{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261005-advance-20261006-r01-order-relation-0001","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"268523ef3d93605d2f4db0ae6382313eef6b3fd984e9fba55cd8a600a0c054f5","family_id":"qf-order-rational-comparison","seed":202610061001,"semantic_template":"qf-order-rational-comparison/{\"inputs\":[\"0/1\",\"0/1\"],\"operation\":\"rational_comparison\"}"},"fields":{"title":"Exact Order of Positive-Denominator Rationals","stem":"Under the usual real order, compare (0)/1 and (0)/1. Both denominators are positive. Give <, =, or > in that order.","answer":{"kind":"short_text","value":"=","explanation":"The exact cross products are 0 and 0, giving =. Positive denominators preserve the comparison direction."},"skills":["Exact Order of Positive-Denominator Rationals"],"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-20261005-advance-20261006-r01-order-relation-0002","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"137d56e54fc0304aa57f7279100e55d4146b2aa16fbb8392a353df537755b00b","family_id":"qf-order-rational-comparison","seed":202610061002,"semantic_template":"qf-order-rational-comparison/{\"inputs\":[\"-2/3\",\"-9/2\"],\"operation\":\"rational_comparison\"}"},"fields":{"title":"Exact Order of Positive-Denominator Rationals","stem":"Under the usual real order, compare (-2)/3 and (-9)/2. Both denominators are positive. Give <, =, or > in that order.","answer":{"kind":"short_text","value":">","explanation":"The exact cross products are -4 and -27, giving >. Positive denominators preserve the comparison direction."},"skills":["Exact Order of Positive-Denominator Rationals"],"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-20261005-advance-20261006-r01-order-relation-0003","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"7ddb06a23254c3671a4b5126f588859debe9cbaafd0f107ab4dde936ccc2de7b","family_id":"qf-order-rational-comparison","seed":202610061003,"semantic_template":"qf-order-rational-comparison/{\"inputs\":[\"3/4\",\"-8/3\"],\"operation\":\"rational_comparison\"}"},"fields":{"title":"Exact Order of Positive-Denominator Rationals","stem":"Under the usual real order, compare (3)/4 and (-8)/3. Both denominators are positive. Give <, =, or > in that order.","answer":{"kind":"short_text","value":">","explanation":"The exact cross products are 9 and -32, giving >. Positive denominators preserve the comparison direction."},"skills":["Exact Order of Positive-Denominator Rationals"],"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-20261005-advance-20261006-r01-order-relation-0004","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"a5e31c63151a88a4d7468e9c80868d2197829e148fcd6e2b64990acecf9b3baf","family_id":"qf-order-rational-comparison","seed":202610061004,"semantic_template":"qf-order-rational-comparison/{\"inputs\":[\"-4/5\",\"-5/4\"],\"operation\":\"rational_comparison\"}"},"fields":{"title":"Exact Order of Positive-Denominator Rationals","stem":"Under the usual real order, compare (-4)/5 and (-5)/4. Both denominators are positive. Give <, =, or > in that order.","answer":{"kind":"short_text","value":">","explanation":"The exact cross products are -16 and -25, giving >. Positive denominators preserve the comparison direction."},"skills":["Exact Order of Positive-Denominator Rationals"],"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-20261005-advance-20261006-r01-order-relation-0005","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"bd1093200b9ae76a380f9a2e1d60b5001ac19d99720d4f44df671dc7ae298826","family_id":"qf-order-rational-comparison","seed":202610061005,"semantic_template":"qf-order-rational-comparison/{\"inputs\":[\"5/6\",\"-6/1\"],\"operation\":\"rational_comparison\"}"},"fields":{"title":"Exact Order of Positive-Denominator Rationals","stem":"Under the usual real order, compare (5)/6 and (-6)/1. Both denominators are positive. Give <, =, or > in that order.","answer":{"kind":"short_text","value":">","explanation":"The exact cross products are 5 and -36, giving >. Positive denominators preserve the comparison direction."},"skills":["Exact Order of Positive-Denominator Rationals"],"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-20261005-advance-20261006-r01-order-relation-0006","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"dcc83a07f49823d18c5e0a3a72b2f06005101230c30aa50b5ca0e2647bc94e55","family_id":"qf-order-rational-comparison","seed":202610061006,"semantic_template":"qf-order-rational-comparison/{\"inputs\":[\"-3/1\",\"-5/2\"],\"operation\":\"rational_comparison\"}"},"fields":{"title":"Exact Order of Positive-Denominator Rationals","stem":"Under the usual real order, compare (-6)/2 and (-5)/2. Both denominators are positive. Give <, =, or > in that order.","answer":{"kind":"short_text","value":"<","explanation":"The exact cross products are -12 and -10, giving <. Positive denominators preserve the comparison direction."},"skills":["Exact Order of Positive-Denominator Rationals"],"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-20261005-advance-20261006-r01-order-relation-0007","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"b4a191c7e23855368a536787285ce236c86ad5338326ca81c3c540bfce11f55c","family_id":"qf-order-rational-comparison","seed":202610061007,"semantic_template":"qf-order-rational-comparison/{\"inputs\":[\"7/3\",\"7/3\"],\"operation\":\"rational_comparison\"}"},"fields":{"title":"Exact Order of Positive-Denominator Rationals","stem":"Under the usual real order, compare (7)/3 and (7)/3. Both denominators are positive. Give <, =, or > in that order.","answer":{"kind":"short_text","value":"=","explanation":"The exact cross products are 21 and 21, giving =. Positive denominators preserve the comparison direction."},"skills":["Exact Order of Positive-Denominator Rationals"],"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-20261005-advance-20261006-r01-order-relation-0008","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"2c209234063b8c9a4e811b06fb407285fc987385d83bca885ae24fed3c5771b1","family_id":"qf-order-rational-comparison","seed":202610061008,"semantic_template":"qf-order-rational-comparison/{\"inputs\":[\"-2/1\",\"-3/4\"],\"operation\":\"rational_comparison\"}"},"fields":{"title":"Exact Order of Positive-Denominator Rationals","stem":"Under the usual real order, compare (-8)/4 and (-3)/4. Both denominators are positive. Give <, =, or > in that order.","answer":{"kind":"short_text","value":"<","explanation":"The exact cross products are -32 and -12, giving <. Positive denominators preserve the comparison direction."},"skills":["Exact Order of Positive-Denominator Rationals"],"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-20261005-advance-20261006-r01-order-relation-0009","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"3004f1beabbc7914d0445829e32d92d2ae10965ecef4f298541df163654deac3","family_id":"qf-order-rational-comparison","seed":202610061009,"semantic_template":"qf-order-rational-comparison/{\"inputs\":[\"9/5\",\"-2/1\"],\"operation\":\"rational_comparison\"}"},"fields":{"title":"Exact Order of Positive-Denominator Rationals","stem":"Under the usual real order, compare (9)/5 and (-2)/1. Both denominators are positive. Give <, =, or > in that order.","answer":{"kind":"short_text","value":">","explanation":"The exact cross products are 9 and -10, giving >. Positive denominators preserve the comparison direction."},"skills":["Exact Order of Positive-Denominator Rationals"],"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-20261005-advance-20261006-r01-order-relation-0010","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"9e12d5482725b186fe649ddf97d80ca025b59a2f25bdb4d3349960936210c6fd","family_id":"qf-order-rational-comparison","seed":202610061010,"semantic_template":"qf-order-rational-comparison/{\"inputs\":[\"-5/3\",\"-11/2\"],\"operation\":\"rational_comparison\"}"},"fields":{"title":"Exact Order of Positive-Denominator Rationals","stem":"Under the usual real order, compare (-10)/6 and (-11)/2. Both denominators are positive. Give <, =, or > in that order.","answer":{"kind":"short_text","value":">","explanation":"The exact cross products are -20 and -66, giving >. Positive denominators preserve the comparison direction."},"skills":["Exact Order of Positive-Denominator Rationals"],"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-20261005-advance-20261006-r01-order-relation-0011","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"5eece9c68b25970f696099da27d4c37ca85bbbc1ef75d1aeffd0b249bba3200b","family_id":"qf-order-rational-comparison","seed":202610061011,"semantic_template":"qf-order-rational-comparison/{\"inputs\":[\"11/2\",\"0/1\"],\"operation\":\"rational_comparison\"}"},"fields":{"title":"Exact Order of Positive-Denominator Rationals","stem":"Under the usual real order, compare (11)/2 and (0)/3. Both denominators are positive. Give <, =, or > in that order.","answer":{"kind":"short_text","value":">","explanation":"The exact cross products are 33 and 0, giving >. Positive denominators preserve the comparison direction."},"skills":["Exact Order of Positive-Denominator Rationals"],"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-20261005-advance-20261006-r01-order-relation-0012","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"a9cb009f05067dca59c1111ca2d3891e0f72d7537410fd36a4f43d9d69e5ba24","family_id":"qf-order-rational-comparison","seed":202610061012,"semantic_template":"qf-order-rational-comparison/{\"inputs\":[\"-4/1\",\"1/4\"],\"operation\":\"rational_comparison\"}"},"fields":{"title":"Exact Order of Positive-Denominator Rationals","stem":"Under the usual real order, compare (-12)/3 and (1)/4. Both denominators are positive. Give <, =, or > in that order.","answer":{"kind":"short_text","value":"<","explanation":"The exact cross products are -48 and 3, giving <. Positive denominators preserve the comparison direction."},"skills":["Exact Order of Positive-Denominator Rationals"],"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-20261005-advance-20261006-r01-order-relation-0013","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"592e60a2d8b5ed8d212c32248f07b49086ef00d8d0d2a530ed54afe065fd3f3c","family_id":"qf-order-rational-comparison","seed":202610061013,"semantic_template":"qf-order-rational-comparison/{\"inputs\":[\"13/4\",\"13/4\"],\"operation\":\"rational_comparison\"}"},"fields":{"title":"Exact Order of Positive-Denominator Rationals","stem":"Under the usual real order, compare (13)/4 and (13)/4. Both denominators are positive. Give <, =, or > in that order.","answer":{"kind":"short_text","value":"=","explanation":"The exact cross products are 52 and 52, giving =. Positive denominators preserve the comparison direction."