_mko_ids":["mko-angle"],"title_zh":"角和對兩門檻的殘差","stem_zh":"精確度數協議；非定向0到180度；a=0、b=0。依序列 (a+b−90, a+b−180, 和是否90, 和是否180)。","answer":{"kind":"expression","value":"(-90, -180, 否, 否)","explanation_zh":"角和雙門檻殘差=(-90, -180, 否, 否)。先加角量，再對兩個不同門檻核差與相等。不由示意圖猜角，有限量值核對非射線度量證明。"},"difficulty":{"band":"primary_foundation","level":1,"skills":["角和對兩門檻的殘差"]},"variant":{"family_id":"qf-density14-angle-pair-defects","seed":202610141051,"parameters":{"a":0,"b":0,"angle_unit":"degrees","domain":"finite_nondirected_degree_protocol","operation":"density14_angle_pair_defects","semantic_template":"qf-density14-angle-pair-defects/0"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-10","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261010-advance-20261014-r01-angle-0052","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","language":"zh-Hant","source_mko_ids":["mko-angle"],"title_zh":"角和對兩門檻的殘差","stem_zh":"精確度數協議；非定向0到180度；a=45、b=45。依序列 (a+b−90, a+b−180, 和是否90, 和是否180)。","answer":{"kind":"expression","value":"(0, -90, 是, 否)","explanation_zh":"角和雙門檻殘差=(0, -90, 是, 否)。先加角量，再對兩個不同門檻核差與相等。不由示意圖猜角，有限量值核對非射線度量證明。"},"difficulty":{"band":"primary_foundation","level":1,"skills":["角和對兩門檻的殘差"]},"variant":{"family_id":"qf-density14-angle-pair-defects","seed":202610141052,"parameters":{"a":45,"b":45,"angle_unit":"degrees","domain":"finite_nondirected_degree_protocol","operation":"density14_angle_pair_defects","semantic_template":"qf-density14-angle-pair-defects/90"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-10","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261010-advance-20261014-r01-angle-0053","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","language":"zh-Hant","source_mko_ids":["mko-angle"],"title_zh":"角和對兩門檻的殘差","stem_zh":"精確度數協議；非定向0到180度；a=90、b=90。依序列 (a+b−90, a+b−180, 和是否90, 和是否180)。","answer":{"kind":"expression","value":"(90, 0, 否, 是)","explanation_zh":"角和雙門檻殘差=(90, 0, 否, 是)。先加角量，再對兩個不同門檻核差與相等。不由示意圖猜角，有限量值核對非射線度量證明。"},"difficulty":{"band":"primary_foundation","level":1,"skills":["角和對兩門檻的殘差"]},"variant":{"family_id":"qf-density14-angle-pair-defects","seed":202610141053,"parameters":{"a":90,"b":90,"angle_unit":"degrees","domain":"finite_nondirected_degree_protocol","operation":"density14_angle_pair_defects","semantic_template":"qf-density14-angle-pair-defects/180"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-10","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261010-advance-20261014-r01-angle-0054","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","language":"zh-Hant","source_mko_ids":["mko-angle"],"title_zh":"角和對兩門檻的殘差","stem_zh":"精確度數協議；非定向0到180度；a=180、b=180。依序列 (a+b−90, a+b−180, 和是否90, 和是否180)。","answer":{"kind":"expression","value":"(270, 180, 否, 否)","explanation_zh":"角和雙門檻殘差=(270, 180, 否, 否)。先加角量，再對兩個不同門檻核差與相等。不由示意圖猜角，有限量值核對非射線度量證明。"},"difficulty":{"band":"primary_foundation","level":1,"skills":["角和對兩門檻的殘差"]},"variant":{"family_id":"qf-density14-angle-pair-defects","seed":202610141054,"parameters":{"a":180,"b":180,"angle_unit":"degrees","domain":"finite_nondirected_degree_protocol","operation":"density14_angle_pair_defects","semantic_template":"qf-density14-angle-pair-defects/360"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-10","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261010-advance-20261014-r01-angle-0055","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","language":"zh-Hant","source_mko_ids":["mko-angle"],"title_zh":"角和對兩門檻的殘差","stem_zh":"精確度數協議；非定向0到180度；a=4、b=0。依序列 (a+b−90, a+b−180, 和是否90, 和是否180)。","answer":{"kind":"expression","value":"(-86, -176, 否, 否)","explanation_zh":"角和雙門檻殘差=(-86, -176, 否, 否)。先加角量，再對兩個不同門檻核差與相等。不由示意圖猜角，有限量值核對非射線度量證明。"},"difficulty":{"band":"primary_foundation","level":1,"skills":["角和對兩門檻的殘差"]},"variant":{"family_id":"qf-density14-angle-pair-defects","seed":202610141055,"parameters":{"a":4,"b":0,"angle_unit":"degrees","domain":"finite_nondirected_degree_protocol","operation":"density14_angle_pair_defects","semantic_template":"qf-density14-angle-pair-defects/4"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-10","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261010-advance-20261014-r01-angle-0056","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","language":"zh-Hant","source_mko_ids":["mko-angle"],"title_zh":"角和對兩門檻的殘差","stem_zh":"精確度數協議；非定向0到180度；a=5、b=0。依序列 (a+b−90, a+b−180, 和是否90, 和是否180)。","answer":{"kind":"expression","value":"(-85, -175, 否, 否)","explanation_zh":"角和雙門檻殘差=(-85, -175, 否, 否)。先加角量，再對兩個不同門檻核差與相等。不由示意圖猜角，有限量值核對非射線度量證明。"},"difficulty":{"band":"primary_foundation","level":1,"skills":["角和對兩門檻的殘差"]},"variant":{"family_id":"qf-density14-angle-pair-defects","seed":202610141056,"parameters":{"a":5,"b":0,"angle_unit":"degrees","domain":"finite_nondirected_degree_protocol","operation":"density14_angle_pair_defects","semantic_template":"qf-density14-angle-pair-defects/5"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-10","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261010-advance-20261014-r01-angle-0057","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","language":"zh-Hant","source_mko_ids":["mko-angle"],"title_zh":"角和對兩門檻的殘差","stem_zh":"精確度數協議；非定向0到180度；a=6、b=0。依序列 (a+b−90, a+b−180, 和是否90, 和是否180)。","answer":{"kind":"expression","value":"(-84, -174, 否, 否)","explanation_zh":"角和雙門檻殘差=(-84, -174, 否, 否)。先加角量，再對兩個不同門檻核差與相等。不由示意圖猜角，有限量值核對非射線度量證明。"