{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261021-r01-mathematical-representation-0001","batch_id":"batch-20261013-advance-20261021-r01-mathematical-representation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"6c62806cde229e174b3cbaa254b21b90cf680f274c4445416bcdbd13bde340db","family_id":"qf-app21-representation-affine-table","seed":202610211001,"semantic_template":"qf-app21-representation-affine-table/{\"a\":-3,\"b\":-12,\"xs\":[-3,-2,0]}"},"fields":{"title":"A Rule-to-Table Bridge on an Explicit Finite Domain","stem":"Use only the explicitly supplied rule, symbols and finite pair table. Graph appearance supplies no values, and agreement on the listed inputs proves no equivalence on unlisted domains. a=-3, b=-12, inputs=[-3, -2, 0]; f(x)=a*x+b. Give (a,b,sorted distinct inputs,every [x,f(x)] row).","answer":{"kind":"expression","value":"(-3, -12, [-3, -2, 0], [[-3, -3], [-2, -6], [0, -12]])","explanation":"Remove repeated inputs, sort numerically and evaluate the rule at every declared input. Do not fill unlisted points from a picture. 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, -12, [-3, -2, 0], [[-3, -3], [-2, -6], [0, -12]])."},"skills":["A Rule-to-Table Bridge on an Explicit Finite Domain"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-r01-mathematical-representation-0002","batch_id":"batch-20261013-advance-20261021-r01-mathematical-representation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"423bc79c18a9a7086ab815e3a96af6e4fc0f2e7d428eff0a098b3cb4152f692d","family_id":"qf-app21-representation-affine-table","seed":202610211002,"semantic_template":"qf-app21-representation-affine-table/{\"a\":-2,\"b\":-11,\"xs\":[-2,-1,1]}"},"fields":{"title":"A Rule-to-Table Bridge on an Explicit Finite Domain","stem":"Use only the explicitly supplied rule, symbols and finite pair table. Graph appearance supplies no values, and agreement on the listed inputs proves no equivalence on unlisted domains. a=-2, b=-11, inputs=[-2, -1, 1]; f(x)=a*x+b. Give (a,b,sorted distinct inputs,every [x,f(x)] row).","answer":{"kind":"expression","value":"(-2, -11, [-2, -1, 1], [[-2, -7], [-1, -9], [1, -13]])","explanation":"Remove repeated inputs, sort numerically and evaluate the rule at every declared input. Do not fill unlisted points from a picture. 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, [-2, -1, 1], [[-2, -7], [-1, -9], [1, -13]])."},"skills":["A Rule-to-Table Bridge on an Explicit Finite Domain"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-r01-mathematical-representation-0003","batch_id":"batch-20261013-advance-20261021-r01-mathematical-representation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"6c3ce33d90f217b3fca5f49a0b4138433d49870e4cdbae7dabd1c963d7a51cc0","family_id":"qf-app21-representation-affine-table","seed":202610211003,"semantic_template":"qf-app21-representation-affine-table/{\"a\":-1,\"b\":-10,\"xs\":[-1,0,2]}"},"fields":{"title":"A Rule-to-Table Bridge on an Explicit Finite Domain","stem":"Use only the explicitly supplied rule, symbols and finite pair table. Graph appearance supplies no values, and agreement on the listed inputs proves no equivalence on unlisted domains. a=-1, b=-10, inputs=[-1, 0, 2]; f(x)=a*x+b. Give (a,b,sorted distinct inputs,every [x,f(x)] row).","answer":{"kind":"expression","value":"(-1, -10, [-1, 0, 2], [[-1, -9], [0, -10], [2, -12]])","explanation":"Remove repeated inputs, sort numerically and evaluate the rule at every declared input. Do not fill unlisted points from a picture. 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, -10, [-1, 0, 2], [[-1, -9], [0, -10], [2, -12]])."},"skills":["A Rule-to-Table Bridge on an Explicit Finite Domain"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-r01-mathematical-representation-0004","batch_id":"batch-20261013-advance-20261021-r01-mathematical-representation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"9487f662fab0dfab33f9de091f76a8ffcf961a4b89fc71fe7c7742e77f6a4104","family_id":"qf-app21-representation-affine-table","seed":202610211004,"semantic_template":"qf-app21-representation-affine-table/{\"a\":0,\"b\":-9,\"xs\":[0,1,3]}"},"fields":{"title":"A Rule-to-Table Bridge on an Explicit Finite Domain","stem":"Use only the explicitly supplied rule, symbols and finite pair table. Graph appearance supplies no values, and agreement on the listed inputs proves no equivalence on unlisted domains. a=0, b=-9, inputs=[0, 1, 3]; f(x)=a*x+b. Give (a,b,sorted distinct inputs,every [x,f(x)] row).","answer":{"kind":"expression","value":"(0, -9, [0, 1, 3], [[0, -9], [1, -9], [3, -9]])","explanation":"Remove repeated inputs, sort numerically and evaluate the rule at every declared input. Do not fill unlisted points from a picture. 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, -9, [0, 1, 3], [[0, -9], [1, -9], [3, -9]])."},"skills":["A Rule-to-Table Bridge on an Explicit Finite Domain"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-r01-mathematical-representation-0005","batch_id":"batch-20261013-advance-20261021-r01-mathematical-representation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"5694f859a1e3d2b4444e2e6e793298c50939da00e195cc5fa4ab6576e3871ecb","family_id":"qf-app21-representation-affine-table","seed":202610211005,"semantic_template":"qf-app21-representation-affine-table/{\"a\":1,\"b\":-8,\"xs\":[1,2,4]}"},"fields":{"title":"A Rule-to-Table Bridge on an Explicit Finite Domain","stem":"Use only the explicitly supplied rule, symbols and finite pair table. Graph appearance supplies no values, and agreement on the listed inputs proves no equivalence on unlisted domains. a=1, b=-8, inputs=[1, 2, 4]; f(x)=a*x+b. Give (a,b,sorted distinct inputs,every [x,f(x)] row).","answer":{"kind":"expression","value":"(1, -8, [1, 2, 4], [[1, -7], [2, -6], [4, -4]])","explanation":"Remove repeated inputs, sort numerically and evaluate the rule at every declared input. Do not fill unlisted points from a picture. 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, -8, [1, 2, 4], [[1, -7], [2, -6], [4, -4]])."},"skills":["A Rule-to-Table Bridge on an Explicit Finite Domain"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-r01-mathematical-representation-0006","batch_id":"batch-20261013-advance-20261021-r01-mathematical-representation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"2a22308f112558c9f61c9aed19707b138bdde85f9dbe86f9b22bba5e0bd02fd1","family_id":"qf-app21-representation-affine-table","seed":202610211006,"semantic_template":"qf-app21-representation-affine-table/{\"a\":2,\"b\":-7,\"xs\":[2,3,5]}"},"fields":{"title":"A Rule-to-Table Bridge on an Explicit Finite Domain","stem":"Use only the explicitly supplied rule, symbols and finite pair table. Graph appearance supplies no values, and agreement on the listed inputs proves no equivalence on unlisted domains. a=2, b=-7, inputs=[2, 3, 5]; f(x)=a*x+b. Give (a,b,sorted distinct inputs,every [x,f(x)] row).","answer":{"kind":"expression","value":"(2, -7, [2, 3, 5], [[2, -3], [3, -1], [5, 3]])","explanation":"Remove repeated inputs, sort numerically and evaluate the rule at every declared input. Do not fill unlisted points from a picture. 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, -7, [2, 3, 5], [[2, -3], [3, -1], [5, 3]])."},"skills":["A Rule-to-Table Bridge on an Explicit Finite Domain"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-r01-mathematical-representation-0007","batch_id":"batch-20261013-advance-20261021-r01-mathematical-representation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"e87a3d5ff9a336c0e9d160e4f08316073e825de8d2986d313977e269b7336ad0","family_id":"qf-app21-representation-affine-table","seed":202610211007,"semantic_template":"qf-app21-representation-affine-table/{\"a\":3,\"b\":-6,\"xs\":[3,4,6]}"},"fields":{"title":"A Rule-to-Table Bridge on an Explicit Finite Domain","stem":"Use only the explicitly supplied rule, symbols and finite pair table. Graph appearance supplies no values, and agreement on the listed inputs proves no equivalence on unlisted domains. a=3, b=-6, inputs=[3, 4, 6]; f(x)=a*x+b. Give (a,b,sorted distinct inputs,every [x,f(x)] row).","answer":{"kind":"expression","value":"(3, -6, [3, 4, 6], [[3, 3], [4, 6], [6, 12]])","explanation":"Remove repeated inputs, sort numerically and evaluate the rule at every declared input. Do not fill unlisted points from a picture. 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, -6, [3, 4, 6], [[3, 3], [4, 6], [6, 12]])."},"skills":["A Rule-to-Table Bridge on an Explicit Finite Domain"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-r01-mathematical-representation-0008","batch_id":"batch-20261013-advance-20261021-r01-mathematical-representation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"78b1866d802977cadaca33a89615eb156377b47a8f4a86d166fd9fcbba9e7971","family_id":"qf-app21-representation-affine-table","seed":202610211008,"semantic_template":"qf-app21-representation-affine-table/{\"a\":-3,\"b\":-5,\"xs\":[-3,-2,0]}"},"fields":{"title":"A Rule-to-Table Bridge on an Explicit Finite Domain","stem":"Use only the explicitly supplied rule, symbols and finite pair table. Graph appearance supplies no values, and agreement on the listed inputs proves no equivalence on unlisted domains. a=-3, b=-5, inputs=[-3, -2, 0]; f(x)=a*x+b. Give (a,b,sorted distinct inputs,every [x,f(x)] row).","answer":{"kind":"expression","value":"(-3, -5, [-3, -2, 0], [[-3, 4], [-2, 1], [0, -5]])","explanation":"Remove repeated inputs, sort numerically and evaluate the rule at every declared input. Do not fill unlisted points from a picture. 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, [-3, -2, 0], [[-3, 4], [-2, 1], [0, -5]])."},"skills":["A Rule-to-Table Bridge on an Explicit Finite Domain"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-r01-mathematical-representation-0009","batch_id":"batch-20261013-advance-20261021-r01-mathematical-representation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"598fd5461c19effa03c2194d3701cae86f2620bbc26f803e87025e8bc1be1991","family_id":"qf-app21-representation-affine-table","seed":202610211009,"semantic_template":"qf-app21-representation-affine-table/{\"a\":-2,\"b\":-4,\"xs\":[-2,-1,1]}"},"fields":{"title":"A Rule-to-Table Bridge on an Explicit Finite Domain","stem":"Use only the explicitly supplied rule, symbols and finite pair table. Graph appearance supplies no values, and agreement on the listed inputs proves no equivalence on unlisted domains. a=-2, b=-4, inputs=[-2, -1, 1]; f(x)=a*x+b. Give (a,b,sorted distinct inputs,every [x,f(x)] row).","answer":{"kind":"expression","value":"(-2, -4, [-2, -1, 1], [[-2, 0], [-1, -2], [1, -6]])","explanation":"Remove repeated inputs, sort numerically and evaluate the rule at every declared input. Do not fill unlisted points from a picture. 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, -1, 1], [[-2, 0], [-1, -2], [1, -6]])."},"skills":["A Rule-to-Table Bridge on an Explicit Finite Domain"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-r01-mathematical-representation-0010","batch_id":"batch-20261013-advance-20261021-r01-mathematical-representation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"035ab33ca28a3089f81ff1d7fbb4a3eb69bfbeebf6f01eb23176912d25a79847","family_id":"qf-app21-representation-affine-table","seed":202610211010,"semantic_template":"qf-app21-representation-affine-table/{\"a\":-1,\"b\":-3,\"xs\":[-1,0,2]}"},"fields":{"title":"A Rule-to-Table Bridge on an Explicit Finite Domain","stem":"Use only the explicitly supplied rule, symbols and finite pair table. Graph appearance supplies no values, and agreement on the listed inputs proves no equivalence on unlisted domains. a=-1, b=-3, inputs=[-1, 0, 2]; f(x)=a*x+b. Give (a,b,sorted distinct inputs,every [x,f(x)] row).","answer":{"kind":"expression","value":"(-1, -3, [-1, 0, 2], [[-1, -2], [0, -3], [2, -5]])","explanation":"Remove repeated inputs, sort numerically and evaluate the rule at every declared input. Do not fill unlisted points from a picture. 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, 0, 2], [[-1, -2], [0, -3], [2, -5]])."},"skills":["A Rule-to-Table Bridge on an Explicit Finite Domain"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-r01-mathematical-representation-0011","batch_id":"batch-20261013-advance-20261021-r01-mathematical-representation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"4c755b79fc87990323502f8737c99375253f969edb1fa748c96c9dfc2c629642","family_id":"qf-app21-representation-affine-table","seed":202610211011,"semantic_template":"qf-app21-representation-affine-table/{\"a\":0,\"b\":-2,\"xs\":[0,1,3]}"},"fields":{"title":"A Rule-to-Table Bridge on an Explicit Finite Domain","stem":"Use only the explicitly supplied rule, symbols and finite pair table. Graph appearance supplies no values, and agreement on the listed inputs proves no equivalence on unlisted domains. a=0, b=-2, inputs=[0, 1, 3]; f(x)=a*x+b. Give (a,b,sorted distinct inputs,every [x,f(x)] row).","answer":{"kind":"expression","value":"(0, -2, [0, 1, 3], [[0, -2], [1, -2], [3, -2]])","explanation":"Remove repeated inputs, sort numerically and evaluate the rule at every declared input. Do not fill unlisted points from a picture. 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, -2, [0, 1, 3], [[0, -2], [1, -2], [3, -2]])."},"skills":["A Rule-to-Table Bridge on an Explicit Finite Domain"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-r01-mathematical-representation-0012","batch_id":"batch-20261013-advance-20261021-r01-mathematical-representation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"a615faebf624f7829db5b9cc1c98c7d68ebf9fd71ef4c87064ed5007cfdfdb47","family_id":"qf-app21-representation-affine-table","seed":202610211012,"semantic_template":"qf-app21-representation-affine-table/{\"a\":1,\"b\":-1,\"xs\":[1,2,4]}"},"fields":{"title":"A Rule-to-Table Bridge on an Explicit Finite Domain","stem":"Use only the explicitly supplied rule, symbols and finite pair table. Graph appearance supplies no values, and agreement on the listed inputs proves no equivalence on unlisted domains. a=1, b=-1, inputs=[1, 2, 4]; f(x)=a*x+b. Give (a,b,sorted distinct inputs,every [x,f(x)] row).","answer":{"kind":"expression","value":"(1, -1, [1, 2, 4], [[1, 0], [2, 1], [4, 3]])","explanation":"Remove repeated inputs, sort numerically and evaluate the rule at every declared input. Do not fill unlisted points from a picture. 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, -1, [1, 2, 4], [[1, 0], [2, 1], [4, 3]])."},"skills":["A Rule-to-Table Bridge on an Explicit Finite Domain"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-r01-mathematical-representation-0013","batch_id":"batch-20261013-advance-20261021-r01-mathematical-representation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"0639ce7aa5833a65a7df2ab5bdbc73c3a09cd5ca712bb8a78a1148e9fd5e2364","family_id":"qf-app21-representation-affine-table","seed":202610211013,"semantic_template":"qf-app21-representation-affine-table/{\"a\":2,\"b\":0,\"xs\":[2,3,5]}"},"fields":{"title":"A Rule-to-Table Bridge on an Explicit Finite Domain","stem":"Use only the explicitly supplied rule, symbols and finite pair table. Graph appearance supplies no values, and agreement on the listed inputs proves no equivalence on unlisted domains. a=2, b=0, inputs=[2, 3, 5]; f(x)=a*x+b. Give (a,b,sorted distinct inputs,every [x,f(x)] row).","answer":{"kind":"expression","value":"(2, 0, [2, 3, 5], [[2, 4], [3, 6], [5, 10]])","explanation":"Remove repeated inputs, sort numerically and evaluate the rule at every declared input. Do not fill unlisted points from a picture. 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, 0, [2, 3, 5], [[2, 4], [3, 6], [5, 10]])."},"skills":["A Rule-to-Table Bridge on an Explicit Finite Domain"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-r01-mathematical-representation-0014","batch_id":"batch-20261013-advance-20261021-r01-mathematical-representation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"ef5d5dfa7e77a83920177b6072f9e738eeb38e3e6a6467516af1ef5f4e124f2f","family_id":"qf-app21-representation-affine-table","seed":202610211014,"semantic_template":"qf-app21-representation-affine-table/{\"a\":3,\"b\":1,\"xs\":[3,4,6]}"},"fields":{"title":"A Rule-to-Table Bridge on an Explicit Finite Domain","stem":"Use only the explicitly supplied rule, symbols and finite pair table. Graph appearance supplies no values, and agreement on the listed inputs proves no equivalence on unlisted domains. a=3, b=1, inputs=[3, 4, 6]; f(x)=a*x+b. Give (a,b,sorted distinct inputs,every [x,f(x)] row).","answer":{"kind":"expression","value":"(3, 1, [3, 4, 6], [[3, 10], [4, 13], [6, 19]])","explanation":"Remove repeated inputs, sort numerically and evaluate the rule at every declared input. Do not fill unlisted points from a picture. 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, [3, 4, 6], [[3, 10], [4, 13], [6, 19]])."},"skills":["A Rule-to-Table Bridge on an Explicit Finite Domain"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-r01-mathematical-representation-0015","batch_id":"batch-20261013-advance-20261021-r01-mathematical-representation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"3f8cf7f3a8873c93170946bc973bd267d7ae7456fb476095c9a77494bd24fa8f","family_id":"qf-app21-representation-affine-table","seed":202610211015,"semantic_template":"qf-app21-representation-affine-table/{\"a\":-3,\"b\":2,\"xs\":[-3,-2,0]}"},"fields":{"title":"A Rule-to-Table Bridge on an Explicit Finite Domain","stem":"Use only the explicitly supplied rule, symbols and finite pair table. Graph appearance supplies no values, and agreement on the listed inputs proves no equivalence on unlisted domains. a=-3, b=2, inputs=[-3, -2, 0]; f(x)=a*x+b. Give (a,b,sorted distinct inputs,every [x,f(x)] row).","answer":{"kind":"expression","value":"(-3, 2, [-3, -2, 0], [[-3, 11], [-2, 8], [0, 2]])","explanation":"Remove repeated inputs, sort numerically and evaluate the rule at every declared input. Do not fill unlisted points from a picture. 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, [-3, -2, 0], [[-3, 11], [-2, 8], [0, 2]])."