},"skills":["Exact Order of Positive-Denominator Rationals"],"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-20261005-advance-20261006-r01-order-relation-0014","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"17a67a25bdc67aa185eddbd2abf16c16a297b78cb7e852bbcbbeec4b33416818","family_id":"qf-order-rational-comparison","seed":202610061014,"semantic_template":"qf-order-rational-comparison/{\"inputs\":[\"-14/5\",\"3/2\"],\"operation\":\"rational_comparison\"}"},"fields":{"title":"Exact Order of Positive-Denominator Rationals","stem":"Under the usual real order, compare (-14)/5 and (3)/2. Both denominators are positive. Give <, =, or > in that order.","answer":{"kind":"short_text","value":"<","explanation":"The exact cross products are -28 and 15, giving <. Positive denominators preserve the comparison direction."},"skills":["Exact Order of Positive-Denominator Rationals"],"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-20261005-advance-20261006-r01-order-relation-0015","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"5c8e3ed6043f6e0d3e6a764d9a07e7c7f836afd968b5a8ef0e05107f6b02bf28","family_id":"qf-order-rational-comparison","seed":202610061015,"semantic_template":"qf-order-rational-comparison/{\"inputs\":[\"5/2\",\"4/3\"],\"operation\":\"rational_comparison\"}"},"fields":{"title":"Exact Order of Positive-Denominator Rationals","stem":"Under the usual real order, compare (15)/6 and (4)/3. Both denominators are positive. Give <, =, or > in that order.","answer":{"kind":"short_text","value":">","explanation":"The exact cross products are 45 and 24, giving >. Positive denominators preserve the comparison direction."},"skills":["Exact Order of Positive-Denominator Rationals"],"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-20261005-advance-20261006-r01-order-relation-0016","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"9c4905117283e8ef6b4c874de7223f2e70f2f0f92f689432a558799091598795","family_id":"qf-order-rational-comparison","seed":202610061016,"semantic_template":"qf-order-rational-comparison/{\"inputs\":[\"-8/1\",\"-17/4\"],\"operation\":\"rational_comparison\"}"},"fields":{"title":"Exact Order of Positive-Denominator Rationals","stem":"Under the usual real order, compare (-16)/2 and (-17)/4. Both denominators are positive. Give <, =, or > in that order.","answer":{"kind":"short_text","value":"<","explanation":"The exact cross products are -64 and -34, giving <. Positive denominators preserve the comparison direction."},"skills":["Exact Order of Positive-Denominator Rationals"],"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-20261005-advance-20261006-r01-order-relation-0017","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"67f4737d1885c4decac3787c5578ebc7cde8bcafd0e031081b15ddcfb7c5be31","family_id":"qf-order-rational-comparison","seed":202610061017,"semantic_template":"qf-order-rational-comparison/{\"inputs\":[\"17/3\",\"6/1\"],\"operation\":\"rational_comparison\"}"},"fields":{"title":"Exact Order of Positive-Denominator Rationals","stem":"Under the usual real order, compare (17)/3 and (6)/1. Both denominators are positive. Give <, =, or > in that order.","answer":{"kind":"short_text","value":"<","explanation":"The exact cross products are 17 and 18, giving <. Positive denominators preserve the comparison direction."},"skills":["Exact Order of Positive-Denominator Rationals"],"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-20261005-advance-20261006-r01-order-relation-0018","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"9069f0026b2077be46da09611da73f44a3bf75669bb3a9e97f6f10eb86a03bea","family_id":"qf-order-rational-comparison","seed":202610061018,"semantic_template":"qf-order-rational-comparison/{\"inputs\":[\"-9/2\",\"7/2\"],\"operation\":\"rational_comparison\"}"},"fields":{"title":"Exact Order of Positive-Denominator Rationals","stem":"Under the usual real order, compare (-18)/4 and (7)/2. Both denominators are positive. Give <, =, or > in that order.","answer":{"kind":"short_text","value":"<","explanation":"The exact cross products are -36 and 28, giving <. Positive denominators preserve the comparison direction."},"skills":["Exact Order of Positive-Denominator Rationals"],"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-20261005-advance-20261006-r01-order-relation-0019","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"75191e2f69d8a8c928579ae54d624d9452c06e572307bcb79efabf3277fe028d","family_id":"qf-order-rational-comparison","seed":202610061019,"semantic_template":"qf-order-rational-comparison/{\"inputs\":[\"19/5\",\"19/5\"],\"operation\":\"rational_comparison\"}"},"fields":{"title":"Exact Order of Positive-Denominator Rationals","stem":"Under the usual real order, compare (19)/5 and (19)/5. Both denominators are positive. Give <, =, or > in that order.","answer":{"kind":"short_text","value":"=","explanation":"The exact cross products are 95 and 95, giving =. Positive denominators preserve the comparison direction."},"skills":["Exact Order of Positive-Denominator Rationals"],"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-20261005-advance-20261006-r01-order-relation-0020","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"1ec970dc90e949d3706b52d75e01a1bcd175ffab4d381fc8f33b89a486d46d11","family_id":"qf-order-rational-comparison","seed":202610061020,"semantic_template":"qf-order-rational-comparison/{\"inputs\":[\"-10/3\",\"9/4\"],\"operation\":\"rational_comparison\"}"},"fields":{"title":"Exact Order of Positive-Denominator Rationals","stem":"Under the usual real order, compare (-20)/6 and (9)/4. Both denominators are positive. Give <, =, or > in that order.","answer":{"kind":"short_text","value":"<","explanation":"The exact cross products are -80 and 54, giving <. Positive denominators preserve the comparison direction."},"skills":["Exact Order of Positive-Denominator Rationals"],"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-20261005-advance-20261006-r01-order-relation-0021","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"8878b5c9eafff79347f84fa2d0d15658f64ffef223bc34b52b3f58c9055a3e7b","family_id":"qf-order-rational-comparison","seed":202610061021,"semantic_template":"qf-order-rational-comparison/{\"inputs\":[\"21/2\",\"10/1\"],\"operation\":\"rational_comparison\"}"},"fields":{"title":"Exact Order of Positive-Denominator Rationals","stem":"Under the usual real order, compare (21)/2 and (10)/1. Both denominators are positive. Give <, =, or > in that order.","answer":{"kind":"short_text","value":">","explanation":"The exact cross products are 21 and 20, giving >. Positive denominators preserve the comparison direction."},"skills":["Exact Order of Positive-Denominator Rationals"],"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-20261005-advance-20261006-r01-order-relation-0022","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"4a2816f5c65750868003363384a9e1c680a55d40d02367b3726ec13535518233","family_id":"qf-order-rational-comparison","seed":202610061022,"semantic_template":"qf-order-rational-comparison/{\"inputs\":[\"-22/3\",\"-23/2\"],\"operation\":\"rational_comparison\"}"},"fields":{"title":"Exact Order of Positive-Denominator Rationals","stem":"Under the usual real order, compare (-22)/3 and (-23)/2. Both denominators are positive. Give <, =, or > in that order.","answer":{"kind":"short_text","value":">","explanation":"The exact cross products are -44 and -69, giving >. Positive denominators preserve the comparison direction."},"skills":["Exact Order of Positive-Denominator Rationals"],"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-20261005-advance-20261006-r01-order-relation-0023","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"27262f38b697c739b5413fdc5e5ed84d45ba5ea9295efa43ff8102128d00a016","family_id":"qf-order-rational-comparison","seed":202610061023,"semantic_template":"qf-order-rational-comparison/{\"inputs\":[\"23/4\",\"4/1\"],\"operation\":\"rational_comparison\"}"},"fields":{"title":"Exact Order of Positive-Denominator Rationals","stem":"Under the usual real order, compare (23)/4 and (12)/3. Both denominators are positive. Give <, =, or > in that order.","answer":{"kind":"short_text","value":">","explanation":"The exact cross products are 69 and 48, giving >. Positive denominators preserve the comparison direction."},"skills":["Exact Order of Positive-Denominator Rationals"],"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-20261005-advance-20261006-r01-order-relation-0024","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"7896de0057ad784c916e2e734eeb74bb709c93a8b72529ebe5b17feb74157499","family_id":"qf-order-rational-comparison","seed":202610061024,"semantic_template":"qf-order-rational-comparison/{\"inputs\":[\"-24/5\",\"13/4\"],\"operation\":\"rational_comparison\"}"},"fields":{"title":"Exact Order of Positive-Denominator Rationals","stem":"Under the usual real order, compare (-24)/5 and (13)/4. Both denominators are positive. Give <, =, or > in that order.","answer":{"kind":"short_text","value":"<","explanation":"The exact cross products are -96 and 65, giving <. Positive denominators preserve the comparison direction."},"skills":["Exact Order of Positive-Denominator Rationals"],"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-20261005-advance-20261006-r01-order-relation-0025","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"1906d29fc3df3f0943bf77028210e01bfe6338e3a836f479e7782456f828b57d","family_id":"qf-order-rational-comparison","seed":202610061025,"semantic_template":"qf-order-rational-comparison/{\"inputs\":[\"25/6\",\"25/6\"],\"operation\":\"rational_comparison\"}"},"fields":{"title":"Exact Order of Positive-Denominator Rationals","stem":"Under the usual real order, compare (25)/6 and (25)/6. Both denominators are positive. Give <, =, or > in that order.","answer":{"kind":"short_text","value":"=","explanation":"The exact cross products are 150 and 150, giving =. Positive denominators preserve the comparison direction."