},"difficulty":{"band":"primary_foundation","level":1,"skills":["角和對兩門檻的殘差"]},"variant":{"family_id":"qf-density14-angle-pair-defects","seed":202610141057,"parameters":{"a":6,"b":0,"angle_unit":"degrees","domain":"finite_nondirected_degree_protocol","operation":"density14_angle_pair_defects","semantic_template":"qf-density14-angle-pair-defects/6"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-10","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261010-advance-20261014-r01-angle-0058","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","language":"zh-Hant","source_mko_ids":["mko-angle"],"title_zh":"角和對兩門檻的殘差","stem_zh":"精確度數協議；非定向0到180度；a=7、b=0。依序列 (a+b−90, a+b−180, 和是否90, 和是否180)。","answer":{"kind":"expression","value":"(-83, -173, 否, 否)","explanation_zh":"角和雙門檻殘差=(-83, -173, 否, 否)。先加角量，再對兩個不同門檻核差與相等。不由示意圖猜角，有限量值核對非射線度量證明。"},"difficulty":{"band":"primary_foundation","level":1,"skills":["角和對兩門檻的殘差"]},"variant":{"family_id":"qf-density14-angle-pair-defects","seed":202610141058,"parameters":{"a":7,"b":0,"angle_unit":"degrees","domain":"finite_nondirected_degree_protocol","operation":"density14_angle_pair_defects","semantic_template":"qf-density14-angle-pair-defects/7"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-10","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261010-advance-20261014-r01-angle-0059","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","language":"zh-Hant","source_mko_ids":["mko-angle"],"title_zh":"角和對兩門檻的殘差","stem_zh":"精確度數協議；非定向0到180度；a=8、b=0。依序列 (a+b−90, a+b−180, 和是否90, 和是否180)。","answer":{"kind":"expression","value":"(-82, -172, 否, 否)","explanation_zh":"角和雙門檻殘差=(-82, -172, 否, 否)。先加角量，再對兩個不同門檻核差與相等。不由示意圖猜角，有限量值核對非射線度量證明。"},"difficulty":{"band":"primary_foundation","level":2,"skills":["角和對兩門檻的殘差"]},"variant":{"family_id":"qf-density14-angle-pair-defects","seed":202610141059,"parameters":{"a":8,"b":0,"angle_unit":"degrees","domain":"finite_nondirected_degree_protocol","operation":"density14_angle_pair_defects","semantic_template":"qf-density14-angle-pair-defects/8"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-10","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261010-advance-20261014-r01-angle-0060","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","language":"zh-Hant","source_mko_ids":["mko-angle"],"title_zh":"角和對兩門檻的殘差","stem_zh":"精確度數協議；非定向0到180度；a=9、b=0。依序列 (a+b−90, a+b−180, 和是否90, 和是否180)。","answer":{"kind":"expression","value":"(-81, -171, 否, 否)","explanation_zh":"角和雙門檻殘差=(-81, -171, 否, 否)。先加角量，再對兩個不同門檻核差與相等。不由示意圖猜角，有限量值核對非射線度量證明。"},"difficulty":{"band":"primary_foundation","level":2,"skills":["角和對兩門檻的殘差"]},"variant":{"family_id":"qf-density14-angle-pair-defects","seed":202610141060,"parameters":{"a":9,"b":0,"angle_unit":"degrees","domain":"finite_nondirected_degree_protocol","operation":"density14_angle_pair_defects","semantic_template":"qf-density14-angle-pair-defects/9"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-10","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261010-advance-20261014-r01-angle-0061","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","language":"zh-Hant","source_mko_ids":["mko-angle"],"title_zh":"角和對兩門檻的殘差","stem_zh":"精確度數協議；非定向0到180度；a=10、b=0。依序列 (a+b−90, a+b−180, 和是否90, 和是否180)。","answer":{"kind":"expression","value":"(-80, -170, 否, 否)","explanation_zh":"角和雙門檻殘差=(-80, -170, 否, 否)。先加角量，再對兩個不同門檻核差與相等。不由示意圖猜角，有限量值核對非射線度量證明。"},"difficulty":{"band":"primary_foundation","level":2,"skills":["角和對兩門檻的殘差"]},"variant":{"family_id":"qf-density14-angle-pair-defects","seed":202610141061,"parameters":{"a":10,"b":0,"angle_unit":"degrees","domain":"finite_nondirected_degree_protocol","operation":"density14_angle_pair_defects","semantic_template":"qf-density14-angle-pair-defects/10"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-10","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261010-advance-20261014-r01-angle-0062","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","language":"zh-Hant","source_mko_ids":["mko-angle"],"title_zh":"角和對兩門檻的殘差","stem_zh":"精確度數協議；非定向0到180度；a=11、b=0。依序列 (a+b−90, a+b−180, 和是否90, 和是否180)。","answer":{"kind":"expression","value":"(-79, -169, 否, 否)","explanation_zh":"角和雙門檻殘差=(-79, -169, 否, 否)。先加角量，再對兩個不同門檻核差與相等。不由示意圖猜角，有限量值核對非射線度量證明。"},"difficulty":{"band":"primary_foundation","level":2,"skills":["角和對兩門檻的殘差"]},"variant":{"family_id":"qf-density14-angle-pair-defects","seed":202610141062,"parameters":{"a":11,"b":0,"angle_unit":"degrees","domain":"finite_nondirected_degree_protocol","operation":"density14_angle_pair_defects","semantic_template":"qf-density14-angle-pair-defects/11"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-10","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261010-advance-20261014-r01-angle-0063","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","language":"zh-Hant","source_mko_ids":["mko-angle"],"title_zh":"角和對兩門檻的殘差","stem_zh":"精確度數協議；非定向0到180度；a=12、b=0。依序列 (a+b−90, a+b−180, 和是否90, 和是否180)。","answer":{"kind":"expression","value":"(-78, -168, 否, 否)","explanation_zh":"角和雙門檻殘差=(-78, -168, 否, 否)。先加角量，再對兩個不同門檻核差與相等。不由示意圖猜角，有限量值核對非射線度量證明。"},"difficulty":{"band":"primary_foundation","level":2,"skills":["角和對兩門檻的殘差"]},"variant":{"family_id":"qf-density14-angle-pair-defects","seed":202610141063,"parameters":{"a":12,"b":0,"angle_unit":"degrees","domain":"finite_nondirected_degree_protocol","operation":"density14_angle_pair_defects","semantic_template":"qf-density14-angle-pair-defects/12"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-10","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261010-advance-20261014-r01-angle-0064","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","language":"zh-Hant","source_mko_ids":["mko-angle"],"title_zh":"角和對兩門檻的殘差","stem_zh":"精確度數協議；非定向0到180度；a=13、b=0。