{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r05-right-triangle-0001","batch_id":"batch-20261008-advance-20261012-r05-right-triangle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"b5feaed84460ffaf35bc4304bdf2a2ac8375983ee7eb094f00d044e6f5b6839d","family_id":"qf-density12-right-triangle-angle-remainder","seed":202610125001,"semantic_template":"qf-density12-right-triangle-angle-remainder/1"},"fields":{"title":"Acute-Angle Remainder in a Given Right Triangle","stem":"Exact degrees: a nondegenerate plane triangle has γ=90° and α=1°. Give (β in degrees, α+β in degrees).","answer":{"kind":"expression","value":"(89, 90)","explanation":"Under the explicit right-angle and triangle-angle-sum premises, subtract α from 90. No tolerance or unstated geometric construction is used. The exact result, retaining the requested order, is (89, 90)."},"skills":["Acute-Angle Remainder in a Given Right Triangle"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r05-right-triangle-0002","batch_id":"batch-20261008-advance-20261012-r05-right-triangle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"52697d0822ca7d03ee4c006444097a9a93f8b9d9fd3d4fda8656f28263a60f3f","family_id":"qf-density12-right-triangle-angle-remainder","seed":202610125002,"semantic_template":"qf-density12-right-triangle-angle-remainder/89"},"fields":{"title":"Acute-Angle Remainder in a Given Right Triangle","stem":"Exact degrees: a nondegenerate plane triangle has γ=90° and α=89°. Give (β in degrees, α+β in degrees).","answer":{"kind":"expression","value":"(1, 90)","explanation":"Under the explicit right-angle and triangle-angle-sum premises, subtract α from 90. No tolerance or unstated geometric construction is used. The exact result, retaining the requested order, is (1, 90)."},"skills":["Acute-Angle Remainder in a Given Right Triangle"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r05-right-triangle-0003","batch_id":"batch-20261008-advance-20261012-r05-right-triangle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"962b63e8c00d93057a351fc328c03e4cbeb13756007de1d276769297177323d1","family_id":"qf-density12-right-triangle-angle-remainder","seed":202610125003,"semantic_template":"qf-density12-right-triangle-angle-remainder/45"},"fields":{"title":"Acute-Angle Remainder in a Given Right Triangle","stem":"Exact degrees: a nondegenerate plane triangle has γ=90° and α=45°. Give (β in degrees, α+β in degrees).","answer":{"kind":"expression","value":"(45, 90)","explanation":"Under the explicit right-angle and triangle-angle-sum premises, subtract α from 90. No tolerance or unstated geometric construction is used. The exact result, retaining the requested order, is (45, 90)."},"skills":["Acute-Angle Remainder in a Given Right Triangle"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r05-right-triangle-0004","batch_id":"batch-20261008-advance-20261012-r05-right-triangle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"c754af542d896a753198a2c00b2ad8d2d4d649d58c657f1d13faf223ab0b2d0b","family_id":"qf-density12-right-triangle-angle-remainder","seed":202610125004,"semantic_template":"qf-density12-right-triangle-angle-remainder/5"},"fields":{"title":"Acute-Angle Remainder in a Given Right Triangle","stem":"Exact degrees: a nondegenerate plane triangle has γ=90° and α=5°. Give (β in degrees, α+β in degrees).","answer":{"kind":"expression","value":"(85, 90)","explanation":"Under the explicit right-angle and triangle-angle-sum premises, subtract α from 90. No tolerance or unstated geometric construction is used. The exact result, retaining the requested order, is (85, 90)."},"skills":["Acute-Angle Remainder in a Given Right Triangle"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r05-right-triangle-0005","batch_id":"batch-20261008-advance-20261012-r05-right-triangle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"0574be14a862f1378b533347e0f711e273b936136287c276371a004e2a8f8660","family_id":"qf-density12-right-triangle-angle-remainder","seed":202610125005,"semantic_template":"qf-density12-right-triangle-angle-remainder/6"},"fields":{"title":"Acute-Angle Remainder in a Given Right Triangle","stem":"Exact degrees: a nondegenerate plane triangle has γ=90° and α=6°. Give (β in degrees, α+β in degrees).","answer":{"kind":"expression","value":"(84, 90)","explanation":"Under the explicit right-angle and triangle-angle-sum premises, subtract α from 90. No tolerance or unstated geometric construction is used. The exact result, retaining the requested order, is (84, 90)."},"skills":["Acute-Angle Remainder in a Given Right Triangle"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r05-right-triangle-0006","batch_id":"batch-20261008-advance-20261012-r05-right-triangle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"8cbc6c9d914287f3c7bdafedf64130bc8252284266b97af6e998c53c10b284c3","family_id":"qf-density12-right-triangle-angle-remainder","seed":202610125006,"semantic_template":"qf-density12-right-triangle-angle-remainder/7"},"fields":{"title":"Acute-Angle Remainder in a Given Right Triangle","stem":"Exact degrees: a nondegenerate plane triangle has γ=90° and α=7°. Give (β in degrees, α+β in degrees).","answer":{"kind":"expression","value":"(83, 90)","explanation":"Under the explicit right-angle and triangle-angle-sum premises, subtract α from 90. No tolerance or unstated geometric construction is used. The exact result, retaining the requested order, is (83, 90)."},"skills":["Acute-Angle Remainder in a Given Right Triangle"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r05-right-triangle-0007","batch_id":"batch-20261008-advance-20261012-r05-right-triangle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"1d42164d8ef63b96fd435bf7f2455ae0b156c0adc87002ea61cc9db4981774d9","family_id":"qf-density12-right-triangle-angle-remainder","seed":202610125007,"semantic_template":"qf-density12-right-triangle-angle-remainder/8"},"fields":{"title":"Acute-Angle Remainder in a Given Right Triangle","stem":"Exact degrees: a nondegenerate plane triangle has γ=90° and α=8°. Give (β in degrees, α+β in degrees).","answer":{"kind":"expression","value":"(82, 90)","explanation":"Under the explicit right-angle and triangle-angle-sum premises, subtract α from 90. No tolerance or unstated geometric construction is used. The exact result, retaining the requested order, is (82, 90)."},"skills":["Acute-Angle Remainder in a Given Right Triangle"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r05-right-triangle-0008","batch_id":"batch-20261008-advance-20261012-r05-right-triangle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"6a878b2b328c8ef1b78e95006f02a4e504872041279ae136c6c0c18e18de8b88","family_id":"qf-density12-right-triangle-angle-remainder","seed":202610125008,"semantic_template":"qf-density12-right-triangle-angle-remainder/9"},"fields":{"title":"Acute-Angle Remainder in a Given Right Triangle","stem":"Exact degrees: a nondegenerate plane triangle has γ=90° and α=9°. Give (β in degrees, α+β in degrees).","answer":{"kind":"expression","value":"(81, 90)","explanation":"Under the explicit right-angle and triangle-angle-sum premises, subtract α from 90. No tolerance or unstated geometric construction is used. The exact result, retaining the requested order, is (81, 90)."},"skills":["Acute-Angle Remainder in a Given Right Triangle"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r05-right-triangle-0009","batch_id":"batch-20261008-advance-20261012-r05-right-triangle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"8e9569898832cfc63d688fbe3bb092957aed88e419a3762562fa18dffd3712a7","family_id":"qf-density12-right-triangle-angle-remainder","seed":202610125009,"semantic_template":"qf-density12-right-triangle-angle-remainder/10"},"fields":{"title":"Acute-Angle Remainder in a Given Right Triangle","stem":"Exact degrees: a nondegenerate plane triangle has γ=90° and α=10°. Give (β in degrees, α+β in degrees).","answer":{"kind":"expression","value":"(80, 90)","explanation":"Under the explicit right-angle and triangle-angle-sum premises, subtract α from 90. No tolerance or unstated geometric construction is used. The exact result, retaining the requested order, is (80, 90)."},"skills":["Acute-Angle Remainder in a Given Right Triangle"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r05-right-triangle-0010","batch_id":"batch-20261008-advance-20261012-r05-right-triangle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"a3db892ce6a63266da4d80c852159a0af275a9f3e7a198b308b9e7cfe601a084","family_id":"qf-density12-right-triangle-angle-remainder","seed":202610125010,"semantic_template":"qf-density12-right-triangle-angle-remainder/11"},"fields":{"title":"Acute-Angle Remainder in a Given Right Triangle","stem":"Exact degrees: a nondegenerate plane triangle has γ=90° and α=11°. Give (β in degrees, α+β in degrees).","answer":{"kind":"expression","value":"(79, 90)","explanation":"Under the explicit right-angle and triangle-angle-sum premises, subtract α from 90. No tolerance or unstated geometric construction is used. The exact result, retaining the requested order, is (79, 90)."},"skills":["Acute-Angle Remainder in a Given Right Triangle"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r05-right-triangle-0011","batch_id":"batch-20261008-advance-20261012-r05-right-triangle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"5086f6ed111b07349a1d50c1a7b178275c7579ff955d760f5d5245e40f306fc2","family_id":"qf-density12-right-triangle-angle-remainder","seed":202610125011,"semantic_template":"qf-density12-right-triangle-angle-remainder/12"},"fields":{"title":"Acute-Angle Remainder in a Given Right Triangle","stem":"Exact degrees: a nondegenerate plane triangle has γ=90° and α=12°. Give (β in degrees, α+β in degrees).","answer":{"kind":"expression","value":"(78, 90)","explanation":"Under the explicit right-angle and triangle-angle-sum premises, subtract α from 90. No tolerance or unstated geometric construction is used. The exact result, retaining the requested order, is (78, 90)."},"skills":["Acute-Angle Remainder in a Given Right Triangle"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r05-right-triangle-0012","batch_id":"batch-20261008-advance-20261012-r05-right-triangle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"822d11027dce7b7131d4a74a90338888a7fd10df87c5570a566058216d79cde3","family_id":"qf-density12-right-triangle-angle-remainder","seed":202610125012,"semantic_template":"qf-density12-right-triangle-angle-remainder/13"},"fields":{"title":"Acute-Angle Remainder in a Given Right Triangle","stem":"Exact degrees: a nondegenerate plane triangle has γ=90° and α=13°. Give (β in degrees, α+β in degrees).","answer":{"kind":"expression","value":"(77, 90)","explanation":"Under the explicit right-angle and triangle-angle-sum premises, subtract α from 90. No tolerance or unstated geometric construction is used. The exact result, retaining the requested order, is (77, 90)."},"skills":["Acute-Angle Remainder in a Given Right Triangle"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r05-right-triangle-0013","batch_id":"batch-20261008-advance-20261012-r05-right-triangle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"81459844c8e772ccbfa4c39f29b67637f372aae9aae137eb1e1c740514c12edb","family_id":"qf-density12-right-triangle-angle-remainder","seed":202610125013,"semantic_template":"qf-density12-right-triangle-angle-remainder/14"},"fields":{"title":"Acute-Angle Remainder in a Given Right Triangle","stem":"Exact degrees: a nondegenerate plane triangle has γ=90° and α=14°. Give (β in degrees, α+β in degrees).","answer":{"kind":"expression","value":"(76, 90)","explanation":"Under the explicit right-angle and triangle-angle-sum premises, subtract α from 90. No tolerance or unstated geometric construction is used. The exact result, retaining the requested order, is (76, 90)."