{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r03-numerical-approximation-error-0001","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"d9eebbcc454aabe631379ca9e996a9721ea48bc5db977a910d7cd05af38987d8","family_id":"qf-app20-error-absolute-error","seed":202610203001,"semantic_template":"qf-app20-error-absolute-error/{\"approximation\":[3,1],\"reference\":[1,1]}"},"fields":{"title":"Exact Absolute Difference from a Specified Reference","stem":"Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. approximation=3/1, reference=1/1. Give (normalized approximation, normalized reference, absolute error).","answer":{"kind":"expression","value":"(3, 1, 2)","explanation":"Take the absolute value of the exact difference, retaining denominator-sign normalization. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (3, 1, 2)."},"skills":["Exact Absolute Difference from a Specified Reference"],"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-20261013-advance-20261020-r03-numerical-approximation-error-0002","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"7044c10e01f95c155216faed7b700c9e21f43aa93198da69e250f838ff7b5f1f","family_id":"qf-app20-error-absolute-error","seed":202610203002,"semantic_template":"qf-app20-error-absolute-error/{\"approximation\":[5,2],\"reference\":[2,2]}"},"fields":{"title":"Exact Absolute Difference from a Specified Reference","stem":"Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. approximation=5/2, reference=2/2. Give (normalized approximation, normalized reference, absolute error).","answer":{"kind":"expression","value":"(5/2, 1, 3/2)","explanation":"Take the absolute value of the exact difference, retaining denominator-sign normalization. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (5/2, 1, 3/2)."},"skills":["Exact Absolute Difference from a Specified Reference"],"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-20261013-advance-20261020-r03-numerical-approximation-error-0003","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"21895f503fc40390749c5565ed8f1d6fc72e560c9aa1a0881a2470327d68aadc","family_id":"qf-app20-error-absolute-error","seed":202610203003,"semantic_template":"qf-app20-error-absolute-error/{\"approximation\":[7,3],\"reference\":[3,3]}"},"fields":{"title":"Exact Absolute Difference from a Specified Reference","stem":"Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. approximation=7/3, reference=3/3. Give (normalized approximation, normalized reference, absolute error).","answer":{"kind":"expression","value":"(7/3, 1, 4/3)","explanation":"Take the absolute value of the exact difference, retaining denominator-sign normalization. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (7/3, 1, 4/3)."},"skills":["Exact Absolute Difference from a Specified Reference"],"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-20261013-advance-20261020-r03-numerical-approximation-error-0004","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"29d0954c3911fdbf2044ce66432b2e06f65aa8d6bd1085293869ae0571e9cf7b","family_id":"qf-app20-error-absolute-error","seed":202610203004,"semantic_template":"qf-app20-error-absolute-error/{\"approximation\":[9,4],\"reference\":[4,4]}"},"fields":{"title":"Exact Absolute Difference from a Specified Reference","stem":"Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. approximation=9/4, reference=4/4. Give (normalized approximation, normalized reference, absolute error).","answer":{"kind":"expression","value":"(9/4, 1, 5/4)","explanation":"Take the absolute value of the exact difference, retaining denominator-sign normalization. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (9/4, 1, 5/4)."},"skills":["Exact Absolute Difference from a Specified Reference"],"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-20261013-advance-20261020-r03-numerical-approximation-error-0005","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"ee045aeb1a31f4ab82499d3a0fe93966cdb999cb68267d85e8aa035c98beaf16","family_id":"qf-app20-error-absolute-error","seed":202610203005,"semantic_template":"qf-app20-error-absolute-error/{\"approximation\":[11,5],\"reference\":[5,1]}"},"fields":{"title":"Exact Absolute Difference from a Specified Reference","stem":"Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. approximation=11/5, reference=5/1. Give (normalized approximation, normalized reference, absolute error).","answer":{"kind":"expression","value":"(11/5, 5, 14/5)","explanation":"Take the absolute value of the exact difference, retaining denominator-sign normalization. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (11/5, 5, 14/5)."},"skills":["Exact Absolute Difference from a Specified Reference"],"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-20261013-advance-20261020-r03-numerical-approximation-error-0006","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"bfb8cb4f83a35ca170a8fb1ebe2c92f8a1154863e04f4b754f80f904de124a80","family_id":"qf-app20-error-absolute-error","seed":202610203006,"semantic_template":"qf-app20-error-absolute-error/{\"approximation\":[13,1],\"reference\":[6,2]}"},"fields":{"title":"Exact Absolute Difference from a Specified Reference","stem":"Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. approximation=13/1, reference=6/2. Give (normalized approximation, normalized reference, absolute error).","answer":{"kind":"expression","value":"(13, 3, 10)","explanation":"Take the absolute value of the exact difference, retaining denominator-sign normalization. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (13, 3, 10)."},"skills":["Exact Absolute Difference from a Specified Reference"],"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-20261013-advance-20261020-r03-numerical-approximation-error-0007","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"242f22cdbb3a9928f80776fa4dd94a36bb8c0ffad3bc2177b7716fa84e58412b","family_id":"qf-app20-error-absolute-error","seed":202610203007,"semantic_template":"qf-app20-error-absolute-error/{\"approximation\":[15,2],\"reference\":[7,3]}"},"fields":{"title":"Exact Absolute Difference from a Specified Reference","stem":"Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. approximation=15/2, reference=7/3. Give (normalized approximation, normalized reference, absolute error).","answer":{"kind":"expression","value":"(15/2, 7/3, 31/6)","explanation":"Take the absolute value of the exact difference, retaining denominator-sign normalization. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (15/2, 7/3, 31/6)."},"skills":["Exact Absolute Difference from a Specified Reference"],"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-20261013-advance-20261020-r03-numerical-approximation-error-0008","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"5a5748a52745bebaddb919030a37560a4bb6c75ae29036701049b9f31e37d5d4","family_id":"qf-app20-error-absolute-error","seed":202610203008,"semantic_template":"qf-app20-error-absolute-error/{\"approximation\":[17,3],\"reference\":[8,4]}"},"fields":{"title":"Exact Absolute Difference from a Specified Reference","stem":"Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. approximation=17/3, reference=8/4. Give (normalized approximation, normalized reference, absolute error).","answer":{"kind":"expression","value":"(17/3, 2, 11/3)","explanation":"Take the absolute value of the exact difference, retaining denominator-sign normalization. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (17/3, 2, 11/3)."},"skills":["Exact Absolute Difference from a Specified Reference"],"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-20261013-advance-20261020-r03-numerical-approximation-error-0009","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"1c5f67e71484edd980583fd72314ff6be293ff0bca42ccc21e55c12fdc08e38d","family_id":"qf-app20-error-absolute-error","seed":202610203009,"semantic_template":"qf-app20-error-absolute-error/{\"approximation\":[19,4],\"reference\":[9,1]}"},"fields":{"title":"Exact Absolute Difference from a Specified Reference","stem":"Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. approximation=19/4, reference=9/1. Give (normalized approximation, normalized reference, absolute error).","answer":{"kind":"expression","value":"(19/4, 9, 17/4)","explanation":"Take the absolute value of the exact difference, retaining denominator-sign normalization. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (19/4, 9, 17/4)."},"skills":["Exact Absolute Difference from a Specified Reference"],"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-20261013-advance-20261020-r03-numerical-approximation-error-0010","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"9b1b8d6b5616c686cdde0b782ecb67ab46ccbc32b2e2a7f3594fcaf549f402fe","family_id":"qf-app20-error-absolute-error","seed":202610203010,"semantic_template":"qf-app20-error-absolute-error/{\"approximation\":[21,5],\"reference\":[1,2]}"},"fields":{"title":"Exact Absolute Difference from a Specified Reference","stem":"Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. approximation=21/5, reference=1/2. Give (normalized approximation, normalized reference, absolute error).","answer":{"kind":"expression","value":"(21/5, 1/2, 37/10)","explanation":"Take the absolute value of the exact difference, retaining denominator-sign normalization. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (21/5, 1/2, 37/10)."},"skills":["Exact Absolute Difference from a Specified Reference"],"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-20261013-advance-20261020-r03-numerical-approximation-error-0011","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"299b83165ad406399bb431af0054029bccec003a41d8028c3785f29d3972a5ad","family_id":"qf-app20-error-absolute-error","seed":202610203011,"semantic_template":"qf-app20-error-absolute-error/{\"approximation\":[23,1],\"reference\":[2,3]}"},"fields":{"title":"Exact Absolute Difference from a Specified Reference","stem":"Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. approximation=23/1, reference=2/3. Give (normalized approximation, normalized reference, absolute error).","answer":{"kind":"expression","value":"(23, 2/3, 67/3)","explanation":"Take the absolute value of the exact difference, retaining denominator-sign normalization. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (23, 2/3, 67/3)."},"skills":["Exact Absolute Difference from a Specified Reference"],"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-20261013-advance-20261020-r03-numerical-approximation-error-0012","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"685c3ca7caeedabf2d89004648911d6fd58de2b7093f0fb6122aa0ec945b6a81","family_id":"qf-app20-error-absolute-error","seed":202610203012,"semantic_template":"qf-app20-error-absolute-error/{\"approximation\":[25,2],\"reference\":[3,4]}"},"fields":{"title":"Exact Absolute Difference from a Specified Reference","stem":"Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. approximation=25/2, reference=3/4. Give (normalized approximation, normalized reference, absolute error).","answer":{"kind":"expression","value":"(25/2, 3/4, 47/4)","explanation":"Take the absolute value of the exact difference, retaining denominator-sign normalization. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (25/2, 3/4, 47/4)."},"skills":["Exact Absolute Difference from a Specified Reference"],"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-20261013-advance-20261020-r03-numerical-approximation-error-0013","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"c90000f6c81d622d9dc24a386032daf090500a37b94471dcbae41fc4e6942804","family_id":"qf-app20-error-absolute-error","seed":202610203013,"semantic_template":"qf-app20-error-absolute-error/{\"approximation\":[27,3],\"reference\":[4,1]}"},"fields":{"title":"Exact Absolute Difference from a Specified Reference","stem":"Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. approximation=27/3, reference=4/1. Give (normalized approximation, normalized reference, absolute error).","answer":{"kind":"expression","value":"(9, 4, 5)","explanation":"Take the absolute value of the exact difference, retaining denominator-sign normalization. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (9, 4, 5)."