{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260928-absolute-value-exact-evaluation-0001","batch_id":"batch-20260928-absolute-value-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"f4b3321d45928b6b0cd3280919ace7a3d309163f73fb7d6764f7db6484a9180b","family_id":"qf-absolute-value-exact-evaluation","seed":20260929,"semantic_template":"qf-absolute-value-exact-evaluation/{\"domain\":\"reals\",\"operation\":\"exact_absolute_value\",\"x\":-12}"},"fields":{"title":"Exact Absolute Value","stem":"Using the piecewise definition over the real numbers, compute |-12| exactly.","answer":{"kind":"short_text","value":"12","explanation":"-12<0, so absolute value takes the additive inverse and |-12|=12."},"skills":["piecewise definition","exact integer computation"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260928-absolute-value-exact-evaluation-0002","batch_id":"batch-20260928-absolute-value-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"e49f71475517295047994cdcdd51b920ea588edabce2765e1967e883722c5f23","family_id":"qf-absolute-value-exact-evaluation","seed":20260930,"semantic_template":"qf-absolute-value-exact-evaluation/{\"domain\":\"reals\",\"operation\":\"exact_absolute_value\",\"x\":-11}"},"fields":{"title":"Exact Absolute Value","stem":"Using the piecewise definition over the real numbers, compute |-11| exactly.","answer":{"kind":"short_text","value":"11","explanation":"-11<0, so absolute value takes the additive inverse and |-11|=11."},"skills":["piecewise definition","exact integer computation"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260928-absolute-value-exact-evaluation-0003","batch_id":"batch-20260928-absolute-value-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"a495c8deeb98030fef0178ce3393ca4ee13c484f917a5b940afb904402b87c2e","family_id":"qf-absolute-value-exact-evaluation","seed":20260931,"semantic_template":"qf-absolute-value-exact-evaluation/{\"domain\":\"reals\",\"operation\":\"exact_absolute_value\",\"x\":-10}"},"fields":{"title":"Exact Absolute Value","stem":"Using the piecewise definition over the real numbers, compute |-10| exactly.","answer":{"kind":"short_text","value":"10","explanation":"-10<0, so absolute value takes the additive inverse and |-10|=10."},"skills":["piecewise definition","exact integer computation"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260928-absolute-value-exact-evaluation-0004","batch_id":"batch-20260928-absolute-value-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"6930598aa4539331cbcbc10cf751ad01836d0bc3d42c87be1536443926c47c7a","family_id":"qf-absolute-value-exact-evaluation","seed":20260932,"semantic_template":"qf-absolute-value-exact-evaluation/{\"domain\":\"reals\",\"operation\":\"exact_absolute_value\",\"x\":-9}"},"fields":{"title":"Exact Absolute Value","stem":"Using the piecewise definition over the real numbers, compute |-9| exactly.","answer":{"kind":"short_text","value":"9","explanation":"-9<0, so absolute value takes the additive inverse and |-9|=9."},"skills":["piecewise definition","exact integer computation"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260928-absolute-value-exact-evaluation-0005","batch_id":"batch-20260928-absolute-value-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"b77000ce3c5eee827b8ab2eb4a982069db55fbf2e603df1368563c3d60f5a113","family_id":"qf-absolute-value-exact-evaluation","seed":20260933,"semantic_template":"qf-absolute-value-exact-evaluation/{\"domain\":\"reals\",\"operation\":\"exact_absolute_value\",\"x\":-8}"},"fields":{"title":"Exact Absolute Value","stem":"Using the piecewise definition over the real numbers, compute |-8| exactly.","answer":{"kind":"short_text","value":"8","explanation":"-8<0, so absolute value takes the additive inverse and |-8|=8."},"skills":["piecewise definition","exact integer computation"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260928-absolute-value-exact-evaluation-0006","batch_id":"batch-20260928-absolute-value-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"a841a31ca5d7caad3d9319f880a64a676d02b587f3bc36ce7c5f6a2c37899f83","family_id":"qf-absolute-value-exact-evaluation","seed":20260934,"semantic_template":"qf-absolute-value-exact-evaluation/{\"domain\":\"reals\",\"operation\":\"exact_absolute_value\",\"x\":-7}"},"fields":{"title":"Exact Absolute Value","stem":"Using the piecewise definition over the real numbers, compute |-7| exactly.","answer":{"kind":"short_text","value":"7","explanation":"-7<0, so absolute value takes the additive inverse and |-7|=7."},"skills":["piecewise definition","exact integer computation"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260928-absolute-value-exact-evaluation-0007","batch_id":"batch-20260928-absolute-value-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"8c825f50100837d70849e7ccdf5592854577643e7ff8e99946a80aa099ba6b44","family_id":"qf-absolute-value-exact-evaluation","seed":20260935,"semantic_template":"qf-absolute-value-exact-evaluation/{\"domain\":\"reals\",\"operation\":\"exact_absolute_value\",\"x\":-6}"},"fields":{"title":"Exact Absolute Value","stem":"Using the piecewise definition over the real numbers, compute |-6| exactly.","answer":{"kind":"short_text","value":"6","explanation":"-6<0, so absolute value takes the additive inverse and |-6|=6."},"skills":["piecewise definition","exact integer computation"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260928-absolute-value-exact-evaluation-0008","batch_id":"batch-20260928-absolute-value-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"e5cd2ce8e7d0ae5fbb70775573f4524e8cc4326e95aec878757b6c0d1066dc26","family_id":"qf-absolute-value-exact-evaluation","seed":20260936,"semantic_template":"qf-absolute-value-exact-evaluation/{\"domain\":\"reals\",\"operation\":\"exact_absolute_value\",\"x\":-5}"},"fields":{"title":"Exact Absolute Value","stem":"Using the piecewise definition over the real numbers, compute |-5| exactly.","answer":{"kind":"short_text","value":"5","explanation":"-5<0, so absolute value takes the additive inverse and |-5|=5."},"skills":["piecewise definition","exact integer computation"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260928-absolute-value-exact-evaluation-0009","batch_id":"batch-20260928-absolute-value-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"bca3a06990d4540cf94b9d009c72e1fdfd466e3741385c66f1220a8198798698","family_id":"qf-absolute-value-exact-evaluation","seed":20260937,"semantic_template":"qf-absolute-value-exact-evaluation/{\"domain\":\"reals\",\"operation\":\"exact_absolute_value\",\"x\":-4}"},"fields":{"title":"Exact Absolute Value","stem":"Using the piecewise definition over the real numbers, compute |-4| exactly.","answer":{"kind":"short_text","value":"4","explanation":"-4<0, so absolute value takes the additive inverse and |-4|=4."},"skills":["piecewise definition","exact integer computation"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260928-absolute-value-exact-evaluation-0010","batch_id":"batch-20260928-absolute-value-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"48a2a501a2dde7d49f2fcbf971eb0f485b501e5d069dc44568bbc881d2c55c04","family_id":"qf-absolute-value-exact-evaluation","seed":20260938,"semantic_template":"qf-absolute-value-exact-evaluation/{\"domain\":\"reals\",\"operation\":\"exact_absolute_value\",\"x\":-3}"},"fields":{"title":"Exact Absolute Value","stem":"Using the piecewise definition over the real numbers, compute |-3| exactly.","answer":{"kind":"short_text","value":"3","explanation":"-3<0, so absolute value takes the additive inverse and |-3|=3."},"skills":["piecewise definition","exact integer computation"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260928-absolute-value-exact-evaluation-0011","batch_id":"batch-20260928-absolute-value-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"2da35d4fcfdd0f8f1ed4c96119a8754d7f9b70ffa88b57ce2637c07109e8a96c","family_id":"qf-absolute-value-exact-evaluation","seed":20260939,"semantic_template":"qf-absolute-value-exact-evaluation/{\"domain\":\"reals\",\"operation\":\"exact_absolute_value\",\"x\":-2}"},"fields":{"title":"Exact Absolute Value","stem":"Using the piecewise definition over the real numbers, compute |-2| exactly.","answer":{"kind":"short_text","value":"2","explanation":"-2<0, so absolute value takes the additive inverse and |-2|=2."},"skills":["piecewise definition","exact integer computation"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260928-absolute-value-exact-evaluation-0012","batch_id":"batch-20260928-absolute-value-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"c1fc0d60b12fc35fba3bd70faf11f3a22cfaa6021e4894dd9f7806d01bb0e5af","family_id":"qf-absolute-value-exact-evaluation","seed":20260940,"semantic_template":"qf-absolute-value-exact-evaluation/{\"domain\":\"reals\",\"operation\":\"exact_absolute_value\",\"x\":-1}"},"fields":{"title":"Exact Absolute Value","stem":"Using the piecewise definition over the real numbers, compute |-1| exactly.","answer":{"kind":"short_text","value":"1","explanation":"-1<0, so absolute value takes the additive inverse and |-1|=1."},"skills":["piecewise definition","exact integer computation"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260928-absolute-value-exact-evaluation-0013","batch_id":"batch-20260928-absolute-value-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"5a75b14bba0202569951d80bc9abfc05190555fb15f98015e1934b85c0f934e1","family_id":"qf-absolute-value-exact-evaluation","seed":20260941,"semantic_template":"qf-absolute-value-exact-evaluation/{\"domain\":\"reals\",\"operation\":\"exact_absolute_value\",\"x\":0}"},"fields":{"title":"Exact Absolute Value","stem":"Using the piecewise definition over the real numbers, compute |0| exactly.","answer":{"kind":"short_text","value":"0","explanation":"0≥0, so absolute value keeps the input and |0|=0."