},"skills":["Acute-Angle Remainder in a Given Right Triangle"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r05-right-triangle-0014","batch_id":"batch-20261008-advance-20261012-r05-right-triangle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"233964f93f60b0e20e0d6c53cfcb07aa2331caa1cacbaeee3d8e170e4c095735","family_id":"qf-density12-right-triangle-angle-remainder","seed":202610125014,"semantic_template":"qf-density12-right-triangle-angle-remainder/15"},"fields":{"title":"Acute-Angle Remainder in a Given Right Triangle","stem":"Exact degrees: a nondegenerate plane triangle has γ=90° and α=15°. Give (β in degrees, α+β in degrees).","answer":{"kind":"expression","value":"(75, 90)","explanation":"Under the explicit right-angle and triangle-angle-sum premises, subtract α from 90. No tolerance or unstated geometric construction is used. The exact result, retaining the requested order, is (75, 90)."},"skills":["Acute-Angle Remainder in a Given Right Triangle"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r05-right-triangle-0015","batch_id":"batch-20261008-advance-20261012-r05-right-triangle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"c52a709dfb25534ac75825b09343615fc915980712c5ff4f6976da5ab9ea5cb2","family_id":"qf-density12-right-triangle-angle-remainder","seed":202610125015,"semantic_template":"qf-density12-right-triangle-angle-remainder/16"},"fields":{"title":"Acute-Angle Remainder in a Given Right Triangle","stem":"Exact degrees: a nondegenerate plane triangle has γ=90° and α=16°. Give (β in degrees, α+β in degrees).","answer":{"kind":"expression","value":"(74, 90)","explanation":"Under the explicit right-angle and triangle-angle-sum premises, subtract α from 90. No tolerance or unstated geometric construction is used. The exact result, retaining the requested order, is (74, 90)."},"skills":["Acute-Angle Remainder in a Given Right Triangle"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r05-right-triangle-0016","batch_id":"batch-20261008-advance-20261012-r05-right-triangle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"0c6642400299cb87c51cf41a38c61634352a7d28b90f29e781bb3f9257fabea8","family_id":"qf-density12-right-triangle-angle-remainder","seed":202610125016,"semantic_template":"qf-density12-right-triangle-angle-remainder/17"},"fields":{"title":"Acute-Angle Remainder in a Given Right Triangle","stem":"Exact degrees: a nondegenerate plane triangle has γ=90° and α=17°. Give (β in degrees, α+β in degrees).","answer":{"kind":"expression","value":"(73, 90)","explanation":"Under the explicit right-angle and triangle-angle-sum premises, subtract α from 90. No tolerance or unstated geometric construction is used. The exact result, retaining the requested order, is (73, 90)."},"skills":["Acute-Angle Remainder in a Given Right Triangle"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r05-right-triangle-0017","batch_id":"batch-20261008-advance-20261012-r05-right-triangle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"4ef56773479dc88a4ba5f0b0d63362c4033041c3d448cd3865b33b34030779ca","family_id":"qf-density12-right-triangle-angle-remainder","seed":202610125017,"semantic_template":"qf-density12-right-triangle-angle-remainder/18"},"fields":{"title":"Acute-Angle Remainder in a Given Right Triangle","stem":"Exact degrees: a nondegenerate plane triangle has γ=90° and α=18°. Give (β in degrees, α+β in degrees).","answer":{"kind":"expression","value":"(72, 90)","explanation":"Under the explicit right-angle and triangle-angle-sum premises, subtract α from 90. No tolerance or unstated geometric construction is used. The exact result, retaining the requested order, is (72, 90)."},"skills":["Acute-Angle Remainder in a Given Right Triangle"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r05-right-triangle-0018","batch_id":"batch-20261008-advance-20261012-r05-right-triangle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"c3fc39969a8a8932ee9c314381e9bdda061db0442b9f3e8e353c4ff91a991650","family_id":"qf-density12-right-triangle-angle-remainder","seed":202610125018,"semantic_template":"qf-density12-right-triangle-angle-remainder/19"},"fields":{"title":"Acute-Angle Remainder in a Given Right Triangle","stem":"Exact degrees: a nondegenerate plane triangle has γ=90° and α=19°. Give (β in degrees, α+β in degrees).","answer":{"kind":"expression","value":"(71, 90)","explanation":"Under the explicit right-angle and triangle-angle-sum premises, subtract α from 90. No tolerance or unstated geometric construction is used. The exact result, retaining the requested order, is (71, 90)."},"skills":["Acute-Angle Remainder in a Given Right Triangle"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r05-right-triangle-0019","batch_id":"batch-20261008-advance-20261012-r05-right-triangle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"6e49d6c65d2722d44a1bf2426ea17510693acaddf0d26a1b896ff1d0a1675a90","family_id":"qf-density12-right-triangle-angle-remainder","seed":202610125019,"semantic_template":"qf-density12-right-triangle-angle-remainder/20"},"fields":{"title":"Acute-Angle Remainder in a Given Right Triangle","stem":"Exact degrees: a nondegenerate plane triangle has γ=90° and α=20°. Give (β in degrees, α+β in degrees).","answer":{"kind":"expression","value":"(70, 90)","explanation":"Under the explicit right-angle and triangle-angle-sum premises, subtract α from 90. No tolerance or unstated geometric construction is used. The exact result, retaining the requested order, is (70, 90)."},"skills":["Acute-Angle Remainder in a Given Right Triangle"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r05-right-triangle-0020","batch_id":"batch-20261008-advance-20261012-r05-right-triangle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"a443ac66733be448a481b1b2d1d8166e767ec3444cece3dfb6a1cd50bec598de","family_id":"qf-density12-right-triangle-angle-remainder","seed":202610125020,"semantic_template":"qf-density12-right-triangle-angle-remainder/21"},"fields":{"title":"Acute-Angle Remainder in a Given Right Triangle","stem":"Exact degrees: a nondegenerate plane triangle has γ=90° and α=21°. Give (β in degrees, α+β in degrees).","answer":{"kind":"expression","value":"(69, 90)","explanation":"Under the explicit right-angle and triangle-angle-sum premises, subtract α from 90. No tolerance or unstated geometric construction is used. The exact result, retaining the requested order, is (69, 90)."},"skills":["Acute-Angle Remainder in a Given Right Triangle"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r05-right-triangle-0021","batch_id":"batch-20261008-advance-20261012-r05-right-triangle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"b6c92936d8051ffcba8cf393320c0eba757d789506318d50a0b7671ef3ddcbb9","family_id":"qf-density12-right-triangle-angle-remainder","seed":202610125021,"semantic_template":"qf-density12-right-triangle-angle-remainder/22"},"fields":{"title":"Acute-Angle Remainder in a Given Right Triangle","stem":"Exact degrees: a nondegenerate plane triangle has γ=90° and α=22°. Give (β in degrees, α+β in degrees).","answer":{"kind":"expression","value":"(68, 90)","explanation":"Under the explicit right-angle and triangle-angle-sum premises, subtract α from 90. No tolerance or unstated geometric construction is used. The exact result, retaining the requested order, is (68, 90)."},"skills":["Acute-Angle Remainder in a Given Right Triangle"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r05-right-triangle-0022","batch_id":"batch-20261008-advance-20261012-r05-right-triangle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"89bfddf1b1b187f984b38c02772518b652b7b2afb7b5f88f3559d6a4fef638b1","family_id":"qf-density12-right-triangle-angle-remainder","seed":202610125022,"semantic_template":"qf-density12-right-triangle-angle-remainder/23"},"fields":{"title":"Acute-Angle Remainder in a Given Right Triangle","stem":"Exact degrees: a nondegenerate plane triangle has γ=90° and α=23°. Give (β in degrees, α+β in degrees).","answer":{"kind":"expression","value":"(67, 90)","explanation":"Under the explicit right-angle and triangle-angle-sum premises, subtract α from 90. No tolerance or unstated geometric construction is used. The exact result, retaining the requested order, is (67, 90)."},"skills":["Acute-Angle Remainder in a Given Right Triangle"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r05-right-triangle-0023","batch_id":"batch-20261008-advance-20261012-r05-right-triangle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"9f50464521f14897dc3eb601825b4ded75ea585ffe8461b51a9393a3d9f18659","family_id":"qf-density12-right-triangle-angle-remainder","seed":202610125023,"semantic_template":"qf-density12-right-triangle-angle-remainder/24"},"fields":{"title":"Acute-Angle Remainder in a Given Right Triangle","stem":"Exact degrees: a nondegenerate plane triangle has γ=90° and α=24°. Give (β in degrees, α+β in degrees).","answer":{"kind":"expression","value":"(66, 90)","explanation":"Under the explicit right-angle and triangle-angle-sum premises, subtract α from 90. No tolerance or unstated geometric construction is used. The exact result, retaining the requested order, is (66, 90)."},"skills":["Acute-Angle Remainder in a Given Right Triangle"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r05-right-triangle-0024","batch_id":"batch-20261008-advance-20261012-r05-right-triangle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"127cb611b4bf8286f39adfd2a5233ee568894ef1672ff11b3930e0fcf63e743c","family_id":"qf-density12-right-triangle-angle-remainder","seed":202610125024,"semantic_template":"qf-density12-right-triangle-angle-remainder/25"},"fields":{"title":"Acute-Angle Remainder in a Given Right Triangle","stem":"Exact degrees: a nondegenerate plane triangle has γ=90° and α=25°. Give (β in degrees, α+β in degrees).","answer":{"kind":"expression","value":"(65, 90)","explanation":"Under the explicit right-angle and triangle-angle-sum premises, subtract α from 90. No tolerance or unstated geometric construction is used. The exact result, retaining the requested order, is (65, 90)."},"skills":["Acute-Angle Remainder in a Given Right Triangle"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r05-right-triangle-0025","batch_id":"batch-20261008-advance-20261012-r05-right-triangle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"dae61c7598d5a55d43a347662725d131450079b5e050597249cbc7d46e9d19ac","family_id":"qf-density12-right-triangle-angle-remainder","seed":202610125025,"semantic_template":"qf-density12-right-triangle-angle-remainder/26"},"fields":{"title":"Acute-Angle Remainder in a Given Right Triangle","stem":"Exact degrees: a nondegenerate plane triangle has γ=90° and α=26°. Give (β in degrees, α+β in degrees).","answer":{"kind":"expression","value":"(64, 90)","explanation":"Under the explicit right-angle and triangle-angle-sum premises, subtract α from 90. No tolerance or unstated geometric construction is used. The exact result, retaining the requested order, is (64, 90)."},"skills":["Acute-Angle Remainder in a Given Right Triangle"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r05-right-triangle-0026","batch_id":"batch-20261008-advance-20261012-r05-right-triangle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"a8f2139a524e17a8af746a643df9d530dea6716abb29546bac3a1a51348ffeee","family_id":"qf-density12-right-triangle-validity-pair","seed":202610125026,"semantic_template":"qf-density12-right-triangle-validity-pair/[0,90,90]"},"fields":{"title":"Candidate Triangle-Angle Qualification","stem":"Exact-degree candidate angles=[90, 90, 0]. Give (all positive with sum 180?, qualified and containing a 90° angle?, signed angle sum−180).","answer":{"kind":"expression","value":"(No, No, 0)","explanation":"Check positivity and the exact sum before the right angle; zero or negative candidate angles may be rejected even if the sum defect is zero. No constructed triangle is claimed. The exact result, retaining the requested order, is (No, No, 0)."