依序列 (a+b−90, a+b−180, 和是否90, 和是否180)。","answer":{"kind":"expression","value":"(-77, -167, 否, 否)","explanation_zh":"角和雙門檻殘差=(-77, -167, 否, 否)。先加角量，再對兩個不同門檻核差與相等。不由示意圖猜角，有限量值核對非射線度量證明。"},"difficulty":{"band":"primary_foundation","level":2,"skills":["角和對兩門檻的殘差"]},"variant":{"family_id":"qf-density14-angle-pair-defects","seed":202610141064,"parameters":{"a":13,"b":0,"angle_unit":"degrees","domain":"finite_nondirected_degree_protocol","operation":"density14_angle_pair_defects","semantic_template":"qf-density14-angle-pair-defects/13"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-10","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261010-advance-20261014-r01-angle-0065","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","language":"zh-Hant","source_mko_ids":["mko-angle"],"title_zh":"角和對兩門檻的殘差","stem_zh":"精確度數協議；非定向0到180度；a=14、b=0。依序列 (a+b−90, a+b−180, 和是否90, 和是否180)。","answer":{"kind":"expression","value":"(-76, -166, 否, 否)","explanation_zh":"角和雙門檻殘差=(-76, -166, 否, 否)。先加角量，再對兩個不同門檻核差與相等。不由示意圖猜角，有限量值核對非射線度量證明。"},"difficulty":{"band":"primary_foundation","level":2,"skills":["角和對兩門檻的殘差"]},"variant":{"family_id":"qf-density14-angle-pair-defects","seed":202610141065,"parameters":{"a":14,"b":0,"angle_unit":"degrees","domain":"finite_nondirected_degree_protocol","operation":"density14_angle_pair_defects","semantic_template":"qf-density14-angle-pair-defects/14"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-10","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261010-advance-20261014-r01-angle-0066","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","language":"zh-Hant","source_mko_ids":["mko-angle"],"title_zh":"角和對兩門檻的殘差","stem_zh":"精確度數協議；非定向0到180度；a=15、b=0。依序列 (a+b−90, a+b−180, 和是否90, 和是否180)。","answer":{"kind":"expression","value":"(-75, -165, 否, 否)","explanation_zh":"角和雙門檻殘差=(-75, -165, 否, 否)。先加角量，再對兩個不同門檻核差與相等。不由示意圖猜角，有限量值核對非射線度量證明。"},"difficulty":{"band":"primary_foundation","level":2,"skills":["角和對兩門檻的殘差"]},"variant":{"family_id":"qf-density14-angle-pair-defects","seed":202610141066,"parameters":{"a":15,"b":0,"angle_unit":"degrees","domain":"finite_nondirected_degree_protocol","operation":"density14_angle_pair_defects","semantic_template":"qf-density14-angle-pair-defects/15"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-10","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261010-advance-20261014-r01-angle-0067","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","language":"zh-Hant","source_mko_ids":["mko-angle"],"title_zh":"角和對兩門檻的殘差","stem_zh":"精確度數協議；非定向0到180度；a=16、b=0。依序列 (a+b−90, a+b−180, 和是否90, 和是否180)。","answer":{"kind":"expression","value":"(-74, -164, 否, 否)","explanation_zh":"角和雙門檻殘差=(-74, -164, 否, 否)。先加角量，再對兩個不同門檻核差與相等。不由示意圖猜角，有限量值核對非射線度量證明。"},"difficulty":{"band":"primary_foundation","level":2,"skills":["角和對兩門檻的殘差"]},"variant":{"family_id":"qf-density14-angle-pair-defects","seed":202610141067,"parameters":{"a":16,"b":0,"angle_unit":"degrees","domain":"finite_nondirected_degree_protocol","operation":"density14_angle_pair_defects","semantic_template":"qf-density14-angle-pair-defects/16"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-10","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261010-advance-20261014-r01-angle-0068","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","language":"zh-Hant","source_mko_ids":["mko-angle"],"title_zh":"角和對兩門檻的殘差","stem_zh":"精確度數協議；非定向0到180度；a=17、b=0。依序列 (a+b−90, a+b−180, 和是否90, 和是否180)。","answer":{"kind":"expression","value":"(-73, -163, 否, 否)","explanation_zh":"角和雙門檻殘差=(-73, -163, 否, 否)。先加角量，再對兩個不同門檻核差與相等。不由示意圖猜角，有限量值核對非射線度量證明。"},"difficulty":{"band":"primary_foundation","level":3,"skills":["角和對兩門檻的殘差"]},"variant":{"family_id":"qf-density14-angle-pair-defects","seed":202610141068,"parameters":{"a":17,"b":0,"angle_unit":"degrees","domain":"finite_nondirected_degree_protocol","operation":"density14_angle_pair_defects","semantic_template":"qf-density14-angle-pair-defects/17"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-10","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261010-advance-20261014-r01-angle-0069","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","language":"zh-Hant","source_mko_ids":["mko-angle"],"title_zh":"角和對兩門檻的殘差","stem_zh":"精確度數協議；非定向0到180度；a=18、b=0。依序列 (a+b−90, a+b−180, 和是否90, 和是否180)。","answer":{"kind":"expression","value":"(-72, -162, 否, 否)","explanation_zh":"角和雙門檻殘差=(-72, -162, 否, 否)。先加角量，再對兩個不同門檻核差與相等。不由示意圖猜角，有限量值核對非射線度量證明。"},"difficulty":{"band":"primary_foundation","level":3,"skills":["角和對兩門檻的殘差"]},"variant":{"family_id":"qf-density14-angle-pair-defects","seed":202610141069,"parameters":{"a":18,"b":0,"angle_unit":"degrees","domain":"finite_nondirected_degree_protocol","operation":"density14_angle_pair_defects","semantic_template":"qf-density14-angle-pair-defects/18"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-10","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261010-advance-20261014-r01-angle-0070","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","language":"zh-Hant","source_mko_ids":["mko-angle"],"title_zh":"角和對兩門檻的殘差","stem_zh":"精確度數協議；非定向0到180度；a=19、b=0。依序列 (a+b−90, a+b−180, 和是否90, 和是否180)。","answer":{"kind":"expression","value":"(-71, -161, 否, 否)","explanation_zh":"角和雙門檻殘差=(-71, -161, 否, 否)。先加角量，再對兩個不同門檻核差與相等。不由示意圖猜角，有限量值核對非射線度量證明。"