},"skills":["A Rule-to-Table Bridge on an Explicit Finite Domain"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-r01-mathematical-representation-0016","batch_id":"batch-20261013-advance-20261021-r01-mathematical-representation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"11687c9e4d41ab680678c66beb05a4572d39ff011401e2d044d33b740b777ad0","family_id":"qf-app21-representation-affine-table","seed":202610211016,"semantic_template":"qf-app21-representation-affine-table/{\"a\":-2,\"b\":3,\"xs\":[-2,-1,1]}"},"fields":{"title":"A Rule-to-Table Bridge on an Explicit Finite Domain","stem":"Use only the explicitly supplied rule, symbols and finite pair table. Graph appearance supplies no values, and agreement on the listed inputs proves no equivalence on unlisted domains. a=-2, b=3, inputs=[-2, -1, 1]; f(x)=a*x+b. Give (a,b,sorted distinct inputs,every [x,f(x)] row).","answer":{"kind":"expression","value":"(-2, 3, [-2, -1, 1], [[-2, 7], [-1, 5], [1, 1]])","explanation":"Remove repeated inputs, sort numerically and evaluate the rule at every declared input. Do not fill unlisted points from a picture. 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, [-2, -1, 1], [[-2, 7], [-1, 5], [1, 1]])."},"skills":["A Rule-to-Table Bridge on an Explicit Finite Domain"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-r01-mathematical-representation-0017","batch_id":"batch-20261013-advance-20261021-r01-mathematical-representation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"6fd2411e92a92f7f0d8b2458d49560bd8732d897180713423da18380f4a2a914","family_id":"qf-app21-representation-affine-table","seed":202610211017,"semantic_template":"qf-app21-representation-affine-table/{\"a\":-1,\"b\":4,\"xs\":[-1,0,2]}"},"fields":{"title":"A Rule-to-Table Bridge on an Explicit Finite Domain","stem":"Use only the explicitly supplied rule, symbols and finite pair table. Graph appearance supplies no values, and agreement on the listed inputs proves no equivalence on unlisted domains. a=-1, b=4, inputs=[-1, 0, 2]; f(x)=a*x+b. Give (a,b,sorted distinct inputs,every [x,f(x)] row).","answer":{"kind":"expression","value":"(-1, 4, [-1, 0, 2], [[-1, 5], [0, 4], [2, 2]])","explanation":"Remove repeated inputs, sort numerically and evaluate the rule at every declared input. Do not fill unlisted points from a picture. 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, 4, [-1, 0, 2], [[-1, 5], [0, 4], [2, 2]])."},"skills":["A Rule-to-Table Bridge on an Explicit Finite Domain"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-r01-mathematical-representation-0018","batch_id":"batch-20261013-advance-20261021-r01-mathematical-representation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"56ae3a020676d2ea83cc3951931de5d7a5c6f6d75aea20cd3feb6f3817006703","family_id":"qf-app21-representation-affine-table","seed":202610211018,"semantic_template":"qf-app21-representation-affine-table/{\"a\":0,\"b\":5,\"xs\":[0,1,3]}"},"fields":{"title":"A Rule-to-Table Bridge on an Explicit Finite Domain","stem":"Use only the explicitly supplied rule, symbols and finite pair table. Graph appearance supplies no values, and agreement on the listed inputs proves no equivalence on unlisted domains. a=0, b=5, inputs=[0, 1, 3]; f(x)=a*x+b. Give (a,b,sorted distinct inputs,every [x,f(x)] row).","answer":{"kind":"expression","value":"(0, 5, [0, 1, 3], [[0, 5], [1, 5], [3, 5]])","explanation":"Remove repeated inputs, sort numerically and evaluate the rule at every declared input. Do not fill unlisted points from a picture. 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, 5, [0, 1, 3], [[0, 5], [1, 5], [3, 5]])."},"skills":["A Rule-to-Table Bridge on an Explicit Finite Domain"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-r01-mathematical-representation-0019","batch_id":"batch-20261013-advance-20261021-r01-mathematical-representation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"b0bcc838fedf69c02b62a037b619dd4302dd642f114c04aa0b6018286323fda6","family_id":"qf-app21-representation-affine-table","seed":202610211019,"semantic_template":"qf-app21-representation-affine-table/{\"a\":1,\"b\":6,\"xs\":[1,2,4]}"},"fields":{"title":"A Rule-to-Table Bridge on an Explicit Finite Domain","stem":"Use only the explicitly supplied rule, symbols and finite pair table. Graph appearance supplies no values, and agreement on the listed inputs proves no equivalence on unlisted domains. a=1, b=6, inputs=[1, 2, 4]; f(x)=a*x+b. Give (a,b,sorted distinct inputs,every [x,f(x)] row).","answer":{"kind":"expression","value":"(1, 6, [1, 2, 4], [[1, 7], [2, 8], [4, 10]])","explanation":"Remove repeated inputs, sort numerically and evaluate the rule at every declared input. Do not fill unlisted points from a picture. 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, 6, [1, 2, 4], [[1, 7], [2, 8], [4, 10]])."},"skills":["A Rule-to-Table Bridge on an Explicit Finite Domain"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-r01-mathematical-representation-0020","batch_id":"batch-20261013-advance-20261021-r01-mathematical-representation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"165d825948f6df03f77464c8b7f038b61ba18ed59f71c58956c246cc8f155eac","family_id":"qf-app21-representation-affine-table","seed":202610211020,"semantic_template":"qf-app21-representation-affine-table/{\"a\":2,\"b\":7,\"xs\":[2,3,5]}"},"fields":{"title":"A Rule-to-Table Bridge on an Explicit Finite Domain","stem":"Use only the explicitly supplied rule, symbols and finite pair table. Graph appearance supplies no values, and agreement on the listed inputs proves no equivalence on unlisted domains. a=2, b=7, inputs=[2, 3, 5]; f(x)=a*x+b. Give (a,b,sorted distinct inputs,every [x,f(x)] row).","answer":{"kind":"expression","value":"(2, 7, [2, 3, 5], [[2, 11], [3, 13], [5, 17]])","explanation":"Remove repeated inputs, sort numerically and evaluate the rule at every declared input. Do not fill unlisted points from a picture. 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, 7, [2, 3, 5], [[2, 11], [3, 13], [5, 17]])."},"skills":["A Rule-to-Table Bridge on an Explicit Finite Domain"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-r01-mathematical-representation-0021","batch_id":"batch-20261013-advance-20261021-r01-mathematical-representation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"3ac8ebb95a2695c730311a526804751592c9412d68c2e0422a6e748da9449ce9","family_id":"qf-app21-representation-affine-table","seed":202610211021,"semantic_template":"qf-app21-representation-affine-table/{\"a\":3,\"b\":8,\"xs\":[3,4,6]}"},"fields":{"title":"A Rule-to-Table Bridge on an Explicit Finite Domain","stem":"Use only the explicitly supplied rule, symbols and finite pair table. Graph appearance supplies no values, and agreement on the listed inputs proves no equivalence on unlisted domains. a=3, b=8, inputs=[3, 4, 6]; f(x)=a*x+b. Give (a,b,sorted distinct inputs,every [x,f(x)] row).","answer":{"kind":"expression","value":"(3, 8, [3, 4, 6], [[3, 17], [4, 20], [6, 26]])","explanation":"Remove repeated inputs, sort numerically and evaluate the rule at every declared input. Do not fill unlisted points from a picture. 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, 8, [3, 4, 6], [[3, 17], [4, 20], [6, 26]])."},"skills":["A Rule-to-Table Bridge on an Explicit Finite Domain"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-r01-mathematical-representation-0022","batch_id":"batch-20261013-advance-20261021-r01-mathematical-representation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"e5a6cdef355ee90d14fef111a23a1c093321757813497e194bdf8b3ebb419747","family_id":"qf-app21-representation-affine-table","seed":202610211022,"semantic_template":"qf-app21-representation-affine-table/{\"a\":-3,\"b\":9,\"xs\":[-3,-2,0]}"},"fields":{"title":"A Rule-to-Table Bridge on an Explicit Finite Domain","stem":"Use only the explicitly supplied rule, symbols and finite pair table. Graph appearance supplies no values, and agreement on the listed inputs proves no equivalence on unlisted domains. a=-3, b=9, inputs=[-3, -2, 0]; f(x)=a*x+b. Give (a,b,sorted distinct inputs,every [x,f(x)] row).","answer":{"kind":"expression","value":"(-3, 9, [-3, -2, 0], [[-3, 18], [-2, 15], [0, 9]])","explanation":"Remove repeated inputs, sort numerically and evaluate the rule at every declared input. Do not fill unlisted points from a picture. 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, [-3, -2, 0], [[-3, 18], [-2, 15], [0, 9]])."},"skills":["A Rule-to-Table Bridge on an Explicit Finite Domain"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-r01-mathematical-representation-0023","batch_id":"batch-20261013-advance-20261021-r01-mathematical-representation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"fcdaf258987c97d53a795975d1eed2c3e305fb53f6c470f99c26d227ae0275d8","family_id":"qf-app21-representation-affine-table","seed":202610211023,"semantic_template":"qf-app21-representation-affine-table/{\"a\":-2,\"b\":10,\"xs\":[-2,-1,1]}"},"fields":{"title":"A Rule-to-Table Bridge on an Explicit Finite Domain","stem":"Use only the explicitly supplied rule, symbols and finite pair table. Graph appearance supplies no values, and agreement on the listed inputs proves no equivalence on unlisted domains. a=-2, b=10, inputs=[-2, -1, 1]; f(x)=a*x+b. Give (a,b,sorted distinct inputs,every [x,f(x)] row).","answer":{"kind":"expression","value":"(-2, 10, [-2, -1, 1], [[-2, 14], [-1, 12], [1, 8]])","explanation":"Remove repeated inputs, sort numerically and evaluate the rule at every declared input. Do not fill unlisted points from a picture. 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, [-2, -1, 1], [[-2, 14], [-1, 12], [1, 8]])."},"skills":["A Rule-to-Table Bridge on an Explicit Finite Domain"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-r01-mathematical-representation-0024","batch_id":"batch-20261013-advance-20261021-r01-mathematical-representation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"0499d317b51be6432cb28fe6ec0588fdf62d5c8ee12785c7d53e4d46f8c82148","family_id":"qf-app21-representation-affine-table","seed":202610211024,"semantic_template":"qf-app21-representation-affine-table/{\"a\":-1,\"b\":11,\"xs\":[-1,0,2]}"},"fields":{"title":"A Rule-to-Table Bridge on an Explicit Finite Domain","stem":"Use only the explicitly supplied rule, symbols and finite pair table. Graph appearance supplies no values, and agreement on the listed inputs proves no equivalence on unlisted domains. a=-1, b=11, inputs=[-1, 0, 2]; f(x)=a*x+b. Give (a,b,sorted distinct inputs,every [x,f(x)] row).","answer":{"kind":"expression","value":"(-1, 11, [-1, 0, 2], [[-1, 12], [0, 11], [2, 9]])","explanation":"Remove repeated inputs, sort numerically and evaluate the rule at every declared input. Do not fill unlisted points from a picture. 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, 11, [-1, 0, 2], [[-1, 12], [0, 11], [2, 9]])."},"skills":["A Rule-to-Table Bridge on an Explicit Finite Domain"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-r01-mathematical-representation-0025","batch_id":"batch-20261013-advance-20261021-r01-mathematical-representation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"cb45c0673eecd0945541ff66689ee8821674fd34e31ab9806555ab0b21b112fe","family_id":"qf-app21-representation-affine-table","seed":202610211025,"semantic_template":"qf-app21-representation-affine-table/{\"a\":0,\"b\":12,\"xs\":[0,1,3]}"},"fields":{"title":"A Rule-to-Table Bridge on an Explicit Finite Domain","stem":"Use only the explicitly supplied rule, symbols and finite pair table. Graph appearance supplies no values, and agreement on the listed inputs proves no equivalence on unlisted domains. a=0, b=12, inputs=[0, 1, 3]; f(x)=a*x+b. Give (a,b,sorted distinct inputs,every [x,f(x)] row).","answer":{"kind":"expression","value":"(0, 12, [0, 1, 3], [[0, 12], [1, 12], [3, 12]])","explanation":"Remove repeated inputs, sort numerically and evaluate the rule at every declared input. Do not fill unlisted points from a picture. 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, 12, [0, 1, 3], [[0, 12], [1, 12], [3, 12]])."},"skills":["A Rule-to-Table Bridge on an Explicit Finite Domain"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-r01-mathematical-representation-0026","batch_id":"batch-20261013-advance-20261021-r01-mathematical-representation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"049662ab7a5b98d65c3ff09039306d38d10e8d4d68d058ce66c8f84cc3686226","family_id":"qf-app21-representation-two-point-rule","seed":202610211026,"semantic_template":"qf-app21-representation-two-point-rule/{\"points\":[[-1,-9],[-2,-6]]}"},"fields":{"title":"The Nonvertical Affine Rule through Two Distinct Inputs","stem":"Use only the explicitly supplied rule, symbols and finite pair table. Graph appearance supplies no values, and agreement on the listed inputs proves no equivalence on unlisted domains. Points=[[-2, -6], [-1, -9]]. Normalize tuple collections by removing identical tuples and sorting their JSON strings with the source’s en-locale comparison. This is canonical record order, not numerical coordinate order; number any output rows from 0 only after that normalization. Require exactly two distinct pairs with different x-coordinates. Give (canonical points,reduced rational slope,intercept), with no /1 for integer results.","answer":{"kind":"expression","value":"([[-1, -9], [-2, -6]], -3, -12)","explanation":"Use the difference quotient for the slope and substitute either point to obtain the intercept; duplicate copies of a point do not create a new point. 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], [-2, -6]], -3, -12)."},"skills":["The Nonvertical Affine Rule through Two Distinct Inputs"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-r01-mathematical-representation-0027","batch_id":"batch-20261013-advance-20261021-r01-mathematical-representation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"903607fdb342c6759dbdf85b74953b808afc1ca5f067e894af551c0f5c249db1","family_id":"qf-app21-representation-two-point-rule","seed":202610211027,"semantic_template":"qf-app21-representation-two-point-rule/{\"points\":[[-1,-9],[1,-13]]}"},"fields":{"title":"The Nonvertical Affine Rule through Two Distinct Inputs","stem":"Use only the explicitly supplied rule, symbols and finite pair table. Graph appearance supplies no values, and agreement on the listed inputs proves no equivalence on unlisted domains. Points=[[-1, -9], [1, -13]]. Normalize tuple collections by removing identical tuples and sorting their JSON strings with the source’s en-locale comparison. This is canonical record order, not numerical coordinate order; number any output rows from 0 only after that normalization. Require exactly two distinct pairs with different x-coordinates. Give (canonical points,reduced rational slope,intercept), with no /1 for integer results.","answer":{"kind":"expression","value":"([[-1, -9], [1, -13]], -2, -11)","explanation":"Use the difference quotient for the slope and substitute either point to obtain the intercept; duplicate copies of a point do not create a new point. 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], [1, -13]], -2, -11)."},"skills":["The Nonvertical Affine Rule through Two Distinct Inputs"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-r01-mathematical-representation-0028","batch_id":"batch-20261013-advance-20261021-r01-mathematical-representation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"9b42bfdde5c6938d7f5fac03b12eb22fe16fe77c71ab71ca3150f83b046ba5b7","family_id":"qf-app21-representation-two-point-rule","seed":202610211028,"semantic_template":"qf-app21-representation-two-point-rule/{\"points\":[[0,-10],[3,-13]]}"},"fields":{"title":"The Nonvertical Affine Rule through Two Distinct Inputs","stem":"Use only the explicitly supplied rule, symbols and finite pair table. Graph appearance supplies no values, and agreement on the listed inputs proves no equivalence on unlisted domains. Points=[[0, -10], [3, -13]]. Normalize tuple collections by removing identical tuples and sorting their JSON strings with the source’s en-locale comparison. This is canonical record order, not numerical coordinate order; number any output rows from 0 only after that normalization. Require exactly two distinct pairs with different x-coordinates. Give (canonical points,reduced rational slope,intercept), with no /1 for integer results.","answer":{"kind":"expression","value":"([[0, -10], [3, -13]], -1, -10)","explanation":"Use the difference quotient for the slope and substitute either point to obtain the intercept; duplicate copies of a point do not create a new point. 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, -10], [3, -13]], -1, -10)."},"skills":["The Nonvertical Affine Rule through Two Distinct Inputs"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-r01-mathematical-representation-0029","batch_id":"batch-20261013-advance-20261021-r01-mathematical-representation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"7c56ca0b80089ddc29743b952cebf0eb21714b24e9c118399ae4f5c07590f3a3","family_id":"qf-app21-representation-two-point-rule","seed":202610211029,"semantic_template":"qf-app21-representation-two-point-rule/{\"points\":[[1,-9],[2,-9]]}"},"fields":{"title":"The Nonvertical Affine Rule through Two Distinct Inputs","stem":"Use only the explicitly supplied rule, symbols and finite pair table. Graph appearance supplies no values, and agreement on the listed inputs proves no equivalence on unlisted domains. Points=[[1, -9], [2, -9]]. Normalize tuple collections by removing identical tuples and sorting their JSON strings with the source’s en-locale comparison. This is canonical record order, not numerical coordinate order; number any output rows from 0 only after that normalization. Require exactly two distinct pairs with different x-coordinates. Give (canonical points,reduced rational slope,intercept), with no /1 for integer results.","answer":{"kind":"expression","value":"([[1, -9], [2, -9]], 0, -9)","explanation":"Use the difference quotient for the slope and substitute either point to obtain the intercept; duplicate copies of a point do not create a new point. 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], [2, -9]], 0, -9)."