},"skills":["Candidate Triangle-Angle Qualification"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r05-right-triangle-0027","batch_id":"batch-20261008-advance-20261012-r05-right-triangle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"591efca1a6f002eb1153d51b52387e3b3f6c9f5034093a9e599b68b6d0460f10","family_id":"qf-density12-right-triangle-validity-pair","seed":202610125027,"semantic_template":"qf-density12-right-triangle-validity-pair/[60,60,60]"},"fields":{"title":"Candidate Triangle-Angle Qualification","stem":"Exact-degree candidate angles=[60, 60, 60]. Give (all positive with sum 180?, qualified and containing a 90° angle?, signed angle sum−180).","answer":{"kind":"expression","value":"(Yes, No, 0)","explanation":"Check positivity and the exact sum before the right angle; zero or negative candidate angles may be rejected even if the sum defect is zero. No constructed triangle is claimed. The exact result, retaining the requested order, is (Yes, No, 0)."},"skills":["Candidate Triangle-Angle Qualification"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r05-right-triangle-0028","batch_id":"batch-20261008-advance-20261012-r05-right-triangle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"d84a6237ceab3c45cf829418605ee1111ae355ef17533a914110378986a7fabd","family_id":"qf-density12-right-triangle-validity-pair","seed":202610125028,"semantic_template":"qf-density12-right-triangle-validity-pair/[30,60,90]"},"fields":{"title":"Candidate Triangle-Angle Qualification","stem":"Exact-degree candidate angles=[90, 30, 60]. Give (all positive with sum 180?, qualified and containing a 90° angle?, signed angle sum−180).","answer":{"kind":"expression","value":"(Yes, Yes, 0)","explanation":"Check positivity and the exact sum before the right angle; zero or negative candidate angles may be rejected even if the sum defect is zero. No constructed triangle is claimed. The exact result, retaining the requested order, is (Yes, Yes, 0)."},"skills":["Candidate Triangle-Angle Qualification"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r05-right-triangle-0029","batch_id":"batch-20261008-advance-20261012-r05-right-triangle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"dfab7df86bc72210d7ee93fad463f43edab88ba2eecb0b5e18d8ecf2deab846c","family_id":"qf-density12-right-triangle-validity-pair","seed":202610125029,"semantic_template":"qf-density12-right-triangle-validity-pair/[-1,90,91]"},"fields":{"title":"Candidate Triangle-Angle Qualification","stem":"Exact-degree candidate angles=[-1, 90, 91]. Give (all positive with sum 180?, qualified and containing a 90° angle?, signed angle sum−180).","answer":{"kind":"expression","value":"(No, No, 0)","explanation":"Check positivity and the exact sum before the right angle; zero or negative candidate angles may be rejected even if the sum defect is zero. No constructed triangle is claimed. The exact result, retaining the requested order, is (No, No, 0)."},"skills":["Candidate Triangle-Angle Qualification"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r05-right-triangle-0030","batch_id":"batch-20261008-advance-20261012-r05-right-triangle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"1f705e73532c6cb6a19871729fce58d2ed1ca5b8b9f38754a48414375b95815f","family_id":"qf-density12-right-triangle-validity-pair","seed":202610125030,"semantic_template":"qf-density12-right-triangle-validity-pair/[45,46,90]"},"fields":{"title":"Candidate Triangle-Angle Qualification","stem":"Exact-degree candidate angles=[90, 45, 46]. Give (all positive with sum 180?, qualified and containing a 90° angle?, signed angle sum−180).","answer":{"kind":"expression","value":"(No, No, 1)","explanation":"Check positivity and the exact sum before the right angle; zero or negative candidate angles may be rejected even if the sum defect is zero. No constructed triangle is claimed. The exact result, retaining the requested order, is (No, No, 1)."},"skills":["Candidate Triangle-Angle Qualification"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r05-right-triangle-0031","batch_id":"batch-20261008-advance-20261012-r05-right-triangle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"3c5a42d62b1076c4616da479c50bae2450ba42bae5aeff6d7aa903a048a92695","family_id":"qf-density12-right-triangle-validity-pair","seed":202610125031,"semantic_template":"qf-density12-right-triangle-validity-pair/[0,0,180]"},"fields":{"title":"Candidate Triangle-Angle Qualification","stem":"Exact-degree candidate angles=[0, 0, 180]. Give (all positive with sum 180?, qualified and containing a 90° angle?, signed angle sum−180).","answer":{"kind":"expression","value":"(No, No, 0)","explanation":"Check positivity and the exact sum before the right angle; zero or negative candidate angles may be rejected even if the sum defect is zero. No constructed triangle is claimed. The exact result, retaining the requested order, is (No, No, 0)."},"skills":["Candidate Triangle-Angle Qualification"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r05-right-triangle-0032","batch_id":"batch-20261008-advance-20261012-r05-right-triangle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"c08b1c74f4d724c9dd61d9913ec913f46dd3125b5e7ee98416511fe7c2988104","family_id":"qf-density12-right-triangle-validity-pair","seed":202610125032,"semantic_template":"qf-density12-right-triangle-validity-pair/[7,83,90]"},"fields":{"title":"Candidate Triangle-Angle Qualification","stem":"Exact-degree candidate angles=[90, 7, 83]. Give (all positive with sum 180?, qualified and containing a 90° angle?, signed angle sum−180).","answer":{"kind":"expression","value":"(Yes, Yes, 0)","explanation":"Check positivity and the exact sum before the right angle; zero or negative candidate angles may be rejected even if the sum defect is zero. No constructed triangle is claimed. The exact result, retaining the requested order, is (Yes, Yes, 0)."},"skills":["Candidate Triangle-Angle Qualification"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r05-right-triangle-0033","batch_id":"batch-20261008-advance-20261012-r05-right-triangle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"5231793461c8b6ba12f1db08dbff578a4980321b63c8ceaa413b2fb8731b34b2","family_id":"qf-density12-right-triangle-validity-pair","seed":202610125033,"semantic_template":"qf-density12-right-triangle-validity-pair/[8,82,90]"},"fields":{"title":"Candidate Triangle-Angle Qualification","stem":"Exact-degree candidate angles=[90, 8, 82]. Give (all positive with sum 180?, qualified and containing a 90° angle?, signed angle sum−180).","answer":{"kind":"expression","value":"(Yes, Yes, 0)","explanation":"Check positivity and the exact sum before the right angle; zero or negative candidate angles may be rejected even if the sum defect is zero. No constructed triangle is claimed. The exact result, retaining the requested order, is (Yes, Yes, 0)."},"skills":["Candidate Triangle-Angle Qualification"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r05-right-triangle-0034","batch_id":"batch-20261008-advance-20261012-r05-right-triangle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"fe49506e3f13532940bda0bf1833bef045b61083f1111c2dfd44bab8957540dd","family_id":"qf-density12-right-triangle-validity-pair","seed":202610125034,"semantic_template":"qf-density12-right-triangle-validity-pair/[9,81,90]"},"fields":{"title":"Candidate Triangle-Angle Qualification","stem":"Exact-degree candidate angles=[90, 9, 81]. Give (all positive with sum 180?, qualified and containing a 90° angle?, signed angle sum−180).","answer":{"kind":"expression","value":"(Yes, Yes, 0)","explanation":"Check positivity and the exact sum before the right angle; zero or negative candidate angles may be rejected even if the sum defect is zero. No constructed triangle is claimed. The exact result, retaining the requested order, is (Yes, Yes, 0)."},"skills":["Candidate Triangle-Angle Qualification"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r05-right-triangle-0035","batch_id":"batch-20261008-advance-20261012-r05-right-triangle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"2fc863f554bfe8a73fec17656c22d006bd49c0951491f61d45697d86d3ee125d","family_id":"qf-density12-right-triangle-validity-pair","seed":202610125035,"semantic_template":"qf-density12-right-triangle-validity-pair/[10,80,90]"},"fields":{"title":"Candidate Triangle-Angle Qualification","stem":"Exact-degree candidate angles=[90, 10, 80]. Give (all positive with sum 180?, qualified and containing a 90° angle?, signed angle sum−180).","answer":{"kind":"expression","value":"(Yes, Yes, 0)","explanation":"Check positivity and the exact sum before the right angle; zero or negative candidate angles may be rejected even if the sum defect is zero. No constructed triangle is claimed. The exact result, retaining the requested order, is (Yes, Yes, 0)."},"skills":["Candidate Triangle-Angle Qualification"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r05-right-triangle-0036","batch_id":"batch-20261008-advance-20261012-r05-right-triangle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"b33b7a409da52de2720afb8813db775605c24b147b20192b339cc4448fff2fc2","family_id":"qf-density12-right-triangle-validity-pair","seed":202610125036,"semantic_template":"qf-density12-right-triangle-validity-pair/[11,79,90]"},"fields":{"title":"Candidate Triangle-Angle Qualification","stem":"Exact-degree candidate angles=[90, 11, 79]. Give (all positive with sum 180?, qualified and containing a 90° angle?, signed angle sum−180).","answer":{"kind":"expression","value":"(Yes, Yes, 0)","explanation":"Check positivity and the exact sum before the right angle; zero or negative candidate angles may be rejected even if the sum defect is zero. No constructed triangle is claimed. The exact result, retaining the requested order, is (Yes, Yes, 0)."},"skills":["Candidate Triangle-Angle Qualification"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r05-right-triangle-0037","batch_id":"batch-20261008-advance-20261012-r05-right-triangle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"8ad4afcf1b1639b445c63d6eea5cc3e63a83105ebf61224cf5fddb31e5e5309e","family_id":"qf-density12-right-triangle-validity-pair","seed":202610125037,"semantic_template":"qf-density12-right-triangle-validity-pair/[12,78,90]"},"fields":{"title":"Candidate Triangle-Angle Qualification","stem":"Exact-degree candidate angles=[90, 12, 78]. Give (all positive with sum 180?, qualified and containing a 90° angle?, signed angle sum−180).","answer":{"kind":"expression","value":"(Yes, Yes, 0)","explanation":"Check positivity and the exact sum before the right angle; zero or negative candidate angles may be rejected even if the sum defect is zero. No constructed triangle is claimed. The exact result, retaining the requested order, is (Yes, Yes, 0)."},"skills":["Candidate Triangle-Angle Qualification"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r05-right-triangle-0038","batch_id":"batch-20261008-advance-20261012-r05-right-triangle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"49e2af1534bb8b3226d243a266683e50985132addc192d124612e8614629b3d8","family_id":"qf-density12-right-triangle-validity-pair","seed":202610125038,"semantic_template":"qf-density12-right-triangle-validity-pair/[13,77,90]"},"fields":{"title":"Candidate Triangle-Angle Qualification","stem":"Exact-degree candidate angles=[90, 13, 77]. Give (all positive with sum 180?, qualified and containing a 90° angle?, signed angle sum−180).","answer":{"kind":"expression","value":"(Yes, Yes, 0)","explanation":"Check positivity and the exact sum before the right angle; zero or negative candidate angles may be rejected even if the sum defect is zero. No constructed triangle is claimed. The exact result, retaining the requested order, is (Yes, Yes, 0)."},"skills":["Candidate Triangle-Angle Qualification"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r05-right-triangle-0039","batch_id":"batch-20261008-advance-20261012-r05-right-triangle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"6f8a0504133a70fb6b945dac143c64a6d23ea2d770e30b0c2d339ae65f953801","family_id":"qf-density12-right-triangle-validity-pair","seed":202610125039,"semantic_template":"qf-density12-right-triangle-validity-pair/[14,76,90]"},"fields":{"title":"Candidate Triangle-Angle Qualification","stem":"Exact-degree candidate angles=[90, 14, 76]. Give (all positive with sum 180?, qualified and containing a 90° angle?, signed angle sum−180).","answer":{"kind":"expression","value":"(Yes, Yes, 0)","explanation":"Check positivity and the exact sum before the right angle; zero or negative candidate angles may be rejected even if the sum defect is zero. No constructed triangle is claimed. The exact result, retaining the requested order, is (Yes, Yes, 0)."