},"skills":["Exact Absolute Difference from a Specified Reference"],"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-20261013-advance-20261020-r03-numerical-approximation-error-0014","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"4465a444df6ba19e1456e930153338b739b9772c6e9ae1b116db5236582d5671","family_id":"qf-app20-error-absolute-error","seed":202610203014,"semantic_template":"qf-app20-error-absolute-error/{\"approximation\":[29,4],\"reference\":[5,2]}"},"fields":{"title":"Exact Absolute Difference from a Specified Reference","stem":"Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. approximation=29/4, reference=5/2. Give (normalized approximation, normalized reference, absolute error).","answer":{"kind":"expression","value":"(29/4, 5/2, 19/4)","explanation":"Take the absolute value of the exact difference, retaining denominator-sign normalization. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (29/4, 5/2, 19/4)."},"skills":["Exact Absolute Difference from a Specified Reference"],"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-20261013-advance-20261020-r03-numerical-approximation-error-0015","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"11aa9d496e954195f9bf151187646ea99a8b9eec1817d6c71ae2d2ab36cb48cf","family_id":"qf-app20-error-absolute-error","seed":202610203015,"semantic_template":"qf-app20-error-absolute-error/{\"approximation\":[31,5],\"reference\":[6,3]}"},"fields":{"title":"Exact Absolute Difference from a Specified Reference","stem":"Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. approximation=31/5, reference=6/3. Give (normalized approximation, normalized reference, absolute error).","answer":{"kind":"expression","value":"(31/5, 2, 21/5)","explanation":"Take the absolute value of the exact difference, retaining denominator-sign normalization. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (31/5, 2, 21/5)."},"skills":["Exact Absolute Difference from a Specified Reference"],"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-20261013-advance-20261020-r03-numerical-approximation-error-0016","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"b4f98d8593ca6f9ac2b4ac732886fb26ef36aab552126bb230972e36f9375a67","family_id":"qf-app20-error-absolute-error","seed":202610203016,"semantic_template":"qf-app20-error-absolute-error/{\"approximation\":[33,1],\"reference\":[7,4]}"},"fields":{"title":"Exact Absolute Difference from a Specified Reference","stem":"Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. approximation=33/1, reference=7/4. Give (normalized approximation, normalized reference, absolute error).","answer":{"kind":"expression","value":"(33, 7/4, 125/4)","explanation":"Take the absolute value of the exact difference, retaining denominator-sign normalization. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (33, 7/4, 125/4)."},"skills":["Exact Absolute Difference from a Specified Reference"],"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-20261013-advance-20261020-r03-numerical-approximation-error-0017","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"4052914881fa8947c3c03cddf5946052427b60769b2b333f96a82750f73d26c5","family_id":"qf-app20-error-absolute-error","seed":202610203017,"semantic_template":"qf-app20-error-absolute-error/{\"approximation\":[35,2],\"reference\":[8,1]}"},"fields":{"title":"Exact Absolute Difference from a Specified Reference","stem":"Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. approximation=35/2, reference=8/1. Give (normalized approximation, normalized reference, absolute error).","answer":{"kind":"expression","value":"(35/2, 8, 19/2)","explanation":"Take the absolute value of the exact difference, retaining denominator-sign normalization. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (35/2, 8, 19/2)."},"skills":["Exact Absolute Difference from a Specified Reference"],"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-20261013-advance-20261020-r03-numerical-approximation-error-0018","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"3c708942ca7d2daa6244c3e72e96bc88f54540ebe76b9c274e8bfeef8b75aeea","family_id":"qf-app20-error-absolute-error","seed":202610203018,"semantic_template":"qf-app20-error-absolute-error/{\"approximation\":[37,3],\"reference\":[9,2]}"},"fields":{"title":"Exact Absolute Difference from a Specified Reference","stem":"Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. approximation=37/3, reference=9/2. Give (normalized approximation, normalized reference, absolute error).","answer":{"kind":"expression","value":"(37/3, 9/2, 47/6)","explanation":"Take the absolute value of the exact difference, retaining denominator-sign normalization. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (37/3, 9/2, 47/6)."},"skills":["Exact Absolute Difference from a Specified Reference"],"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-20261013-advance-20261020-r03-numerical-approximation-error-0019","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"86418bee10104e66d1250d3a2684a3643302f36803bf3951795e5032a7f073bf","family_id":"qf-app20-error-absolute-error","seed":202610203019,"semantic_template":"qf-app20-error-absolute-error/{\"approximation\":[39,4],\"reference\":[1,3]}"},"fields":{"title":"Exact Absolute Difference from a Specified Reference","stem":"Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. approximation=39/4, reference=1/3. Give (normalized approximation, normalized reference, absolute error).","answer":{"kind":"expression","value":"(39/4, 1/3, 113/12)","explanation":"Take the absolute value of the exact difference, retaining denominator-sign normalization. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (39/4, 1/3, 113/12)."},"skills":["Exact Absolute Difference from a Specified Reference"],"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-20261013-advance-20261020-r03-numerical-approximation-error-0020","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"9920104cb8fab85db870cfaad3ffb695d2b28daaadf10da05c4487c7b7b11635","family_id":"qf-app20-error-absolute-error","seed":202610203020,"semantic_template":"qf-app20-error-absolute-error/{\"approximation\":[41,5],\"reference\":[2,4]}"},"fields":{"title":"Exact Absolute Difference from a Specified Reference","stem":"Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. approximation=41/5, reference=2/4. Give (normalized approximation, normalized reference, absolute error).","answer":{"kind":"expression","value":"(41/5, 1/2, 77/10)","explanation":"Take the absolute value of the exact difference, retaining denominator-sign normalization. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (41/5, 1/2, 77/10)."},"skills":["Exact Absolute Difference from a Specified Reference"],"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-20261013-advance-20261020-r03-numerical-approximation-error-0021","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"4bf0533a49a1effb276449cecaa43cfed10972ac6be50e0529272b327dfafea9","family_id":"qf-app20-error-absolute-error","seed":202610203021,"semantic_template":"qf-app20-error-absolute-error/{\"approximation\":[43,1],\"reference\":[3,1]}"},"fields":{"title":"Exact Absolute Difference from a Specified Reference","stem":"Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. approximation=43/1, reference=3/1. Give (normalized approximation, normalized reference, absolute error).","answer":{"kind":"expression","value":"(43, 3, 40)","explanation":"Take the absolute value of the exact difference, retaining denominator-sign normalization. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (43, 3, 40)."},"skills":["Exact Absolute Difference from a Specified Reference"],"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-20261013-advance-20261020-r03-numerical-approximation-error-0022","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"2aaabe99364fe4c80f9314ddb55498c893aa9a424697e962551b98acf47cebe7","family_id":"qf-app20-error-absolute-error","seed":202610203022,"semantic_template":"qf-app20-error-absolute-error/{\"approximation\":[45,2],\"reference\":[4,2]}"},"fields":{"title":"Exact Absolute Difference from a Specified Reference","stem":"Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. approximation=45/2, reference=4/2. Give (normalized approximation, normalized reference, absolute error).","answer":{"kind":"expression","value":"(45/2, 2, 41/2)","explanation":"Take the absolute value of the exact difference, retaining denominator-sign normalization. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (45/2, 2, 41/2)."},"skills":["Exact Absolute Difference from a Specified Reference"],"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-20261013-advance-20261020-r03-numerical-approximation-error-0023","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"87dea1cf4036e1192d3ffa4fe09dfaf0a780c7e6cf37467ab81eb67a3663de03","family_id":"qf-app20-error-absolute-error","seed":202610203023,"semantic_template":"qf-app20-error-absolute-error/{\"approximation\":[47,3],\"reference\":[5,3]}"},"fields":{"title":"Exact Absolute Difference from a Specified Reference","stem":"Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. approximation=47/3, reference=5/3. Give (normalized approximation, normalized reference, absolute error).","answer":{"kind":"expression","value":"(47/3, 5/3, 14)","explanation":"Take the absolute value of the exact difference, retaining denominator-sign normalization. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (47/3, 5/3, 14)."},"skills":["Exact Absolute Difference from a Specified Reference"],"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-20261013-advance-20261020-r03-numerical-approximation-error-0024","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"11eb44e8d44df55bf35a7568309a4328ce45dfca214831d0bde758dba2d5d958","family_id":"qf-app20-error-absolute-error","seed":202610203024,"semantic_template":"qf-app20-error-absolute-error/{\"approximation\":[49,4],\"reference\":[6,4]}"},"fields":{"title":"Exact Absolute Difference from a Specified Reference","stem":"Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. approximation=49/4, reference=6/4. Give (normalized approximation, normalized reference, absolute error).","answer":{"kind":"expression","value":"(49/4, 3/2, 43/4)","explanation":"Take the absolute value of the exact difference, retaining denominator-sign normalization. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (49/4, 3/2, 43/4)."},"skills":["Exact Absolute Difference from a Specified Reference"],"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-20261013-advance-20261020-r03-numerical-approximation-error-0025","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"e9e481ea4c906013eafc2a8ebb0602fbe8f03ebad60fcdb800f1b0d2ecf6f5f0","family_id":"qf-app20-error-absolute-error","seed":202610203025,"semantic_template":"qf-app20-error-absolute-error/{\"approximation\":[51,5],\"reference\":[7,1]}"},"fields":{"title":"Exact Absolute Difference from a Specified Reference","stem":"Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. approximation=51/5, reference=7/1. Give (normalized approximation, normalized reference, absolute error).","answer":{"kind":"expression","value":"(51/5, 7, 16/5)","explanation":"Take the absolute value of the exact difference, retaining denominator-sign normalization. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (51/5, 7, 16/5)."},"skills":["Exact Absolute Difference from a Specified Reference"],"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-20261013-advance-20261020-r03-numerical-approximation-error-0026","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"1131aa7d37e47c7db670d14b163c91e36960cae5470d8dc888a543c0eda4156b","family_id":"qf-app20-error-relative-error","seed":202610203026,"semantic_template":"qf-app20-error-relative-error/{\"approximation\":[3,1],\"reference\":[1,1]}"},"fields":{"title":"Relative Error with an Explicit Nonzero Reference","stem":"Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. approximation=3/1, reference=1/1 is required to be nonzero. Give (approximation, reference, absolute error, absolute error divided by absolute reference). Do not convert the ratio to a percentage.","answer":{"kind":"expression","value":"(3, 1, 2, 2)","explanation":"Check the nonzero-reference premise and use its absolute value, including for a negative reference. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (3, 1, 2, 2)."