{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260925-triangle-explicit-validity-0001","batch_id":"batch-20260925-triangle-object-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"c2ca32fbbccc4a8ee0f7bef27bf06365631c001eb4252f9c5c12b2d2752b4481","family_id":"qf-triangle-explicit-validity","seed":20260926,"semantic_template":"qf-triangle-explicit-validity/{\"noncollinear\":false,\"operation\":\"validity\",\"vertices\":[\"A\",\"A\",\"C\"]}"},"fields":{"title":"Triangle Validity from Explicit Conditions","stem":"The three points in order are A, A, C; the prompt explicitly states that they are collinear. Using only the distinctness and noncollinearity conditions, do they form a nondegenerate triangle?","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"The vertices are not all distinct, so they do not form the nondegenerate triangle of this entry."},"skills":["distinct vertices","noncollinearity"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260925-triangle-explicit-validity-0002","batch_id":"batch-20260925-triangle-object-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"caa48c96cf2c50e86cba09463837f88d21cba4628ebbf3c0b7da391551538a0d","family_id":"qf-triangle-explicit-validity","seed":20260927,"semantic_template":"qf-triangle-explicit-validity/{\"noncollinear\":true,\"operation\":\"validity\",\"vertices\":[\"D\",\"E\",\"F\"]}"},"fields":{"title":"Triangle Validity from Explicit Conditions","stem":"The three points in order are D, E, F; the prompt explicitly states that they are noncollinear. Using only the distinctness and noncollinearity conditions, do they form a nondegenerate triangle?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"The three vertices are distinct and noncollinear, so they form a nondegenerate triangle."},"skills":["distinct vertices","noncollinearity"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260925-triangle-explicit-validity-0003","batch_id":"batch-20260925-triangle-object-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"76e52a7e7aeff3bc8af0631a60b319bbd8fda6d361d81540042537e9258e361f","family_id":"qf-triangle-explicit-validity","seed":20260928,"semantic_template":"qf-triangle-explicit-validity/{\"noncollinear\":true,\"operation\":\"validity\",\"vertices\":[\"G\",\"H\",\"I\"]}"},"fields":{"title":"Triangle Validity from Explicit Conditions","stem":"The three points in order are G, H, I; the prompt explicitly states that they are noncollinear. Using only the distinctness and noncollinearity conditions, do they form a nondegenerate triangle?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"The three vertices are distinct and noncollinear, so they form a nondegenerate triangle."},"skills":["distinct vertices","noncollinearity"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260925-triangle-explicit-validity-0004","batch_id":"batch-20260925-triangle-object-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"ab8fa2477d779a57b87bec36bcf090b7d525085c341e68efb0632b9cd2bc9111","family_id":"qf-triangle-explicit-validity","seed":20260929,"semantic_template":"qf-triangle-explicit-validity/{\"noncollinear\":true,\"operation\":\"validity\",\"vertices\":[\"J\",\"K\",\"L\"]}"},"fields":{"title":"Triangle Validity from Explicit Conditions","stem":"The three points in order are J, K, L; the prompt explicitly states that they are noncollinear. Using only the distinctness and noncollinearity conditions, do they form a nondegenerate triangle?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"The three vertices are distinct and noncollinear, so they form a nondegenerate triangle."},"skills":["distinct vertices","noncollinearity"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260925-triangle-explicit-validity-0005","batch_id":"batch-20260925-triangle-object-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"72a5026432655d2d3f54efac90701a69791fbbe0323ffc7b36c30a2ac572ca24","family_id":"qf-triangle-explicit-validity","seed":20260930,"semantic_template":"qf-triangle-explicit-validity/{\"noncollinear\":false,\"operation\":\"validity\",\"vertices\":[\"M\",\"M\",\"P\"]}"},"fields":{"title":"Triangle Validity from Explicit Conditions","stem":"The three points in order are M, M, P; the prompt explicitly states that they are collinear. Using only the distinctness and noncollinearity conditions, do they form a nondegenerate triangle?","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"The vertices are not all distinct, so they do not form the nondegenerate triangle of this entry."},"skills":["distinct vertices","noncollinearity"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260925-triangle-explicit-validity-0006","batch_id":"batch-20260925-triangle-object-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"de00960b4c30d49363662e5a5aedcc1f8963569ee133e93cf1da1e6591a8d6d6","family_id":"qf-triangle-explicit-validity","seed":20260931,"semantic_template":"qf-triangle-explicit-validity/{\"noncollinear\":false,\"operation\":\"validity\",\"vertices\":[\"Q\",\"R\",\"S\"]}"},"fields":{"title":"Triangle Validity from Explicit Conditions","stem":"The three points in order are Q, R, S; the prompt explicitly states that they are collinear. Using only the distinctness and noncollinearity conditions, do they form a nondegenerate triangle?","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"The vertices are distinct but collinear, so they do not form the nondegenerate triangle of this entry."