},"skills":["Candidate Triangle-Angle Qualification"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r05-right-triangle-0040","batch_id":"batch-20261008-advance-20261012-r05-right-triangle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"d57e07b91794652bc1014a5c34ea72ada3d8680f3773049384dbff47ad2355c1","family_id":"qf-density12-right-triangle-validity-pair","seed":202610125040,"semantic_template":"qf-density12-right-triangle-validity-pair/[15,75,90]"},"fields":{"title":"Candidate Triangle-Angle Qualification","stem":"Exact-degree candidate angles=[90, 15, 75]. Give (all positive with sum 180?, qualified and containing a 90° angle?, signed angle sum−180).","answer":{"kind":"expression","value":"(Yes, Yes, 0)","explanation":"Check positivity and the exact sum before the right angle; zero or negative candidate angles may be rejected even if the sum defect is zero. No constructed triangle is claimed. The exact result, retaining the requested order, is (Yes, Yes, 0)."},"skills":["Candidate Triangle-Angle Qualification"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r05-right-triangle-0041","batch_id":"batch-20261008-advance-20261012-r05-right-triangle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"b92c2ae270f9a66bd679a64a0c003a98f43d240c71e255bafd4e95f1afba8d5b","family_id":"qf-density12-right-triangle-validity-pair","seed":202610125041,"semantic_template":"qf-density12-right-triangle-validity-pair/[16,74,90]"},"fields":{"title":"Candidate Triangle-Angle Qualification","stem":"Exact-degree candidate angles=[90, 16, 74]. Give (all positive with sum 180?, qualified and containing a 90° angle?, signed angle sum−180).","answer":{"kind":"expression","value":"(Yes, Yes, 0)","explanation":"Check positivity and the exact sum before the right angle; zero or negative candidate angles may be rejected even if the sum defect is zero. No constructed triangle is claimed. The exact result, retaining the requested order, is (Yes, Yes, 0)."},"skills":["Candidate Triangle-Angle Qualification"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r05-right-triangle-0042","batch_id":"batch-20261008-advance-20261012-r05-right-triangle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"ff7ef37f481ac22256006684a02b49b17170a1eb3f87e28c162baa1beb7aab8e","family_id":"qf-density12-right-triangle-validity-pair","seed":202610125042,"semantic_template":"qf-density12-right-triangle-validity-pair/[17,73,90]"},"fields":{"title":"Candidate Triangle-Angle Qualification","stem":"Exact-degree candidate angles=[90, 17, 73]. Give (all positive with sum 180?, qualified and containing a 90° angle?, signed angle sum−180).","answer":{"kind":"expression","value":"(Yes, Yes, 0)","explanation":"Check positivity and the exact sum before the right angle; zero or negative candidate angles may be rejected even if the sum defect is zero. No constructed triangle is claimed. The exact result, retaining the requested order, is (Yes, Yes, 0)."},"skills":["Candidate Triangle-Angle Qualification"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r05-right-triangle-0043","batch_id":"batch-20261008-advance-20261012-r05-right-triangle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"facd1484b12ef9382556df7a6f83b2779c59a9df2e9cc2bbd2ef2385cd7343c3","family_id":"qf-density12-right-triangle-validity-pair","seed":202610125043,"semantic_template":"qf-density12-right-triangle-validity-pair/[18,72,90]"},"fields":{"title":"Candidate Triangle-Angle Qualification","stem":"Exact-degree candidate angles=[90, 18, 72]. Give (all positive with sum 180?, qualified and containing a 90° angle?, signed angle sum−180).","answer":{"kind":"expression","value":"(Yes, Yes, 0)","explanation":"Check positivity and the exact sum before the right angle; zero or negative candidate angles may be rejected even if the sum defect is zero. No constructed triangle is claimed. The exact result, retaining the requested order, is (Yes, Yes, 0)."},"skills":["Candidate Triangle-Angle Qualification"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r05-right-triangle-0044","batch_id":"batch-20261008-advance-20261012-r05-right-triangle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"6db5b14f8bdf673acfdbcd503f9bd1ed2638c75ddfec9cfe083c0f0081b931af","family_id":"qf-density12-right-triangle-validity-pair","seed":202610125044,"semantic_template":"qf-density12-right-triangle-validity-pair/[19,71,90]"},"fields":{"title":"Candidate Triangle-Angle Qualification","stem":"Exact-degree candidate angles=[90, 19, 71]. Give (all positive with sum 180?, qualified and containing a 90° angle?, signed angle sum−180).","answer":{"kind":"expression","value":"(Yes, Yes, 0)","explanation":"Check positivity and the exact sum before the right angle; zero or negative candidate angles may be rejected even if the sum defect is zero. No constructed triangle is claimed. The exact result, retaining the requested order, is (Yes, Yes, 0)."},"skills":["Candidate Triangle-Angle Qualification"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r05-right-triangle-0045","batch_id":"batch-20261008-advance-20261012-r05-right-triangle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"c4e3133b2957bb2fb573663c6858e7f38a418dac29c72b7166c92be61e177569","family_id":"qf-density12-right-triangle-validity-pair","seed":202610125045,"semantic_template":"qf-density12-right-triangle-validity-pair/[20,70,90]"},"fields":{"title":"Candidate Triangle-Angle Qualification","stem":"Exact-degree candidate angles=[90, 20, 70]. Give (all positive with sum 180?, qualified and containing a 90° angle?, signed angle sum−180).","answer":{"kind":"expression","value":"(Yes, Yes, 0)","explanation":"Check positivity and the exact sum before the right angle; zero or negative candidate angles may be rejected even if the sum defect is zero. No constructed triangle is claimed. The exact result, retaining the requested order, is (Yes, Yes, 0)."},"skills":["Candidate Triangle-Angle Qualification"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r05-right-triangle-0046","batch_id":"batch-20261008-advance-20261012-r05-right-triangle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"e1624b8ccf72b99d8ba6d7c0c1d8b667960ff01058026432c62fd4c50a18c5af","family_id":"qf-density12-right-triangle-validity-pair","seed":202610125046,"semantic_template":"qf-density12-right-triangle-validity-pair/[21,69,90]"},"fields":{"title":"Candidate Triangle-Angle Qualification","stem":"Exact-degree candidate angles=[90, 21, 69]. Give (all positive with sum 180?, qualified and containing a 90° angle?, signed angle sum−180).","answer":{"kind":"expression","value":"(Yes, Yes, 0)","explanation":"Check positivity and the exact sum before the right angle; zero or negative candidate angles may be rejected even if the sum defect is zero. No constructed triangle is claimed. The exact result, retaining the requested order, is (Yes, Yes, 0)."},"skills":["Candidate Triangle-Angle Qualification"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r05-right-triangle-0047","batch_id":"batch-20261008-advance-20261012-r05-right-triangle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"c68e3cfcaf450f08fcdac9828e24cf2d134bb6305898a056a08c68ad60b30f10","family_id":"qf-density12-right-triangle-validity-pair","seed":202610125047,"semantic_template":"qf-density12-right-triangle-validity-pair/[22,68,90]"},"fields":{"title":"Candidate Triangle-Angle Qualification","stem":"Exact-degree candidate angles=[90, 22, 68]. Give (all positive with sum 180?, qualified and containing a 90° angle?, signed angle sum−180).","answer":{"kind":"expression","value":"(Yes, Yes, 0)","explanation":"Check positivity and the exact sum before the right angle; zero or negative candidate angles may be rejected even if the sum defect is zero. No constructed triangle is claimed. The exact result, retaining the requested order, is (Yes, Yes, 0)."},"skills":["Candidate Triangle-Angle Qualification"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r05-right-triangle-0048","batch_id":"batch-20261008-advance-20261012-r05-right-triangle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"1a9a8142553eb6682723975093275df6fb966fd58f1d1034a53f3e16b2e72082","family_id":"qf-density12-right-triangle-validity-pair","seed":202610125048,"semantic_template":"qf-density12-right-triangle-validity-pair/[23,67,90]"},"fields":{"title":"Candidate Triangle-Angle Qualification","stem":"Exact-degree candidate angles=[90, 23, 67]. Give (all positive with sum 180?, qualified and containing a 90° angle?, signed angle sum−180).","answer":{"kind":"expression","value":"(Yes, Yes, 0)","explanation":"Check positivity and the exact sum before the right angle; zero or negative candidate angles may be rejected even if the sum defect is zero. No constructed triangle is claimed. The exact result, retaining the requested order, is (Yes, Yes, 0)."},"skills":["Candidate Triangle-Angle Qualification"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r05-right-triangle-0049","batch_id":"batch-20261008-advance-20261012-r05-right-triangle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"e2a36e3c89a3325391762c6849d8d57a3900cdb82819d70139e4c57dcde7e708","family_id":"qf-density12-right-triangle-validity-pair","seed":202610125049,"semantic_template":"qf-density12-right-triangle-validity-pair/[24,66,90]"},"fields":{"title":"Candidate Triangle-Angle Qualification","stem":"Exact-degree candidate angles=[90, 24, 66]. Give (all positive with sum 180?, qualified and containing a 90° angle?, signed angle sum−180).","answer":{"kind":"expression","value":"(Yes, Yes, 0)","explanation":"Check positivity and the exact sum before the right angle; zero or negative candidate angles may be rejected even if the sum defect is zero. No constructed triangle is claimed. The exact result, retaining the requested order, is (Yes, Yes, 0)."},"skills":["Candidate Triangle-Angle Qualification"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r05-right-triangle-0050","batch_id":"batch-20261008-advance-20261012-r05-right-triangle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"b59580d646c47026f05442df6b692d5bd2b6e31a24030ba8e42d180601dc7f28","family_id":"qf-density12-right-triangle-validity-pair","seed":202610125050,"semantic_template":"qf-density12-right-triangle-validity-pair/[25,65,90]"},"fields":{"title":"Candidate Triangle-Angle Qualification","stem":"Exact-degree candidate angles=[90, 25, 65]. Give (all positive with sum 180?, qualified and containing a 90° angle?, signed angle sum−180).","answer":{"kind":"expression","value":"(Yes, Yes, 0)","explanation":"Check positivity and the exact sum before the right angle; zero or negative candidate angles may be rejected even if the sum defect is zero. No constructed triangle is claimed. The exact result, retaining the requested order, is (Yes, Yes, 0)."},"skills":["Candidate Triangle-Angle Qualification"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r05-right-triangle-0051","batch_id":"batch-20261008-advance-20261012-r05-right-triangle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"54c2456a8ed1d915a61c9ddde68fdb128d67017f7aeba319a9a137c3ac729678","family_id":"qf-density12-right-triangle-marked-vertices","seed":202610125051,"semantic_template":"qf-density12-right-triangle-marked-vertices/[90,45,45]"},"fields":{"title":"Labeled Right Vertex and Opposite Side","stem":"Exact degrees: vertex indices 1,2,3 have ordered angles=[90, 45, 45], already required positive, summing to 180, with a unique 90°. Give (right-vertex index, other two endpoint indices, their ordered acute angles).","answer":{"kind":"expression","value":"(1, [2, 3], [45, 45])","explanation":"Find the right angle in label order; the opposite side uses the other two vertex labels. Do not reorder angles or infer a construction proof. The exact result, retaining the requested order, is (1, [2, 3], [45, 45])."