},"skills":["Relative Error with an Explicit Nonzero Reference"],"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-20261013-advance-20261020-r03-numerical-approximation-error-0027","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"65273e9bb5b0d4b34a035e59d67dce4ed232b77a91cd6f630835b510580f0b32","family_id":"qf-app20-error-relative-error","seed":202610203027,"semantic_template":"qf-app20-error-relative-error/{\"approximation\":[5,2],\"reference\":[2,2]}"},"fields":{"title":"Relative Error with an Explicit Nonzero Reference","stem":"Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. approximation=5/2, reference=2/2 is required to be nonzero. Give (approximation, reference, absolute error, absolute error divided by absolute reference). Do not convert the ratio to a percentage.","answer":{"kind":"expression","value":"(5/2, 1, 3/2, 3/2)","explanation":"Check the nonzero-reference premise and use its absolute value, including for a negative reference. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (5/2, 1, 3/2, 3/2)."},"skills":["Relative Error with an Explicit Nonzero Reference"],"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-20261013-advance-20261020-r03-numerical-approximation-error-0028","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"ae78c74872e56cfe6755c77c6ef762cde259779b4cfff152a51df36af52d291a","family_id":"qf-app20-error-relative-error","seed":202610203028,"semantic_template":"qf-app20-error-relative-error/{\"approximation\":[7,3],\"reference\":[3,3]}"},"fields":{"title":"Relative Error with an Explicit Nonzero Reference","stem":"Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. approximation=7/3, reference=3/3 is required to be nonzero. Give (approximation, reference, absolute error, absolute error divided by absolute reference). Do not convert the ratio to a percentage.","answer":{"kind":"expression","value":"(7/3, 1, 4/3, 4/3)","explanation":"Check the nonzero-reference premise and use its absolute value, including for a negative reference. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (7/3, 1, 4/3, 4/3)."},"skills":["Relative Error with an Explicit Nonzero Reference"],"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-20261013-advance-20261020-r03-numerical-approximation-error-0029","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"4e8c0cc72837e25aa6e31216a986d30ca1754a5365087511e618c65b84d387f5","family_id":"qf-app20-error-relative-error","seed":202610203029,"semantic_template":"qf-app20-error-relative-error/{\"approximation\":[9,4],\"reference\":[4,4]}"},"fields":{"title":"Relative Error with an Explicit Nonzero Reference","stem":"Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. approximation=9/4, reference=4/4 is required to be nonzero. Give (approximation, reference, absolute error, absolute error divided by absolute reference). Do not convert the ratio to a percentage.","answer":{"kind":"expression","value":"(9/4, 1, 5/4, 5/4)","explanation":"Check the nonzero-reference premise and use its absolute value, including for a negative reference. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (9/4, 1, 5/4, 5/4)."},"skills":["Relative Error with an Explicit Nonzero Reference"],"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-20261013-advance-20261020-r03-numerical-approximation-error-0030","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"8f1a802bdfbb0fb8df726a04ee55b36d789c5c04003988b2a420b575c4cf0e0a","family_id":"qf-app20-error-relative-error","seed":202610203030,"semantic_template":"qf-app20-error-relative-error/{\"approximation\":[11,5],\"reference\":[5,1]}"},"fields":{"title":"Relative Error with an Explicit Nonzero Reference","stem":"Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. approximation=11/5, reference=5/1 is required to be nonzero. Give (approximation, reference, absolute error, absolute error divided by absolute reference). Do not convert the ratio to a percentage.","answer":{"kind":"expression","value":"(11/5, 5, 14/5, 14/25)","explanation":"Check the nonzero-reference premise and use its absolute value, including for a negative reference. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (11/5, 5, 14/5, 14/25)."},"skills":["Relative Error with an Explicit Nonzero Reference"],"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-20261013-advance-20261020-r03-numerical-approximation-error-0031","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"4cf447c144c7f984e6c8de72ff34b3488a2704b7efc2b5a90b38052836114f1d","family_id":"qf-app20-error-relative-error","seed":202610203031,"semantic_template":"qf-app20-error-relative-error/{\"approximation\":[13,1],\"reference\":[6,2]}"},"fields":{"title":"Relative Error with an Explicit Nonzero Reference","stem":"Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. approximation=13/1, reference=6/2 is required to be nonzero. Give (approximation, reference, absolute error, absolute error divided by absolute reference). Do not convert the ratio to a percentage.","answer":{"kind":"expression","value":"(13, 3, 10, 10/3)","explanation":"Check the nonzero-reference premise and use its absolute value, including for a negative reference. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (13, 3, 10, 10/3)."},"skills":["Relative Error with an Explicit Nonzero Reference"],"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-20261013-advance-20261020-r03-numerical-approximation-error-0032","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"109fb47743d3a3934ab1f2325c8233cc25aca0331da334a26ffab3e4546e0dc3","family_id":"qf-app20-error-relative-error","seed":202610203032,"semantic_template":"qf-app20-error-relative-error/{\"approximation\":[15,2],\"reference\":[7,3]}"},"fields":{"title":"Relative Error with an Explicit Nonzero Reference","stem":"Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. approximation=15/2, reference=7/3 is required to be nonzero. Give (approximation, reference, absolute error, absolute error divided by absolute reference). Do not convert the ratio to a percentage.","answer":{"kind":"expression","value":"(15/2, 7/3, 31/6, 31/14)","explanation":"Check the nonzero-reference premise and use its absolute value, including for a negative reference. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (15/2, 7/3, 31/6, 31/14)."},"skills":["Relative Error with an Explicit Nonzero Reference"],"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-20261013-advance-20261020-r03-numerical-approximation-error-0033","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"4f13b07f9b1ebe5f0d7fdba82be72354fd1f673db7a3251db73c62e513f6789e","family_id":"qf-app20-error-relative-error","seed":202610203033,"semantic_template":"qf-app20-error-relative-error/{\"approximation\":[17,3],\"reference\":[8,4]}"},"fields":{"title":"Relative Error with an Explicit Nonzero Reference","stem":"Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. approximation=17/3, reference=8/4 is required to be nonzero. Give (approximation, reference, absolute error, absolute error divided by absolute reference). Do not convert the ratio to a percentage.","answer":{"kind":"expression","value":"(17/3, 2, 11/3, 11/6)","explanation":"Check the nonzero-reference premise and use its absolute value, including for a negative reference. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (17/3, 2, 11/3, 11/6)."},"skills":["Relative Error with an Explicit Nonzero Reference"],"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-20261013-advance-20261020-r03-numerical-approximation-error-0034","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"2c3faa1fa0ddd325859da2fa8dffbfa3d5fbc975aa2153331e58ea1b1cca32d0","family_id":"qf-app20-error-relative-error","seed":202610203034,"semantic_template":"qf-app20-error-relative-error/{\"approximation\":[19,4],\"reference\":[9,1]}"},"fields":{"title":"Relative Error with an Explicit Nonzero Reference","stem":"Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. approximation=19/4, reference=9/1 is required to be nonzero. Give (approximation, reference, absolute error, absolute error divided by absolute reference). Do not convert the ratio to a percentage.","answer":{"kind":"expression","value":"(19/4, 9, 17/4, 17/36)","explanation":"Check the nonzero-reference premise and use its absolute value, including for a negative reference. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (19/4, 9, 17/4, 17/36)."},"skills":["Relative Error with an Explicit Nonzero Reference"],"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-20261013-advance-20261020-r03-numerical-approximation-error-0035","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"da51c17e2adacabfaa2d3812792317b5c656c85a2758a487219318c603cb1c42","family_id":"qf-app20-error-relative-error","seed":202610203035,"semantic_template":"qf-app20-error-relative-error/{\"approximation\":[21,5],\"reference\":[1,2]}"},"fields":{"title":"Relative Error with an Explicit Nonzero Reference","stem":"Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. approximation=21/5, reference=1/2 is required to be nonzero. Give (approximation, reference, absolute error, absolute error divided by absolute reference). Do not convert the ratio to a percentage.","answer":{"kind":"expression","value":"(21/5, 1/2, 37/10, 37/5)","explanation":"Check the nonzero-reference premise and use its absolute value, including for a negative reference. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (21/5, 1/2, 37/10, 37/5)."},"skills":["Relative Error with an Explicit Nonzero Reference"],"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-20261013-advance-20261020-r03-numerical-approximation-error-0036","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"6a0a38abc5d294b7937625c93aa90d08f58367d9a97dce717fd5516b7df9a732","family_id":"qf-app20-error-relative-error","seed":202610203036,"semantic_template":"qf-app20-error-relative-error/{\"approximation\":[23,1],\"reference\":[2,3]}"},"fields":{"title":"Relative Error with an Explicit Nonzero Reference","stem":"Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. approximation=23/1, reference=2/3 is required to be nonzero. Give (approximation, reference, absolute error, absolute error divided by absolute reference). Do not convert the ratio to a percentage.","answer":{"kind":"expression","value":"(23, 2/3, 67/3, 67/2)","explanation":"Check the nonzero-reference premise and use its absolute value, including for a negative reference. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (23, 2/3, 67/3, 67/2)."},"skills":["Relative Error with an Explicit Nonzero Reference"],"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-20261013-advance-20261020-r03-numerical-approximation-error-0037","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"40487212a1a8c26b54cec7a60a59dfa19fed5c4fb12e8a651654df11e90fd1d1","family_id":"qf-app20-error-relative-error","seed":202610203037,"semantic_template":"qf-app20-error-relative-error/{\"approximation\":[25,2],\"reference\":[3,4]}"},"fields":{"title":"Relative Error with an Explicit Nonzero Reference","stem":"Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. approximation=25/2, reference=3/4 is required to be nonzero. Give (approximation, reference, absolute error, absolute error divided by absolute reference). Do not convert the ratio to a percentage.","answer":{"kind":"expression","value":"(25/2, 3/4, 47/4, 47/3)","explanation":"Check the nonzero-reference premise and use its absolute value, including for a negative reference. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (25/2, 3/4, 47/4, 47/3)."},"skills":["Relative Error with an Explicit Nonzero Reference"],"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-20261013-advance-20261020-r03-numerical-approximation-error-0038","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"e0a77fe12e6b354fd56202b6cbcec05194fd1452fde3e8066f5958f22e86b2ed","family_id":"qf-app20-error-relative-error","seed":202610203038,"semantic_template":"qf-app20-error-relative-error/{\"approximation\":[27,3],\"reference\":[4,1]}"},"fields":{"title":"Relative Error with an Explicit Nonzero Reference","stem":"Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. approximation=27/3, reference=4/1 is required to be nonzero. Give (approximation, reference, absolute error, absolute error divided by absolute reference). Do not convert the ratio to a percentage.","answer":{"kind":"expression","value":"(9, 4, 5, 5/4)","explanation":"Check the nonzero-reference premise and use its absolute value, including for a negative reference. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (9, 4, 5, 5/4)."