},"skills":["Exact Order of Positive-Denominator Rationals"],"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-20261005-advance-20261006-r01-order-relation-0026","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"12c2ed1d9e9e2f216ae108f3240a33ee08023a0c5770114a4979561dc025e77f","family_id":"qf-order-finite-extrema","seed":202610061026,"semantic_template":"qf-order-finite-extrema/{\"inputs\":[\"0\",\"0\"],\"operation\":\"finite_extrema\"}"},"fields":{"title":"Minimum and Maximum of a Finite Real Set","stem":"Under the usual real order, the explicit finite nonempty set has elements {0}. Give (minimum, maximum).","answer":{"kind":"expression","value":"(0, 0)","explanation":"Order the given elements to obtain (0, 0). Listing order is irrelevant; a singleton has equal extrema, while this rule does not assign extrema to an empty set."},"skills":["Minimum and Maximum of a Finite Real Set"],"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-20261005-advance-20261006-r01-order-relation-0027","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"b7d67da55399a957af310519308ec27d6b4333cee183ba02db98551db9149514","family_id":"qf-order-finite-extrema","seed":202610061027,"semantic_template":"qf-order-finite-extrema/{\"inputs\":[\"-1\",\"3\"],\"operation\":\"finite_extrema\"}"},"fields":{"title":"Minimum and Maximum of a Finite Real Set","stem":"Under the usual real order, the explicit finite nonempty set has elements {-1, 0, 3}. Give (minimum, maximum).","answer":{"kind":"expression","value":"(-1, 3)","explanation":"Order the given elements to obtain (-1, 3). Listing order is irrelevant; a singleton has equal extrema, while this rule does not assign extrema to an empty set."},"skills":["Minimum and Maximum of a Finite Real Set"],"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-20261005-advance-20261006-r01-order-relation-0028","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"3abe26b4ef624f6eae098b50f496345eb936935da751b1edc9d3eceb04a1d6ae","family_id":"qf-order-finite-extrema","seed":202610061028,"semantic_template":"qf-order-finite-extrema/{\"inputs\":[\"-2\",\"4\"],\"operation\":\"finite_extrema\"}"},"fields":{"title":"Minimum and Maximum of a Finite Real Set","stem":"Under the usual real order, the explicit finite nonempty set has elements {-2, 0, 4}. Give (minimum, maximum).","answer":{"kind":"expression","value":"(-2, 4)","explanation":"Order the given elements to obtain (-2, 4). Listing order is irrelevant; a singleton has equal extrema, while this rule does not assign extrema to an empty set."},"skills":["Minimum and Maximum of a Finite Real Set"],"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-20261005-advance-20261006-r01-order-relation-0029","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"5edaac0223ef201e6fadade4b8fe8bdf527c81b08e95fc9f2908c618d3b2ed3d","family_id":"qf-order-finite-extrema","seed":202610061029,"semantic_template":"qf-order-finite-extrema/{\"inputs\":[\"-3\",\"5\"],\"operation\":\"finite_extrema\"}"},"fields":{"title":"Minimum and Maximum of a Finite Real Set","stem":"Under the usual real order, the explicit finite nonempty set has elements {-3, 0, 5}. Give (minimum, maximum).","answer":{"kind":"expression","value":"(-3, 5)","explanation":"Order the given elements to obtain (-3, 5). Listing order is irrelevant; a singleton has equal extrema, while this rule does not assign extrema to an empty set."},"skills":["Minimum and Maximum of a Finite Real Set"],"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-20261005-advance-20261006-r01-order-relation-0030","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"632c6a5b96fbdaa9483cf9587b65acaea1568d93b97acfb930b65bc08e10e1bb","family_id":"qf-order-finite-extrema","seed":202610061030,"semantic_template":"qf-order-finite-extrema/{\"inputs\":[\"-7\",\"-4\"],\"operation\":\"finite_extrema\"}"},"fields":{"title":"Minimum and Maximum of a Finite Real Set","stem":"Under the usual real order, the explicit finite nonempty set has elements {-7, -6, -4}. Give (minimum, maximum).","answer":{"kind":"expression","value":"(-7, -4)","explanation":"Order the given elements to obtain (-7, -4). Listing order is irrelevant; a singleton has equal extrema, while this rule does not assign extrema to an empty set."},"skills":["Minimum and Maximum of a Finite Real Set"],"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-20261005-advance-20261006-r01-order-relation-0031","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"9a9a92ef4a9dce23278f83de28b43d36ed774c10df251de032198193a7118cc7","family_id":"qf-order-finite-extrema","seed":202610061031,"semantic_template":"qf-order-finite-extrema/{\"inputs\":[\"-5\",\"7\"],\"operation\":\"finite_extrema\"}"},"fields":{"title":"Minimum and Maximum of a Finite Real Set","stem":"Under the usual real order, the explicit finite nonempty set has elements {-5, 0, 7}. Give (minimum, maximum).","answer":{"kind":"expression","value":"(-5, 7)","explanation":"Order the given elements to obtain (-5, 7). Listing order is irrelevant; a singleton has equal extrema, while this rule does not assign extrema to an empty set."},"skills":["Minimum and Maximum of a Finite Real Set"],"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-20261005-advance-20261006-r01-order-relation-0032","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"0773db03971fd7955823b3fed8792ae68a5cbf530c3aeb26ed7fb80311505a7e","family_id":"qf-order-finite-extrema","seed":202610061032,"semantic_template":"qf-order-finite-extrema/{\"inputs\":[\"-6\",\"8\"],\"operation\":\"finite_extrema\"}"},"fields":{"title":"Minimum and Maximum of a Finite Real Set","stem":"Under the usual real order, the explicit finite nonempty set has elements {-6, 0, 8}. Give (minimum, maximum).","answer":{"kind":"expression","value":"(-6, 8)","explanation":"Order the given elements to obtain (-6, 8). Listing order is irrelevant; a singleton has equal extrema, while this rule does not assign extrema to an empty set."},"skills":["Minimum and Maximum of a Finite Real Set"],"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-20261005-advance-20261006-r01-order-relation-0033","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"436ad9251d3c4473e38f5fbfcd89ec2ea120f97c7a67521f80eaa52e092da1e8","family_id":"qf-order-finite-extrema","seed":202610061033,"semantic_template":"qf-order-finite-extrema/{\"inputs\":[\"-7\",\"9\"],\"operation\":\"finite_extrema\"}"},"fields":{"title":"Minimum and Maximum of a Finite Real Set","stem":"Under the usual real order, the explicit finite nonempty set has elements {-7, 0, 9}. Give (minimum, maximum).","answer":{"kind":"expression","value":"(-7, 9)","explanation":"Order the given elements to obtain (-7, 9). Listing order is irrelevant; a singleton has equal extrema, while this rule does not assign extrema to an empty set."},"skills":["Minimum and Maximum of a Finite Real Set"],"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-20261005-advance-20261006-r01-order-relation-0034","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"bc9266cd7f1133e0bb62e93aa12ca948c917e23645a0ac6e7558cc173df91e1a","family_id":"qf-order-finite-extrema","seed":202610061034,"semantic_template":"qf-order-finite-extrema/{\"inputs\":[\"-11\",\"-8\"],\"operation\":\"finite_extrema\"}"},"fields":{"title":"Minimum and Maximum of a Finite Real Set","stem":"Under the usual real order, the explicit finite nonempty set has elements {-11, -10, -8}. Give (minimum, maximum).","answer":{"kind":"expression","value":"(-11, -8)","explanation":"Order the given elements to obtain (-11, -8). Listing order is irrelevant; a singleton has equal extrema, while this rule does not assign extrema to an empty set."},"skills":["Minimum and Maximum of a Finite Real Set"],"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-20261005-advance-20261006-r01-order-relation-0035","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"ba7dcee08fc6f5fac4c022311818580135e0c86b0ddcf5845efe3a883eab68a2","family_id":"qf-order-finite-extrema","seed":202610061035,"semantic_template":"qf-order-finite-extrema/{\"inputs\":[\"-9\",\"11\"],\"operation\":\"finite_extrema\"}"},"fields":{"title":"Minimum and Maximum of a Finite Real Set","stem":"Under the usual real order, the explicit finite nonempty set has elements {-9, 0, 11}. Give (minimum, maximum).","answer":{"kind":"expression","value":"(-9, 11)","explanation":"Order the given elements to obtain (-9, 11). Listing order is irrelevant; a singleton has equal extrema, while this rule does not assign extrema to an empty set."},"skills":["Minimum and Maximum of a Finite Real Set"],"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-20261005-advance-20261006-r01-order-relation-0036","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"8e1ef0329a1355a46a9cabb15a89fccff42ab4066befd7cb12868eb0960a1a7e","family_id":"qf-order-finite-extrema","seed":202610061036,"semantic_template":"qf-order-finite-extrema/{\"inputs\":[\"-10\",\"12\"],\"operation\":\"finite_extrema\"}"},"fields":{"title":"Minimum and Maximum of a Finite Real Set","stem":"Under the usual real order, the explicit finite nonempty set has elements {-10, 0, 12}. Give (minimum, maximum).","answer":{"kind":"expression","value":"(-10, 12)","explanation":"Order the given elements to obtain (-10, 12). Listing order is irrelevant; a singleton has equal extrema, while this rule does not assign extrema to an empty set."},"skills":["Minimum and Maximum of a Finite Real Set"],"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-20261005-advance-20261006-r01-order-relation-0037","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"37001e74fd3b9fa3c4ba2a1c7fb06b8320530072dba40f3ffaa9dd17bebab496","family_id":"qf-order-finite-extrema","seed":202610061037,"semantic_template":"qf-order-finite-extrema/{\"inputs\":[\"-11\",\"13\"],\"operation\":\"finite_extrema\"}"},"fields":{"title":"Minimum and Maximum of a Finite Real Set","stem":"Under the usual real order, the explicit finite nonempty set has elements {-11, 0, 13}. Give (minimum, maximum).","answer":{"kind":"expression","value":"(-11, 13)","explanation":"Order the given elements to obtain (-11, 13). Listing order is irrelevant; a singleton has equal extrema, while this rule does not assign extrema to an empty set."