},"difficulty":{"band":"primary_foundation","level":3,"skills":["角和對兩門檻的殘差"]},"variant":{"family_id":"qf-density14-angle-pair-defects","seed":202610141070,"parameters":{"a":19,"b":0,"angle_unit":"degrees","domain":"finite_nondirected_degree_protocol","operation":"density14_angle_pair_defects","semantic_template":"qf-density14-angle-pair-defects/19"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-10","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261010-advance-20261014-r01-angle-0071","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","language":"zh-Hant","source_mko_ids":["mko-angle"],"title_zh":"角和對兩門檻的殘差","stem_zh":"精確度數協議；非定向0到180度；a=20、b=0。依序列 (a+b−90, a+b−180, 和是否90, 和是否180)。","answer":{"kind":"expression","value":"(-70, -160, 否, 否)","explanation_zh":"角和雙門檻殘差=(-70, -160, 否, 否)。先加角量，再對兩個不同門檻核差與相等。不由示意圖猜角，有限量值核對非射線度量證明。"},"difficulty":{"band":"primary_foundation","level":3,"skills":["角和對兩門檻的殘差"]},"variant":{"family_id":"qf-density14-angle-pair-defects","seed":202610141071,"parameters":{"a":20,"b":0,"angle_unit":"degrees","domain":"finite_nondirected_degree_protocol","operation":"density14_angle_pair_defects","semantic_template":"qf-density14-angle-pair-defects/20"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-10","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261010-advance-20261014-r01-angle-0072","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","language":"zh-Hant","source_mko_ids":["mko-angle"],"title_zh":"角和對兩門檻的殘差","stem_zh":"精確度數協議；非定向0到180度；a=21、b=0。依序列 (a+b−90, a+b−180, 和是否90, 和是否180)。","answer":{"kind":"expression","value":"(-69, -159, 否, 否)","explanation_zh":"角和雙門檻殘差=(-69, -159, 否, 否)。先加角量，再對兩個不同門檻核差與相等。不由示意圖猜角，有限量值核對非射線度量證明。"},"difficulty":{"band":"primary_foundation","level":3,"skills":["角和對兩門檻的殘差"]},"variant":{"family_id":"qf-density14-angle-pair-defects","seed":202610141072,"parameters":{"a":21,"b":0,"angle_unit":"degrees","domain":"finite_nondirected_degree_protocol","operation":"density14_angle_pair_defects","semantic_template":"qf-density14-angle-pair-defects/21"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-10","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261010-advance-20261014-r01-angle-0073","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","language":"zh-Hant","source_mko_ids":["mko-angle"],"title_zh":"角和對兩門檻的殘差","stem_zh":"精確度數協議；非定向0到180度；a=22、b=0。依序列 (a+b−90, a+b−180, 和是否90, 和是否180)。","answer":{"kind":"expression","value":"(-68, -158, 否, 否)","explanation_zh":"角和雙門檻殘差=(-68, -158, 否, 否)。先加角量，再對兩個不同門檻核差與相等。不由示意圖猜角，有限量值核對非射線度量證明。"},"difficulty":{"band":"primary_foundation","level":3,"skills":["角和對兩門檻的殘差"]},"variant":{"family_id":"qf-density14-angle-pair-defects","seed":202610141073,"parameters":{"a":22,"b":0,"angle_unit":"degrees","domain":"finite_nondirected_degree_protocol","operation":"density14_angle_pair_defects","semantic_template":"qf-density14-angle-pair-defects/22"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-10","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261010-advance-20261014-r01-angle-0074","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","language":"zh-Hant","source_mko_ids":["mko-angle"],"title_zh":"角和對兩門檻的殘差","stem_zh":"精確度數協議；非定向0到180度；a=23、b=0。依序列 (a+b−90, a+b−180, 和是否90, 和是否180)。","answer":{"kind":"expression","value":"(-67, -157, 否, 否)","explanation_zh":"角和雙門檻殘差=(-67, -157, 否, 否)。先加角量，再對兩個不同門檻核差與相等。不由示意圖猜角，有限量值核對非射線度量證明。"},"difficulty":{"band":"primary_foundation","level":3,"skills":["角和對兩門檻的殘差"]},"variant":{"family_id":"qf-density14-angle-pair-defects","seed":202610141074,"parameters":{"a":23,"b":0,"angle_unit":"degrees","domain":"finite_nondirected_degree_protocol","operation":"density14_angle_pair_defects","semantic_template":"qf-density14-angle-pair-defects/23"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-10","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261010-advance-20261014-r01-angle-0075","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","language":"zh-Hant","source_mko_ids":["mko-angle"],"title_zh":"角和對兩門檻的殘差","stem_zh":"精確度數協議；非定向0到180度；a=24、b=0。依序列 (a+b−90, a+b−180, 和是否90, 和是否180)。","answer":{"kind":"expression","value":"(-66, -156, 否, 否)","explanation_zh":"角和雙門檻殘差=(-66, -156, 否, 否)。先加角量，再對兩個不同門檻核差與相等。不由示意圖猜角，有限量值核對非射線度量證明。"},"difficulty":{"band":"primary_foundation","level":3,"skills":["角和對兩門檻的殘差"]},"variant":{"family_id":"qf-density14-angle-pair-defects","seed":202610141075,"parameters":{"a":24,"b":0,"angle_unit":"degrees","domain":"finite_nondirected_degree_protocol","operation":"density14_angle_pair_defects","semantic_template":"qf-density14-angle-pair-defects/24"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-10","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261010-advance-20261014-r01-angle-0076","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","language":"zh-Hant","source_mko_ids":["mko-angle"],"title_zh":"三段角量的有序預算","stem_zh":"精確度數協議；非定向0到180度；parts=[0, 0, 0]、target=180。依序答 (三個累加前綴, 總累加≤180資格, target−總累加)。","answer":{"kind":"expression","value":"([0, 0, 0], 是, 180)","explanation_zh":"三段預算前綴與資格=([0, 0, 0], 是, 180)。逐段累加而不重新取模；超界累加量不是本條目角。不由示意圖猜角，有限量值核對非射線度量證明。"},"difficulty":{"band":"primary_foundation","level":1,"skills":["三段角量的有序預算"]},"variant":{"family_id":"qf-density14-angle-three-part-budget","seed":202610141076,"parameters":{"parts":[0,0,0],"target":180,"angle_unit":"degrees","domain":"finite_nondirected_degree_protocol","operation":"density14_angle_three_part_budget","semantic_template":"qf-density14-angle-three-part-budget/[[0,0,0],180]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-10","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261010-advance-20261014-r01-angle-0077","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","language":"zh-Hant","source_mko_ids":["mko-angle"],"title_zh":"三段角量的有序預算","stem_zh":"精確度數協議；非定向0到180度；parts=[90, 90, 0]、target=90。