},"skills":["Labeled Right Vertex and Opposite Side"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r05-right-triangle-0052","batch_id":"batch-20261008-advance-20261012-r05-right-triangle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"0e4745dbdb2603dcad7798ae47abd9ca80c6468b31c5e214f227a283dc364591","family_id":"qf-density12-right-triangle-marked-vertices","seed":202610125052,"semantic_template":"qf-density12-right-triangle-marked-vertices/[1,90,89]"},"fields":{"title":"Labeled Right Vertex and Opposite Side","stem":"Exact degrees: vertex indices 1,2,3 have ordered angles=[1, 90, 89], already required positive, summing to 180, with a unique 90°. Give (right-vertex index, other two endpoint indices, their ordered acute angles).","answer":{"kind":"expression","value":"(2, [1, 3], [1, 89])","explanation":"Find the right angle in label order; the opposite side uses the other two vertex labels. Do not reorder angles or infer a construction proof. The exact result, retaining the requested order, is (2, [1, 3], [1, 89])."},"skills":["Labeled Right Vertex and Opposite Side"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r05-right-triangle-0053","batch_id":"batch-20261008-advance-20261012-r05-right-triangle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"4511311085fb4a44c2faa7835101aadb4d54316f4f8a6657568d6341340b06b8","family_id":"qf-density12-right-triangle-marked-vertices","seed":202610125053,"semantic_template":"qf-density12-right-triangle-marked-vertices/[3,87,90]"},"fields":{"title":"Labeled Right Vertex and Opposite Side","stem":"Exact degrees: vertex indices 1,2,3 have ordered angles=[3, 87, 90], already required positive, summing to 180, with a unique 90°. Give (right-vertex index, other two endpoint indices, their ordered acute angles).","answer":{"kind":"expression","value":"(3, [1, 2], [3, 87])","explanation":"Find the right angle in label order; the opposite side uses the other two vertex labels. Do not reorder angles or infer a construction proof. The exact result, retaining the requested order, is (3, [1, 2], [3, 87])."},"skills":["Labeled Right Vertex and Opposite Side"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r05-right-triangle-0054","batch_id":"batch-20261008-advance-20261012-r05-right-triangle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"4545c812f2e14f4c191b53a9bac5dc65807fa1ebccf499ac4aebdcf784eb2344","family_id":"qf-density12-right-triangle-marked-vertices","seed":202610125054,"semantic_template":"qf-density12-right-triangle-marked-vertices/[90,4,86]"},"fields":{"title":"Labeled Right Vertex and Opposite Side","stem":"Exact degrees: vertex indices 1,2,3 have ordered angles=[90, 4, 86], already required positive, summing to 180, with a unique 90°. Give (right-vertex index, other two endpoint indices, their ordered acute angles).","answer":{"kind":"expression","value":"(1, [2, 3], [4, 86])","explanation":"Find the right angle in label order; the opposite side uses the other two vertex labels. Do not reorder angles or infer a construction proof. The exact result, retaining the requested order, is (1, [2, 3], [4, 86])."},"skills":["Labeled Right Vertex and Opposite Side"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r05-right-triangle-0055","batch_id":"batch-20261008-advance-20261012-r05-right-triangle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"da23913c2c0a9d2e4a96881df7a60588e9e34cdd19713147bc8bf0b36cb31a44","family_id":"qf-density12-right-triangle-marked-vertices","seed":202610125055,"semantic_template":"qf-density12-right-triangle-marked-vertices/[5,90,85]"},"fields":{"title":"Labeled Right Vertex and Opposite Side","stem":"Exact degrees: vertex indices 1,2,3 have ordered angles=[5, 90, 85], already required positive, summing to 180, with a unique 90°. Give (right-vertex index, other two endpoint indices, their ordered acute angles).","answer":{"kind":"expression","value":"(2, [1, 3], [5, 85])","explanation":"Find the right angle in label order; the opposite side uses the other two vertex labels. Do not reorder angles or infer a construction proof. The exact result, retaining the requested order, is (2, [1, 3], [5, 85])."},"skills":["Labeled Right Vertex and Opposite Side"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r05-right-triangle-0056","batch_id":"batch-20261008-advance-20261012-r05-right-triangle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"03989612213351ddfa9788e7a945766a6873722ae224cce6cd90b7c2e106780d","family_id":"qf-density12-right-triangle-marked-vertices","seed":202610125056,"semantic_template":"qf-density12-right-triangle-marked-vertices/[6,84,90]"},"fields":{"title":"Labeled Right Vertex and Opposite Side","stem":"Exact degrees: vertex indices 1,2,3 have ordered angles=[6, 84, 90], already required positive, summing to 180, with a unique 90°. Give (right-vertex index, other two endpoint indices, their ordered acute angles).","answer":{"kind":"expression","value":"(3, [1, 2], [6, 84])","explanation":"Find the right angle in label order; the opposite side uses the other two vertex labels. Do not reorder angles or infer a construction proof. The exact result, retaining the requested order, is (3, [1, 2], [6, 84])."},"skills":["Labeled Right Vertex and Opposite Side"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r05-right-triangle-0057","batch_id":"batch-20261008-advance-20261012-r05-right-triangle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"329632e5e044f1db5b35e07f6eef9ee46a9ca66dfc3eba6de8d9177d89df0b72","family_id":"qf-density12-right-triangle-marked-vertices","seed":202610125057,"semantic_template":"qf-density12-right-triangle-marked-vertices/[90,7,83]"},"fields":{"title":"Labeled Right Vertex and Opposite Side","stem":"Exact degrees: vertex indices 1,2,3 have ordered angles=[90, 7, 83], already required positive, summing to 180, with a unique 90°. Give (right-vertex index, other two endpoint indices, their ordered acute angles).","answer":{"kind":"expression","value":"(1, [2, 3], [7, 83])","explanation":"Find the right angle in label order; the opposite side uses the other two vertex labels. Do not reorder angles or infer a construction proof. The exact result, retaining the requested order, is (1, [2, 3], [7, 83])."},"skills":["Labeled Right Vertex and Opposite Side"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r05-right-triangle-0058","batch_id":"batch-20261008-advance-20261012-r05-right-triangle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"560d6e89da0d5563d23c4f85f4e05565d5ac09ffd40fc2948861d52232086766","family_id":"qf-density12-right-triangle-marked-vertices","seed":202610125058,"semantic_template":"qf-density12-right-triangle-marked-vertices/[8,90,82]"},"fields":{"title":"Labeled Right Vertex and Opposite Side","stem":"Exact degrees: vertex indices 1,2,3 have ordered angles=[8, 90, 82], already required positive, summing to 180, with a unique 90°. Give (right-vertex index, other two endpoint indices, their ordered acute angles).","answer":{"kind":"expression","value":"(2, [1, 3], [8, 82])","explanation":"Find the right angle in label order; the opposite side uses the other two vertex labels. Do not reorder angles or infer a construction proof. The exact result, retaining the requested order, is (2, [1, 3], [8, 82])."},"skills":["Labeled Right Vertex and Opposite Side"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r05-right-triangle-0059","batch_id":"batch-20261008-advance-20261012-r05-right-triangle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"2570b5139133bcc7106b223dcb00653c6911c74bfc542adbf49c2f6364e30e73","family_id":"qf-density12-right-triangle-marked-vertices","seed":202610125059,"semantic_template":"qf-density12-right-triangle-marked-vertices/[9,81,90]"},"fields":{"title":"Labeled Right Vertex and Opposite Side","stem":"Exact degrees: vertex indices 1,2,3 have ordered angles=[9, 81, 90], already required positive, summing to 180, with a unique 90°. Give (right-vertex index, other two endpoint indices, their ordered acute angles).","answer":{"kind":"expression","value":"(3, [1, 2], [9, 81])","explanation":"Find the right angle in label order; the opposite side uses the other two vertex labels. Do not reorder angles or infer a construction proof. The exact result, retaining the requested order, is (3, [1, 2], [9, 81])."},"skills":["Labeled Right Vertex and Opposite Side"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r05-right-triangle-0060","batch_id":"batch-20261008-advance-20261012-r05-right-triangle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"2fcf01adfae2f5ca2fc3fd04d75fc78ff11a3550b82e7ca59369a17108b33389","family_id":"qf-density12-right-triangle-marked-vertices","seed":202610125060,"semantic_template":"qf-density12-right-triangle-marked-vertices/[90,10,80]"},"fields":{"title":"Labeled Right Vertex and Opposite Side","stem":"Exact degrees: vertex indices 1,2,3 have ordered angles=[90, 10, 80], already required positive, summing to 180, with a unique 90°. Give (right-vertex index, other two endpoint indices, their ordered acute angles).","answer":{"kind":"expression","value":"(1, [2, 3], [10, 80])","explanation":"Find the right angle in label order; the opposite side uses the other two vertex labels. Do not reorder angles or infer a construction proof. The exact result, retaining the requested order, is (1, [2, 3], [10, 80])."},"skills":["Labeled Right Vertex and Opposite Side"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r05-right-triangle-0061","batch_id":"batch-20261008-advance-20261012-r05-right-triangle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"136ea1c8971517aafdefea17acf104e5fa33f209d095f8582b4dbd7cb4de40b3","family_id":"qf-density12-right-triangle-marked-vertices","seed":202610125061,"semantic_template":"qf-density12-right-triangle-marked-vertices/[11,90,79]"},"fields":{"title":"Labeled Right Vertex and Opposite Side","stem":"Exact degrees: vertex indices 1,2,3 have ordered angles=[11, 90, 79], already required positive, summing to 180, with a unique 90°. Give (right-vertex index, other two endpoint indices, their ordered acute angles).","answer":{"kind":"expression","value":"(2, [1, 3], [11, 79])","explanation":"Find the right angle in label order; the opposite side uses the other two vertex labels. Do not reorder angles or infer a construction proof. The exact result, retaining the requested order, is (2, [1, 3], [11, 79])."},"skills":["Labeled Right Vertex and Opposite Side"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r05-right-triangle-0062","batch_id":"batch-20261008-advance-20261012-r05-right-triangle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"dcac69233b720830a7422f78c27bf67dcde6f99ec7d4dc1f20b6211ac1ec5712","family_id":"qf-density12-right-triangle-marked-vertices","seed":202610125062,"semantic_template":"qf-density12-right-triangle-marked-vertices/[12,78,90]"},"fields":{"title":"Labeled Right Vertex and Opposite Side","stem":"Exact degrees: vertex indices 1,2,3 have ordered angles=[12, 78, 90], already required positive, summing to 180, with a unique 90°. Give (right-vertex index, other two endpoint indices, their ordered acute angles).","answer":{"kind":"expression","value":"(3, [1, 2], [12, 78])","explanation":"Find the right angle in label order; the opposite side uses the other two vertex labels. Do not reorder angles or infer a construction proof. The exact result, retaining the requested order, is (3, [1, 2], [12, 78])."},"skills":["Labeled Right Vertex and Opposite Side"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r05-right-triangle-0063","batch_id":"batch-20261008-advance-20261012-r05-right-triangle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"bc6fef7a48938e5ca605a82dd2801ac73e8ddd32acaee73c0bd56d1d46a3158d","family_id":"qf-density12-right-triangle-marked-vertices","seed":202610125063,"semantic_template":"qf-density12-right-triangle-marked-vertices/[90,13,77]"},"fields":{"title":"Labeled Right Vertex and Opposite Side","stem":"Exact degrees: vertex indices 1,2,3 have ordered angles=[90, 13, 77], already required positive, summing to 180, with a unique 90°. Give (right-vertex index, other two endpoint indices, their ordered acute angles).","answer":{"kind":"expression","value":"(1, [2, 3], [13, 77])","explanation":"Find the right angle in label order; the opposite side uses the other two vertex labels. Do not reorder angles or infer a construction proof. The exact result, retaining the requested order, is (1, [2, 3], [13, 77])."