{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r03-variable-expression-0001","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"eac2e4d58b94837a6dddb257f787bfba15f29063065f6c8c1a45f4e67fd8e365","family_id":"qf-density11-expression-two-env-values","seed":202610113001,"semantic_template":"qf-density11-expression-two-env-values/[\"constant\",-3]"},"fields":{"title":"Affine Expression in Two Environments","stem":"All operations and evaluations are exact in Q, not truncated natural-number arithmetic. E(x)=(0)x+(-3) is an expression, not an equation. Ordered x environments=[0/3, -1/2]. Give the two E values. Use exact reduced fractions with positive denominators, retaining /1 for integers.","answer":{"kind":"expression","value":"(-3/1, -3/1)","explanation":"Evaluate the same expression separately in both environments; a constant ignores x, and evaluation is not equation solving. The exact result, retaining the requested order, is (-3/1, -3/1)."},"skills":["Affine Expression in Two Environments"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r03-variable-expression-0002","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"25a3c13ced61653566ead167f86e650f0750354a82392a588ff4153fe0ee62f0","family_id":"qf-density11-expression-two-env-values","seed":202610113002,"semantic_template":"qf-density11-expression-two-env-values/[-1,-6,[\"1/3\",\"-1/1\"]]"},"fields":{"title":"Affine Expression in Two Environments","stem":"All operations and evaluations are exact in Q, not truncated natural-number arithmetic. E(x)=(-1)x+(-6) is an expression, not an equation. Ordered x environments=[1/3, -2/2]. Give the two E values. Use exact reduced fractions with positive denominators, retaining /1 for integers.","answer":{"kind":"expression","value":"(-19/3, -5/1)","explanation":"Evaluate the same expression separately in both environments; a constant ignores x, and evaluation is not equation solving. The exact result, retaining the requested order, is (-19/3, -5/1)."},"skills":["Affine Expression in Two Environments"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r03-variable-expression-0003","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"00ffc50c7779ef8f94de83330ac2cd4038f49819fcd9d1e66ef72cf94fe021bf","family_id":"qf-density11-expression-two-env-values","seed":202610113003,"semantic_template":"qf-density11-expression-two-env-values/[2,-5,[\"2/3\",\"-3/2\"]]"},"fields":{"title":"Affine Expression in Two Environments","stem":"All operations and evaluations are exact in Q, not truncated natural-number arithmetic. E(x)=(2)x+(-5) is an expression, not an equation. Ordered x environments=[2/3, -3/2]. Give the two E values. Use exact reduced fractions with positive denominators, retaining /1 for integers.","answer":{"kind":"expression","value":"(-11/3, -8/1)","explanation":"Evaluate the same expression separately in both environments; a constant ignores x, and evaluation is not equation solving. The exact result, retaining the requested order, is (-11/3, -8/1)."},"skills":["Affine Expression in Two Environments"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r03-variable-expression-0004","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"28ab262679d1fe5c9e2f5cafac1c06650328a6567522b10fc6eb07161f94666e","family_id":"qf-density11-expression-two-env-values","seed":202610113004,"semantic_template":"qf-density11-expression-two-env-values/[-3,-4,[\"1/1\",\"-2/1\"]]"},"fields":{"title":"Affine Expression in Two Environments","stem":"All operations and evaluations are exact in Q, not truncated natural-number arithmetic. E(x)=(-3)x+(-4) is an expression, not an equation. Ordered x environments=[3/3, -4/2]. Give the two E values. Use exact reduced fractions with positive denominators, retaining /1 for integers.","answer":{"kind":"expression","value":"(-7/1, 2/1)","explanation":"Evaluate the same expression separately in both environments; a constant ignores x, and evaluation is not equation solving. The exact result, retaining the requested order, is (-7/1, 2/1)."},"skills":["Affine Expression in Two Environments"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r03-variable-expression-0005","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"0b1f6f08ef6309b62980cd23c48a4666d32e05656efd40cb2c7a688681b6a797","family_id":"qf-density11-expression-two-env-values","seed":202610113005,"semantic_template":"qf-density11-expression-two-env-values/[4,-3,[\"4/3\",\"-5/2\"]]"},"fields":{"title":"Affine Expression in Two Environments","stem":"All operations and evaluations are exact in Q, not truncated natural-number arithmetic. E(x)=(4)x+(-3) is an expression, not an equation. Ordered x environments=[4/3, -5/2]. Give the two E values. Use exact reduced fractions with positive denominators, retaining /1 for integers.","answer":{"kind":"expression","value":"(7/3, -13/1)","explanation":"Evaluate the same expression separately in both environments; a constant ignores x, and evaluation is not equation solving. The exact result, retaining the requested order, is (7/3, -13/1)."},"skills":["Affine Expression in Two Environments"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r03-variable-expression-0006","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"dfa2cb6fedf51604bce64acb4bcc44bb09094ce71179447e214177da604ddf8f","family_id":"qf-density11-expression-two-env-values","seed":202610113006,"semantic_template":"qf-density11-expression-two-env-values/[-5,-2,[\"5/3\",\"-3/1\"]]"},"fields":{"title":"Affine Expression in Two Environments","stem":"All operations and evaluations are exact in Q, not truncated natural-number arithmetic. E(x)=(-5)x+(-2) is an expression, not an equation. Ordered x environments=[5/3, -6/2]. Give the two E values. Use exact reduced fractions with positive denominators, retaining /1 for integers.","answer":{"kind":"expression","value":"(-31/3, 13/1)","explanation":"Evaluate the same expression separately in both environments; a constant ignores x, and evaluation is not equation solving. The exact result, retaining the requested order, is (-31/3, 13/1)."},"skills":["Affine Expression in Two Environments"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r03-variable-expression-0007","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"b7079c44dfbeb5a87616d5d443f19bc513061b9adb01595c1878f8ebd64ecbed","family_id":"qf-density11-expression-two-env-values","seed":202610113007,"semantic_template":"qf-density11-expression-two-env-values/[6,-1,[\"2/1\",\"-7/2\"]]"},"fields":{"title":"Affine Expression in Two Environments","stem":"All operations and evaluations are exact in Q, not truncated natural-number arithmetic. E(x)=(6)x+(-1) is an expression, not an equation. Ordered x environments=[6/3, -7/2]. Give the two E values. Use exact reduced fractions with positive denominators, retaining /1 for integers.","answer":{"kind":"expression","value":"(11/1, -22/1)","explanation":"Evaluate the same expression separately in both environments; a constant ignores x, and evaluation is not equation solving. The exact result, retaining the requested order, is (11/1, -22/1)."},"skills":["Affine Expression in Two Environments"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r03-variable-expression-0008","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"4b309fc913807298647e63a85107de6b4882070a8b94dd4f848f007163e37272","family_id":"qf-density11-expression-two-env-values","seed":202610113008,"semantic_template":"qf-density11-expression-two-env-values/[-7,0,[\"7/3\",\"-4/1\"]]"},"fields":{"title":"Affine Expression in Two Environments","stem":"All operations and evaluations are exact in Q, not truncated natural-number arithmetic. E(x)=(-7)x+(0) is an expression, not an equation. Ordered x environments=[7/3, -8/2]. Give the two E values. Use exact reduced fractions with positive denominators, retaining /1 for integers.","answer":{"kind":"expression","value":"(-49/3, 28/1)","explanation":"Evaluate the same expression separately in both environments; a constant ignores x, and evaluation is not equation solving. The exact result, retaining the requested order, is (-49/3, 28/1)."},"skills":["Affine Expression in Two Environments"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r03-variable-expression-0009","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"d4900abe8673f632866548778cabac72efc17416b42fddd8425b9b3f8cb03a89","family_id":"qf-density11-expression-two-env-values","seed":202610113009,"semantic_template":"qf-density11-expression-two-env-values/[8,1,[\"8/3\",\"-9/2\"]]"},"fields":{"title":"Affine Expression in Two Environments","stem":"All operations and evaluations are exact in Q, not truncated natural-number arithmetic. E(x)=(8)x+(1) is an expression, not an equation. Ordered x environments=[8/3, -9/2]. Give the two E values. Use exact reduced fractions with positive denominators, retaining /1 for integers.","answer":{"kind":"expression","value":"(67/3, -35/1)","explanation":"Evaluate the same expression separately in both environments; a constant ignores x, and evaluation is not equation solving. The exact result, retaining the requested order, is (67/3, -35/1)."},"skills":["Affine Expression in Two Environments"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r03-variable-expression-0010","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"87d5e5aa514ecbafbee0f663399a4d97680aab500fc6c4ddff181d044f562ab3","family_id":"qf-density11-expression-two-env-values","seed":202610113010,"semantic_template":"qf-density11-expression-two-env-values/[-9,2,[\"3/1\",\"-5/1\"]]"},"fields":{"title":"Affine Expression in Two Environments","stem":"All operations and evaluations are exact in Q, not truncated natural-number arithmetic. E(x)=(-9)x+(2) is an expression, not an equation. Ordered x environments=[9/3, -10/2]. Give the two E values. Use exact reduced fractions with positive denominators, retaining /1 for integers.","answer":{"kind":"expression","value":"(-25/1, 47/1)","explanation":"Evaluate the same expression separately in both environments; a constant ignores x, and evaluation is not equation solving. The exact result, retaining the requested order, is (-25/1, 47/1)."},"skills":["Affine Expression in Two Environments"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r03-variable-expression-0011","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"56ae9635577ede2bc9d30f0f03eab7e40d32178579b9912a35fcdc18dabfb2fe","family_id":"qf-density11-expression-two-env-values","seed":202610113011,"semantic_template":"qf-density11-expression-two-env-values/[10,3,[\"10/3\",\"-11/2\"]]"},"fields":{"title":"Affine Expression in Two Environments","stem":"All operations and evaluations are exact in Q, not truncated natural-number arithmetic. E(x)=(10)x+(3) is an expression, not an equation. Ordered x environments=[10/3, -11/2]. Give the two E values. Use exact reduced fractions with positive denominators, retaining /1 for integers.","answer":{"kind":"expression","value":"(109/3, -52/1)","explanation":"Evaluate the same expression separately in both environments; a constant ignores x, and evaluation is not equation solving. The exact result, retaining the requested order, is (109/3, -52/1)."},"skills":["Affine Expression in Two Environments"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r03-variable-expression-0012","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"f4d3787947901e4b526d06a02acb6a5b476933a5fe0817fff5af0e044b41afb8","family_id":"qf-density11-expression-two-env-values","seed":202610113012,"semantic_template":"qf-density11-expression-two-env-values/[-11,4,[\"11/3\",\"-6/1\"]]"},"fields":{"title":"Affine Expression in Two Environments","stem":"All operations and evaluations are exact in Q, not truncated natural-number arithmetic. E(x)=(-11)x+(4) is an expression, not an equation. Ordered x environments=[11/3, -12/2]. Give the two E values. Use exact reduced fractions with positive denominators, retaining /1 for integers.","answer":{"kind":"expression","value":"(-109/3, 70/1)","explanation":"Evaluate the same expression separately in both environments; a constant ignores x, and evaluation is not equation solving. The exact result, retaining the requested order, is (-109/3, 70/1)."