依序答 (三個累加前綴, 總累加≤180資格, target−總累加)。","answer":{"kind":"expression","value":"([90, 180, 180], 是, -90)","explanation_zh":"三段預算前綴與資格=([90, 180, 180], 是, -90)。逐段累加而不重新取模；超界累加量不是本條目角。不由示意圖猜角，有限量值核對非射線度量證明。"},"difficulty":{"band":"primary_foundation","level":1,"skills":["三段角量的有序預算"]},"variant":{"family_id":"qf-density14-angle-three-part-budget","seed":202610141077,"parameters":{"parts":[90,90,0],"target":90,"angle_unit":"degrees","domain":"finite_nondirected_degree_protocol","operation":"density14_angle_three_part_budget","semantic_template":"qf-density14-angle-three-part-budget/[[90,90,0],90]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-10","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261010-advance-20261014-r01-angle-0078","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","language":"zh-Hant","source_mko_ids":["mko-angle"],"title_zh":"三段角量的有序預算","stem_zh":"精確度數協議；非定向0到180度；parts=[90, 90, 90]、target=180。依序答 (三個累加前綴, 總累加≤180資格, target−總累加)。","answer":{"kind":"expression","value":"([90, 180, 270], 否, -90)","explanation_zh":"三段預算前綴與資格=([90, 180, 270], 否, -90)。逐段累加而不重新取模；超界累加量不是本條目角。不由示意圖猜角，有限量值核對非射線度量證明。"},"difficulty":{"band":"primary_foundation","level":1,"skills":["三段角量的有序預算"]},"variant":{"family_id":"qf-density14-angle-three-part-budget","seed":202610141078,"parameters":{"parts":[90,90,90],"target":180,"angle_unit":"degrees","domain":"finite_nondirected_degree_protocol","operation":"density14_angle_three_part_budget","semantic_template":"qf-density14-angle-three-part-budget/[[90,90,90],180]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-10","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261010-advance-20261014-r01-angle-0079","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","language":"zh-Hant","source_mko_ids":["mko-angle"],"title_zh":"三段角量的有序預算","stem_zh":"精確度數協議；非定向0到180度；parts=[180, 1, 0]、target=90。依序答 (三個累加前綴, 總累加≤180資格, target−總累加)。","answer":{"kind":"expression","value":"([180, 181, 181], 否, -91)","explanation_zh":"三段預算前綴與資格=([180, 181, 181], 否, -91)。逐段累加而不重新取模；超界累加量不是本條目角。不由示意圖猜角，有限量值核對非射線度量證明。"},"difficulty":{"band":"primary_foundation","level":1,"skills":["三段角量的有序預算"]},"variant":{"family_id":"qf-density14-angle-three-part-budget","seed":202610141079,"parameters":{"parts":[180,1,0],"target":90,"angle_unit":"degrees","domain":"finite_nondirected_degree_protocol","operation":"density14_angle_three_part_budget","semantic_template":"qf-density14-angle-three-part-budget/[[180,1,0],90]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-10","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261010-advance-20261014-r01-angle-0080","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","language":"zh-Hant","source_mko_ids":["mko-angle"],"title_zh":"三段角量的有序預算","stem_zh":"精確度數協議；非定向0到180度；parts=[4, 90, 5]、target=180。依序答 (三個累加前綴, 總累加≤180資格, target−總累加)。","answer":{"kind":"expression","value":"([4, 94, 99], 是, 81)","explanation_zh":"三段預算前綴與資格=([4, 94, 99], 是, 81)。逐段累加而不重新取模；超界累加量不是本條目角。不由示意圖猜角，有限量值核對非射線度量證明。"},"difficulty":{"band":"primary_foundation","level":1,"skills":["三段角量的有序預算"]},"variant":{"family_id":"qf-density14-angle-three-part-budget","seed":202610141080,"parameters":{"parts":[4,90,5],"target":180,"angle_unit":"degrees","domain":"finite_nondirected_degree_protocol","operation":"density14_angle_three_part_budget","semantic_template":"qf-density14-angle-three-part-budget/[[4,90,5],180]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-10","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261010-advance-20261014-r01-angle-0081","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","language":"zh-Hant","source_mko_ids":["mko-angle"],"title_zh":"三段角量的有序預算","stem_zh":"精確度數協議；非定向0到180度；parts=[5, 90, 6]、target=90。依序答 (三個累加前綴, 總累加≤180資格, target−總累加)。","answer":{"kind":"expression","value":"([5, 95, 101], 是, -11)","explanation_zh":"三段預算前綴與資格=([5, 95, 101], 是, -11)。逐段累加而不重新取模；超界累加量不是本條目角。不由示意圖猜角，有限量值核對非射線度量證明。"},"difficulty":{"band":"primary_foundation","level":1,"skills":["三段角量的有序預算"]},"variant":{"family_id":"qf-density14-angle-three-part-budget","seed":202610141081,"parameters":{"parts":[5,90,6],"target":90,"angle_unit":"degrees","domain":"finite_nondirected_degree_protocol","operation":"density14_angle_three_part_budget","semantic_template":"qf-density14-angle-three-part-budget/[[5,90,6],90]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-10","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261010-advance-20261014-r01-angle-0082","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","language":"zh-Hant","source_mko_ids":["mko-angle"],"title_zh":"三段角量的有序預算","stem_zh":"精確度數協議；非定向0到180度；parts=[6, 90, 7]、target=180。依序答 (三個累加前綴, 總累加≤180資格, target−總累加)。","answer":{"kind":"expression","value":"([6, 96, 103], 是, 77)","explanation_zh":"三段預算前綴與資格=([6, 96, 103], 是, 77)。逐段累加而不重新取模；超界累加量不是本條目角。不由示意圖猜角，有限量值核對非射線度量證明。"},"difficulty":{"band":"primary_foundation","level":1,"skills":["三段角量的有序預算"]},"variant":{"family_id":"qf-density14-angle-three-part-budget","seed":202610141082,"parameters":{"parts":[6,90,7],"target":180,"angle_unit":"degrees","domain":"finite_nondirected_degree_protocol","operation":"density14_angle_three_part_budget","semantic_template":"qf-density14-angle-three-part-budget/[[6,90,7],180]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-10","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261010-advance-20261014-r01-angle-0083","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","language":"zh-Hant","source_mko_ids":["mko-angle"],"title_zh":"三段角量的有序預算","stem_zh":"精確度數協議；非定向0到180度；parts=[7, 90, 8]、target=90。