},"skills":["The Nonvertical Affine Rule through Two Distinct Inputs"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-r01-mathematical-representation-0030","batch_id":"batch-20261013-advance-20261021-r01-mathematical-representation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"45fcfd2c1a3a971a53804e1a9ac0df81dce6819c910d61f50367ad47c0f345c2","family_id":"qf-app21-representation-two-point-rule","seed":202610211030,"semantic_template":"qf-app21-representation-two-point-rule/{\"points\":[[2,-6],[4,-4]]}"},"fields":{"title":"The Nonvertical Affine Rule through Two Distinct Inputs","stem":"Use only the explicitly supplied rule, symbols and finite pair table. Graph appearance supplies no values, and agreement on the listed inputs proves no equivalence on unlisted domains. Points=[[2, -6], [4, -4]]. Normalize tuple collections by removing identical tuples and sorting their JSON strings with the source’s en-locale comparison. This is canonical record order, not numerical coordinate order; number any output rows from 0 only after that normalization. Require exactly two distinct pairs with different x-coordinates. Give (canonical points,reduced rational slope,intercept), with no /1 for integer results.","answer":{"kind":"expression","value":"([[2, -6], [4, -4]], 1, -8)","explanation":"Use the difference quotient for the slope and substitute either point to obtain the intercept; duplicate copies of a point do not create a new point. 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], [4, -4]], 1, -8)."},"skills":["The Nonvertical Affine Rule through Two Distinct Inputs"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-r01-mathematical-representation-0031","batch_id":"batch-20261013-advance-20261021-r01-mathematical-representation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"1583cfe09e3de882d917ca51be7835ea8ca0a7e31c853e74561d2be5eeed0b36","family_id":"qf-app21-representation-two-point-rule","seed":202610211031,"semantic_template":"qf-app21-representation-two-point-rule/{\"points\":[[-2,-11],[1,-5]]}"},"fields":{"title":"The Nonvertical Affine Rule through Two Distinct Inputs","stem":"Use only the explicitly supplied rule, symbols and finite pair table. Graph appearance supplies no values, and agreement on the listed inputs proves no equivalence on unlisted domains. Points=[[-2, -11], [1, -5]]. Normalize tuple collections by removing identical tuples and sorting their JSON strings with the source’s en-locale comparison. This is canonical record order, not numerical coordinate order; number any output rows from 0 only after that normalization. Require exactly two distinct pairs with different x-coordinates. Give (canonical points,reduced rational slope,intercept), with no /1 for integer results.","answer":{"kind":"expression","value":"([[-2, -11], [1, -5]], 2, -7)","explanation":"Use the difference quotient for the slope and substitute either point to obtain the intercept; duplicate copies of a point do not create a new point. 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], [1, -5]], 2, -7)."},"skills":["The Nonvertical Affine Rule through Two Distinct Inputs"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-r01-mathematical-representation-0032","batch_id":"batch-20261013-advance-20261021-r01-mathematical-representation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"93c92a84a265e3d21a94f2448bc16a19d1c57f4607043e20dda445a2de956d25","family_id":"qf-app21-representation-two-point-rule","seed":202610211032,"semantic_template":"qf-app21-representation-two-point-rule/{\"points\":[[-1,-9],[0,-6]]}"},"fields":{"title":"The Nonvertical Affine Rule through Two Distinct Inputs","stem":"Use only the explicitly supplied rule, symbols and finite pair table. Graph appearance supplies no values, and agreement on the listed inputs proves no equivalence on unlisted domains. Points=[[-1, -9], [0, -6]]. Normalize tuple collections by removing identical tuples and sorting their JSON strings with the source’s en-locale comparison. This is canonical record order, not numerical coordinate order; number any output rows from 0 only after that normalization. Require exactly two distinct pairs with different x-coordinates. Give (canonical points,reduced rational slope,intercept), with no /1 for integer results.","answer":{"kind":"expression","value":"([[-1, -9], [0, -6]], 3, -6)","explanation":"Use the difference quotient for the slope and substitute either point to obtain the intercept; duplicate copies of a point do not create a new point. 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, -6]], 3, -6)."},"skills":["The Nonvertical Affine Rule through Two Distinct Inputs"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-r01-mathematical-representation-0033","batch_id":"batch-20261013-advance-20261021-r01-mathematical-representation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"702a4998b6c3df9877e0e3c55ffc2955d93e2a20bfd6cd922f752cf3e5ba6842","family_id":"qf-app21-representation-two-point-rule","seed":202610211033,"semantic_template":"qf-app21-representation-two-point-rule/{\"points\":[[0,-5],[2,-11]]}"},"fields":{"title":"The Nonvertical Affine Rule through Two Distinct Inputs","stem":"Use only the explicitly supplied rule, symbols and finite pair table. Graph appearance supplies no values, and agreement on the listed inputs proves no equivalence on unlisted domains. Points=[[0, -5], [2, -11]]. Normalize tuple collections by removing identical tuples and sorting their JSON strings with the source’s en-locale comparison. This is canonical record order, not numerical coordinate order; number any output rows from 0 only after that normalization. Require exactly two distinct pairs with different x-coordinates. Give (canonical points,reduced rational slope,intercept), with no /1 for integer results.","answer":{"kind":"expression","value":"([[0, -5], [2, -11]], -3, -5)","explanation":"Use the difference quotient for the slope and substitute either point to obtain the intercept; duplicate copies of a point do not create a new point. 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, -5], [2, -11]], -3, -5)."},"skills":["The Nonvertical Affine Rule through Two Distinct Inputs"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-r01-mathematical-representation-0034","batch_id":"batch-20261013-advance-20261021-r01-mathematical-representation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"bdc7ab7043a4609732592832dba32e0c3039eb231d7a51ab07d91dbf462ac658","family_id":"qf-app21-representation-two-point-rule","seed":202610211034,"semantic_template":"qf-app21-representation-two-point-rule/{\"points\":[[1,-6],[4,-12]]}"},"fields":{"title":"The Nonvertical Affine Rule through Two Distinct Inputs","stem":"Use only the explicitly supplied rule, symbols and finite pair table. Graph appearance supplies no values, and agreement on the listed inputs proves no equivalence on unlisted domains. Points=[[1, -6], [4, -12]]. Normalize tuple collections by removing identical tuples and sorting their JSON strings with the source’s en-locale comparison. This is canonical record order, not numerical coordinate order; number any output rows from 0 only after that normalization. Require exactly two distinct pairs with different x-coordinates. Give (canonical points,reduced rational slope,intercept), with no /1 for integer results.","answer":{"kind":"expression","value":"([[1, -6], [4, -12]], -2, -4)","explanation":"Use the difference quotient for the slope and substitute either point to obtain the intercept; duplicate copies of a point do not create a new point. 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, -6], [4, -12]], -2, -4)."},"skills":["The Nonvertical Affine Rule through Two Distinct Inputs"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-r01-mathematical-representation-0035","batch_id":"batch-20261013-advance-20261021-r01-mathematical-representation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"830bedc300d8298f48cceee4a923e4a9c0f302e1dcb5c893b1915746e1b6cc17","family_id":"qf-app21-representation-two-point-rule","seed":202610211035,"semantic_template":"qf-app21-representation-two-point-rule/{\"points\":[[2,-5],[3,-6]]}"},"fields":{"title":"The Nonvertical Affine Rule through Two Distinct Inputs","stem":"Use only the explicitly supplied rule, symbols and finite pair table. Graph appearance supplies no values, and agreement on the listed inputs proves no equivalence on unlisted domains. Points=[[2, -5], [3, -6]]. Normalize tuple collections by removing identical tuples and sorting their JSON strings with the source’s en-locale comparison. This is canonical record order, not numerical coordinate order; number any output rows from 0 only after that normalization. Require exactly two distinct pairs with different x-coordinates. Give (canonical points,reduced rational slope,intercept), with no /1 for integer results.","answer":{"kind":"expression","value":"([[2, -5], [3, -6]], -1, -3)","explanation":"Use the difference quotient for the slope and substitute either point to obtain the intercept; duplicate copies of a point do not create a new point. 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, -5], [3, -6]], -1, -3)."},"skills":["The Nonvertical Affine Rule through Two Distinct Inputs"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-r01-mathematical-representation-0036","batch_id":"batch-20261013-advance-20261021-r01-mathematical-representation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"38fd3fade23007dea1a5bf8402f9307dcf11f0e959b1518b61025fa4fb3d0d39","family_id":"qf-app21-representation-two-point-rule","seed":202610211036,"semantic_template":"qf-app21-representation-two-point-rule/{\"points\":[[-2,-2],[0,-2]]}"},"fields":{"title":"The Nonvertical Affine Rule through Two Distinct Inputs","stem":"Use only the explicitly supplied rule, symbols and finite pair table. Graph appearance supplies no values, and agreement on the listed inputs proves no equivalence on unlisted domains. Points=[[-2, -2], [0, -2]]. Normalize tuple collections by removing identical tuples and sorting their JSON strings with the source’s en-locale comparison. This is canonical record order, not numerical coordinate order; number any output rows from 0 only after that normalization. Require exactly two distinct pairs with different x-coordinates. Give (canonical points,reduced rational slope,intercept), with no /1 for integer results.","answer":{"kind":"expression","value":"([[-2, -2], [0, -2]], 0, -2)","explanation":"Use the difference quotient for the slope and substitute either point to obtain the intercept; duplicate copies of a point do not create a new point. 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], [0, -2]], 0, -2)."},"skills":["The Nonvertical Affine Rule through Two Distinct Inputs"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-r01-mathematical-representation-0037","batch_id":"batch-20261013-advance-20261021-r01-mathematical-representation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"81f7cd295a7f4569fb09b409e1c51da79e9c8a3102af7797f8eea4719db3bbc2","family_id":"qf-app21-representation-two-point-rule","seed":202610211037,"semantic_template":"qf-app21-representation-two-point-rule/{\"points\":[[-1,-2],[2,1]]}"},"fields":{"title":"The Nonvertical Affine Rule through Two Distinct Inputs","stem":"Use only the explicitly supplied rule, symbols and finite pair table. Graph appearance supplies no values, and agreement on the listed inputs proves no equivalence on unlisted domains. Points=[[-1, -2], [2, 1]]. Normalize tuple collections by removing identical tuples and sorting their JSON strings with the source’s en-locale comparison. This is canonical record order, not numerical coordinate order; number any output rows from 0 only after that normalization. Require exactly two distinct pairs with different x-coordinates. Give (canonical points,reduced rational slope,intercept), with no /1 for integer results.","answer":{"kind":"expression","value":"([[-1, -2], [2, 1]], 1, -1)","explanation":"Use the difference quotient for the slope and substitute either point to obtain the intercept; duplicate copies of a point do not create a new point. 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, 1]], 1, -1)."},"skills":["The Nonvertical Affine Rule through Two Distinct Inputs"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-r01-mathematical-representation-0038","batch_id":"batch-20261013-advance-20261021-r01-mathematical-representation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"4b6cf810b99cfbc7be2f4998ee2fdf90ea6e2967af1a8d2d5999a66d1f98d535","family_id":"qf-app21-representation-two-point-rule","seed":202610211038,"semantic_template":"qf-app21-representation-two-point-rule/{\"points\":[[0,0],[1,2]]}"},"fields":{"title":"The Nonvertical Affine Rule through Two Distinct Inputs","stem":"Use only the explicitly supplied rule, symbols and finite pair table. Graph appearance supplies no values, and agreement on the listed inputs proves no equivalence on unlisted domains. Points=[[0, 0], [1, 2]]. Normalize tuple collections by removing identical tuples and sorting their JSON strings with the source’s en-locale comparison. This is canonical record order, not numerical coordinate order; number any output rows from 0 only after that normalization. Require exactly two distinct pairs with different x-coordinates. Give (canonical points,reduced rational slope,intercept), with no /1 for integer results.","answer":{"kind":"expression","value":"([[0, 0], [1, 2]], 2, 0)","explanation":"Use the difference quotient for the slope and substitute either point to obtain the intercept; duplicate copies of a point do not create a new point. 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, 0], [1, 2]], 2, 0)."},"skills":["The Nonvertical Affine Rule through Two Distinct Inputs"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-r01-mathematical-representation-0039","batch_id":"batch-20261013-advance-20261021-r01-mathematical-representation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"49b83e50eabec8f1466042a2c505bd0b29d17e4aa0f16464657408e75a5659fa","family_id":"qf-app21-representation-two-point-rule","seed":202610211039,"semantic_template":"qf-app21-representation-two-point-rule/{\"points\":[[1,4],[3,10]]}"},"fields":{"title":"The Nonvertical Affine Rule through Two Distinct Inputs","stem":"Use only the explicitly supplied rule, symbols and finite pair table. Graph appearance supplies no values, and agreement on the listed inputs proves no equivalence on unlisted domains. Points=[[1, 4], [3, 10]]. Normalize tuple collections by removing identical tuples and sorting their JSON strings with the source’s en-locale comparison. This is canonical record order, not numerical coordinate order; number any output rows from 0 only after that normalization. Require exactly two distinct pairs with different x-coordinates. Give (canonical points,reduced rational slope,intercept), with no /1 for integer results.","answer":{"kind":"expression","value":"([[1, 4], [3, 10]], 3, 1)","explanation":"Use the difference quotient for the slope and substitute either point to obtain the intercept; duplicate copies of a point do not create a new point. 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, 4], [3, 10]], 3, 1)."},"skills":["The Nonvertical Affine Rule through Two Distinct Inputs"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-r01-mathematical-representation-0040","batch_id":"batch-20261013-advance-20261021-r01-mathematical-representation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"29d9e47e9ebaa0e6faae50759f7e7d63584da46d3f7f30767d4223fb8338cb04","family_id":"qf-app21-representation-two-point-rule","seed":202610211040,"semantic_template":"qf-app21-representation-two-point-rule/{\"points\":[[2,-4],[5,-13]]}"},"fields":{"title":"The Nonvertical Affine Rule through Two Distinct Inputs","stem":"Use only the explicitly supplied rule, symbols and finite pair table. Graph appearance supplies no values, and agreement on the listed inputs proves no equivalence on unlisted domains. Points=[[2, -4], [5, -13]]. Normalize tuple collections by removing identical tuples and sorting their JSON strings with the source’s en-locale comparison. This is canonical record order, not numerical coordinate order; number any output rows from 0 only after that normalization. Require exactly two distinct pairs with different x-coordinates. Give (canonical points,reduced rational slope,intercept), with no /1 for integer results.","answer":{"kind":"expression","value":"([[2, -4], [5, -13]], -3, 2)","explanation":"Use the difference quotient for the slope and substitute either point to obtain the intercept; duplicate copies of a point do not create a new point. 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], [5, -13]], -3, 2)."},"skills":["The Nonvertical Affine Rule through Two Distinct Inputs"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-r01-mathematical-representation-0041","batch_id":"batch-20261013-advance-20261021-r01-mathematical-representation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"e48a19cc6f921ff3e76518aad69c3ec44619bcc177be63f620fb08537888738c","family_id":"qf-app21-representation-two-point-rule","seed":202610211041,"semantic_template":"qf-app21-representation-two-point-rule/{\"points\":[[-1,5],[-2,7]]}"},"fields":{"title":"The Nonvertical Affine Rule through Two Distinct Inputs","stem":"Use only the explicitly supplied rule, symbols and finite pair table. Graph appearance supplies no values, and agreement on the listed inputs proves no equivalence on unlisted domains. Points=[[-2, 7], [-1, 5]]. Normalize tuple collections by removing identical tuples and sorting their JSON strings with the source’s en-locale comparison. This is canonical record order, not numerical coordinate order; number any output rows from 0 only after that normalization. Require exactly two distinct pairs with different x-coordinates. Give (canonical points,reduced rational slope,intercept), with no /1 for integer results.","answer":{"kind":"expression","value":"([[-1, 5], [-2, 7]], -2, 3)","explanation":"Use the difference quotient for the slope and substitute either point to obtain the intercept; duplicate copies of a point do not create a new point. 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], [-2, 7]], -2, 3)."