},"skills":["Relative Error with an Explicit Nonzero Reference"],"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-20261013-advance-20261020-r03-numerical-approximation-error-0039","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"ecda04efe3d40c583738fb3e47043bc758f2ace9f7ef4be19f0f3064ad9da913","family_id":"qf-app20-error-relative-error","seed":202610203039,"semantic_template":"qf-app20-error-relative-error/{\"approximation\":[29,4],\"reference\":[5,2]}"},"fields":{"title":"Relative Error with an Explicit Nonzero Reference","stem":"Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. approximation=29/4, reference=5/2 is required to be nonzero. Give (approximation, reference, absolute error, absolute error divided by absolute reference). Do not convert the ratio to a percentage.","answer":{"kind":"expression","value":"(29/4, 5/2, 19/4, 19/10)","explanation":"Check the nonzero-reference premise and use its absolute value, including for a negative reference. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (29/4, 5/2, 19/4, 19/10)."},"skills":["Relative Error with an Explicit Nonzero Reference"],"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-20261013-advance-20261020-r03-numerical-approximation-error-0040","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"a0fd2438fdc5ebb1a1b93d4c3fec032f9a2425efd6b8fd0517c710c37001c898","family_id":"qf-app20-error-relative-error","seed":202610203040,"semantic_template":"qf-app20-error-relative-error/{\"approximation\":[31,5],\"reference\":[6,3]}"},"fields":{"title":"Relative Error with an Explicit Nonzero Reference","stem":"Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. approximation=31/5, reference=6/3 is required to be nonzero. Give (approximation, reference, absolute error, absolute error divided by absolute reference). Do not convert the ratio to a percentage.","answer":{"kind":"expression","value":"(31/5, 2, 21/5, 21/10)","explanation":"Check the nonzero-reference premise and use its absolute value, including for a negative reference. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (31/5, 2, 21/5, 21/10)."},"skills":["Relative Error with an Explicit Nonzero Reference"],"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-20261013-advance-20261020-r03-numerical-approximation-error-0041","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"9865b97d247dd4c8e5495da682f850af4fc8cad0533b289ba917926957d2447d","family_id":"qf-app20-error-relative-error","seed":202610203041,"semantic_template":"qf-app20-error-relative-error/{\"approximation\":[33,1],\"reference\":[7,4]}"},"fields":{"title":"Relative Error with an Explicit Nonzero Reference","stem":"Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. approximation=33/1, reference=7/4 is required to be nonzero. Give (approximation, reference, absolute error, absolute error divided by absolute reference). Do not convert the ratio to a percentage.","answer":{"kind":"expression","value":"(33, 7/4, 125/4, 125/7)","explanation":"Check the nonzero-reference premise and use its absolute value, including for a negative reference. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (33, 7/4, 125/4, 125/7)."},"skills":["Relative Error with an Explicit Nonzero Reference"],"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-20261013-advance-20261020-r03-numerical-approximation-error-0042","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"264c144a2aeb2ed630e154309507c8b9aff95a46f93358646799a28f9121eb0b","family_id":"qf-app20-error-relative-error","seed":202610203042,"semantic_template":"qf-app20-error-relative-error/{\"approximation\":[35,2],\"reference\":[8,1]}"},"fields":{"title":"Relative Error with an Explicit Nonzero Reference","stem":"Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. approximation=35/2, reference=8/1 is required to be nonzero. Give (approximation, reference, absolute error, absolute error divided by absolute reference). Do not convert the ratio to a percentage.","answer":{"kind":"expression","value":"(35/2, 8, 19/2, 19/16)","explanation":"Check the nonzero-reference premise and use its absolute value, including for a negative reference. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (35/2, 8, 19/2, 19/16)."},"skills":["Relative Error with an Explicit Nonzero Reference"],"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-20261013-advance-20261020-r03-numerical-approximation-error-0043","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"2fe568b1f2861b49e150d573e205dc9ea2a32f92b9f54e65447261bdadb64817","family_id":"qf-app20-error-relative-error","seed":202610203043,"semantic_template":"qf-app20-error-relative-error/{\"approximation\":[37,3],\"reference\":[9,2]}"},"fields":{"title":"Relative Error with an Explicit Nonzero Reference","stem":"Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. approximation=37/3, reference=9/2 is required to be nonzero. Give (approximation, reference, absolute error, absolute error divided by absolute reference). Do not convert the ratio to a percentage.","answer":{"kind":"expression","value":"(37/3, 9/2, 47/6, 47/27)","explanation":"Check the nonzero-reference premise and use its absolute value, including for a negative reference. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (37/3, 9/2, 47/6, 47/27)."},"skills":["Relative Error with an Explicit Nonzero Reference"],"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-20261013-advance-20261020-r03-numerical-approximation-error-0044","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"79bb628a81fb814357f6206cc07e405fd8a6c59a7d89f282b4f133723e2e7653","family_id":"qf-app20-error-relative-error","seed":202610203044,"semantic_template":"qf-app20-error-relative-error/{\"approximation\":[39,4],\"reference\":[1,3]}"},"fields":{"title":"Relative Error with an Explicit Nonzero Reference","stem":"Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. approximation=39/4, reference=1/3 is required to be nonzero. Give (approximation, reference, absolute error, absolute error divided by absolute reference). Do not convert the ratio to a percentage.","answer":{"kind":"expression","value":"(39/4, 1/3, 113/12, 113/4)","explanation":"Check the nonzero-reference premise and use its absolute value, including for a negative reference. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (39/4, 1/3, 113/12, 113/4)."},"skills":["Relative Error with an Explicit Nonzero Reference"],"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-20261013-advance-20261020-r03-numerical-approximation-error-0045","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"c0c93be5e42887901e4432d07a08db0be75a233c0f2b595030f0ff2f1f86faa6","family_id":"qf-app20-error-relative-error","seed":202610203045,"semantic_template":"qf-app20-error-relative-error/{\"approximation\":[41,5],\"reference\":[2,4]}"},"fields":{"title":"Relative Error with an Explicit Nonzero Reference","stem":"Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. approximation=41/5, reference=2/4 is required to be nonzero. Give (approximation, reference, absolute error, absolute error divided by absolute reference). Do not convert the ratio to a percentage.","answer":{"kind":"expression","value":"(41/5, 1/2, 77/10, 77/5)","explanation":"Check the nonzero-reference premise and use its absolute value, including for a negative reference. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (41/5, 1/2, 77/10, 77/5)."},"skills":["Relative Error with an Explicit Nonzero Reference"],"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-20261013-advance-20261020-r03-numerical-approximation-error-0046","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"3838c4e62e39553ee93957860f29d401e29a5bfb3d07d5408c8ee67d1f9ff06b","family_id":"qf-app20-error-relative-error","seed":202610203046,"semantic_template":"qf-app20-error-relative-error/{\"approximation\":[43,1],\"reference\":[3,1]}"},"fields":{"title":"Relative Error with an Explicit Nonzero Reference","stem":"Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. approximation=43/1, reference=3/1 is required to be nonzero. Give (approximation, reference, absolute error, absolute error divided by absolute reference). Do not convert the ratio to a percentage.","answer":{"kind":"expression","value":"(43, 3, 40, 40/3)","explanation":"Check the nonzero-reference premise and use its absolute value, including for a negative reference. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (43, 3, 40, 40/3)."},"skills":["Relative Error with an Explicit Nonzero Reference"],"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-20261013-advance-20261020-r03-numerical-approximation-error-0047","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"9f2b3676af43ae6b09300390111d98f11a9a6a39901c2285495ae6972284282d","family_id":"qf-app20-error-relative-error","seed":202610203047,"semantic_template":"qf-app20-error-relative-error/{\"approximation\":[45,2],\"reference\":[4,2]}"},"fields":{"title":"Relative Error with an Explicit Nonzero Reference","stem":"Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. approximation=45/2, reference=4/2 is required to be nonzero. Give (approximation, reference, absolute error, absolute error divided by absolute reference). Do not convert the ratio to a percentage.","answer":{"kind":"expression","value":"(45/2, 2, 41/2, 41/4)","explanation":"Check the nonzero-reference premise and use its absolute value, including for a negative reference. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (45/2, 2, 41/2, 41/4)."},"skills":["Relative Error with an Explicit Nonzero Reference"],"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-20261013-advance-20261020-r03-numerical-approximation-error-0048","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"b0e2e756ce66c985f2484383924052fbb8208ee8bcbbc5bb70ae834a3d4c3d21","family_id":"qf-app20-error-relative-error","seed":202610203048,"semantic_template":"qf-app20-error-relative-error/{\"approximation\":[47,3],\"reference\":[5,3]}"},"fields":{"title":"Relative Error with an Explicit Nonzero Reference","stem":"Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. approximation=47/3, reference=5/3 is required to be nonzero. Give (approximation, reference, absolute error, absolute error divided by absolute reference). Do not convert the ratio to a percentage.","answer":{"kind":"expression","value":"(47/3, 5/3, 14, 42/5)","explanation":"Check the nonzero-reference premise and use its absolute value, including for a negative reference. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (47/3, 5/3, 14, 42/5)."},"skills":["Relative Error with an Explicit Nonzero Reference"],"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-20261013-advance-20261020-r03-numerical-approximation-error-0049","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"0667128baff21406b60783af2d69dc995dbd3fa4931c5d7bc3eec7ae126d3a38","family_id":"qf-app20-error-relative-error","seed":202610203049,"semantic_template":"qf-app20-error-relative-error/{\"approximation\":[49,4],\"reference\":[6,4]}"},"fields":{"title":"Relative Error with an Explicit Nonzero Reference","stem":"Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. approximation=49/4, reference=6/4 is required to be nonzero. Give (approximation, reference, absolute error, absolute error divided by absolute reference). Do not convert the ratio to a percentage.","answer":{"kind":"expression","value":"(49/4, 3/2, 43/4, 43/6)","explanation":"Check the nonzero-reference premise and use its absolute value, including for a negative reference. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (49/4, 3/2, 43/4, 43/6)."},"skills":["Relative Error with an Explicit Nonzero Reference"],"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-20261013-advance-20261020-r03-numerical-approximation-error-0050","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"7debcd1d52ed8d755272cfff8578298c49fb18ba7fc75dfd5e65fe93b1a6e697","family_id":"qf-app20-error-relative-error","seed":202610203050,"semantic_template":"qf-app20-error-relative-error/{\"approximation\":[51,5],\"reference\":[7,1]}"},"fields":{"title":"Relative Error with an Explicit Nonzero Reference","stem":"Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. approximation=51/5, reference=7/1 is required to be nonzero. Give (approximation, reference, absolute error, absolute error divided by absolute reference). Do not convert the ratio to a percentage.","answer":{"kind":"expression","value":"(51/5, 7, 16/5, 16/35)","explanation":"Check the nonzero-reference premise and use its absolute value, including for a negative reference. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (51/5, 7, 16/5, 16/35)."