{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0001","batch_id":"batch-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"280926db42c7e32f243e9db3a1d24b299b8c5dba2fc382c1a381a5264aaf0682","family_id":"qf-app21-diagnostic-integer-sum-record","seed":202610212001,"semantic_template":"qf-app21-diagnostic-integer-sum-record/{\"a\":-12,\"b\":-9,\"response\":-20}"},"fields":{"title":"Synthetic Integer-Sum Response and Its Rule Code","stem":"Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. a=-12, b=-9, response=-20. Give (a,b,response,a+b,match?,matches_rule_expected or differs_from_rule_expected).","answer":{"kind":"expression","value":"(-12, -9, -20, -21, No, differs_from_rule_expected)","explanation":"Recompute the exact integer sum. A mismatched response licenses only the stated rule code, not a diagnosis of its author. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (-12, -9, -20, -21, No, differs_from_rule_expected)."},"skills":["Synthetic Integer-Sum Response and Its Rule Code"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0002","batch_id":"batch-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"a4d240fb6aa7fcec7ca0610c81ac354222e5720f38d5faa3dc0e39513adef792","family_id":"qf-app21-diagnostic-integer-sum-record","seed":202610212002,"semantic_template":"qf-app21-diagnostic-integer-sum-record/{\"a\":-11,\"b\":-7,\"response\":-18}"},"fields":{"title":"Synthetic Integer-Sum Response and Its Rule Code","stem":"Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. a=-11, b=-7, response=-18. Give (a,b,response,a+b,match?,matches_rule_expected or differs_from_rule_expected).","answer":{"kind":"expression","value":"(-11, -7, -18, -18, Yes, matches_rule_expected)","explanation":"Recompute the exact integer sum. A mismatched response licenses only the stated rule code, not a diagnosis of its author. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (-11, -7, -18, -18, Yes, matches_rule_expected)."},"skills":["Synthetic Integer-Sum Response and Its Rule Code"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0003","batch_id":"batch-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"05b462573efd9251ce30143bbd20a7344933c78165fcc5edad5c8445d1554df4","family_id":"qf-app21-diagnostic-integer-sum-record","seed":202610212003,"semantic_template":"qf-app21-diagnostic-integer-sum-record/{\"a\":-10,\"b\":-5,\"response\":-15}"},"fields":{"title":"Synthetic Integer-Sum Response and Its Rule Code","stem":"Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. a=-10, b=-5, response=-15. Give (a,b,response,a+b,match?,matches_rule_expected or differs_from_rule_expected).","answer":{"kind":"expression","value":"(-10, -5, -15, -15, Yes, matches_rule_expected)","explanation":"Recompute the exact integer sum. A mismatched response licenses only the stated rule code, not a diagnosis of its author. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (-10, -5, -15, -15, Yes, matches_rule_expected)."},"skills":["Synthetic Integer-Sum Response and Its Rule Code"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0004","batch_id":"batch-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"54a2baf840eb0797bab33d2c270579928dfaea4f0f49abc46469de4f4cbf7f37","family_id":"qf-app21-diagnostic-integer-sum-record","seed":202610212004,"semantic_template":"qf-app21-diagnostic-integer-sum-record/{\"a\":-9,\"b\":-3,\"response\":-11}"},"fields":{"title":"Synthetic Integer-Sum Response and Its Rule Code","stem":"Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. a=-9, b=-3, response=-11. Give (a,b,response,a+b,match?,matches_rule_expected or differs_from_rule_expected).","answer":{"kind":"expression","value":"(-9, -3, -11, -12, No, differs_from_rule_expected)","explanation":"Recompute the exact integer sum. A mismatched response licenses only the stated rule code, not a diagnosis of its author. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (-9, -3, -11, -12, No, differs_from_rule_expected)."},"skills":["Synthetic Integer-Sum Response and Its Rule Code"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0005","batch_id":"batch-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"114f5b07a1e2a946b700c507eaec92788a671a912211642b431407b78322f4ef","family_id":"qf-app21-diagnostic-integer-sum-record","seed":202610212005,"semantic_template":"qf-app21-diagnostic-integer-sum-record/{\"a\":-8,\"b\":-1,\"response\":-9}"},"fields":{"title":"Synthetic Integer-Sum Response and Its Rule Code","stem":"Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. a=-8, b=-1, response=-9. Give (a,b,response,a+b,match?,matches_rule_expected or differs_from_rule_expected).","answer":{"kind":"expression","value":"(-8, -1, -9, -9, Yes, matches_rule_expected)","explanation":"Recompute the exact integer sum. A mismatched response licenses only the stated rule code, not a diagnosis of its author. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (-8, -1, -9, -9, Yes, matches_rule_expected)."},"skills":["Synthetic Integer-Sum Response and Its Rule Code"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0006","batch_id":"batch-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"d8736e8e700b668779ca15dc3246e9a62586c9e91a66cf9d57b12b397da1a154","family_id":"qf-app21-diagnostic-integer-sum-record","seed":202610212006,"semantic_template":"qf-app21-diagnostic-integer-sum-record/{\"a\":-7,\"b\":1,\"response\":-6}"},"fields":{"title":"Synthetic Integer-Sum Response and Its Rule Code","stem":"Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. a=-7, b=1, response=-6. Give (a,b,response,a+b,match?,matches_rule_expected or differs_from_rule_expected).","answer":{"kind":"expression","value":"(-7, 1, -6, -6, Yes, matches_rule_expected)","explanation":"Recompute the exact integer sum. A mismatched response licenses only the stated rule code, not a diagnosis of its author. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (-7, 1, -6, -6, Yes, matches_rule_expected)."},"skills":["Synthetic Integer-Sum Response and Its Rule Code"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0007","batch_id":"batch-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"2f8481a130d5fe7eeb3ef864ceea7736b892652de42042b403b06e1f591b76f1","family_id":"qf-app21-diagnostic-integer-sum-record","seed":202610212007,"semantic_template":"qf-app21-diagnostic-integer-sum-record/{\"a\":-6,\"b\":3,\"response\":-2}"},"fields":{"title":"Synthetic Integer-Sum Response and Its Rule Code","stem":"Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. a=-6, b=3, response=-2. Give (a,b,response,a+b,match?,matches_rule_expected or differs_from_rule_expected).","answer":{"kind":"expression","value":"(-6, 3, -2, -3, No, differs_from_rule_expected)","explanation":"Recompute the exact integer sum. A mismatched response licenses only the stated rule code, not a diagnosis of its author. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (-6, 3, -2, -3, No, differs_from_rule_expected)."},"skills":["Synthetic Integer-Sum Response and Its Rule Code"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0008","batch_id":"batch-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"000766ff8f66086931b6e42d0f5bd18d2fa4b1a0d5f9bcbf3b79a57fe45e63c3","family_id":"qf-app21-diagnostic-integer-sum-record","seed":202610212008,"semantic_template":"qf-app21-diagnostic-integer-sum-record/{\"a\":-5,\"b\":5,\"response\":0}"},"fields":{"title":"Synthetic Integer-Sum Response and Its Rule Code","stem":"Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. a=-5, b=5, response=0. Give (a,b,response,a+b,match?,matches_rule_expected or differs_from_rule_expected).","answer":{"kind":"expression","value":"(-5, 5, 0, 0, Yes, matches_rule_expected)","explanation":"Recompute the exact integer sum. A mismatched response licenses only the stated rule code, not a diagnosis of its author. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (-5, 5, 0, 0, Yes, matches_rule_expected)."},"skills":["Synthetic Integer-Sum Response and Its Rule Code"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0009","batch_id":"batch-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"a54818406021b6b7a1dc44fd7bebb80e939c8e856a1eb23631f7e7ca0f1be1bf","family_id":"qf-app21-diagnostic-integer-sum-record","seed":202610212009,"semantic_template":"qf-app21-diagnostic-integer-sum-record/{\"a\":-4,\"b\":7,\"response\":3}"},"fields":{"title":"Synthetic Integer-Sum Response and Its Rule Code","stem":"Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. a=-4, b=7, response=3. Give (a,b,response,a+b,match?,matches_rule_expected or differs_from_rule_expected).","answer":{"kind":"expression","value":"(-4, 7, 3, 3, Yes, matches_rule_expected)","explanation":"Recompute the exact integer sum. A mismatched response licenses only the stated rule code, not a diagnosis of its author. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (-4, 7, 3, 3, Yes, matches_rule_expected)."},"skills":["Synthetic Integer-Sum Response and Its Rule Code"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0010","batch_id":"batch-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"f0287f9b6c5a02264a7737b46742c3b7dd7590e0addbf5e43c0aaf65551f86d2","family_id":"qf-app21-diagnostic-integer-sum-record","seed":202610212010,"semantic_template":"qf-app21-diagnostic-integer-sum-record/{\"a\":-3,\"b\":9,\"response\":7}"},"fields":{"title":"Synthetic Integer-Sum Response and Its Rule Code","stem":"Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. a=-3, b=9, response=7. Give (a,b,response,a+b,match?,matches_rule_expected or differs_from_rule_expected).","answer":{"kind":"expression","value":"(-3, 9, 7, 6, No, differs_from_rule_expected)","explanation":"Recompute the exact integer sum. A mismatched response licenses only the stated rule code, not a diagnosis of its author. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (-3, 9, 7, 6, No, differs_from_rule_expected)."},"skills":["Synthetic Integer-Sum Response and Its Rule Code"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0011","batch_id":"batch-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"ad3970c67455c2cdbada2895195222eb0ed930fbd1db2330f5dd8263643eb05d","family_id":"qf-app21-diagnostic-integer-sum-record","seed":202610212011,"semantic_template":"qf-app21-diagnostic-integer-sum-record/{\"a\":-2,\"b\":11,\"response\":9}"},"fields":{"title":"Synthetic Integer-Sum Response and Its Rule Code","stem":"Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. a=-2, b=11, response=9. Give (a,b,response,a+b,match?,matches_rule_expected or differs_from_rule_expected).","answer":{"kind":"expression","value":"(-2, 11, 9, 9, Yes, matches_rule_expected)","explanation":"Recompute the exact integer sum. A mismatched response licenses only the stated rule code, not a diagnosis of its author. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (-2, 11, 9, 9, Yes, matches_rule_expected)."},"skills":["Synthetic Integer-Sum Response and Its Rule Code"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0012","batch_id":"batch-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"3b935da3f1c78dfd44b35f70367729bd4052ffe0587f46ccf4e7ae57941a577d","family_id":"qf-app21-diagnostic-integer-sum-record","seed":202610212012,"semantic_template":"qf-app21-diagnostic-integer-sum-record/{\"a\":-1,\"b\":13,\"response\":12}"},"fields":{"title":"Synthetic Integer-Sum Response and Its Rule Code","stem":"Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. a=-1, b=13, response=12. Give (a,b,response,a+b,match?,matches_rule_expected or differs_from_rule_expected).","answer":{"kind":"expression","value":"(-1, 13, 12, 12, Yes, matches_rule_expected)","explanation":"Recompute the exact integer sum. A mismatched response licenses only the stated rule code, not a diagnosis of its author. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (-1, 13, 12, 12, Yes, matches_rule_expected)."},"skills":["Synthetic Integer-Sum Response and Its Rule Code"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0013","batch_id":"batch-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"3dc28aaa4ff1fa55ac05a3d10461316a7640974ef4bd8ee8f31d96cd8ffa7238","family_id":"qf-app21-diagnostic-integer-sum-record","seed":202610212013,"semantic_template":"qf-app21-diagnostic-integer-sum-record/{\"a\":0,\"b\":15,\"response\":16}"},"fields":{"title":"Synthetic Integer-Sum Response and Its Rule Code","stem":"Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. a=0, b=15, response=16. Give (a,b,response,a+b,match?,matches_rule_expected or differs_from_rule_expected).","answer":{"kind":"expression","value":"(0, 15, 16, 15, No, differs_from_rule_expected)","explanation":"Recompute the exact integer sum. A mismatched response licenses only the stated rule code, not a diagnosis of its author. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (0, 15, 16, 15, No, differs_from_rule_expected)."},"skills":["Synthetic Integer-Sum Response and Its Rule Code"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0014","batch_id":"batch-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"704170834b628a9cc2aacf4c89e0305ff5d9c07c6643a17c9ca8ec1a569764ca","family_id":"qf-app21-diagnostic-integer-sum-record","seed":202610212014,"semantic_template":"qf-app21-diagnostic-integer-sum-record/{\"a\":1,\"b\":17,\"response\":18}"},"fields":{"title":"Synthetic Integer-Sum Response and Its Rule Code","stem":"Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. a=1, b=17, response=18. Give (a,b,response,a+b,match?,matches_rule_expected or differs_from_rule_expected).","answer":{"kind":"expression","value":"(1, 17, 18, 18, Yes, matches_rule_expected)","explanation":"Recompute the exact integer sum. A mismatched response licenses only the stated rule code, not a diagnosis of its author. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (1, 17, 18, 18, Yes, matches_rule_expected)."