},"skills":["Minimum and Maximum of a Finite Real Set"],"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-20261005-advance-20261006-r01-order-relation-0038","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"78f3ac35316426c19616158223633ed5d52a4c9ed5419c0fc9e952dab16d3088","family_id":"qf-order-finite-extrema","seed":202610061038,"semantic_template":"qf-order-finite-extrema/{\"inputs\":[\"-15\",\"-12\"],\"operation\":\"finite_extrema\"}"},"fields":{"title":"Minimum and Maximum of a Finite Real Set","stem":"Under the usual real order, the explicit finite nonempty set has elements {-15, -14, -12}. Give (minimum, maximum).","answer":{"kind":"expression","value":"(-15, -12)","explanation":"Order the given elements to obtain (-15, -12). Listing order is irrelevant; a singleton has equal extrema, while this rule does not assign extrema to an empty set."},"skills":["Minimum and Maximum of a Finite Real Set"],"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-20261005-advance-20261006-r01-order-relation-0039","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"92e11d0407ea37dbdee70b2bea24691b39febf9178caf73b7b7964a8af6a2815","family_id":"qf-order-finite-extrema","seed":202610061039,"semantic_template":"qf-order-finite-extrema/{\"inputs\":[\"-13\",\"15\"],\"operation\":\"finite_extrema\"}"},"fields":{"title":"Minimum and Maximum of a Finite Real Set","stem":"Under the usual real order, the explicit finite nonempty set has elements {-13, 0, 15}. Give (minimum, maximum).","answer":{"kind":"expression","value":"(-13, 15)","explanation":"Order the given elements to obtain (-13, 15). Listing order is irrelevant; a singleton has equal extrema, while this rule does not assign extrema to an empty set."},"skills":["Minimum and Maximum of a Finite Real Set"],"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-20261005-advance-20261006-r01-order-relation-0040","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"eafb14583c3282bb14ddf99ff02fdd5ca283b29d12b6102abdfd77d8239aaca8","family_id":"qf-order-finite-extrema","seed":202610061040,"semantic_template":"qf-order-finite-extrema/{\"inputs\":[\"-14\",\"16\"],\"operation\":\"finite_extrema\"}"},"fields":{"title":"Minimum and Maximum of a Finite Real Set","stem":"Under the usual real order, the explicit finite nonempty set has elements {-14, 0, 16}. Give (minimum, maximum).","answer":{"kind":"expression","value":"(-14, 16)","explanation":"Order the given elements to obtain (-14, 16). Listing order is irrelevant; a singleton has equal extrema, while this rule does not assign extrema to an empty set."},"skills":["Minimum and Maximum of a Finite Real Set"],"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-20261005-advance-20261006-r01-order-relation-0041","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"e18343be4bf527d873b15fa977344d519ddf76cb4673bed89dfcbd4759ca68db","family_id":"qf-order-finite-extrema","seed":202610061041,"semantic_template":"qf-order-finite-extrema/{\"inputs\":[\"-15\",\"17\"],\"operation\":\"finite_extrema\"}"},"fields":{"title":"Minimum and Maximum of a Finite Real Set","stem":"Under the usual real order, the explicit finite nonempty set has elements {-15, 0, 17}. Give (minimum, maximum).","answer":{"kind":"expression","value":"(-15, 17)","explanation":"Order the given elements to obtain (-15, 17). Listing order is irrelevant; a singleton has equal extrema, while this rule does not assign extrema to an empty set."},"skills":["Minimum and Maximum of a Finite Real Set"],"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-20261005-advance-20261006-r01-order-relation-0042","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"a72d6168738da50b030cecb4ccf85707a8bb985d88ff16113484ad1c600e492c","family_id":"qf-order-finite-extrema","seed":202610061042,"semantic_template":"qf-order-finite-extrema/{\"inputs\":[\"-19\",\"-16\"],\"operation\":\"finite_extrema\"}"},"fields":{"title":"Minimum and Maximum of a Finite Real Set","stem":"Under the usual real order, the explicit finite nonempty set has elements {-19, -18, -16}. Give (minimum, maximum).","answer":{"kind":"expression","value":"(-19, -16)","explanation":"Order the given elements to obtain (-19, -16). Listing order is irrelevant; a singleton has equal extrema, while this rule does not assign extrema to an empty set."},"skills":["Minimum and Maximum of a Finite Real Set"],"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-20261005-advance-20261006-r01-order-relation-0043","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"90da6aa74b5f7048ef5fbfddce4751e5b396c3e51754d9cc451b3d781796c5e5","family_id":"qf-order-finite-extrema","seed":202610061043,"semantic_template":"qf-order-finite-extrema/{\"inputs\":[\"-17\",\"19\"],\"operation\":\"finite_extrema\"}"},"fields":{"title":"Minimum and Maximum of a Finite Real Set","stem":"Under the usual real order, the explicit finite nonempty set has elements {-17, 0, 19}. Give (minimum, maximum).","answer":{"kind":"expression","value":"(-17, 19)","explanation":"Order the given elements to obtain (-17, 19). Listing order is irrelevant; a singleton has equal extrema, while this rule does not assign extrema to an empty set."},"skills":["Minimum and Maximum of a Finite Real Set"],"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-20261005-advance-20261006-r01-order-relation-0044","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"6e4005d1b0b1f5169e868323f80475a4753a3447162cb2972c1f86147d9187cf","family_id":"qf-order-finite-extrema","seed":202610061044,"semantic_template":"qf-order-finite-extrema/{\"inputs\":[\"-18\",\"20\"],\"operation\":\"finite_extrema\"}"},"fields":{"title":"Minimum and Maximum of a Finite Real Set","stem":"Under the usual real order, the explicit finite nonempty set has elements {-18, 0, 20}. Give (minimum, maximum).","answer":{"kind":"expression","value":"(-18, 20)","explanation":"Order the given elements to obtain (-18, 20). Listing order is irrelevant; a singleton has equal extrema, while this rule does not assign extrema to an empty set."},"skills":["Minimum and Maximum of a Finite Real Set"],"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-20261005-advance-20261006-r01-order-relation-0045","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"0301f29bbf3f74d35e213ed65fac400547dbdcfa6d7cb394ec572ce26871223a","family_id":"qf-order-finite-extrema","seed":202610061045,"semantic_template":"qf-order-finite-extrema/{\"inputs\":[\"-19\",\"21\"],\"operation\":\"finite_extrema\"}"},"fields":{"title":"Minimum and Maximum of a Finite Real Set","stem":"Under the usual real order, the explicit finite nonempty set has elements {-19, 0, 21}. Give (minimum, maximum).","answer":{"kind":"expression","value":"(-19, 21)","explanation":"Order the given elements to obtain (-19, 21). Listing order is irrelevant; a singleton has equal extrema, while this rule does not assign extrema to an empty set."},"skills":["Minimum and Maximum of a Finite Real Set"],"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-20261005-advance-20261006-r01-order-relation-0046","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"29c8e75a5cc85c00ec16548ed50d0d49d2cef6f3d1d8d34fbd6645cb8f0db0b6","family_id":"qf-order-finite-extrema","seed":202610061046,"semantic_template":"qf-order-finite-extrema/{\"inputs\":[\"-23\",\"-20\"],\"operation\":\"finite_extrema\"}"},"fields":{"title":"Minimum and Maximum of a Finite Real Set","stem":"Under the usual real order, the explicit finite nonempty set has elements {-23, -22, -20}. Give (minimum, maximum).","answer":{"kind":"expression","value":"(-23, -20)","explanation":"Order the given elements to obtain (-23, -20). Listing order is irrelevant; a singleton has equal extrema, while this rule does not assign extrema to an empty set."},"skills":["Minimum and Maximum of a Finite Real Set"],"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-20261005-advance-20261006-r01-order-relation-0047","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"91eb23762fb79ac31a6e7e1eacd28f36362c20d26f03a520dceb3d264535a4a1","family_id":"qf-order-finite-extrema","seed":202610061047,"semantic_template":"qf-order-finite-extrema/{\"inputs\":[\"-21\",\"23\"],\"operation\":\"finite_extrema\"}"},"fields":{"title":"Minimum and Maximum of a Finite Real Set","stem":"Under the usual real order, the explicit finite nonempty set has elements {-21, 0, 23}. Give (minimum, maximum).","answer":{"kind":"expression","value":"(-21, 23)","explanation":"Order the given elements to obtain (-21, 23). Listing order is irrelevant; a singleton has equal extrema, while this rule does not assign extrema to an empty set."},"skills":["Minimum and Maximum of a Finite Real Set"],"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-20261005-advance-20261006-r01-order-relation-0048","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"97a6b51ba06ce5eae092cf6774f247a1e7b8ead342d8fe1d3ba23bbab9a42d52","family_id":"qf-order-finite-extrema","seed":202610061048,"semantic_template":"qf-order-finite-extrema/{\"inputs\":[\"-22\",\"24\"],\"operation\":\"finite_extrema\"}"},"fields":{"title":"Minimum and Maximum of a Finite Real Set","stem":"Under the usual real order, the explicit finite nonempty set has elements {-22, 0, 24}. Give (minimum, maximum).","answer":{"kind":"expression","value":"(-22, 24)","explanation":"Order the given elements to obtain (-22, 24). Listing order is irrelevant; a singleton has equal extrema, while this rule does not assign extrema to an empty set."},"skills":["Minimum and Maximum of a Finite Real Set"],"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-20261005-advance-20261006-r01-order-relation-0049","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"28c6bba987bcc0d103f8a43f3a3214de7e2166ce609305ffa88b8ca986ec376c","family_id":"qf-order-finite-extrema","seed":202610061049,"semantic_template":"qf-order-finite-extrema/{\"inputs\":[\"-23\",\"25\"],\"operation\":\"finite_extrema\"}"},"fields":{"title":"Minimum and Maximum of a Finite Real Set","stem":"Under the usual real order, the explicit finite nonempty set has elements {-23, 0, 25}. Give (minimum, maximum).","answer":{"kind":"expression","value":"(-23, 25)","explanation":"Order the given elements to obtain (-23, 25). Listing order is irrelevant; a singleton has equal extrema, while this rule does not assign extrema to an empty set."