},"skills":["Relative Error with an Explicit Nonzero Reference"],"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-20261013-advance-20261020-r03-numerical-approximation-error-0051","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"f7d3416e6fddc650ff15595f9a5718fe0e76b49b054f17ff7215e03684968a38","family_id":"qf-app20-error-tolerance-audit","seed":202610203051,"semantic_template":"qf-app20-error-tolerance-audit/{\"approximation\":[3,1],\"reference\":[1,1],\"tolerance\":[1,2]}"},"fields":{"title":"Inclusive Absolute-Error Tolerance","stem":"Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. approximation=3/1, reference=1/1, tolerance=1/2≥0. Give (approximation, reference, absolute error, tolerance, error≤tolerance?).","answer":{"kind":"expression","value":"(3, 1, 2, 1/2, No)","explanation":"The tolerance comparison includes equality; a negative tolerance is not admitted. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (3, 1, 2, 1/2, No)."},"skills":["Inclusive Absolute-Error Tolerance"],"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-20261013-advance-20261020-r03-numerical-approximation-error-0052","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"1bbd8ecdc414b9534a1fd46881fdaf967d92feb362e049feeb8e87dfb54f6b7d","family_id":"qf-app20-error-tolerance-audit","seed":202610203052,"semantic_template":"qf-app20-error-tolerance-audit/{\"approximation\":[5,2],\"reference\":[2,2],\"tolerance\":[2,3]}"},"fields":{"title":"Inclusive Absolute-Error Tolerance","stem":"Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. approximation=5/2, reference=2/2, tolerance=2/3≥0. Give (approximation, reference, absolute error, tolerance, error≤tolerance?).","answer":{"kind":"expression","value":"(5/2, 1, 3/2, 2/3, No)","explanation":"The tolerance comparison includes equality; a negative tolerance is not admitted. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (5/2, 1, 3/2, 2/3, No)."},"skills":["Inclusive Absolute-Error Tolerance"],"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-20261013-advance-20261020-r03-numerical-approximation-error-0053","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"db3a8642bca61ff86fee21de1a1f3a2b0f1fbf5950b68cf93bae63530201e769","family_id":"qf-app20-error-tolerance-audit","seed":202610203053,"semantic_template":"qf-app20-error-tolerance-audit/{\"approximation\":[7,3],\"reference\":[3,3],\"tolerance\":[3,4]}"},"fields":{"title":"Inclusive Absolute-Error Tolerance","stem":"Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. approximation=7/3, reference=3/3, tolerance=3/4≥0. Give (approximation, reference, absolute error, tolerance, error≤tolerance?).","answer":{"kind":"expression","value":"(7/3, 1, 4/3, 3/4, No)","explanation":"The tolerance comparison includes equality; a negative tolerance is not admitted. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (7/3, 1, 4/3, 3/4, No)."},"skills":["Inclusive Absolute-Error Tolerance"],"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-20261013-advance-20261020-r03-numerical-approximation-error-0054","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"1c3da935d0b4629c43bf176a85a11a21d5a8955234312157b88da8ddafcfa5e1","family_id":"qf-app20-error-tolerance-audit","seed":202610203054,"semantic_template":"qf-app20-error-tolerance-audit/{\"approximation\":[9,4],\"reference\":[4,4],\"tolerance\":[4,5]}"},"fields":{"title":"Inclusive Absolute-Error Tolerance","stem":"Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. approximation=9/4, reference=4/4, tolerance=4/5≥0. Give (approximation, reference, absolute error, tolerance, error≤tolerance?).","answer":{"kind":"expression","value":"(9/4, 1, 5/4, 4/5, No)","explanation":"The tolerance comparison includes equality; a negative tolerance is not admitted. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (9/4, 1, 5/4, 4/5, No)."},"skills":["Inclusive Absolute-Error Tolerance"],"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-20261013-advance-20261020-r03-numerical-approximation-error-0055","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"59a80efac87484f63a3dcd242bace4ec9e4fb967b98fc3e9e864ffc2673e077e","family_id":"qf-app20-error-tolerance-audit","seed":202610203055,"semantic_template":"qf-app20-error-tolerance-audit/{\"approximation\":[11,5],\"reference\":[5,1],\"tolerance\":[5,6]}"},"fields":{"title":"Inclusive Absolute-Error Tolerance","stem":"Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. approximation=11/5, reference=5/1, tolerance=5/6≥0. Give (approximation, reference, absolute error, tolerance, error≤tolerance?).","answer":{"kind":"expression","value":"(11/5, 5, 14/5, 5/6, No)","explanation":"The tolerance comparison includes equality; a negative tolerance is not admitted. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (11/5, 5, 14/5, 5/6, No)."},"skills":["Inclusive Absolute-Error Tolerance"],"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-20261013-advance-20261020-r03-numerical-approximation-error-0056","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"3aa8f3c46988231e55edb945cd82e0bc4f8d80204160517a682548103fb83a0b","family_id":"qf-app20-error-tolerance-audit","seed":202610203056,"semantic_template":"qf-app20-error-tolerance-audit/{\"approximation\":[13,1],\"reference\":[6,2],\"tolerance\":[6,7]}"},"fields":{"title":"Inclusive Absolute-Error Tolerance","stem":"Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. approximation=13/1, reference=6/2, tolerance=6/7≥0. Give (approximation, reference, absolute error, tolerance, error≤tolerance?).","answer":{"kind":"expression","value":"(13, 3, 10, 6/7, No)","explanation":"The tolerance comparison includes equality; a negative tolerance is not admitted. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (13, 3, 10, 6/7, No)."},"skills":["Inclusive Absolute-Error Tolerance"],"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-20261013-advance-20261020-r03-numerical-approximation-error-0057","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"86d98a95567682a36dee1303550b49017fedcce6c257cc92731c3eb038bf3a20","family_id":"qf-app20-error-tolerance-audit","seed":202610203057,"semantic_template":"qf-app20-error-tolerance-audit/{\"approximation\":[15,2],\"reference\":[7,3],\"tolerance\":[1,8]}"},"fields":{"title":"Inclusive Absolute-Error Tolerance","stem":"Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. approximation=15/2, reference=7/3, tolerance=1/8≥0. Give (approximation, reference, absolute error, tolerance, error≤tolerance?).","answer":{"kind":"expression","value":"(15/2, 7/3, 31/6, 1/8, No)","explanation":"The tolerance comparison includes equality; a negative tolerance is not admitted. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (15/2, 7/3, 31/6, 1/8, No)."},"skills":["Inclusive Absolute-Error Tolerance"],"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-20261013-advance-20261020-r03-numerical-approximation-error-0058","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"06eb01ee62de41d44987aa2f2ceb672764b2628c5f48a96031e7dab1be1592d1","family_id":"qf-app20-error-tolerance-audit","seed":202610203058,"semantic_template":"qf-app20-error-tolerance-audit/{\"approximation\":[17,3],\"reference\":[8,4],\"tolerance\":[2,2]}"},"fields":{"title":"Inclusive Absolute-Error Tolerance","stem":"Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. approximation=17/3, reference=8/4, tolerance=2/2≥0. Give (approximation, reference, absolute error, tolerance, error≤tolerance?).","answer":{"kind":"expression","value":"(17/3, 2, 11/3, 1, No)","explanation":"The tolerance comparison includes equality; a negative tolerance is not admitted. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (17/3, 2, 11/3, 1, No)."},"skills":["Inclusive Absolute-Error Tolerance"],"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-20261013-advance-20261020-r03-numerical-approximation-error-0059","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"a003b6f26db1fe475d4173bc5d14edcb3259da901b32f1f9a7ec54460598f3a0","family_id":"qf-app20-error-tolerance-audit","seed":202610203059,"semantic_template":"qf-app20-error-tolerance-audit/{\"approximation\":[19,4],\"reference\":[9,1],\"tolerance\":[3,3]}"},"fields":{"title":"Inclusive Absolute-Error Tolerance","stem":"Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. approximation=19/4, reference=9/1, tolerance=3/3≥0. Give (approximation, reference, absolute error, tolerance, error≤tolerance?).","answer":{"kind":"expression","value":"(19/4, 9, 17/4, 1, No)","explanation":"The tolerance comparison includes equality; a negative tolerance is not admitted. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (19/4, 9, 17/4, 1, No)."},"skills":["Inclusive Absolute-Error Tolerance"],"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-20261013-advance-20261020-r03-numerical-approximation-error-0060","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"99f74c43bf2c8e0ca38d7e86759242c53790eba209264ca555458392a641763e","family_id":"qf-app20-error-tolerance-audit","seed":202610203060,"semantic_template":"qf-app20-error-tolerance-audit/{\"approximation\":[21,5],\"reference\":[1,2],\"tolerance\":[4,4]}"},"fields":{"title":"Inclusive Absolute-Error Tolerance","stem":"Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. approximation=21/5, reference=1/2, tolerance=4/4≥0. Give (approximation, reference, absolute error, tolerance, error≤tolerance?).","answer":{"kind":"expression","value":"(21/5, 1/2, 37/10, 1, No)","explanation":"The tolerance comparison includes equality; a negative tolerance is not admitted. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (21/5, 1/2, 37/10, 1, No)."},"skills":["Inclusive Absolute-Error Tolerance"],"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-20261013-advance-20261020-r03-numerical-approximation-error-0061","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"4124f5b7283d039ff945f367c6258594456ea4120ee388b99673a8fbe3512628","family_id":"qf-app20-error-tolerance-audit","seed":202610203061,"semantic_template":"qf-app20-error-tolerance-audit/{\"approximation\":[23,1],\"reference\":[2,3],\"tolerance\":[5,5]}"},"fields":{"title":"Inclusive Absolute-Error Tolerance","stem":"Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. approximation=23/1, reference=2/3, tolerance=5/5≥0. Give (approximation, reference, absolute error, tolerance, error≤tolerance?).","answer":{"kind":"expression","value":"(23, 2/3, 67/3, 1, No)","explanation":"The tolerance comparison includes equality; a negative tolerance is not admitted. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (23, 2/3, 67/3, 1, No)."},"skills":["Inclusive Absolute-Error Tolerance"],"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-20261013-advance-20261020-r03-numerical-approximation-error-0062","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"91521dddffd2cdf5d84aaaf7facffbe7efe319950fd4280e8c2327e050681fe7","family_id":"qf-app20-error-tolerance-audit","seed":202610203062,"semantic_template":"qf-app20-error-tolerance-audit/{\"approximation\":[25,2],\"reference\":[3,4],\"tolerance\":[6,6]}"},"fields":{"title":"Inclusive Absolute-Error Tolerance","stem":"Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. approximation=25/2, reference=3/4, tolerance=6/6≥0. Give (approximation, reference, absolute error, tolerance, error≤tolerance?).","answer":{"kind":"expression","value":"(25/2, 3/4, 47/4, 1, No)","explanation":"The tolerance comparison includes equality; a negative tolerance is not admitted. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (25/2, 3/4, 47/4, 1, No)."},"skills":["Inclusive Absolute-Error Tolerance"],"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-20261013-advance-20261020-r03-numerical-approximation-error-0063","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"4464dd78d5841336d193193aa6c3bd7d40edb22a9fa60341a05f026eb9c84af6","family_id":"qf-app20-error-tolerance-audit","seed":202610203063,"semantic_template":"qf-app20-error-tolerance-audit/{\"approximation\":[27,3],\"reference\":[4,1],\"tolerance\":[1,7]}"},"fields":{"title":"Inclusive Absolute-Error Tolerance","stem":"Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. approximation=27/3, reference=4/1, tolerance=1/7≥0. Give (approximation, reference, absolute error, tolerance, error≤tolerance?).","answer":{"kind":"expression","value":"(9, 4, 5, 1/7, No)","explanation":"The tolerance comparison includes equality; a negative tolerance is not admitted. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (9, 4, 5, 1/7, No)."