},"skills":["Affine Expression in Two Environments"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r03-variable-expression-0013","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"8c9bcd3de93fcd2bf7d91d05fd167f7e78e655a944d9a5670e6ecb6cce940641","family_id":"qf-density11-expression-two-env-values","seed":202610113013,"semantic_template":"qf-density11-expression-two-env-values/[12,5,[\"4/1\",\"-13/2\"]]"},"fields":{"title":"Affine Expression in Two Environments","stem":"All operations and evaluations are exact in Q, not truncated natural-number arithmetic. E(x)=(12)x+(5) is an expression, not an equation. Ordered x environments=[12/3, -13/2]. Give the two E values. Use exact reduced fractions with positive denominators, retaining /1 for integers.","answer":{"kind":"expression","value":"(53/1, -73/1)","explanation":"Evaluate the same expression separately in both environments; a constant ignores x, and evaluation is not equation solving. The exact result, retaining the requested order, is (53/1, -73/1)."},"skills":["Affine Expression in Two Environments"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r03-variable-expression-0014","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"ac12805ddd7613cb9a27dd61a7fcba86c56f61a3c82b7e879e8550fa11271216","family_id":"qf-density11-expression-two-env-values","seed":202610113014,"semantic_template":"qf-density11-expression-two-env-values/[-13,6,[\"13/3\",\"-7/1\"]]"},"fields":{"title":"Affine Expression in Two Environments","stem":"All operations and evaluations are exact in Q, not truncated natural-number arithmetic. E(x)=(-13)x+(6) is an expression, not an equation. Ordered x environments=[13/3, -14/2]. Give the two E values. Use exact reduced fractions with positive denominators, retaining /1 for integers.","answer":{"kind":"expression","value":"(-151/3, 97/1)","explanation":"Evaluate the same expression separately in both environments; a constant ignores x, and evaluation is not equation solving. The exact result, retaining the requested order, is (-151/3, 97/1)."},"skills":["Affine Expression in Two Environments"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r03-variable-expression-0015","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"9fc3b38351e89f4804987c5a9b03d61c373ef30993c7cdb7f580c0f7d1b0a941","family_id":"qf-density11-expression-two-env-values","seed":202610113015,"semantic_template":"qf-density11-expression-two-env-values/[14,7,[\"14/3\",\"-15/2\"]]"},"fields":{"title":"Affine Expression in Two Environments","stem":"All operations and evaluations are exact in Q, not truncated natural-number arithmetic. E(x)=(14)x+(7) is an expression, not an equation. Ordered x environments=[14/3, -15/2]. Give the two E values. Use exact reduced fractions with positive denominators, retaining /1 for integers.","answer":{"kind":"expression","value":"(217/3, -98/1)","explanation":"Evaluate the same expression separately in both environments; a constant ignores x, and evaluation is not equation solving. The exact result, retaining the requested order, is (217/3, -98/1)."},"skills":["Affine Expression in Two Environments"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r03-variable-expression-0016","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"a28a8406b80b71259be3521666ddcc3904028451a2c5144afa9ff4f2384a4723","family_id":"qf-density11-expression-two-env-values","seed":202610113016,"semantic_template":"qf-density11-expression-two-env-values/[-15,8,[\"5/1\",\"-8/1\"]]"},"fields":{"title":"Affine Expression in Two Environments","stem":"All operations and evaluations are exact in Q, not truncated natural-number arithmetic. E(x)=(-15)x+(8) is an expression, not an equation. Ordered x environments=[15/3, -16/2]. Give the two E values. Use exact reduced fractions with positive denominators, retaining /1 for integers.","answer":{"kind":"expression","value":"(-67/1, 128/1)","explanation":"Evaluate the same expression separately in both environments; a constant ignores x, and evaluation is not equation solving. The exact result, retaining the requested order, is (-67/1, 128/1)."},"skills":["Affine Expression in Two Environments"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r03-variable-expression-0017","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"d602fe310fe50719c46ea91e43cbf12705c41bca3d85696ed5d0fe6c9e9acfed","family_id":"qf-density11-expression-two-env-values","seed":202610113017,"semantic_template":"qf-density11-expression-two-env-values/[16,9,[\"16/3\",\"-17/2\"]]"},"fields":{"title":"Affine Expression in Two Environments","stem":"All operations and evaluations are exact in Q, not truncated natural-number arithmetic. E(x)=(16)x+(9) is an expression, not an equation. Ordered x environments=[16/3, -17/2]. Give the two E values. Use exact reduced fractions with positive denominators, retaining /1 for integers.","answer":{"kind":"expression","value":"(283/3, -127/1)","explanation":"Evaluate the same expression separately in both environments; a constant ignores x, and evaluation is not equation solving. The exact result, retaining the requested order, is (283/3, -127/1)."},"skills":["Affine Expression in Two Environments"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r03-variable-expression-0018","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"deab5143c320910bf333292bd3f1d967bee02616dfa165d25b28733e0fa9ab2f","family_id":"qf-density11-expression-two-env-values","seed":202610113018,"semantic_template":"qf-density11-expression-two-env-values/[-17,10,[\"17/3\",\"-9/1\"]]"},"fields":{"title":"Affine Expression in Two Environments","stem":"All operations and evaluations are exact in Q, not truncated natural-number arithmetic. E(x)=(-17)x+(10) is an expression, not an equation. Ordered x environments=[17/3, -18/2]. Give the two E values. Use exact reduced fractions with positive denominators, retaining /1 for integers.","answer":{"kind":"expression","value":"(-259/3, 163/1)","explanation":"Evaluate the same expression separately in both environments; a constant ignores x, and evaluation is not equation solving. The exact result, retaining the requested order, is (-259/3, 163/1)."},"skills":["Affine Expression in Two Environments"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r03-variable-expression-0019","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"20349c9921ba224d124a71165040bf666d1da1acef0aeb904f2f53dbc36e3e19","family_id":"qf-density11-expression-two-env-values","seed":202610113019,"semantic_template":"qf-density11-expression-two-env-values/[18,11,[\"6/1\",\"-19/2\"]]"},"fields":{"title":"Affine Expression in Two Environments","stem":"All operations and evaluations are exact in Q, not truncated natural-number arithmetic. E(x)=(18)x+(11) is an expression, not an equation. Ordered x environments=[18/3, -19/2]. Give the two E values. Use exact reduced fractions with positive denominators, retaining /1 for integers.","answer":{"kind":"expression","value":"(119/1, -160/1)","explanation":"Evaluate the same expression separately in both environments; a constant ignores x, and evaluation is not equation solving. The exact result, retaining the requested order, is (119/1, -160/1)."},"skills":["Affine Expression in Two Environments"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r03-variable-expression-0020","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"677050c6f76185db98c86df1b9f1f98114d0957ce694f2355c98532d749d2f8f","family_id":"qf-density11-expression-two-env-values","seed":202610113020,"semantic_template":"qf-density11-expression-two-env-values/[-19,12,[\"19/3\",\"-10/1\"]]"},"fields":{"title":"Affine Expression in Two Environments","stem":"All operations and evaluations are exact in Q, not truncated natural-number arithmetic. E(x)=(-19)x+(12) is an expression, not an equation. Ordered x environments=[19/3, -20/2]. Give the two E values. Use exact reduced fractions with positive denominators, retaining /1 for integers.","answer":{"kind":"expression","value":"(-325/3, 202/1)","explanation":"Evaluate the same expression separately in both environments; a constant ignores x, and evaluation is not equation solving. The exact result, retaining the requested order, is (-325/3, 202/1)."},"skills":["Affine Expression in Two Environments"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r03-variable-expression-0021","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"4c5d6d8c677a42dae088ec4f57f33a936157aaf73fcf1ed7c7a5e78b1371cfe5","family_id":"qf-density11-expression-two-env-values","seed":202610113021,"semantic_template":"qf-density11-expression-two-env-values/[20,13,[\"20/3\",\"-21/2\"]]"},"fields":{"title":"Affine Expression in Two Environments","stem":"All operations and evaluations are exact in Q, not truncated natural-number arithmetic. E(x)=(20)x+(13) is an expression, not an equation. Ordered x environments=[20/3, -21/2]. Give the two E values. Use exact reduced fractions with positive denominators, retaining /1 for integers.","answer":{"kind":"expression","value":"(439/3, -197/1)","explanation":"Evaluate the same expression separately in both environments; a constant ignores x, and evaluation is not equation solving. The exact result, retaining the requested order, is (439/3, -197/1)."},"skills":["Affine Expression in Two Environments"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r03-variable-expression-0022","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"3bac66abfdc3678b3f4ddabce0261b8637eaaf7d9cf6f3a0f41c3bd714490115","family_id":"qf-density11-expression-two-env-values","seed":202610113022,"semantic_template":"qf-density11-expression-two-env-values/[-21,14,[\"7/1\",\"-11/1\"]]"},"fields":{"title":"Affine Expression in Two Environments","stem":"All operations and evaluations are exact in Q, not truncated natural-number arithmetic. E(x)=(-21)x+(14) is an expression, not an equation. Ordered x environments=[21/3, -22/2]. Give the two E values. Use exact reduced fractions with positive denominators, retaining /1 for integers.","answer":{"kind":"expression","value":"(-133/1, 245/1)","explanation":"Evaluate the same expression separately in both environments; a constant ignores x, and evaluation is not equation solving. The exact result, retaining the requested order, is (-133/1, 245/1)."},"skills":["Affine Expression in Two Environments"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r03-variable-expression-0023","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"4b074794d038787ef51665b141088e5e9ee7d887e508c0322628ed5b822685b8","family_id":"qf-density11-expression-two-env-values","seed":202610113023,"semantic_template":"qf-density11-expression-two-env-values/[22,15,[\"22/3\",\"-23/2\"]]"},"fields":{"title":"Affine Expression in Two Environments","stem":"All operations and evaluations are exact in Q, not truncated natural-number arithmetic. E(x)=(22)x+(15) is an expression, not an equation. Ordered x environments=[22/3, -23/2]. Give the two E values. Use exact reduced fractions with positive denominators, retaining /1 for integers.","answer":{"kind":"expression","value":"(529/3, -238/1)","explanation":"Evaluate the same expression separately in both environments; a constant ignores x, and evaluation is not equation solving. The exact result, retaining the requested order, is (529/3, -238/1)."},"skills":["Affine Expression in Two Environments"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r03-variable-expression-0024","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"063666a7f931d8605ba9326432a5f2d572ee6ba18397572390b960ebdb467382","family_id":"qf-density11-expression-two-env-values","seed":202610113024,"semantic_template":"qf-density11-expression-two-env-values/[-23,16,[\"23/3\",\"-12/1\"]]"},"fields":{"title":"Affine Expression in Two Environments","stem":"All operations and evaluations are exact in Q, not truncated natural-number arithmetic. E(x)=(-23)x+(16) is an expression, not an equation. Ordered x environments=[23/3, -24/2]. Give the two E values. Use exact reduced fractions with positive denominators, retaining /1 for integers.","answer":{"kind":"expression","value":"(-481/3, 292/1)","explanation":"Evaluate the same expression separately in both environments; a constant ignores x, and evaluation is not equation solving. The exact result, retaining the requested order, is (-481/3, 292/1)."