依序答 (三個累加前綴, 總累加≤180資格, target−總累加)。","answer":{"kind":"expression","value":"([7, 97, 105], 是, -15)","explanation_zh":"三段預算前綴與資格=([7, 97, 105], 是, -15)。逐段累加而不重新取模；超界累加量不是本條目角。不由示意圖猜角，有限量值核對非射線度量證明。"},"difficulty":{"band":"primary_foundation","level":1,"skills":["三段角量的有序預算"]},"variant":{"family_id":"qf-density14-angle-three-part-budget","seed":202610141083,"parameters":{"parts":[7,90,8],"target":90,"angle_unit":"degrees","domain":"finite_nondirected_degree_protocol","operation":"density14_angle_three_part_budget","semantic_template":"qf-density14-angle-three-part-budget/[[7,90,8],90]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-10","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261010-advance-20261014-r01-angle-0084","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","language":"zh-Hant","source_mko_ids":["mko-angle"],"title_zh":"三段角量的有序預算","stem_zh":"精確度數協議；非定向0到180度；parts=[8, 90, 9]、target=180。依序答 (三個累加前綴, 總累加≤180資格, target−總累加)。","answer":{"kind":"expression","value":"([8, 98, 107], 是, 73)","explanation_zh":"三段預算前綴與資格=([8, 98, 107], 是, 73)。逐段累加而不重新取模；超界累加量不是本條目角。不由示意圖猜角，有限量值核對非射線度量證明。"},"difficulty":{"band":"primary_foundation","level":2,"skills":["三段角量的有序預算"]},"variant":{"family_id":"qf-density14-angle-three-part-budget","seed":202610141084,"parameters":{"parts":[8,90,9],"target":180,"angle_unit":"degrees","domain":"finite_nondirected_degree_protocol","operation":"density14_angle_three_part_budget","semantic_template":"qf-density14-angle-three-part-budget/[[8,90,9],180]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-10","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261010-advance-20261014-r01-angle-0085","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","language":"zh-Hant","source_mko_ids":["mko-angle"],"title_zh":"三段角量的有序預算","stem_zh":"精確度數協議；非定向0到180度；parts=[9, 90, 10]、target=90。依序答 (三個累加前綴, 總累加≤180資格, target−總累加)。","answer":{"kind":"expression","value":"([9, 99, 109], 是, -19)","explanation_zh":"三段預算前綴與資格=([9, 99, 109], 是, -19)。逐段累加而不重新取模；超界累加量不是本條目角。不由示意圖猜角，有限量值核對非射線度量證明。"},"difficulty":{"band":"primary_foundation","level":2,"skills":["三段角量的有序預算"]},"variant":{"family_id":"qf-density14-angle-three-part-budget","seed":202610141085,"parameters":{"parts":[9,90,10],"target":90,"angle_unit":"degrees","domain":"finite_nondirected_degree_protocol","operation":"density14_angle_three_part_budget","semantic_template":"qf-density14-angle-three-part-budget/[[9,90,10],90]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-10","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261010-advance-20261014-r01-angle-0086","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","language":"zh-Hant","source_mko_ids":["mko-angle"],"title_zh":"三段角量的有序預算","stem_zh":"精確度數協議；非定向0到180度；parts=[10, 90, 11]、target=180。依序答 (三個累加前綴, 總累加≤180資格, target−總累加)。","answer":{"kind":"expression","value":"([10, 100, 111], 是, 69)","explanation_zh":"三段預算前綴與資格=([10, 100, 111], 是, 69)。逐段累加而不重新取模；超界累加量不是本條目角。不由示意圖猜角，有限量值核對非射線度量證明。"},"difficulty":{"band":"primary_foundation","level":2,"skills":["三段角量的有序預算"]},"variant":{"family_id":"qf-density14-angle-three-part-budget","seed":202610141086,"parameters":{"parts":[10,90,11],"target":180,"angle_unit":"degrees","domain":"finite_nondirected_degree_protocol","operation":"density14_angle_three_part_budget","semantic_template":"qf-density14-angle-three-part-budget/[[10,90,11],180]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-10","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261010-advance-20261014-r01-angle-0087","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","language":"zh-Hant","source_mko_ids":["mko-angle"],"title_zh":"三段角量的有序預算","stem_zh":"精確度數協議；非定向0到180度；parts=[11, 90, 12]、target=90。依序答 (三個累加前綴, 總累加≤180資格, target−總累加)。","answer":{"kind":"expression","value":"([11, 101, 113], 是, -23)","explanation_zh":"三段預算前綴與資格=([11, 101, 113], 是, -23)。逐段累加而不重新取模；超界累加量不是本條目角。不由示意圖猜角，有限量值核對非射線度量證明。"},"difficulty":{"band":"primary_foundation","level":2,"skills":["三段角量的有序預算"]},"variant":{"family_id":"qf-density14-angle-three-part-budget","seed":202610141087,"parameters":{"parts":[11,90,12],"target":90,"angle_unit":"degrees","domain":"finite_nondirected_degree_protocol","operation":"density14_angle_three_part_budget","semantic_template":"qf-density14-angle-three-part-budget/[[11,90,12],90]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-10","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261010-advance-20261014-r01-angle-0088","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","language":"zh-Hant","source_mko_ids":["mko-angle"],"title_zh":"三段角量的有序預算","stem_zh":"精確度數協議；非定向0到180度；parts=[12, 90, 13]、target=180。依序答 (三個累加前綴, 總累加≤180資格, target−總累加)。","answer":{"kind":"expression","value":"([12, 102, 115], 是, 65)","explanation_zh":"三段預算前綴與資格=([12, 102, 115], 是, 65)。逐段累加而不重新取模；超界累加量不是本條目角。不由示意圖猜角，有限量值核對非射線度量證明。"},"difficulty":{"band":"primary_foundation","level":2,"skills":["三段角量的有序預算"]},"variant":{"family_id":"qf-density14-angle-three-part-budget","seed":202610141088,"parameters":{"parts":[12,90,13],"target":180,"angle_unit":"degrees","domain":"finite_nondirected_degree_protocol","operation":"density14_angle_three_part_budget","semantic_template":"qf-density14-angle-three-part-budget/[[12,90,13],180]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-10","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261010-advance-20261014-r01-angle-0089","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","language":"zh-Hant","source_mko_ids":["mko-angle"],"title_zh":"三段角量的有序預算","stem_zh":"精確度數協議；非定向0到180度；parts=[13, 90, 14]、target=90。