},"skills":["piecewise definition","exact integer computation"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260928-absolute-value-exact-evaluation-0014","batch_id":"batch-20260928-absolute-value-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"07f0220ee185f693914240c39544a040ec6df32029a74676dc4886547ed89e2d","family_id":"qf-absolute-value-exact-evaluation","seed":20260942,"semantic_template":"qf-absolute-value-exact-evaluation/{\"domain\":\"reals\",\"operation\":\"exact_absolute_value\",\"x\":1}"},"fields":{"title":"Exact Absolute Value","stem":"Using the piecewise definition over the real numbers, compute |1| exactly.","answer":{"kind":"short_text","value":"1","explanation":"1≥0, so absolute value keeps the input and |1|=1."},"skills":["piecewise definition","exact integer computation"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260928-absolute-value-exact-evaluation-0015","batch_id":"batch-20260928-absolute-value-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"5622f75f3d779d7ad91926457a522437f35dc576b0f1f086dfc0a58c89a9adae","family_id":"qf-absolute-value-exact-evaluation","seed":20260943,"semantic_template":"qf-absolute-value-exact-evaluation/{\"domain\":\"reals\",\"operation\":\"exact_absolute_value\",\"x\":2}"},"fields":{"title":"Exact Absolute Value","stem":"Using the piecewise definition over the real numbers, compute |2| exactly.","answer":{"kind":"short_text","value":"2","explanation":"2≥0, so absolute value keeps the input and |2|=2."},"skills":["piecewise definition","exact integer computation"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260928-absolute-value-exact-evaluation-0016","batch_id":"batch-20260928-absolute-value-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"9c4ac7c1b22b0a96430fa3243b41ca6c5c5b590200731ffe6532e2fe16a6dbfe","family_id":"qf-absolute-value-exact-evaluation","seed":20260944,"semantic_template":"qf-absolute-value-exact-evaluation/{\"domain\":\"reals\",\"operation\":\"exact_absolute_value\",\"x\":3}"},"fields":{"title":"Exact Absolute Value","stem":"Using the piecewise definition over the real numbers, compute |3| exactly.","answer":{"kind":"short_text","value":"3","explanation":"3≥0, so absolute value keeps the input and |3|=3."},"skills":["piecewise definition","exact integer computation"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260928-absolute-value-exact-evaluation-0017","batch_id":"batch-20260928-absolute-value-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"5d849d57e74214b1d4d31ed37a185e1ffa2ce7478e6a212d016a96078540fa07","family_id":"qf-absolute-value-exact-evaluation","seed":20260945,"semantic_template":"qf-absolute-value-exact-evaluation/{\"domain\":\"reals\",\"operation\":\"exact_absolute_value\",\"x\":4}"},"fields":{"title":"Exact Absolute Value","stem":"Using the piecewise definition over the real numbers, compute |4| exactly.","answer":{"kind":"short_text","value":"4","explanation":"4≥0, so absolute value keeps the input and |4|=4."},"skills":["piecewise definition","exact integer computation"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260928-absolute-value-exact-evaluation-0018","batch_id":"batch-20260928-absolute-value-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"173ad74988b6826e3896da72425d2b6d8d59fd49d5e8cd1a9ffdfacddbb98358","family_id":"qf-absolute-value-exact-evaluation","seed":20260946,"semantic_template":"qf-absolute-value-exact-evaluation/{\"domain\":\"reals\",\"operation\":\"exact_absolute_value\",\"x\":5}"},"fields":{"title":"Exact Absolute Value","stem":"Using the piecewise definition over the real numbers, compute |5| exactly.","answer":{"kind":"short_text","value":"5","explanation":"5≥0, so absolute value keeps the input and |5|=5."},"skills":["piecewise definition","exact integer computation"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260928-absolute-value-exact-evaluation-0019","batch_id":"batch-20260928-absolute-value-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"e765504adb409a77ba02cf96e202319beef1c94fda4f4dbefe00f75e6581f0f8","family_id":"qf-absolute-value-exact-evaluation","seed":20260947,"semantic_template":"qf-absolute-value-exact-evaluation/{\"domain\":\"reals\",\"operation\":\"exact_absolute_value\",\"x\":6}"},"fields":{"title":"Exact Absolute Value","stem":"Using the piecewise definition over the real numbers, compute |6| exactly.","answer":{"kind":"short_text","value":"6","explanation":"6≥0, so absolute value keeps the input and |6|=6."},"skills":["piecewise definition","exact integer computation"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260928-absolute-value-exact-evaluation-0020","batch_id":"batch-20260928-absolute-value-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"6851e66ed2e591a6ce079e508407d0a450ae669beab70147577a3aab82671358","family_id":"qf-absolute-value-exact-evaluation","seed":20260948,"semantic_template":"qf-absolute-value-exact-evaluation/{\"domain\":\"reals\",\"operation\":\"exact_absolute_value\",\"x\":7}"},"fields":{"title":"Exact Absolute Value","stem":"Using the piecewise definition over the real numbers, compute |7| exactly.","answer":{"kind":"short_text","value":"7","explanation":"7≥0, so absolute value keeps the input and |7|=7."},"skills":["piecewise definition","exact integer computation"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260928-absolute-value-exact-evaluation-0021","batch_id":"batch-20260928-absolute-value-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"2ffd6f912f4f66a89af7ad19ec229c52525d4056e49945cfa8b32ed736bf3db2","family_id":"qf-absolute-value-exact-evaluation","seed":20260949,"semantic_template":"qf-absolute-value-exact-evaluation/{\"domain\":\"reals\",\"operation\":\"exact_absolute_value\",\"x\":8}"},"fields":{"title":"Exact Absolute Value","stem":"Using the piecewise definition over the real numbers, compute |8| exactly.","answer":{"kind":"short_text","value":"8","explanation":"8≥0, so absolute value keeps the input and |8|=8."},"skills":["piecewise definition","exact integer computation"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260928-absolute-value-exact-evaluation-0022","batch_id":"batch-20260928-absolute-value-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"51fbf2df6e161adad3a0beaa58a9eb2147fc19f4c20114b68c95287ce760a46f","family_id":"qf-absolute-value-exact-evaluation","seed":20260950,"semantic_template":"qf-absolute-value-exact-evaluation/{\"domain\":\"reals\",\"operation\":\"exact_absolute_value\",\"x\":9}"},"fields":{"title":"Exact Absolute Value","stem":"Using the piecewise definition over the real numbers, compute |9| exactly.","answer":{"kind":"short_text","value":"9","explanation":"9≥0, so absolute value keeps the input and |9|=9."},"skills":["piecewise definition","exact integer computation"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260928-absolute-value-exact-evaluation-0023","batch_id":"batch-20260928-absolute-value-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"0f69314433f148290d3cdb0fddb7e318d9419f1b0b55b212cbc74b8723da4691","family_id":"qf-absolute-value-exact-evaluation","seed":20260951,"semantic_template":"qf-absolute-value-exact-evaluation/{\"domain\":\"reals\",\"operation\":\"exact_absolute_value\",\"x\":10}"},"fields":{"title":"Exact Absolute Value","stem":"Using the piecewise definition over the real numbers, compute |10| exactly.","answer":{"kind":"short_text","value":"10","explanation":"10≥0, so absolute value keeps the input and |10|=10."},"skills":["piecewise definition","exact integer computation"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260928-absolute-value-exact-evaluation-0024","batch_id":"batch-20260928-absolute-value-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"ba6ecff462eeff865885f113c67f42c460f324a8db701603147f799019ac88e7","family_id":"qf-absolute-value-exact-evaluation","seed":20260952,"semantic_template":"qf-absolute-value-exact-evaluation/{\"domain\":\"reals\",\"operation\":\"exact_absolute_value\",\"x\":11}"},"fields":{"title":"Exact Absolute Value","stem":"Using the piecewise definition over the real numbers, compute |11| exactly.","answer":{"kind":"short_text","value":"11","explanation":"11≥0, so absolute value keeps the input and |11|=11."},"skills":["piecewise definition","exact integer computation"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260928-absolute-value-exact-evaluation-0025","batch_id":"batch-20260928-absolute-value-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"00fa74673dbe4fa917c15ff9b9c68c8ea90c3558596be64922990d062df1551a","family_id":"qf-absolute-value-exact-evaluation","seed":20260953,"semantic_template":"qf-absolute-value-exact-evaluation/{\"domain\":\"reals\",\"operation\":\"exact_absolute_value\",\"x\":12}"},"fields":{"title":"Exact Absolute Value","stem":"Using the piecewise definition over the real numbers, compute |12| exactly.","answer":{"kind":"short_text","value":"12","explanation":"12≥0, so absolute value keeps the input and |12|=12."},"skills":["piecewise definition","exact integer computation"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260928-absolute-value-piecewise-branch-0001","batch_id":"batch-20260928-absolute-value-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"3560a0a386f4b88bbae922ec72c180674e886ff49492ee7e1a18e9463ca2ff47","family_id":"qf-absolute-value-piecewise-branch","seed":20261029,"semantic_template":"qf-absolute-value-piecewise-branch/{\"domain\":\"reals\",\"operation\":\"piecewise_branch\",\"x\":12}"},"fields":{"title":"Piecewise Branch of Absolute Value","stem":"For the real number x=12, which branch of the piecewise definition of |x| applies?","answer":{"kind":"short_text","value":"nonnegative branch x","explanation":"x=12≥0, so use the nonnegative branch x and obtain |x|=12."