},"skills":["Minimum and Maximum of a Finite Real Set"],"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-20261005-advance-20261006-r01-order-relation-0050","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"cff9b01ca1ec781f891a3b5cce8bbc3fdede0dd1e5c9afb0261bde5d135b5aef","family_id":"qf-order-finite-extrema","seed":202610061050,"semantic_template":"qf-order-finite-extrema/{\"inputs\":[\"-27\",\"-24\"],\"operation\":\"finite_extrema\"}"},"fields":{"title":"Minimum and Maximum of a Finite Real Set","stem":"Under the usual real order, the explicit finite nonempty set has elements {-27, -26, -24}. Give (minimum, maximum).","answer":{"kind":"expression","value":"(-27, -24)","explanation":"Order the given elements to obtain (-27, -24). Listing order is irrelevant; a singleton has equal extrema, while this rule does not assign extrema to an empty set."},"skills":["Minimum and Maximum of a Finite Real Set"],"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-20261005-advance-20261006-r01-order-relation-0051","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"66678a2aa9cab171ef38cb8fb94095f4a7c96c2a7f2f63a1f4530eafdae4f57b","family_id":"qf-order-closed-interval","seed":202610061051,"semantic_template":"qf-order-closed-interval/{\"inputs\":[\"0/1\",\"0\",\"0\"],\"operation\":\"closed_interval\"}"},"fields":{"title":"Membership Including Closed Endpoints","stem":"Under the usual real order, is (0)/1 in the closed interval [0, 0]? The denominator is positive and both endpoints are included.","answer":{"kind":"short_text","value":"Yes","explanation":"Check 0·1≤0≤0·1 exactly, obtaining Yes. A singleton closed interval still contains its endpoint."},"skills":["Membership Including Closed Endpoints"],"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-20261005-advance-20261006-r01-order-relation-0052","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"b21ed0e85608f3064fc09ac6499b914bb43d01acf2bd09b9e0a3420495ed2142","family_id":"qf-order-closed-interval","seed":202610061052,"semantic_template":"qf-order-closed-interval/{\"inputs\":[\"3/1\",\"-1\",\"3\"],\"operation\":\"closed_interval\"}"},"fields":{"title":"Membership Including Closed Endpoints","stem":"Under the usual real order, is (6)/2 in the closed interval [-1, 3]? The denominator is positive and both endpoints are included.","answer":{"kind":"short_text","value":"Yes","explanation":"Check -1·2≤6≤3·2 exactly, obtaining Yes. A singleton closed interval still contains its endpoint."},"skills":["Membership Including Closed Endpoints"],"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-20261005-advance-20261006-r01-order-relation-0053","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"d7e5c99926fa793869933dc6427ad000bbce90d3b89cbee48198b05c3c39c56d","family_id":"qf-order-closed-interval","seed":202610061053,"semantic_template":"qf-order-closed-interval/{\"inputs\":[\"-7/3\",\"-2\",\"4\"],\"operation\":\"closed_interval\"}"},"fields":{"title":"Membership Including Closed Endpoints","stem":"Under the usual real order, is (-7)/3 in the closed interval [-2, 4]? The denominator is positive and both endpoints are included.","answer":{"kind":"short_text","value":"No","explanation":"Check -2·3≤-7≤4·3 exactly, obtaining No. A singleton closed interval still contains its endpoint."},"skills":["Membership Including Closed Endpoints"],"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-20261005-advance-20261006-r01-order-relation-0054","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"38526084951d31422387a99341353d9679f35db2b2223d36eca3c24d85d81e94","family_id":"qf-order-closed-interval","seed":202610061054,"semantic_template":"qf-order-closed-interval/{\"inputs\":[\"21/4\",\"-3\",\"5\"],\"operation\":\"closed_interval\"}"},"fields":{"title":"Membership Including Closed Endpoints","stem":"Under the usual real order, is (21)/4 in the closed interval [-3, 5]? The denominator is positive and both endpoints are included.","answer":{"kind":"short_text","value":"No","explanation":"Check -3·4≤21≤5·4 exactly, obtaining No. A singleton closed interval still contains its endpoint."},"skills":["Membership Including Closed Endpoints"],"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-20261005-advance-20261006-r01-order-relation-0055","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"89ac70916b6a40583a2695975157771623ac893f41ee817289b94feeae987b51","family_id":"qf-order-closed-interval","seed":202610061055,"semantic_template":"qf-order-closed-interval/{\"inputs\":[\"1/1\",\"-4\",\"6\"],\"operation\":\"closed_interval\"}"},"fields":{"title":"Membership Including Closed Endpoints","stem":"Under the usual real order, is (1)/1 in the closed interval [-4, 6]? The denominator is positive and both endpoints are included.","answer":{"kind":"short_text","value":"Yes","explanation":"Check -4·1≤1≤6·1 exactly, obtaining Yes. A singleton closed interval still contains its endpoint."},"skills":["Membership Including Closed Endpoints"],"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-20261005-advance-20261006-r01-order-relation-0056","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"d1ffe5982e51e1b42e1c05e74971d0e72a25ddf893b368b1a549b47a4a8e102a","family_id":"qf-order-closed-interval","seed":202610061056,"semantic_template":"qf-order-closed-interval/{\"inputs\":[\"-5/1\",\"-5\",\"7\"],\"operation\":\"closed_interval\"}"},"fields":{"title":"Membership Including Closed Endpoints","stem":"Under the usual real order, is (-10)/2 in the closed interval [-5, 7]? The denominator is positive and both endpoints are included.","answer":{"kind":"short_text","value":"Yes","explanation":"Check -5·2≤-10≤7·2 exactly, obtaining Yes. A singleton closed interval still contains its endpoint."},"skills":["Membership Including Closed Endpoints"],"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-20261005-advance-20261006-r01-order-relation-0057","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"136f0b0fbd57d41911c6383ffcd2f8d164c02457a7dfd5893e5abc0f23f6455e","family_id":"qf-order-closed-interval","seed":202610061057,"semantic_template":"qf-order-closed-interval/{\"inputs\":[\"8/1\",\"-6\",\"8\"],\"operation\":\"closed_interval\"}"},"fields":{"title":"Membership Including Closed Endpoints","stem":"Under the usual real order, is (24)/3 in the closed interval [-6, 8]? The denominator is positive and both endpoints are included.","answer":{"kind":"short_text","value":"Yes","explanation":"Check -6·3≤24≤8·3 exactly, obtaining Yes. A singleton closed interval still contains its endpoint."},"skills":["Membership Including Closed Endpoints"],"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-20261005-advance-20261006-r01-order-relation-0058","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"19125d61f699a4d54b15fca96f3731386ac8748e57b2e0b08cb660546548a1e8","family_id":"qf-order-closed-interval","seed":202610061058,"semantic_template":"qf-order-closed-interval/{\"inputs\":[\"-29/4\",\"-7\",\"9\"],\"operation\":\"closed_interval\"}"},"fields":{"title":"Membership Including Closed Endpoints","stem":"Under the usual real order, is (-29)/4 in the closed interval [-7, 9]? The denominator is positive and both endpoints are included.","answer":{"kind":"short_text","value":"No","explanation":"Check -7·4≤-29≤9·4 exactly, obtaining No. A singleton closed interval still contains its endpoint."},"skills":["Membership Including Closed Endpoints"],"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-20261005-advance-20261006-r01-order-relation-0059","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"2a010bf8b7c3e480935585c9cd3d1aa24ce11d8b4bc1b0c513784deb3bf4f300","family_id":"qf-order-closed-interval","seed":202610061059,"semantic_template":"qf-order-closed-interval/{\"inputs\":[\"11/1\",\"-8\",\"10\"],\"operation\":\"closed_interval\"}"},"fields":{"title":"Membership Including Closed Endpoints","stem":"Under the usual real order, is (11)/1 in the closed interval [-8, 10]? The denominator is positive and both endpoints are included.","answer":{"kind":"short_text","value":"No","explanation":"Check -8·1≤11≤10·1 exactly, obtaining No. A singleton closed interval still contains its endpoint."},"skills":["Membership Including Closed Endpoints"],"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-20261005-advance-20261006-r01-order-relation-0060","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"23b6646bbf5513d64f28a972aaf9e7fb5a295120d305d7bb10e93681739170c0","family_id":"qf-order-closed-interval","seed":202610061060,"semantic_template":"qf-order-closed-interval/{\"inputs\":[\"1/2\",\"-9\",\"11\"],\"operation\":\"closed_interval\"}"},"fields":{"title":"Membership Including Closed Endpoints","stem":"Under the usual real order, is (1)/2 in the closed interval [-9, 11]? The denominator is positive and both endpoints are included.","answer":{"kind":"short_text","value":"Yes","explanation":"Check -9·2≤1≤11·2 exactly, obtaining Yes. A singleton closed interval still contains its endpoint."},"skills":["Membership Including Closed Endpoints"],"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-20261005-advance-20261006-r01-order-relation-0061","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"1262feb30fcd37c1e45dd98e9732420ecb1f703e03ec2089f909a24352c0b5dc","family_id":"qf-order-closed-interval","seed":202610061061,"semantic_template":"qf-order-closed-interval/{\"inputs\":[\"-10/1\",\"-10\",\"12\"],\"operation\":\"closed_interval\"}"},"fields":{"title":"Membership Including Closed Endpoints","stem":"Under the usual real order, is (-30)/3 in the closed interval [-10, 12]? The denominator is positive and both endpoints are included.","answer":{"kind":"short_text","value":"Yes","explanation":"Check -10·3≤-30≤12·3 exactly, obtaining Yes. A singleton closed interval still contains its endpoint."},"skills":["Membership Including Closed Endpoints"],"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-20261005-advance-20261006-r01-order-relation-0062","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"d907422d5ab09f4bc6b1378a319f8d548288c13592c3a036ffd83b82ae0ed1ce","family_id":"qf-order-closed-interval","seed":202610061062,"semantic_template":"qf-order-closed-interval/{\"inputs\":[\"13/1\",\"-11\",\"13\"],\"operation\":\"closed_interval\"}"},"fields":{"title":"Membership Including Closed Endpoints","stem":"Under the usual real order, is (52)/4 in the closed interval [-11, 13]? The denominator is positive and both endpoints are included.","answer":{"kind":"short_text","value":"Yes","explanation":"Check -11·4≤52≤13·4 exactly, obtaining Yes. A singleton closed interval still contains its endpoint."