},"skills":["Labeled Right Vertex and Opposite Side"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r05-right-triangle-0064","batch_id":"batch-20261008-advance-20261012-r05-right-triangle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"52200a83e951e2f0d2029723d88fb8e019069b962b1b0ffe7b819b0bc4fffeb3","family_id":"qf-density12-right-triangle-marked-vertices","seed":202610125064,"semantic_template":"qf-density12-right-triangle-marked-vertices/[14,90,76]"},"fields":{"title":"Labeled Right Vertex and Opposite Side","stem":"Exact degrees: vertex indices 1,2,3 have ordered angles=[14, 90, 76], already required positive, summing to 180, with a unique 90°. Give (right-vertex index, other two endpoint indices, their ordered acute angles).","answer":{"kind":"expression","value":"(2, [1, 3], [14, 76])","explanation":"Find the right angle in label order; the opposite side uses the other two vertex labels. Do not reorder angles or infer a construction proof. The exact result, retaining the requested order, is (2, [1, 3], [14, 76])."},"skills":["Labeled Right Vertex and Opposite Side"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r05-right-triangle-0065","batch_id":"batch-20261008-advance-20261012-r05-right-triangle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"ebb65e06e76e046750393559ab531ab8b990636b7553e302137628def8d71a0b","family_id":"qf-density12-right-triangle-marked-vertices","seed":202610125065,"semantic_template":"qf-density12-right-triangle-marked-vertices/[15,75,90]"},"fields":{"title":"Labeled Right Vertex and Opposite Side","stem":"Exact degrees: vertex indices 1,2,3 have ordered angles=[15, 75, 90], already required positive, summing to 180, with a unique 90°. Give (right-vertex index, other two endpoint indices, their ordered acute angles).","answer":{"kind":"expression","value":"(3, [1, 2], [15, 75])","explanation":"Find the right angle in label order; the opposite side uses the other two vertex labels. Do not reorder angles or infer a construction proof. The exact result, retaining the requested order, is (3, [1, 2], [15, 75])."},"skills":["Labeled Right Vertex and Opposite Side"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r05-right-triangle-0066","batch_id":"batch-20261008-advance-20261012-r05-right-triangle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"e9d9b1618eab227d59cd53ee38ef7415007d2feb947ea6d5098f9c35818d064c","family_id":"qf-density12-right-triangle-marked-vertices","seed":202610125066,"semantic_template":"qf-density12-right-triangle-marked-vertices/[90,16,74]"},"fields":{"title":"Labeled Right Vertex and Opposite Side","stem":"Exact degrees: vertex indices 1,2,3 have ordered angles=[90, 16, 74], already required positive, summing to 180, with a unique 90°. Give (right-vertex index, other two endpoint indices, their ordered acute angles).","answer":{"kind":"expression","value":"(1, [2, 3], [16, 74])","explanation":"Find the right angle in label order; the opposite side uses the other two vertex labels. Do not reorder angles or infer a construction proof. The exact result, retaining the requested order, is (1, [2, 3], [16, 74])."},"skills":["Labeled Right Vertex and Opposite Side"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r05-right-triangle-0067","batch_id":"batch-20261008-advance-20261012-r05-right-triangle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"b1ea3c2cf81b7d003120889c77b6fd4beee4a92615363bf23ff33306cd595bc1","family_id":"qf-density12-right-triangle-marked-vertices","seed":202610125067,"semantic_template":"qf-density12-right-triangle-marked-vertices/[17,90,73]"},"fields":{"title":"Labeled Right Vertex and Opposite Side","stem":"Exact degrees: vertex indices 1,2,3 have ordered angles=[17, 90, 73], already required positive, summing to 180, with a unique 90°. Give (right-vertex index, other two endpoint indices, their ordered acute angles).","answer":{"kind":"expression","value":"(2, [1, 3], [17, 73])","explanation":"Find the right angle in label order; the opposite side uses the other two vertex labels. Do not reorder angles or infer a construction proof. The exact result, retaining the requested order, is (2, [1, 3], [17, 73])."},"skills":["Labeled Right Vertex and Opposite Side"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r05-right-triangle-0068","batch_id":"batch-20261008-advance-20261012-r05-right-triangle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"9898f03e4a54f6711dad6ac7d541fc2a39d662885511fbb21201a2ea2ba6c2b6","family_id":"qf-density12-right-triangle-marked-vertices","seed":202610125068,"semantic_template":"qf-density12-right-triangle-marked-vertices/[18,72,90]"},"fields":{"title":"Labeled Right Vertex and Opposite Side","stem":"Exact degrees: vertex indices 1,2,3 have ordered angles=[18, 72, 90], already required positive, summing to 180, with a unique 90°. Give (right-vertex index, other two endpoint indices, their ordered acute angles).","answer":{"kind":"expression","value":"(3, [1, 2], [18, 72])","explanation":"Find the right angle in label order; the opposite side uses the other two vertex labels. Do not reorder angles or infer a construction proof. The exact result, retaining the requested order, is (3, [1, 2], [18, 72])."},"skills":["Labeled Right Vertex and Opposite Side"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r05-right-triangle-0069","batch_id":"batch-20261008-advance-20261012-r05-right-triangle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"5a8d9ef6ab39a0110252d3959d93d864b258582f2ce93c7483979e02f2ed7836","family_id":"qf-density12-right-triangle-marked-vertices","seed":202610125069,"semantic_template":"qf-density12-right-triangle-marked-vertices/[90,19,71]"},"fields":{"title":"Labeled Right Vertex and Opposite Side","stem":"Exact degrees: vertex indices 1,2,3 have ordered angles=[90, 19, 71], already required positive, summing to 180, with a unique 90°. Give (right-vertex index, other two endpoint indices, their ordered acute angles).","answer":{"kind":"expression","value":"(1, [2, 3], [19, 71])","explanation":"Find the right angle in label order; the opposite side uses the other two vertex labels. Do not reorder angles or infer a construction proof. The exact result, retaining the requested order, is (1, [2, 3], [19, 71])."},"skills":["Labeled Right Vertex and Opposite Side"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r05-right-triangle-0070","batch_id":"batch-20261008-advance-20261012-r05-right-triangle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"9aaa0525a6713b367c9e31c0e0a8d90ab3f9b2f7059582b542b203c9d2632c38","family_id":"qf-density12-right-triangle-marked-vertices","seed":202610125070,"semantic_template":"qf-density12-right-triangle-marked-vertices/[20,90,70]"},"fields":{"title":"Labeled Right Vertex and Opposite Side","stem":"Exact degrees: vertex indices 1,2,3 have ordered angles=[20, 90, 70], already required positive, summing to 180, with a unique 90°. Give (right-vertex index, other two endpoint indices, their ordered acute angles).","answer":{"kind":"expression","value":"(2, [1, 3], [20, 70])","explanation":"Find the right angle in label order; the opposite side uses the other two vertex labels. Do not reorder angles or infer a construction proof. The exact result, retaining the requested order, is (2, [1, 3], [20, 70])."},"skills":["Labeled Right Vertex and Opposite Side"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r05-right-triangle-0071","batch_id":"batch-20261008-advance-20261012-r05-right-triangle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"73bfbd8790aee09828f53fb963650a757ec6e18f452130e83a4ec46e3910228e","family_id":"qf-density12-right-triangle-marked-vertices","seed":202610125071,"semantic_template":"qf-density12-right-triangle-marked-vertices/[21,69,90]"},"fields":{"title":"Labeled Right Vertex and Opposite Side","stem":"Exact degrees: vertex indices 1,2,3 have ordered angles=[21, 69, 90], already required positive, summing to 180, with a unique 90°. Give (right-vertex index, other two endpoint indices, their ordered acute angles).","answer":{"kind":"expression","value":"(3, [1, 2], [21, 69])","explanation":"Find the right angle in label order; the opposite side uses the other two vertex labels. Do not reorder angles or infer a construction proof. The exact result, retaining the requested order, is (3, [1, 2], [21, 69])."},"skills":["Labeled Right Vertex and Opposite Side"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r05-right-triangle-0072","batch_id":"batch-20261008-advance-20261012-r05-right-triangle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"8c34a02f8a47658de373f5871eee168d9d6eefc9257aa7db4097adb9a794cfb5","family_id":"qf-density12-right-triangle-marked-vertices","seed":202610125072,"semantic_template":"qf-density12-right-triangle-marked-vertices/[90,22,68]"},"fields":{"title":"Labeled Right Vertex and Opposite Side","stem":"Exact degrees: vertex indices 1,2,3 have ordered angles=[90, 22, 68], already required positive, summing to 180, with a unique 90°. Give (right-vertex index, other two endpoint indices, their ordered acute angles).","answer":{"kind":"expression","value":"(1, [2, 3], [22, 68])","explanation":"Find the right angle in label order; the opposite side uses the other two vertex labels. Do not reorder angles or infer a construction proof. The exact result, retaining the requested order, is (1, [2, 3], [22, 68])."},"skills":["Labeled Right Vertex and Opposite Side"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r05-right-triangle-0073","batch_id":"batch-20261008-advance-20261012-r05-right-triangle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"2bb32f65a4251e41ab859be1403c388684a65891ce6d70f8b7dac76dee90fa2d","family_id":"qf-density12-right-triangle-marked-vertices","seed":202610125073,"semantic_template":"qf-density12-right-triangle-marked-vertices/[23,90,67]"},"fields":{"title":"Labeled Right Vertex and Opposite Side","stem":"Exact degrees: vertex indices 1,2,3 have ordered angles=[23, 90, 67], already required positive, summing to 180, with a unique 90°. Give (right-vertex index, other two endpoint indices, their ordered acute angles).","answer":{"kind":"expression","value":"(2, [1, 3], [23, 67])","explanation":"Find the right angle in label order; the opposite side uses the other two vertex labels. Do not reorder angles or infer a construction proof. The exact result, retaining the requested order, is (2, [1, 3], [23, 67])."},"skills":["Labeled Right Vertex and Opposite Side"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r05-right-triangle-0074","batch_id":"batch-20261008-advance-20261012-r05-right-triangle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"8fc14ca5072eb94cda61d23b7256000da825b0b30e2721f911b8362d192bcdfa","family_id":"qf-density12-right-triangle-marked-vertices","seed":202610125074,"semantic_template":"qf-density12-right-triangle-marked-vertices/[24,66,90]"},"fields":{"title":"Labeled Right Vertex and Opposite Side","stem":"Exact degrees: vertex indices 1,2,3 have ordered angles=[24, 66, 90], already required positive, summing to 180, with a unique 90°. Give (right-vertex index, other two endpoint indices, their ordered acute angles).","answer":{"kind":"expression","value":"(3, [1, 2], [24, 66])","explanation":"Find the right angle in label order; the opposite side uses the other two vertex labels. Do not reorder angles or infer a construction proof. The exact result, retaining the requested order, is (3, [1, 2], [24, 66])."