},"skills":["The Nonvertical Affine Rule through Two Distinct Inputs"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-r01-mathematical-representation-0042","batch_id":"batch-20261013-advance-20261021-r01-mathematical-representation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"0cd9d273abf4df23145775be071c8c6ddcb1f09e9b5b5222fcffa9d404eb303e","family_id":"qf-app21-representation-two-point-rule","seed":202610211042,"semantic_template":"qf-app21-representation-two-point-rule/{\"points\":[[-1,5],[1,3]]}"},"fields":{"title":"The Nonvertical Affine Rule through Two Distinct Inputs","stem":"Use only the explicitly supplied rule, symbols and finite pair table. Graph appearance supplies no values, and agreement on the listed inputs proves no equivalence on unlisted domains. Points=[[-1, 5], [1, 3]]. Normalize tuple collections by removing identical tuples and sorting their JSON strings with the source’s en-locale comparison. This is canonical record order, not numerical coordinate order; number any output rows from 0 only after that normalization. Require exactly two distinct pairs with different x-coordinates. Give (canonical points,reduced rational slope,intercept), with no /1 for integer results.","answer":{"kind":"expression","value":"([[-1, 5], [1, 3]], -1, 4)","explanation":"Use the difference quotient for the slope and substitute either point to obtain the intercept; duplicate copies of a point do not create a new point. 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, 3]], -1, 4)."},"skills":["The Nonvertical Affine Rule through Two Distinct Inputs"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-r01-mathematical-representation-0043","batch_id":"batch-20261013-advance-20261021-r01-mathematical-representation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"2b03121d6ed61057b60313c725f5d2cb839967b021783b1ed75e79f461dc09d9","family_id":"qf-app21-representation-two-point-rule","seed":202610211043,"semantic_template":"qf-app21-representation-two-point-rule/{\"points\":[[0,5],[3,5]]}"},"fields":{"title":"The Nonvertical Affine Rule through Two Distinct Inputs","stem":"Use only the explicitly supplied rule, symbols and finite pair table. Graph appearance supplies no values, and agreement on the listed inputs proves no equivalence on unlisted domains. Points=[[0, 5], [3, 5]]. Normalize tuple collections by removing identical tuples and sorting their JSON strings with the source’s en-locale comparison. This is canonical record order, not numerical coordinate order; number any output rows from 0 only after that normalization. Require exactly two distinct pairs with different x-coordinates. Give (canonical points,reduced rational slope,intercept), with no /1 for integer results.","answer":{"kind":"expression","value":"([[0, 5], [3, 5]], 0, 5)","explanation":"Use the difference quotient for the slope and substitute either point to obtain the intercept; duplicate copies of a point do not create a new point. 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, 5], [3, 5]], 0, 5)."},"skills":["The Nonvertical Affine Rule through Two Distinct Inputs"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-r01-mathematical-representation-0044","batch_id":"batch-20261013-advance-20261021-r01-mathematical-representation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"b552986ccdbf3a16058b1df49048b7c96784d3bf3e7e893e6d94e4293cef90fc","family_id":"qf-app21-representation-two-point-rule","seed":202610211044,"semantic_template":"qf-app21-representation-two-point-rule/{\"points\":[[1,7],[2,8]]}"},"fields":{"title":"The Nonvertical Affine Rule through Two Distinct Inputs","stem":"Use only the explicitly supplied rule, symbols and finite pair table. Graph appearance supplies no values, and agreement on the listed inputs proves no equivalence on unlisted domains. Points=[[1, 7], [2, 8]]. Normalize tuple collections by removing identical tuples and sorting their JSON strings with the source’s en-locale comparison. This is canonical record order, not numerical coordinate order; number any output rows from 0 only after that normalization. Require exactly two distinct pairs with different x-coordinates. Give (canonical points,reduced rational slope,intercept), with no /1 for integer results.","answer":{"kind":"expression","value":"([[1, 7], [2, 8]], 1, 6)","explanation":"Use the difference quotient for the slope and substitute either point to obtain the intercept; duplicate copies of a point do not create a new point. 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, 8]], 1, 6)."},"skills":["The Nonvertical Affine Rule through Two Distinct Inputs"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-r01-mathematical-representation-0045","batch_id":"batch-20261013-advance-20261021-r01-mathematical-representation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"54118ac0e3d53352d766597bc953e6070cb7eaaf0e63cad15ef4d2a7c18fd336","family_id":"qf-app21-representation-two-point-rule","seed":202610211045,"semantic_template":"qf-app21-representation-two-point-rule/{\"points\":[[2,11],[4,15]]}"},"fields":{"title":"The Nonvertical Affine Rule through Two Distinct Inputs","stem":"Use only the explicitly supplied rule, symbols and finite pair table. Graph appearance supplies no values, and agreement on the listed inputs proves no equivalence on unlisted domains. Points=[[2, 11], [4, 15]]. Normalize tuple collections by removing identical tuples and sorting their JSON strings with the source’s en-locale comparison. This is canonical record order, not numerical coordinate order; number any output rows from 0 only after that normalization. Require exactly two distinct pairs with different x-coordinates. Give (canonical points,reduced rational slope,intercept), with no /1 for integer results.","answer":{"kind":"expression","value":"([[2, 11], [4, 15]], 2, 7)","explanation":"Use the difference quotient for the slope and substitute either point to obtain the intercept; duplicate copies of a point do not create a new point. 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], [4, 15]], 2, 7)."},"skills":["The Nonvertical Affine Rule through Two Distinct Inputs"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-r01-mathematical-representation-0046","batch_id":"batch-20261013-advance-20261021-r01-mathematical-representation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"e2514742e75186c7c49956476fd2d9670a21066be2237259df52197d054df479","family_id":"qf-app21-representation-two-point-rule","seed":202610211046,"semantic_template":"qf-app21-representation-two-point-rule/{\"points\":[[-2,2],[1,11]]}"},"fields":{"title":"The Nonvertical Affine Rule through Two Distinct Inputs","stem":"Use only the explicitly supplied rule, symbols and finite pair table. Graph appearance supplies no values, and agreement on the listed inputs proves no equivalence on unlisted domains. Points=[[-2, 2], [1, 11]]. Normalize tuple collections by removing identical tuples and sorting their JSON strings with the source’s en-locale comparison. This is canonical record order, not numerical coordinate order; number any output rows from 0 only after that normalization. Require exactly two distinct pairs with different x-coordinates. Give (canonical points,reduced rational slope,intercept), with no /1 for integer results.","answer":{"kind":"expression","value":"([[-2, 2], [1, 11]], 3, 8)","explanation":"Use the difference quotient for the slope and substitute either point to obtain the intercept; duplicate copies of a point do not create a new point. 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], [1, 11]], 3, 8)."},"skills":["The Nonvertical Affine Rule through Two Distinct Inputs"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-r01-mathematical-representation-0047","batch_id":"batch-20261013-advance-20261021-r01-mathematical-representation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"2ef43245044c80f1510c2137a1d8073fb80b9b4130b7bfe4ce4dcf93a3198101","family_id":"qf-app21-representation-two-point-rule","seed":202610211047,"semantic_template":"qf-app21-representation-two-point-rule/{\"points\":[[-1,12],[0,9]]}"},"fields":{"title":"The Nonvertical Affine Rule through Two Distinct Inputs","stem":"Use only the explicitly supplied rule, symbols and finite pair table. Graph appearance supplies no values, and agreement on the listed inputs proves no equivalence on unlisted domains. Points=[[-1, 12], [0, 9]]. Normalize tuple collections by removing identical tuples and sorting their JSON strings with the source’s en-locale comparison. This is canonical record order, not numerical coordinate order; number any output rows from 0 only after that normalization. Require exactly two distinct pairs with different x-coordinates. Give (canonical points,reduced rational slope,intercept), with no /1 for integer results.","answer":{"kind":"expression","value":"([[-1, 12], [0, 9]], -3, 9)","explanation":"Use the difference quotient for the slope and substitute either point to obtain the intercept; duplicate copies of a point do not create a new point. 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], [0, 9]], -3, 9)."},"skills":["The Nonvertical Affine Rule through Two Distinct Inputs"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-r01-mathematical-representation-0048","batch_id":"batch-20261013-advance-20261021-r01-mathematical-representation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"cc287a5e1b3387abbf1e54ef241adcaa0e1a004c851650e79db3ec5d5e3f771f","family_id":"qf-app21-representation-two-point-rule","seed":202610211048,"semantic_template":"qf-app21-representation-two-point-rule/{\"points\":[[0,10],[2,6]]}"},"fields":{"title":"The Nonvertical Affine Rule through Two Distinct Inputs","stem":"Use only the explicitly supplied rule, symbols and finite pair table. Graph appearance supplies no values, and agreement on the listed inputs proves no equivalence on unlisted domains. Points=[[0, 10], [2, 6]]. Normalize tuple collections by removing identical tuples and sorting their JSON strings with the source’s en-locale comparison. This is canonical record order, not numerical coordinate order; number any output rows from 0 only after that normalization. Require exactly two distinct pairs with different x-coordinates. Give (canonical points,reduced rational slope,intercept), with no /1 for integer results.","answer":{"kind":"expression","value":"([[0, 10], [2, 6]], -2, 10)","explanation":"Use the difference quotient for the slope and substitute either point to obtain the intercept; duplicate copies of a point do not create a new point. 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, 10], [2, 6]], -2, 10)."},"skills":["The Nonvertical Affine Rule through Two Distinct Inputs"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-r01-mathematical-representation-0049","batch_id":"batch-20261013-advance-20261021-r01-mathematical-representation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"92ba5e9245656eeef017174bb6fa754bf8a21e9417e37e5c6d740d6bf4b90b7d","family_id":"qf-app21-representation-two-point-rule","seed":202610211049,"semantic_template":"qf-app21-representation-two-point-rule/{\"points\":[[1,10],[4,7]]}"},"fields":{"title":"The Nonvertical Affine Rule through Two Distinct Inputs","stem":"Use only the explicitly supplied rule, symbols and finite pair table. Graph appearance supplies no values, and agreement on the listed inputs proves no equivalence on unlisted domains. Points=[[1, 10], [4, 7]]. Normalize tuple collections by removing identical tuples and sorting their JSON strings with the source’s en-locale comparison. This is canonical record order, not numerical coordinate order; number any output rows from 0 only after that normalization. Require exactly two distinct pairs with different x-coordinates. Give (canonical points,reduced rational slope,intercept), with no /1 for integer results.","answer":{"kind":"expression","value":"([[1, 10], [4, 7]], -1, 11)","explanation":"Use the difference quotient for the slope and substitute either point to obtain the intercept; duplicate copies of a point do not create a new point. 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, 10], [4, 7]], -1, 11)."},"skills":["The Nonvertical Affine Rule through Two Distinct Inputs"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-r01-mathematical-representation-0050","batch_id":"batch-20261013-advance-20261021-r01-mathematical-representation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"6e37cc4893e82308307b951bcc4925ee30527035d04ac83c6956f9231703c49b","family_id":"qf-app21-representation-two-point-rule","seed":202610211050,"semantic_template":"qf-app21-representation-two-point-rule/{\"points\":[[2,12],[3,12]]}"},"fields":{"title":"The Nonvertical Affine Rule through Two Distinct Inputs","stem":"Use only the explicitly supplied rule, symbols and finite pair table. Graph appearance supplies no values, and agreement on the listed inputs proves no equivalence on unlisted domains. Points=[[2, 12], [3, 12]]. Normalize tuple collections by removing identical tuples and sorting their JSON strings with the source’s en-locale comparison. This is canonical record order, not numerical coordinate order; number any output rows from 0 only after that normalization. Require exactly two distinct pairs with different x-coordinates. Give (canonical points,reduced rational slope,intercept), with no /1 for integer results.","answer":{"kind":"expression","value":"([[2, 12], [3, 12]], 0, 12)","explanation":"Use the difference quotient for the slope and substitute either point to obtain the intercept; duplicate copies of a point do not create a new point. 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, 12], [3, 12]], 0, 12)."},"skills":["The Nonvertical Affine Rule through Two Distinct Inputs"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-r01-mathematical-representation-0051","batch_id":"batch-20261013-advance-20261021-r01-mathematical-representation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"0778b8ba737e04eb1e053145796c46dbf1833cd0d074fb371d2987531f7a1ea1","family_id":"qf-app21-representation-function-audit","seed":202610211051,"semantic_template":"qf-app21-representation-function-audit/{\"pairs\":[[0,-12],[1,-10],[1,-11],[2,-5]]}"},"fields":{"title":"Repeated Inputs versus a Single-Valued Pair Table","stem":"Use only the explicitly supplied rule, symbols and finite pair table. Graph appearance supplies no values, and agreement on the listed inputs proves no equivalence on unlisted domains. Pairs=[[0, -12], [1, -11], [1, -10], [2, -5]]. Normalize tuple collections by removing identical tuples and sorting their JSON strings with the source’s en-locale comparison. This is canonical record order, not numerical coordinate order; number any output rows from 0 only after that normalization. Give (canonical pairs,sorted distinct domain,inputs having multiple distinct outputs,is the table a function on its domain?). List conflicts in first-appearance order in the canonical pair table.","answer":{"kind":"expression","value":"([[0, -12], [1, -10], [1, -11], [2, -5]], [0, 1, 2], [1], No)","explanation":"Identical duplicate pairs are harmless; one input with distinct outputs violates the function condition. Domain order and canonical pair order are separate. 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, -12], [1, -10], [1, -11], [2, -5]], [0, 1, 2], [1], No)."},"skills":["Repeated Inputs versus a Single-Valued Pair Table"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-r01-mathematical-representation-0052","batch_id":"batch-20261013-advance-20261021-r01-mathematical-representation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"05311c344d1267883e9bd335bff0806be2f87e7ab4fa627f0e999b58e111371c","family_id":"qf-app21-representation-function-audit","seed":202610211052,"semantic_template":"qf-app21-representation-function-audit/{\"pairs\":[[0,-11],[1,-10],[2,-3]]}"},"fields":{"title":"Repeated Inputs versus a Single-Valued Pair Table","stem":"Use only the explicitly supplied rule, symbols and finite pair table. Graph appearance supplies no values, and agreement on the listed inputs proves no equivalence on unlisted domains. Pairs=[[0, -11], [1, -10], [1, -10], [2, -3]]. Normalize tuple collections by removing identical tuples and sorting their JSON strings with the source’s en-locale comparison. This is canonical record order, not numerical coordinate order; number any output rows from 0 only after that normalization. Give (canonical pairs,sorted distinct domain,inputs having multiple distinct outputs,is the table a function on its domain?). List conflicts in first-appearance order in the canonical pair table.","answer":{"kind":"expression","value":"([[0, -11], [1, -10], [2, -3]], [0, 1, 2], [], Yes)","explanation":"Identical duplicate pairs are harmless; one input with distinct outputs violates the function condition. Domain order and canonical pair order are separate. 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, -11], [1, -10], [2, -3]], [0, 1, 2], [], Yes)."},"skills":["Repeated Inputs versus a Single-Valued Pair Table"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-r01-mathematical-representation-0053","batch_id":"batch-20261013-advance-20261021-r01-mathematical-representation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"355ada3eb938782025aa03b99205f8eff400f7379a9a5768e44074217b2ecb9c","family_id":"qf-app21-representation-function-audit","seed":202610211053,"semantic_template":"qf-app21-representation-function-audit/{\"pairs\":[[0,-10],[1,-9],[2,-1]]}"},"fields":{"title":"Repeated Inputs versus a Single-Valued Pair Table","stem":"Use only the explicitly supplied rule, symbols and finite pair table. Graph appearance supplies no values, and agreement on the listed inputs proves no equivalence on unlisted domains. Pairs=[[0, -10], [1, -9], [1, -9], [2, -1]]. Normalize tuple collections by removing identical tuples and sorting their JSON strings with the source’s en-locale comparison. This is canonical record order, not numerical coordinate order; number any output rows from 0 only after that normalization. Give (canonical pairs,sorted distinct domain,inputs having multiple distinct outputs,is the table a function on its domain?). List conflicts in first-appearance order in the canonical pair table.","answer":{"kind":"expression","value":"([[0, -10], [1, -9], [2, -1]], [0, 1, 2], [], Yes)","explanation":"Identical duplicate pairs are harmless; one input with distinct outputs violates the function condition. Domain order and canonical pair order are separate. 