},"skills":["Affine Expression in Two Environments"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r03-variable-expression-0025","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"a3d9ce917b04ab1b8fcb7ad90f4cfc14b1dbe61080996d80d717190bb711c8b4","family_id":"qf-density11-expression-two-env-values","seed":202610113025,"semantic_template":"qf-density11-expression-two-env-values/[24,17,[\"8/1\",\"-25/2\"]]"},"fields":{"title":"Affine Expression in Two Environments","stem":"All operations and evaluations are exact in Q, not truncated natural-number arithmetic. E(x)=(24)x+(17) is an expression, not an equation. Ordered x environments=[24/3, -25/2]. Give the two E values. Use exact reduced fractions with positive denominators, retaining /1 for integers.","answer":{"kind":"expression","value":"(209/1, -283/1)","explanation":"Evaluate the same expression separately in both environments; a constant ignores x, and evaluation is not equation solving. The exact result, retaining the requested order, is (209/1, -283/1)."},"skills":["Affine Expression in Two Environments"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r03-variable-expression-0026","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"e9aaf11fcc1db86009f73ae1b1dbca02b84e5a664bccc98c8faffde7a1c2378a","family_id":"qf-density11-expression-simultaneous-swap","seed":202610113026,"semantic_template":"qf-density11-expression-simultaneous-swap/[\"zero_pair\"]"},"fields":{"title":"Simultaneous Variable Swap","stem":"All operations and evaluations are exact in Q, not truncated natural-number arithmetic. E(x,y)=(0)x+(0)y, x=1, y=2. Swap x and y simultaneously; give (original value, swapped value) as integers.","answer":{"kind":"expression","value":"(0, 0)","explanation":"Both new bindings come from the original environment; sequential overwriting is not simultaneous substitution. The exact result, retaining the requested order, is (0, 0)."},"skills":["Simultaneous Variable Swap"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r03-variable-expression-0027","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"a77b968baafe11d03fc6b4ac949a8d7eaa0c28eb49a9fd7a4572ab3a212e60c8","family_id":"qf-density11-expression-simultaneous-swap","seed":202610113027,"semantic_template":"qf-density11-expression-simultaneous-swap/[\"equal_coefficients\",\"2\",\"2\"]"},"fields":{"title":"Simultaneous Variable Swap","stem":"All operations and evaluations are exact in Q, not truncated natural-number arithmetic. E(x,y)=(2)x+(2)y, x=-1, y=3. Swap x and y simultaneously; give (original value, swapped value) as integers.","answer":{"kind":"expression","value":"(4, 4)","explanation":"Both new bindings come from the original environment; sequential overwriting is not simultaneous substitution. The exact result, retaining the requested order, is (4, 4)."},"skills":["Simultaneous Variable Swap"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r03-variable-expression-0028","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"add19f01c61a66e664c5691e3b0beb5eb1c5166ab5dc8d0d3dbf2f5427fd8425","family_id":"qf-density11-expression-simultaneous-swap","seed":202610113028,"semantic_template":"qf-density11-expression-simultaneous-swap/[\"equal_environment\",\"-3\"]"},"fields":{"title":"Simultaneous Variable Swap","stem":"All operations and evaluations are exact in Q, not truncated natural-number arithmetic. E(x,y)=(1)x+(-2)y, x=3, y=3. Swap x and y simultaneously; give (original value, swapped value) as integers.","answer":{"kind":"expression","value":"(-3, -3)","explanation":"Both new bindings come from the original environment; sequential overwriting is not simultaneous substitution. The exact result, retaining the requested order, is (-3, -3)."},"skills":["Simultaneous Variable Swap"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r03-variable-expression-0029","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"e2f8a76e59a63b52fe17270b8dd23dbdd48b93ce968c63875180bb99bb1d9279","family_id":"qf-density11-expression-simultaneous-swap","seed":202610113029,"semantic_template":"qf-density11-expression-simultaneous-swap/[-3,4,6,1]"},"fields":{"title":"Simultaneous Variable Swap","stem":"All operations and evaluations are exact in Q, not truncated natural-number arithmetic. E(x,y)=(4)x+(-3)y, x=1, y=6. Swap x and y simultaneously; give (original value, swapped value) as integers.","answer":{"kind":"expression","value":"(-14, 21)","explanation":"Both new bindings come from the original environment; sequential overwriting is not simultaneous substitution. The exact result, retaining the requested order, is (-14, 21)."},"skills":["Simultaneous Variable Swap"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r03-variable-expression-0030","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"f8e11a68b5d4bb11cd6422677ff3a1a9341670d056b66004c10faf679198d928","family_id":"qf-density11-expression-simultaneous-swap","seed":202610113030,"semantic_template":"qf-density11-expression-simultaneous-swap/[-4,5,7,2]"},"fields":{"title":"Simultaneous Variable Swap","stem":"All operations and evaluations are exact in Q, not truncated natural-number arithmetic. E(x,y)=(5)x+(-4)y, x=2, y=7. Swap x and y simultaneously; give (original value, swapped value) as integers.","answer":{"kind":"expression","value":"(-18, 27)","explanation":"Both new bindings come from the original environment; sequential overwriting is not simultaneous substitution. The exact result, retaining the requested order, is (-18, 27)."},"skills":["Simultaneous Variable Swap"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r03-variable-expression-0031","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"e84c1c5f472181fe8903b10e1f63f715bb911e366c11527584783478a1853ab5","family_id":"qf-density11-expression-simultaneous-swap","seed":202610113031,"semantic_template":"qf-density11-expression-simultaneous-swap/[-5,6,8,-2]"},"fields":{"title":"Simultaneous Variable Swap","stem":"All operations and evaluations are exact in Q, not truncated natural-number arithmetic. E(x,y)=(6)x+(-5)y, x=-2, y=8. Swap x and y simultaneously; give (original value, swapped value) as integers.","answer":{"kind":"expression","value":"(-52, 58)","explanation":"Both new bindings come from the original environment; sequential overwriting is not simultaneous substitution. The exact result, retaining the requested order, is (-52, 58)."},"skills":["Simultaneous Variable Swap"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r03-variable-expression-0032","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"61c03ba3744cde6c98fc0275e51f4bc68e3a43305ae3df81806038c6e87de92d","family_id":"qf-density11-expression-simultaneous-swap","seed":202610113032,"semantic_template":"qf-density11-expression-simultaneous-swap/[-6,7,9,-1]"},"fields":{"title":"Simultaneous Variable Swap","stem":"All operations and evaluations are exact in Q, not truncated natural-number arithmetic. E(x,y)=(7)x+(-6)y, x=-1, y=9. Swap x and y simultaneously; give (original value, swapped value) as integers.","answer":{"kind":"expression","value":"(-61, 69)","explanation":"Both new bindings come from the original environment; sequential overwriting is not simultaneous substitution. The exact result, retaining the requested order, is (-61, 69)."},"skills":["Simultaneous Variable Swap"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r03-variable-expression-0033","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"c4a966725e755c6a74758e9a1c7bfeb44dc98a4ac4a265a34b93c1820851bc03","family_id":"qf-density11-expression-simultaneous-swap","seed":202610113033,"semantic_template":"qf-density11-expression-simultaneous-swap/[-7,8,10,0]"},"fields":{"title":"Simultaneous Variable Swap","stem":"All operations and evaluations are exact in Q, not truncated natural-number arithmetic. E(x,y)=(8)x+(-7)y, x=0, y=10. Swap x and y simultaneously; give (original value, swapped value) as integers.","answer":{"kind":"expression","value":"(-70, 80)","explanation":"Both new bindings come from the original environment; sequential overwriting is not simultaneous substitution. The exact result, retaining the requested order, is (-70, 80)."},"skills":["Simultaneous Variable Swap"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r03-variable-expression-0034","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"5b4539c770f65f958278026ccd85bbf463cad35b03f6aabc587b4cc517efb246","family_id":"qf-density11-expression-simultaneous-swap","seed":202610113034,"semantic_template":"qf-density11-expression-simultaneous-swap/[-8,9,11,1]"},"fields":{"title":"Simultaneous Variable Swap","stem":"All operations and evaluations are exact in Q, not truncated natural-number arithmetic. E(x,y)=(9)x+(-8)y, x=1, y=11. Swap x and y simultaneously; give (original value, swapped value) as integers.","answer":{"kind":"expression","value":"(-79, 91)","explanation":"Both new bindings come from the original environment; sequential overwriting is not simultaneous substitution. The exact result, retaining the requested order, is (-79, 91)."},"skills":["Simultaneous Variable Swap"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r03-variable-expression-0035","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"59668f94bdccb008cc662c505222f2126b53a5d97472b5ef3a0c8bc8c0657004","family_id":"qf-density11-expression-simultaneous-swap","seed":202610113035,"semantic_template":"qf-density11-expression-simultaneous-swap/[-9,10,12,2]"},"fields":{"title":"Simultaneous Variable Swap","stem":"All operations and evaluations are exact in Q, not truncated natural-number arithmetic. E(x,y)=(10)x+(-9)y, x=2, y=12. Swap x and y simultaneously; give (original value, swapped value) as integers.","answer":{"kind":"expression","value":"(-88, 102)","explanation":"Both new bindings come from the original environment; sequential overwriting is not simultaneous substitution. The exact result, retaining the requested order, is (-88, 102)."},"skills":["Simultaneous Variable Swap"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r03-variable-expression-0036","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"f8ccb9f82023751078abf0368072a2b8d77b4ac5a32c742fd0c78bea71c838d5","family_id":"qf-density11-expression-simultaneous-swap","seed":202610113036,"semantic_template":"qf-density11-expression-simultaneous-swap/[-10,11,13,-2]"},"fields":{"title":"Simultaneous Variable Swap","stem":"All operations and evaluations are exact in Q, not truncated natural-number arithmetic. E(x,y)=(11)x+(-10)y, x=-2, y=13. Swap x and y simultaneously; give (original value, swapped value) as integers.","answer":{"kind":"expression","value":"(-152, 163)","explanation":"Both new bindings come from the original environment; sequential overwriting is not simultaneous substitution. The exact result, retaining the requested order, is (-152, 163)."},"skills":["Simultaneous Variable Swap"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r03-variable-expression-0037","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"0c7f45a43158558955028736180d957a5f83132a95a3f1e85010405a9f7b6fff","family_id":"qf-density11-expression-simultaneous-swap","seed":202610113037,"semantic_template":"qf-density11-expression-simultaneous-swap/[-11,12,14,-1]"},"fields":{"title":"Simultaneous Variable Swap","stem":"All operations and evaluations are exact in Q, not truncated natural-number arithmetic. E(x,y)=(12)x+(-11)y, x=-1, y=14. Swap x and y simultaneously; give (original value, swapped value) as integers.","answer":{"kind":"expression","value":"(-166, 179)","explanation":"Both new bindings come from the original environment; sequential overwriting is not simultaneous substitution. The exact result, retaining the requested order, is (-166, 179)."},"skills":["Simultaneous Variable Swap"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r03-variable-expression-0038","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"a2d95ffe760a2e330007ddc16dc12a5c117e83e92be5a5d745a8e3f0de663c00","family_id":"qf-density11-expression-simultaneous-swap","seed":202610113038,"semantic_template":"qf-density11-expression-simultaneous-swap/[-12,13,15,0]"},"fields":{"title":"Simultaneous Variable Swap","stem":"All operations and evaluations are exact in Q, not truncated natural-number arithmetic. E(x,y)=(13)x+(-12)y, x=0, y=15. Swap x and y simultaneously; give (original value, swapped value) as integers.","answer":{"kind":"expression","value":"(-180, 195)","explanation":"Both new bindings come from the original environment; sequential overwriting is not simultaneous substitution. The exact result, retaining the requested order, is (-180, 195)."