},"skills":["Membership Including Closed Endpoints"],"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-20261005-advance-20261006-r01-order-relation-0063","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"6fdb3284648f373075c21d29bb0e3119fede9a1870a202a566684cd9154b0042","family_id":"qf-order-closed-interval","seed":202610061063,"semantic_template":"qf-order-closed-interval/{\"inputs\":[\"-13/1\",\"-12\",\"14\"],\"operation\":\"closed_interval\"}"},"fields":{"title":"Membership Including Closed Endpoints","stem":"Under the usual real order, is (-13)/1 in the closed interval [-12, 14]? The denominator is positive and both endpoints are included.","answer":{"kind":"short_text","value":"No","explanation":"Check -12·1≤-13≤14·1 exactly, obtaining No. A singleton closed interval still contains its endpoint."},"skills":["Membership Including Closed Endpoints"],"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-20261005-advance-20261006-r01-order-relation-0064","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"db397584f3a64b881cfa2e3bcea194204d64eeefb69badce67cef95a2fa8c8d2","family_id":"qf-order-closed-interval","seed":202610061064,"semantic_template":"qf-order-closed-interval/{\"inputs\":[\"31/2\",\"-13\",\"15\"],\"operation\":\"closed_interval\"}"},"fields":{"title":"Membership Including Closed Endpoints","stem":"Under the usual real order, is (31)/2 in the closed interval [-13, 15]? The denominator is positive and both endpoints are included.","answer":{"kind":"short_text","value":"No","explanation":"Check -13·2≤31≤15·2 exactly, obtaining No. A singleton closed interval still contains its endpoint."},"skills":["Membership Including Closed Endpoints"],"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-20261005-advance-20261006-r01-order-relation-0065","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"96531dd880af03f890ff3f8ac1a94dfc652d27a75dd4dd9df1c867f0a7d0ee28","family_id":"qf-order-closed-interval","seed":202610061065,"semantic_template":"qf-order-closed-interval/{\"inputs\":[\"1/3\",\"-14\",\"16\"],\"operation\":\"closed_interval\"}"},"fields":{"title":"Membership Including Closed Endpoints","stem":"Under the usual real order, is (1)/3 in the closed interval [-14, 16]? The denominator is positive and both endpoints are included.","answer":{"kind":"short_text","value":"Yes","explanation":"Check -14·3≤1≤16·3 exactly, obtaining Yes. A singleton closed interval still contains its endpoint."},"skills":["Membership Including Closed Endpoints"],"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-20261005-advance-20261006-r01-order-relation-0066","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"fd664921a25770fd294049f9efe170cf6a199afac9e91221cdd2f61cee23a36c","family_id":"qf-order-closed-interval","seed":202610061066,"semantic_template":"qf-order-closed-interval/{\"inputs\":[\"-15/1\",\"-15\",\"17\"],\"operation\":\"closed_interval\"}"},"fields":{"title":"Membership Including Closed Endpoints","stem":"Under the usual real order, is (-60)/4 in the closed interval [-15, 17]? The denominator is positive and both endpoints are included.","answer":{"kind":"short_text","value":"Yes","explanation":"Check -15·4≤-60≤17·4 exactly, obtaining Yes. A singleton closed interval still contains its endpoint."},"skills":["Membership Including Closed Endpoints"],"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-20261005-advance-20261006-r01-order-relation-0067","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"fd7e7bcb1e305abe576b90568f20225015dcb4a2a222275e32a50cde26adab80","family_id":"qf-order-closed-interval","seed":202610061067,"semantic_template":"qf-order-closed-interval/{\"inputs\":[\"18/1\",\"-16\",\"18\"],\"operation\":\"closed_interval\"}"},"fields":{"title":"Membership Including Closed Endpoints","stem":"Under the usual real order, is (18)/1 in the closed interval [-16, 18]? The denominator is positive and both endpoints are included.","answer":{"kind":"short_text","value":"Yes","explanation":"Check -16·1≤18≤18·1 exactly, obtaining Yes. A singleton closed interval still contains its endpoint."},"skills":["Membership Including Closed Endpoints"],"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-20261005-advance-20261006-r01-order-relation-0068","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"8ca06707b7e431dce98b3b8f445ba8eed822614f6f41ebe2a247f50007a4da4e","family_id":"qf-order-closed-interval","seed":202610061068,"semantic_template":"qf-order-closed-interval/{\"inputs\":[\"-35/2\",\"-17\",\"19\"],\"operation\":\"closed_interval\"}"},"fields":{"title":"Membership Including Closed Endpoints","stem":"Under the usual real order, is (-35)/2 in the closed interval [-17, 19]? The denominator is positive and both endpoints are included.","answer":{"kind":"short_text","value":"No","explanation":"Check -17·2≤-35≤19·2 exactly, obtaining No. A singleton closed interval still contains its endpoint."},"skills":["Membership Including Closed Endpoints"],"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-20261005-advance-20261006-r01-order-relation-0069","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"470ae0cae336045e447c5750bcbcaf34b90a2fb29834c3593a03cbfe4669ad38","family_id":"qf-order-closed-interval","seed":202610061069,"semantic_template":"qf-order-closed-interval/{\"inputs\":[\"61/3\",\"-18\",\"20\"],\"operation\":\"closed_interval\"}"},"fields":{"title":"Membership Including Closed Endpoints","stem":"Under the usual real order, is (61)/3 in the closed interval [-18, 20]? The denominator is positive and both endpoints are included.","answer":{"kind":"short_text","value":"No","explanation":"Check -18·3≤61≤20·3 exactly, obtaining No. A singleton closed interval still contains its endpoint."},"skills":["Membership Including Closed Endpoints"],"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-20261005-advance-20261006-r01-order-relation-0070","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"1f05f8a8b77e9d74626127598e9e874a767fa0486862c1160d5fe2a5ca897f0f","family_id":"qf-order-closed-interval","seed":202610061070,"semantic_template":"qf-order-closed-interval/{\"inputs\":[\"1/4\",\"-19\",\"21\"],\"operation\":\"closed_interval\"}"},"fields":{"title":"Membership Including Closed Endpoints","stem":"Under the usual real order, is (1)/4 in the closed interval [-19, 21]? The denominator is positive and both endpoints are included.","answer":{"kind":"short_text","value":"Yes","explanation":"Check -19·4≤1≤21·4 exactly, obtaining Yes. A singleton closed interval still contains its endpoint."},"skills":["Membership Including Closed Endpoints"],"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-20261005-advance-20261006-r01-order-relation-0071","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"a240b7d8a1564d4ea6b6964da3357408714a24073df3ae4122ba4db90d383fb1","family_id":"qf-order-closed-interval","seed":202610061071,"semantic_template":"qf-order-closed-interval/{\"inputs\":[\"-20/1\",\"-20\",\"22\"],\"operation\":\"closed_interval\"}"},"fields":{"title":"Membership Including Closed Endpoints","stem":"Under the usual real order, is (-20)/1 in the closed interval [-20, 22]? The denominator is positive and both endpoints are included.","answer":{"kind":"short_text","value":"Yes","explanation":"Check -20·1≤-20≤22·1 exactly, obtaining Yes. A singleton closed interval still contains its endpoint."},"skills":["Membership Including Closed Endpoints"],"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-20261005-advance-20261006-r01-order-relation-0072","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"9cd0006495774dfc33cdd301641a9176f1402fdc5f9711ea2ad094bdb3ccfb19","family_id":"qf-order-closed-interval","seed":202610061072,"semantic_template":"qf-order-closed-interval/{\"inputs\":[\"23/1\",\"-21\",\"23\"],\"operation\":\"closed_interval\"}"},"fields":{"title":"Membership Including Closed Endpoints","stem":"Under the usual real order, is (46)/2 in the closed interval [-21, 23]? The denominator is positive and both endpoints are included.","answer":{"kind":"short_text","value":"Yes","explanation":"Check -21·2≤46≤23·2 exactly, obtaining Yes. A singleton closed interval still contains its endpoint."},"skills":["Membership Including Closed Endpoints"],"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-20261005-advance-20261006-r01-order-relation-0073","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"87aaf5e2e51190a1c861e454bc4881b69314bbe1f4af50be9140ab54cf26ae27","family_id":"qf-order-closed-interval","seed":202610061073,"semantic_template":"qf-order-closed-interval/{\"inputs\":[\"-67/3\",\"-22\",\"24\"],\"operation\":\"closed_interval\"}"},"fields":{"title":"Membership Including Closed Endpoints","stem":"Under the usual real order, is (-67)/3 in the closed interval [-22, 24]? The denominator is positive and both endpoints are included.","answer":{"kind":"short_text","value":"No","explanation":"Check -22·3≤-67≤24·3 exactly, obtaining No. A singleton closed interval still contains its endpoint."},"skills":["Membership Including Closed Endpoints"],"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-20261005-advance-20261006-r01-order-relation-0074","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"b10e2ba5e619c298887a764df572804b691ed1c3c0f165ae083435faf13b0480","family_id":"qf-order-closed-interval","seed":202610061074,"semantic_template":"qf-order-closed-interval/{\"inputs\":[\"101/4\",\"-23\",\"25\"],\"operation\":\"closed_interval\"}"},"fields":{"title":"Membership Including Closed Endpoints","stem":"Under the usual real order, is (101)/4 in the closed interval [-23, 25]? The denominator is positive and both endpoints are included.","answer":{"kind":"short_text","value":"No","explanation":"Check -23·4≤101≤25·4 exactly, obtaining No. A singleton closed interval still contains its endpoint."