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, -10], [1, -9], [2, -1]], [0, 1, 2], [], Yes)."},"skills":["Repeated Inputs versus a Single-Valued Pair Table"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-r01-mathematical-representation-0054","batch_id":"batch-20261013-advance-20261021-r01-mathematical-representation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"56d80bf9282e33f9d559e4ebc32975dbe1e8333fba98e583b8ed85b4dd1a7ea7","family_id":"qf-app21-representation-function-audit","seed":202610211054,"semantic_template":"qf-app21-representation-function-audit/{\"pairs\":[[0,-9],[1,-8],[2,1]]}"},"fields":{"title":"Repeated Inputs versus a Single-Valued Pair Table","stem":"Use only the explicitly supplied rule, symbols and finite pair table. Graph appearance supplies no values, and agreement on the listed inputs proves no equivalence on unlisted domains. Pairs=[[0, -9], [1, -8], [1, -8], [2, 1]]. Normalize tuple collections by removing identical tuples and sorting their JSON strings with the source’s en-locale comparison. This is canonical record order, not numerical coordinate order; number any output rows from 0 only after that normalization. Give (canonical pairs,sorted distinct domain,inputs having multiple distinct outputs,is the table a function on its domain?). List conflicts in first-appearance order in the canonical pair table.","answer":{"kind":"expression","value":"([[0, -9], [1, -8], [2, 1]], [0, 1, 2], [], Yes)","explanation":"Identical duplicate pairs are harmless; one input with distinct outputs violates the function condition. Domain order and canonical pair order are separate. 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, -9], [1, -8], [2, 1]], [0, 1, 2], [], Yes)."},"skills":["Repeated Inputs versus a Single-Valued Pair Table"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-r01-mathematical-representation-0055","batch_id":"batch-20261013-advance-20261021-r01-mathematical-representation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"f2338d8713ce072f7908c2a909479532744cfea37ab72f8ce4da77bd08553002","family_id":"qf-app21-representation-function-audit","seed":202610211055,"semantic_template":"qf-app21-representation-function-audit/{\"pairs\":[[0,-8],[1,-6],[1,-7],[2,3]]}"},"fields":{"title":"Repeated Inputs versus a Single-Valued Pair Table","stem":"Use only the explicitly supplied rule, symbols and finite pair table. Graph appearance supplies no values, and agreement on the listed inputs proves no equivalence on unlisted domains. Pairs=[[0, -8], [1, -7], [1, -6], [2, 3]]. Normalize tuple collections by removing identical tuples and sorting their JSON strings with the source’s en-locale comparison. This is canonical record order, not numerical coordinate order; number any output rows from 0 only after that normalization. Give (canonical pairs,sorted distinct domain,inputs having multiple distinct outputs,is the table a function on its domain?). List conflicts in first-appearance order in the canonical pair table.","answer":{"kind":"expression","value":"([[0, -8], [1, -6], [1, -7], [2, 3]], [0, 1, 2], [1], No)","explanation":"Identical duplicate pairs are harmless; one input with distinct outputs violates the function condition. Domain order and canonical pair order are separate. 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, -6], [1, -7], [2, 3]], [0, 1, 2], [1], No)."},"skills":["Repeated Inputs versus a Single-Valued Pair Table"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-r01-mathematical-representation-0056","batch_id":"batch-20261013-advance-20261021-r01-mathematical-representation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"3ad17e354cb6f27d7682f906c8f108ef55d2b427f82195a8f3ec60b1008d89c1","family_id":"qf-app21-representation-function-audit","seed":202610211056,"semantic_template":"qf-app21-representation-function-audit/{\"pairs\":[[0,-7],[1,-6],[2,5]]}"},"fields":{"title":"Repeated Inputs versus a Single-Valued Pair Table","stem":"Use only the explicitly supplied rule, symbols and finite pair table. Graph appearance supplies no values, and agreement on the listed inputs proves no equivalence on unlisted domains. Pairs=[[0, -7], [1, -6], [1, -6], [2, 5]]. Normalize tuple collections by removing identical tuples and sorting their JSON strings with the source’s en-locale comparison. This is canonical record order, not numerical coordinate order; number any output rows from 0 only after that normalization. Give (canonical pairs,sorted distinct domain,inputs having multiple distinct outputs,is the table a function on its domain?). List conflicts in first-appearance order in the canonical pair table.","answer":{"kind":"expression","value":"([[0, -7], [1, -6], [2, 5]], [0, 1, 2], [], Yes)","explanation":"Identical duplicate pairs are harmless; one input with distinct outputs violates the function condition. Domain order and canonical pair order are separate. 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, -7], [1, -6], [2, 5]], [0, 1, 2], [], Yes)."},"skills":["Repeated Inputs versus a Single-Valued Pair Table"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-r01-mathematical-representation-0057","batch_id":"batch-20261013-advance-20261021-r01-mathematical-representation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"97d79dbccd8007cafdc2e7621dc39d17a0819cf6177ae692065fa329602c16ca","family_id":"qf-app21-representation-function-audit","seed":202610211057,"semantic_template":"qf-app21-representation-function-audit/{\"pairs\":[[0,-6],[1,-5],[2,7]]}"},"fields":{"title":"Repeated Inputs versus a Single-Valued Pair Table","stem":"Use only the explicitly supplied rule, symbols and finite pair table. Graph appearance supplies no values, and agreement on the listed inputs proves no equivalence on unlisted domains. Pairs=[[0, -6], [1, -5], [1, -5], [2, 7]]. Normalize tuple collections by removing identical tuples and sorting their JSON strings with the source’s en-locale comparison. This is canonical record order, not numerical coordinate order; number any output rows from 0 only after that normalization. Give (canonical pairs,sorted distinct domain,inputs having multiple distinct outputs,is the table a function on its domain?). List conflicts in first-appearance order in the canonical pair table.","answer":{"kind":"expression","value":"([[0, -6], [1, -5], [2, 7]], [0, 1, 2], [], Yes)","explanation":"Identical duplicate pairs are harmless; one input with distinct outputs violates the function condition. Domain order and canonical pair order are separate. 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], [1, -5], [2, 7]], [0, 1, 2], [], Yes)."},"skills":["Repeated Inputs versus a Single-Valued Pair Table"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-r01-mathematical-representation-0058","batch_id":"batch-20261013-advance-20261021-r01-mathematical-representation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"6e959ea3213193f3c8e38fd5f48730f5feaeedbffeadd00e4718269e1b1f41c0","family_id":"qf-app21-representation-function-audit","seed":202610211058,"semantic_template":"qf-app21-representation-function-audit/{\"pairs\":[[0,-5],[1,-4],[2,9]]}"},"fields":{"title":"Repeated Inputs versus a Single-Valued Pair Table","stem":"Use only the explicitly supplied rule, symbols and finite pair table. Graph appearance supplies no values, and agreement on the listed inputs proves no equivalence on unlisted domains. Pairs=[[0, -5], [1, -4], [1, -4], [2, 9]]. Normalize tuple collections by removing identical tuples and sorting their JSON strings with the source’s en-locale comparison. This is canonical record order, not numerical coordinate order; number any output rows from 0 only after that normalization. Give (canonical pairs,sorted distinct domain,inputs having multiple distinct outputs,is the table a function on its domain?). List conflicts in first-appearance order in the canonical pair table.","answer":{"kind":"expression","value":"([[0, -5], [1, -4], [2, 9]], [0, 1, 2], [], Yes)","explanation":"Identical duplicate pairs are harmless; one input with distinct outputs violates the function condition. Domain order and canonical pair order are separate. 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, -5], [1, -4], [2, 9]], [0, 1, 2], [], Yes)."},"skills":["Repeated Inputs versus a Single-Valued Pair Table"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-r01-mathematical-representation-0059","batch_id":"batch-20261013-advance-20261021-r01-mathematical-representation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"ce0896756c113d6113f3cb151bfc697eea86dda14226a75dce6fd376646cacff","family_id":"qf-app21-representation-function-audit","seed":202610211059,"semantic_template":"qf-app21-representation-function-audit/{\"pairs\":[[0,-4],[1,-2],[1,-3],[2,11]]}"},"fields":{"title":"Repeated Inputs versus a Single-Valued Pair Table","stem":"Use only the explicitly supplied rule, symbols and finite pair table. Graph appearance supplies no values, and agreement on the listed inputs proves no equivalence on unlisted domains. Pairs=[[0, -4], [1, -3], [1, -2], [2, 11]]. Normalize tuple collections by removing identical tuples and sorting their JSON strings with the source’s en-locale comparison. This is canonical record order, not numerical coordinate order; number any output rows from 0 only after that normalization. Give (canonical pairs,sorted distinct domain,inputs having multiple distinct outputs,is the table a function on its domain?). List conflicts in first-appearance order in the canonical pair table.","answer":{"kind":"expression","value":"([[0, -4], [1, -2], [1, -3], [2, 11]], [0, 1, 2], [1], No)","explanation":"Identical duplicate pairs are harmless; one input with distinct outputs violates the function condition. Domain order and canonical pair order are separate. 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], [1, -3], [2, 11]], [0, 1, 2], [1], No)."},"skills":["Repeated Inputs versus a Single-Valued Pair Table"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-r01-mathematical-representation-0060","batch_id":"batch-20261013-advance-20261021-r01-mathematical-representation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"0f92454b2b72acadaa581a58d9666307d546b55bc79cbda1b4486bb10e9ded85","family_id":"qf-app21-representation-function-audit","seed":202610211060,"semantic_template":"qf-app21-representation-function-audit/{\"pairs\":[[0,-3],[1,-2],[2,13]]}"},"fields":{"title":"Repeated Inputs versus a Single-Valued Pair Table","stem":"Use only the explicitly supplied rule, symbols and finite pair table. Graph appearance supplies no values, and agreement on the listed inputs proves no equivalence on unlisted domains. Pairs=[[0, -3], [1, -2], [1, -2], [2, 13]]. Normalize tuple collections by removing identical tuples and sorting their JSON strings with the source’s en-locale comparison. This is canonical record order, not numerical coordinate order; number any output rows from 0 only after that normalization. Give (canonical pairs,sorted distinct domain,inputs having multiple distinct outputs,is the table a function on its domain?). List conflicts in first-appearance order in the canonical pair table.","answer":{"kind":"expression","value":"([[0, -3], [1, -2], [2, 13]], [0, 1, 2], [], Yes)","explanation":"Identical duplicate pairs are harmless; one input with distinct outputs violates the function condition. Domain order and canonical pair order are separate. 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, -3], [1, -2], [2, 13]], [0, 1, 2], [], Yes)."},"skills":["Repeated Inputs versus a Single-Valued Pair Table"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-r01-mathematical-representation-0061","batch_id":"batch-20261013-advance-20261021-r01-mathematical-representation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"3459463263e1a3070c16feefa3272c54dda86012c2b70a86a27e7eb4aed1474f","family_id":"qf-app21-representation-function-audit","seed":202610211061,"semantic_template":"qf-app21-representation-function-audit/{\"pairs\":[[0,-2],[1,-1],[2,15]]}"},"fields":{"title":"Repeated Inputs versus a Single-Valued Pair Table","stem":"Use only the explicitly supplied rule, symbols and finite pair table. Graph appearance supplies no values, and agreement on the listed inputs proves no equivalence on unlisted domains. Pairs=[[0, -2], [1, -1], [1, -1], [2, 15]]. Normalize tuple collections by removing identical tuples and sorting their JSON strings with the source’s en-locale comparison. This is canonical record order, not numerical coordinate order; number any output rows from 0 only after that normalization. Give (canonical pairs,sorted distinct domain,inputs having multiple distinct outputs,is the table a function on its domain?). List conflicts in first-appearance order in the canonical pair table.","answer":{"kind":"expression","value":"([[0, -2], [1, -1], [2, 15]], [0, 1, 2], [], Yes)","explanation":"Identical duplicate pairs are harmless; one input with distinct outputs violates the function condition. Domain order and canonical pair order are separate. 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, -2], [1, -1], [2, 15]], [0, 1, 2], [], Yes)."},"skills":["Repeated Inputs versus a Single-Valued Pair Table"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-r01-mathematical-representation-0062","batch_id":"batch-20261013-advance-20261021-r01-mathematical-representation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"35b0e9df29e892195651c0a1fa25662fea45f421c375741674f8cb74ec0b8949","family_id":"qf-app21-representation-function-audit","seed":202610211062,"semantic_template":"qf-app21-representation-function-audit/{\"pairs\":[[0,-1],[1,0],[2,17]]}"},"fields":{"title":"Repeated Inputs versus a Single-Valued Pair Table","stem":"Use only the explicitly supplied rule, symbols and finite pair table. Graph appearance supplies no values, and agreement on the listed inputs proves no equivalence on unlisted domains. Pairs=[[0, -1], [1, 0], [1, 0], [2, 17]]. Normalize tuple collections by removing identical tuples and sorting their JSON strings with the source’s en-locale comparison. This is canonical record order, not numerical coordinate order; number any output rows from 0 only after that normalization. Give (canonical pairs,sorted distinct domain,inputs having multiple distinct outputs,is the table a function on its domain?). List conflicts in first-appearance order in the canonical pair table.","answer":{"kind":"expression","value":"([[0, -1], [1, 0], [2, 17]], [0, 1, 2], [], Yes)","explanation":"Identical duplicate pairs are harmless; one input with distinct outputs violates the function condition. Domain order and canonical pair order are separate. 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], [1, 0], [2, 17]], [0, 1, 2], [], Yes)."},"skills":["Repeated Inputs versus a Single-Valued Pair Table"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-r01-mathematical-representation-0063","batch_id":"batch-20261013-advance-20261021-r01-mathematical-representation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"c975d1acf5a4d7682d5d16b5dd165be962a1c0accd1a85ba99a28af88cf45c60","family_id":"qf-app21-representation-function-audit","seed":202610211063,"semantic_template":"qf-app21-representation-function-audit/{\"pairs\":[[0,0],[1,1],[1,2],[2,19]]}"},"fields":{"title":"Repeated Inputs versus a Single-Valued Pair Table","stem":"Use only the explicitly supplied rule, symbols and finite pair table. Graph appearance supplies no values, and agreement on the listed inputs proves no equivalence on unlisted domains. Pairs=[[0, 0], [1, 1], [1, 2], [2, 19]]. Normalize tuple collections by removing identical tuples and sorting their JSON strings with the source’s en-locale comparison. This is canonical record order, not numerical coordinate order; number any output rows from 0 only after that normalization. Give (canonical pairs,sorted distinct domain,inputs having multiple distinct outputs,is the table a function on its domain?). List conflicts in first-appearance order in the canonical pair table.","answer":{"kind":"expression","value":"([[0, 0], [1, 1], [1, 2], [2, 19]], [0, 1, 2], [1], No)","explanation":"Identical duplicate pairs are harmless; one input with distinct outputs violates the function condition. Domain order and canonical pair order are separate. 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, 0], [1, 1], [1, 2], [2, 19]], [0, 1, 2], [1], No)."},"skills":["Repeated Inputs versus a Single-Valued Pair Table"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-r01-mathematical-representation-0064","batch_id":"batch-20261013-advance-20261021-r01-mathematical-representation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"46b89047a20711de8d7102bd7c036bf4db67a3641961539ffd033a572cd12733","family_id":"qf-app21-representation-function-audit","seed":202610211064,"semantic_template":"qf-app21-representation-function-audit/{\"pairs\":[[0,1],[1,2],[2,21]]}"},"fields":{"title":"Repeated Inputs versus a Single-Valued Pair Table","stem":"Use only the explicitly supplied rule, symbols and finite pair table. Graph appearance supplies no values, and agreement on the listed inputs proves no equivalence on unlisted domains. Pairs=[[0, 1], [1, 2], [1, 2], [2, 21]]. Normalize tuple collections by removing identical tuples and sorting their JSON strings with the source’s en-locale comparison. This is canonical record order, not numerical coordinate order; number any output rows from 0 only after that normalization. Give (canonical pairs,sorted distinct domain,inputs having multiple distinct outputs,is the table a function on its domain?). List conflicts in first-appearance order in the canonical pair table.","answer":{"kind":"expression","value":"([[0, 1], [1, 2], [2, 21]], [0, 1, 2], [], Yes)","explanation":"Identical duplicate pairs are harmless; one input with distinct outputs violates the function condition. Domain order and canonical pair order are separate. 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], [1, 2], [2, 21]], [0, 1, 2], [], Yes)."