},"skills":["Simultaneous Variable Swap"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r03-variable-expression-0039","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"c60d2481faa252afa351c2fd83eb397e2aab92e2ef12e65842ade1fb1464fd84","family_id":"qf-density11-expression-simultaneous-swap","seed":202610113039,"semantic_template":"qf-density11-expression-simultaneous-swap/[-13,14,16,1]"},"fields":{"title":"Simultaneous Variable Swap","stem":"All operations and evaluations are exact in Q, not truncated natural-number arithmetic. E(x,y)=(14)x+(-13)y, x=1, y=16. Swap x and y simultaneously; give (original value, swapped value) as integers.","answer":{"kind":"expression","value":"(-194, 211)","explanation":"Both new bindings come from the original environment; sequential overwriting is not simultaneous substitution. The exact result, retaining the requested order, is (-194, 211)."},"skills":["Simultaneous Variable Swap"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r03-variable-expression-0040","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"39ee0fcbc71e5e2898fbb58b6ebd9ec74124c85cc8e430b968f207828946450f","family_id":"qf-density11-expression-simultaneous-swap","seed":202610113040,"semantic_template":"qf-density11-expression-simultaneous-swap/[-14,15,17,2]"},"fields":{"title":"Simultaneous Variable Swap","stem":"All operations and evaluations are exact in Q, not truncated natural-number arithmetic. E(x,y)=(15)x+(-14)y, x=2, y=17. Swap x and y simultaneously; give (original value, swapped value) as integers.","answer":{"kind":"expression","value":"(-208, 227)","explanation":"Both new bindings come from the original environment; sequential overwriting is not simultaneous substitution. The exact result, retaining the requested order, is (-208, 227)."},"skills":["Simultaneous Variable Swap"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r03-variable-expression-0041","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"498a6d38d43b62566b293a2c63c5bd45b06352665ce5b8aa806c1ad3ea5c357e","family_id":"qf-density11-expression-simultaneous-swap","seed":202610113041,"semantic_template":"qf-density11-expression-simultaneous-swap/[-15,16,18,-2]"},"fields":{"title":"Simultaneous Variable Swap","stem":"All operations and evaluations are exact in Q, not truncated natural-number arithmetic. E(x,y)=(16)x+(-15)y, x=-2, y=18. Swap x and y simultaneously; give (original value, swapped value) as integers.","answer":{"kind":"expression","value":"(-302, 318)","explanation":"Both new bindings come from the original environment; sequential overwriting is not simultaneous substitution. The exact result, retaining the requested order, is (-302, 318)."},"skills":["Simultaneous Variable Swap"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r03-variable-expression-0042","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"ccddda16d41dbc5eaa795d2f0fe2c36bc189d008d446fa1241fddc582e15480d","family_id":"qf-density11-expression-simultaneous-swap","seed":202610113042,"semantic_template":"qf-density11-expression-simultaneous-swap/[-16,17,19,-1]"},"fields":{"title":"Simultaneous Variable Swap","stem":"All operations and evaluations are exact in Q, not truncated natural-number arithmetic. E(x,y)=(17)x+(-16)y, x=-1, y=19. Swap x and y simultaneously; give (original value, swapped value) as integers.","answer":{"kind":"expression","value":"(-321, 339)","explanation":"Both new bindings come from the original environment; sequential overwriting is not simultaneous substitution. The exact result, retaining the requested order, is (-321, 339)."},"skills":["Simultaneous Variable Swap"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r03-variable-expression-0043","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"8ad3cc8a3d18d953d7b193d0667c9e98a364cb5532c6fe5ca2aa394e10e83f4c","family_id":"qf-density11-expression-simultaneous-swap","seed":202610113043,"semantic_template":"qf-density11-expression-simultaneous-swap/[-17,18,20,0]"},"fields":{"title":"Simultaneous Variable Swap","stem":"All operations and evaluations are exact in Q, not truncated natural-number arithmetic. E(x,y)=(18)x+(-17)y, x=0, y=20. Swap x and y simultaneously; give (original value, swapped value) as integers.","answer":{"kind":"expression","value":"(-340, 360)","explanation":"Both new bindings come from the original environment; sequential overwriting is not simultaneous substitution. The exact result, retaining the requested order, is (-340, 360)."},"skills":["Simultaneous Variable Swap"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r03-variable-expression-0044","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"c0db12738cfe4ecacdae73beb1959e9f4ca75b0726dcbf1233258629352c5385","family_id":"qf-density11-expression-simultaneous-swap","seed":202610113044,"semantic_template":"qf-density11-expression-simultaneous-swap/[-18,19,21,1]"},"fields":{"title":"Simultaneous Variable Swap","stem":"All operations and evaluations are exact in Q, not truncated natural-number arithmetic. E(x,y)=(19)x+(-18)y, x=1, y=21. Swap x and y simultaneously; give (original value, swapped value) as integers.","answer":{"kind":"expression","value":"(-359, 381)","explanation":"Both new bindings come from the original environment; sequential overwriting is not simultaneous substitution. The exact result, retaining the requested order, is (-359, 381)."},"skills":["Simultaneous Variable Swap"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r03-variable-expression-0045","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"fcb4c235eeaa16c0ec4067c0d1ae9832d8a9f69aac2e1fdfd3c98ec5b2952b27","family_id":"qf-density11-expression-simultaneous-swap","seed":202610113045,"semantic_template":"qf-density11-expression-simultaneous-swap/[-19,20,22,2]"},"fields":{"title":"Simultaneous Variable Swap","stem":"All operations and evaluations are exact in Q, not truncated natural-number arithmetic. E(x,y)=(20)x+(-19)y, x=2, y=22. Swap x and y simultaneously; give (original value, swapped value) as integers.","answer":{"kind":"expression","value":"(-378, 402)","explanation":"Both new bindings come from the original environment; sequential overwriting is not simultaneous substitution. The exact result, retaining the requested order, is (-378, 402)."},"skills":["Simultaneous Variable Swap"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r03-variable-expression-0046","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"6ad9ebcf33af04cb3d314571dcb2dc2831d207d6fb581ef5f78a6039d5127357","family_id":"qf-density11-expression-simultaneous-swap","seed":202610113046,"semantic_template":"qf-density11-expression-simultaneous-swap/[-20,21,23,-2]"},"fields":{"title":"Simultaneous Variable Swap","stem":"All operations and evaluations are exact in Q, not truncated natural-number arithmetic. E(x,y)=(21)x+(-20)y, x=-2, y=23. Swap x and y simultaneously; give (original value, swapped value) as integers.","answer":{"kind":"expression","value":"(-502, 523)","explanation":"Both new bindings come from the original environment; sequential overwriting is not simultaneous substitution. The exact result, retaining the requested order, is (-502, 523)."},"skills":["Simultaneous Variable Swap"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r03-variable-expression-0047","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"44d18893395f2209ab04474bdf79eac28347d48c10054b178236673be8f6ed4b","family_id":"qf-density11-expression-simultaneous-swap","seed":202610113047,"semantic_template":"qf-density11-expression-simultaneous-swap/[-21,22,24,-1]"},"fields":{"title":"Simultaneous Variable Swap","stem":"All operations and evaluations are exact in Q, not truncated natural-number arithmetic. E(x,y)=(22)x+(-21)y, x=-1, y=24. Swap x and y simultaneously; give (original value, swapped value) as integers.","answer":{"kind":"expression","value":"(-526, 549)","explanation":"Both new bindings come from the original environment; sequential overwriting is not simultaneous substitution. The exact result, retaining the requested order, is (-526, 549)."},"skills":["Simultaneous Variable Swap"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r03-variable-expression-0048","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"3e48622d8c87fa00728371ca5760d7898417647a51a838b80a5240bc821ab1a0","family_id":"qf-density11-expression-simultaneous-swap","seed":202610113048,"semantic_template":"qf-density11-expression-simultaneous-swap/[-22,23,25,0]"},"fields":{"title":"Simultaneous Variable Swap","stem":"All operations and evaluations are exact in Q, not truncated natural-number arithmetic. E(x,y)=(23)x+(-22)y, x=0, y=25. Swap x and y simultaneously; give (original value, swapped value) as integers.","answer":{"kind":"expression","value":"(-550, 575)","explanation":"Both new bindings come from the original environment; sequential overwriting is not simultaneous substitution. The exact result, retaining the requested order, is (-550, 575)."},"skills":["Simultaneous Variable Swap"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r03-variable-expression-0049","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"054dd3984ff1522f83f1e888499731b7ea4179d3c7d1444b2e0a241dc457ec19","family_id":"qf-density11-expression-simultaneous-swap","seed":202610113049,"semantic_template":"qf-density11-expression-simultaneous-swap/[-23,24,26,1]"},"fields":{"title":"Simultaneous Variable Swap","stem":"All operations and evaluations are exact in Q, not truncated natural-number arithmetic. E(x,y)=(24)x+(-23)y, x=1, y=26. Swap x and y simultaneously; give (original value, swapped value) as integers.","answer":{"kind":"expression","value":"(-574, 601)","explanation":"Both new bindings come from the original environment; sequential overwriting is not simultaneous substitution. The exact result, retaining the requested order, is (-574, 601)."},"skills":["Simultaneous Variable Swap"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r03-variable-expression-0050","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"6453e34d1d180591e404df8dd093b74108b2ad641df715d9f1f63d26f12525ea","family_id":"qf-density11-expression-simultaneous-swap","seed":202610113050,"semantic_template":"qf-density11-expression-simultaneous-swap/[-24,25,27,2]"},"fields":{"title":"Simultaneous Variable Swap","stem":"All operations and evaluations are exact in Q, not truncated natural-number arithmetic. E(x,y)=(25)x+(-24)y, x=2, y=27. Swap x and y simultaneously; give (original value, swapped value) as integers.","answer":{"kind":"expression","value":"(-598, 627)","explanation":"Both new bindings come from the original environment; sequential overwriting is not simultaneous substitution. The exact result, retaining the requested order, is (-598, 627)."},"skills":["Simultaneous Variable Swap"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r03-variable-expression-0051","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"567194f8cc0784213b71c63b462bc9b2bcae786ec58fac8ae128d3ea6177499b","family_id":"qf-density11-expression-local-shadow-pair","seed":202610113051,"semantic_template":"qf-density11-expression-local-shadow-pair/[0,0,1]"},"fields":{"title":"Outer and Lexically Shadowed Values","stem":"All operations and evaluations are exact in Q, not truncated natural-number arithmetic. Outer x=0, locally shadowing inner x=0, c=1. Give (outer x+c, inner x+c) as integers; the inner binding does not mutate the outer one.","answer":{"kind":"expression","value":"(1, 1)","explanation":"Use each scope’s own binding before adding c; lexical shadowing is not assignment to the outer environment. The exact result, retaining the requested order, is (1, 1)."},"skills":["Outer and Lexically Shadowed Values"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r03-variable-expression-0052","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"c45ad749cab108339ec0f6d50738c10252af4f639764cec4ad2969701c12ee2a","family_id":"qf-density11-expression-local-shadow-pair","seed":202610113052,"semantic_template":"qf-density11-expression-local-shadow-pair/[3,-2,4]"},"fields":{"title":"Outer and Lexically Shadowed Values","stem":"All operations and evaluations are exact in Q, not truncated natural-number arithmetic. Outer x=3, locally shadowing inner x=-2, c=4. Give (outer x+c, inner x+c) as integers; the inner binding does not mutate the outer one.","answer":{"kind":"expression","value":"(7, 2)","explanation":"Use each scope’s own binding before adding c; lexical shadowing is not assignment to the outer environment. The exact result, retaining the requested order, is (7, 2)."