},"skills":["Synthetic Integer-Sum Response and Its Rule Code"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0015","batch_id":"batch-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"685b2d32991406ac4f4deb19d6dbbfc1c782c720c249fdac58e62fed1fe688cc","family_id":"qf-app21-diagnostic-integer-sum-record","seed":202610212015,"semantic_template":"qf-app21-diagnostic-integer-sum-record/{\"a\":2,\"b\":19,\"response\":21}"},"fields":{"title":"Synthetic Integer-Sum Response and Its Rule Code","stem":"Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. a=2, b=19, response=21. Give (a,b,response,a+b,match?,matches_rule_expected or differs_from_rule_expected).","answer":{"kind":"expression","value":"(2, 19, 21, 21, Yes, matches_rule_expected)","explanation":"Recompute the exact integer sum. A mismatched response licenses only the stated rule code, not a diagnosis of its author. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (2, 19, 21, 21, Yes, matches_rule_expected)."},"skills":["Synthetic Integer-Sum Response and Its Rule Code"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0016","batch_id":"batch-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"3ac06007ed4fb0fa03346645aa3124772dd50c3b0a4677427e7cff92712a4c08","family_id":"qf-app21-diagnostic-integer-sum-record","seed":202610212016,"semantic_template":"qf-app21-diagnostic-integer-sum-record/{\"a\":3,\"b\":21,\"response\":25}"},"fields":{"title":"Synthetic Integer-Sum Response and Its Rule Code","stem":"Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. a=3, b=21, response=25. Give (a,b,response,a+b,match?,matches_rule_expected or differs_from_rule_expected).","answer":{"kind":"expression","value":"(3, 21, 25, 24, No, differs_from_rule_expected)","explanation":"Recompute the exact integer sum. A mismatched response licenses only the stated rule code, not a diagnosis of its author. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (3, 21, 25, 24, No, differs_from_rule_expected)."},"skills":["Synthetic Integer-Sum Response and Its Rule Code"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0017","batch_id":"batch-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"401c9cf9d4fe369525ce8e8b05d2b684610c9592809fab415b8d6bab9a4ad59a","family_id":"qf-app21-diagnostic-integer-sum-record","seed":202610212017,"semantic_template":"qf-app21-diagnostic-integer-sum-record/{\"a\":4,\"b\":23,\"response\":27}"},"fields":{"title":"Synthetic Integer-Sum Response and Its Rule Code","stem":"Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. a=4, b=23, response=27. Give (a,b,response,a+b,match?,matches_rule_expected or differs_from_rule_expected).","answer":{"kind":"expression","value":"(4, 23, 27, 27, Yes, matches_rule_expected)","explanation":"Recompute the exact integer sum. A mismatched response licenses only the stated rule code, not a diagnosis of its author. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (4, 23, 27, 27, Yes, matches_rule_expected)."},"skills":["Synthetic Integer-Sum Response and Its Rule Code"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0018","batch_id":"batch-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"be75e18eb149f6d44d7fd5b867dedcf304ab210470108f343c9c824324ba8215","family_id":"qf-app21-diagnostic-integer-sum-record","seed":202610212018,"semantic_template":"qf-app21-diagnostic-integer-sum-record/{\"a\":5,\"b\":25,\"response\":30}"},"fields":{"title":"Synthetic Integer-Sum Response and Its Rule Code","stem":"Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. a=5, b=25, response=30. Give (a,b,response,a+b,match?,matches_rule_expected or differs_from_rule_expected).","answer":{"kind":"expression","value":"(5, 25, 30, 30, Yes, matches_rule_expected)","explanation":"Recompute the exact integer sum. A mismatched response licenses only the stated rule code, not a diagnosis of its author. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (5, 25, 30, 30, Yes, matches_rule_expected)."},"skills":["Synthetic Integer-Sum Response and Its Rule Code"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0019","batch_id":"batch-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"7b58ab4a97ea56d0c33752c9bb26d34215caf94d92cfe6b5eec35d465813f9fc","family_id":"qf-app21-diagnostic-integer-sum-record","seed":202610212019,"semantic_template":"qf-app21-diagnostic-integer-sum-record/{\"a\":6,\"b\":27,\"response\":34}"},"fields":{"title":"Synthetic Integer-Sum Response and Its Rule Code","stem":"Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. a=6, b=27, response=34. Give (a,b,response,a+b,match?,matches_rule_expected or differs_from_rule_expected).","answer":{"kind":"expression","value":"(6, 27, 34, 33, No, differs_from_rule_expected)","explanation":"Recompute the exact integer sum. A mismatched response licenses only the stated rule code, not a diagnosis of its author. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (6, 27, 34, 33, No, differs_from_rule_expected)."},"skills":["Synthetic Integer-Sum Response and Its Rule Code"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0020","batch_id":"batch-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"b9fc5ded904931dcf2fbad350269cf5b3943cc2f80c414c7a3682267a20b452d","family_id":"qf-app21-diagnostic-integer-sum-record","seed":202610212020,"semantic_template":"qf-app21-diagnostic-integer-sum-record/{\"a\":7,\"b\":29,\"response\":36}"},"fields":{"title":"Synthetic Integer-Sum Response and Its Rule Code","stem":"Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. a=7, b=29, response=36. Give (a,b,response,a+b,match?,matches_rule_expected or differs_from_rule_expected).","answer":{"kind":"expression","value":"(7, 29, 36, 36, Yes, matches_rule_expected)","explanation":"Recompute the exact integer sum. A mismatched response licenses only the stated rule code, not a diagnosis of its author. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (7, 29, 36, 36, Yes, matches_rule_expected)."},"skills":["Synthetic Integer-Sum Response and Its Rule Code"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0021","batch_id":"batch-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"acfe97f683a259487b8f6c4b2b823a3da1ed5fc9ccebe61b03f7eaf0ac8a3a77","family_id":"qf-app21-diagnostic-integer-sum-record","seed":202610212021,"semantic_template":"qf-app21-diagnostic-integer-sum-record/{\"a\":8,\"b\":31,\"response\":39}"},"fields":{"title":"Synthetic Integer-Sum Response and Its Rule Code","stem":"Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. a=8, b=31, response=39. Give (a,b,response,a+b,match?,matches_rule_expected or differs_from_rule_expected).","answer":{"kind":"expression","value":"(8, 31, 39, 39, Yes, matches_rule_expected)","explanation":"Recompute the exact integer sum. A mismatched response licenses only the stated rule code, not a diagnosis of its author. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (8, 31, 39, 39, Yes, matches_rule_expected)."},"skills":["Synthetic Integer-Sum Response and Its Rule Code"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0022","batch_id":"batch-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"ef86b5d0219123113943c78864eeb89bb9550fcb3af241bc82796107e4b5cb8a","family_id":"qf-app21-diagnostic-integer-sum-record","seed":202610212022,"semantic_template":"qf-app21-diagnostic-integer-sum-record/{\"a\":9,\"b\":33,\"response\":43}"},"fields":{"title":"Synthetic Integer-Sum Response and Its Rule Code","stem":"Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. a=9, b=33, response=43. Give (a,b,response,a+b,match?,matches_rule_expected or differs_from_rule_expected).","answer":{"kind":"expression","value":"(9, 33, 43, 42, No, differs_from_rule_expected)","explanation":"Recompute the exact integer sum. A mismatched response licenses only the stated rule code, not a diagnosis of its author. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (9, 33, 43, 42, No, differs_from_rule_expected)."},"skills":["Synthetic Integer-Sum Response and Its Rule Code"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0023","batch_id":"batch-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"a2b7caecd9caad244d6e3191013829f35446fd15048c458e03c75ce3fc8ab0d4","family_id":"qf-app21-diagnostic-integer-sum-record","seed":202610212023,"semantic_template":"qf-app21-diagnostic-integer-sum-record/{\"a\":10,\"b\":35,\"response\":45}"},"fields":{"title":"Synthetic Integer-Sum Response and Its Rule Code","stem":"Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. a=10, b=35, response=45. Give (a,b,response,a+b,match?,matches_rule_expected or differs_from_rule_expected).","answer":{"kind":"expression","value":"(10, 35, 45, 45, Yes, matches_rule_expected)","explanation":"Recompute the exact integer sum. A mismatched response licenses only the stated rule code, not a diagnosis of its author. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (10, 35, 45, 45, Yes, matches_rule_expected)."},"skills":["Synthetic Integer-Sum Response and Its Rule Code"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0024","batch_id":"batch-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"9c45ce6c422e96831590de40fadd9970099d7c31339dd81ba57576449621f0af","family_id":"qf-app21-diagnostic-integer-sum-record","seed":202610212024,"semantic_template":"qf-app21-diagnostic-integer-sum-record/{\"a\":11,\"b\":37,\"response\":48}"},"fields":{"title":"Synthetic Integer-Sum Response and Its Rule Code","stem":"Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. a=11, b=37, response=48. Give (a,b,response,a+b,match?,matches_rule_expected or differs_from_rule_expected).","answer":{"kind":"expression","value":"(11, 37, 48, 48, Yes, matches_rule_expected)","explanation":"Recompute the exact integer sum. A mismatched response licenses only the stated rule code, not a diagnosis of its author. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (11, 37, 48, 48, Yes, matches_rule_expected)."},"skills":["Synthetic Integer-Sum Response and Its Rule Code"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0025","batch_id":"batch-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"b08084f3ca897dde67888292ce670177d906113abfa6b795d67ff2c8c6c3aeb5","family_id":"qf-app21-diagnostic-integer-sum-record","seed":202610212025,"semantic_template":"qf-app21-diagnostic-integer-sum-record/{\"a\":12,\"b\":39,\"response\":52}"},"fields":{"title":"Synthetic Integer-Sum Response and Its Rule Code","stem":"Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. a=12, b=39, response=52. Give (a,b,response,a+b,match?,matches_rule_expected or differs_from_rule_expected).","answer":{"kind":"expression","value":"(12, 39, 52, 51, No, differs_from_rule_expected)","explanation":"Recompute the exact integer sum. A mismatched response licenses only the stated rule code, not a diagnosis of its author. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (12, 39, 52, 51, No, differs_from_rule_expected)."},"skills":["Synthetic Integer-Sum Response and Its Rule Code"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0026","batch_id":"batch-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"2d2e465382e84b80a429f7d872a9483d87710bd3877f9a878b1591f2dc9182e3","family_id":"qf-app21-diagnostic-fraction-equivalence-record","seed":202610212026,"semantic_template":"qf-app21-diagnostic-fraction-equivalence-record/{\"p\":-8,\"q\":1,\"r\":-7,\"response\":true,\"s\":1}"},"fields":{"title":"Synthetic Fraction-Equivalence Response with Nonzero Denominators","stem":"Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. Fractions p/q and r/s have p=-8, q=1≠0, r=-7, s=1≠0; Boolean response=true. Give (p,q,r,s,p*s,r*q,equivalent?,response,match?,rule code). Preserve the signed original numerator/denominator values in these fields.","answer":{"kind":"expression","value":"(-8, 1, -7, 1, -8, -7, No, Yes, No, differs_from_rule_expected)","explanation":"Cross products test equivalence exactly, including negative denominators; compare that truth value with the synthetic response without replacing the record’s raw fractions. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (-8, 1, -7, 1, -8, -7, No, Yes, No, differs_from_rule_expected)."},"skills":["Synthetic Fraction-Equivalence Response with Nonzero Denominators"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0027","batch_id":"batch-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"97df03cd8c56e1ab97ce2f3410db5ec7d2993679210a085a23df34db223a630d","family_id":"qf-app21-diagnostic-fraction-equivalence-record","seed":202610212027,"semantic_template":"qf-app21-diagnostic-fraction-equivalence-record/{\"p\":-7,\"q\":2,\"r\":-14,\"response\":false,\"s\":2}"},"fields":{"title":"Synthetic Fraction-Equivalence Response with Nonzero Denominators","stem":"Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. Fractions p/q and r/s have p=-7, q=2≠0, r=-14, s=2≠0; Boolean response=false. Give (p,q,r,s,p*s,r*q,equivalent?,response,match?,rule code). Preserve the signed original numerator/denominator values in these fields.","answer":{"kind":"expression","value":"(-7, 2, -14, 2, -14, -28, No, No, Yes, matches_rule_expected)","explanation":"Cross products test equivalence exactly, including negative denominators; compare that truth value with the synthetic response without replacing the record’s raw fractions. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (-7, 2, -14, 2, -14, -28, No, No, Yes, matches_rule_expected)."},"skills":["Synthetic Fraction-Equivalence Response with Nonzero Denominators"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0028","batch_id":"batch-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"3e2007938d11103e194518ef7b3a22bb5c2a0dbd4b6d89ca6b410d5bda00b359","family_id":"qf-app21-diagnostic-fraction-equivalence-record","seed":202610212028,"semantic_template":"qf-app21-diagnostic-fraction-equivalence-record/{\"p\":-6,\"q\":3,\"r\":-17,\"response\":false,\"s\":3}"},"fields":{"title":"Synthetic Fraction-Equivalence Response with Nonzero Denominators","stem":"Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. Fractions p/q and r/s have p=-6, q=3≠0, r=-17, s=3≠0; Boolean response=false. Give (p,q,r,s,p*s,r*q,equivalent?,response,match?,rule code). Preserve the signed original numerator/denominator values in these fields.","answer":{"kind":"expression","value":"(-6, 3, -17, 3, -18, -51, No, No, Yes, matches_rule_expected)","explanation":"Cross products test equivalence exactly, including negative denominators; compare that truth value with the synthetic response without replacing the record’s raw fractions. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (-6, 3, -17, 3, -18, -51, No, No, Yes, matches_rule_expected)."},"skills":["Synthetic Fraction-Equivalence Response with Nonzero Denominators"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0029","batch_id":"batch-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"f9b42ca50549f9fc5c4d2c26b567ed11a4d7befdbf11fc5efa698764a0715f2c","family_id":"qf-app21-diagnostic-fraction-equivalence-record","seed":202610212029,"semantic_template":"qf-app21-diagnostic-fraction-equivalence-record/{\"p\":-5,\"q\":4,\"r\":-20,\"response\":false,\"s\":4}"},"fields":{"title":"Synthetic Fraction-Equivalence Response with Nonzero Denominators","stem":"Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. Fractions p/q and r/s have p=-5, q=4≠0, r=-20, s=4≠0; Boolean response=false. Give (p,q,r,s,p*s,r*q,equivalent?,response,match?,rule code). Preserve the signed original numerator/denominator values in these fields.","answer":{"kind":"expression","value":"(-5, 4, -20, 4, -20, -80, No, No, Yes, matches_rule_expected)","explanation":"Cross products test equivalence exactly, including negative denominators; compare that truth value with the synthetic response without replacing the record’s raw fractions. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (-5, 4, -20, 4, -20, -80, No, No, Yes, matches_rule_expected)."},"skills":["Synthetic Fraction-Equivalence Response with Nonzero Denominators"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0030","batch_id":"batch-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"c55b7eb97d0dc6cbeaca7097a303a5ee9cb32ece8b4639c528b583215d0acbd4","family_id":"qf-app21-diagnostic-fraction-equivalence-record","seed":202610212030,"semantic_template":"qf-app21-diagnostic-fraction-equivalence-record/{\"p\":-4,\"q\":5,\"r\":-19,\"response\":true,\"s\":5}"},"fields":{"title":"Synthetic Fraction-Equivalence Response with Nonzero Denominators","stem":"Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. Fractions p/q and r/s have p=-4, q=5≠0, r=-19, s=5≠0; Boolean response=true. Give (p,q,r,s,p*s,r*q,equivalent?,response,match?,rule code). Preserve the signed original numerator/denominator values in these fields.","answer":{"kind":"expression","value":"(-4, 5, -19, 5, -20, -95, No, Yes, No, differs_from_rule_expected)","explanation":"Cross products test equivalence exactly, including negative denominators; compare that truth value with the synthetic response without replacing the record’s raw fractions. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (-4, 5, -19, 5, -20, -95, No, Yes, No, differs_from_rule_expected)."},"skills":["Synthetic Fraction-Equivalence Response with Nonzero Denominators"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0031","batch_id":"batch-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"0a1b4c2d103304836b3076043edcce71514058ef1b259e2f9c066a24cbd02da0","family_id":"qf-app21-diagnostic-fraction-equivalence-record","seed":202610212031,"semantic_template":"qf-app21-diagnostic-fraction-equivalence-record/{\"p\":-3,\"q\":1,\"r\":-18,\"response\":true,\"s\":6}"},"fields":{"title":"Synthetic Fraction-Equivalence Response with Nonzero Denominators","stem":"Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. Fractions p/q and r/s have p=-3, q=1≠0, r=-18, s=6≠0; Boolean response=true. Give (p,q,r,s,p*s,r*q,equivalent?,response,match?,rule code). Preserve the signed original numerator/denominator values in these fields.","answer":{"kind":"expression","value":"(-3, 1, -18, 6, -18, -18, Yes, Yes, Yes, matches_rule_expected)","explanation":"Cross products test equivalence exactly, including negative denominators; compare that truth value with the synthetic response without replacing the record’s raw fractions. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (-3, 1, -18, 6, -18, -18, Yes, Yes, Yes, matches_rule_expected)."},"skills":["Synthetic Fraction-Equivalence Response with Nonzero Denominators"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0032","batch_id":"batch-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"a8438fbcff327c1ddeadf1d11236fa0f0b48f0ea9165a9f296f12958ab1cde79","family_id":"qf-app21-diagnostic-fraction-equivalence-record","seed":202610212032,"semantic_template":"qf-app21-diagnostic-fraction-equivalence-record/{\"p\":-2,\"q\":2,\"r\":-13,\"response\":false,\"s\":7}"},"fields":{"title":"Synthetic Fraction-Equivalence Response with Nonzero Denominators","stem":"Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. Fractions p/q and r/s have p=-2, q=2≠0, r=-13, s=7≠0; Boolean response=false. Give (p,q,r,s,p*s,r*q,equivalent?,response,match?,rule code). Preserve the signed original numerator/denominator values in these fields.","answer":{"kind":"expression","value":"(-2, 2, -13, 7, -14, -26, No, No, Yes, matches_rule_expected)","explanation":"Cross products test equivalence exactly, including negative denominators; compare that truth value with the synthetic response without replacing the record’s raw fractions. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (-2, 2, -13, 7, -14, -26, No, No, Yes, matches_rule_expected)."},"skills":["Synthetic Fraction-Equivalence Response with Nonzero Denominators"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0033","batch_id":"batch-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"33e972b91df96598dc7cc004f65376d8693a40b5271701139d82631e2fccd700","family_id":"qf-app21-diagnostic-fraction-equivalence-record","seed":202610212033,"semantic_template":"qf-app21-diagnostic-fraction-equivalence-record/{\"p\":-1,\"q\":3,\"r\":-1,\"response\":false,\"s\":1}"},"fields":{"title":"Synthetic Fraction-Equivalence Response with Nonzero Denominators","stem":"Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. Fractions p/q and r/s have p=-1, q=3≠0, r=-1, s=1≠0; Boolean response=false. Give (p,q,r,s,p*s,r*q,equivalent?,response,match?,rule code). Preserve the signed original numerator/denominator values in these fields.","answer":{"kind":"expression","value":"(-1, 3, -1, 1, -1, -3, No, No, Yes, matches_rule_expected)","explanation":"Cross products test equivalence exactly, including negative denominators; compare that truth value with the synthetic response without replacing the record’s raw fractions. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (-1, 3, -1, 1, -1, -3, No, No, Yes, matches_rule_expected)."},"skills":["Synthetic Fraction-Equivalence Response with Nonzero Denominators"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0034","batch_id":"batch-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"cf23b9ab149d341f20d5d0c90d73c0a9350f1c4311bb24f82e6f6d5f772eaaeb","family_id":"qf-app21-diagnostic-fraction-equivalence-record","seed":202610212034,"semantic_template":"qf-app21-diagnostic-fraction-equivalence-record/{\"p\":0,\"q\":4,\"r\":1,\"response\":true,\"s\":2}"},"fields":{"title":"Synthetic Fraction-Equivalence Response with Nonzero Denominators","stem":"Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. Fractions p/q and r/s have p=0, q=4≠0, r=1, s=2≠0; Boolean response=true. Give (p,q,r,s,p*s,r*q,equivalent?,response,match?,rule code). Preserve the signed original numerator/denominator values in these fields.","answer":{"kind":"expression","value":"(0, 4, 1, 2, 0, 4, No, Yes, No, differs_from_rule_expected)","explanation":"Cross products test equivalence exactly, including negative denominators; compare that truth value with the synthetic response without replacing the record’s raw fractions. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (0, 4, 1, 2, 0, 4, No, Yes, No, differs_from_rule_expected)."},"skills":["Synthetic Fraction-Equivalence Response with Nonzero Denominators"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0035","batch_id":"batch-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"5822de9ee798d0d8216ba973c334955503331d423adae1d8eef4793aa71127e0","family_id":"qf-app21-diagnostic-fraction-equivalence-record","seed":202610212035,"semantic_template":"qf-app21-diagnostic-fraction-equivalence-record/{\"p\":1,\"q\":5,\"r\":3,\"response\":false,\"s\":3}"},"fields":{"title":"Synthetic Fraction-Equivalence Response with Nonzero Denominators","stem":"Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. Fractions p/q and r/s have p=1, q=5≠0, r=3, s=3≠0; Boolean response=false. Give (p,q,r,s,p*s,r*q,equivalent?,response,match?,rule code). Preserve the signed original numerator/denominator values in these fields.","answer":{"kind":"expression","value":"(1, 5, 3, 3, 3, 15, No, No, Yes, matches_rule_expected)","explanation":"Cross products test equivalence exactly, including negative denominators; compare that truth value with the synthetic response without replacing the record’s raw fractions. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (1, 5, 3, 3, 3, 15, No, No, Yes, matches_rule_expected)."},"skills":["Synthetic Fraction-Equivalence Response with Nonzero Denominators"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0036","batch_id":"batch-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"134aee40fb6f404c13ede7d6eb6df80f3c79cb9f4eb8d3ee4ab355b689bf6f3b","family_id":"qf-app21-diagnostic-fraction-equivalence-record","seed":202610212036,"semantic_template":"qf-app21-diagnostic-fraction-equivalence-record/{\"p\":2,\"q\":1,\"r\":9,\"response\":false,\"s\":4}"},"fields":{"title":"Synthetic Fraction-Equivalence Response with Nonzero Denominators","stem":"Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. Fractions p/q and r/s have p=2, q=1≠0, r=9, s=4≠0; Boolean response=false. Give (p,q,r,s,p*s,r*q,equivalent?,response,match?,rule code). Preserve the signed original numerator/denominator values in these fields.","answer":{"kind":"expression","value":"(2, 1, 9, 4, 8, 9, No, No, Yes, matches_rule_expected)","explanation":"Cross products test equivalence exactly, including negative denominators; compare that truth value with the synthetic response without replacing the record’s raw fractions. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (2, 1, 9, 4, 8, 9, No, No, Yes, matches_rule_expected)."},"skills":["Synthetic Fraction-Equivalence Response with Nonzero Denominators"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0037","batch_id":"batch-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"4c26a302b07e600e045f56a66d4619d0a37968079364490cc7a3e2b8ad4a1eb2","family_id":"qf-app21-diagnostic-fraction-equivalence-record","seed":202610212037,"semantic_template":"qf-app21-diagnostic-fraction-equivalence-record/{\"p\":3,\"q\":2,\"r\":15,\"response\":false,\"s\":5}"},"fields":{"title":"Synthetic Fraction-Equivalence Response with Nonzero Denominators","stem":"Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. Fractions p/q and r/s have p=3, q=2≠0, r=15, s=5≠0; Boolean response=false. Give (p,q,r,s,p*s,r*q,equivalent?,response,match?,rule code). Preserve the signed original numerator/denominator values in these fields.","answer":{"kind":"expression","value":"(3, 2, 15, 5, 15, 30, No, No, Yes, matches_rule_expected)","explanation":"Cross products test equivalence exactly, including negative denominators; compare that truth value with the synthetic response without replacing the record’s raw fractions. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (3, 2, 15, 5, 15, 30, No, No, Yes, matches_rule_expected)."},"skills":["Synthetic Fraction-Equivalence Response with Nonzero Denominators"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0038","batch_id":"batch-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"0db8afab207e3ea4908e9be39c26ea60751963048c59e672acd33a5d166a8a50","family_id":"qf-app21-diagnostic-fraction-equivalence-record","seed":202610212038,"semantic_template":"qf-app21-diagnostic-fraction-equivalence-record/{\"p\":4,\"q\":3,\"r\":25,\"response\":true,\"s\":6}"},"fields":{"title":"Synthetic Fraction-Equivalence Response with Nonzero Denominators","stem":"Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. Fractions p/q and r/s have p=4, q=3≠0, r=25, s=6≠0; Boolean response=true. Give (p,q,r,s,p*s,r*q,equivalent?,response,match?,rule code). Preserve the signed original numerator/denominator values in these fields.","answer":{"kind":"expression","value":"(4, 3, 25, 6, 24, 75, No, Yes, No, differs_from_rule_expected)","explanation":"Cross products test equivalence exactly, including negative denominators; compare that truth value with the synthetic response without replacing the record’s raw fractions. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (4, 3, 25, 6, 24, 75, No, Yes, No, differs_from_rule_expected)."},"skills":["Synthetic Fraction-Equivalence Response with Nonzero Denominators"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0039","batch_id":"batch-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"3c5b1a91ff6251655a19e101c1a0756b86dccd6561b91fd7240883d4385e4c2f","family_id":"qf-app21-diagnostic-fraction-equivalence-record","seed":202610212039,"semantic_template":"qf-app21-diagnostic-fraction-equivalence-record/{\"p\":5,\"q\":4,\"r\":35,\"response\":false,\"s\":7}"},"fields":{"title":"Synthetic Fraction-Equivalence Response with Nonzero Denominators","stem":"Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. Fractions p/q and r/s have p=5, q=4≠0, r=35, s=7≠0; Boolean response=false. Give (p,q,r,s,p*s,r*q,equivalent?,response,match?,rule code). Preserve the signed original numerator/denominator values in these fields.","answer":{"kind":"expression","value":"(5, 4, 35, 7, 35, 140, No, No, Yes, matches_rule_expected)","explanation":"Cross products test equivalence exactly, including negative denominators; compare that truth value with the synthetic response without replacing the record’s raw fractions. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (5, 4, 35, 7, 35, 140, No, No, Yes, matches_rule_expected)."},"skills":["Synthetic Fraction-Equivalence Response with Nonzero Denominators"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0040","batch_id":"batch-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"097ef4955c4980267a113ef837ac8f1ceaf996bc78385505be07f59282ad8afb","family_id":"qf-app21-diagnostic-fraction-equivalence-record","seed":202610212040,"semantic_template":"qf-app21-diagnostic-fraction-equivalence-record/{\"p\":6,\"q\":5,\"r\":7,\"response\":false,\"s\":1}"},"fields":{"title":"Synthetic Fraction-Equivalence Response with Nonzero Denominators","stem":"Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. Fractions p/q and r/s have p=6, q=5≠0, r=7, s=1≠0; Boolean response=false. Give (p,q,r,s,p*s,r*q,equivalent?,response,match?,rule code). Preserve the signed original numerator/denominator values in these fields.","answer":{"kind":"expression","value":"(6, 5, 7, 1, 6, 35, No, No, Yes, matches_rule_expected)","explanation":"Cross products test equivalence exactly, including negative denominators; compare that truth value with the synthetic response without replacing the record’s raw fractions. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (6, 5, 7, 1, 6, 35, No, No, Yes, matches_rule_expected)."},"skills":["Synthetic Fraction-Equivalence Response with Nonzero Denominators"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0041","batch_id":"batch-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"a466283033f0502315d8221673b1002e765e17c96294280523f8b61a4db4e27e","family_id":"qf-app21-diagnostic-fraction-equivalence-record","seed":202610212041,"semantic_template":"qf-app21-diagnostic-fraction-equivalence-record/{\"p\":7,\"q\":1,\"r\":14,\"response\":true,\"s\":2}"},"fields":{"title":"Synthetic Fraction-Equivalence Response with Nonzero Denominators","stem":"Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. Fractions p/q and r/s have p=7, q=1≠0, r=14, s=2≠0; Boolean response=true. Give (p,q,r,s,p*s,r*q,equivalent?,response,match?,rule code). Preserve the signed original numerator/denominator values in these fields.","answer":{"kind":"expression","value":"(7, 1, 14, 2, 14, 14, Yes, Yes, Yes, matches_rule_expected)","explanation":"Cross products test equivalence exactly, including negative denominators; compare that truth value with the synthetic response without replacing the record’s raw fractions. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (7, 1, 14, 2, 14, 14, Yes, Yes, Yes, matches_rule_expected)."},"skills":["Synthetic Fraction-Equivalence Response with Nonzero Denominators"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0042","batch_id":"batch-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"cd4fe24d40fbfd392ab711d82bd54366324e318079c6ae85b869656d90595e49","family_id":"qf-app21-diagnostic-fraction-equivalence-record","seed":202610212042,"semantic_template":"qf-app21-diagnostic-fraction-equivalence-record/{\"p\":8,\"q\":2,\"r\":25,\"response\":true,\"s\":3}"},"fields":{"title":"Synthetic Fraction-Equivalence Response with Nonzero Denominators","stem":"Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. Fractions p/q and r/s have p=8, q=2≠0, r=25, s=3≠0; Boolean response=true. Give (p,q,r,s,p*s,r*q,equivalent?,response,match?,rule code). Preserve the signed original numerator/denominator values in these fields.","answer":{"kind":"expression","value":"(8, 2, 25, 3, 24, 50, No, Yes, No, differs_from_rule_expected)","explanation":"Cross products test equivalence exactly, including negative denominators; compare that truth value with the synthetic response without replacing the record’s raw fractions. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (8, 2, 25, 3, 24, 50, No, Yes, No, differs_from_rule_expected)."},"skills":["Synthetic Fraction-Equivalence Response with Nonzero Denominators"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0043","batch_id":"batch-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"7e08b8e433106b24a84db8f543f60411496d7682b8cf3eb81d9e5b689f5cc674","family_id":"qf-app21-diagnostic-fraction-equivalence-record","seed":202610212043,"semantic_template":"qf-app21-diagnostic-fraction-equivalence-record/{\"p\":9,\"q\":3,\"r\":36,\"response\":false,\"s\":4}"},"fields":{"title":"Synthetic Fraction-Equivalence Response with Nonzero Denominators","stem":"Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. Fractions p/q and r/s have p=9, q=3≠0, r=36, s=4≠0; Boolean response=false. Give (p,q,r,s,p*s,r*q,equivalent?,response,match?,rule code). Preserve the signed original numerator/denominator values in these fields.","answer":{"kind":"expression","value":"(9, 3, 36, 4, 36, 108, No, No, Yes, matches_rule_expected)","explanation":"Cross products test equivalence exactly, including negative denominators; compare that truth value with the synthetic response without replacing the record’s raw fractions. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (9, 3, 36, 4, 36, 108, No, No, Yes, matches_rule_expected)."},"skills":["Synthetic Fraction-Equivalence Response with Nonzero Denominators"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0044","batch_id":"batch-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"54abc107d5c2d23463f269be0c0a2a4ce1fb361f2127be67597d90bb1d802ec3","family_id":"qf-app21-diagnostic-fraction-equivalence-record","seed":202610212044,"semantic_template":"qf-app21-diagnostic-fraction-equivalence-record/{\"p\":10,\"q\":4,\"r\":51,\"response\":false,\"s\":5}"},"fields":{"title":"Synthetic Fraction-Equivalence Response with Nonzero Denominators","stem":"Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. Fractions p/q and r/s have p=10, q=4≠0, r=51, s=5≠0; Boolean response=false. Give (p,q,r,s,p*s,r*q,equivalent?,response,match?,rule code). Preserve the signed original numerator/denominator values in these fields.","answer":{"kind":"expression","value":"(10, 4, 51, 5, 50, 204, No, No, Yes, matches_rule_expected)","explanation":"Cross products test equivalence exactly, including negative denominators; compare that truth value with the synthetic response without replacing the record’s raw fractions. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (10, 4, 51, 5, 50, 204, No, No, Yes, matches_rule_expected)."},"skills":["Synthetic Fraction-Equivalence Response with Nonzero Denominators"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0045","batch_id":"batch-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"a1b72eced20ecd15ae6fe19f1290585c86fda94dcd96bf2cf5ab221ead79abf2","family_id":"qf-app21-diagnostic-fraction-equivalence-record","seed":202610212045,"semantic_template":"qf-app21-diagnostic-fraction-equivalence-record/{\"p\":11,\"q\":5,\"r\":66,\"response\":false,\"s\":6}"},"fields":{"title":"Synthetic Fraction-Equivalence Response with Nonzero Denominators","stem":"Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. Fractions p/q and r/s have p=11, q=5≠0, r=66, s=6≠0; Boolean response=false. Give (p,q,r,s,p*s,r*q,equivalent?,response,match?,rule code). Preserve the signed original numerator/denominator values in these fields.","answer":{"kind":"expression","value":"(11, 5, 66, 6, 66, 330, No, No, Yes, matches_rule_expected)","explanation":"Cross products test equivalence exactly, including negative denominators; compare that truth value with the synthetic response without replacing the record’s raw fractions. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (11, 5, 66, 6, 66, 330, No, No, Yes, matches_rule_expected)."},"skills":["Synthetic Fraction-Equivalence Response with Nonzero Denominators"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0046","batch_id":"batch-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"6d4be9c37d0fa12e5fe1103fa57614941fc74ef38c804e2bdf90c4d9ac8867f5","family_id":"qf-app21-diagnostic-fraction-equivalence-record","seed":202610212046,"semantic_template":"qf-app21-diagnostic-fraction-equivalence-record/{\"p\":12,\"q\":1,\"r\":85,\"response\":true,\"s\":7}"},"fields":{"title":"Synthetic Fraction-Equivalence Response with Nonzero Denominators","stem":"Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. Fractions p/q and r/s have p=12, q=1≠0, r=85, s=7≠0; Boolean response=true. Give (p,q,r,s,p*s,r*q,equivalent?,response,match?,rule code). Preserve the signed original numerator/denominator values in these fields.","answer":{"kind":"expression","value":"(12, 1, 85, 7, 84, 85, No, Yes, No, differs_from_rule_expected)","explanation":"Cross products test equivalence exactly, including negative denominators; compare that truth value with the synthetic response without replacing the record’s raw fractions. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (12, 1, 85, 7, 84, 85, No, Yes, No, differs_from_rule_expected)."},"skills":["Synthetic Fraction-Equivalence Response with Nonzero Denominators"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0047","batch_id":"batch-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"96ea478d37f0441541aa0512b8772ab21b9263ba78ed3cbe14274e146380750f","family_id":"qf-app21-diagnostic-fraction-equivalence-record","seed":202610212047,"semantic_template":"qf-app21-diagnostic-fraction-equivalence-record/{\"p\":13,\"q\":2,\"r\":13,\"response\":false,\"s\":1}"},"fields":{"title":"Synthetic Fraction-Equivalence Response with Nonzero Denominators","stem":"Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. Fractions p/q and r/s have p=13, q=2≠0, r=13, s=1≠0; Boolean response=false. Give (p,q,r,s,p*s,r*q,equivalent?,response,match?,rule code). Preserve the signed original numerator/denominator values in these fields.","answer":{"kind":"expression","value":"(13, 2, 13, 1, 13, 26, No, No, Yes, matches_rule_expected)","explanation":"Cross products test equivalence exactly, including negative denominators; compare that truth value with the synthetic response without replacing the record’s raw fractions. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (13, 2, 13, 1, 13, 26, No, No, Yes, matches_rule_expected)."},"skills":["Synthetic Fraction-Equivalence Response with Nonzero Denominators"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0048","batch_id":"batch-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"2d62917a638b1761906dce0e91e87f4af24c33c8c83004fc2b3b117d8d1819c9","family_id":"qf-app21-diagnostic-fraction-equivalence-record","seed":202610212048,"semantic_template":"qf-app21-diagnostic-fraction-equivalence-record/{\"p\":14,\"q\":3,\"r\":29,\"response\":false,\"s\":2}"},"fields":{"title":"Synthetic Fraction-Equivalence Response with Nonzero Denominators","stem":"Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. Fractions p/q and r/s have p=14, q=3≠0, r=29, s=2≠0; Boolean response=false. Give (p,q,r,s,p*s,r*q,equivalent?,response,match?,rule code). Preserve the signed original numerator/denominator values in these fields.","answer":{"kind":"expression","value":"(14, 3, 29, 2, 28, 87, No, No, Yes, matches_rule_expected)","explanation":"Cross products test equivalence exactly, including negative denominators; compare that truth value with the synthetic response without replacing the record’s raw fractions. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (14, 3, 29, 2, 28, 87, No, No, Yes, matches_rule_expected)."},"skills":["Synthetic Fraction-Equivalence Response with Nonzero Denominators"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0049","batch_id":"batch-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"ddedbee5d5754a5297f85f02b77da9666cf887ed3ed5a8f6c4410ba8ba7a6f03","family_id":"qf-app21-diagnostic-fraction-equivalence-record","seed":202610212049,"semantic_template":"qf-app21-diagnostic-fraction-equivalence-record/{\"p\":15,\"q\":4,\"r\":45,\"response\":false,\"s\":3}"},"fields":{"title":"Synthetic Fraction-Equivalence Response with Nonzero Denominators","stem":"Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. Fractions p/q and r/s have p=15, q=4≠0, r=45, s=3≠0; Boolean response=false. Give (p,q,r,s,p*s,r*q,equivalent?,response,match?,rule code). Preserve the signed original numerator/denominator values in these fields.","answer":{"kind":"expression","value":"(15, 4, 45, 3, 45, 180, No, No, Yes, matches_rule_expected)","explanation":"Cross products test equivalence exactly, including negative denominators; compare that truth value with the synthetic response without replacing the record’s raw fractions. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (15, 4, 45, 3, 45, 180, No, No, Yes, matches_rule_expected)."},"skills":["Synthetic Fraction-Equivalence Response with Nonzero Denominators"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0050","batch_id":"batch-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"524eef7bcb14210b5c06f68712587fc116070584d1c53b7f67ebf738afc5836b","family_id":"qf-app21-diagnostic-fraction-equivalence-record","seed":202610212050,"semantic_template":"qf-app21-diagnostic-fraction-equivalence-record/{\"p\":16,\"q\":5,\"r\":65,\"response\":true,\"s\":4}"},"fields":{"title":"Synthetic Fraction-Equivalence Response with Nonzero Denominators","stem":"Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. Fractions p/q and r/s have p=16, q=5≠0, r=65, s=4≠0; Boolean response=true. Give (p,q,r,s,p*s,r*q,equivalent?,response,match?,rule code). Preserve the signed original numerator/denominator values in these fields.","answer":{"kind":"expression","value":"(16, 5, 65, 4, 64, 325, No, Yes, No, differs_from_rule_expected)","explanation":"Cross products test equivalence exactly, including negative denominators; compare that truth value with the synthetic response without replacing the record’s raw fractions. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (16, 5, 65, 4, 64, 325, No, Yes, No, differs_from_rule_expected)."},"skills":["Synthetic Fraction-Equivalence Response with Nonzero Denominators"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0051","batch_id":"batch-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"540fe5f9ff968f101556544380d9d0e5a0c03f7a8d0f475d48996b261537a653","family_id":"qf-app21-diagnostic-linear-substitution-record","seed":202610212051,"semantic_template":"qf-app21-diagnostic-linear-substitution-record/{\"a\":-3,\"b\":-11,\"response\":-6,\"x\":-2}"},"fields":{"title":"Synthetic Response to a Declared Substitution","stem":"Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. a=-3, b=-11, x=-2, response=-6. Give (a,b,x,response,a*x+b,match?,rule code).","answer":{"kind":"expression","value":"(-3, -11, -2, -6, -5, No, differs_from_rule_expected)","explanation":"Evaluate the declared expression, compare values and retain only a rule-agreement status. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (-3, -11, -2, -6, -5, No, differs_from_rule_expected)."},"skills":["Synthetic Response to a Declared Substitution"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0052","batch_id":"batch-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"a563239d30eb9e42869abaf9182c0a9a7f8a71a806d2ed68ba5eea44253d8550","family_id":"qf-app21-diagnostic-linear-substitution-record","seed":202610212052,"semantic_template":"qf-app21-diagnostic-linear-substitution-record/{\"a\":-2,\"b\":-10,\"response\":-8,\"x\":-1}"},"fields":{"title":"Synthetic Response to a Declared Substitution","stem":"Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. a=-2, b=-10, x=-1, response=-8. Give (a,b,x,response,a*x+b,match?,rule code).","answer":{"kind":"expression","value":"(-2, -10, -1, -8, -8, Yes, matches_rule_expected)","explanation":"Evaluate the declared expression, compare values and retain only a rule-agreement status. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (-2, -10, -1, -8, -8, Yes, matches_rule_expected)."},"skills":["Synthetic Response to a Declared Substitution"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0053","batch_id":"batch-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"f42fa4a575af791f03924f4d18240c5588f86a9098ff4b2e2432839b845dc5bc","family_id":"qf-app21-diagnostic-linear-substitution-record","seed":202610212053,"semantic_template":"qf-app21-diagnostic-linear-substitution-record/{\"a\":-1,\"b\":-9,\"response\":-9,\"x\":0}"},"fields":{"title":"Synthetic Response to a Declared Substitution","stem":"Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. a=-1, b=-9, x=0, response=-9. Give (a,b,x,response,a*x+b,match?,rule code).","answer":{"kind":"expression","value":"(-1, -9, 0, -9, -9, Yes, matches_rule_expected)","explanation":"Evaluate the declared expression, compare values and retain only a rule-agreement status. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (-1, -9, 0, -9, -9, Yes, matches_rule_expected)."},"skills":["Synthetic Response to a Declared Substitution"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0054","batch_id":"batch-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"f9436cef19b9c576b0f818b87eb8b462780e900ceea261ec41da21549c37bb5f","family_id":"qf-app21-diagnostic-linear-substitution-record","seed":202610212054,"semantic_template":"qf-app21-diagnostic-linear-substitution-record/{\"a\":0,\"b\":-8,\"response\":-9,\"x\":1}"},"fields":{"title":"Synthetic Response to a Declared Substitution","stem":"Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. a=0, b=-8, x=1, response=-9. Give (a,b,x,response,a*x+b,match?,rule code).","answer":{"kind":"expression","value":"(0, -8, 1, -9, -8, No, differs_from_rule_expected)","explanation":"Evaluate the declared expression, compare values and retain only a rule-agreement status. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (0, -8, 1, -9, -8, No, differs_from_rule_expected)."},"skills":["Synthetic Response to a Declared Substitution"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0055","batch_id":"batch-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"6a2f37afd72ea2ec6f2909caba73f3ad2ad52cdbfb6eb6cd709d10611df55475","family_id":"qf-app21-diagnostic-linear-substitution-record","seed":202610212055,"semantic_template":"qf-app21-diagnostic-linear-substitution-record/{\"a\":1,\"b\":-7,\"response\":-5,\"x\":2}"},"fields":{"title":"Synthetic Response to a Declared Substitution","stem":"Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. a=1, b=-7, x=2, response=-5. Give (a,b,x,response,a*x+b,match?,rule code).","answer":{"kind":"expression","value":"(1, -7, 2, -5, -5, Yes, matches_rule_expected)","explanation":"Evaluate the declared expression, compare values and retain only a rule-agreement status. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (1, -7, 2, -5, -5, Yes, matches_rule_expected)."},"skills":["Synthetic Response to a Declared Substitution"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0056","batch_id":"batch-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"83646eaa6090605d0a746da828e58dc2925ba28be5c4b3671f98fe978bfe0280","family_id":"qf-app21-diagnostic-linear-substitution-record","seed":202610212056,"semantic_template":"qf-app21-diagnostic-linear-substitution-record/{\"a\":2,\"b\":-6,\"response\":-10,\"x\":-2}"},"fields":{"title":"Synthetic Response to a Declared Substitution","stem":"Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. a=2, b=-6, x=-2, response=-10. Give (a,b,x,response,a*x+b,match?,rule code).","answer":{"kind":"expression","value":"(2, -6, -2, -10, -10, Yes, matches_rule_expected)","explanation":"Evaluate the declared expression, compare values and retain only a rule-agreement status. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (2, -6, -2, -10, -10, Yes, matches_rule_expected)."},"skills":["Synthetic Response to a Declared Substitution"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0057","batch_id":"batch-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"eca674986a442052f84dd7cc52d317a210e5826d02d07c71e5751af7a3fb927b","family_id":"qf-app21-diagnostic-linear-substitution-record","seed":202610212057,"semantic_template":"qf-app21-diagnostic-linear-substitution-record/{\"a\":3,\"b\":-5,\"response\":-9,\"x\":-1}"},"fields":{"title":"Synthetic Response to a Declared Substitution","stem":"Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. a=3, b=-5, x=-1, response=-9. Give (a,b,x,response,a*x+b,match?,rule code).","answer":{"kind":"expression","value":"(3, -5, -1, -9, -8, No, differs_from_rule_expected)","explanation":"Evaluate the declared expression, compare values and retain only a rule-agreement status. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (3, -5, -1, -9, -8, No, differs_from_rule_expected)."},"skills":["Synthetic Response to a Declared Substitution"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0058","batch_id":"batch-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"44d818378975973b6521cafcf84c527b5d73671cb34b42d375e3f9236505adb9","family_id":"qf-app21-diagnostic-linear-substitution-record","seed":202610212058,"semantic_template":"qf-app21-diagnostic-linear-substitution-record/{\"a\":-3,\"b\":-4,\"response\":-4,\"x\":0}"},"fields":{"title":"Synthetic Response to a Declared Substitution","stem":"Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. a=-3, b=-4, x=0, response=-4. Give (a,b,x,response,a*x+b,match?,rule code).","answer":{"kind":"expression","value":"(-3, -4, 0, -4, -4, Yes, matches_rule_expected)","explanation":"Evaluate the declared expression, compare values and retain only a rule-agreement status. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (-3, -4, 0, -4, -4, Yes, matches_rule_expected)."},"skills":["Synthetic Response to a Declared Substitution"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0059","batch_id":"batch-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"45ae21e26bc31c02c960efbec732a7665b9488d16396a9bde1a4531bddc3cc64","family_id":"qf-app21-diagnostic-linear-substitution-record","seed":202610212059,"semantic_template":"qf-app21-diagnostic-linear-substitution-record/{\"a\":-2,\"b\":-3,\"response\":-5,\"x\":1}"},"fields":{"title":"Synthetic Response to a Declared Substitution","stem":"Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. a=-2, b=-3, x=1, response=-5. Give (a,b,x,response,a*x+b,match?,rule code).","answer":{"kind":"expression","value":"(-2, -3, 1, -5, -5, Yes, matches_rule_expected)","explanation":"Evaluate the declared expression, compare values and retain only a rule-agreement status. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (-2, -3, 1, -5, -5, Yes, matches_rule_expected)."},"skills":["Synthetic Response to a Declared Substitution"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0060","batch_id":"batch-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"142966e7f45c1bb31759b2c1b21fdcfa549788394daa36b7e9c3350d999e13bd","family_id":"qf-app21-diagnostic-linear-substitution-record","seed":202610212060,"semantic_template":"qf-app21-diagnostic-linear-substitution-record/{\"a\":-1,\"b\":-2,\"response\":-5,\"x\":2}"},"fields":{"title":"Synthetic Response to a Declared Substitution","stem":"Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. a=-1, b=-2, x=2, response=-5. Give (a,b,x,response,a*x+b,match?,rule code).","answer":{"kind":"expression","value":"(-1, -2, 2, -5, -4, No, differs_from_rule_expected)","explanation":"Evaluate the declared expression, compare values and retain only a rule-agreement status. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (-1, -2, 2, -5, -4, No, differs_from_rule_expected)."},"skills":["Synthetic Response to a Declared Substitution"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0061","batch_id":"batch-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"01b3f4676bc190172c93e9be432bf04bd106caf361bf6c10ac7e95d28dd368e6","family_id":"qf-app21-diagnostic-linear-substitution-record","seed":202610212061,"semantic_template":"qf-app21-diagnostic-linear-substitution-record/{\"a\":0,\"b\":-1,\"response\":-1,\"x\":-2}"},"fields":{"title":"Synthetic Response to a Declared Substitution","stem":"Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. a=0, b=-1, x=-2, response=-1. Give (a,b,x,response,a*x+b,match?,rule code).","answer":{"kind":"expression","value":"(0, -1, -2, -1, -1, Yes, matches_rule_expected)","explanation":"Evaluate the declared expression, compare values and retain only a rule-agreement status. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (0, -1, -2, -1, -1, Yes, matches_rule_expected)."},"skills":["Synthetic Response to a Declared Substitution"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0062","batch_id":"batch-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"472dfb84c63572a32561b68125ab884c6e514967cee9c71b0f16c217e66e31aa","family_id":"qf-app21-diagnostic-linear-substitution-record","seed":202610212062,"semantic_template":"qf-app21-diagnostic-linear-substitution-record/{\"a\":1,\"b\":0,\"response\":-1,\"x\":-1}"},"fields":{"title":"Synthetic Response to a Declared Substitution","stem":"Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. a=1, b=0, x=-1, response=-1. Give (a,b,x,response,a*x+b,match?,rule code).","answer":{"kind":"expression","value":"(1, 0, -1, -1, -1, Yes, matches_rule_expected)","explanation":"Evaluate the declared expression, compare values and retain only a rule-agreement status. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (1, 0, -1, -1, -1, Yes, matches_rule_expected)."},"skills":["Synthetic Response to a Declared Substitution"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0063","batch_id":"batch-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"90b8786ec253330920f0c5dbee35bb2f5660f12df4f7f7441f4d88dd4c2fb19b","family_id":"qf-app21-diagnostic-linear-substitution-record","seed":202610212063,"semantic_template":"qf-app21-diagnostic-linear-substitution-record/{\"a\":2,\"b\":1,\"response\":0,\"x\":0}"},"fields":{"title":"Synthetic Response to a Declared Substitution","stem":"Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. a=2, b=1, x=0, response=0. Give (a,b,x,response,a*x+b,match?,rule code).","answer":{"kind":"expression","value":"(2, 1, 0, 0, 1, No, differs_from_rule_expected)","explanation":"Evaluate the declared expression, compare values and retain only a rule-agreement status. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (2, 1, 0, 0, 1, No, differs_from_rule_expected)."},"skills":["Synthetic Response to a Declared Substitution"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0064","batch_id":"batch-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"c2dfa401792b93741d24e2c80757811a69349430efd2ded2752403f83a39735a","family_id":"qf-app21-diagnostic-linear-substitution-record","seed":202610212064,"semantic_template":"qf-app21-diagnostic-linear-substitution-record/{\"a\":3,\"b\":2,\"response\":5,\"x\":1}"},"fields":{"title":"Synthetic Response to a Declared Substitution","stem":"Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. a=3, b=2, x=1, response=5. Give (a,b,x,response,a*x+b,match?,rule code).","answer":{"kind":"expression","value":"(3, 2, 1, 5, 5, Yes, matches_rule_expected)","explanation":"Evaluate the declared expression, compare values and retain only a rule-agreement status. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (3, 2, 1, 5, 5, Yes, matches_rule_expected)."},"skills":["Synthetic Response to a Declared Substitution"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0065","batch_id":"batch-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"978225f490aef288ab159c287a67d9dc4d83a53d1d05e777fd4e9c5d63fea475","family_id":"qf-app21-diagnostic-linear-substitution-record","seed":202610212065,"semantic_template":"qf-app21-diagnostic-linear-substitution-record/{\"a\":-3,\"b\":3,\"response\":-3,\"x\":2}"},"fields":{"title":"Synthetic Response to a Declared Substitution","stem":"Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. a=-3, b=3, x=2, response=-3. Give (a,b,x,response,a*x+b,match?,rule code).","answer":{"kind":"expression","value":"(-3, 3, 2, -3, -3, Yes, matches_rule_expected)","explanation":"Evaluate the declared expression, compare values and retain only a rule-agreement status. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (-3, 3, 2, -3, -3, Yes, matches_rule_expected)."},"skills":["Synthetic Response to a Declared Substitution"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0066","batch_id":"batch-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"08caddfb24965e8afdcbb65e8202d3785677db4ec96926cf08559db724855e98","family_id":"qf-app21-diagnostic-linear-substitution-record","seed":202610212066,"semantic_template":"qf-app21-diagnostic-linear-substitution-record/{\"a\":-2,\"b\":4,\"response\":7,\"x\":-2}"},"fields":{"title":"Synthetic Response to a Declared Substitution","stem":"Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. a=-2, b=4, x=-2, response=7. Give (a,b,x,response,a*x+b,match?,rule code).","answer":{"kind":"expression","value":"(-2, 4, -2, 7, 8, No, differs_from_rule_expected)","explanation":"Evaluate the declared expression, compare values and retain only a rule-agreement status. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (-2, 4, -2, 7, 8, No, differs_from_rule_expected)."},"skills":["Synthetic Response to a Declared Substitution"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0067","batch_id":"batch-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"46f694815e96674c36338948d7b2f4996246dd1e179d59fc54f17939492001da","family_id":"qf-app21-diagnostic-linear-substitution-record","seed":202610212067,"semantic_template":"qf-app21-diagnostic-linear-substitution-record/{\"a\":-1,\"b\":5,\"response\":6,\"x\":-1}"},"fields":{"title":"Synthetic Response to a Declared Substitution","stem":"Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. a=-1, b=5, x=-1, response=6. Give (a,b,x,response,a*x+b,match?,rule code).","answer":{"kind":"expression","value":"(-1, 5, -1, 6, 6, Yes, matches_rule_expected)","explanation":"Evaluate the declared expression, compare values and retain only a rule-agreement status. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (-1, 5, -1, 6, 6, Yes, matches_rule_expected)."},"skills":["Synthetic Response to a Declared Substitution"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0068","batch_id":"batch-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"82af031f6e7a19f0ac6ccab40b76ac03fe458164ed6c9d5f09edcd89e575be91","family_id":"qf-app21-diagnostic-linear-substitution-record","seed":202610212068,"semantic_template":"qf-app21-diagnostic-linear-substitution-record/{\"a\":0,\"b\":6,\"response\":6,\"x\":0}"},"fields":{"title":"Synthetic Response to a Declared Substitution","stem":"Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. a=0, b=6, x=0, response=6. Give (a,b,x,response,a*x+b,match?,rule code).","answer":{"kind":"expression","value":"(0, 6, 0, 6, 6, Yes, matches_rule_expected)","explanation":"Evaluate the declared expression, compare values and retain only a rule-agreement status. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (0, 6, 0, 6, 6, Yes, matches_rule_expected)."},"skills":["Synthetic Response to a Declared Substitution"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0069","batch_id":"batch-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"ae66172935533bd7ecc3e5e08d2b115333be1800cf18af33142896a4a95a326c","family_id":"qf-app21-diagnostic-linear-substitution-record","seed":202610212069,"semantic_template":"qf-app21-diagnostic-linear-substitution-record/{\"a\":1,\"b\":7,\"response\":7,\"x\":1}"},"fields":{"title":"Synthetic Response to a Declared Substitution","stem":"Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. a=1, b=7, x=1, response=7. Give (a,b,x,response,a*x+b,match?,rule code).","answer":{"kind":"expression","value":"(1, 7, 1, 7, 8, No, differs_from_rule_expected)","explanation":"Evaluate the declared expression, compare values and retain only a rule-agreement status. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (1, 7, 1, 7, 8, No, differs_from_rule_expected)."},"skills":["Synthetic Response to a Declared Substitution"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0070","batch_id":"batch-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"daf278511eb9c6083ce462ef532ec0eae3637bda6433d05889db0fd991ce10ac","family_id":"qf-app21-diagnostic-linear-substitution-record","seed":202610212070,"semantic_template":"qf-app21-diagnostic-linear-substitution-record/{\"a\":2,\"b\":8,\"response\":12,\"x\":2}"},"fields":{"title":"Synthetic Response to a Declared Substitution","stem":"Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. a=2, b=8, x=2, response=12. Give (a,b,x,response,a*x+b,match?,rule code).","answer":{"kind":"expression","value":"(2, 8, 2, 12, 12, Yes, matches_rule_expected)","explanation":"Evaluate the declared expression, compare values and retain only a rule-agreement status. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (2, 8, 2, 12, 12, Yes, matches_rule_expected)."},"skills":["Synthetic Response to a Declared Substitution"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0071","batch_id":"batch-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"7b84896c0aae3023cc19a2b1ab6584532630b7c6b7104afc7294537c493919c7","family_id":"qf-app21-diagnostic-linear-substitution-record","seed":202610212071,"semantic_template":"qf-app21-diagnostic-linear-substitution-record/{\"a\":3,\"b\":9,\"response\":3,\"x\":-2}"},"fields":{"title":"Synthetic Response to a Declared Substitution","stem":"Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. a=3, b=9, x=-2, response=3. Give (a,b,x,response,a*x+b,match?,rule code).","answer":{"kind":"expression","value":"(3, 9, -2, 3, 3, Yes, matches_rule_expected)","explanation":"Evaluate the declared expression, compare values and retain only a rule-agreement status. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (3, 9, -2, 3, 3, Yes, matches_rule_expected)."},"skills":["Synthetic Response to a Declared Substitution"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0072","batch_id":"batch-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"5630d08178ab0b0c3368a86362e4717632b61b5a2f565b353dbd7d1418c38e5f","family_id":"qf-app21-diagnostic-linear-substitution-record","seed":202610212072,"semantic_template":"qf-app21-diagnostic-linear-substitution-record/{\"a\":-3,\"b\":10,\"response\":12,\"x\":-1}"},"fields":{"title":"Synthetic Response to a Declared Substitution","stem":"Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. a=-3, b=10, x=-1, response=12. Give (a,b,x,response,a*x+b,match?,rule code).","answer":{"kind":"expression","value":"(-3, 10, -1, 12, 13, No, differs_from_rule_expected)","explanation":"Evaluate the declared expression, compare values and retain only a rule-agreement status. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (-3, 10, -1, 12, 13, No, differs_from_rule_expected)."},"skills":["Synthetic Response to a Declared Substitution"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0073","batch_id":"batch-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"5c92a709799ebcd7de77b69689e418fabc6d05334cca128323e84f1a1366cfd7","family_id":"qf-app21-diagnostic-linear-substitution-record","seed":202610212073,"semantic_template":"qf-app21-diagnostic-linear-substitution-record/{\"a\":-2,\"b\":11,\"response\":11,\"x\":0}"},"fields":{"title":"Synthetic Response to a Declared Substitution","stem":"Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. a=-2, b=11, x=0, response=11. Give (a,b,x,response,a*x+b,match?,rule code).","answer":{"kind":"expression","value":"(-2, 11, 0, 11, 11, Yes, matches_rule_expected)","explanation":"Evaluate the declared expression, compare values and retain only a rule-agreement status. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (-2, 11, 0, 11, 11, Yes, matches_rule_expected)."},"skills":["Synthetic Response to a Declared Substitution"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0074","batch_id":"batch-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"771b25a53d4e2afc731ebf40da1d28709fac69115d92f3b31aabfe5d4a0d1e42","family_id":"qf-app21-diagnostic-linear-substitution-record","seed":202610212074,"semantic_template":"qf-app21-diagnostic-linear-substitution-record/{\"a\":-1,\"b\":12,\"response\":11,\"x\":1}"},"fields":{"title":"Synthetic Response to a Declared Substitution","stem":"Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. a=-1, b=12, x=1, response=11. Give (a,b,x,response,a*x+b,match?,rule code).","answer":{"kind":"expression","value":"(-1, 12, 1, 11, 11, Yes, matches_rule_expected)","explanation":"Evaluate the declared expression, compare values and retain only a rule-agreement status. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (-1, 12, 1, 11, 11, Yes, matches_rule_expected)."},"skills":["Synthetic Response to a Declared Substitution"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0075","batch_id":"batch-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"47974020fd37ba8183fd38586070a97bfbbe4a79643268b2e9b09f5237f7dfed","family_id":"qf-app21-diagnostic-linear-substitution-record","seed":202610212075,"semantic_template":"qf-app21-diagnostic-linear-substitution-record/{\"a\":0,\"b\":13,\"response\":12,\"x\":2}"},"fields":{"title":"Synthetic Response to a Declared Substitution","stem":"Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. a=0, b=13, x=2, response=12. Give (a,b,x,response,a*x+b,match?,rule code).","answer":{"kind":"expression","value":"(0, 13, 2, 12, 13, No, differs_from_rule_expected)","explanation":"Evaluate the declared expression, compare values and retain only a rule-agreement status. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (0, 13, 2, 12, 13, No, differs_from_rule_expected)."},"skills":["Synthetic Response to a Declared Substitution"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0076","batch_id":"batch-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"df0fd740231cb043a62943c9dc63c378585b382c14482f3a94d184c697e638bf","family_id":"qf-app21-diagnostic-record-completeness","seed":202610212076,"semantic_template":"qf-app21-diagnostic-record-completeness/{\"expected_present\":false,\"item_id\":21000,\"prompt_present\":true,\"response_present\":false,\"rule_present\":false}"},"fields":{"title":"Presence Flags for a Replayable Synthetic Record","stem":"Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. item_id=21000; prompt_present=true, expected_present=false, response_present=false, rule_present=false. Give (item id,prompt flag,expected flag,response flag,rule flag,all present?,synthetic_record_complete or synthetic_record_incomplete).","answer":{"kind":"expression","value":"(21000, Yes, No, No, No, No, synthetic_record_incomplete)","explanation":"Completeness requires every explicitly Boolean field-presence flag. A complete record alone proves neither response correctness nor educational effectiveness. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (21000, Yes, No, No, No, No, synthetic_record_incomplete)."},"skills":["Presence Flags for a Replayable Synthetic Record"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0077","batch_id":"batch-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"bf725bf4872145afea2cbb3299cfadb7816b729d44772d79768676627b3fc416","family_id":"qf-app21-diagnostic-record-completeness","seed":202610212077,"semantic_template":"qf-app21-diagnostic-record-completeness/{\"expected_present\":true,\"item_id\":21001,\"prompt_present\":true,\"response_present\":true,\"rule_present\":true}"},"fields":{"title":"Presence Flags for a Replayable Synthetic Record","stem":"Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. item_id=21001; prompt_present=true, expected_present=true, response_present=true, rule_present=true. Give (item id,prompt flag,expected flag,response flag,rule flag,all present?,synthetic_record_complete or synthetic_record_incomplete).","answer":{"kind":"expression","value":"(21001, Yes, Yes, Yes, Yes, Yes, synthetic_record_complete)","explanation":"Completeness requires every explicitly Boolean field-presence flag. A complete record alone proves neither response correctness nor educational effectiveness. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (21001, Yes, Yes, Yes, Yes, Yes, synthetic_record_complete)."},"skills":["Presence Flags for a Replayable Synthetic Record"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0078","batch_id":"batch-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"863d9cf357afc94e11bf11435a2d893f21ffcb3c313d026c4de04c5344c96c44","family_id":"qf-app21-diagnostic-record-completeness","seed":202610212078,"semantic_template":"qf-app21-diagnostic-record-completeness/{\"expected_present\":true,\"item_id\":21002,\"prompt_present\":true,\"response_present\":true,\"rule_present\":true}"},"fields":{"title":"Presence Flags for a Replayable Synthetic Record","stem":"Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. item_id=21002; prompt_present=true, expected_present=true, response_present=true, rule_present=true. Give (item id,prompt flag,expected flag,response flag,rule flag,all present?,synthetic_record_complete or synthetic_record_incomplete).","answer":{"kind":"expression","value":"(21002, Yes, Yes, Yes, Yes, Yes, synthetic_record_complete)","explanation":"Completeness requires every explicitly Boolean field-presence flag. A complete record alone proves neither response correctness nor educational effectiveness. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (21002, Yes, Yes, Yes, Yes, Yes, synthetic_record_complete)."