},"skills":["Labeled Right Vertex and Opposite Side"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r05-right-triangle-0075","batch_id":"batch-20261008-advance-20261012-r05-right-triangle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"1f88a6dbddfd7fc5ca7ba1d8c41a3f3c7e108cc2f8321abcf14489816a62c85e","family_id":"qf-density12-right-triangle-marked-vertices","seed":202610125075,"semantic_template":"qf-density12-right-triangle-marked-vertices/[90,25,65]"},"fields":{"title":"Labeled Right Vertex and Opposite Side","stem":"Exact degrees: vertex indices 1,2,3 have ordered angles=[90, 25, 65], already required positive, summing to 180, with a unique 90°. Give (right-vertex index, other two endpoint indices, their ordered acute angles).","answer":{"kind":"expression","value":"(1, [2, 3], [25, 65])","explanation":"Find the right angle in label order; the opposite side uses the other two vertex labels. Do not reorder angles or infer a construction proof. The exact result, retaining the requested order, is (1, [2, 3], [25, 65])."},"skills":["Labeled Right Vertex and Opposite Side"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r05-right-triangle-0076","batch_id":"batch-20261008-advance-20261012-r05-right-triangle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"ab169f1ade130e5a2b73954d2fb7c06c10244bdb7c4d345cbec247d5b9bba150","family_id":"qf-density12-right-triangle-pi-multiple","seed":202610125076,"semantic_template":"qf-density12-right-triangle-pi-multiple/\"1/2\""},"fields":{"title":"Exact π-Multiple Candidate without Periodic Wrapping","stem":"Candidate θ=(1/2)π radians. Give (exact degree value, does it equal exactly 90°?), without taking a modulus or wrapping a period.","answer":{"kind":"expression","value":"(90/1, Yes)","explanation":"Multiply the rational π coefficient by 180 and reduce exactly; 450° is not 90°, with no floating-point π or tolerance. The exact result, retaining the requested order, is (90/1, Yes)."},"skills":["Exact π-Multiple Candidate without Periodic Wrapping"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r05-right-triangle-0077","batch_id":"batch-20261008-advance-20261012-r05-right-triangle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"33a78f4bf6bff587dee811f3ee2a4703d2c38daf80eb15ecb52d1ca8ff194c38","family_id":"qf-density12-right-triangle-pi-multiple","seed":202610125077,"semantic_template":"qf-density12-right-triangle-pi-multiple/\"5/2\""},"fields":{"title":"Exact π-Multiple Candidate without Periodic Wrapping","stem":"Candidate θ=(5/2)π radians. Give (exact degree value, does it equal exactly 90°?), without taking a modulus or wrapping a period.","answer":{"kind":"expression","value":"(450/1, No)","explanation":"Multiply the rational π coefficient by 180 and reduce exactly; 450° is not 90°, with no floating-point π or tolerance. The exact result, retaining the requested order, is (450/1, No)."},"skills":["Exact π-Multiple Candidate without Periodic Wrapping"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r05-right-triangle-0078","batch_id":"batch-20261008-advance-20261012-r05-right-triangle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"f27ddd9dbe186bf58ed9c83ce30ce903f893242f1c3c47b4a62901f8f8834aaf","family_id":"qf-density12-right-triangle-pi-multiple","seed":202610125078,"semantic_template":"qf-density12-right-triangle-pi-multiple/\"0/1\""},"fields":{"title":"Exact π-Multiple Candidate without Periodic Wrapping","stem":"Candidate θ=(0/1)π radians. Give (exact degree value, does it equal exactly 90°?), without taking a modulus or wrapping a period.","answer":{"kind":"expression","value":"(0/1, No)","explanation":"Multiply the rational π coefficient by 180 and reduce exactly; 450° is not 90°, with no floating-point π or tolerance. The exact result, retaining the requested order, is (0/1, No)."},"skills":["Exact π-Multiple Candidate without Periodic Wrapping"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r05-right-triangle-0079","batch_id":"batch-20261008-advance-20261012-r05-right-triangle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"1b48c2d36658c5708473cf28aef725cd873eaef511e62b5aaa0c27f73d3e3c95","family_id":"qf-density12-right-triangle-pi-multiple","seed":202610125079,"semantic_template":"qf-density12-right-triangle-pi-multiple/\"-1/2\""},"fields":{"title":"Exact π-Multiple Candidate without Periodic Wrapping","stem":"Candidate θ=(-1/2)π radians. Give (exact degree value, does it equal exactly 90°?), without taking a modulus or wrapping a period.","answer":{"kind":"expression","value":"(-90/1, No)","explanation":"Multiply the rational π coefficient by 180 and reduce exactly; 450° is not 90°, with no floating-point π or tolerance. The exact result, retaining the requested order, is (-90/1, No)."},"skills":["Exact π-Multiple Candidate without Periodic Wrapping"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r05-right-triangle-0080","batch_id":"batch-20261008-advance-20261012-r05-right-triangle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"cbf3e50f151da7f60ebde488bb05031a3dcd2fa9609ce99314b965f0e51e8166","family_id":"qf-density12-right-triangle-pi-multiple","seed":202610125080,"semantic_template":"qf-density12-right-triangle-pi-multiple/\"1/7\""},"fields":{"title":"Exact π-Multiple Candidate without Periodic Wrapping","stem":"Candidate θ=(1/7)π radians. Give (exact degree value, does it equal exactly 90°?), without taking a modulus or wrapping a period.","answer":{"kind":"expression","value":"(180/7, No)","explanation":"Multiply the rational π coefficient by 180 and reduce exactly; 450° is not 90°, with no floating-point π or tolerance. The exact result, retaining the requested order, is (180/7, No)."},"skills":["Exact π-Multiple Candidate without Periodic Wrapping"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r05-right-triangle-0081","batch_id":"batch-20261008-advance-20261012-r05-right-triangle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"706badc21cc0137a285a6534f51b45fbd0541ee1cabdf271a20dd8b9909b6f5b","family_id":"qf-density12-right-triangle-pi-multiple","seed":202610125081,"semantic_template":"qf-density12-right-triangle-pi-multiple/\"2/7\""},"fields":{"title":"Exact π-Multiple Candidate without Periodic Wrapping","stem":"Candidate θ=(2/7)π radians. Give (exact degree value, does it equal exactly 90°?), without taking a modulus or wrapping a period.","answer":{"kind":"expression","value":"(360/7, No)","explanation":"Multiply the rational π coefficient by 180 and reduce exactly; 450° is not 90°, with no floating-point π or tolerance. The exact result, retaining the requested order, is (360/7, No)."},"skills":["Exact π-Multiple Candidate without Periodic Wrapping"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r05-right-triangle-0082","batch_id":"batch-20261008-advance-20261012-r05-right-triangle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"578845f260f94d5eab30d43be4fbf76df07fb4a0779c71752bb6e00fdabb4615","family_id":"qf-density12-right-triangle-pi-multiple","seed":202610125082,"semantic_template":"qf-density12-right-triangle-pi-multiple/\"3/7\""},"fields":{"title":"Exact π-Multiple Candidate without Periodic Wrapping","stem":"Candidate θ=(3/7)π radians. Give (exact degree value, does it equal exactly 90°?), without taking a modulus or wrapping a period.","answer":{"kind":"expression","value":"(540/7, No)","explanation":"Multiply the rational π coefficient by 180 and reduce exactly; 450° is not 90°, with no floating-point π or tolerance. The exact result, retaining the requested order, is (540/7, No)."},"skills":["Exact π-Multiple Candidate without Periodic Wrapping"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r05-right-triangle-0083","batch_id":"batch-20261008-advance-20261012-r05-right-triangle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"3176593801b3a719d44a247e5693e8a8169b489d4981df128c10448715e14794","family_id":"qf-density12-right-triangle-pi-multiple","seed":202610125083,"semantic_template":"qf-density12-right-triangle-pi-multiple/\"4/7\""},"fields":{"title":"Exact π-Multiple Candidate without Periodic Wrapping","stem":"Candidate θ=(4/7)π radians. Give (exact degree value, does it equal exactly 90°?), without taking a modulus or wrapping a period.","answer":{"kind":"expression","value":"(720/7, No)","explanation":"Multiply the rational π coefficient by 180 and reduce exactly; 450° is not 90°, with no floating-point π or tolerance. The exact result, retaining the requested order, is (720/7, No)."},"skills":["Exact π-Multiple Candidate without Periodic Wrapping"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r05-right-triangle-0084","batch_id":"batch-20261008-advance-20261012-r05-right-triangle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"0f9ee9efd5f54010140ef8c6d7c60b7c47214b153f73085512807841e2aadb64","family_id":"qf-density12-right-triangle-pi-multiple","seed":202610125084,"semantic_template":"qf-density12-right-triangle-pi-multiple/\"5/7\""},"fields":{"title":"Exact π-Multiple Candidate without Periodic Wrapping","stem":"Candidate θ=(5/7)π radians. Give (exact degree value, does it equal exactly 90°?), without taking a modulus or wrapping a period.","answer":{"kind":"expression","value":"(900/7, No)","explanation":"Multiply the rational π coefficient by 180 and reduce exactly; 450° is not 90°, with no floating-point π or tolerance. The exact result, retaining the requested order, is (900/7, No)."},"skills":["Exact π-Multiple Candidate without Periodic Wrapping"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r05-right-triangle-0085","batch_id":"batch-20261008-advance-20261012-r05-right-triangle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"5de1c48ac71ab196948bb9832c392daf87c6be5b05d6d322c6c8a884a51185c4","family_id":"qf-density12-right-triangle-pi-multiple","seed":202610125085,"semantic_template":"qf-density12-right-triangle-pi-multiple/\"6/7\""},"fields":{"title":"Exact π-Multiple Candidate without Periodic Wrapping","stem":"Candidate θ=(6/7)π radians. Give (exact degree value, does it equal exactly 90°?), without taking a modulus or wrapping a period.","answer":{"kind":"expression","value":"(1080/7, No)","explanation":"Multiply the rational π coefficient by 180 and reduce exactly; 450° is not 90°, with no floating-point π or tolerance. The exact result, retaining the requested order, is (1080/7, No)."},"skills":["Exact π-Multiple Candidate without Periodic Wrapping"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r05-right-triangle-0086","batch_id":"batch-20261008-advance-20261012-r05-right-triangle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"ae26e0eddcf89ce677177d776c00fef78734417ed48dae15bb59df2ab22f59eb","family_id":"qf-density12-right-triangle-pi-multiple","seed":202610125086,"semantic_template":"qf-density12-right-triangle-pi-multiple/\"1/1\""},"fields":{"title":"Exact π-Multiple Candidate without Periodic Wrapping","stem":"Candidate θ=(7/7)π radians. Give (exact degree value, does it equal exactly 90°?), without taking a modulus or wrapping a period.","answer":{"kind":"expression","value":"(180/1, No)","explanation":"Multiply the rational π coefficient by 180 and reduce exactly; 450° is not 90°, with no floating-point π or tolerance. The exact result, retaining the requested order, is (180/1, No)."},"skills":["Exact π-Multiple Candidate without Periodic Wrapping"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r05-right-triangle-0087","batch_id":"batch-20261008-advance-20261012-r05-right-triangle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"0562fd54957f66537d8f3d1df0b9b3c8f58598214ad6db607a7fd77b8dc0a206","family_id":"qf-density12-right-triangle-pi-multiple","seed":202610125087,"semantic_template":"qf-density12-right-triangle-pi-multiple/\"8/7\""},"fields":{"title":"Exact π-Multiple Candidate without Periodic Wrapping","stem":"Candidate θ=(8/7)π radians. Give (exact degree value, does it equal exactly 90°?), without taking a modulus or wrapping a period.","answer":{"kind":"expression","value":"(1440/7, No)","explanation":"Multiply the rational π coefficient by 180 and reduce exactly; 450° is not 90°, with no floating-point π or tolerance. The exact result, retaining the requested order, is (1440/7, No)."