},"skills":["Outer and Lexically Shadowed Values"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r03-variable-expression-0053","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"6b85b3fd9c899914c7f32db3259bc062318de77cc99cd0e9f2886445b9488729","family_id":"qf-density11-expression-local-shadow-pair","seed":202610113053,"semantic_template":"qf-density11-expression-local-shadow-pair/[-10,-1,0]"},"fields":{"title":"Outer and Lexically Shadowed Values","stem":"All operations and evaluations are exact in Q, not truncated natural-number arithmetic. Outer x=-10, locally shadowing inner x=-1, c=0. Give (outer x+c, inner x+c) as integers; the inner binding does not mutate the outer one.","answer":{"kind":"expression","value":"(-10, -1)","explanation":"Use each scope’s own binding before adding c; lexical shadowing is not assignment to the outer environment. The exact result, retaining the requested order, is (-10, -1)."},"skills":["Outer and Lexically Shadowed Values"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r03-variable-expression-0054","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"3d617ed7078be5133fe392fcd5c5d3daed53d5b923439882793e708ca6f57a47","family_id":"qf-density11-expression-local-shadow-pair","seed":202610113054,"semantic_template":"qf-density11-expression-local-shadow-pair/[-9,-2,1]"},"fields":{"title":"Outer and Lexically Shadowed Values","stem":"All operations and evaluations are exact in Q, not truncated natural-number arithmetic. Outer x=-9, locally shadowing inner x=-2, c=1. Give (outer x+c, inner x+c) as integers; the inner binding does not mutate the outer one.","answer":{"kind":"expression","value":"(-8, -1)","explanation":"Use each scope’s own binding before adding c; lexical shadowing is not assignment to the outer environment. The exact result, retaining the requested order, is (-8, -1)."},"skills":["Outer and Lexically Shadowed Values"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r03-variable-expression-0055","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"ce43680d87943a315fb66013024ea2f4f56f2602f9eb669c93b64dbbd2538821","family_id":"qf-density11-expression-local-shadow-pair","seed":202610113055,"semantic_template":"qf-density11-expression-local-shadow-pair/[-8,-3,-2]"},"fields":{"title":"Outer and Lexically Shadowed Values","stem":"All operations and evaluations are exact in Q, not truncated natural-number arithmetic. Outer x=-8, locally shadowing inner x=-3, c=-2. Give (outer x+c, inner x+c) as integers; the inner binding does not mutate the outer one.","answer":{"kind":"expression","value":"(-10, -5)","explanation":"Use each scope’s own binding before adding c; lexical shadowing is not assignment to the outer environment. The exact result, retaining the requested order, is (-10, -5)."},"skills":["Outer and Lexically Shadowed Values"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r03-variable-expression-0056","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"dc17ee685826096c1e603604a80ebec4ec86333308db8ae5cc3fd3c1ccc95844","family_id":"qf-density11-expression-local-shadow-pair","seed":202610113056,"semantic_template":"qf-density11-expression-local-shadow-pair/[-7,-4,-1]"},"fields":{"title":"Outer and Lexically Shadowed Values","stem":"All operations and evaluations are exact in Q, not truncated natural-number arithmetic. Outer x=-7, locally shadowing inner x=-4, c=-1. Give (outer x+c, inner x+c) as integers; the inner binding does not mutate the outer one.","answer":{"kind":"expression","value":"(-8, -5)","explanation":"Use each scope’s own binding before adding c; lexical shadowing is not assignment to the outer environment. The exact result, retaining the requested order, is (-8, -5)."},"skills":["Outer and Lexically Shadowed Values"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r03-variable-expression-0057","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"6b9fab33cf9b6e3311473cece9e8d4386324f90fae9c8d65b40d703472701db6","family_id":"qf-density11-expression-local-shadow-pair","seed":202610113057,"semantic_template":"qf-density11-expression-local-shadow-pair/[-6,-5,0]"},"fields":{"title":"Outer and Lexically Shadowed Values","stem":"All operations and evaluations are exact in Q, not truncated natural-number arithmetic. Outer x=-6, locally shadowing inner x=-5, c=0. Give (outer x+c, inner x+c) as integers; the inner binding does not mutate the outer one.","answer":{"kind":"expression","value":"(-6, -5)","explanation":"Use each scope’s own binding before adding c; lexical shadowing is not assignment to the outer environment. The exact result, retaining the requested order, is (-6, -5)."},"skills":["Outer and Lexically Shadowed Values"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r03-variable-expression-0058","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"a398f35939d1ad92e61a8eb7348625c976a7b4870679fcddc85ec45173326396","family_id":"qf-density11-expression-local-shadow-pair","seed":202610113058,"semantic_template":"qf-density11-expression-local-shadow-pair/[-5,-6,1]"},"fields":{"title":"Outer and Lexically Shadowed Values","stem":"All operations and evaluations are exact in Q, not truncated natural-number arithmetic. Outer x=-5, locally shadowing inner x=-6, c=1. Give (outer x+c, inner x+c) as integers; the inner binding does not mutate the outer one.","answer":{"kind":"expression","value":"(-4, -5)","explanation":"Use each scope’s own binding before adding c; lexical shadowing is not assignment to the outer environment. The exact result, retaining the requested order, is (-4, -5)."},"skills":["Outer and Lexically Shadowed Values"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r03-variable-expression-0059","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"dd7856baaa9c24ab76acb3c80bd14010ceb1105142cb1646b9fe13a0c5007544","family_id":"qf-density11-expression-local-shadow-pair","seed":202610113059,"semantic_template":"qf-density11-expression-local-shadow-pair/[-4,-7,-2]"},"fields":{"title":"Outer and Lexically Shadowed Values","stem":"All operations and evaluations are exact in Q, not truncated natural-number arithmetic. Outer x=-4, locally shadowing inner x=-7, c=-2. Give (outer x+c, inner x+c) as integers; the inner binding does not mutate the outer one.","answer":{"kind":"expression","value":"(-6, -9)","explanation":"Use each scope’s own binding before adding c; lexical shadowing is not assignment to the outer environment. The exact result, retaining the requested order, is (-6, -9)."},"skills":["Outer and Lexically Shadowed Values"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r03-variable-expression-0060","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"57f84983649cdd3ea44cf942fdcc89f4db0bbb82ead528b55a83d1363fa608e7","family_id":"qf-density11-expression-local-shadow-pair","seed":202610113060,"semantic_template":"qf-density11-expression-local-shadow-pair/[-3,-8,-1]"},"fields":{"title":"Outer and Lexically Shadowed Values","stem":"All operations and evaluations are exact in Q, not truncated natural-number arithmetic. Outer x=-3, locally shadowing inner x=-8, c=-1. Give (outer x+c, inner x+c) as integers; the inner binding does not mutate the outer one.","answer":{"kind":"expression","value":"(-4, -9)","explanation":"Use each scope’s own binding before adding c; lexical shadowing is not assignment to the outer environment. The exact result, retaining the requested order, is (-4, -9)."},"skills":["Outer and Lexically Shadowed Values"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r03-variable-expression-0061","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"a30957de28b5016f82a847a176bb08caa3d11edd1061a6eccbd40c902b92aad9","family_id":"qf-density11-expression-local-shadow-pair","seed":202610113061,"semantic_template":"qf-density11-expression-local-shadow-pair/[-2,-9,0]"},"fields":{"title":"Outer and Lexically Shadowed Values","stem":"All operations and evaluations are exact in Q, not truncated natural-number arithmetic. Outer x=-2, locally shadowing inner x=-9, c=0. Give (outer x+c, inner x+c) as integers; the inner binding does not mutate the outer one.","answer":{"kind":"expression","value":"(-2, -9)","explanation":"Use each scope’s own binding before adding c; lexical shadowing is not assignment to the outer environment. The exact result, retaining the requested order, is (-2, -9)."},"skills":["Outer and Lexically Shadowed Values"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r03-variable-expression-0062","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"ba6d2d07bbffc714daf63069d7caecbbb8855d96644f3f35f8514aa3bf94d4ee","family_id":"qf-density11-expression-local-shadow-pair","seed":202610113062,"semantic_template":"qf-density11-expression-local-shadow-pair/[-1,-10,1]"},"fields":{"title":"Outer and Lexically Shadowed Values","stem":"All operations and evaluations are exact in Q, not truncated natural-number arithmetic. Outer x=-1, locally shadowing inner x=-10, c=1. Give (outer x+c, inner x+c) as integers; the inner binding does not mutate the outer one.","answer":{"kind":"expression","value":"(0, -9)","explanation":"Use each scope’s own binding before adding c; lexical shadowing is not assignment to the outer environment. The exact result, retaining the requested order, is (0, -9)."},"skills":["Outer and Lexically Shadowed Values"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r03-variable-expression-0063","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"00c85adb40f3ea4ec2f33c9e67e2037bba07fd6beee99d5a62abca9ce74cae09","family_id":"qf-density11-expression-local-shadow-pair","seed":202610113063,"semantic_template":"qf-density11-expression-local-shadow-pair/[0,-11,-2]"},"fields":{"title":"Outer and Lexically Shadowed Values","stem":"All operations and evaluations are exact in Q, not truncated natural-number arithmetic. Outer x=0, locally shadowing inner x=-11, c=-2. Give (outer x+c, inner x+c) as integers; the inner binding does not mutate the outer one.","answer":{"kind":"expression","value":"(-2, -13)","explanation":"Use each scope’s own binding before adding c; lexical shadowing is not assignment to the outer environment. The exact result, retaining the requested order, is (-2, -13)."},"skills":["Outer and Lexically Shadowed Values"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r03-variable-expression-0064","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"29b79e89f7c25280b3bb7c61c604ba220aebcaf7058fc3bb65e08757822f2967","family_id":"qf-density11-expression-local-shadow-pair","seed":202610113064,"semantic_template":"qf-density11-expression-local-shadow-pair/[1,-12,-1]"},"fields":{"title":"Outer and Lexically Shadowed Values","stem":"All operations and evaluations are exact in Q, not truncated natural-number arithmetic. Outer x=1, locally shadowing inner x=-12, c=-1. Give (outer x+c, inner x+c) as integers; the inner binding does not mutate the outer one.","answer":{"kind":"expression","value":"(0, -13)","explanation":"Use each scope’s own binding before adding c; lexical shadowing is not assignment to the outer environment. The exact result, retaining the requested order, is (0, -13)."},"skills":["Outer and Lexically Shadowed Values"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r03-variable-expression-0065","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"0e96309b6c30ef65922483729aa6f171dfb4b28db61c51443eac972cb85ace3b","family_id":"qf-density11-expression-local-shadow-pair","seed":202610113065,"semantic_template":"qf-density11-expression-local-shadow-pair/[2,-13,0]"},"fields":{"title":"Outer and Lexically Shadowed Values","stem":"All operations and evaluations are exact in Q, not truncated natural-number arithmetic. Outer x=2, locally shadowing inner x=-13, c=0. Give (outer x+c, inner x+c) as integers; the inner binding does not mutate the outer one.","answer":{"kind":"expression","value":"(2, -13)","explanation":"Use each scope’s own binding before adding c; lexical shadowing is not assignment to the outer environment. The exact result, retaining the requested order, is (2, -13)."