},"skills":["Presence Flags for a Replayable Synthetic Record"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0079","batch_id":"batch-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"7729aab7006cb17fae62b60dfcc33cdb4621b1884acea45cda1faf5eb450b543","family_id":"qf-app21-diagnostic-record-completeness","seed":202610212079,"semantic_template":"qf-app21-diagnostic-record-completeness/{\"expected_present\":true,\"item_id\":21003,\"prompt_present\":true,\"response_present\":true,\"rule_present\":false}"},"fields":{"title":"Presence Flags for a Replayable Synthetic Record","stem":"Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. item_id=21003; prompt_present=true, expected_present=true, response_present=true, rule_present=false. Give (item id,prompt flag,expected flag,response flag,rule flag,all present?,synthetic_record_complete or synthetic_record_incomplete).","answer":{"kind":"expression","value":"(21003, Yes, Yes, Yes, No, No, synthetic_record_incomplete)","explanation":"Completeness requires every explicitly Boolean field-presence flag. A complete record alone proves neither response correctness nor educational effectiveness. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (21003, Yes, Yes, Yes, No, No, synthetic_record_incomplete)."},"skills":["Presence Flags for a Replayable Synthetic Record"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0080","batch_id":"batch-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"9e871760dc51b4d23b61f4604f55b654995e65126fdded42dd2f1ae8daea17e5","family_id":"qf-app21-diagnostic-record-completeness","seed":202610212080,"semantic_template":"qf-app21-diagnostic-record-completeness/{\"expected_present\":true,\"item_id\":21004,\"prompt_present\":true,\"response_present\":false,\"rule_present\":true}"},"fields":{"title":"Presence Flags for a Replayable Synthetic Record","stem":"Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. item_id=21004; prompt_present=true, expected_present=true, response_present=false, rule_present=true. Give (item id,prompt flag,expected flag,response flag,rule flag,all present?,synthetic_record_complete or synthetic_record_incomplete).","answer":{"kind":"expression","value":"(21004, Yes, Yes, No, Yes, No, synthetic_record_incomplete)","explanation":"Completeness requires every explicitly Boolean field-presence flag. A complete record alone proves neither response correctness nor educational effectiveness. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (21004, Yes, Yes, No, Yes, No, synthetic_record_incomplete)."},"skills":["Presence Flags for a Replayable Synthetic Record"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0081","batch_id":"batch-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"68a112b590f5bd0cf9f658375627846c5a73f95c33e66a0a7634f01c48367da9","family_id":"qf-app21-diagnostic-record-completeness","seed":202610212081,"semantic_template":"qf-app21-diagnostic-record-completeness/{\"expected_present\":false,\"item_id\":21005,\"prompt_present\":true,\"response_present\":true,\"rule_present\":true}"},"fields":{"title":"Presence Flags for a Replayable Synthetic Record","stem":"Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. item_id=21005; prompt_present=true, expected_present=false, response_present=true, rule_present=true. Give (item id,prompt flag,expected flag,response flag,rule flag,all present?,synthetic_record_complete or synthetic_record_incomplete).","answer":{"kind":"expression","value":"(21005, Yes, No, Yes, Yes, No, synthetic_record_incomplete)","explanation":"Completeness requires every explicitly Boolean field-presence flag. A complete record alone proves neither response correctness nor educational effectiveness. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (21005, Yes, No, Yes, Yes, No, synthetic_record_incomplete)."},"skills":["Presence Flags for a Replayable Synthetic Record"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0082","batch_id":"batch-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"6431f5ef0de1ae00ee0223feedb5fbbaaa4a58b94b9cab3ba4349a41e93989d2","family_id":"qf-app21-diagnostic-record-completeness","seed":202610212082,"semantic_template":"qf-app21-diagnostic-record-completeness/{\"expected_present\":true,\"item_id\":21006,\"prompt_present\":true,\"response_present\":true,\"rule_present\":false}"},"fields":{"title":"Presence Flags for a Replayable Synthetic Record","stem":"Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. item_id=21006; prompt_present=true, expected_present=true, response_present=true, rule_present=false. Give (item id,prompt flag,expected flag,response flag,rule flag,all present?,synthetic_record_complete or synthetic_record_incomplete).","answer":{"kind":"expression","value":"(21006, Yes, Yes, Yes, No, No, synthetic_record_incomplete)","explanation":"Completeness requires every explicitly Boolean field-presence flag. A complete record alone proves neither response correctness nor educational effectiveness. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (21006, Yes, Yes, Yes, No, No, synthetic_record_incomplete)."},"skills":["Presence Flags for a Replayable Synthetic Record"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0083","batch_id":"batch-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"2370ee298ea3537dbac044744348084b0c499ea06f2bf5577c4994d79c8ae2e5","family_id":"qf-app21-diagnostic-record-completeness","seed":202610212083,"semantic_template":"qf-app21-diagnostic-record-completeness/{\"expected_present\":true,\"item_id\":21007,\"prompt_present\":true,\"response_present\":true,\"rule_present\":true}"},"fields":{"title":"Presence Flags for a Replayable Synthetic Record","stem":"Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. item_id=21007; prompt_present=true, expected_present=true, response_present=true, rule_present=true. Give (item id,prompt flag,expected flag,response flag,rule flag,all present?,synthetic_record_complete or synthetic_record_incomplete).","answer":{"kind":"expression","value":"(21007, Yes, Yes, Yes, Yes, Yes, synthetic_record_complete)","explanation":"Completeness requires every explicitly Boolean field-presence flag. A complete record alone proves neither response correctness nor educational effectiveness. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (21007, Yes, Yes, Yes, Yes, Yes, synthetic_record_complete)."},"skills":["Presence Flags for a Replayable Synthetic Record"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0084","batch_id":"batch-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"2aec260e959443b7168eec39e74aff2aad112f6fa7e599f0a4f5e2c33b58e164","family_id":"qf-app21-diagnostic-record-completeness","seed":202610212084,"semantic_template":"qf-app21-diagnostic-record-completeness/{\"expected_present\":true,\"item_id\":21008,\"prompt_present\":true,\"response_present\":false,\"rule_present\":true}"},"fields":{"title":"Presence Flags for a Replayable Synthetic Record","stem":"Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. item_id=21008; prompt_present=true, expected_present=true, response_present=false, rule_present=true. Give (item id,prompt flag,expected flag,response flag,rule flag,all present?,synthetic_record_complete or synthetic_record_incomplete).","answer":{"kind":"expression","value":"(21008, Yes, Yes, No, Yes, No, synthetic_record_incomplete)","explanation":"Completeness requires every explicitly Boolean field-presence flag. A complete record alone proves neither response correctness nor educational effectiveness. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (21008, Yes, Yes, No, Yes, No, synthetic_record_incomplete)."},"skills":["Presence Flags for a Replayable Synthetic Record"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0085","batch_id":"batch-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"12f45318e6fc887972f71cafa34f3e60999a778c6af8a4f5a99384d9beaee45f","family_id":"qf-app21-diagnostic-record-completeness","seed":202610212085,"semantic_template":"qf-app21-diagnostic-record-completeness/{\"expected_present\":true,\"item_id\":21009,\"prompt_present\":true,\"response_present\":true,\"rule_present\":false}"},"fields":{"title":"Presence Flags for a Replayable Synthetic Record","stem":"Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. item_id=21009; prompt_present=true, expected_present=true, response_present=true, rule_present=false. Give (item id,prompt flag,expected flag,response flag,rule flag,all present?,synthetic_record_complete or synthetic_record_incomplete).","answer":{"kind":"expression","value":"(21009, Yes, Yes, Yes, No, No, synthetic_record_incomplete)","explanation":"Completeness requires every explicitly Boolean field-presence flag. A complete record alone proves neither response correctness nor educational effectiveness. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (21009, Yes, Yes, Yes, No, No, synthetic_record_incomplete)."},"skills":["Presence Flags for a Replayable Synthetic Record"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0086","batch_id":"batch-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"4a7a552c702651d7f38408b9e19faea0ba25a5c57e5a48657e22ea881218989a","family_id":"qf-app21-diagnostic-record-completeness","seed":202610212086,"semantic_template":"qf-app21-diagnostic-record-completeness/{\"expected_present\":false,\"item_id\":21010,\"prompt_present\":true,\"response_present\":true,\"rule_present\":true}"},"fields":{"title":"Presence Flags for a Replayable Synthetic Record","stem":"Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. item_id=21010; prompt_present=true, expected_present=false, response_present=true, rule_present=true. Give (item id,prompt flag,expected flag,response flag,rule flag,all present?,synthetic_record_complete or synthetic_record_incomplete).","answer":{"kind":"expression","value":"(21010, Yes, No, Yes, Yes, No, synthetic_record_incomplete)","explanation":"Completeness requires every explicitly Boolean field-presence flag. A complete record alone proves neither response correctness nor educational effectiveness. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (21010, Yes, No, Yes, Yes, No, synthetic_record_incomplete)."},"skills":["Presence Flags for a Replayable Synthetic Record"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0087","batch_id":"batch-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"6a71b084de53aa554d1318e942278e0a14a6249ae6c00995a5d3dbcc59269747","family_id":"qf-app21-diagnostic-record-completeness","seed":202610212087,"semantic_template":"qf-app21-diagnostic-record-completeness/{\"expected_present\":true,\"item_id\":21011,\"prompt_present\":true,\"response_present\":true,\"rule_present\":true}"},"fields":{"title":"Presence Flags for a Replayable Synthetic Record","stem":"Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. item_id=21011; prompt_present=true, expected_present=true, response_present=true, rule_present=true. Give (item id,prompt flag,expected flag,response flag,rule flag,all present?,synthetic_record_complete or synthetic_record_incomplete).","answer":{"kind":"expression","value":"(21011, Yes, Yes, Yes, Yes, Yes, synthetic_record_complete)","explanation":"Completeness requires every explicitly Boolean field-presence flag. A complete record alone proves neither response correctness nor educational effectiveness. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (21011, Yes, Yes, Yes, Yes, Yes, synthetic_record_complete)."},"skills":["Presence Flags for a Replayable Synthetic Record"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0088","batch_id":"batch-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"289bd0ecfb8ee8b33ecf3ce79be75b8bc80cd0ccbff536e495b9f8444b7029e5","family_id":"qf-app21-diagnostic-record-completeness","seed":202610212088,"semantic_template":"qf-app21-diagnostic-record-completeness/{\"expected_present\":true,\"item_id\":21012,\"prompt_present\":true,\"response_present\":false,\"rule_present\":false}"},"fields":{"title":"Presence Flags for a Replayable Synthetic Record","stem":"Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. item_id=21012; prompt_present=true, expected_present=true, response_present=false, rule_present=false. Give (item id,prompt flag,expected flag,response flag,rule flag,all present?,synthetic_record_complete or synthetic_record_incomplete).","answer":{"kind":"expression","value":"(21012, Yes, Yes, No, No, No, synthetic_record_incomplete)","explanation":"Completeness requires every explicitly Boolean field-presence flag. A complete record alone proves neither response correctness nor educational effectiveness. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (21012, Yes, Yes, No, No, No, synthetic_record_incomplete)."},"skills":["Presence Flags for a Replayable Synthetic Record"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0089","batch_id":"batch-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"c8bf7176f83a6eef2fe0a6f16a512cb099238221bae1ddd3f0a089d152fee754","family_id":"qf-app21-diagnostic-record-completeness","seed":202610212089,"semantic_template":"qf-app21-diagnostic-record-completeness/{\"expected_present\":true,\"item_id\":21013,\"prompt_present\":true,\"response_present\":true,\"rule_present\":true}"},"fields":{"title":"Presence Flags for a Replayable Synthetic Record","stem":"Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. item_id=21013; prompt_present=true, expected_present=true, response_present=true, rule_present=true. Give (item id,prompt flag,expected flag,response flag,rule flag,all present?,synthetic_record_complete or synthetic_record_incomplete).","answer":{"kind":"expression","value":"(21013, Yes, Yes, Yes, Yes, Yes, synthetic_record_complete)","explanation":"Completeness requires every explicitly Boolean field-presence flag. A complete record alone proves neither response correctness nor educational effectiveness. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (21013, Yes, Yes, Yes, Yes, Yes, synthetic_record_complete)."