},"skills":["distinct vertices","noncollinearity"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260925-triangle-explicit-validity-0007","batch_id":"batch-20260925-triangle-object-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"ad3a4e770484a9a6fe77c490b498ca922dec221bbc97f1408e50e6f75121c157","family_id":"qf-triangle-explicit-validity","seed":20260932,"semantic_template":"qf-triangle-explicit-validity/{\"noncollinear\":true,\"operation\":\"validity\",\"vertices\":[\"T\",\"U\",\"V\"]}"},"fields":{"title":"Triangle Validity from Explicit Conditions","stem":"The three points in order are T, U, V; the prompt explicitly states that they are noncollinear. Using only the distinctness and noncollinearity conditions, do they form a nondegenerate triangle?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"The three vertices are distinct and noncollinear, so they form a nondegenerate triangle."},"skills":["distinct vertices","noncollinearity"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260925-triangle-explicit-validity-0008","batch_id":"batch-20260925-triangle-object-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"4a7ca29a2fe0cd5149c7a85af322cf939c22898a47a9ccdd1e4550edb796376b","family_id":"qf-triangle-explicit-validity","seed":20260933,"semantic_template":"qf-triangle-explicit-validity/{\"noncollinear\":true,\"operation\":\"validity\",\"vertices\":[\"W\",\"X\",\"Y\"]}"},"fields":{"title":"Triangle Validity from Explicit Conditions","stem":"The three points in order are W, X, Y; the prompt explicitly states that they are noncollinear. Using only the distinctness and noncollinearity conditions, do they form a nondegenerate triangle?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"The three vertices are distinct and noncollinear, so they form a nondegenerate triangle."},"skills":["distinct vertices","noncollinearity"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260925-triangle-explicit-validity-0009","batch_id":"batch-20260925-triangle-object-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"580e23952dac862196b08684a52f7542ebe03d222d8cc5e15795d595ab97c038","family_id":"qf-triangle-explicit-validity","seed":20260934,"semantic_template":"qf-triangle-explicit-validity/{\"noncollinear\":false,\"operation\":\"validity\",\"vertices\":[\"A\",\"A\",\"D\"]}"},"fields":{"title":"Triangle Validity from Explicit Conditions","stem":"The three points in order are A, A, D; the prompt explicitly states that they are collinear. Using only the distinctness and noncollinearity conditions, do they form a nondegenerate triangle?","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"The vertices are not all distinct, so they do not form the nondegenerate triangle of this entry."},"skills":["distinct vertices","noncollinearity"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260925-triangle-explicit-validity-0010","batch_id":"batch-20260925-triangle-object-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"b4bfdb817921e399dd551c157e5dee03ae7adf080238ddc03e2acd01a1379711","family_id":"qf-triangle-explicit-validity","seed":20260935,"semantic_template":"qf-triangle-explicit-validity/{\"noncollinear\":true,\"operation\":\"validity\",\"vertices\":[\"A\",\"C\",\"E\"]}"},"fields":{"title":"Triangle Validity from Explicit Conditions","stem":"The three points in order are A, C, E; the prompt explicitly states that they are noncollinear. Using only the distinctness and noncollinearity conditions, do they form a nondegenerate triangle?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"The three vertices are distinct and noncollinear, so they form a nondegenerate triangle."},"skills":["distinct vertices","noncollinearity"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260925-triangle-explicit-validity-0011","batch_id":"batch-20260925-triangle-object-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"3d109dbfbc9e4950550c317d1ebaa62bd37c3c73747f7b3fea2041fd1bc095d7","family_id":"qf-triangle-explicit-validity","seed":20260936,"semantic_template":"qf-triangle-explicit-validity/{\"noncollinear\":false,\"operation\":\"validity\",\"vertices\":[\"B\",\"D\",\"F\"]}"},"fields":{"title":"Triangle Validity from Explicit Conditions","stem":"The three points in order are B, D, F; the prompt explicitly states that they are collinear. Using only the distinctness and noncollinearity conditions, do they form a nondegenerate triangle?","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"The vertices are distinct but collinear, so they do not form the nondegenerate triangle of this entry."},"skills":["distinct vertices","noncollinearity"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260925-triangle-explicit-validity-0012","batch_id":"batch-20260925-triangle-object-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"162494ae1a6092a76f3e0403daeb949af3ca3d8b05ff72d80dc82e146f8da573","family_id":"qf-triangle-explicit-validity","seed":20260937,"semantic_template":"qf-triangle-explicit-validity/{\"noncollinear\":true,\"operation\":\"validity\",\"vertices\":[\"C\",\"E\",\"G\"]}"},"fields":{"title":"Triangle Validity from Explicit Conditions","stem":"The three points in order are C, E, G; the prompt explicitly states that they are noncollinear. Using only the distinctness and noncollinearity conditions, do they form a nondegenerate triangle?