},"skills":["Outer and Lexically Shadowed Values"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r03-variable-expression-0066","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"becdf595b6203f2e36227afebf828165001dbef67f61a9b1d1dae5f1337fce8e","family_id":"qf-density11-expression-local-shadow-pair","seed":202610113066,"semantic_template":"qf-density11-expression-local-shadow-pair/[3,-14,1]"},"fields":{"title":"Outer and Lexically Shadowed Values","stem":"All operations and evaluations are exact in Q, not truncated natural-number arithmetic. Outer x=3, locally shadowing inner x=-14, c=1. Give (outer x+c, inner x+c) as integers; the inner binding does not mutate the outer one.","answer":{"kind":"expression","value":"(4, -13)","explanation":"Use each scope’s own binding before adding c; lexical shadowing is not assignment to the outer environment. The exact result, retaining the requested order, is (4, -13)."},"skills":["Outer and Lexically Shadowed Values"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r03-variable-expression-0067","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"49d0807590ea71700b306851af808e8bebc719ba06ea8ba12f67181d148298c0","family_id":"qf-density11-expression-local-shadow-pair","seed":202610113067,"semantic_template":"qf-density11-expression-local-shadow-pair/[4,-15,-2]"},"fields":{"title":"Outer and Lexically Shadowed Values","stem":"All operations and evaluations are exact in Q, not truncated natural-number arithmetic. Outer x=4, locally shadowing inner x=-15, c=-2. Give (outer x+c, inner x+c) as integers; the inner binding does not mutate the outer one.","answer":{"kind":"expression","value":"(2, -17)","explanation":"Use each scope’s own binding before adding c; lexical shadowing is not assignment to the outer environment. The exact result, retaining the requested order, is (2, -17)."},"skills":["Outer and Lexically Shadowed Values"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r03-variable-expression-0068","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"457606ff7e7911741671cf8076c8ddccc710cd8aada4aa07a2ea1fa1585f0894","family_id":"qf-density11-expression-local-shadow-pair","seed":202610113068,"semantic_template":"qf-density11-expression-local-shadow-pair/[5,-16,-1]"},"fields":{"title":"Outer and Lexically Shadowed Values","stem":"All operations and evaluations are exact in Q, not truncated natural-number arithmetic. Outer x=5, locally shadowing inner x=-16, c=-1. Give (outer x+c, inner x+c) as integers; the inner binding does not mutate the outer one.","answer":{"kind":"expression","value":"(4, -17)","explanation":"Use each scope’s own binding before adding c; lexical shadowing is not assignment to the outer environment. The exact result, retaining the requested order, is (4, -17)."},"skills":["Outer and Lexically Shadowed Values"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r03-variable-expression-0069","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"a32d089e8ec4b6d97a78956dc50a6c04829a04df819abaf0c11e5bdb7bc9df1d","family_id":"qf-density11-expression-local-shadow-pair","seed":202610113069,"semantic_template":"qf-density11-expression-local-shadow-pair/[6,-17,0]"},"fields":{"title":"Outer and Lexically Shadowed Values","stem":"All operations and evaluations are exact in Q, not truncated natural-number arithmetic. Outer x=6, locally shadowing inner x=-17, c=0. Give (outer x+c, inner x+c) as integers; the inner binding does not mutate the outer one.","answer":{"kind":"expression","value":"(6, -17)","explanation":"Use each scope’s own binding before adding c; lexical shadowing is not assignment to the outer environment. The exact result, retaining the requested order, is (6, -17)."},"skills":["Outer and Lexically Shadowed Values"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r03-variable-expression-0070","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"a0caf624e6d57e2b19cda6de2d0e50c23430b542eb200f91f4d6b1c3a4ae18c0","family_id":"qf-density11-expression-local-shadow-pair","seed":202610113070,"semantic_template":"qf-density11-expression-local-shadow-pair/[7,-18,1]"},"fields":{"title":"Outer and Lexically Shadowed Values","stem":"All operations and evaluations are exact in Q, not truncated natural-number arithmetic. Outer x=7, locally shadowing inner x=-18, c=1. Give (outer x+c, inner x+c) as integers; the inner binding does not mutate the outer one.","answer":{"kind":"expression","value":"(8, -17)","explanation":"Use each scope’s own binding before adding c; lexical shadowing is not assignment to the outer environment. The exact result, retaining the requested order, is (8, -17)."},"skills":["Outer and Lexically Shadowed Values"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r03-variable-expression-0071","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"65de72e45ce0c19c8a0a237ec6752d516bcc5d1ea1d24852f565683d59eacc38","family_id":"qf-density11-expression-local-shadow-pair","seed":202610113071,"semantic_template":"qf-density11-expression-local-shadow-pair/[8,-19,-2]"},"fields":{"title":"Outer and Lexically Shadowed Values","stem":"All operations and evaluations are exact in Q, not truncated natural-number arithmetic. Outer x=8, locally shadowing inner x=-19, c=-2. Give (outer x+c, inner x+c) as integers; the inner binding does not mutate the outer one.","answer":{"kind":"expression","value":"(6, -21)","explanation":"Use each scope’s own binding before adding c; lexical shadowing is not assignment to the outer environment. The exact result, retaining the requested order, is (6, -21)."},"skills":["Outer and Lexically Shadowed Values"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r03-variable-expression-0072","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"22203a756ab143fa849547723155604b6a38d6ec02e85bd4a65851f3e7468249","family_id":"qf-density11-expression-local-shadow-pair","seed":202610113072,"semantic_template":"qf-density11-expression-local-shadow-pair/[9,-20,-1]"},"fields":{"title":"Outer and Lexically Shadowed Values","stem":"All operations and evaluations are exact in Q, not truncated natural-number arithmetic. Outer x=9, locally shadowing inner x=-20, c=-1. Give (outer x+c, inner x+c) as integers; the inner binding does not mutate the outer one.","answer":{"kind":"expression","value":"(8, -21)","explanation":"Use each scope’s own binding before adding c; lexical shadowing is not assignment to the outer environment. The exact result, retaining the requested order, is (8, -21)."},"skills":["Outer and Lexically Shadowed Values"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r03-variable-expression-0073","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"1cecd8d78a13d5b9aa200b9775c01403a94f91e34384522d948d3639581a495a","family_id":"qf-density11-expression-local-shadow-pair","seed":202610113073,"semantic_template":"qf-density11-expression-local-shadow-pair/[10,-21,0]"},"fields":{"title":"Outer and Lexically Shadowed Values","stem":"All operations and evaluations are exact in Q, not truncated natural-number arithmetic. Outer x=10, locally shadowing inner x=-21, c=0. Give (outer x+c, inner x+c) as integers; the inner binding does not mutate the outer one.","answer":{"kind":"expression","value":"(10, -21)","explanation":"Use each scope’s own binding before adding c; lexical shadowing is not assignment to the outer environment. The exact result, retaining the requested order, is (10, -21)."},"skills":["Outer and Lexically Shadowed Values"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r03-variable-expression-0074","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"d9902c8e432e3754b3ed898b5e95094c979bdf11f490395e55254a171478b786","family_id":"qf-density11-expression-local-shadow-pair","seed":202610113074,"semantic_template":"qf-density11-expression-local-shadow-pair/[11,-22,1]"},"fields":{"title":"Outer and Lexically Shadowed Values","stem":"All operations and evaluations are exact in Q, not truncated natural-number arithmetic. Outer x=11, locally shadowing inner x=-22, c=1. Give (outer x+c, inner x+c) as integers; the inner binding does not mutate the outer one.","answer":{"kind":"expression","value":"(12, -21)","explanation":"Use each scope’s own binding before adding c; lexical shadowing is not assignment to the outer environment. The exact result, retaining the requested order, is (12, -21)."},"skills":["Outer and Lexically Shadowed Values"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r03-variable-expression-0075","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"7e58c922badcd96f73728315010dfe716877fab62ef0c6fc26e8dfee0234ed40","family_id":"qf-density11-expression-local-shadow-pair","seed":202610113075,"semantic_template":"qf-density11-expression-local-shadow-pair/[12,-23,-2]"},"fields":{"title":"Outer and Lexically Shadowed Values","stem":"All operations and evaluations are exact in Q, not truncated natural-number arithmetic. Outer x=12, locally shadowing inner x=-23, c=-2. Give (outer x+c, inner x+c) as integers; the inner binding does not mutate the outer one.","answer":{"kind":"expression","value":"(10, -25)","explanation":"Use each scope’s own binding before adding c; lexical shadowing is not assignment to the outer environment. The exact result, retaining the requested order, is (10, -25)."},"skills":["Outer and Lexically Shadowed Values"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r03-variable-expression-0076","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"eb12dd99ef6492efe2b570e98b06185dd6b411450bd1a1274d0402a2c122542d","family_id":"qf-density11-expression-domain-candidate","seed":202610113076,"semantic_template":"qf-density11-expression-domain-candidate/[\"zero_numerator\",[\"hole\",\"valid\",\"valid\"]]"},"fields":{"title":"Original Rational-Expression Domain Guard","stem":"All operations and evaluations are exact in Q, not truncated natural-number arithmetic. The original expression is E(x)=(0)/(x−(1)), excluding x=1. Ordered candidates=[1/1, 2/1, 0/1]. Give (three domain-eligibility values, three E values or undefined).","answer":{"kind":"expression","value":"([No, Yes, Yes], [undefined, 0/1, 0/1])","explanation":"Check the original excluded point before evaluating; even a zero numerator cannot fill a denominator-zero hole or extend the original domain. The exact result, retaining the requested order, is ([No, Yes, Yes], [undefined, 0/1, 0/1])."},"skills":["Original Rational-Expression Domain Guard"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r03-variable-expression-0077","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"23d7afab8cc0a4f7b8935ce5ea1a5a1989c475ada08c8ad3f25fe6430a4690fe","family_id":"qf-density11-expression-domain-candidate","seed":202610113077,"semantic_template":"qf-density11-expression-domain-candidate/[\"all_holes\"]"},"fields":{"title":"Original Rational-Expression Domain Guard","stem":"All operations and evaluations are exact in Q, not truncated natural-number arithmetic. The original expression is E(x)=(5)/(x−(-2)), excluding x=-2. Ordered candidates=[-2/1, -2/1, -2/1]. Give (three domain-eligibility values, three E values or undefined).","answer":{"kind":"expression","value":"([No, No, No], [undefined, undefined, undefined])","explanation":"Check the original excluded point before evaluating; even a zero numerator cannot fill a denominator-zero hole or extend the original domain. The exact result, retaining the requested order, is ([No, No, No], [undefined, undefined, undefined])."},"skills":["Original Rational-Expression Domain Guard"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r03-variable-expression-0078","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"67c495f500be04df215770bf3d86d730cba934f704924e1874d43e7378d69c97","family_id":"qf-density11-expression-domain-candidate","seed":202610113078,"semantic_template":"qf-density11-expression-domain-candidate/[2,[\"0/1\",\"1/1\",\"-1/1\"]]"},"fields":{"title":"Original Rational-Expression Domain Guard","stem":"All operations and evaluations are exact in Q, not truncated natural-number arithmetic. The original expression is E(x)=(2)/(x−(0)), excluding x=0. Ordered candidates=[0/1, 1/1, -1/1]. Give (three domain-eligibility values, three E values or undefined).","answer":{"kind":"expression","value":"([No, Yes, Yes], [undefined, 2/1, -2/1])","explanation":"Check the original excluded point before evaluating; even a zero numerator cannot fill a denominator-zero hole or extend the original domain. The exact result, retaining the requested order, is ([No, Yes, Yes], [undefined, 2/1, -2/1])."