},"skills":["zero boundary","piecewise functions"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260928-absolute-value-piecewise-branch-0002","batch_id":"batch-20260928-absolute-value-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"5942d6919ccd014510e147b910ae9b65ab90a3a26ae00e8ba17b26892f615acf","family_id":"qf-absolute-value-piecewise-branch","seed":20261030,"semantic_template":"qf-absolute-value-piecewise-branch/{\"domain\":\"reals\",\"operation\":\"piecewise_branch\",\"x\":11}"},"fields":{"title":"Piecewise Branch of Absolute Value","stem":"For the real number x=11, which branch of the piecewise definition of |x| applies?","answer":{"kind":"short_text","value":"nonnegative branch x","explanation":"x=11≥0, so use the nonnegative branch x and obtain |x|=11."},"skills":["zero boundary","piecewise functions"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260928-absolute-value-piecewise-branch-0003","batch_id":"batch-20260928-absolute-value-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"53013aa0b6f45acdfcb1ddf15ce195959dddd307de75c9f3b369114257c3e762","family_id":"qf-absolute-value-piecewise-branch","seed":20261031,"semantic_template":"qf-absolute-value-piecewise-branch/{\"domain\":\"reals\",\"operation\":\"piecewise_branch\",\"x\":10}"},"fields":{"title":"Piecewise Branch of Absolute Value","stem":"For the real number x=10, which branch of the piecewise definition of |x| applies?","answer":{"kind":"short_text","value":"nonnegative branch x","explanation":"x=10≥0, so use the nonnegative branch x and obtain |x|=10."},"skills":["zero boundary","piecewise functions"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260928-absolute-value-piecewise-branch-0004","batch_id":"batch-20260928-absolute-value-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"80cd79cf80acf535428f7b2b85de74b9d6760e68b1abb0a0a87425687590e40c","family_id":"qf-absolute-value-piecewise-branch","seed":20261032,"semantic_template":"qf-absolute-value-piecewise-branch/{\"domain\":\"reals\",\"operation\":\"piecewise_branch\",\"x\":9}"},"fields":{"title":"Piecewise Branch of Absolute Value","stem":"For the real number x=9, which branch of the piecewise definition of |x| applies?","answer":{"kind":"short_text","value":"nonnegative branch x","explanation":"x=9≥0, so use the nonnegative branch x and obtain |x|=9."},"skills":["zero boundary","piecewise functions"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260928-absolute-value-piecewise-branch-0005","batch_id":"batch-20260928-absolute-value-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"9cf278a2b851109f8fd729444689e748f0ce75a97183c79b9f41d7294a68f4fc","family_id":"qf-absolute-value-piecewise-branch","seed":20261033,"semantic_template":"qf-absolute-value-piecewise-branch/{\"domain\":\"reals\",\"operation\":\"piecewise_branch\",\"x\":8}"},"fields":{"title":"Piecewise Branch of Absolute Value","stem":"For the real number x=8, which branch of the piecewise definition of |x| applies?","answer":{"kind":"short_text","value":"nonnegative branch x","explanation":"x=8≥0, so use the nonnegative branch x and obtain |x|=8."},"skills":["zero boundary","piecewise functions"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260928-absolute-value-piecewise-branch-0006","batch_id":"batch-20260928-absolute-value-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"9c22c59878e0044e5e7223685717f4978f3d3368c2285916297f5410ea868f98","family_id":"qf-absolute-value-piecewise-branch","seed":20261034,"semantic_template":"qf-absolute-value-piecewise-branch/{\"domain\":\"reals\",\"operation\":\"piecewise_branch\",\"x\":7}"},"fields":{"title":"Piecewise Branch of Absolute Value","stem":"For the real number x=7, which branch of the piecewise definition of |x| applies?","answer":{"kind":"short_text","value":"nonnegative branch x","explanation":"x=7≥0, so use the nonnegative branch x and obtain |x|=7."},"skills":["zero boundary","piecewise functions"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260928-absolute-value-piecewise-branch-0007","batch_id":"batch-20260928-absolute-value-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"9e59fc98de7ef30d7d6f3011730e7e1cb924d95059b7dae8d3510b45d0723df4","family_id":"qf-absolute-value-piecewise-branch","seed":20261035,"semantic_template":"qf-absolute-value-piecewise-branch/{\"domain\":\"reals\",\"operation\":\"piecewise_branch\",\"x\":6}"},"fields":{"title":"Piecewise Branch of Absolute Value","stem":"For the real number x=6, which branch of the piecewise definition of |x| applies?","answer":{"kind":"short_text","value":"nonnegative branch x","explanation":"x=6≥0, so use the nonnegative branch x and obtain |x|=6."},"skills":["zero boundary","piecewise functions"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260928-absolute-value-piecewise-branch-0008","batch_id":"batch-20260928-absolute-value-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"c6ae220c7324df1bd4a0784a5472fdf8908a25c48506051f941715fc07860b99","family_id":"qf-absolute-value-piecewise-branch","seed":20261036,"semantic_template":"qf-absolute-value-piecewise-branch/{\"domain\":\"reals\",\"operation\":\"piecewise_branch\",\"x\":5}"},"fields":{"title":"Piecewise Branch of Absolute Value","stem":"For the real number x=5, which branch of the piecewise definition of |x| applies?","answer":{"kind":"short_text","value":"nonnegative branch x","explanation":"x=5≥0, so use the nonnegative branch x and obtain |x|=5."},"skills":["zero boundary","piecewise functions"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260928-absolute-value-piecewise-branch-0009","batch_id":"batch-20260928-absolute-value-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"9d852b38441dbccba318e8325cb40d093b9bb5f6c89912aee3c5c7e21c3dc028","family_id":"qf-absolute-value-piecewise-branch","seed":20261037,"semantic_template":"qf-absolute-value-piecewise-branch/{\"domain\":\"reals\",\"operation\":\"piecewise_branch\",\"x\":4}"},"fields":{"title":"Piecewise Branch of Absolute Value","stem":"For the real number x=4, which branch of the piecewise definition of |x| applies?","answer":{"kind":"short_text","value":"nonnegative branch x","explanation":"x=4≥0, so use the nonnegative branch x and obtain |x|=4."},"skills":["zero boundary","piecewise functions"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260928-absolute-value-piecewise-branch-0010","batch_id":"batch-20260928-absolute-value-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"3993dc24a2c2c0672e998ae1a2a68ab3d5127c1188d1a5a5bc801d034fcf005a","family_id":"qf-absolute-value-piecewise-branch","seed":20261038,"semantic_template":"qf-absolute-value-piecewise-branch/{\"domain\":\"reals\",\"operation\":\"piecewise_branch\",\"x\":3}"},"fields":{"title":"Piecewise Branch of Absolute Value","stem":"For the real number x=3, which branch of the piecewise definition of |x| applies?","answer":{"kind":"short_text","value":"nonnegative branch x","explanation":"x=3≥0, so use the nonnegative branch x and obtain |x|=3."},"skills":["zero boundary","piecewise functions"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260928-absolute-value-piecewise-branch-0011","batch_id":"batch-20260928-absolute-value-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"077b852715bc109f476a4dd02b60b7a6cc4f70e901629936e9eec90d9b03ed5c","family_id":"qf-absolute-value-piecewise-branch","seed":20261039,"semantic_template":"qf-absolute-value-piecewise-branch/{\"domain\":\"reals\",\"operation\":\"piecewise_branch\",\"x\":2}"},"fields":{"title":"Piecewise Branch of Absolute Value","stem":"For the real number x=2, which branch of the piecewise definition of |x| applies?","answer":{"kind":"short_text","value":"nonnegative branch x","explanation":"x=2≥0, so use the nonnegative branch x and obtain |x|=2."},"skills":["zero boundary","piecewise functions"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260928-absolute-value-piecewise-branch-0012","batch_id":"batch-20260928-absolute-value-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"c1b5481bb5e975d248e72d0f7dfe0574163ed8b9d64ddff7a9c492b46557941c","family_id":"qf-absolute-value-piecewise-branch","seed":20261040,"semantic_template":"qf-absolute-value-piecewise-branch/{\"domain\":\"reals\",\"operation\":\"piecewise_branch\",\"x\":1}"},"fields":{"title":"Piecewise Branch of Absolute Value","stem":"For the real number x=1, which branch of the piecewise definition of |x| applies?","answer":{"kind":"short_text","value":"nonnegative branch x","explanation":"x=1≥0, so use the nonnegative branch x and obtain |x|=1."},"skills":["zero boundary","piecewise functions"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260928-absolute-value-piecewise-branch-0013","batch_id":"batch-20260928-absolute-value-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"19225e999674d464b5264528d47aba2d8899dcd1665788192f64694cae90a935","family_id":"qf-absolute-value-piecewise-branch","seed":20261041,"semantic_template":"qf-absolute-value-piecewise-branch/{\"domain\":\"reals\",\"operation\":\"piecewise_branch\",\"x\":0}"},"fields":{"title":"Piecewise Branch of Absolute Value","stem":"For the real number x=0, which branch of the piecewise definition of |x| applies?","answer":{"kind":"short_text","value":"nonnegative branch x","explanation":"x=0≥0, so use the nonnegative branch x and obtain |x|=0."