},"skills":["Repeated Inputs versus a Single-Valued Pair Table"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-r01-mathematical-representation-0065","batch_id":"batch-20261013-advance-20261021-r01-mathematical-representation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"229aa48d5b2beb002812efa2a4af1fbd9454b3c82fa231fdfabb8b9e592f7ac4","family_id":"qf-app21-representation-function-audit","seed":202610211065,"semantic_template":"qf-app21-representation-function-audit/{\"pairs\":[[0,2],[1,3],[2,23]]}"},"fields":{"title":"Repeated Inputs versus a Single-Valued Pair Table","stem":"Use only the explicitly supplied rule, symbols and finite pair table. Graph appearance supplies no values, and agreement on the listed inputs proves no equivalence on unlisted domains. Pairs=[[0, 2], [1, 3], [1, 3], [2, 23]]. Normalize tuple collections by removing identical tuples and sorting their JSON strings with the source’s en-locale comparison. This is canonical record order, not numerical coordinate order; number any output rows from 0 only after that normalization. Give (canonical pairs,sorted distinct domain,inputs having multiple distinct outputs,is the table a function on its domain?). List conflicts in first-appearance order in the canonical pair table.","answer":{"kind":"expression","value":"([[0, 2], [1, 3], [2, 23]], [0, 1, 2], [], Yes)","explanation":"Identical duplicate pairs are harmless; one input with distinct outputs violates the function condition. Domain order and canonical pair order are separate. 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, 2], [1, 3], [2, 23]], [0, 1, 2], [], Yes)."},"skills":["Repeated Inputs versus a Single-Valued Pair Table"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-r01-mathematical-representation-0066","batch_id":"batch-20261013-advance-20261021-r01-mathematical-representation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"fcb7bb2c3ceefa5be1c9dd197efd326667c6ecf2a15976b93089c974aeb4b1ac","family_id":"qf-app21-representation-function-audit","seed":202610211066,"semantic_template":"qf-app21-representation-function-audit/{\"pairs\":[[0,3],[1,4],[2,25]]}"},"fields":{"title":"Repeated Inputs versus a Single-Valued Pair Table","stem":"Use only the explicitly supplied rule, symbols and finite pair table. Graph appearance supplies no values, and agreement on the listed inputs proves no equivalence on unlisted domains. Pairs=[[0, 3], [1, 4], [1, 4], [2, 25]]. Normalize tuple collections by removing identical tuples and sorting their JSON strings with the source’s en-locale comparison. This is canonical record order, not numerical coordinate order; number any output rows from 0 only after that normalization. Give (canonical pairs,sorted distinct domain,inputs having multiple distinct outputs,is the table a function on its domain?). List conflicts in first-appearance order in the canonical pair table.","answer":{"kind":"expression","value":"([[0, 3], [1, 4], [2, 25]], [0, 1, 2], [], Yes)","explanation":"Identical duplicate pairs are harmless; one input with distinct outputs violates the function condition. Domain order and canonical pair order are separate. 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, 3], [1, 4], [2, 25]], [0, 1, 2], [], Yes)."},"skills":["Repeated Inputs versus a Single-Valued Pair Table"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-r01-mathematical-representation-0067","batch_id":"batch-20261013-advance-20261021-r01-mathematical-representation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"d028b9f92d9984b71e891a35ba8a6e63336a20c8d06deed98dfec9a4c71faa7d","family_id":"qf-app21-representation-function-audit","seed":202610211067,"semantic_template":"qf-app21-representation-function-audit/{\"pairs\":[[0,4],[1,5],[1,6],[2,27]]}"},"fields":{"title":"Repeated Inputs versus a Single-Valued Pair Table","stem":"Use only the explicitly supplied rule, symbols and finite pair table. Graph appearance supplies no values, and agreement on the listed inputs proves no equivalence on unlisted domains. Pairs=[[0, 4], [1, 5], [1, 6], [2, 27]]. Normalize tuple collections by removing identical tuples and sorting their JSON strings with the source’s en-locale comparison. This is canonical record order, not numerical coordinate order; number any output rows from 0 only after that normalization. Give (canonical pairs,sorted distinct domain,inputs having multiple distinct outputs,is the table a function on its domain?). List conflicts in first-appearance order in the canonical pair table.","answer":{"kind":"expression","value":"([[0, 4], [1, 5], [1, 6], [2, 27]], [0, 1, 2], [1], No)","explanation":"Identical duplicate pairs are harmless; one input with distinct outputs violates the function condition. Domain order and canonical pair order are separate. 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, 5], [1, 6], [2, 27]], [0, 1, 2], [1], No)."},"skills":["Repeated Inputs versus a Single-Valued Pair Table"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-r01-mathematical-representation-0068","batch_id":"batch-20261013-advance-20261021-r01-mathematical-representation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"fc285787a85b5cce8041821d19504b879f869b6a9141c314eda3bacca413e1d2","family_id":"qf-app21-representation-function-audit","seed":202610211068,"semantic_template":"qf-app21-representation-function-audit/{\"pairs\":[[0,5],[1,6],[2,29]]}"},"fields":{"title":"Repeated Inputs versus a Single-Valued Pair Table","stem":"Use only the explicitly supplied rule, symbols and finite pair table. Graph appearance supplies no values, and agreement on the listed inputs proves no equivalence on unlisted domains. Pairs=[[0, 5], [1, 6], [1, 6], [2, 29]]. Normalize tuple collections by removing identical tuples and sorting their JSON strings with the source’s en-locale comparison. This is canonical record order, not numerical coordinate order; number any output rows from 0 only after that normalization. Give (canonical pairs,sorted distinct domain,inputs having multiple distinct outputs,is the table a function on its domain?). List conflicts in first-appearance order in the canonical pair table.","answer":{"kind":"expression","value":"([[0, 5], [1, 6], [2, 29]], [0, 1, 2], [], Yes)","explanation":"Identical duplicate pairs are harmless; one input with distinct outputs violates the function condition. Domain order and canonical pair order are separate. 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, 5], [1, 6], [2, 29]], [0, 1, 2], [], Yes)."},"skills":["Repeated Inputs versus a Single-Valued Pair Table"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-r01-mathematical-representation-0069","batch_id":"batch-20261013-advance-20261021-r01-mathematical-representation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"55750e6baea7d1dc2c10ee848877e1bf84f907af089c60c0f5115dc5bc2425a9","family_id":"qf-app21-representation-function-audit","seed":202610211069,"semantic_template":"qf-app21-representation-function-audit/{\"pairs\":[[0,6],[1,7],[2,31]]}"},"fields":{"title":"Repeated Inputs versus a Single-Valued Pair Table","stem":"Use only the explicitly supplied rule, symbols and finite pair table. Graph appearance supplies no values, and agreement on the listed inputs proves no equivalence on unlisted domains. Pairs=[[0, 6], [1, 7], [1, 7], [2, 31]]. Normalize tuple collections by removing identical tuples and sorting their JSON strings with the source’s en-locale comparison. This is canonical record order, not numerical coordinate order; number any output rows from 0 only after that normalization. Give (canonical pairs,sorted distinct domain,inputs having multiple distinct outputs,is the table a function on its domain?). List conflicts in first-appearance order in the canonical pair table.","answer":{"kind":"expression","value":"([[0, 6], [1, 7], [2, 31]], [0, 1, 2], [], Yes)","explanation":"Identical duplicate pairs are harmless; one input with distinct outputs violates the function condition. Domain order and canonical pair order are separate. 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], [1, 7], [2, 31]], [0, 1, 2], [], Yes)."},"skills":["Repeated Inputs versus a Single-Valued Pair Table"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-r01-mathematical-representation-0070","batch_id":"batch-20261013-advance-20261021-r01-mathematical-representation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"ad35b3a9707a0bbf75c91fafcf816ac1f7fbe33d861fe8259bdd0d7b48b697a0","family_id":"qf-app21-representation-function-audit","seed":202610211070,"semantic_template":"qf-app21-representation-function-audit/{\"pairs\":[[0,7],[1,8],[2,33]]}"},"fields":{"title":"Repeated Inputs versus a Single-Valued Pair Table","stem":"Use only the explicitly supplied rule, symbols and finite pair table. Graph appearance supplies no values, and agreement on the listed inputs proves no equivalence on unlisted domains. Pairs=[[0, 7], [1, 8], [1, 8], [2, 33]]. Normalize tuple collections by removing identical tuples and sorting their JSON strings with the source’s en-locale comparison. This is canonical record order, not numerical coordinate order; number any output rows from 0 only after that normalization. Give (canonical pairs,sorted distinct domain,inputs having multiple distinct outputs,is the table a function on its domain?). List conflicts in first-appearance order in the canonical pair table.","answer":{"kind":"expression","value":"([[0, 7], [1, 8], [2, 33]], [0, 1, 2], [], Yes)","explanation":"Identical duplicate pairs are harmless; one input with distinct outputs violates the function condition. Domain order and canonical pair order are separate. 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, 7], [1, 8], [2, 33]], [0, 1, 2], [], Yes)."},"skills":["Repeated Inputs versus a Single-Valued Pair Table"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-r01-mathematical-representation-0071","batch_id":"batch-20261013-advance-20261021-r01-mathematical-representation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"d033ec51e77a90a405ce76cc6828ca6419d758c3edf7c683b8c1c774a8cfc477","family_id":"qf-app21-representation-function-audit","seed":202610211071,"semantic_template":"qf-app21-representation-function-audit/{\"pairs\":[[0,8],[1,10],[1,9],[2,35]]}"},"fields":{"title":"Repeated Inputs versus a Single-Valued Pair Table","stem":"Use only the explicitly supplied rule, symbols and finite pair table. Graph appearance supplies no values, and agreement on the listed inputs proves no equivalence on unlisted domains. Pairs=[[0, 8], [1, 9], [1, 10], [2, 35]]. Normalize tuple collections by removing identical tuples and sorting their JSON strings with the source’s en-locale comparison. This is canonical record order, not numerical coordinate order; number any output rows from 0 only after that normalization. Give (canonical pairs,sorted distinct domain,inputs having multiple distinct outputs,is the table a function on its domain?). List conflicts in first-appearance order in the canonical pair table.","answer":{"kind":"expression","value":"([[0, 8], [1, 10], [1, 9], [2, 35]], [0, 1, 2], [1], No)","explanation":"Identical duplicate pairs are harmless; one input with distinct outputs violates the function condition. Domain order and canonical pair order are separate. 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, 10], [1, 9], [2, 35]], [0, 1, 2], [1], No)."},"skills":["Repeated Inputs versus a Single-Valued Pair Table"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-r01-mathematical-representation-0072","batch_id":"batch-20261013-advance-20261021-r01-mathematical-representation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"a72ab8b9d0c50192aa623dd4609946c3b05e41349feca99cd6a7aaf3e21644b5","family_id":"qf-app21-representation-function-audit","seed":202610211072,"semantic_template":"qf-app21-representation-function-audit/{\"pairs\":[[0,9],[1,10],[2,37]]}"},"fields":{"title":"Repeated Inputs versus a Single-Valued Pair Table","stem":"Use only the explicitly supplied rule, symbols and finite pair table. Graph appearance supplies no values, and agreement on the listed inputs proves no equivalence on unlisted domains. Pairs=[[0, 9], [1, 10], [1, 10], [2, 37]]. Normalize tuple collections by removing identical tuples and sorting their JSON strings with the source’s en-locale comparison. This is canonical record order, not numerical coordinate order; number any output rows from 0 only after that normalization. Give (canonical pairs,sorted distinct domain,inputs having multiple distinct outputs,is the table a function on its domain?). List conflicts in first-appearance order in the canonical pair table.","answer":{"kind":"expression","value":"([[0, 9], [1, 10], [2, 37]], [0, 1, 2], [], Yes)","explanation":"Identical duplicate pairs are harmless; one input with distinct outputs violates the function condition. Domain order and canonical pair order are separate. 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, 9], [1, 10], [2, 37]], [0, 1, 2], [], Yes)."},"skills":["Repeated Inputs versus a Single-Valued Pair Table"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-r01-mathematical-representation-0073","batch_id":"batch-20261013-advance-20261021-r01-mathematical-representation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"5c874c106aa4d37d4aa8cdf4df1289609e890fa63292e9aec3c6408b936ddbdd","family_id":"qf-app21-representation-function-audit","seed":202610211073,"semantic_template":"qf-app21-representation-function-audit/{\"pairs\":[[0,10],[1,11],[2,39]]}"},"fields":{"title":"Repeated Inputs versus a Single-Valued Pair Table","stem":"Use only the explicitly supplied rule, symbols and finite pair table. Graph appearance supplies no values, and agreement on the listed inputs proves no equivalence on unlisted domains. Pairs=[[0, 10], [1, 11], [1, 11], [2, 39]]. Normalize tuple collections by removing identical tuples and sorting their JSON strings with the source’s en-locale comparison. This is canonical record order, not numerical coordinate order; number any output rows from 0 only after that normalization. Give (canonical pairs,sorted distinct domain,inputs having multiple distinct outputs,is the table a function on its domain?). List conflicts in first-appearance order in the canonical pair table.","answer":{"kind":"expression","value":"([[0, 10], [1, 11], [2, 39]], [0, 1, 2], [], Yes)","explanation":"Identical duplicate pairs are harmless; one input with distinct outputs violates the function condition. Domain order and canonical pair order are separate. 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, 10], [1, 11], [2, 39]], [0, 1, 2], [], Yes)."},"skills":["Repeated Inputs versus a Single-Valued Pair Table"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-r01-mathematical-representation-0074","batch_id":"batch-20261013-advance-20261021-r01-mathematical-representation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"823aaa46a24524e61f97803f5e5f00673032adb405af605382369f4b7bdafadc","family_id":"qf-app21-representation-function-audit","seed":202610211074,"semantic_template":"qf-app21-representation-function-audit/{\"pairs\":[[0,11],[1,12],[2,41]]}"},"fields":{"title":"Repeated Inputs versus a Single-Valued Pair Table","stem":"Use only the explicitly supplied rule, symbols and finite pair table. Graph appearance supplies no values, and agreement on the listed inputs proves no equivalence on unlisted domains. Pairs=[[0, 11], [1, 12], [1, 12], [2, 41]]. Normalize tuple collections by removing identical tuples and sorting their JSON strings with the source’s en-locale comparison. This is canonical record order, not numerical coordinate order; number any output rows from 0 only after that normalization. Give (canonical pairs,sorted distinct domain,inputs having multiple distinct outputs,is the table a function on its domain?). List conflicts in first-appearance order in the canonical pair table.","answer":{"kind":"expression","value":"([[0, 11], [1, 12], [2, 41]], [0, 1, 2], [], Yes)","explanation":"Identical duplicate pairs are harmless; one input with distinct outputs violates the function condition. Domain order and canonical pair order are separate. 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, 11], [1, 12], [2, 41]], [0, 1, 2], [], Yes)."},"skills":["Repeated Inputs versus a Single-Valued Pair Table"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-r01-mathematical-representation-0075","batch_id":"batch-20261013-advance-20261021-r01-mathematical-representation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"74726f4512084eef1da88256506e11947cffd52a893718140cdf0484e329c8fc","family_id":"qf-app21-representation-function-audit","seed":202610211075,"semantic_template":"qf-app21-representation-function-audit/{\"pairs\":[[0,12],[1,13],[1,14],[2,43]]}"},"fields":{"title":"Repeated Inputs versus a Single-Valued Pair Table","stem":"Use only the explicitly supplied rule, symbols and finite pair table. Graph appearance supplies no values, and agreement on the listed inputs proves no equivalence on unlisted domains. Pairs=[[0, 12], [1, 13], [1, 14], [2, 43]]. Normalize tuple collections by removing identical tuples and sorting their JSON strings with the source’s en-locale comparison. This is canonical record order, not numerical coordinate order; number any output rows from 0 only after that normalization. Give (canonical pairs,sorted distinct domain,inputs having multiple distinct outputs,is the table a function on its domain?). List conflicts in first-appearance order in the canonical pair table.","answer":{"kind":"expression","value":"([[0, 12], [1, 13], [1, 14], [2, 43]], [0, 1, 2], [1], No)","explanation":"Identical duplicate pairs are harmless; one input with distinct outputs violates the function condition. Domain order and canonical pair order are separate. 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, 12], [1, 13], [1, 14], [2, 43]], [0, 1, 2], [1], No)."