},"skills":["Original Rational-Expression Domain Guard"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r03-variable-expression-0079","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"1fe974faba012190454cb42c464060038014aff85e020a0ec0049a9f52bdc4fa","family_id":"qf-density11-expression-domain-candidate","seed":202610113079,"semantic_template":"qf-density11-expression-domain-candidate/[2,[\"0/1\",\"2/1\",\"-5/1\"]]"},"fields":{"title":"Original Rational-Expression Domain Guard","stem":"All operations and evaluations are exact in Q, not truncated natural-number arithmetic. The original expression is E(x)=(2)/(x−(1)), excluding x=1. Ordered candidates=[1/1, 6/2, -4/1]. Give (three domain-eligibility values, three E values or undefined).","answer":{"kind":"expression","value":"([No, Yes, Yes], [undefined, 1/1, -2/5])","explanation":"Check the original excluded point before evaluating; even a zero numerator cannot fill a denominator-zero hole or extend the original domain. The exact result, retaining the requested order, is ([No, Yes, Yes], [undefined, 1/1, -2/5])."},"skills":["Original Rational-Expression Domain Guard"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r03-variable-expression-0080","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"4217d6db71a15677515435c2f42b2e330a6b7132e638470373185c887f65bcaf","family_id":"qf-density11-expression-domain-candidate","seed":202610113080,"semantic_template":"qf-density11-expression-domain-candidate/[3,[\"0/1\",\"5/2\",\"-6/1\"]]"},"fields":{"title":"Original Rational-Expression Domain Guard","stem":"All operations and evaluations are exact in Q, not truncated natural-number arithmetic. The original expression is E(x)=(3)/(x−(2)), excluding x=2. Ordered candidates=[2/1, 9/2, -4/1]. Give (three domain-eligibility values, three E values or undefined).","answer":{"kind":"expression","value":"([No, Yes, Yes], [undefined, 6/5, -1/2])","explanation":"Check the original excluded point before evaluating; even a zero numerator cannot fill a denominator-zero hole or extend the original domain. The exact result, retaining the requested order, is ([No, Yes, Yes], [undefined, 6/5, -1/2])."},"skills":["Original Rational-Expression Domain Guard"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r03-variable-expression-0081","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"a81fd33fb2e52ecacd372a10fc1b3cb83f826e189d9fdbb7fe75d271f6c67a77","family_id":"qf-density11-expression-domain-candidate","seed":202610113081,"semantic_template":"qf-density11-expression-domain-candidate/[4,[\"0/1\",\"3/1\",\"-7/1\"]]"},"fields":{"title":"Original Rational-Expression Domain Guard","stem":"All operations and evaluations are exact in Q, not truncated natural-number arithmetic. The original expression is E(x)=(4)/(x−(-2)), excluding x=-2. Ordered candidates=[-2/1, 2/2, -9/1]. Give (three domain-eligibility values, three E values or undefined).","answer":{"kind":"expression","value":"([No, Yes, Yes], [undefined, 4/3, -4/7])","explanation":"Check the original excluded point before evaluating; even a zero numerator cannot fill a denominator-zero hole or extend the original domain. The exact result, retaining the requested order, is ([No, Yes, Yes], [undefined, 4/3, -4/7])."},"skills":["Original Rational-Expression Domain Guard"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r03-variable-expression-0082","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"4e2024136e1745b6ec8a9b37daf26a2eb023fb2a34169e802b830af4f2df57ef","family_id":"qf-density11-expression-domain-candidate","seed":202610113082,"semantic_template":"qf-density11-expression-domain-candidate/[5,[\"0/1\",\"7/2\",\"-8/1\"]]"},"fields":{"title":"Original Rational-Expression Domain Guard","stem":"All operations and evaluations are exact in Q, not truncated natural-number arithmetic. The original expression is E(x)=(5)/(x−(-1)), excluding x=-1. Ordered candidates=[-1/1, 5/2, -9/1]. Give (three domain-eligibility values, three E values or undefined).","answer":{"kind":"expression","value":"([No, Yes, Yes], [undefined, 10/7, -5/8])","explanation":"Check the original excluded point before evaluating; even a zero numerator cannot fill a denominator-zero hole or extend the original domain. The exact result, retaining the requested order, is ([No, Yes, Yes], [undefined, 10/7, -5/8])."},"skills":["Original Rational-Expression Domain Guard"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r03-variable-expression-0083","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"c07bf517038b026c611b507e6ac27b0df05df57d9e5905750bd79164dd4634fe","family_id":"qf-density11-expression-domain-candidate","seed":202610113083,"semantic_template":"qf-density11-expression-domain-candidate/[6,[\"0/1\",\"4/1\",\"-9/1\"]]"},"fields":{"title":"Original Rational-Expression Domain Guard","stem":"All operations and evaluations are exact in Q, not truncated natural-number arithmetic. The original expression is E(x)=(6)/(x−(0)), excluding x=0. Ordered candidates=[0/1, 8/2, -9/1]. Give (three domain-eligibility values, three E values or undefined).","answer":{"kind":"expression","value":"([No, Yes, Yes], [undefined, 3/2, -2/3])","explanation":"Check the original excluded point before evaluating; even a zero numerator cannot fill a denominator-zero hole or extend the original domain. The exact result, retaining the requested order, is ([No, Yes, Yes], [undefined, 3/2, -2/3])."},"skills":["Original Rational-Expression Domain Guard"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r03-variable-expression-0084","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"a8d421af7ec5af99b0daf9fa56874671aa28012edcd3f4f5787feb01c2cb39f8","family_id":"qf-density11-expression-domain-candidate","seed":202610113084,"semantic_template":"qf-density11-expression-domain-candidate/[7,[\"0/1\",\"9/2\",\"-10/1\"]]"},"fields":{"title":"Original Rational-Expression Domain Guard","stem":"All operations and evaluations are exact in Q, not truncated natural-number arithmetic. The original expression is E(x)=(7)/(x−(1)), excluding x=1. Ordered candidates=[1/1, 11/2, -9/1]. Give (three domain-eligibility values, three E values or undefined).","answer":{"kind":"expression","value":"([No, Yes, Yes], [undefined, 14/9, -7/10])","explanation":"Check the original excluded point before evaluating; even a zero numerator cannot fill a denominator-zero hole or extend the original domain. The exact result, retaining the requested order, is ([No, Yes, Yes], [undefined, 14/9, -7/10])."},"skills":["Original Rational-Expression Domain Guard"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r03-variable-expression-0085","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"54fe10a96460ac189ea937efcb063d1c1493a702809a11a53e6ddab4fb90f80c","family_id":"qf-density11-expression-domain-candidate","seed":202610113085,"semantic_template":"qf-density11-expression-domain-candidate/[8,[\"0/1\",\"5/1\",\"-11/1\"]]"},"fields":{"title":"Original Rational-Expression Domain Guard","stem":"All operations and evaluations are exact in Q, not truncated natural-number arithmetic. The original expression is E(x)=(8)/(x−(2)), excluding x=2. Ordered candidates=[2/1, 14/2, -9/1]. Give (three domain-eligibility values, three E values or undefined).","answer":{"kind":"expression","value":"([No, Yes, Yes], [undefined, 8/5, -8/11])","explanation":"Check the original excluded point before evaluating; even a zero numerator cannot fill a denominator-zero hole or extend the original domain. The exact result, retaining the requested order, is ([No, Yes, Yes], [undefined, 8/5, -8/11])."},"skills":["Original Rational-Expression Domain Guard"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r03-variable-expression-0086","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"cdb97dbf745818980aab4f2589d4046c28f24b90f93074753a2bc49765eb16be","family_id":"qf-density11-expression-domain-candidate","seed":202610113086,"semantic_template":"qf-density11-expression-domain-candidate/[9,[\"0/1\",\"11/2\",\"-12/1\"]]"},"fields":{"title":"Original Rational-Expression Domain Guard","stem":"All operations and evaluations are exact in Q, not truncated natural-number arithmetic. The original expression is E(x)=(9)/(x−(-2)), excluding x=-2. Ordered candidates=[-2/1, 7/2, -14/1]. Give (three domain-eligibility values, three E values or undefined).","answer":{"kind":"expression","value":"([No, Yes, Yes], [undefined, 18/11, -3/4])","explanation":"Check the original excluded point before evaluating; even a zero numerator cannot fill a denominator-zero hole or extend the original domain. The exact result, retaining the requested order, is ([No, Yes, Yes], [undefined, 18/11, -3/4])."},"skills":["Original Rational-Expression Domain Guard"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r03-variable-expression-0087","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"5178b09d60b0a457848f8248a1e9cf7a0c58dbea9a3568854ac5350ae67b41cc","family_id":"qf-density11-expression-domain-candidate","seed":202610113087,"semantic_template":"qf-density11-expression-domain-candidate/[10,[\"0/1\",\"6/1\",\"-13/1\"]]"},"fields":{"title":"Original Rational-Expression Domain Guard","stem":"All operations and evaluations are exact in Q, not truncated natural-number arithmetic. The original expression is E(x)=(10)/(x−(-1)), excluding x=-1. Ordered candidates=[-1/1, 10/2, -14/1]. Give (three domain-eligibility values, three E values or undefined).","answer":{"kind":"expression","value":"([No, Yes, Yes], [undefined, 5/3, -10/13])","explanation":"Check the original excluded point before evaluating; even a zero numerator cannot fill a denominator-zero hole or extend the original domain. The exact result, retaining the requested order, is ([No, Yes, Yes], [undefined, 5/3, -10/13])."},"skills":["Original Rational-Expression Domain Guard"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r03-variable-expression-0088","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"a146de269fed7e6890f52fe4f8670fc4e767eca6b491ab214c2a353e66af941a","family_id":"qf-density11-expression-domain-candidate","seed":202610113088,"semantic_template":"qf-density11-expression-domain-candidate/[11,[\"0/1\",\"13/2\",\"-14/1\"]]"},"fields":{"title":"Original Rational-Expression Domain Guard","stem":"All operations and evaluations are exact in Q, not truncated natural-number arithmetic. The original expression is E(x)=(11)/(x−(0)), excluding x=0. Ordered candidates=[0/1, 13/2, -14/1]. Give (three domain-eligibility values, three E values or undefined).","answer":{"kind":"expression","value":"([No, Yes, Yes], [undefined, 22/13, -11/14])","explanation":"Check the original excluded point before evaluating; even a zero numerator cannot fill a denominator-zero hole or extend the original domain. The exact result, retaining the requested order, is ([No, Yes, Yes], [undefined, 22/13, -11/14])."},"skills":["Original Rational-Expression Domain Guard"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r03-variable-expression-0089","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"a0b0e5b1f1d9c435fd77328661f7a325ef621426f7ca31ef435dcf3d6b346cd2","family_id":"qf-density11-expression-domain-candidate","seed":202610113089,"semantic_template":"qf-density11-expression-domain-candidate/[12,[\"0/1\",\"7/1\",\"-15/1\"]]"},"fields":{"title":"Original Rational-Expression Domain Guard","stem":"All operations and evaluations are exact in Q, not truncated natural-number arithmetic. The original expression is E(x)=(12)/(x−(1)), excluding x=1. Ordered candidates=[1/1, 16/2, -14/1]. Give (three domain-eligibility values, three E values or undefined).","answer":{"kind":"expression","value":"([No, Yes, Yes], [undefined, 12/7, -4/5])","explanation":"Check the original excluded point before evaluating; even a zero numerator cannot fill a denominator-zero hole or extend the original domain. The exact result, retaining the requested order, is ([No, Yes, Yes], [undefined, 12/7, -4/5])."