},"skills":["zero boundary","piecewise functions"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260928-absolute-value-piecewise-branch-0014","batch_id":"batch-20260928-absolute-value-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"88c46e689740ba253b0e341f1936416b51f5892946fbc46d85cd3658722117a8","family_id":"qf-absolute-value-piecewise-branch","seed":20261042,"semantic_template":"qf-absolute-value-piecewise-branch/{\"domain\":\"reals\",\"operation\":\"piecewise_branch\",\"x\":-1}"},"fields":{"title":"Piecewise Branch of Absolute Value","stem":"For the real number x=-1, which branch of the piecewise definition of |x| applies?","answer":{"kind":"short_text","value":"negative branch -x","explanation":"x=-1<0, so use the negative branch -x and obtain |x|=1."},"skills":["zero boundary","piecewise functions"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260928-absolute-value-piecewise-branch-0015","batch_id":"batch-20260928-absolute-value-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"98740d388ba7ec0b9b21dc2d866167b579d581c6c256190b3f40d4071d5698bf","family_id":"qf-absolute-value-piecewise-branch","seed":20261043,"semantic_template":"qf-absolute-value-piecewise-branch/{\"domain\":\"reals\",\"operation\":\"piecewise_branch\",\"x\":-2}"},"fields":{"title":"Piecewise Branch of Absolute Value","stem":"For the real number x=-2, which branch of the piecewise definition of |x| applies?","answer":{"kind":"short_text","value":"negative branch -x","explanation":"x=-2<0, so use the negative branch -x and obtain |x|=2."},"skills":["zero boundary","piecewise functions"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260928-absolute-value-piecewise-branch-0016","batch_id":"batch-20260928-absolute-value-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"88e763479e4eb745536a55c2f2ccdf9f755335766006264e2fcf92494c14c20a","family_id":"qf-absolute-value-piecewise-branch","seed":20261044,"semantic_template":"qf-absolute-value-piecewise-branch/{\"domain\":\"reals\",\"operation\":\"piecewise_branch\",\"x\":-3}"},"fields":{"title":"Piecewise Branch of Absolute Value","stem":"For the real number x=-3, which branch of the piecewise definition of |x| applies?","answer":{"kind":"short_text","value":"negative branch -x","explanation":"x=-3<0, so use the negative branch -x and obtain |x|=3."},"skills":["zero boundary","piecewise functions"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260928-absolute-value-piecewise-branch-0017","batch_id":"batch-20260928-absolute-value-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"5f2db66a5a82f8291c5f6b5610079be0231413911aa481c39e21f8917de26235","family_id":"qf-absolute-value-piecewise-branch","seed":20261045,"semantic_template":"qf-absolute-value-piecewise-branch/{\"domain\":\"reals\",\"operation\":\"piecewise_branch\",\"x\":-4}"},"fields":{"title":"Piecewise Branch of Absolute Value","stem":"For the real number x=-4, which branch of the piecewise definition of |x| applies?","answer":{"kind":"short_text","value":"negative branch -x","explanation":"x=-4<0, so use the negative branch -x and obtain |x|=4."},"skills":["zero boundary","piecewise functions"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260928-absolute-value-piecewise-branch-0018","batch_id":"batch-20260928-absolute-value-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"2baaeb02ad1a99a89a79ce36e0926474f84620440173c3f4ca5189398df3a660","family_id":"qf-absolute-value-piecewise-branch","seed":20261046,"semantic_template":"qf-absolute-value-piecewise-branch/{\"domain\":\"reals\",\"operation\":\"piecewise_branch\",\"x\":-5}"},"fields":{"title":"Piecewise Branch of Absolute Value","stem":"For the real number x=-5, which branch of the piecewise definition of |x| applies?","answer":{"kind":"short_text","value":"negative branch -x","explanation":"x=-5<0, so use the negative branch -x and obtain |x|=5."},"skills":["zero boundary","piecewise functions"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260928-absolute-value-piecewise-branch-0019","batch_id":"batch-20260928-absolute-value-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"3b79d0df8b542deb26564f6897bdd3a66f7c0078fda45f48b395e50e5030e6dc","family_id":"qf-absolute-value-piecewise-branch","seed":20261047,"semantic_template":"qf-absolute-value-piecewise-branch/{\"domain\":\"reals\",\"operation\":\"piecewise_branch\",\"x\":-6}"},"fields":{"title":"Piecewise Branch of Absolute Value","stem":"For the real number x=-6, which branch of the piecewise definition of |x| applies?","answer":{"kind":"short_text","value":"negative branch -x","explanation":"x=-6<0, so use the negative branch -x and obtain |x|=6."},"skills":["zero boundary","piecewise functions"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260928-absolute-value-piecewise-branch-0020","batch_id":"batch-20260928-absolute-value-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"d16d23119cc7366156ef5c7118ce4f4052a91273453ba16bdaf2adbd15cc90a4","family_id":"qf-absolute-value-piecewise-branch","seed":20261048,"semantic_template":"qf-absolute-value-piecewise-branch/{\"domain\":\"reals\",\"operation\":\"piecewise_branch\",\"x\":-7}"},"fields":{"title":"Piecewise Branch of Absolute Value","stem":"For the real number x=-7, which branch of the piecewise definition of |x| applies?","answer":{"kind":"short_text","value":"negative branch -x","explanation":"x=-7<0, so use the negative branch -x and obtain |x|=7."},"skills":["zero boundary","piecewise functions"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260928-absolute-value-piecewise-branch-0021","batch_id":"batch-20260928-absolute-value-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"fc682b4e8efccb122a9ef5d3acf4e2b4329adc6d9fbeec9fa1611ccddd507f5c","family_id":"qf-absolute-value-piecewise-branch","seed":20261049,"semantic_template":"qf-absolute-value-piecewise-branch/{\"domain\":\"reals\",\"operation\":\"piecewise_branch\",\"x\":-8}"},"fields":{"title":"Piecewise Branch of Absolute Value","stem":"For the real number x=-8, which branch of the piecewise definition of |x| applies?","answer":{"kind":"short_text","value":"negative branch -x","explanation":"x=-8<0, so use the negative branch -x and obtain |x|=8."},"skills":["zero boundary","piecewise functions"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260928-absolute-value-piecewise-branch-0022","batch_id":"batch-20260928-absolute-value-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"b9aaaf46d2610b62d6e82844e0e9be0b1abe78f167222121062707bb535f6081","family_id":"qf-absolute-value-piecewise-branch","seed":20261050,"semantic_template":"qf-absolute-value-piecewise-branch/{\"domain\":\"reals\",\"operation\":\"piecewise_branch\",\"x\":-9}"},"fields":{"title":"Piecewise Branch of Absolute Value","stem":"For the real number x=-9, which branch of the piecewise definition of |x| applies?","answer":{"kind":"short_text","value":"negative branch -x","explanation":"x=-9<0, so use the negative branch -x and obtain |x|=9."},"skills":["zero boundary","piecewise functions"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260928-absolute-value-piecewise-branch-0023","batch_id":"batch-20260928-absolute-value-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"b891fdff91b9556c0e3964c2d9b73b9ccc5da52fd0e770aaaf9022020732d102","family_id":"qf-absolute-value-piecewise-branch","seed":20261051,"semantic_template":"qf-absolute-value-piecewise-branch/{\"domain\":\"reals\",\"operation\":\"piecewise_branch\",\"x\":-10}"},"fields":{"title":"Piecewise Branch of Absolute Value","stem":"For the real number x=-10, which branch of the piecewise definition of |x| applies?","answer":{"kind":"short_text","value":"negative branch -x","explanation":"x=-10<0, so use the negative branch -x and obtain |x|=10."},"skills":["zero boundary","piecewise functions"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260928-absolute-value-piecewise-branch-0024","batch_id":"batch-20260928-absolute-value-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"7b6d20ddee3af81f9e28c22c847756acec0f256c08f5ecd95f5de1998f11641c","family_id":"qf-absolute-value-piecewise-branch","seed":20261052,"semantic_template":"qf-absolute-value-piecewise-branch/{\"domain\":\"reals\",\"operation\":\"piecewise_branch\",\"x\":-11}"},"fields":{"title":"Piecewise Branch of Absolute Value","stem":"For the real number x=-11, which branch of the piecewise definition of |x| applies?","answer":{"kind":"short_text","value":"negative branch -x","explanation":"x=-11<0, so use the negative branch -x and obtain |x|=11."},"skills":["zero boundary","piecewise functions"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260928-absolute-value-piecewise-branch-0025","batch_id":"batch-20260928-absolute-value-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"3f8c4d15f207db16d0ceaa6f60d36512cb16facb00b5eac3a3f4f20e6597c48d","family_id":"qf-absolute-value-piecewise-branch","seed":20261053,"semantic_template":"qf-absolute-value-piecewise-branch/{\"domain\":\"reals\",\"operation\":\"piecewise_branch\",\"x\":-12}"},"fields":{"title":"Piecewise Branch of Absolute Value","stem":"For the real number x=-12, which branch of the piecewise definition of |x| applies?","answer":{"kind":"short_text","value":"negative branch -x","explanation":"x=-12<0, so use the negative branch -x and obtain |x|=12."},"skills":["zero boundary","piecewise functions"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260928-absolute-value-distance-0001","batch_id":"batch-20260928-absolute-value-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"424dd022232d0b8011d99f2332b3b40c22d0e965eb53a3941e883b003d2b1152","family_id":"qf-absolute-value-distance","seed":20261129,"semantic_template":"qf-absolute-value-distance/{\"a\":-12,\"b\":-15,\"domain\":\"reals\",\"operation\":\"number_line_distance\"}"},"fields":{"title":"Distance on the Real Number Line","stem":"On the real number line, a=-12 and b=-15. Compute the distance |a-b| exactly.","answer":{"kind":"short_text","value":"3","explanation":"|a-b|=|-12-(-15)|=|3|=3; exchanging the endpoints gives the same distance."