},"skills":["Repeated Inputs versus a Single-Valued Pair Table"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-r01-mathematical-representation-0076","batch_id":"batch-20261013-advance-20261021-r01-mathematical-representation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"3d66e90bd0380aefc6571bcd66039956af640fdd0c902d148de87f0d8c1654d0","family_id":"qf-app21-representation-consistency-audit","seed":202610211076,"semantic_template":"qf-app21-representation-consistency-audit/{\"a\":-2,\"b\":-10,\"pairs\":[[0,-10],[1,-12],[2,-13]]}"},"fields":{"title":"Audit Every Table Row against an Affine Rule","stem":"Use only the explicitly supplied rule, symbols and finite pair table. Graph appearance supplies no values, and agreement on the listed inputs proves no equivalence on unlisted domains. a=-2, b=-10, pairs=[[0, -10], [1, -12], [2, -13]]. Normalize tuple collections by removing identical tuples and sorting their JSON strings with the source’s en-locale comparison. This is canonical record order, not numerical coordinate order; number any output rows from 0 only after that normalization. Give (a,b,every [x,listed y,a*x+b,match?] row,all rows match?).","answer":{"kind":"expression","value":"(-2, -10, [[0, -10, -10, Yes], [1, -12, -12, Yes], [2, -13, -14, No]], No)","explanation":"Compare actual numeric entries with the rule rather than judging a plotted line’s appearance. 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, [[0, -10, -10, Yes], [1, -12, -12, Yes], [2, -13, -14, No]], No)."},"skills":["Audit Every Table Row against an Affine Rule"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-r01-mathematical-representation-0077","batch_id":"batch-20261013-advance-20261021-r01-mathematical-representation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"a550dcdd0666a61f4bfb0391d2cd8ddbffa239cb7bc8a16e044445b389e66f9d","family_id":"qf-app21-representation-consistency-audit","seed":202610211077,"semantic_template":"qf-app21-representation-consistency-audit/{\"a\":-1,\"b\":-9,\"pairs\":[[0,-9],[1,-10],[2,-11]]}"},"fields":{"title":"Audit Every Table Row against an Affine Rule","stem":"Use only the explicitly supplied rule, symbols and finite pair table. Graph appearance supplies no values, and agreement on the listed inputs proves no equivalence on unlisted domains. a=-1, b=-9, pairs=[[0, -9], [1, -10], [2, -11]]. Normalize tuple collections by removing identical tuples and sorting their JSON strings with the source’s en-locale comparison. This is canonical record order, not numerical coordinate order; number any output rows from 0 only after that normalization. Give (a,b,every [x,listed y,a*x+b,match?] row,all rows match?).","answer":{"kind":"expression","value":"(-1, -9, [[0, -9, -9, Yes], [1, -10, -10, Yes], [2, -11, -11, Yes]], Yes)","explanation":"Compare actual numeric entries with the rule rather than judging a plotted line’s appearance. 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], [1, -10, -10, Yes], [2, -11, -11, Yes]], Yes)."},"skills":["Audit Every Table Row against an Affine Rule"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-r01-mathematical-representation-0078","batch_id":"batch-20261013-advance-20261021-r01-mathematical-representation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"594df9783f51ce435816187fca9aa6b83a0ed209c8c9ef11dac6f65b93903932","family_id":"qf-app21-representation-consistency-audit","seed":202610211078,"semantic_template":"qf-app21-representation-consistency-audit/{\"a\":0,\"b\":-8,\"pairs\":[[0,-8],[1,-8],[2,-8]]}"},"fields":{"title":"Audit Every Table Row against an Affine Rule","stem":"Use only the explicitly supplied rule, symbols and finite pair table. Graph appearance supplies no values, and agreement on the listed inputs proves no equivalence on unlisted domains. a=0, b=-8, pairs=[[0, -8], [1, -8], [2, -8]]. Normalize tuple collections by removing identical tuples and sorting their JSON strings with the source’s en-locale comparison. This is canonical record order, not numerical coordinate order; number any output rows from 0 only after that normalization. Give (a,b,every [x,listed y,a*x+b,match?] row,all rows match?).","answer":{"kind":"expression","value":"(0, -8, [[0, -8, -8, Yes], [1, -8, -8, Yes], [2, -8, -8, Yes]], Yes)","explanation":"Compare actual numeric entries with the rule rather than judging a plotted line’s appearance. 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, [[0, -8, -8, Yes], [1, -8, -8, Yes], [2, -8, -8, Yes]], Yes)."},"skills":["Audit Every Table Row against an Affine Rule"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-r01-mathematical-representation-0079","batch_id":"batch-20261013-advance-20261021-r01-mathematical-representation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"49956a8cb15a4961b4c652bc5f51774f7bf9d190e895ae477a5f525fd632e575","family_id":"qf-app21-representation-consistency-audit","seed":202610211079,"semantic_template":"qf-app21-representation-consistency-audit/{\"a\":1,\"b\":-7,\"pairs\":[[0,-7],[1,-6],[2,-5]]}"},"fields":{"title":"Audit Every Table Row against an Affine Rule","stem":"Use only the explicitly supplied rule, symbols and finite pair table. Graph appearance supplies no values, and agreement on the listed inputs proves no equivalence on unlisted domains. a=1, b=-7, pairs=[[0, -7], [1, -6], [2, -5]]. Normalize tuple collections by removing identical tuples and sorting their JSON strings with the source’s en-locale comparison. This is canonical record order, not numerical coordinate order; number any output rows from 0 only after that normalization. Give (a,b,every [x,listed y,a*x+b,match?] row,all rows match?).","answer":{"kind":"expression","value":"(1, -7, [[0, -7, -7, Yes], [1, -6, -6, Yes], [2, -5, -5, Yes]], Yes)","explanation":"Compare actual numeric entries with the rule rather than judging a plotted line’s appearance. 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, [[0, -7, -7, Yes], [1, -6, -6, Yes], [2, -5, -5, Yes]], Yes)."},"skills":["Audit Every Table Row against an Affine Rule"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-r01-mathematical-representation-0080","batch_id":"batch-20261013-advance-20261021-r01-mathematical-representation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"e216474bdb03565d85c13cbe6497ba067ff5bab13485546059a5c2ed24ff7357","family_id":"qf-app21-representation-consistency-audit","seed":202610211080,"semantic_template":"qf-app21-representation-consistency-audit/{\"a\":2,\"b\":-6,\"pairs\":[[0,-6],[1,-4],[2,-1]]}"},"fields":{"title":"Audit Every Table Row against an Affine Rule","stem":"Use only the explicitly supplied rule, symbols and finite pair table. Graph appearance supplies no values, and agreement on the listed inputs proves no equivalence on unlisted domains. a=2, b=-6, pairs=[[0, -6], [1, -4], [2, -1]]. Normalize tuple collections by removing identical tuples and sorting their JSON strings with the source’s en-locale comparison. This is canonical record order, not numerical coordinate order; number any output rows from 0 only after that normalization. Give (a,b,every [x,listed y,a*x+b,match?] row,all rows match?).","answer":{"kind":"expression","value":"(2, -6, [[0, -6, -6, Yes], [1, -4, -4, Yes], [2, -1, -2, No]], No)","explanation":"Compare actual numeric entries with the rule rather than judging a plotted line’s appearance. 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, [[0, -6, -6, Yes], [1, -4, -4, Yes], [2, -1, -2, No]], No)."},"skills":["Audit Every Table Row against an Affine Rule"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-r01-mathematical-representation-0081","batch_id":"batch-20261013-advance-20261021-r01-mathematical-representation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"20e53ad07a56b6b03fc6717dc5fc446314b9efc91386c078a9782476a9372b00","family_id":"qf-app21-representation-consistency-audit","seed":202610211081,"semantic_template":"qf-app21-representation-consistency-audit/{\"a\":-2,\"b\":-5,\"pairs\":[[0,-5],[1,-7],[2,-9]]}"},"fields":{"title":"Audit Every Table Row against an Affine Rule","stem":"Use only the explicitly supplied rule, symbols and finite pair table. Graph appearance supplies no values, and agreement on the listed inputs proves no equivalence on unlisted domains. a=-2, b=-5, pairs=[[0, -5], [1, -7], [2, -9]]. Normalize tuple collections by removing identical tuples and sorting their JSON strings with the source’s en-locale comparison. This is canonical record order, not numerical coordinate order; number any output rows from 0 only after that normalization. Give (a,b,every [x,listed y,a*x+b,match?] row,all rows match?).","answer":{"kind":"expression","value":"(-2, -5, [[0, -5, -5, Yes], [1, -7, -7, Yes], [2, -9, -9, Yes]], Yes)","explanation":"Compare actual numeric entries with the rule rather than judging a plotted line’s appearance. 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, -5, [[0, -5, -5, Yes], [1, -7, -7, Yes], [2, -9, -9, Yes]], Yes)."},"skills":["Audit Every Table Row against an Affine Rule"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-r01-mathematical-representation-0082","batch_id":"batch-20261013-advance-20261021-r01-mathematical-representation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"f765245d23de519f6cac01568d8a8dcf4190cec3d8220e4d3cba3a4b6fe248fc","family_id":"qf-app21-representation-consistency-audit","seed":202610211082,"semantic_template":"qf-app21-representation-consistency-audit/{\"a\":-1,\"b\":-4,\"pairs\":[[0,-4],[1,-5],[2,-6]]}"},"fields":{"title":"Audit Every Table Row against an Affine Rule","stem":"Use only the explicitly supplied rule, symbols and finite pair table. Graph appearance supplies no values, and agreement on the listed inputs proves no equivalence on unlisted domains. a=-1, b=-4, pairs=[[0, -4], [1, -5], [2, -6]]. Normalize tuple collections by removing identical tuples and sorting their JSON strings with the source’s en-locale comparison. This is canonical record order, not numerical coordinate order; number any output rows from 0 only after that normalization. Give (a,b,every [x,listed y,a*x+b,match?] row,all rows match?).","answer":{"kind":"expression","value":"(-1, -4, [[0, -4, -4, Yes], [1, -5, -5, Yes], [2, -6, -6, Yes]], Yes)","explanation":"Compare actual numeric entries with the rule rather than judging a plotted line’s appearance. 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, -4, [[0, -4, -4, Yes], [1, -5, -5, Yes], [2, -6, -6, Yes]], Yes)."},"skills":["Audit Every Table Row against an Affine Rule"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-r01-mathematical-representation-0083","batch_id":"batch-20261013-advance-20261021-r01-mathematical-representation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"a155ec29e9f0add16ccecbd009a9f802bc4c683e6a87121f83d3755406109b72","family_id":"qf-app21-representation-consistency-audit","seed":202610211083,"semantic_template":"qf-app21-representation-consistency-audit/{\"a\":0,\"b\":-3,\"pairs\":[[0,-3],[1,-3],[2,-3]]}"},"fields":{"title":"Audit Every Table Row against an Affine Rule","stem":"Use only the explicitly supplied rule, symbols and finite pair table. Graph appearance supplies no values, and agreement on the listed inputs proves no equivalence on unlisted domains. a=0, b=-3, pairs=[[0, -3], [1, -3], [2, -3]]. Normalize tuple collections by removing identical tuples and sorting their JSON strings with the source’s en-locale comparison. This is canonical record order, not numerical coordinate order; number any output rows from 0 only after that normalization. Give (a,b,every [x,listed y,a*x+b,match?] row,all rows match?).","answer":{"kind":"expression","value":"(0, -3, [[0, -3, -3, Yes], [1, -3, -3, Yes], [2, -3, -3, Yes]], Yes)","explanation":"Compare actual numeric entries with the rule rather than judging a plotted line’s appearance. 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, -3, [[0, -3, -3, Yes], [1, -3, -3, Yes], [2, -3, -3, Yes]], Yes)."},"skills":["Audit Every Table Row against an Affine Rule"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-r01-mathematical-representation-0084","batch_id":"batch-20261013-advance-20261021-r01-mathematical-representation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"5c9eead840d9202353b1a1b6ff4cf9f0922fe113b23716b7259041ba00fab518","family_id":"qf-app21-representation-consistency-audit","seed":202610211084,"semantic_template":"qf-app21-representation-consistency-audit/{\"a\":1,\"b\":-2,\"pairs\":[[0,-2],[1,-1],[2,1]]}"},"fields":{"title":"Audit Every Table Row against an Affine Rule","stem":"Use only the explicitly supplied rule, symbols and finite pair table. Graph appearance supplies no values, and agreement on the listed inputs proves no equivalence on unlisted domains. a=1, b=-2, pairs=[[0, -2], [1, -1], [2, 1]]. Normalize tuple collections by removing identical tuples and sorting their JSON strings with the source’s en-locale comparison. This is canonical record order, not numerical coordinate order; number any output rows from 0 only after that normalization. Give (a,b,every [x,listed y,a*x+b,match?] row,all rows match?).","answer":{"kind":"expression","value":"(1, -2, [[0, -2, -2, Yes], [1, -1, -1, Yes], [2, 1, 0, No]], No)","explanation":"Compare actual numeric entries with the rule rather than judging a plotted line’s appearance. 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, [[0, -2, -2, Yes], [1, -1, -1, Yes], [2, 1, 0, No]], No)."},"skills":["Audit Every Table Row against an Affine Rule"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-r01-mathematical-representation-0085","batch_id":"batch-20261013-advance-20261021-r01-mathematical-representation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"33974222fbbe467de661360910be9336c11336171f0d434a8dab1f55316d7817","family_id":"qf-app21-representation-consistency-audit","seed":202610211085,"semantic_template":"qf-app21-representation-consistency-audit/{\"a\":2,\"b\":-1,\"pairs\":[[0,-1],[1,1],[2,3]]}"},"fields":{"title":"Audit Every Table Row against an Affine Rule","stem":"Use only the explicitly supplied rule, symbols and finite pair table. Graph appearance supplies no values, and agreement on the listed inputs proves no equivalence on unlisted domains. a=2, b=-1, pairs=[[0, -1], [1, 1], [2, 3]]. Normalize tuple collections by removing identical tuples and sorting their JSON strings with the source’s en-locale comparison. This is canonical record order, not numerical coordinate order; number any output rows from 0 only after that normalization. Give (a,b,every [x,listed y,a*x+b,match?] row,all rows match?).","answer":{"kind":"expression","value":"(2, -1, [[0, -1, -1, Yes], [1, 1, 1, Yes], [2, 3, 3, Yes]], Yes)","explanation":"Compare actual numeric entries with the rule rather than judging a plotted line’s appearance. 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, -1, -1, Yes], [1, 1, 1, Yes], [2, 3, 3, Yes]], Yes)."},"skills":["Audit Every Table Row against an Affine Rule"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-r01-mathematical-representation-0086","batch_id":"batch-20261013-advance-20261021-r01-mathematical-representation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"c6670e2ec4325d3bb2ef2a612db33869730a8d7d99949980612f6626d80cca56","family_id":"qf-app21-representation-consistency-audit","seed":202610211086,"semantic_template":"qf-app21-representation-consistency-audit/{\"a\":-2,\"b\":0,\"pairs\":[[0,0],[1,-2],[2,-4]]}"},"fields":{"title":"Audit Every Table Row against an Affine Rule","stem":"Use only the explicitly supplied rule, symbols and finite pair table. Graph appearance supplies no values, and agreement on the listed inputs proves no equivalence on unlisted domains. a=-2, b=0, pairs=[[0, 0], [1, -2], [2, -4]]. Normalize tuple collections by removing identical tuples and sorting their JSON strings with the source’s en-locale comparison. This is canonical record order, not numerical coordinate order; number any output rows from 0 only after that normalization. Give (a,b,every [x,listed y,a*x+b,match?] row,all rows match?).","answer":{"kind":"expression","value":"(-2, 0, [[0, 0, 0, Yes], [1, -2, -2, Yes], [2, -4, -4, Yes]], Yes)","explanation":"Compare actual numeric entries with the rule rather than judging a plotted line’s appearance. 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, 0, [[0, 0, 0, Yes], [1, -2, -2, Yes], [2, -4, -4, Yes]], Yes)."},"skills":["Audit Every Table Row against an Affine Rule"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-r01-mathematical-representation-0087","batch_id":"batch-20261013-advance-20261021-r01-mathematical-representation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"cca1135605104f5f27bd0c68fe2ae9e12d4e20fc0c767b25d3d928979941dad5","family_id":"qf-app21-representation-consistency-audit","seed":202610211087,"semantic_template":"qf-app21-representation-consistency-audit/{\"a\":-1,\"b\":1,\"pairs\":[[0,1],[1,0],[2,-1]]}"},"fields":{"title":"Audit Every Table Row against an Affine Rule","stem":"Use only the explicitly supplied rule, symbols and finite pair table. Graph appearance supplies no values, and agreement on the listed inputs proves no equivalence on unlisted domains. a=-1, b=1, pairs=[[0, 1], [1, 0], [2, -1]]. Normalize tuple collections by removing identical tuples and sorting their JSON strings with the source’s en-locale comparison. This is canonical record order, not numerical coordinate order; number any output rows from 0 only after that normalization. Give (a,b,every [x,listed y,a*x+b,match?] row,all rows match?).","answer":{"kind":"expression","value":"(-1, 1, [[0, 1, 1, Yes], [1, 0, 0, Yes], [2, -1, -1, Yes]], Yes)","explanation":"Compare actual numeric entries with the rule rather than judging a plotted line’s appearance. 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, 1, [[0, 1, 1, Yes], [1, 0, 0, Yes], [2, -1, -1, Yes]], Yes)."},"skills":["Audit Every Table Row against an Affine Rule"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-r01-mathematical-representation-0088","batch_id":"batch-20261013-advance-20261021-r01-mathematical-representation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"2d8f776d8c868293d687d2a0e5d1f71c00bed0869b3b6b6616c3b1b0d4d2284b","family_id":"qf-app21-representation-consistency-audit","seed":202610211088,"semantic_template":"qf-app21-representation-consistency-audit/{\"a\":0,\"b\":2,\"pairs\":[[0,2],[1,2],[2,3]]}"},"fields":{"title":"Audit Every Table Row against an Affine Rule","stem":"Use only the explicitly supplied rule, symbols and finite pair table. Graph appearance supplies no values, and agreement on the listed inputs proves no equivalence on unlisted domains. a=0, b=2, pairs=[[0, 2], [1, 2], [2, 3]]. Normalize tuple collections by removing identical tuples and sorting their JSON strings with the source’s en-locale comparison. This is canonical record order, not numerical coordinate order; number any output rows from 0 only after that normalization. Give (a,b,every [x,listed y,a*x+b,match?] row,all rows match?).","answer":{"kind":"expression","value":"(0, 2, [[0, 2, 2, Yes], [1, 2, 2, Yes], [2, 3, 2, No]], No)","explanation":"Compare actual numeric entries with the rule rather than judging a plotted line’s appearance. 