},"skills":["Inclusive Absolute-Error Tolerance"],"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-20261013-advance-20261020-r03-numerical-approximation-error-0064","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"0af792b0821d57ab480791c56db882f7fe278747871e1c2e004c4183498b8092","family_id":"qf-app20-error-tolerance-audit","seed":202610203064,"semantic_template":"qf-app20-error-tolerance-audit/{\"approximation\":[29,4],\"reference\":[5,2],\"tolerance\":[2,8]}"},"fields":{"title":"Inclusive Absolute-Error Tolerance","stem":"Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. approximation=29/4, reference=5/2, tolerance=2/8≥0. Give (approximation, reference, absolute error, tolerance, error≤tolerance?).","answer":{"kind":"expression","value":"(29/4, 5/2, 19/4, 1/4, No)","explanation":"The tolerance comparison includes equality; a negative tolerance is not admitted. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (29/4, 5/2, 19/4, 1/4, No)."},"skills":["Inclusive Absolute-Error Tolerance"],"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-20261013-advance-20261020-r03-numerical-approximation-error-0065","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"4c0f2dc0d21784f3d6a2ed61fc4f80f91947d9d6427c67940135273998a25918","family_id":"qf-app20-error-tolerance-audit","seed":202610203065,"semantic_template":"qf-app20-error-tolerance-audit/{\"approximation\":[31,5],\"reference\":[6,3],\"tolerance\":[3,2]}"},"fields":{"title":"Inclusive Absolute-Error Tolerance","stem":"Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. approximation=31/5, reference=6/3, tolerance=3/2≥0. Give (approximation, reference, absolute error, tolerance, error≤tolerance?).","answer":{"kind":"expression","value":"(31/5, 2, 21/5, 3/2, No)","explanation":"The tolerance comparison includes equality; a negative tolerance is not admitted. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (31/5, 2, 21/5, 3/2, No)."},"skills":["Inclusive Absolute-Error Tolerance"],"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-20261013-advance-20261020-r03-numerical-approximation-error-0066","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"2cf957ce943082aed9a2cab195f653fa6a28fad7dbc247fa8d1a5ae5d965db8f","family_id":"qf-app20-error-tolerance-audit","seed":202610203066,"semantic_template":"qf-app20-error-tolerance-audit/{\"approximation\":[33,1],\"reference\":[7,4],\"tolerance\":[4,3]}"},"fields":{"title":"Inclusive Absolute-Error Tolerance","stem":"Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. approximation=33/1, reference=7/4, tolerance=4/3≥0. Give (approximation, reference, absolute error, tolerance, error≤tolerance?).","answer":{"kind":"expression","value":"(33, 7/4, 125/4, 4/3, No)","explanation":"The tolerance comparison includes equality; a negative tolerance is not admitted. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (33, 7/4, 125/4, 4/3, No)."},"skills":["Inclusive Absolute-Error Tolerance"],"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-20261013-advance-20261020-r03-numerical-approximation-error-0067","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"399a1fbf5213c61d383d4b479a9e7b6d178704262b592d6ae53e9c64725eff62","family_id":"qf-app20-error-tolerance-audit","seed":202610203067,"semantic_template":"qf-app20-error-tolerance-audit/{\"approximation\":[35,2],\"reference\":[8,1],\"tolerance\":[5,4]}"},"fields":{"title":"Inclusive Absolute-Error Tolerance","stem":"Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. approximation=35/2, reference=8/1, tolerance=5/4≥0. Give (approximation, reference, absolute error, tolerance, error≤tolerance?).","answer":{"kind":"expression","value":"(35/2, 8, 19/2, 5/4, No)","explanation":"The tolerance comparison includes equality; a negative tolerance is not admitted. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (35/2, 8, 19/2, 5/4, No)."},"skills":["Inclusive Absolute-Error Tolerance"],"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-20261013-advance-20261020-r03-numerical-approximation-error-0068","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"3b686164231190c67661e381d33726179dc507c2c9d5a69abebe9af93a953843","family_id":"qf-app20-error-tolerance-audit","seed":202610203068,"semantic_template":"qf-app20-error-tolerance-audit/{\"approximation\":[37,3],\"reference\":[9,2],\"tolerance\":[6,5]}"},"fields":{"title":"Inclusive Absolute-Error Tolerance","stem":"Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. approximation=37/3, reference=9/2, tolerance=6/5≥0. Give (approximation, reference, absolute error, tolerance, error≤tolerance?).","answer":{"kind":"expression","value":"(37/3, 9/2, 47/6, 6/5, No)","explanation":"The tolerance comparison includes equality; a negative tolerance is not admitted. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (37/3, 9/2, 47/6, 6/5, No)."},"skills":["Inclusive Absolute-Error Tolerance"],"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-20261013-advance-20261020-r03-numerical-approximation-error-0069","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"aafa246447f4184ee0aba3bde0c8c0f9e25b12921e2c52119198b552cd661f75","family_id":"qf-app20-error-tolerance-audit","seed":202610203069,"semantic_template":"qf-app20-error-tolerance-audit/{\"approximation\":[39,4],\"reference\":[1,3],\"tolerance\":[1,6]}"},"fields":{"title":"Inclusive Absolute-Error Tolerance","stem":"Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. approximation=39/4, reference=1/3, tolerance=1/6≥0. Give (approximation, reference, absolute error, tolerance, error≤tolerance?).","answer":{"kind":"expression","value":"(39/4, 1/3, 113/12, 1/6, No)","explanation":"The tolerance comparison includes equality; a negative tolerance is not admitted. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (39/4, 1/3, 113/12, 1/6, No)."},"skills":["Inclusive Absolute-Error Tolerance"],"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-20261013-advance-20261020-r03-numerical-approximation-error-0070","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"988d9931babcc3b0ee2030e00cec17c186c293af097ed8d9ae4e79e55541c582","family_id":"qf-app20-error-tolerance-audit","seed":202610203070,"semantic_template":"qf-app20-error-tolerance-audit/{\"approximation\":[41,5],\"reference\":[2,4],\"tolerance\":[2,7]}"},"fields":{"title":"Inclusive Absolute-Error Tolerance","stem":"Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. approximation=41/5, reference=2/4, tolerance=2/7≥0. Give (approximation, reference, absolute error, tolerance, error≤tolerance?).","answer":{"kind":"expression","value":"(41/5, 1/2, 77/10, 2/7, No)","explanation":"The tolerance comparison includes equality; a negative tolerance is not admitted. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (41/5, 1/2, 77/10, 2/7, No)."},"skills":["Inclusive Absolute-Error Tolerance"],"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-20261013-advance-20261020-r03-numerical-approximation-error-0071","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"0f9b07e9ebe7536a4fa3e5c801b0ff68bed0022de8207595d8b9a4380f53f843","family_id":"qf-app20-error-tolerance-audit","seed":202610203071,"semantic_template":"qf-app20-error-tolerance-audit/{\"approximation\":[43,1],\"reference\":[3,1],\"tolerance\":[3,8]}"},"fields":{"title":"Inclusive Absolute-Error Tolerance","stem":"Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. approximation=43/1, reference=3/1, tolerance=3/8≥0. Give (approximation, reference, absolute error, tolerance, error≤tolerance?).","answer":{"kind":"expression","value":"(43, 3, 40, 3/8, No)","explanation":"The tolerance comparison includes equality; a negative tolerance is not admitted. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (43, 3, 40, 3/8, No)."},"skills":["Inclusive Absolute-Error Tolerance"],"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-20261013-advance-20261020-r03-numerical-approximation-error-0072","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"ed00d1645ad2882fcbdb3c3bc9f6d6e74ad41b3139ead58d7f37c276b57e6918","family_id":"qf-app20-error-tolerance-audit","seed":202610203072,"semantic_template":"qf-app20-error-tolerance-audit/{\"approximation\":[45,2],\"reference\":[4,2],\"tolerance\":[4,2]}"},"fields":{"title":"Inclusive Absolute-Error Tolerance","stem":"Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. approximation=45/2, reference=4/2, tolerance=4/2≥0. Give (approximation, reference, absolute error, tolerance, error≤tolerance?).","answer":{"kind":"expression","value":"(45/2, 2, 41/2, 2, No)","explanation":"The tolerance comparison includes equality; a negative tolerance is not admitted. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (45/2, 2, 41/2, 2, No)."},"skills":["Inclusive Absolute-Error Tolerance"],"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-20261013-advance-20261020-r03-numerical-approximation-error-0073","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"cdf8f52367e9d5faf9449d44baa5cf35985716723eee73ba3119da7d6cc0f245","family_id":"qf-app20-error-tolerance-audit","seed":202610203073,"semantic_template":"qf-app20-error-tolerance-audit/{\"approximation\":[47,3],\"reference\":[5,3],\"tolerance\":[5,3]}"},"fields":{"title":"Inclusive Absolute-Error Tolerance","stem":"Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. approximation=47/3, reference=5/3, tolerance=5/3≥0. Give (approximation, reference, absolute error, tolerance, error≤tolerance?).","answer":{"kind":"expression","value":"(47/3, 5/3, 14, 5/3, No)","explanation":"The tolerance comparison includes equality; a negative tolerance is not admitted. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (47/3, 5/3, 14, 5/3, No)."},"skills":["Inclusive Absolute-Error Tolerance"],"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-20261013-advance-20261020-r03-numerical-approximation-error-0074","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"18ecc76ef0f0bfdfdff304f255be8e1955e3fe4bf31d5ef7585322758635bf0c","family_id":"qf-app20-error-tolerance-audit","seed":202610203074,"semantic_template":"qf-app20-error-tolerance-audit/{\"approximation\":[49,4],\"reference\":[6,4],\"tolerance\":[6,4]}"},"fields":{"title":"Inclusive Absolute-Error Tolerance","stem":"Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. approximation=49/4, reference=6/4, tolerance=6/4≥0. Give (approximation, reference, absolute error, tolerance, error≤tolerance?).","answer":{"kind":"expression","value":"(49/4, 3/2, 43/4, 3/2, No)","explanation":"The tolerance comparison includes equality; a negative tolerance is not admitted. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (49/4, 3/2, 43/4, 3/2, No)."},"skills":["Inclusive Absolute-Error Tolerance"],"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-20261013-advance-20261020-r03-numerical-approximation-error-0075","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"c936cda528a31a0ed5a19f43de5ba7261d7693e11cf730ea7507461fe41a7949","family_id":"qf-app20-error-tolerance-audit","seed":202610203075,"semantic_template":"qf-app20-error-tolerance-audit/{\"approximation\":[51,5],\"reference\":[7,1],\"tolerance\":[1,5]}"},"fields":{"title":"Inclusive Absolute-Error Tolerance","stem":"Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. approximation=51/5, reference=7/1, tolerance=1/5≥0. Give (approximation, reference, absolute error, tolerance, error≤tolerance?).","answer":{"kind":"expression","value":"(51/5, 7, 16/5, 1/5, No)","explanation":"The tolerance comparison includes equality; a negative tolerance is not admitted. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (51/5, 7, 16/5, 1/5, No)."},"skills":["Inclusive Absolute-Error Tolerance"],"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-20261013-advance-20261020-r03-numerical-approximation-error-0076","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"642d640f66cc09e02627577c3ba8c89053d44cd90971b3a9159b84f850690269","family_id":"qf-app20-error-error-interval","seed":202610203076,"semantic_template":"qf-app20-error-error-interval/{\"candidate\":[1,1],\"reference\":[1,1],\"tolerance\":[1,2]}"},"fields":{"title":"Inclusive Error Interval and a Candidate Boundary","stem":"Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. reference=1/1, tolerance=1/2≥0, candidate=1/1. Give (reference, tolerance, reference−tolerance, reference+tolerance, candidate, inside the inclusive interval?).","answer":{"kind":"expression","value":"(1, 1/2, 1/2, 3/2, 1, Yes)","explanation":"Check both exact endpoint inequalities; boundary points are within tolerance. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (1, 1/2, 1/2, 3/2, 1, Yes)."