},"skills":["number-line distance","absolute value of a difference"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260928-absolute-value-distance-0002","batch_id":"batch-20260928-absolute-value-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"1a6f444d4db59f41b2dc8895eea5266dc0e070eafea9d983257409b26594f03c","family_id":"qf-absolute-value-distance","seed":20261130,"semantic_template":"qf-absolute-value-distance/{\"a\":-11,\"b\":-8,\"domain\":\"reals\",\"operation\":\"number_line_distance\"}"},"fields":{"title":"Distance on the Real Number Line","stem":"On the real number line, a=-11 and b=-8. Compute the distance |a-b| exactly.","answer":{"kind":"short_text","value":"3","explanation":"|a-b|=|-11-(-8)|=|-3|=3; exchanging the endpoints gives the same distance."},"skills":["number-line distance","absolute value of a difference"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260928-absolute-value-distance-0003","batch_id":"batch-20260928-absolute-value-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"1749f82e664fc54a4e2a7d3c9bccc001bf28020cf06db760adcd3de71f061c14","family_id":"qf-absolute-value-distance","seed":20261131,"semantic_template":"qf-absolute-value-distance/{\"a\":-10,\"b\":-1,\"domain\":\"reals\",\"operation\":\"number_line_distance\"}"},"fields":{"title":"Distance on the Real Number Line","stem":"On the real number line, a=-10 and b=-1. Compute the distance |a-b| exactly.","answer":{"kind":"short_text","value":"9","explanation":"|a-b|=|-10-(-1)|=|-9|=9; exchanging the endpoints gives the same distance."},"skills":["number-line distance","absolute value of a difference"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260928-absolute-value-distance-0004","batch_id":"batch-20260928-absolute-value-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"72764b0aa18633eac45972266e002eb2c67faa5a275e20522c4e6d496acae300","family_id":"qf-absolute-value-distance","seed":20261132,"semantic_template":"qf-absolute-value-distance/{\"a\":-9,\"b\":6,\"domain\":\"reals\",\"operation\":\"number_line_distance\"}"},"fields":{"title":"Distance on the Real Number Line","stem":"On the real number line, a=-9 and b=6. Compute the distance |a-b| exactly.","answer":{"kind":"short_text","value":"15","explanation":"|a-b|=|-9-(6)|=|-15|=15; exchanging the endpoints gives the same distance."},"skills":["number-line distance","absolute value of a difference"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260928-absolute-value-distance-0005","batch_id":"batch-20260928-absolute-value-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"65d4e949916de8b86d79c85ae28a2464d84cdc0ec5e7e1d968928ee3c1ee0b41","family_id":"qf-absolute-value-distance","seed":20261133,"semantic_template":"qf-absolute-value-distance/{\"a\":-8,\"b\":13,\"domain\":\"reals\",\"operation\":\"number_line_distance\"}"},"fields":{"title":"Distance on the Real Number Line","stem":"On the real number line, a=-8 and b=13. Compute the distance |a-b| exactly.","answer":{"kind":"short_text","value":"21","explanation":"|a-b|=|-8-(13)|=|-21|=21; exchanging the endpoints gives the same distance."},"skills":["number-line distance","absolute value of a difference"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260928-absolute-value-distance-0006","batch_id":"batch-20260928-absolute-value-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"d8f2b78e41e422049b304af35f8eba9a85b9e79626b0b99eb20d76387cf47dbb","family_id":"qf-absolute-value-distance","seed":20261134,"semantic_template":"qf-absolute-value-distance/{\"a\":-7,\"b\":-11,\"domain\":\"reals\",\"operation\":\"number_line_distance\"}"},"fields":{"title":"Distance on the Real Number Line","stem":"On the real number line, a=-7 and b=-11. Compute the distance |a-b| exactly.","answer":{"kind":"short_text","value":"4","explanation":"|a-b|=|-7-(-11)|=|4|=4; exchanging the endpoints gives the same distance."},"skills":["number-line distance","absolute value of a difference"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260928-absolute-value-distance-0007","batch_id":"batch-20260928-absolute-value-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"f55409685cffa739ff84125d75733791ef68deeeace0f47a2196bb86dbe71848","family_id":"qf-absolute-value-distance","seed":20261135,"semantic_template":"qf-absolute-value-distance/{\"a\":-6,\"b\":-4,\"domain\":\"reals\",\"operation\":\"number_line_distance\"}"},"fields":{"title":"Distance on the Real Number Line","stem":"On the real number line, a=-6 and b=-4. Compute the distance |a-b| exactly.","answer":{"kind":"short_text","value":"2","explanation":"|a-b|=|-6-(-4)|=|-2|=2; exchanging the endpoints gives the same distance."},"skills":["number-line distance","absolute value of a difference"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260928-absolute-value-distance-0008","batch_id":"batch-20260928-absolute-value-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"6253d007d608383869c8150beeb08a24d9f0f17bd7c2dfe53bd55f729ff5a28e","family_id":"qf-absolute-value-distance","seed":20261136,"semantic_template":"qf-absolute-value-distance/{\"a\":-5,\"b\":3,\"domain\":\"reals\",\"operation\":\"number_line_distance\"}"},"fields":{"title":"Distance on the Real Number Line","stem":"On the real number line, a=-5 and b=3. Compute the distance |a-b| exactly.","answer":{"kind":"short_text","value":"8","explanation":"|a-b|=|-5-(3)|=|-8|=8; exchanging the endpoints gives the same distance."},"skills":["number-line distance","absolute value of a difference"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260928-absolute-value-distance-0009","batch_id":"batch-20260928-absolute-value-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"8cc10e4530a8de617305832195aac1876c63e1dce2483e21060d555903d1c532","family_id":"qf-absolute-value-distance","seed":20261137,"semantic_template":"qf-absolute-value-distance/{\"a\":-4,\"b\":10,\"domain\":\"reals\",\"operation\":\"number_line_distance\"}"},"fields":{"title":"Distance on the Real Number Line","stem":"On the real number line, a=-4 and b=10. Compute the distance |a-b| exactly.","answer":{"kind":"short_text","value":"14","explanation":"|a-b|=|-4-(10)|=|-14|=14; exchanging the endpoints gives the same distance."},"skills":["number-line distance","absolute value of a difference"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260928-absolute-value-distance-0010","batch_id":"batch-20260928-absolute-value-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"7221f53df383f4ca4ff175bbf84e4c419bde1f20d660604c4abf0a578fd010c8","family_id":"qf-absolute-value-distance","seed":20261138,"semantic_template":"qf-absolute-value-distance/{\"a\":-3,\"b\":-14,\"domain\":\"reals\",\"operation\":\"number_line_distance\"}"},"fields":{"title":"Distance on the Real Number Line","stem":"On the real number line, a=-3 and b=-14. Compute the distance |a-b| exactly.","answer":{"kind":"short_text","value":"11","explanation":"|a-b|=|-3-(-14)|=|11|=11; exchanging the endpoints gives the same distance."},"skills":["number-line distance","absolute value of a difference"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260928-absolute-value-distance-0011","batch_id":"batch-20260928-absolute-value-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"29717b59a2f3559c4d3c716c13765ba8b34757ae54972e1feacb32a6c3febcfc","family_id":"qf-absolute-value-distance","seed":20261139,"semantic_template":"qf-absolute-value-distance/{\"a\":-2,\"b\":-7,\"domain\":\"reals\",\"operation\":\"number_line_distance\"}"},"fields":{"title":"Distance on the Real Number Line","stem":"On the real number line, a=-2 and b=-7. Compute the distance |a-b| exactly.","answer":{"kind":"short_text","value":"5","explanation":"|a-b|=|-2-(-7)|=|5|=5; exchanging the endpoints gives the same distance."},"skills":["number-line distance","absolute value of a difference"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260928-absolute-value-distance-0012","batch_id":"batch-20260928-absolute-value-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"edc47f57dc6e6280dea47874fc59aab77ac4bdff8a4219ab851145e5e089017b","family_id":"qf-absolute-value-distance","seed":20261140,"semantic_template":"qf-absolute-value-distance/{\"a\":-1,\"b\":0,\"domain\":\"reals\",\"operation\":\"number_line_distance\"}"},"fields":{"title":"Distance on the Real Number Line","stem":"On the real number line, a=-1 and b=0. Compute the distance |a-b| exactly.","answer":{"kind":"short_text","value":"1","explanation":"|a-b|=|-1-(0)|=|-1|=1; exchanging the endpoints gives the same distance."},"skills":["number-line distance","absolute value of a difference"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260928-absolute-value-distance-0013","batch_id":"batch-20260928-absolute-value-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"665d51ac2ec92740daa403ab5c445214759a0f2a055f825041baf87f36991e43","family_id":"qf-absolute-value-distance","seed":20261141,"semantic_template":"qf-absolute-value-distance/{\"a\":0,\"b\":7,\"domain\":\"reals\",\"operation\":\"number_line_distance\"}"},"fields":{"title":"Distance on the Real Number Line","stem":"On the real number line, a=0 and b=7. Compute the distance |a-b| exactly.","answer":{"kind":"short_text","value":"7","explanation":"|a-b|=|0-(7)|=|-7|=7; exchanging the endpoints gives the same distance."