依序答 (三個累加前綴, 總累加≤180資格, target−總累加)。","answer":{"kind":"expression","value":"([13, 103, 117], 是, -27)","explanation_zh":"三段預算前綴與資格=([13, 103, 117], 是, -27)。逐段累加而不重新取模；超界累加量不是本條目角。不由示意圖猜角，有限量值核對非射線度量證明。"},"difficulty":{"band":"primary_foundation","level":2,"skills":["三段角量的有序預算"]},"variant":{"family_id":"qf-density14-angle-three-part-budget","seed":202610141089,"parameters":{"parts":[13,90,14],"target":90,"angle_unit":"degrees","domain":"finite_nondirected_degree_protocol","operation":"density14_angle_three_part_budget","semantic_template":"qf-density14-angle-three-part-budget/[[13,90,14],90]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-10","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261010-advance-20261014-r01-angle-0090","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","language":"zh-Hant","source_mko_ids":["mko-angle"],"title_zh":"三段角量的有序預算","stem_zh":"精確度數協議；非定向0到180度；parts=[14, 90, 15]、target=180。依序答 (三個累加前綴, 總累加≤180資格, target−總累加)。","answer":{"kind":"expression","value":"([14, 104, 119], 是, 61)","explanation_zh":"三段預算前綴與資格=([14, 104, 119], 是, 61)。逐段累加而不重新取模；超界累加量不是本條目角。不由示意圖猜角，有限量值核對非射線度量證明。"},"difficulty":{"band":"primary_foundation","level":2,"skills":["三段角量的有序預算"]},"variant":{"family_id":"qf-density14-angle-three-part-budget","seed":202610141090,"parameters":{"parts":[14,90,15],"target":180,"angle_unit":"degrees","domain":"finite_nondirected_degree_protocol","operation":"density14_angle_three_part_budget","semantic_template":"qf-density14-angle-three-part-budget/[[14,90,15],180]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-10","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261010-advance-20261014-r01-angle-0091","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","language":"zh-Hant","source_mko_ids":["mko-angle"],"title_zh":"三段角量的有序預算","stem_zh":"精確度數協議；非定向0到180度；parts=[15, 90, 16]、target=90。依序答 (三個累加前綴, 總累加≤180資格, target−總累加)。","answer":{"kind":"expression","value":"([15, 105, 121], 是, -31)","explanation_zh":"三段預算前綴與資格=([15, 105, 121], 是, -31)。逐段累加而不重新取模；超界累加量不是本條目角。不由示意圖猜角，有限量值核對非射線度量證明。"},"difficulty":{"band":"primary_foundation","level":2,"skills":["三段角量的有序預算"]},"variant":{"family_id":"qf-density14-angle-three-part-budget","seed":202610141091,"parameters":{"parts":[15,90,16],"target":90,"angle_unit":"degrees","domain":"finite_nondirected_degree_protocol","operation":"density14_angle_three_part_budget","semantic_template":"qf-density14-angle-three-part-budget/[[15,90,16],90]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-10","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261010-advance-20261014-r01-angle-0092","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","language":"zh-Hant","source_mko_ids":["mko-angle"],"title_zh":"三段角量的有序預算","stem_zh":"精確度數協議；非定向0到180度；parts=[16, 90, 17]、target=180。依序答 (三個累加前綴, 總累加≤180資格, target−總累加)。","answer":{"kind":"expression","value":"([16, 106, 123], 是, 57)","explanation_zh":"三段預算前綴與資格=([16, 106, 123], 是, 57)。逐段累加而不重新取模；超界累加量不是本條目角。不由示意圖猜角，有限量值核對非射線度量證明。"},"difficulty":{"band":"primary_foundation","level":2,"skills":["三段角量的有序預算"]},"variant":{"family_id":"qf-density14-angle-three-part-budget","seed":202610141092,"parameters":{"parts":[16,90,17],"target":180,"angle_unit":"degrees","domain":"finite_nondirected_degree_protocol","operation":"density14_angle_three_part_budget","semantic_template":"qf-density14-angle-three-part-budget/[[16,90,17],180]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-10","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261010-advance-20261014-r01-angle-0093","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","language":"zh-Hant","source_mko_ids":["mko-angle"],"title_zh":"三段角量的有序預算","stem_zh":"精確度數協議；非定向0到180度；parts=[17, 90, 18]、target=90。依序答 (三個累加前綴, 總累加≤180資格, target−總累加)。","answer":{"kind":"expression","value":"([17, 107, 125], 是, -35)","explanation_zh":"三段預算前綴與資格=([17, 107, 125], 是, -35)。逐段累加而不重新取模；超界累加量不是本條目角。不由示意圖猜角，有限量值核對非射線度量證明。"},"difficulty":{"band":"primary_foundation","level":3,"skills":["三段角量的有序預算"]},"variant":{"family_id":"qf-density14-angle-three-part-budget","seed":202610141093,"parameters":{"parts":[17,90,18],"target":90,"angle_unit":"degrees","domain":"finite_nondirected_degree_protocol","operation":"density14_angle_three_part_budget","semantic_template":"qf-density14-angle-three-part-budget/[[17,90,18],90]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-10","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261010-advance-20261014-r01-angle-0094","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","language":"zh-Hant","source_mko_ids":["mko-angle"],"title_zh":"三段角量的有序預算","stem_zh":"精確度數協議；非定向0到180度；parts=[18, 90, 19]、target=180。依序答 (三個累加前綴, 總累加≤180資格, target−總累加)。","answer":{"kind":"expression","value":"([18, 108, 127], 是, 53)","explanation_zh":"三段預算前綴與資格=([18, 108, 127], 是, 53)。逐段累加而不重新取模；超界累加量不是本條目角。不由示意圖猜角，有限量值核對非射線度量證明。"},"difficulty":{"band":"primary_foundation","level":3,"skills":["三段角量的有序預算"]},"variant":{"family_id":"qf-density14-angle-three-part-budget","seed":202610141094,"parameters":{"parts":[18,90,19],"target":180,"angle_unit":"degrees","domain":"finite_nondirected_degree_protocol","operation":"density14_angle_three_part_budget","semantic_template":"qf-density14-angle-three-part-budget/[[18,90,19],180]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-10","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261010-advance-20261014-r01-angle-0095","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","language":"zh-Hant","source_mko_ids":["mko-angle"],"title_zh":"三段角量的有序預算","stem_zh":"精確度數協議；非定向0到180度；parts=[19, 90, 20]、target=90。