},"skills":["Membership Including Closed Endpoints"],"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-20261005-advance-20261006-r01-order-relation-0075","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"6e1b0d3a7d115188e59d3d90054fc7b4c25b5ddc0595258dad56e03c353719eb","family_id":"qf-order-closed-interval","seed":202610061075,"semantic_template":"qf-order-closed-interval/{\"inputs\":[\"1/1\",\"-24\",\"26\"],\"operation\":\"closed_interval\"}"},"fields":{"title":"Membership Including Closed Endpoints","stem":"Under the usual real order, is (1)/1 in the closed interval [-24, 26]? The denominator is positive and both endpoints are included.","answer":{"kind":"short_text","value":"Yes","explanation":"Check -24·1≤1≤26·1 exactly, obtaining Yes. A singleton closed interval still contains its endpoint."},"skills":["Membership Including Closed Endpoints"],"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-20261005-advance-20261006-r01-order-relation-0076","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"e78673acee229d18b5edbae97e65e28cfb1f83d9d381679e58ab88976d1c351c","family_id":"qf-order-common-translation","seed":202610061076,"semantic_template":"qf-order-common-translation/{\"inputs\":[\"0\",\"0\"],\"operation\":\"common_translation\"}"},"fields":{"title":"Order after a Common Addend","stem":"Under the usual real order, a=0, b=0, and c=-12. Compare a+c and b+c, giving <, =, or > in that order.","answer":{"kind":"short_text","value":"=","explanation":"The translated values are -12 and -12, with relation =. A common addend preserves the original order, including equality."},"skills":["Order after a Common Addend"],"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-20261005-advance-20261006-r01-order-relation-0077","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"5dd31f5953c6987d01b36f9f31331d5b44663458404c8f12b9e41a7f709cfd30","family_id":"qf-order-common-translation","seed":202610061077,"semantic_template":"qf-order-common-translation/{\"inputs\":[\"-3\",\"2\"],\"operation\":\"common_translation\"}"},"fields":{"title":"Order after a Common Addend","stem":"Under the usual real order, a=-3, b=2, and c=-11. Compare a+c and b+c, giving <, =, or > in that order.","answer":{"kind":"short_text","value":"<","explanation":"The translated values are -14 and -9, with relation <. A common addend preserves the original order, including equality."},"skills":["Order after a Common Addend"],"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-20261005-advance-20261006-r01-order-relation-0078","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"ded582d7f578895fbc2985842f2fd55b7aedead0661999b342ef8a53f54568b9","family_id":"qf-order-common-translation","seed":202610061078,"semantic_template":"qf-order-common-translation/{\"inputs\":[\"-4\",\"-8\"],\"operation\":\"common_translation\"}"},"fields":{"title":"Order after a Common Addend","stem":"Under the usual real order, a=-4, b=-8, and c=-10. Compare a+c and b+c, giving <, =, or > in that order.","answer":{"kind":"short_text","value":">","explanation":"The translated values are -14 and -18, with relation >. A common addend preserves the original order, including equality."},"skills":["Order after a Common Addend"],"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-20261005-advance-20261006-r01-order-relation-0079","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"5225b6a7837e7ff64d022f10eff6c08140fc33968f4d95a1706df310fe711150","family_id":"qf-order-common-translation","seed":202610061079,"semantic_template":"qf-order-common-translation/{\"inputs\":[\"-5\",\"-5\"],\"operation\":\"common_translation\"}"},"fields":{"title":"Order after a Common Addend","stem":"Under the usual real order, a=-5, b=-5, and c=-9. Compare a+c and b+c, giving <, =, or > in that order.","answer":{"kind":"short_text","value":"=","explanation":"The translated values are -14 and -14, with relation =. A common addend preserves the original order, including equality."},"skills":["Order after a Common Addend"],"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-20261005-advance-20261006-r01-order-relation-0080","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"1a476716f54047b03d7fc4bd1eefc29dff702683c5d151b6cf308c4ab43c8ed3","family_id":"qf-order-common-translation","seed":202610061080,"semantic_template":"qf-order-common-translation/{\"inputs\":[\"-6\",\"5\"],\"operation\":\"common_translation\"}"},"fields":{"title":"Order after a Common Addend","stem":"Under the usual real order, a=-6, b=5, and c=-8. Compare a+c and b+c, giving <, =, or > in that order.","answer":{"kind":"short_text","value":"<","explanation":"The translated values are -14 and -3, with relation <. A common addend preserves the original order, including equality."},"skills":["Order after a Common Addend"],"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-20261005-advance-20261006-r01-order-relation-0081","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"2804372a8bf2ea22a8397ae41651fbb0919362615e929595969371f8d750aaf9","family_id":"qf-order-common-translation","seed":202610061081,"semantic_template":"qf-order-common-translation/{\"inputs\":[\"-7\",\"-14\"],\"operation\":\"common_translation\"}"},"fields":{"title":"Order after a Common Addend","stem":"Under the usual real order, a=-7, b=-14, and c=-7. Compare a+c and b+c, giving <, =, or > in that order.","answer":{"kind":"short_text","value":">","explanation":"The translated values are -14 and -21, with relation >. A common addend preserves the original order, including equality."},"skills":["Order after a Common Addend"],"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-20261005-advance-20261006-r01-order-relation-0082","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"0204b220eedf20bc3606a2a4fa08c6bdcc9d30825074e863d63ecae90088beaf","family_id":"qf-order-common-translation","seed":202610061082,"semantic_template":"qf-order-common-translation/{\"inputs\":[\"-8\",\"-8\"],\"operation\":\"common_translation\"}"},"fields":{"title":"Order after a Common Addend","stem":"Under the usual real order, a=-8, b=-8, and c=-6. Compare a+c and b+c, giving <, =, or > in that order.","answer":{"kind":"short_text","value":"=","explanation":"The translated values are -14 and -14, with relation =. A common addend preserves the original order, including equality."},"skills":["Order after a Common Addend"],"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-20261005-advance-20261006-r01-order-relation-0083","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"60bc6048d55218e7e73330d49f382635de563c041658ec00f37c6ab238fb31c9","family_id":"qf-order-common-translation","seed":202610061083,"semantic_template":"qf-order-common-translation/{\"inputs\":[\"-9\",\"8\"],\"operation\":\"common_translation\"}"},"fields":{"title":"Order after a Common Addend","stem":"Under the usual real order, a=-9, b=8, and c=-5. Compare a+c and b+c, giving <, =, or > in that order.","answer":{"kind":"short_text","value":"<","explanation":"The translated values are -14 and 3, with relation <. A common addend preserves the original order, including equality."},"skills":["Order after a Common Addend"],"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-20261005-advance-20261006-r01-order-relation-0084","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"7561a314ee7a74277a1a5809dfa98d44deca61cf4b6968f76bd745103e636b84","family_id":"qf-order-common-translation","seed":202610061084,"semantic_template":"qf-order-common-translation/{\"inputs\":[\"-10\",\"-20\"],\"operation\":\"common_translation\"}"},"fields":{"title":"Order after a Common Addend","stem":"Under the usual real order, a=-10, b=-20, and c=-4. Compare a+c and b+c, giving <, =, or > in that order.","answer":{"kind":"short_text","value":">","explanation":"The translated values are -14 and -24, with relation >. A common addend preserves the original order, including equality."},"skills":["Order after a Common Addend"],"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-20261005-advance-20261006-r01-order-relation-0085","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"bb65cc592c0876c51b8c344c16251e349247613430b6edf698c8647f92762d68","family_id":"qf-order-common-translation","seed":202610061085,"semantic_template":"qf-order-common-translation/{\"inputs\":[\"-11\",\"-11\"],\"operation\":\"common_translation\"}"},"fields":{"title":"Order after a Common Addend","stem":"Under the usual real order, a=-11, b=-11, and c=-3. Compare a+c and b+c, giving <, =, or > in that order.","answer":{"kind":"short_text","value":"=","explanation":"The translated values are -14 and -14, with relation =. A common addend preserves the original order, including equality."},"skills":["Order after a Common Addend"],"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-20261005-advance-20261006-r01-order-relation-0086","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"82743ce8a1da8cedeacd43c9caba40abf2339d552ed277cfac656ba342cf1b3b","family_id":"qf-order-common-translation","seed":202610061086,"semantic_template":"qf-order-common-translation/{\"inputs\":[\"-12\",\"11\"],\"operation\":\"common_translation\"}"},"fields":{"title":"Order after a Common Addend","stem":"Under the usual real order, a=-12, b=11, and c=-2. Compare a+c and b+c, giving <, =, or > in that order.","answer":{"kind":"short_text","value":"<","explanation":"The translated values are -14 and 9, with relation <. A common addend preserves the original order, including equality."},"skills":["Order after a Common Addend"],"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-20261005-advance-20261006-r01-order-relation-0087","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"16f4f5519f0048f7716ba87288874cfc2e4ac713cfa1e708196f29db50809443","family_id":"qf-order-common-translation","seed":202610061087,"semantic_template":"qf-order-common-translation/{\"inputs\":[\"-13\",\"-26\"],\"operation\":\"common_translation\"}"},"fields":{"title":"Order after a Common Addend","stem":"Under the usual real order, a=-13, b=-26, and c=-1. Compare a+c and b+c, giving <, =, or > in that order.","answer":{"kind":"short_text","value":">","explanation":"The translated values are -14 and -27, with relation >. A common addend preserves the original order, including equality."