},"skills":["number-line distance","absolute value of a difference"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260928-absolute-value-distance-0014","batch_id":"batch-20260928-absolute-value-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"c9a32fb9bbc4bc94f3ee9e8b67c0917b8dbfb11a4091a3148e9985e7214729ce","family_id":"qf-absolute-value-distance","seed":20261142,"semantic_template":"qf-absolute-value-distance/{\"a\":1,\"b\":14,\"domain\":\"reals\",\"operation\":\"number_line_distance\"}"},"fields":{"title":"Distance on the Real Number Line","stem":"On the real number line, a=1 and b=14. Compute the distance |a-b| exactly.","answer":{"kind":"short_text","value":"13","explanation":"|a-b|=|1-(14)|=|-13|=13; exchanging the endpoints gives the same distance."},"skills":["number-line distance","absolute value of a difference"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260928-absolute-value-distance-0015","batch_id":"batch-20260928-absolute-value-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"f5049c8b2395b40f59127ed6327587bdfc53a4bf597c8513ec9a0b901a657b37","family_id":"qf-absolute-value-distance","seed":20261143,"semantic_template":"qf-absolute-value-distance/{\"a\":2,\"b\":-10,\"domain\":\"reals\",\"operation\":\"number_line_distance\"}"},"fields":{"title":"Distance on the Real Number Line","stem":"On the real number line, a=2 and b=-10. Compute the distance |a-b| exactly.","answer":{"kind":"short_text","value":"12","explanation":"|a-b|=|2-(-10)|=|12|=12; exchanging the endpoints gives the same distance."},"skills":["number-line distance","absolute value of a difference"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260928-absolute-value-distance-0016","batch_id":"batch-20260928-absolute-value-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"3fb113a71b313a6d95bbd858547bf76a3e4f5b97ecd4d12fa0a5551e65b3d05f","family_id":"qf-absolute-value-distance","seed":20261144,"semantic_template":"qf-absolute-value-distance/{\"a\":3,\"b\":-3,\"domain\":\"reals\",\"operation\":\"number_line_distance\"}"},"fields":{"title":"Distance on the Real Number Line","stem":"On the real number line, a=3 and b=-3. Compute the distance |a-b| exactly.","answer":{"kind":"short_text","value":"6","explanation":"|a-b|=|3-(-3)|=|6|=6; exchanging the endpoints gives the same distance."},"skills":["number-line distance","absolute value of a difference"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260928-absolute-value-distance-0017","batch_id":"batch-20260928-absolute-value-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"0dbcb350448c703a78b6399bb4aa3819f16a74b5615300d23c5508579a9ac7d8","family_id":"qf-absolute-value-distance","seed":20261145,"semantic_template":"qf-absolute-value-distance/{\"a\":4,\"b\":4,\"domain\":\"reals\",\"operation\":\"number_line_distance\"}"},"fields":{"title":"Distance on the Real Number Line","stem":"On the real number line, a=4 and b=4. Compute the distance |a-b| exactly.","answer":{"kind":"short_text","value":"0","explanation":"|a-b|=|4-(4)|=|0|=0; exchanging the endpoints gives the same distance."},"skills":["number-line distance","absolute value of a difference"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260928-absolute-value-distance-0018","batch_id":"batch-20260928-absolute-value-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"603efbb3b661d758d07f0990ca483c224d155e75fdfb2397ca8b5cceb982c7d1","family_id":"qf-absolute-value-distance","seed":20261146,"semantic_template":"qf-absolute-value-distance/{\"a\":5,\"b\":11,\"domain\":\"reals\",\"operation\":\"number_line_distance\"}"},"fields":{"title":"Distance on the Real Number Line","stem":"On the real number line, a=5 and b=11. Compute the distance |a-b| exactly.","answer":{"kind":"short_text","value":"6","explanation":"|a-b|=|5-(11)|=|-6|=6; exchanging the endpoints gives the same distance."},"skills":["number-line distance","absolute value of a difference"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260928-absolute-value-distance-0019","batch_id":"batch-20260928-absolute-value-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"26c53c854bb36e2662cdec933bcbedc9e91972a86906b2f66c996d2a17263a2f","family_id":"qf-absolute-value-distance","seed":20261147,"semantic_template":"qf-absolute-value-distance/{\"a\":6,\"b\":-13,\"domain\":\"reals\",\"operation\":\"number_line_distance\"}"},"fields":{"title":"Distance on the Real Number Line","stem":"On the real number line, a=6 and b=-13. Compute the distance |a-b| exactly.","answer":{"kind":"short_text","value":"19","explanation":"|a-b|=|6-(-13)|=|19|=19; exchanging the endpoints gives the same distance."},"skills":["number-line distance","absolute value of a difference"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260928-absolute-value-distance-0020","batch_id":"batch-20260928-absolute-value-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"f2d8cb3c97ebe7b68ffc5438f18271a3ed8aa64fe0fe60823a4db4e45f68f5f2","family_id":"qf-absolute-value-distance","seed":20261148,"semantic_template":"qf-absolute-value-distance/{\"a\":7,\"b\":-6,\"domain\":\"reals\",\"operation\":\"number_line_distance\"}"},"fields":{"title":"Distance on the Real Number Line","stem":"On the real number line, a=7 and b=-6. Compute the distance |a-b| exactly.","answer":{"kind":"short_text","value":"13","explanation":"|a-b|=|7-(-6)|=|13|=13; exchanging the endpoints gives the same distance."},"skills":["number-line distance","absolute value of a difference"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260928-absolute-value-distance-0021","batch_id":"batch-20260928-absolute-value-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"dee1109aafca7dd500085dd79b44e2cc82101daaee68def3d01ae57607436c30","family_id":"qf-absolute-value-distance","seed":20261149,"semantic_template":"qf-absolute-value-distance/{\"a\":8,\"b\":1,\"domain\":\"reals\",\"operation\":\"number_line_distance\"}"},"fields":{"title":"Distance on the Real Number Line","stem":"On the real number line, a=8 and b=1. Compute the distance |a-b| exactly.","answer":{"kind":"short_text","value":"7","explanation":"|a-b|=|8-(1)|=|7|=7; exchanging the endpoints gives the same distance."},"skills":["number-line distance","absolute value of a difference"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260928-absolute-value-distance-0022","batch_id":"batch-20260928-absolute-value-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"e875bf4e4b2be68c519abff80da72d7ee0b06ce346075cfa2ad1676c044465bc","family_id":"qf-absolute-value-distance","seed":20261150,"semantic_template":"qf-absolute-value-distance/{\"a\":9,\"b\":8,\"domain\":\"reals\",\"operation\":\"number_line_distance\"}"},"fields":{"title":"Distance on the Real Number Line","stem":"On the real number line, a=9 and b=8. Compute the distance |a-b| exactly.","answer":{"kind":"short_text","value":"1","explanation":"|a-b|=|9-(8)|=|1|=1; exchanging the endpoints gives the same distance."},"skills":["number-line distance","absolute value of a difference"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260928-absolute-value-distance-0023","batch_id":"batch-20260928-absolute-value-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"e0035cb11f38f9d932621f282d5125a40f6ea11b3e09e5570c519980e8c079cd","family_id":"qf-absolute-value-distance","seed":20261151,"semantic_template":"qf-absolute-value-distance/{\"a\":10,\"b\":15,\"domain\":\"reals\",\"operation\":\"number_line_distance\"}"},"fields":{"title":"Distance on the Real Number Line","stem":"On the real number line, a=10 and b=15. Compute the distance |a-b| exactly.","answer":{"kind":"short_text","value":"5","explanation":"|a-b|=|10-(15)|=|-5|=5; exchanging the endpoints gives the same distance."},"skills":["number-line distance","absolute value of a difference"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260928-absolute-value-distance-0024","batch_id":"batch-20260928-absolute-value-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"b4ef10ec742eb6dc9f7df85fce4c8b60333edf02108450c0223ee6a650281d12","family_id":"qf-absolute-value-distance","seed":20261152,"semantic_template":"qf-absolute-value-distance/{\"a\":11,\"b\":-9,\"domain\":\"reals\",\"operation\":\"number_line_distance\"}"},"fields":{"title":"Distance on the Real Number Line","stem":"On the real number line, a=11 and b=-9. Compute the distance |a-b| exactly.","answer":{"kind":"short_text","value":"20","explanation":"|a-b|=|11-(-9)|=|20|=20; exchanging the endpoints gives the same distance."},"skills":["number-line distance","absolute value of a difference"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260928-absolute-value-distance-0025","batch_id":"batch-20260928-absolute-value-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"9b5ddf2c1de8d8d9b27b856365c17a9e39907aa96624334523d1f6dd9f8ba0d6","family_id":"qf-absolute-value-distance","seed":20261153,"semantic_template":"qf-absolute-value-distance/{\"a\":12,\"b\":-2,\"domain\":\"reals\",\"operation\":\"number_line_distance\"}"},"fields":{"title":"Distance on the Real Number Line","stem":"On the real number line, a=12 and b=-2. Compute the distance |a-b| exactly.","answer":{"kind":"short_text","value":"14","explanation":"|a-b|=|12-(-2)|=|14|=14; exchanging the endpoints gives the same distance."},"skills":["number-line distance","absolute value of a difference"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260928-absolute-value-equation-class-0001","batch_id":"batch-20260928-absolute-value-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"9332e3b39d3aef528befff161ad0e31cab8374a04c9a07853be3f398251b9be2","family_id":"qf-absolute-value-equation-class","seed":20261229,"semantic_template":"qf-absolute-value-equation-class/{\"c\":-4,\"domain\":\"reals\",\"operation\":\"absolute_equation_solution_class\"}"},"fields":{"title":"Solution Classification of an Absolute-Value Equation","stem":"Over the real numbers, classify the solution set of |x|=-4.","answer":{"kind":"short_text","value":"no solution","explanation":"Absolute value is nonnegative and cannot equal -4, so there is no solution."