},"skills":["Exact π-Multiple Candidate without Periodic Wrapping"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r05-right-triangle-0088","batch_id":"batch-20261008-advance-20261012-r05-right-triangle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"a4d08d6178a1df07b0e28b5af60a45c1ec56e9ba692fe773fb6d78caa0420e7a","family_id":"qf-density12-right-triangle-pi-multiple","seed":202610125088,"semantic_template":"qf-density12-right-triangle-pi-multiple/\"9/7\""},"fields":{"title":"Exact π-Multiple Candidate without Periodic Wrapping","stem":"Candidate θ=(9/7)π radians. Give (exact degree value, does it equal exactly 90°?), without taking a modulus or wrapping a period.","answer":{"kind":"expression","value":"(1620/7, No)","explanation":"Multiply the rational π coefficient by 180 and reduce exactly; 450° is not 90°, with no floating-point π or tolerance. The exact result, retaining the requested order, is (1620/7, No)."},"skills":["Exact π-Multiple Candidate without Periodic Wrapping"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r05-right-triangle-0089","batch_id":"batch-20261008-advance-20261012-r05-right-triangle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"f2eac34d84ae340ce2670a18d7a217b2b4003bd30d7f32f004be59070fbf0f0c","family_id":"qf-density12-right-triangle-pi-multiple","seed":202610125089,"semantic_template":"qf-density12-right-triangle-pi-multiple/\"10/7\""},"fields":{"title":"Exact π-Multiple Candidate without Periodic Wrapping","stem":"Candidate θ=(10/7)π radians. Give (exact degree value, does it equal exactly 90°?), without taking a modulus or wrapping a period.","answer":{"kind":"expression","value":"(1800/7, No)","explanation":"Multiply the rational π coefficient by 180 and reduce exactly; 450° is not 90°, with no floating-point π or tolerance. The exact result, retaining the requested order, is (1800/7, No)."},"skills":["Exact π-Multiple Candidate without Periodic Wrapping"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r05-right-triangle-0090","batch_id":"batch-20261008-advance-20261012-r05-right-triangle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"f03f39e13c169e4186fd018c7bd3dc4482a7dba12fc9a577b7d9063a3e693061","family_id":"qf-density12-right-triangle-pi-multiple","seed":202610125090,"semantic_template":"qf-density12-right-triangle-pi-multiple/\"11/7\""},"fields":{"title":"Exact π-Multiple Candidate without Periodic Wrapping","stem":"Candidate θ=(11/7)π radians. Give (exact degree value, does it equal exactly 90°?), without taking a modulus or wrapping a period.","answer":{"kind":"expression","value":"(1980/7, No)","explanation":"Multiply the rational π coefficient by 180 and reduce exactly; 450° is not 90°, with no floating-point π or tolerance. The exact result, retaining the requested order, is (1980/7, No)."},"skills":["Exact π-Multiple Candidate without Periodic Wrapping"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r05-right-triangle-0091","batch_id":"batch-20261008-advance-20261012-r05-right-triangle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"9853b985ff0ddd42f923a7435593c4979a1c78ea0866e26d8ea0841df570be9c","family_id":"qf-density12-right-triangle-pi-multiple","seed":202610125091,"semantic_template":"qf-density12-right-triangle-pi-multiple/\"12/7\""},"fields":{"title":"Exact π-Multiple Candidate without Periodic Wrapping","stem":"Candidate θ=(12/7)π radians. Give (exact degree value, does it equal exactly 90°?), without taking a modulus or wrapping a period.","answer":{"kind":"expression","value":"(2160/7, No)","explanation":"Multiply the rational π coefficient by 180 and reduce exactly; 450° is not 90°, with no floating-point π or tolerance. The exact result, retaining the requested order, is (2160/7, No)."},"skills":["Exact π-Multiple Candidate without Periodic Wrapping"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r05-right-triangle-0092","batch_id":"batch-20261008-advance-20261012-r05-right-triangle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"b581cdb5ebc7930e7f6f81290a7980eeff9f942b96b7050898a1c152a5813232","family_id":"qf-density12-right-triangle-pi-multiple","seed":202610125092,"semantic_template":"qf-density12-right-triangle-pi-multiple/\"13/7\""},"fields":{"title":"Exact π-Multiple Candidate without Periodic Wrapping","stem":"Candidate θ=(13/7)π radians. Give (exact degree value, does it equal exactly 90°?), without taking a modulus or wrapping a period.","answer":{"kind":"expression","value":"(2340/7, No)","explanation":"Multiply the rational π coefficient by 180 and reduce exactly; 450° is not 90°, with no floating-point π or tolerance. The exact result, retaining the requested order, is (2340/7, No)."},"skills":["Exact π-Multiple Candidate without Periodic Wrapping"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r05-right-triangle-0093","batch_id":"batch-20261008-advance-20261012-r05-right-triangle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"2f7bad0e3c1c00d1aa102dbab5cdb4a4d248aa8ec2ce8008bd931a3c0a556825","family_id":"qf-density12-right-triangle-pi-multiple","seed":202610125093,"semantic_template":"qf-density12-right-triangle-pi-multiple/\"2/1\""},"fields":{"title":"Exact π-Multiple Candidate without Periodic Wrapping","stem":"Candidate θ=(14/7)π radians. Give (exact degree value, does it equal exactly 90°?), without taking a modulus or wrapping a period.","answer":{"kind":"expression","value":"(360/1, No)","explanation":"Multiply the rational π coefficient by 180 and reduce exactly; 450° is not 90°, with no floating-point π or tolerance. The exact result, retaining the requested order, is (360/1, No)."},"skills":["Exact π-Multiple Candidate without Periodic Wrapping"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r05-right-triangle-0094","batch_id":"batch-20261008-advance-20261012-r05-right-triangle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"59dd66660cc86c72cabce32c23c96e2de3790e141152d28dba43986117da98a1","family_id":"qf-density12-right-triangle-pi-multiple","seed":202610125094,"semantic_template":"qf-density12-right-triangle-pi-multiple/\"15/7\""},"fields":{"title":"Exact π-Multiple Candidate without Periodic Wrapping","stem":"Candidate θ=(15/7)π radians. Give (exact degree value, does it equal exactly 90°?), without taking a modulus or wrapping a period.","answer":{"kind":"expression","value":"(2700/7, No)","explanation":"Multiply the rational π coefficient by 180 and reduce exactly; 450° is not 90°, with no floating-point π or tolerance. The exact result, retaining the requested order, is (2700/7, No)."},"skills":["Exact π-Multiple Candidate without Periodic Wrapping"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r05-right-triangle-0095","batch_id":"batch-20261008-advance-20261012-r05-right-triangle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"bcf7f339f16b2afa60a8b63df9fc5d59995239d06c20f24d548a4f780bdb6d5e","family_id":"qf-density12-right-triangle-pi-multiple","seed":202610125095,"semantic_template":"qf-density12-right-triangle-pi-multiple/\"16/7\""},"fields":{"title":"Exact π-Multiple Candidate without Periodic Wrapping","stem":"Candidate θ=(16/7)π radians. Give (exact degree value, does it equal exactly 90°?), without taking a modulus or wrapping a period.","answer":{"kind":"expression","value":"(2880/7, No)","explanation":"Multiply the rational π coefficient by 180 and reduce exactly; 450° is not 90°, with no floating-point π or tolerance. The exact result, retaining the requested order, is (2880/7, No)."},"skills":["Exact π-Multiple Candidate without Periodic Wrapping"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r05-right-triangle-0096","batch_id":"batch-20261008-advance-20261012-r05-right-triangle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"42dbc3dad02921797a6da8fa6fa94a9ddfedd5cffeb8e4da92aa5cbe4eabbc7f","family_id":"qf-density12-right-triangle-pi-multiple","seed":202610125096,"semantic_template":"qf-density12-right-triangle-pi-multiple/\"17/7\""},"fields":{"title":"Exact π-Multiple Candidate without Periodic Wrapping","stem":"Candidate θ=(17/7)π radians. Give (exact degree value, does it equal exactly 90°?), without taking a modulus or wrapping a period.","answer":{"kind":"expression","value":"(3060/7, No)","explanation":"Multiply the rational π coefficient by 180 and reduce exactly; 450° is not 90°, with no floating-point π or tolerance. The exact result, retaining the requested order, is (3060/7, No)."},"skills":["Exact π-Multiple Candidate without Periodic Wrapping"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r05-right-triangle-0097","batch_id":"batch-20261008-advance-20261012-r05-right-triangle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"aee1772560b3da1a8f974b7f53d1d9562203f51a07cd2e9e4391e564235c1e89","family_id":"qf-density12-right-triangle-pi-multiple","seed":202610125097,"semantic_template":"qf-density12-right-triangle-pi-multiple/\"18/7\""},"fields":{"title":"Exact π-Multiple Candidate without Periodic Wrapping","stem":"Candidate θ=(18/7)π radians. Give (exact degree value, does it equal exactly 90°?), without taking a modulus or wrapping a period.","answer":{"kind":"expression","value":"(3240/7, No)","explanation":"Multiply the rational π coefficient by 180 and reduce exactly; 450° is not 90°, with no floating-point π or tolerance. The exact result, retaining the requested order, is (3240/7, No)."},"skills":["Exact π-Multiple Candidate without Periodic Wrapping"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r05-right-triangle-0098","batch_id":"batch-20261008-advance-20261012-r05-right-triangle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"65a6554dc679c257128e5da79854f41773f5b370facb7b39226ded695842f292","family_id":"qf-density12-right-triangle-pi-multiple","seed":202610125098,"semantic_template":"qf-density12-right-triangle-pi-multiple/\"19/7\""},"fields":{"title":"Exact π-Multiple Candidate without Periodic Wrapping","stem":"Candidate θ=(19/7)π radians. Give (exact degree value, does it equal exactly 90°?), without taking a modulus or wrapping a period.","answer":{"kind":"expression","value":"(3420/7, No)","explanation":"Multiply the rational π coefficient by 180 and reduce exactly; 450° is not 90°, with no floating-point π or tolerance. The exact result, retaining the requested order, is (3420/7, No)."},"skills":["Exact π-Multiple Candidate without Periodic Wrapping"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r05-right-triangle-0099","batch_id":"batch-20261008-advance-20261012-r05-right-triangle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"1c0934d74feb7f4eb261b9d763854a562bd269794b0ae732bc5aa81e4813a72d","family_id":"qf-density12-right-triangle-pi-multiple","seed":202610125099,"semantic_template":"qf-density12-right-triangle-pi-multiple/\"20/7\""},"fields":{"title":"Exact π-Multiple Candidate without Periodic Wrapping","stem":"Candidate θ=(20/7)π radians. Give (exact degree value, does it equal exactly 90°?), without taking a modulus or wrapping a period.","answer":{"kind":"expression","value":"(3600/7, No)","explanation":"Multiply the rational π coefficient by 180 and reduce exactly; 450° is not 90°, with no floating-point π or tolerance. The exact result, retaining the requested order, is (3600/7, No)."},"skills":["Exact π-Multiple Candidate without Periodic Wrapping"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261012-r05-right-triangle-0100","batch_id":"batch-20261008-advance-20261012-r05-right-triangle-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"aa1449b9384110dba7aa1687d1f83037db0df33a90224593e56dc7a692636c68","family_id":"qf-density12-right-triangle-pi-multiple","seed":202610125100,"semantic_template":"qf-density12-right-triangle-pi-multiple/\"3/1\""},"fields":{"title":"Exact π-Multiple Candidate without Periodic Wrapping","stem":"Candidate θ=(21/7)π radians. Give (exact degree value, does it equal exactly 90°?), without taking a modulus or wrapping a period.","answer":{"kind":"expression","value":"(540/1, No)","explanation":"Multiply the rational π coefficient by 180 and reduce exactly; 450° is not 90°, with no floating-point π or tolerance. The exact result, retaining the requested order, is (540/1, No)."},"skills":["Exact π-Multiple Candidate without Periodic Wrapping"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}