},"skills":["Order after a Common Addend"],"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-20261005-advance-20261006-r01-order-relation-0088","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"d8fe1529785afb05d216fb61100012a7d68fd0262b9800e36e504d394814604b","family_id":"qf-order-common-translation","seed":202610061088,"semantic_template":"qf-order-common-translation/{\"inputs\":[\"-14\",\"-14\"],\"operation\":\"common_translation\"}"},"fields":{"title":"Order after a Common Addend","stem":"Under the usual real order, a=-14, b=-14, and c=0. Compare a+c and b+c, giving <, =, or > in that order.","answer":{"kind":"short_text","value":"=","explanation":"The translated values are -14 and -14, with relation =. A common addend preserves the original order, including equality."},"skills":["Order after a Common Addend"],"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-20261005-advance-20261006-r01-order-relation-0089","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"8fc115fc45e79806e619dcbe5dde60e6f6ca601605e03bbdbb68e5f307e34089","family_id":"qf-order-common-translation","seed":202610061089,"semantic_template":"qf-order-common-translation/{\"inputs\":[\"-15\",\"14\"],\"operation\":\"common_translation\"}"},"fields":{"title":"Order after a Common Addend","stem":"Under the usual real order, a=-15, b=14, and c=1. Compare a+c and b+c, giving <, =, or > in that order.","answer":{"kind":"short_text","value":"<","explanation":"The translated values are -14 and 15, with relation <. A common addend preserves the original order, including equality."},"skills":["Order after a Common Addend"],"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-20261005-advance-20261006-r01-order-relation-0090","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"6d39969c127ccc9f6f30942ceaa7bd7d87ba47479bc796ad24f7d3e276d5b408","family_id":"qf-order-common-translation","seed":202610061090,"semantic_template":"qf-order-common-translation/{\"inputs\":[\"-16\",\"-32\"],\"operation\":\"common_translation\"}"},"fields":{"title":"Order after a Common Addend","stem":"Under the usual real order, a=-16, b=-32, and c=2. Compare a+c and b+c, giving <, =, or > in that order.","answer":{"kind":"short_text","value":">","explanation":"The translated values are -14 and -30, with relation >. A common addend preserves the original order, including equality."},"skills":["Order after a Common Addend"],"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-20261005-advance-20261006-r01-order-relation-0091","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"44d604b668031a52e5537750c4613c531d2d1fcc15929d3a8a847b5a1fbb0c14","family_id":"qf-order-common-translation","seed":202610061091,"semantic_template":"qf-order-common-translation/{\"inputs\":[\"-17\",\"-17\"],\"operation\":\"common_translation\"}"},"fields":{"title":"Order after a Common Addend","stem":"Under the usual real order, a=-17, b=-17, and c=3. Compare a+c and b+c, giving <, =, or > in that order.","answer":{"kind":"short_text","value":"=","explanation":"The translated values are -14 and -14, with relation =. A common addend preserves the original order, including equality."},"skills":["Order after a Common Addend"],"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-20261005-advance-20261006-r01-order-relation-0092","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"6ab617e382a54b992e5b98ab885ee3ed8024ea7d53171884d8525480d22a20f5","family_id":"qf-order-common-translation","seed":202610061092,"semantic_template":"qf-order-common-translation/{\"inputs\":[\"-18\",\"17\"],\"operation\":\"common_translation\"}"},"fields":{"title":"Order after a Common Addend","stem":"Under the usual real order, a=-18, b=17, and c=4. Compare a+c and b+c, giving <, =, or > in that order.","answer":{"kind":"short_text","value":"<","explanation":"The translated values are -14 and 21, with relation <. A common addend preserves the original order, including equality."},"skills":["Order after a Common Addend"],"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-20261005-advance-20261006-r01-order-relation-0093","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"89189876bd41f39d33b95fef660b8eb31d40fa2438d3d5fcc1b1467479466d17","family_id":"qf-order-common-translation","seed":202610061093,"semantic_template":"qf-order-common-translation/{\"inputs\":[\"-19\",\"-38\"],\"operation\":\"common_translation\"}"},"fields":{"title":"Order after a Common Addend","stem":"Under the usual real order, a=-19, b=-38, and c=5. Compare a+c and b+c, giving <, =, or > in that order.","answer":{"kind":"short_text","value":">","explanation":"The translated values are -14 and -33, with relation >. A common addend preserves the original order, including equality."},"skills":["Order after a Common Addend"],"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-20261005-advance-20261006-r01-order-relation-0094","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"8a470f9ec20c875161064616ee5aca7ee1b9e2383d7b6ac3e5643e6662e0fb43","family_id":"qf-order-common-translation","seed":202610061094,"semantic_template":"qf-order-common-translation/{\"inputs\":[\"-20\",\"-20\"],\"operation\":\"common_translation\"}"},"fields":{"title":"Order after a Common Addend","stem":"Under the usual real order, a=-20, b=-20, and c=6. Compare a+c and b+c, giving <, =, or > in that order.","answer":{"kind":"short_text","value":"=","explanation":"The translated values are -14 and -14, with relation =. A common addend preserves the original order, including equality."},"skills":["Order after a Common Addend"],"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-20261005-advance-20261006-r01-order-relation-0095","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"b1ddbde4cf72d64fe0f8c2c6a51769c727843629c4c1e74b0fee73b8e551648a","family_id":"qf-order-common-translation","seed":202610061095,"semantic_template":"qf-order-common-translation/{\"inputs\":[\"-21\",\"20\"],\"operation\":\"common_translation\"}"},"fields":{"title":"Order after a Common Addend","stem":"Under the usual real order, a=-21, b=20, and c=7. Compare a+c and b+c, giving <, =, or > in that order.","answer":{"kind":"short_text","value":"<","explanation":"The translated values are -14 and 27, with relation <. A common addend preserves the original order, including equality."},"skills":["Order after a Common Addend"],"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-20261005-advance-20261006-r01-order-relation-0096","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"4b07b5a222fe61aea45dd655ee0a2f2602778954ef5ce9b28d6a4fcbbe7a8829","family_id":"qf-order-common-translation","seed":202610061096,"semantic_template":"qf-order-common-translation/{\"inputs\":[\"-22\",\"-44\"],\"operation\":\"common_translation\"}"},"fields":{"title":"Order after a Common Addend","stem":"Under the usual real order, a=-22, b=-44, and c=8. Compare a+c and b+c, giving <, =, or > in that order.","answer":{"kind":"short_text","value":">","explanation":"The translated values are -14 and -36, with relation >. A common addend preserves the original order, including equality."},"skills":["Order after a Common Addend"],"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-20261005-advance-20261006-r01-order-relation-0097","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"19276074ca0d32d6265755d88052a31f5bc82cdb0c16b114894b7c1c9eab86d3","family_id":"qf-order-common-translation","seed":202610061097,"semantic_template":"qf-order-common-translation/{\"inputs\":[\"-23\",\"-23\"],\"operation\":\"common_translation\"}"},"fields":{"title":"Order after a Common Addend","stem":"Under the usual real order, a=-23, b=-23, and c=9. Compare a+c and b+c, giving <, =, or > in that order.","answer":{"kind":"short_text","value":"=","explanation":"The translated values are -14 and -14, with relation =. A common addend preserves the original order, including equality."},"skills":["Order after a Common Addend"],"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-20261005-advance-20261006-r01-order-relation-0098","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"34def5d8fe3350193a720c7b5a6358a2247154a3415b6ffe200b2684e18c4cfc","family_id":"qf-order-common-translation","seed":202610061098,"semantic_template":"qf-order-common-translation/{\"inputs\":[\"-24\",\"23\"],\"operation\":\"common_translation\"}"},"fields":{"title":"Order after a Common Addend","stem":"Under the usual real order, a=-24, b=23, and c=10. Compare a+c and b+c, giving <, =, or > in that order.","answer":{"kind":"short_text","value":"<","explanation":"The translated values are -14 and 33, with relation <. A common addend preserves the original order, including equality."},"skills":["Order after a Common Addend"],"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-20261005-advance-20261006-r01-order-relation-0099","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"fb0d7b55e7d7c108c8532bbdff6f64987898180e205f9980a023f33eec3a9b72","family_id":"qf-order-common-translation","seed":202610061099,"semantic_template":"qf-order-common-translation/{\"inputs\":[\"-25\",\"-50\"],\"operation\":\"common_translation\"}"},"fields":{"title":"Order after a Common Addend","stem":"Under the usual real order, a=-25, b=-50, and c=11. Compare a+c and b+c, giving <, =, or > in that order.","answer":{"kind":"short_text","value":">","explanation":"The translated values are -14 and -39, with relation >. A common addend preserves the original order, including equality."},"skills":["Order after a Common Addend"],"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-20261005-advance-20261006-r01-order-relation-0100","batch_id":"batch-20261005-advance-20261006-r01-order-relation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"0fd5dfaedffd7d157c0035b33c7119c67cb0fc4f2413a2fdb6f6e37e94024f7b","family_id":"qf-order-common-translation","seed":202610061100,"semantic_template":"qf-order-common-translation/{\"inputs\":[\"-26\",\"-26\"],\"operation\":\"common_translation\"}"},"fields":{"title":"Order after a Common Addend","stem":"Under the usual real order, a=-26, b=-26, and c=12. Compare a+c and b+c, giving <, =, or > in that order.","answer":{"kind":"short_text","value":"=","explanation":"The translated values are -14 and -14, with relation =. A common addend preserves the original order, including equality."},"skills":["Order after a Common Addend"],"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."}}