},"skills":["absolute-value equations","solution-set classification"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260928-absolute-value-equation-class-0002","batch_id":"batch-20260928-absolute-value-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"d0f7b362915e8632cbc3da86b0d1c0578d2381183f69d5a966aed449b159c62c","family_id":"qf-absolute-value-equation-class","seed":20261230,"semantic_template":"qf-absolute-value-equation-class/{\"c\":-3,\"domain\":\"reals\",\"operation\":\"absolute_equation_solution_class\"}"},"fields":{"title":"Solution Classification of an Absolute-Value Equation","stem":"Over the real numbers, classify the solution set of |x|=-3.","answer":{"kind":"short_text","value":"no solution","explanation":"Absolute value is nonnegative and cannot equal -3, so there is no solution."},"skills":["absolute-value equations","solution-set classification"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260928-absolute-value-equation-class-0003","batch_id":"batch-20260928-absolute-value-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"3eed105fc0e647db81cb491549fc65ca78c9b8dec691037379d523566114e667","family_id":"qf-absolute-value-equation-class","seed":20261231,"semantic_template":"qf-absolute-value-equation-class/{\"c\":-2,\"domain\":\"reals\",\"operation\":\"absolute_equation_solution_class\"}"},"fields":{"title":"Solution Classification of an Absolute-Value Equation","stem":"Over the real numbers, classify the solution set of |x|=-2.","answer":{"kind":"short_text","value":"no solution","explanation":"Absolute value is nonnegative and cannot equal -2, so there is no solution."},"skills":["absolute-value equations","solution-set classification"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260928-absolute-value-equation-class-0004","batch_id":"batch-20260928-absolute-value-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"03d4ac85666e6fdfe7358a4382b03afcf0c4c037267c11e5ba5ac7fff4a3e188","family_id":"qf-absolute-value-equation-class","seed":20261232,"semantic_template":"qf-absolute-value-equation-class/{\"c\":-1,\"domain\":\"reals\",\"operation\":\"absolute_equation_solution_class\"}"},"fields":{"title":"Solution Classification of an Absolute-Value Equation","stem":"Over the real numbers, classify the solution set of |x|=-1.","answer":{"kind":"short_text","value":"no solution","explanation":"Absolute value is nonnegative and cannot equal -1, so there is no solution."},"skills":["absolute-value equations","solution-set classification"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260928-absolute-value-equation-class-0005","batch_id":"batch-20260928-absolute-value-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"c321b86eb534c6542f9805fcc72888ec687008cf2c2438b659f6ea2e11d88736","family_id":"qf-absolute-value-equation-class","seed":20261233,"semantic_template":"qf-absolute-value-equation-class/{\"c\":0,\"domain\":\"reals\",\"operation\":\"absolute_equation_solution_class\"}"},"fields":{"title":"Solution Classification of an Absolute-Value Equation","stem":"Over the real numbers, classify the solution set of |x|=0.","answer":{"kind":"short_text","value":"unique solution x=0","explanation":"|x|=0 holds exactly at x=0."},"skills":["absolute-value equations","solution-set classification"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260928-absolute-value-equation-class-0006","batch_id":"batch-20260928-absolute-value-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"b02d87e91041a1279f877195c5499c84d441cbd4de8322e19ac91d2b5b11b01d","family_id":"qf-absolute-value-equation-class","seed":20261234,"semantic_template":"qf-absolute-value-equation-class/{\"c\":1,\"domain\":\"reals\",\"operation\":\"absolute_equation_solution_class\"}"},"fields":{"title":"Solution Classification of an Absolute-Value Equation","stem":"Over the real numbers, classify the solution set of |x|=1.","answer":{"kind":"short_text","value":"two solutions x=-1, 1","explanation":"The real numbers at distance 1 from 0 are x=-1 and x=1."},"skills":["absolute-value equations","solution-set classification"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260928-absolute-value-equation-class-0007","batch_id":"batch-20260928-absolute-value-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"bf71ff504fab640814d4d48cccf51c9a93685b8e0c04738c4bf9f1c8b7cf7ee4","family_id":"qf-absolute-value-equation-class","seed":20261235,"semantic_template":"qf-absolute-value-equation-class/{\"c\":2,\"domain\":\"reals\",\"operation\":\"absolute_equation_solution_class\"}"},"fields":{"title":"Solution Classification of an Absolute-Value Equation","stem":"Over the real numbers, classify the solution set of |x|=2.","answer":{"kind":"short_text","value":"two solutions x=-2, 2","explanation":"The real numbers at distance 2 from 0 are x=-2 and x=2."},"skills":["absolute-value equations","solution-set classification"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260928-absolute-value-equation-class-0008","batch_id":"batch-20260928-absolute-value-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"5533ffaa60159f6b01234753a7436e2cf75314d9d37c46d391bf1cd371322165","family_id":"qf-absolute-value-equation-class","seed":20261236,"semantic_template":"qf-absolute-value-equation-class/{\"c\":3,\"domain\":\"reals\",\"operation\":\"absolute_equation_solution_class\"}"},"fields":{"title":"Solution Classification of an Absolute-Value Equation","stem":"Over the real numbers, classify the solution set of |x|=3.","answer":{"kind":"short_text","value":"two solutions x=-3, 3","explanation":"The real numbers at distance 3 from 0 are x=-3 and x=3."},"skills":["absolute-value equations","solution-set classification"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260928-absolute-value-equation-class-0009","batch_id":"batch-20260928-absolute-value-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"eea8fe9002c526741f26f382ece9ca8619f0b1ce44f9b5024b00ca575756e982","family_id":"qf-absolute-value-equation-class","seed":20261237,"semantic_template":"qf-absolute-value-equation-class/{\"c\":4,\"domain\":\"reals\",\"operation\":\"absolute_equation_solution_class\"}"},"fields":{"title":"Solution Classification of an Absolute-Value Equation","stem":"Over the real numbers, classify the solution set of |x|=4.","answer":{"kind":"short_text","value":"two solutions x=-4, 4","explanation":"The real numbers at distance 4 from 0 are x=-4 and x=4."},"skills":["absolute-value equations","solution-set classification"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260928-absolute-value-equation-class-0010","batch_id":"batch-20260928-absolute-value-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"31093ae7d26916b332fd399ef9c380b56ce980e3502a76dc04c83ba01fdddbb9","family_id":"qf-absolute-value-equation-class","seed":20261238,"semantic_template":"qf-absolute-value-equation-class/{\"c\":5,\"domain\":\"reals\",\"operation\":\"absolute_equation_solution_class\"}"},"fields":{"title":"Solution Classification of an Absolute-Value Equation","stem":"Over the real numbers, classify the solution set of |x|=5.","answer":{"kind":"short_text","value":"two solutions x=-5, 5","explanation":"The real numbers at distance 5 from 0 are x=-5 and x=5."},"skills":["absolute-value equations","solution-set classification"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260928-absolute-value-equation-class-0011","batch_id":"batch-20260928-absolute-value-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"e6d1caa891ba71536bcc8065b085ad47e140fcc192ab17836d8c658e758d271b","family_id":"qf-absolute-value-equation-class","seed":20261239,"semantic_template":"qf-absolute-value-equation-class/{\"c\":6,\"domain\":\"reals\",\"operation\":\"absolute_equation_solution_class\"}"},"fields":{"title":"Solution Classification of an Absolute-Value Equation","stem":"Over the real numbers, classify the solution set of |x|=6.","answer":{"kind":"short_text","value":"two solutions x=-6, 6","explanation":"The real numbers at distance 6 from 0 are x=-6 and x=6."},"skills":["absolute-value equations","solution-set classification"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260928-absolute-value-equation-class-0012","batch_id":"batch-20260928-absolute-value-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"558688256a5bfdef368631d221c6b25c2b9545decb4e191188355d3068f49ed0","family_id":"qf-absolute-value-equation-class","seed":20261240,"semantic_template":"qf-absolute-value-equation-class/{\"c\":7,\"domain\":\"reals\",\"operation\":\"absolute_equation_solution_class\"}"},"fields":{"title":"Solution Classification of an Absolute-Value Equation","stem":"Over the real numbers, classify the solution set of |x|=7.","answer":{"kind":"short_text","value":"two solutions x=-7, 7","explanation":"The real numbers at distance 7 from 0 are x=-7 and x=7."},"skills":["absolute-value equations","solution-set classification"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260928-absolute-value-equation-class-0013","batch_id":"batch-20260928-absolute-value-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"6400342e1ecd175b99b75ec7de3d54067135333b8d9492e1d3162230e7398354","family_id":"qf-absolute-value-equation-class","seed":20261241,"semantic_template":"qf-absolute-value-equation-class/{\"c\":8,\"domain\":\"reals\",\"operation\":\"absolute_equation_solution_class\"}"},"fields":{"title":"Solution Classification of an Absolute-Value Equation","stem":"Over the real numbers, classify the solution set of |x|=8.","answer":{"kind":"short_text","value":"two solutions x=-8, 8","explanation":"The real numbers at distance 8 from 0 are x=-8 and x=8."