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, 2, [[0, 2, 2, Yes], [1, 2, 2, Yes], [2, 3, 2, No]], No)."},"skills":["Audit Every Table Row against an Affine Rule"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-r01-mathematical-representation-0089","batch_id":"batch-20261013-advance-20261021-r01-mathematical-representation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"4f008cedf3da75a96ed4187b05d42a6f469e9dd1a18a72c11fa3f308b8dfb183","family_id":"qf-app21-representation-consistency-audit","seed":202610211089,"semantic_template":"qf-app21-representation-consistency-audit/{\"a\":1,\"b\":3,\"pairs\":[[0,3],[1,4],[2,5]]}"},"fields":{"title":"Audit Every Table Row against an Affine Rule","stem":"Use only the explicitly supplied rule, symbols and finite pair table. Graph appearance supplies no values, and agreement on the listed inputs proves no equivalence on unlisted domains. a=1, b=3, pairs=[[0, 3], [1, 4], [2, 5]]. Normalize tuple collections by removing identical tuples and sorting their JSON strings with the source’s en-locale comparison. This is canonical record order, not numerical coordinate order; number any output rows from 0 only after that normalization. Give (a,b,every [x,listed y,a*x+b,match?] row,all rows match?).","answer":{"kind":"expression","value":"(1, 3, [[0, 3, 3, Yes], [1, 4, 4, Yes], [2, 5, 5, Yes]], Yes)","explanation":"Compare actual numeric entries with the rule rather than judging a plotted line’s appearance. 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, [[0, 3, 3, Yes], [1, 4, 4, Yes], [2, 5, 5, Yes]], Yes)."},"skills":["Audit Every Table Row against an Affine Rule"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-r01-mathematical-representation-0090","batch_id":"batch-20261013-advance-20261021-r01-mathematical-representation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"679c1338608e4ade09c2a066c06c58eee6e1f493a67c8adc47f9862539a4c768","family_id":"qf-app21-representation-consistency-audit","seed":202610211090,"semantic_template":"qf-app21-representation-consistency-audit/{\"a\":2,\"b\":4,\"pairs\":[[0,4],[1,6],[2,8]]}"},"fields":{"title":"Audit Every Table Row against an Affine Rule","stem":"Use only the explicitly supplied rule, symbols and finite pair table. Graph appearance supplies no values, and agreement on the listed inputs proves no equivalence on unlisted domains. a=2, b=4, pairs=[[0, 4], [1, 6], [2, 8]]. Normalize tuple collections by removing identical tuples and sorting their JSON strings with the source’s en-locale comparison. This is canonical record order, not numerical coordinate order; number any output rows from 0 only after that normalization. Give (a,b,every [x,listed y,a*x+b,match?] row,all rows match?).","answer":{"kind":"expression","value":"(2, 4, [[0, 4, 4, Yes], [1, 6, 6, Yes], [2, 8, 8, Yes]], Yes)","explanation":"Compare actual numeric entries with the rule rather than judging a plotted line’s appearance. 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, [[0, 4, 4, Yes], [1, 6, 6, Yes], [2, 8, 8, Yes]], Yes)."},"skills":["Audit Every Table Row against an Affine Rule"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-r01-mathematical-representation-0091","batch_id":"batch-20261013-advance-20261021-r01-mathematical-representation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"82e5c41836e99a04108149a31669f77bf508db7eefa4bc31115bd8e12523d2c6","family_id":"qf-app21-representation-consistency-audit","seed":202610211091,"semantic_template":"qf-app21-representation-consistency-audit/{\"a\":-2,\"b\":5,\"pairs\":[[0,5],[1,3],[2,1]]}"},"fields":{"title":"Audit Every Table Row against an Affine Rule","stem":"Use only the explicitly supplied rule, symbols and finite pair table. Graph appearance supplies no values, and agreement on the listed inputs proves no equivalence on unlisted domains. a=-2, b=5, pairs=[[0, 5], [1, 3], [2, 1]]. Normalize tuple collections by removing identical tuples and sorting their JSON strings with the source’s en-locale comparison. This is canonical record order, not numerical coordinate order; number any output rows from 0 only after that normalization. Give (a,b,every [x,listed y,a*x+b,match?] row,all rows match?).","answer":{"kind":"expression","value":"(-2, 5, [[0, 5, 5, Yes], [1, 3, 3, Yes], [2, 1, 1, Yes]], Yes)","explanation":"Compare actual numeric entries with the rule rather than judging a plotted line’s appearance. 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, 5, [[0, 5, 5, Yes], [1, 3, 3, Yes], [2, 1, 1, Yes]], Yes)."},"skills":["Audit Every Table Row against an Affine Rule"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-r01-mathematical-representation-0092","batch_id":"batch-20261013-advance-20261021-r01-mathematical-representation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"1ec73270719f0ac734032775e49f1de6ea46ae664abf2b52aded2587683258c5","family_id":"qf-app21-representation-consistency-audit","seed":202610211092,"semantic_template":"qf-app21-representation-consistency-audit/{\"a\":-1,\"b\":6,\"pairs\":[[0,6],[1,5],[2,5]]}"},"fields":{"title":"Audit Every Table Row against an Affine Rule","stem":"Use only the explicitly supplied rule, symbols and finite pair table. Graph appearance supplies no values, and agreement on the listed inputs proves no equivalence on unlisted domains. a=-1, b=6, pairs=[[0, 6], [1, 5], [2, 5]]. Normalize tuple collections by removing identical tuples and sorting their JSON strings with the source’s en-locale comparison. This is canonical record order, not numerical coordinate order; number any output rows from 0 only after that normalization. Give (a,b,every [x,listed y,a*x+b,match?] row,all rows match?).","answer":{"kind":"expression","value":"(-1, 6, [[0, 6, 6, Yes], [1, 5, 5, Yes], [2, 5, 4, No]], No)","explanation":"Compare actual numeric entries with the rule rather than judging a plotted line’s appearance. 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, 6, [[0, 6, 6, Yes], [1, 5, 5, Yes], [2, 5, 4, No]], No)."},"skills":["Audit Every Table Row against an Affine Rule"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-r01-mathematical-representation-0093","batch_id":"batch-20261013-advance-20261021-r01-mathematical-representation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"5689be1f4e1ed9ea3ce30bd8c1b07746f085f28e606f8b65380e76118baa8f71","family_id":"qf-app21-representation-consistency-audit","seed":202610211093,"semantic_template":"qf-app21-representation-consistency-audit/{\"a\":0,\"b\":7,\"pairs\":[[0,7],[1,7],[2,7]]}"},"fields":{"title":"Audit Every Table Row against an Affine Rule","stem":"Use only the explicitly supplied rule, symbols and finite pair table. Graph appearance supplies no values, and agreement on the listed inputs proves no equivalence on unlisted domains. a=0, b=7, pairs=[[0, 7], [1, 7], [2, 7]]. Normalize tuple collections by removing identical tuples and sorting their JSON strings with the source’s en-locale comparison. This is canonical record order, not numerical coordinate order; number any output rows from 0 only after that normalization. Give (a,b,every [x,listed y,a*x+b,match?] row,all rows match?).","answer":{"kind":"expression","value":"(0, 7, [[0, 7, 7, Yes], [1, 7, 7, Yes], [2, 7, 7, Yes]], Yes)","explanation":"Compare actual numeric entries with the rule rather than judging a plotted line’s appearance. 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, 7, [[0, 7, 7, Yes], [1, 7, 7, Yes], [2, 7, 7, Yes]], Yes)."},"skills":["Audit Every Table Row against an Affine Rule"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-r01-mathematical-representation-0094","batch_id":"batch-20261013-advance-20261021-r01-mathematical-representation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"e3fd184d92f717ff5278e434d2cbc65fcdf4fe51f8499430a72897472e8cd34d","family_id":"qf-app21-representation-consistency-audit","seed":202610211094,"semantic_template":"qf-app21-representation-consistency-audit/{\"a\":1,\"b\":8,\"pairs\":[[0,8],[1,9],[2,10]]}"},"fields":{"title":"Audit Every Table Row against an Affine Rule","stem":"Use only the explicitly supplied rule, symbols and finite pair table. Graph appearance supplies no values, and agreement on the listed inputs proves no equivalence on unlisted domains. a=1, b=8, pairs=[[0, 8], [1, 9], [2, 10]]. Normalize tuple collections by removing identical tuples and sorting their JSON strings with the source’s en-locale comparison. This is canonical record order, not numerical coordinate order; number any output rows from 0 only after that normalization. Give (a,b,every [x,listed y,a*x+b,match?] row,all rows match?).","answer":{"kind":"expression","value":"(1, 8, [[0, 8, 8, Yes], [1, 9, 9, Yes], [2, 10, 10, Yes]], Yes)","explanation":"Compare actual numeric entries with the rule rather than judging a plotted line’s appearance. 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, 8, [[0, 8, 8, Yes], [1, 9, 9, Yes], [2, 10, 10, Yes]], Yes)."},"skills":["Audit Every Table Row against an Affine Rule"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-r01-mathematical-representation-0095","batch_id":"batch-20261013-advance-20261021-r01-mathematical-representation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"ce705e2c72ceb3a2ac5031689763f18c8379a5b6de7898b4f4a6eb478ed3d774","family_id":"qf-app21-representation-consistency-audit","seed":202610211095,"semantic_template":"qf-app21-representation-consistency-audit/{\"a\":2,\"b\":9,\"pairs\":[[0,9],[1,11],[2,13]]}"},"fields":{"title":"Audit Every Table Row against an Affine Rule","stem":"Use only the explicitly supplied rule, symbols and finite pair table. Graph appearance supplies no values, and agreement on the listed inputs proves no equivalence on unlisted domains. a=2, b=9, pairs=[[0, 9], [1, 11], [2, 13]]. Normalize tuple collections by removing identical tuples and sorting their JSON strings with the source’s en-locale comparison. This is canonical record order, not numerical coordinate order; number any output rows from 0 only after that normalization. Give (a,b,every [x,listed y,a*x+b,match?] row,all rows match?).","answer":{"kind":"expression","value":"(2, 9, [[0, 9, 9, Yes], [1, 11, 11, Yes], [2, 13, 13, Yes]], Yes)","explanation":"Compare actual numeric entries with the rule rather than judging a plotted line’s appearance. 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, 9, [[0, 9, 9, Yes], [1, 11, 11, Yes], [2, 13, 13, Yes]], Yes)."},"skills":["Audit Every Table Row against an Affine Rule"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-r01-mathematical-representation-0096","batch_id":"batch-20261013-advance-20261021-r01-mathematical-representation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"91057430a23324a62fd59cb324e5fcd2a553689c7103f05430590763a65a52f8","family_id":"qf-app21-representation-consistency-audit","seed":202610211096,"semantic_template":"qf-app21-representation-consistency-audit/{\"a\":-2,\"b\":10,\"pairs\":[[0,10],[1,8],[2,7]]}"},"fields":{"title":"Audit Every Table Row against an Affine Rule","stem":"Use only the explicitly supplied rule, symbols and finite pair table. Graph appearance supplies no values, and agreement on the listed inputs proves no equivalence on unlisted domains. a=-2, b=10, pairs=[[0, 10], [1, 8], [2, 7]]. Normalize tuple collections by removing identical tuples and sorting their JSON strings with the source’s en-locale comparison. This is canonical record order, not numerical coordinate order; number any output rows from 0 only after that normalization. Give (a,b,every [x,listed y,a*x+b,match?] row,all rows match?).","answer":{"kind":"expression","value":"(-2, 10, [[0, 10, 10, Yes], [1, 8, 8, Yes], [2, 7, 6, No]], No)","explanation":"Compare actual numeric entries with the rule rather than judging a plotted line’s appearance. 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, [[0, 10, 10, Yes], [1, 8, 8, Yes], [2, 7, 6, No]], No)."},"skills":["Audit Every Table Row against an Affine Rule"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-r01-mathematical-representation-0097","batch_id":"batch-20261013-advance-20261021-r01-mathematical-representation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"d8be8bd4795d9f7841cb6fc0c689cc2b6c882a5624573f712a840959ada8d0df","family_id":"qf-app21-representation-consistency-audit","seed":202610211097,"semantic_template":"qf-app21-representation-consistency-audit/{\"a\":-1,\"b\":11,\"pairs\":[[0,11],[1,10],[2,9]]}"},"fields":{"title":"Audit Every Table Row against an Affine Rule","stem":"Use only the explicitly supplied rule, symbols and finite pair table. Graph appearance supplies no values, and agreement on the listed inputs proves no equivalence on unlisted domains. a=-1, b=11, pairs=[[0, 11], [1, 10], [2, 9]]. Normalize tuple collections by removing identical tuples and sorting their JSON strings with the source’s en-locale comparison. This is canonical record order, not numerical coordinate order; number any output rows from 0 only after that normalization. Give (a,b,every [x,listed y,a*x+b,match?] row,all rows match?).","answer":{"kind":"expression","value":"(-1, 11, [[0, 11, 11, Yes], [1, 10, 10, Yes], [2, 9, 9, Yes]], Yes)","explanation":"Compare actual numeric entries with the rule rather than judging a plotted line’s appearance. 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, 11, [[0, 11, 11, Yes], [1, 10, 10, Yes], [2, 9, 9, Yes]], Yes)."},"skills":["Audit Every Table Row against an Affine Rule"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-r01-mathematical-representation-0098","batch_id":"batch-20261013-advance-20261021-r01-mathematical-representation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"42eae71d83864e2e89b8ad021cd289604ac4156c66093bf93342c23174b9aff1","family_id":"qf-app21-representation-consistency-audit","seed":202610211098,"semantic_template":"qf-app21-representation-consistency-audit/{\"a\":0,\"b\":12,\"pairs\":[[0,12],[1,12],[2,12]]}"},"fields":{"title":"Audit Every Table Row against an Affine Rule","stem":"Use only the explicitly supplied rule, symbols and finite pair table. Graph appearance supplies no values, and agreement on the listed inputs proves no equivalence on unlisted domains. a=0, b=12, pairs=[[0, 12], [1, 12], [2, 12]]. Normalize tuple collections by removing identical tuples and sorting their JSON strings with the source’s en-locale comparison. This is canonical record order, not numerical coordinate order; number any output rows from 0 only after that normalization. Give (a,b,every [x,listed y,a*x+b,match?] row,all rows match?).","answer":{"kind":"expression","value":"(0, 12, [[0, 12, 12, Yes], [1, 12, 12, Yes], [2, 12, 12, Yes]], Yes)","explanation":"Compare actual numeric entries with the rule rather than judging a plotted line’s appearance. 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, 12, [[0, 12, 12, Yes], [1, 12, 12, Yes], [2, 12, 12, Yes]], Yes)."},"skills":["Audit Every Table Row against an Affine Rule"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-r01-mathematical-representation-0099","batch_id":"batch-20261013-advance-20261021-r01-mathematical-representation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"d07efc23527c03f8a4b903c9baee95674f41c763016cea0719cdf30e2180e22f","family_id":"qf-app21-representation-consistency-audit","seed":202610211099,"semantic_template":"qf-app21-representation-consistency-audit/{\"a\":1,\"b\":13,\"pairs\":[[0,13],[1,14],[2,15]]}"},"fields":{"title":"Audit Every Table Row against an Affine Rule","stem":"Use only the explicitly supplied rule, symbols and finite pair table. Graph appearance supplies no values, and agreement on the listed inputs proves no equivalence on unlisted domains. a=1, b=13, pairs=[[0, 13], [1, 14], [2, 15]]. Normalize tuple collections by removing identical tuples and sorting their JSON strings with the source’s en-locale comparison. This is canonical record order, not numerical coordinate order; number any output rows from 0 only after that normalization. Give (a,b,every [x,listed y,a*x+b,match?] row,all rows match?).","answer":{"kind":"expression","value":"(1, 13, [[0, 13, 13, Yes], [1, 14, 14, Yes], [2, 15, 15, Yes]], Yes)","explanation":"Compare actual numeric entries with the rule rather than judging a plotted line’s appearance. 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, [[0, 13, 13, Yes], [1, 14, 14, Yes], [2, 15, 15, Yes]], Yes)."},"skills":["Audit Every Table Row against an Affine Rule"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the 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-r01-mathematical-representation-0100","batch_id":"batch-20261013-advance-20261021-r01-mathematical-representation-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"ae77a00de0f106be8d5b995bf7e0f76f36f7219ecff4330c6e069faee436f382","family_id":"qf-app21-representation-consistency-audit","seed":202610211100,"semantic_template":"qf-app21-representation-consistency-audit/{\"a\":2,\"b\":14,\"pairs\":[[0,14],[1,16],[2,19]]}"},"fields":{"title":"Audit Every Table Row against an Affine Rule","stem":"Use only the explicitly supplied rule, symbols and finite pair table. Graph appearance supplies no values, and agreement on the listed inputs proves no equivalence on unlisted domains. a=2, b=14, pairs=[[0, 14], [1, 16], [2, 19]]. Normalize tuple collections by removing identical tuples and sorting their JSON strings with the source’s en-locale comparison. This is canonical record order, not numerical coordinate order; number any output rows from 0 only after that normalization. Give (a,b,every [x,listed y,a*x+b,match?] row,all rows match?).","answer":{"kind":"expression","value":"(2, 14, [[0, 14, 14, Yes], [1, 16, 16, Yes], [2, 19, 18, No]], No)","explanation":"Compare actual numeric entries with the rule rather than judging a plotted line’s appearance. 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, 14, [[0, 14, 14, Yes], [1, 16, 16, Yes], [2, 19, 18, No]], No)."},"skills":["Audit Every Table Row against an Affine Rule"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}