},"skills":["Original Rational-Expression Domain Guard"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r03-variable-expression-0090","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"4d8b3d5ffdcb8c17c723d8265d757ae934168ab1604a0aee8d3092366c189de1","family_id":"qf-density11-expression-domain-candidate","seed":202610113090,"semantic_template":"qf-density11-expression-domain-candidate/[13,[\"0/1\",\"15/2\",\"-16/1\"]]"},"fields":{"title":"Original Rational-Expression Domain Guard","stem":"All operations and evaluations are exact in Q, not truncated natural-number arithmetic. The original expression is E(x)=(13)/(x−(2)), excluding x=2. Ordered candidates=[2/1, 19/2, -14/1]. Give (three domain-eligibility values, three E values or undefined).","answer":{"kind":"expression","value":"([No, Yes, Yes], [undefined, 26/15, -13/16])","explanation":"Check the original excluded point before evaluating; even a zero numerator cannot fill a denominator-zero hole or extend the original domain. The exact result, retaining the requested order, is ([No, Yes, Yes], [undefined, 26/15, -13/16])."},"skills":["Original Rational-Expression Domain Guard"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r03-variable-expression-0091","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"4edfe36360c67e594c34ccaa485b0ffee38aa90f1eabb3d14b48e641c66a1f4d","family_id":"qf-density11-expression-domain-candidate","seed":202610113091,"semantic_template":"qf-density11-expression-domain-candidate/[14,[\"0/1\",\"8/1\",\"-17/1\"]]"},"fields":{"title":"Original Rational-Expression Domain Guard","stem":"All operations and evaluations are exact in Q, not truncated natural-number arithmetic. The original expression is E(x)=(14)/(x−(-2)), excluding x=-2. Ordered candidates=[-2/1, 12/2, -19/1]. Give (three domain-eligibility values, three E values or undefined).","answer":{"kind":"expression","value":"([No, Yes, Yes], [undefined, 7/4, -14/17])","explanation":"Check the original excluded point before evaluating; even a zero numerator cannot fill a denominator-zero hole or extend the original domain. The exact result, retaining the requested order, is ([No, Yes, Yes], [undefined, 7/4, -14/17])."},"skills":["Original Rational-Expression Domain Guard"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r03-variable-expression-0092","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"2739472cf60c0b162627cbfb2ddcedbb94048e64cff1f84b90a8b2fc624355eb","family_id":"qf-density11-expression-domain-candidate","seed":202610113092,"semantic_template":"qf-density11-expression-domain-candidate/[15,[\"0/1\",\"17/2\",\"-18/1\"]]"},"fields":{"title":"Original Rational-Expression Domain Guard","stem":"All operations and evaluations are exact in Q, not truncated natural-number arithmetic. The original expression is E(x)=(15)/(x−(-1)), excluding x=-1. Ordered candidates=[-1/1, 15/2, -19/1]. Give (three domain-eligibility values, three E values or undefined).","answer":{"kind":"expression","value":"([No, Yes, Yes], [undefined, 30/17, -5/6])","explanation":"Check the original excluded point before evaluating; even a zero numerator cannot fill a denominator-zero hole or extend the original domain. The exact result, retaining the requested order, is ([No, Yes, Yes], [undefined, 30/17, -5/6])."},"skills":["Original Rational-Expression Domain Guard"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r03-variable-expression-0093","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"6bd3e91e91eb08d0826aa0685235448d586180a6dcf14642d871361f85975195","family_id":"qf-density11-expression-domain-candidate","seed":202610113093,"semantic_template":"qf-density11-expression-domain-candidate/[16,[\"0/1\",\"9/1\",\"-19/1\"]]"},"fields":{"title":"Original Rational-Expression Domain Guard","stem":"All operations and evaluations are exact in Q, not truncated natural-number arithmetic. The original expression is E(x)=(16)/(x−(0)), excluding x=0. Ordered candidates=[0/1, 18/2, -19/1]. Give (three domain-eligibility values, three E values or undefined).","answer":{"kind":"expression","value":"([No, Yes, Yes], [undefined, 16/9, -16/19])","explanation":"Check the original excluded point before evaluating; even a zero numerator cannot fill a denominator-zero hole or extend the original domain. The exact result, retaining the requested order, is ([No, Yes, Yes], [undefined, 16/9, -16/19])."},"skills":["Original Rational-Expression Domain Guard"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r03-variable-expression-0094","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"8c894c1b4cc51b439a030073ea65dced92fde2e9407a859519850aaab74d9be6","family_id":"qf-density11-expression-domain-candidate","seed":202610113094,"semantic_template":"qf-density11-expression-domain-candidate/[17,[\"0/1\",\"19/2\",\"-20/1\"]]"},"fields":{"title":"Original Rational-Expression Domain Guard","stem":"All operations and evaluations are exact in Q, not truncated natural-number arithmetic. The original expression is E(x)=(17)/(x−(1)), excluding x=1. Ordered candidates=[1/1, 21/2, -19/1]. Give (three domain-eligibility values, three E values or undefined).","answer":{"kind":"expression","value":"([No, Yes, Yes], [undefined, 34/19, -17/20])","explanation":"Check the original excluded point before evaluating; even a zero numerator cannot fill a denominator-zero hole or extend the original domain. The exact result, retaining the requested order, is ([No, Yes, Yes], [undefined, 34/19, -17/20])."},"skills":["Original Rational-Expression Domain Guard"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r03-variable-expression-0095","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"507a126860f2afa6060133fe8ad845637f563d7b42f75e29b00b2feca136e545","family_id":"qf-density11-expression-domain-candidate","seed":202610113095,"semantic_template":"qf-density11-expression-domain-candidate/[18,[\"0/1\",\"10/1\",\"-21/1\"]]"},"fields":{"title":"Original Rational-Expression Domain Guard","stem":"All operations and evaluations are exact in Q, not truncated natural-number arithmetic. The original expression is E(x)=(18)/(x−(2)), excluding x=2. Ordered candidates=[2/1, 24/2, -19/1]. Give (three domain-eligibility values, three E values or undefined).","answer":{"kind":"expression","value":"([No, Yes, Yes], [undefined, 9/5, -6/7])","explanation":"Check the original excluded point before evaluating; even a zero numerator cannot fill a denominator-zero hole or extend the original domain. The exact result, retaining the requested order, is ([No, Yes, Yes], [undefined, 9/5, -6/7])."},"skills":["Original Rational-Expression Domain Guard"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r03-variable-expression-0096","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"337d6cef2db71bf613255b571089e43564fa5752d2615184dbf45fb093fafce0","family_id":"qf-density11-expression-domain-candidate","seed":202610113096,"semantic_template":"qf-density11-expression-domain-candidate/[19,[\"0/1\",\"21/2\",\"-22/1\"]]"},"fields":{"title":"Original Rational-Expression Domain Guard","stem":"All operations and evaluations are exact in Q, not truncated natural-number arithmetic. The original expression is E(x)=(19)/(x−(-2)), excluding x=-2. Ordered candidates=[-2/1, 17/2, -24/1]. Give (three domain-eligibility values, three E values or undefined).","answer":{"kind":"expression","value":"([No, Yes, Yes], [undefined, 38/21, -19/22])","explanation":"Check the original excluded point before evaluating; even a zero numerator cannot fill a denominator-zero hole or extend the original domain. The exact result, retaining the requested order, is ([No, Yes, Yes], [undefined, 38/21, -19/22])."},"skills":["Original Rational-Expression Domain Guard"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r03-variable-expression-0097","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"4c8d8770adfec052b06f4df3f8e13bedcc77994c677aefe7d694b2b0ad49d97d","family_id":"qf-density11-expression-domain-candidate","seed":202610113097,"semantic_template":"qf-density11-expression-domain-candidate/[20,[\"0/1\",\"11/1\",\"-23/1\"]]"},"fields":{"title":"Original Rational-Expression Domain Guard","stem":"All operations and evaluations are exact in Q, not truncated natural-number arithmetic. The original expression is E(x)=(20)/(x−(-1)), excluding x=-1. Ordered candidates=[-1/1, 20/2, -24/1]. Give (three domain-eligibility values, three E values or undefined).","answer":{"kind":"expression","value":"([No, Yes, Yes], [undefined, 20/11, -20/23])","explanation":"Check the original excluded point before evaluating; even a zero numerator cannot fill a denominator-zero hole or extend the original domain. The exact result, retaining the requested order, is ([No, Yes, Yes], [undefined, 20/11, -20/23])."},"skills":["Original Rational-Expression Domain Guard"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r03-variable-expression-0098","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"3e7c9530ad76ca79f61f233ad0ada2e5efdc572071f2a9eec84abe963b7a2a47","family_id":"qf-density11-expression-domain-candidate","seed":202610113098,"semantic_template":"qf-density11-expression-domain-candidate/[21,[\"0/1\",\"23/2\",\"-24/1\"]]"},"fields":{"title":"Original Rational-Expression Domain Guard","stem":"All operations and evaluations are exact in Q, not truncated natural-number arithmetic. The original expression is E(x)=(21)/(x−(0)), excluding x=0. Ordered candidates=[0/1, 23/2, -24/1]. Give (three domain-eligibility values, three E values or undefined).","answer":{"kind":"expression","value":"([No, Yes, Yes], [undefined, 42/23, -7/8])","explanation":"Check the original excluded point before evaluating; even a zero numerator cannot fill a denominator-zero hole or extend the original domain. The exact result, retaining the requested order, is ([No, Yes, Yes], [undefined, 42/23, -7/8])."},"skills":["Original Rational-Expression Domain Guard"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r03-variable-expression-0099","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"01f2844a23920bf4e0913b9ad834a2ea933bb97b26bd51bd5d710655a79a3163","family_id":"qf-density11-expression-domain-candidate","seed":202610113099,"semantic_template":"qf-density11-expression-domain-candidate/[22,[\"0/1\",\"12/1\",\"-25/1\"]]"},"fields":{"title":"Original Rational-Expression Domain Guard","stem":"All operations and evaluations are exact in Q, not truncated natural-number arithmetic. The original expression is E(x)=(22)/(x−(1)), excluding x=1. Ordered candidates=[1/1, 26/2, -24/1]. Give (three domain-eligibility values, three E values or undefined).","answer":{"kind":"expression","value":"([No, Yes, Yes], [undefined, 11/6, -22/25])","explanation":"Check the original excluded point before evaluating; even a zero numerator cannot fill a denominator-zero hole or extend the original domain. The exact result, retaining the requested order, is ([No, Yes, Yes], [undefined, 11/6, -22/25])."},"skills":["Original Rational-Expression Domain Guard"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261008-advance-20261011-r03-variable-expression-0100","batch_id":"batch-20261008-advance-20261011-r03-variable-expression-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"4ab66bd0896522bb644290841383aa6bd3c8a2d15c522521d7b722ead6983fdf","family_id":"qf-density11-expression-domain-candidate","seed":202610113100,"semantic_template":"qf-density11-expression-domain-candidate/[23,[\"0/1\",\"25/2\",\"-26/1\"]]"},"fields":{"title":"Original Rational-Expression Domain Guard","stem":"All operations and evaluations are exact in Q, not truncated natural-number arithmetic. The original expression is E(x)=(23)/(x−(2)), excluding x=2. Ordered candidates=[2/1, 29/2, -24/1]. Give (three domain-eligibility values, three E values or undefined).","answer":{"kind":"expression","value":"([No, Yes, Yes], [undefined, 46/25, -23/26])","explanation":"Check the original excluded point before evaluating; even a zero numerator cannot fill a denominator-zero hole or extend the original domain. The exact result, retaining the requested order, is ([No, Yes, Yes], [undefined, 46/25, -23/26])."},"skills":["Original Rational-Expression Domain Guard"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}