},"skills":["Presence Flags for a Replayable Synthetic Record"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0090","batch_id":"batch-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"d9caf95495083af15530cc8ff65ea5818c6051fab94316fe8190277954a19a31","family_id":"qf-app21-diagnostic-record-completeness","seed":202610212090,"semantic_template":"qf-app21-diagnostic-record-completeness/{\"expected_present\":true,\"item_id\":21014,\"prompt_present\":true,\"response_present\":true,\"rule_present\":true}"},"fields":{"title":"Presence Flags for a Replayable Synthetic Record","stem":"Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. item_id=21014; prompt_present=true, expected_present=true, response_present=true, rule_present=true. Give (item id,prompt flag,expected flag,response flag,rule flag,all present?,synthetic_record_complete or synthetic_record_incomplete).","answer":{"kind":"expression","value":"(21014, Yes, Yes, Yes, Yes, Yes, synthetic_record_complete)","explanation":"Completeness requires every explicitly Boolean field-presence flag. A complete record alone proves neither response correctness nor educational effectiveness. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (21014, Yes, Yes, Yes, Yes, Yes, synthetic_record_complete)."},"skills":["Presence Flags for a Replayable Synthetic Record"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0091","batch_id":"batch-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"ca18d3e6a54167c4c24747fe885b3b814f298986caa1beb25de7e74f85dfac4e","family_id":"qf-app21-diagnostic-record-completeness","seed":202610212091,"semantic_template":"qf-app21-diagnostic-record-completeness/{\"expected_present\":false,\"item_id\":21015,\"prompt_present\":true,\"response_present\":true,\"rule_present\":false}"},"fields":{"title":"Presence Flags for a Replayable Synthetic Record","stem":"Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. item_id=21015; prompt_present=true, expected_present=false, response_present=true, rule_present=false. Give (item id,prompt flag,expected flag,response flag,rule flag,all present?,synthetic_record_complete or synthetic_record_incomplete).","answer":{"kind":"expression","value":"(21015, Yes, No, Yes, No, No, synthetic_record_incomplete)","explanation":"Completeness requires every explicitly Boolean field-presence flag. A complete record alone proves neither response correctness nor educational effectiveness. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (21015, Yes, No, Yes, No, No, synthetic_record_incomplete)."},"skills":["Presence Flags for a Replayable Synthetic Record"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0092","batch_id":"batch-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"00c42685b9eb05a526b7ed840228fd5f6728970ee90b4f29dcf556b51aa0daa3","family_id":"qf-app21-diagnostic-record-completeness","seed":202610212092,"semantic_template":"qf-app21-diagnostic-record-completeness/{\"expected_present\":true,\"item_id\":21016,\"prompt_present\":true,\"response_present\":false,\"rule_present\":true}"},"fields":{"title":"Presence Flags for a Replayable Synthetic Record","stem":"Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. item_id=21016; prompt_present=true, expected_present=true, response_present=false, rule_present=true. Give (item id,prompt flag,expected flag,response flag,rule flag,all present?,synthetic_record_complete or synthetic_record_incomplete).","answer":{"kind":"expression","value":"(21016, Yes, Yes, No, Yes, No, synthetic_record_incomplete)","explanation":"Completeness requires every explicitly Boolean field-presence flag. A complete record alone proves neither response correctness nor educational effectiveness. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (21016, Yes, Yes, No, Yes, No, synthetic_record_incomplete)."},"skills":["Presence Flags for a Replayable Synthetic Record"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0093","batch_id":"batch-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"bb331a5bf6a3c890231df0cbc21040ea16f9931a1d9085351de9dc31dbf32830","family_id":"qf-app21-diagnostic-record-completeness","seed":202610212093,"semantic_template":"qf-app21-diagnostic-record-completeness/{\"expected_present\":true,\"item_id\":21017,\"prompt_present\":true,\"response_present\":true,\"rule_present\":true}"},"fields":{"title":"Presence Flags for a Replayable Synthetic Record","stem":"Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. item_id=21017; prompt_present=true, expected_present=true, response_present=true, rule_present=true. Give (item id,prompt flag,expected flag,response flag,rule flag,all present?,synthetic_record_complete or synthetic_record_incomplete).","answer":{"kind":"expression","value":"(21017, Yes, Yes, Yes, Yes, Yes, synthetic_record_complete)","explanation":"Completeness requires every explicitly Boolean field-presence flag. A complete record alone proves neither response correctness nor educational effectiveness. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (21017, Yes, Yes, Yes, Yes, Yes, synthetic_record_complete)."},"skills":["Presence Flags for a Replayable Synthetic Record"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0094","batch_id":"batch-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"d1d7357bd3a04367ab5f2a6749feb081dc1fd86347e88786d00fd00e89129672","family_id":"qf-app21-diagnostic-record-completeness","seed":202610212094,"semantic_template":"qf-app21-diagnostic-record-completeness/{\"expected_present\":true,\"item_id\":21018,\"prompt_present\":true,\"response_present\":true,\"rule_present\":false}"},"fields":{"title":"Presence Flags for a Replayable Synthetic Record","stem":"Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. item_id=21018; prompt_present=true, expected_present=true, response_present=true, rule_present=false. Give (item id,prompt flag,expected flag,response flag,rule flag,all present?,synthetic_record_complete or synthetic_record_incomplete).","answer":{"kind":"expression","value":"(21018, Yes, Yes, Yes, No, No, synthetic_record_incomplete)","explanation":"Completeness requires every explicitly Boolean field-presence flag. A complete record alone proves neither response correctness nor educational effectiveness. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (21018, Yes, Yes, Yes, No, No, synthetic_record_incomplete)."},"skills":["Presence Flags for a Replayable Synthetic Record"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0095","batch_id":"batch-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"9b0f5c35a71a617462a937d579babbf02da1064c0a8c17a3aba5fa46b2ee4db3","family_id":"qf-app21-diagnostic-record-completeness","seed":202610212095,"semantic_template":"qf-app21-diagnostic-record-completeness/{\"expected_present\":true,\"item_id\":21019,\"prompt_present\":true,\"response_present\":true,\"rule_present\":true}"},"fields":{"title":"Presence Flags for a Replayable Synthetic Record","stem":"Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. item_id=21019; prompt_present=true, expected_present=true, response_present=true, rule_present=true. Give (item id,prompt flag,expected flag,response flag,rule flag,all present?,synthetic_record_complete or synthetic_record_incomplete).","answer":{"kind":"expression","value":"(21019, Yes, Yes, Yes, Yes, Yes, synthetic_record_complete)","explanation":"Completeness requires every explicitly Boolean field-presence flag. A complete record alone proves neither response correctness nor educational effectiveness. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (21019, Yes, Yes, Yes, Yes, Yes, synthetic_record_complete)."},"skills":["Presence Flags for a Replayable Synthetic Record"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0096","batch_id":"batch-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"f47a0fc8803e8ebe74f9bbe3097bcbb5ccf9d95f427aad31754eb83451dfa2ef","family_id":"qf-app21-diagnostic-record-completeness","seed":202610212096,"semantic_template":"qf-app21-diagnostic-record-completeness/{\"expected_present\":false,\"item_id\":21020,\"prompt_present\":true,\"response_present\":false,\"rule_present\":true}"},"fields":{"title":"Presence Flags for a Replayable Synthetic Record","stem":"Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. item_id=21020; prompt_present=true, expected_present=false, response_present=false, rule_present=true. Give (item id,prompt flag,expected flag,response flag,rule flag,all present?,synthetic_record_complete or synthetic_record_incomplete).","answer":{"kind":"expression","value":"(21020, Yes, No, No, Yes, No, synthetic_record_incomplete)","explanation":"Completeness requires every explicitly Boolean field-presence flag. A complete record alone proves neither response correctness nor educational effectiveness. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (21020, Yes, No, No, Yes, No, synthetic_record_incomplete)."},"skills":["Presence Flags for a Replayable Synthetic Record"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0097","batch_id":"batch-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"c241cfa686760ec63d9ec202fcad2ad7e75fe1a03703a9efeb4bcf341d614efb","family_id":"qf-app21-diagnostic-record-completeness","seed":202610212097,"semantic_template":"qf-app21-diagnostic-record-completeness/{\"expected_present\":true,\"item_id\":21021,\"prompt_present\":true,\"response_present\":true,\"rule_present\":false}"},"fields":{"title":"Presence Flags for a Replayable Synthetic Record","stem":"Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. item_id=21021; prompt_present=true, expected_present=true, response_present=true, rule_present=false. Give (item id,prompt flag,expected flag,response flag,rule flag,all present?,synthetic_record_complete or synthetic_record_incomplete).","answer":{"kind":"expression","value":"(21021, Yes, Yes, Yes, No, No, synthetic_record_incomplete)","explanation":"Completeness requires every explicitly Boolean field-presence flag. A complete record alone proves neither response correctness nor educational effectiveness. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (21021, Yes, Yes, Yes, No, No, synthetic_record_incomplete)."},"skills":["Presence Flags for a Replayable Synthetic Record"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0098","batch_id":"batch-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"9c1db480aeac56379393e1ae6822326dc4004168a08671d2d6ae00521293cddc","family_id":"qf-app21-diagnostic-record-completeness","seed":202610212098,"semantic_template":"qf-app21-diagnostic-record-completeness/{\"expected_present\":true,\"item_id\":21022,\"prompt_present\":true,\"response_present\":true,\"rule_present\":true}"},"fields":{"title":"Presence Flags for a Replayable Synthetic Record","stem":"Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. item_id=21022; prompt_present=true, expected_present=true, response_present=true, rule_present=true. Give (item id,prompt flag,expected flag,response flag,rule flag,all present?,synthetic_record_complete or synthetic_record_incomplete).","answer":{"kind":"expression","value":"(21022, Yes, Yes, Yes, Yes, Yes, synthetic_record_complete)","explanation":"Completeness requires every explicitly Boolean field-presence flag. A complete record alone proves neither response correctness nor educational effectiveness. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (21022, Yes, Yes, Yes, Yes, Yes, synthetic_record_complete)."},"skills":["Presence Flags for a Replayable Synthetic Record"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0099","batch_id":"batch-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"56cd75e6da55617c9397170cc8ea8c0b13865feb7eaf64da97d6757257596fcc","family_id":"qf-app21-diagnostic-record-completeness","seed":202610212099,"semantic_template":"qf-app21-diagnostic-record-completeness/{\"expected_present\":true,\"item_id\":21023,\"prompt_present\":true,\"response_present\":true,\"rule_present\":true}"},"fields":{"title":"Presence Flags for a Replayable Synthetic Record","stem":"Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. item_id=21023; prompt_present=true, expected_present=true, response_present=true, rule_present=true. Give (item id,prompt flag,expected flag,response flag,rule flag,all present?,synthetic_record_complete or synthetic_record_incomplete).","answer":{"kind":"expression","value":"(21023, Yes, Yes, Yes, Yes, Yes, synthetic_record_complete)","explanation":"Completeness requires every explicitly Boolean field-presence flag. A complete record alone proves neither response correctness nor educational effectiveness. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (21023, Yes, Yes, Yes, Yes, Yes, synthetic_record_complete)."},"skills":["Presence Flags for a Replayable Synthetic Record"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0100","batch_id":"batch-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"453118b3b2d843705299d5028d7168f14ee5a52535be1813a9b1cfed6f85201a","family_id":"qf-app21-diagnostic-record-completeness","seed":202610212100,"semantic_template":"qf-app21-diagnostic-record-completeness/{\"expected_present\":true,\"item_id\":21024,\"prompt_present\":true,\"response_present\":false,\"rule_present\":false}"},"fields":{"title":"Presence Flags for a Replayable Synthetic Record","stem":"Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. item_id=21024; prompt_present=true, expected_present=true, response_present=false, rule_present=false. Give (item id,prompt flag,expected flag,response flag,rule flag,all present?,synthetic_record_complete or synthetic_record_incomplete).","answer":{"kind":"expression","value":"(21024, Yes, Yes, No, No, No, synthetic_record_incomplete)","explanation":"Completeness requires every explicitly Boolean field-presence flag. A complete record alone proves neither response correctness nor educational effectiveness. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (21024, Yes, Yes, No, No, No, synthetic_record_incomplete)."},"skills":["Presence Flags for a Replayable Synthetic Record"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}