},"skills":["Inclusive Error Interval and a Candidate Boundary"],"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-20261013-advance-20261020-r03-numerical-approximation-error-0077","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"b4500858a1c877a938d050824972791796d4854794946344832ee32c7439a37e","family_id":"qf-app20-error-error-interval","seed":202610203077,"semantic_template":"qf-app20-error-error-interval/{\"candidate\":[3,2],\"reference\":[2,2],\"tolerance\":[2,3]}"},"fields":{"title":"Inclusive Error Interval and a Candidate Boundary","stem":"Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. reference=2/2, tolerance=2/3≥0, candidate=3/2. Give (reference, tolerance, reference−tolerance, reference+tolerance, candidate, inside the inclusive interval?).","answer":{"kind":"expression","value":"(1, 2/3, 1/3, 5/3, 3/2, Yes)","explanation":"Check both exact endpoint inequalities; boundary points are within tolerance. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (1, 2/3, 1/3, 5/3, 3/2, Yes)."},"skills":["Inclusive Error Interval and a Candidate Boundary"],"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-20261013-advance-20261020-r03-numerical-approximation-error-0078","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"a7a018c7c7946e54bb07ba3c8f00136ed1035b33e37785400b33e3d38bdaa9bb","family_id":"qf-app20-error-error-interval","seed":202610203078,"semantic_template":"qf-app20-error-error-interval/{\"candidate\":[5,3],\"reference\":[3,3],\"tolerance\":[3,4]}"},"fields":{"title":"Inclusive Error Interval and a Candidate Boundary","stem":"Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. reference=3/3, tolerance=3/4≥0, candidate=5/3. Give (reference, tolerance, reference−tolerance, reference+tolerance, candidate, inside the inclusive interval?).","answer":{"kind":"expression","value":"(1, 3/4, 1/4, 7/4, 5/3, Yes)","explanation":"Check both exact endpoint inequalities; boundary points are within tolerance. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (1, 3/4, 1/4, 7/4, 5/3, Yes)."},"skills":["Inclusive Error Interval and a Candidate Boundary"],"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-20261013-advance-20261020-r03-numerical-approximation-error-0079","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"a3cab8e3a9aa90d335ecd467a4c83403068fb864ab4ea429f55f8a4d6a81a89f","family_id":"qf-app20-error-error-interval","seed":202610203079,"semantic_template":"qf-app20-error-error-interval/{\"candidate\":[7,4],\"reference\":[4,4],\"tolerance\":[4,5]}"},"fields":{"title":"Inclusive Error Interval and a Candidate Boundary","stem":"Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. reference=4/4, tolerance=4/5≥0, candidate=7/4. Give (reference, tolerance, reference−tolerance, reference+tolerance, candidate, inside the inclusive interval?).","answer":{"kind":"expression","value":"(1, 4/5, 1/5, 9/5, 7/4, Yes)","explanation":"Check both exact endpoint inequalities; boundary points are within tolerance. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (1, 4/5, 1/5, 9/5, 7/4, Yes)."},"skills":["Inclusive Error Interval and a Candidate Boundary"],"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-20261013-advance-20261020-r03-numerical-approximation-error-0080","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"6607a03bd01fd2a1c7e2649535a72773b7e3ff004bc13e99e37c57d227f96da5","family_id":"qf-app20-error-error-interval","seed":202610203080,"semantic_template":"qf-app20-error-error-interval/{\"candidate\":[9,5],\"reference\":[5,1],\"tolerance\":[5,6]}"},"fields":{"title":"Inclusive Error Interval and a Candidate Boundary","stem":"Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. reference=5/1, tolerance=5/6≥0, candidate=9/5. Give (reference, tolerance, reference−tolerance, reference+tolerance, candidate, inside the inclusive interval?).","answer":{"kind":"expression","value":"(5, 5/6, 25/6, 35/6, 9/5, No)","explanation":"Check both exact endpoint inequalities; boundary points are within tolerance. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (5, 5/6, 25/6, 35/6, 9/5, No)."},"skills":["Inclusive Error Interval and a Candidate Boundary"],"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-20261013-advance-20261020-r03-numerical-approximation-error-0081","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"69795d2c819c22bdbd2ef5ac8c5298caf54fbc785f0bfc49bb2783b3f39cf041","family_id":"qf-app20-error-error-interval","seed":202610203081,"semantic_template":"qf-app20-error-error-interval/{\"candidate\":[11,1],\"reference\":[6,2],\"tolerance\":[6,7]}"},"fields":{"title":"Inclusive Error Interval and a Candidate Boundary","stem":"Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. reference=6/2, tolerance=6/7≥0, candidate=11/1. Give (reference, tolerance, reference−tolerance, reference+tolerance, candidate, inside the inclusive interval?).","answer":{"kind":"expression","value":"(3, 6/7, 15/7, 27/7, 11, No)","explanation":"Check both exact endpoint inequalities; boundary points are within tolerance. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (3, 6/7, 15/7, 27/7, 11, No)."},"skills":["Inclusive Error Interval and a Candidate Boundary"],"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-20261013-advance-20261020-r03-numerical-approximation-error-0082","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"10bd19a9c082b32e9a065ee3392beeadffbc2b9e0942df14e635bc227ee76169","family_id":"qf-app20-error-error-interval","seed":202610203082,"semantic_template":"qf-app20-error-error-interval/{\"candidate\":[13,2],\"reference\":[7,3],\"tolerance\":[1,8]}"},"fields":{"title":"Inclusive Error Interval and a Candidate Boundary","stem":"Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. reference=7/3, tolerance=1/8≥0, candidate=13/2. Give (reference, tolerance, reference−tolerance, reference+tolerance, candidate, inside the inclusive interval?).","answer":{"kind":"expression","value":"(7/3, 1/8, 53/24, 59/24, 13/2, No)","explanation":"Check both exact endpoint inequalities; boundary points are within tolerance. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (7/3, 1/8, 53/24, 59/24, 13/2, No)."},"skills":["Inclusive Error Interval and a Candidate Boundary"],"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-20261013-advance-20261020-r03-numerical-approximation-error-0083","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"34bb5258eab53631ef1c5b5dc18e963395165b3de96ba476ade503bf38db560e","family_id":"qf-app20-error-error-interval","seed":202610203083,"semantic_template":"qf-app20-error-error-interval/{\"candidate\":[15,3],\"reference\":[8,4],\"tolerance\":[2,2]}"},"fields":{"title":"Inclusive Error Interval and a Candidate Boundary","stem":"Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. reference=8/4, tolerance=2/2≥0, candidate=15/3. Give (reference, tolerance, reference−tolerance, reference+tolerance, candidate, inside the inclusive interval?).","answer":{"kind":"expression","value":"(2, 1, 1, 3, 5, No)","explanation":"Check both exact endpoint inequalities; boundary points are within tolerance. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (2, 1, 1, 3, 5, No)."},"skills":["Inclusive Error Interval and a Candidate Boundary"],"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-20261013-advance-20261020-r03-numerical-approximation-error-0084","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"e515a12a44c7812f2d729e2d42f5a4dccb5836635f89a3d6cea76800bc456da4","family_id":"qf-app20-error-error-interval","seed":202610203084,"semantic_template":"qf-app20-error-error-interval/{\"candidate\":[17,4],\"reference\":[9,1],\"tolerance\":[3,3]}"},"fields":{"title":"Inclusive Error Interval and a Candidate Boundary","stem":"Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. reference=9/1, tolerance=3/3≥0, candidate=17/4. Give (reference, tolerance, reference−tolerance, reference+tolerance, candidate, inside the inclusive interval?).","answer":{"kind":"expression","value":"(9, 1, 8, 10, 17/4, No)","explanation":"Check both exact endpoint inequalities; boundary points are within tolerance. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (9, 1, 8, 10, 17/4, No)."},"skills":["Inclusive Error Interval and a Candidate Boundary"],"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-20261013-advance-20261020-r03-numerical-approximation-error-0085","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"583850f918d87b838dd1361d11d475140af9294895421000676bace2183463b8","family_id":"qf-app20-error-error-interval","seed":202610203085,"semantic_template":"qf-app20-error-error-interval/{\"candidate\":[19,5],\"reference\":[1,2],\"tolerance\":[4,4]}"},"fields":{"title":"Inclusive Error Interval and a Candidate Boundary","stem":"Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. reference=1/2, tolerance=4/4≥0, candidate=19/5. Give (reference, tolerance, reference−tolerance, reference+tolerance, candidate, inside the inclusive interval?).","answer":{"kind":"expression","value":"(1/2, 1, -1/2, 3/2, 19/5, No)","explanation":"Check both exact endpoint inequalities; boundary points are within tolerance. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (1/2, 1, -1/2, 3/2, 19/5, No)."},"skills":["Inclusive Error Interval and a Candidate Boundary"],"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-20261013-advance-20261020-r03-numerical-approximation-error-0086","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"047a3aac350ed093f20744101cd3cba4dec356d306321c2caf78dcd4e9fea974","family_id":"qf-app20-error-error-interval","seed":202610203086,"semantic_template":"qf-app20-error-error-interval/{\"candidate\":[21,1],\"reference\":[2,3],\"tolerance\":[5,5]}"},"fields":{"title":"Inclusive Error Interval and a Candidate Boundary","stem":"Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. reference=2/3, tolerance=5/5≥0, candidate=21/1. Give (reference, tolerance, reference−tolerance, reference+tolerance, candidate, inside the inclusive interval?).","answer":{"kind":"expression","value":"(2/3, 1, -1/3, 5/3, 21, No)","explanation":"Check both exact endpoint inequalities; boundary points are within tolerance. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (2/3, 1, -1/3, 5/3, 21, No)."},"skills":["Inclusive Error Interval and a Candidate Boundary"],"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-20261013-advance-20261020-r03-numerical-approximation-error-0087","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"4a533f2d3639b85649c1d2cab94bad9d3aeb68193e28f4e0d8aae6b6dd62ab71","family_id":"qf-app20-error-error-interval","seed":202610203087,"semantic_template":"qf-app20-error-error-interval/{\"candidate\":[23,2],\"reference\":[3,4],\"tolerance\":[6,6]}"},"fields":{"title":"Inclusive Error Interval and a Candidate Boundary","stem":"Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. reference=3/4, tolerance=6/6≥0, candidate=23/2. Give (reference, tolerance, reference−tolerance, reference+tolerance, candidate, inside the inclusive interval?).","answer":{"kind":"expression","value":"(3/4, 1, -1/4, 7/4, 23/2, No)","explanation":"Check both exact endpoint inequalities; boundary points are within tolerance. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (3/4, 1, -1/4, 7/4, 23/2, No)."},"skills":["Inclusive Error Interval and a Candidate Boundary"],"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-20261013-advance-20261020-r03-numerical-approximation-error-0088","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"d584c466ee0dcddfcda4447d6c71257fa3646b4fc57679840a2ce7cb2648824f","family_id":"qf-app20-error-error-interval","seed":202610203088,"semantic_template":"qf-app20-error-error-interval/{\"candidate\":[25,3],\"reference\":[4,1],\"tolerance\":[1,7]}"},"fields":{"title":"Inclusive Error Interval and a Candidate Boundary","stem":"Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. reference=4/1, tolerance=1/7≥0, candidate=25/3. Give (reference, tolerance, reference−tolerance, reference+tolerance, candidate, inside the inclusive interval?).","answer":{"kind":"expression","value":"(4, 1/7, 27/7, 29/7, 25/3, No)","explanation":"Check both exact endpoint inequalities; boundary points are within tolerance. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (4, 1/7, 27/7, 29/7, 25/3, No)."