依序答 (三個累加前綴, 總累加≤180資格, target−總累加)。","answer":{"kind":"expression","value":"([19, 109, 129], 是, -39)","explanation_zh":"三段預算前綴與資格=([19, 109, 129], 是, -39)。逐段累加而不重新取模；超界累加量不是本條目角。不由示意圖猜角，有限量值核對非射線度量證明。"},"difficulty":{"band":"primary_foundation","level":3,"skills":["三段角量的有序預算"]},"variant":{"family_id":"qf-density14-angle-three-part-budget","seed":202610141095,"parameters":{"parts":[19,90,20],"target":90,"angle_unit":"degrees","domain":"finite_nondirected_degree_protocol","operation":"density14_angle_three_part_budget","semantic_template":"qf-density14-angle-three-part-budget/[[19,90,20],90]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-10","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261010-advance-20261014-r01-angle-0096","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","language":"zh-Hant","source_mko_ids":["mko-angle"],"title_zh":"三段角量的有序預算","stem_zh":"精確度數協議；非定向0到180度；parts=[20, 90, 21]、target=180。依序答 (三個累加前綴, 總累加≤180資格, target−總累加)。","answer":{"kind":"expression","value":"([20, 110, 131], 是, 49)","explanation_zh":"三段預算前綴與資格=([20, 110, 131], 是, 49)。逐段累加而不重新取模；超界累加量不是本條目角。不由示意圖猜角，有限量值核對非射線度量證明。"},"difficulty":{"band":"primary_foundation","level":3,"skills":["三段角量的有序預算"]},"variant":{"family_id":"qf-density14-angle-three-part-budget","seed":202610141096,"parameters":{"parts":[20,90,21],"target":180,"angle_unit":"degrees","domain":"finite_nondirected_degree_protocol","operation":"density14_angle_three_part_budget","semantic_template":"qf-density14-angle-three-part-budget/[[20,90,21],180]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-10","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261010-advance-20261014-r01-angle-0097","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","language":"zh-Hant","source_mko_ids":["mko-angle"],"title_zh":"三段角量的有序預算","stem_zh":"精確度數協議；非定向0到180度；parts=[21, 90, 22]、target=90。依序答 (三個累加前綴, 總累加≤180資格, target−總累加)。","answer":{"kind":"expression","value":"([21, 111, 133], 是, -43)","explanation_zh":"三段預算前綴與資格=([21, 111, 133], 是, -43)。逐段累加而不重新取模；超界累加量不是本條目角。不由示意圖猜角，有限量值核對非射線度量證明。"},"difficulty":{"band":"primary_foundation","level":3,"skills":["三段角量的有序預算"]},"variant":{"family_id":"qf-density14-angle-three-part-budget","seed":202610141097,"parameters":{"parts":[21,90,22],"target":90,"angle_unit":"degrees","domain":"finite_nondirected_degree_protocol","operation":"density14_angle_three_part_budget","semantic_template":"qf-density14-angle-three-part-budget/[[21,90,22],90]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-10","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261010-advance-20261014-r01-angle-0098","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","language":"zh-Hant","source_mko_ids":["mko-angle"],"title_zh":"三段角量的有序預算","stem_zh":"精確度數協議；非定向0到180度；parts=[22, 90, 23]、target=180。依序答 (三個累加前綴, 總累加≤180資格, target−總累加)。","answer":{"kind":"expression","value":"([22, 112, 135], 是, 45)","explanation_zh":"三段預算前綴與資格=([22, 112, 135], 是, 45)。逐段累加而不重新取模；超界累加量不是本條目角。不由示意圖猜角，有限量值核對非射線度量證明。"},"difficulty":{"band":"primary_foundation","level":3,"skills":["三段角量的有序預算"]},"variant":{"family_id":"qf-density14-angle-three-part-budget","seed":202610141098,"parameters":{"parts":[22,90,23],"target":180,"angle_unit":"degrees","domain":"finite_nondirected_degree_protocol","operation":"density14_angle_three_part_budget","semantic_template":"qf-density14-angle-three-part-budget/[[22,90,23],180]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-10","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261010-advance-20261014-r01-angle-0099","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","language":"zh-Hant","source_mko_ids":["mko-angle"],"title_zh":"三段角量的有序預算","stem_zh":"精確度數協議；非定向0到180度；parts=[23, 90, 24]、target=90。依序答 (三個累加前綴, 總累加≤180資格, target−總累加)。","answer":{"kind":"expression","value":"([23, 113, 137], 是, -47)","explanation_zh":"三段預算前綴與資格=([23, 113, 137], 是, -47)。逐段累加而不重新取模；超界累加量不是本條目角。不由示意圖猜角，有限量值核對非射線度量證明。"},"difficulty":{"band":"primary_foundation","level":3,"skills":["三段角量的有序預算"]},"variant":{"family_id":"qf-density14-angle-three-part-budget","seed":202610141099,"parameters":{"parts":[23,90,24],"target":90,"angle_unit":"degrees","domain":"finite_nondirected_degree_protocol","operation":"density14_angle_three_part_budget","semantic_template":"qf-density14-angle-three-part-budget/[[23,90,24],90]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-10","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261010-advance-20261014-r01-angle-0100","batch_id":"batch-20261010-advance-20261014-r01-angle-foundations","language":"zh-Hant","source_mko_ids":["mko-angle"],"title_zh":"三段角量的有序預算","stem_zh":"精確度數協議；非定向0到180度；parts=[24, 90, 25]、target=180。依序答 (三個累加前綴, 總累加≤180資格, target−總累加)。","answer":{"kind":"expression","value":"([24, 114, 139], 是, 41)","explanation_zh":"三段預算前綴與資格=([24, 114, 139], 是, 41)。逐段累加而不重新取模；超界累加量不是本條目角。不由示意圖猜角，有限量值核對非射線度量證明。"},"difficulty":{"band":"primary_foundation","level":3,"skills":["三段角量的有序預算"]},"variant":{"family_id":"qf-density14-angle-three-part-budget","seed":202610141100,"parameters":{"parts":[24,90,25],"target":180,"angle_unit":"degrees","domain":"finite_nondirected_degree_protocol","operation":"density14_angle_three_part_budget","semantic_template":"qf-density14-angle-three-part-budget/[[24,90,25],180]"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-10","contract_version":"ocme-question-factory-v0.1"}}