},"skills":["absolute-value equations","solution-set classification"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260928-absolute-value-equation-class-0014","batch_id":"batch-20260928-absolute-value-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"a65ea7e22b72e3a4e7b3e8bd508f24daa2fbe8423b1750296097f85e5bb536d8","family_id":"qf-absolute-value-equation-class","seed":20261242,"semantic_template":"qf-absolute-value-equation-class/{\"c\":9,\"domain\":\"reals\",\"operation\":\"absolute_equation_solution_class\"}"},"fields":{"title":"Solution Classification of an Absolute-Value Equation","stem":"Over the real numbers, classify the solution set of |x|=9.","answer":{"kind":"short_text","value":"two solutions x=-9, 9","explanation":"The real numbers at distance 9 from 0 are x=-9 and x=9."},"skills":["absolute-value equations","solution-set classification"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260928-absolute-value-equation-class-0015","batch_id":"batch-20260928-absolute-value-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"fc2cd870edeb85a6397fcb66759295cf709db574d2a8622449c2f5466406001e","family_id":"qf-absolute-value-equation-class","seed":20261243,"semantic_template":"qf-absolute-value-equation-class/{\"c\":10,\"domain\":\"reals\",\"operation\":\"absolute_equation_solution_class\"}"},"fields":{"title":"Solution Classification of an Absolute-Value Equation","stem":"Over the real numbers, classify the solution set of |x|=10.","answer":{"kind":"short_text","value":"two solutions x=-10, 10","explanation":"The real numbers at distance 10 from 0 are x=-10 and x=10."},"skills":["absolute-value equations","solution-set classification"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260928-absolute-value-equation-class-0016","batch_id":"batch-20260928-absolute-value-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"c483c2b4e55268f24ead8f4a602d23430e3572a0f3f0d471aca5946bfc32ac27","family_id":"qf-absolute-value-equation-class","seed":20261244,"semantic_template":"qf-absolute-value-equation-class/{\"c\":11,\"domain\":\"reals\",\"operation\":\"absolute_equation_solution_class\"}"},"fields":{"title":"Solution Classification of an Absolute-Value Equation","stem":"Over the real numbers, classify the solution set of |x|=11.","answer":{"kind":"short_text","value":"two solutions x=-11, 11","explanation":"The real numbers at distance 11 from 0 are x=-11 and x=11."},"skills":["absolute-value equations","solution-set classification"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260928-absolute-value-equation-class-0017","batch_id":"batch-20260928-absolute-value-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"4e714bbae22d41373025dde2fee65cf9db3231e83f4e91e80152a2f394228447","family_id":"qf-absolute-value-equation-class","seed":20261245,"semantic_template":"qf-absolute-value-equation-class/{\"c\":12,\"domain\":\"reals\",\"operation\":\"absolute_equation_solution_class\"}"},"fields":{"title":"Solution Classification of an Absolute-Value Equation","stem":"Over the real numbers, classify the solution set of |x|=12.","answer":{"kind":"short_text","value":"two solutions x=-12, 12","explanation":"The real numbers at distance 12 from 0 are x=-12 and x=12."},"skills":["absolute-value equations","solution-set classification"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260928-absolute-value-equation-class-0018","batch_id":"batch-20260928-absolute-value-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"31c6adde887061effc35211724e017efe238ad32c104b07ac210c4861081fb34","family_id":"qf-absolute-value-equation-class","seed":20261246,"semantic_template":"qf-absolute-value-equation-class/{\"c\":13,\"domain\":\"reals\",\"operation\":\"absolute_equation_solution_class\"}"},"fields":{"title":"Solution Classification of an Absolute-Value Equation","stem":"Over the real numbers, classify the solution set of |x|=13.","answer":{"kind":"short_text","value":"two solutions x=-13, 13","explanation":"The real numbers at distance 13 from 0 are x=-13 and x=13."},"skills":["absolute-value equations","solution-set classification"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260928-absolute-value-equation-class-0019","batch_id":"batch-20260928-absolute-value-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"e6c9454a9c408d1538517ab96b4bf288dca47f27cc094219d5f1b570d8826a6f","family_id":"qf-absolute-value-equation-class","seed":20261247,"semantic_template":"qf-absolute-value-equation-class/{\"c\":14,\"domain\":\"reals\",\"operation\":\"absolute_equation_solution_class\"}"},"fields":{"title":"Solution Classification of an Absolute-Value Equation","stem":"Over the real numbers, classify the solution set of |x|=14.","answer":{"kind":"short_text","value":"two solutions x=-14, 14","explanation":"The real numbers at distance 14 from 0 are x=-14 and x=14."},"skills":["absolute-value equations","solution-set classification"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260928-absolute-value-equation-class-0020","batch_id":"batch-20260928-absolute-value-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"8a23b807c0dcc76b0a88b0a1c84072df167976c8ca0e20e77620623e52f56927","family_id":"qf-absolute-value-equation-class","seed":20261248,"semantic_template":"qf-absolute-value-equation-class/{\"c\":15,\"domain\":\"reals\",\"operation\":\"absolute_equation_solution_class\"}"},"fields":{"title":"Solution Classification of an Absolute-Value Equation","stem":"Over the real numbers, classify the solution set of |x|=15.","answer":{"kind":"short_text","value":"two solutions x=-15, 15","explanation":"The real numbers at distance 15 from 0 are x=-15 and x=15."},"skills":["absolute-value equations","solution-set classification"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260928-absolute-value-equation-class-0021","batch_id":"batch-20260928-absolute-value-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"64887d484c07bcc9469cd20463cb22bdcf1c0e06b3750a4a4be4e9b7791d4383","family_id":"qf-absolute-value-equation-class","seed":20261249,"semantic_template":"qf-absolute-value-equation-class/{\"c\":16,\"domain\":\"reals\",\"operation\":\"absolute_equation_solution_class\"}"},"fields":{"title":"Solution Classification of an Absolute-Value Equation","stem":"Over the real numbers, classify the solution set of |x|=16.","answer":{"kind":"short_text","value":"two solutions x=-16, 16","explanation":"The real numbers at distance 16 from 0 are x=-16 and x=16."},"skills":["absolute-value equations","solution-set classification"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260928-absolute-value-equation-class-0022","batch_id":"batch-20260928-absolute-value-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"c45f9f974c8c5cb1b455a431664b6644e53aeef07214706c0e6f5732667166dd","family_id":"qf-absolute-value-equation-class","seed":20261250,"semantic_template":"qf-absolute-value-equation-class/{\"c\":17,\"domain\":\"reals\",\"operation\":\"absolute_equation_solution_class\"}"},"fields":{"title":"Solution Classification of an Absolute-Value Equation","stem":"Over the real numbers, classify the solution set of |x|=17.","answer":{"kind":"short_text","value":"two solutions x=-17, 17","explanation":"The real numbers at distance 17 from 0 are x=-17 and x=17."},"skills":["absolute-value equations","solution-set classification"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260928-absolute-value-equation-class-0023","batch_id":"batch-20260928-absolute-value-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"55242f33f6896a9168b46c173730550d8a24dc3f429977402cfd80fe6ea76784","family_id":"qf-absolute-value-equation-class","seed":20261251,"semantic_template":"qf-absolute-value-equation-class/{\"c\":18,\"domain\":\"reals\",\"operation\":\"absolute_equation_solution_class\"}"},"fields":{"title":"Solution Classification of an Absolute-Value Equation","stem":"Over the real numbers, classify the solution set of |x|=18.","answer":{"kind":"short_text","value":"two solutions x=-18, 18","explanation":"The real numbers at distance 18 from 0 are x=-18 and x=18."},"skills":["absolute-value equations","solution-set classification"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260928-absolute-value-equation-class-0024","batch_id":"batch-20260928-absolute-value-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"2b2009affc36749a51cb1cca877d5b296fca7d9ba359a9d309970c8ad73f3679","family_id":"qf-absolute-value-equation-class","seed":20261252,"semantic_template":"qf-absolute-value-equation-class/{\"c\":19,\"domain\":\"reals\",\"operation\":\"absolute_equation_solution_class\"}"},"fields":{"title":"Solution Classification of an Absolute-Value Equation","stem":"Over the real numbers, classify the solution set of |x|=19.","answer":{"kind":"short_text","value":"two solutions x=-19, 19","explanation":"The real numbers at distance 19 from 0 are x=-19 and x=19."},"skills":["absolute-value equations","solution-set classification"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260928-absolute-value-equation-class-0025","batch_id":"batch-20260928-absolute-value-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"bffdde188408469d711173b5a9f06b58034ca91989670fef55254d6a09d72d53","family_id":"qf-absolute-value-equation-class","seed":20261253,"semantic_template":"qf-absolute-value-equation-class/{\"c\":20,\"domain\":\"reals\",\"operation\":\"absolute_equation_solution_class\"}"},"fields":{"title":"Solution Classification of an Absolute-Value Equation","stem":"Over the real numbers, classify the solution set of |x|=20.","answer":{"kind":"short_text","value":"two solutions x=-20, 20","explanation":"The real numbers at distance 20 from 0 are x=-20 and x=20."},"skills":["absolute-value equations","solution-set classification"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}