},"skills":["Inclusive Error Interval and a Candidate Boundary"],"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-20261013-advance-20261020-r03-numerical-approximation-error-0089","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"19900aa5a54c81d7013a5dc24b64a6c3f0e89dd18dcdc8972affb78c91944d27","family_id":"qf-app20-error-error-interval","seed":202610203089,"semantic_template":"qf-app20-error-error-interval/{\"candidate\":[27,4],\"reference\":[5,2],\"tolerance\":[2,8]}"},"fields":{"title":"Inclusive Error Interval and a Candidate Boundary","stem":"Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. reference=5/2, tolerance=2/8≥0, candidate=27/4. Give (reference, tolerance, reference−tolerance, reference+tolerance, candidate, inside the inclusive interval?).","answer":{"kind":"expression","value":"(5/2, 1/4, 9/4, 11/4, 27/4, No)","explanation":"Check both exact endpoint inequalities; boundary points are within tolerance. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (5/2, 1/4, 9/4, 11/4, 27/4, No)."},"skills":["Inclusive Error Interval and a Candidate Boundary"],"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-20261013-advance-20261020-r03-numerical-approximation-error-0090","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"f9f1ea93a6290ba6d2b409290f464920d8a190bb2e95a25415f2b1706826e535","family_id":"qf-app20-error-error-interval","seed":202610203090,"semantic_template":"qf-app20-error-error-interval/{\"candidate\":[29,5],\"reference\":[6,3],\"tolerance\":[3,2]}"},"fields":{"title":"Inclusive Error Interval and a Candidate Boundary","stem":"Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. reference=6/3, tolerance=3/2≥0, candidate=29/5. Give (reference, tolerance, reference−tolerance, reference+tolerance, candidate, inside the inclusive interval?).","answer":{"kind":"expression","value":"(2, 3/2, 1/2, 7/2, 29/5, No)","explanation":"Check both exact endpoint inequalities; boundary points are within tolerance. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (2, 3/2, 1/2, 7/2, 29/5, No)."},"skills":["Inclusive Error Interval and a Candidate Boundary"],"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-20261013-advance-20261020-r03-numerical-approximation-error-0091","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"c362a346a791a1913dbd2beef363ef0dd919f82e28cc8da91b4f0704ac710f8f","family_id":"qf-app20-error-error-interval","seed":202610203091,"semantic_template":"qf-app20-error-error-interval/{\"candidate\":[31,1],\"reference\":[7,4],\"tolerance\":[4,3]}"},"fields":{"title":"Inclusive Error Interval and a Candidate Boundary","stem":"Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. reference=7/4, tolerance=4/3≥0, candidate=31/1. Give (reference, tolerance, reference−tolerance, reference+tolerance, candidate, inside the inclusive interval?).","answer":{"kind":"expression","value":"(7/4, 4/3, 5/12, 37/12, 31, No)","explanation":"Check both exact endpoint inequalities; boundary points are within tolerance. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (7/4, 4/3, 5/12, 37/12, 31, No)."},"skills":["Inclusive Error Interval and a Candidate Boundary"],"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-20261013-advance-20261020-r03-numerical-approximation-error-0092","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"8deb495ba84ebde0f5e8a896a8fbe41b79c6cd6ca1b6df4780b97b61b69b04dd","family_id":"qf-app20-error-error-interval","seed":202610203092,"semantic_template":"qf-app20-error-error-interval/{\"candidate\":[33,2],\"reference\":[8,1],\"tolerance\":[5,4]}"},"fields":{"title":"Inclusive Error Interval and a Candidate Boundary","stem":"Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. reference=8/1, tolerance=5/4≥0, candidate=33/2. Give (reference, tolerance, reference−tolerance, reference+tolerance, candidate, inside the inclusive interval?).","answer":{"kind":"expression","value":"(8, 5/4, 27/4, 37/4, 33/2, No)","explanation":"Check both exact endpoint inequalities; boundary points are within tolerance. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (8, 5/4, 27/4, 37/4, 33/2, No)."},"skills":["Inclusive Error Interval and a Candidate Boundary"],"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-20261013-advance-20261020-r03-numerical-approximation-error-0093","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"20eb5551cdca362a3668e79b56548104c64d38ed9cbb5017883082414f38d5de","family_id":"qf-app20-error-error-interval","seed":202610203093,"semantic_template":"qf-app20-error-error-interval/{\"candidate\":[35,3],\"reference\":[9,2],\"tolerance\":[6,5]}"},"fields":{"title":"Inclusive Error Interval and a Candidate Boundary","stem":"Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. reference=9/2, tolerance=6/5≥0, candidate=35/3. Give (reference, tolerance, reference−tolerance, reference+tolerance, candidate, inside the inclusive interval?).","answer":{"kind":"expression","value":"(9/2, 6/5, 33/10, 57/10, 35/3, No)","explanation":"Check both exact endpoint inequalities; boundary points are within tolerance. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (9/2, 6/5, 33/10, 57/10, 35/3, No)."},"skills":["Inclusive Error Interval and a Candidate Boundary"],"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-20261013-advance-20261020-r03-numerical-approximation-error-0094","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"1c8d431ad8b2a2f8ae0f4a349574b88e6468a3cfe48c7935ab41cf9dd852a471","family_id":"qf-app20-error-error-interval","seed":202610203094,"semantic_template":"qf-app20-error-error-interval/{\"candidate\":[37,4],\"reference\":[1,3],\"tolerance\":[1,6]}"},"fields":{"title":"Inclusive Error Interval and a Candidate Boundary","stem":"Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. reference=1/3, tolerance=1/6≥0, candidate=37/4. Give (reference, tolerance, reference−tolerance, reference+tolerance, candidate, inside the inclusive interval?).","answer":{"kind":"expression","value":"(1/3, 1/6, 1/6, 1/2, 37/4, No)","explanation":"Check both exact endpoint inequalities; boundary points are within tolerance. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (1/3, 1/6, 1/6, 1/2, 37/4, No)."},"skills":["Inclusive Error Interval and a Candidate Boundary"],"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-20261013-advance-20261020-r03-numerical-approximation-error-0095","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"3bd1027b01172cffc38693a034d3aa3c01f7a5c0f92e568034c7307c94d79d7f","family_id":"qf-app20-error-error-interval","seed":202610203095,"semantic_template":"qf-app20-error-error-interval/{\"candidate\":[39,5],\"reference\":[2,4],\"tolerance\":[2,7]}"},"fields":{"title":"Inclusive Error Interval and a Candidate Boundary","stem":"Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. reference=2/4, tolerance=2/7≥0, candidate=39/5. Give (reference, tolerance, reference−tolerance, reference+tolerance, candidate, inside the inclusive interval?).","answer":{"kind":"expression","value":"(1/2, 2/7, 3/14, 11/14, 39/5, No)","explanation":"Check both exact endpoint inequalities; boundary points are within tolerance. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (1/2, 2/7, 3/14, 11/14, 39/5, No)."},"skills":["Inclusive Error Interval and a Candidate Boundary"],"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-20261013-advance-20261020-r03-numerical-approximation-error-0096","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"bd740cf0eba5183212362d7d0b6a46e8b3204cfe22ba17c86a49aac9805be1d3","family_id":"qf-app20-error-error-interval","seed":202610203096,"semantic_template":"qf-app20-error-error-interval/{\"candidate\":[41,1],\"reference\":[3,1],\"tolerance\":[3,8]}"},"fields":{"title":"Inclusive Error Interval and a Candidate Boundary","stem":"Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. reference=3/1, tolerance=3/8≥0, candidate=41/1. Give (reference, tolerance, reference−tolerance, reference+tolerance, candidate, inside the inclusive interval?).","answer":{"kind":"expression","value":"(3, 3/8, 21/8, 27/8, 41, No)","explanation":"Check both exact endpoint inequalities; boundary points are within tolerance. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (3, 3/8, 21/8, 27/8, 41, No)."},"skills":["Inclusive Error Interval and a Candidate Boundary"],"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-20261013-advance-20261020-r03-numerical-approximation-error-0097","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"616b950faf61287cd63028783fc8980a56a3771da44c70241e900934eb59eb64","family_id":"qf-app20-error-error-interval","seed":202610203097,"semantic_template":"qf-app20-error-error-interval/{\"candidate\":[43,2],\"reference\":[4,2],\"tolerance\":[4,2]}"},"fields":{"title":"Inclusive Error Interval and a Candidate Boundary","stem":"Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. reference=4/2, tolerance=4/2≥0, candidate=43/2. Give (reference, tolerance, reference−tolerance, reference+tolerance, candidate, inside the inclusive interval?).","answer":{"kind":"expression","value":"(2, 2, 0, 4, 43/2, No)","explanation":"Check both exact endpoint inequalities; boundary points are within tolerance. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (2, 2, 0, 4, 43/2, No)."},"skills":["Inclusive Error Interval and a Candidate Boundary"],"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-20261013-advance-20261020-r03-numerical-approximation-error-0098","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"21c2b3c3bb8e67c5107ed3e1c8f1706aee5ae205c4c7fec75d18c1549501a2df","family_id":"qf-app20-error-error-interval","seed":202610203098,"semantic_template":"qf-app20-error-error-interval/{\"candidate\":[45,3],\"reference\":[5,3],\"tolerance\":[5,3]}"},"fields":{"title":"Inclusive Error Interval and a Candidate Boundary","stem":"Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. reference=5/3, tolerance=5/3≥0, candidate=45/3. Give (reference, tolerance, reference−tolerance, reference+tolerance, candidate, inside the inclusive interval?).","answer":{"kind":"expression","value":"(5/3, 5/3, 0, 10/3, 15, No)","explanation":"Check both exact endpoint inequalities; boundary points are within tolerance. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (5/3, 5/3, 0, 10/3, 15, No)."},"skills":["Inclusive Error Interval and a Candidate Boundary"],"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-20261013-advance-20261020-r03-numerical-approximation-error-0099","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"76f143f4cc68117744d6f7ded18386b28349799eb4cae0998df50f27e036115b","family_id":"qf-app20-error-error-interval","seed":202610203099,"semantic_template":"qf-app20-error-error-interval/{\"candidate\":[47,4],\"reference\":[6,4],\"tolerance\":[6,4]}"},"fields":{"title":"Inclusive Error Interval and a Candidate Boundary","stem":"Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. reference=6/4, tolerance=6/4≥0, candidate=47/4. Give (reference, tolerance, reference−tolerance, reference+tolerance, candidate, inside the inclusive interval?).","answer":{"kind":"expression","value":"(3/2, 3/2, 0, 3, 47/4, No)","explanation":"Check both exact endpoint inequalities; boundary points are within tolerance. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (3/2, 3/2, 0, 3, 47/4, No)."},"skills":["Inclusive Error Interval and a Candidate Boundary"],"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-20261013-advance-20261020-r03-numerical-approximation-error-0100","batch_id":"batch-20261013-advance-20261020-r03-numerical-approximation-error-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"81220a1da9be1a111265c6c1f4ba5ff440bec554db5250a46602da776b59fd96","family_id":"qf-app20-error-error-interval","seed":202610203100,"semantic_template":"qf-app20-error-error-interval/{\"candidate\":[49,5],\"reference\":[7,1],\"tolerance\":[1,5]}"},"fields":{"title":"Inclusive Error Interval and a Candidate Boundary","stem":"Use exact rational inputs. Normalize denominator signs and reduce output fractions; print integers without /1. These specified-value checks do not identify truncation, rounding, measurement or model-error causes. reference=7/1, tolerance=1/5≥0, candidate=49/5. Give (reference, tolerance, reference−tolerance, reference+tolerance, candidate, inside the inclusive interval?).","answer":{"kind":"expression","value":"(7, 1/5, 34/5, 36/5, 49/5, No)","explanation":"Check both exact endpoint inequalities; boundary points are within tolerance. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is (7, 1/5, 34/5, 36/5, 49/5, No)."},"skills":["Inclusive Error Interval and a Candidate Boundary"],"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."}}