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"The three vertices are distinct and noncollinear, so they form a nondegenerate triangle."},"skills":["distinct vertices","noncollinearity"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260925-triangle-explicit-validity-0013","batch_id":"batch-20260925-triangle-object-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"72fe679ca060fe6ffb120a932c225183090eddf8e3f4a9a1bdc6ac1837ca154a","family_id":"qf-triangle-explicit-validity","seed":20260938,"semantic_template":"qf-triangle-explicit-validity/{\"noncollinear\":false,\"operation\":\"validity\",\"vertices\":[\"D\",\"D\",\"H\"]}"},"fields":{"title":"Triangle Validity from Explicit Conditions","stem":"The three points in order are D, D, H; the prompt explicitly states that they are collinear. Using only the distinctness and noncollinearity conditions, do they form a nondegenerate triangle?","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"The vertices are not all distinct, so they do not form the nondegenerate triangle of this entry."},"skills":["distinct vertices","noncollinearity"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260925-triangle-explicit-validity-0014","batch_id":"batch-20260925-triangle-object-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"b9910795b55ddbb83fd435861d1a0f71a44b33bdfad9ab17b8740d1ab33cf117","family_id":"qf-triangle-explicit-validity","seed":20260939,"semantic_template":"qf-triangle-explicit-validity/{\"noncollinear\":true,\"operation\":\"validity\",\"vertices\":[\"E\",\"G\",\"I\"]}"},"fields":{"title":"Triangle Validity from Explicit Conditions","stem":"The three points in order are E, G, I; the prompt explicitly states that they are noncollinear. Using only the distinctness and noncollinearity conditions, do they form a nondegenerate triangle?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"The three vertices are distinct and noncollinear, so they form a nondegenerate triangle."},"skills":["distinct vertices","noncollinearity"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260925-triangle-explicit-validity-0015","batch_id":"batch-20260925-triangle-object-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"b35207a14bf4a98f72c83b9bf7aaa10af43c2c316de9207f9604e9c39d30ceba","family_id":"qf-triangle-explicit-validity","seed":20260940,"semantic_template":"qf-triangle-explicit-validity/{\"noncollinear\":true,\"operation\":\"validity\",\"vertices\":[\"F\",\"H\",\"J\"]}"},"fields":{"title":"Triangle Validity from Explicit Conditions","stem":"The three points in order are F, H, J; the prompt explicitly states that they are noncollinear. Using only the distinctness and noncollinearity conditions, do they form a nondegenerate triangle?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"The three vertices are distinct and noncollinear, so they form a nondegenerate triangle."},"skills":["distinct vertices","noncollinearity"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260925-triangle-explicit-validity-0016","batch_id":"batch-20260925-triangle-object-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"5b245b28141744da6bef23a6f970d6022468a216cf9fc7060083e3260b6acb65","family_id":"qf-triangle-explicit-validity","seed":20260941,"semantic_template":"qf-triangle-explicit-validity/{\"noncollinear\":false,\"operation\":\"validity\",\"vertices\":[\"G\",\"I\",\"K\"]}"},"fields":{"title":"Triangle Validity from Explicit Conditions","stem":"The three points in order are G, I, K; the prompt explicitly states that they are collinear. Using only the distinctness and noncollinearity conditions, do they form a nondegenerate triangle?","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"The vertices are distinct but collinear, so they do not form the nondegenerate triangle of this entry."},"skills":["distinct vertices","noncollinearity"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260925-triangle-explicit-validity-0017","batch_id":"batch-20260925-triangle-object-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"f3a93b088b1c78627115f0cc0f69dd8c2a10655b45803870798cf969eaed6bab","family_id":"qf-triangle-explicit-validity","seed":20260942,"semantic_template":"qf-triangle-explicit-validity/{\"noncollinear\":false,\"operation\":\"validity\",\"vertices\":[\"H\",\"H\",\"L\"]}"},"fields":{"title":"Triangle Validity from Explicit Conditions","stem":"The three points in order are H, H, L; the prompt explicitly states that they are collinear. Using only the distinctness and noncollinearity conditions, do they form a nondegenerate triangle?","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"The vertices are not all distinct, so they do not form the nondegenerate triangle of this entry."},"skills":["distinct vertices","noncollinearity"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260925-triangle-explicit-validity-0018","batch_id":"batch-20260925-triangle-object-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"9aca977ae00f2acf586a5e1a9a49d4821ecad1c038a691bc364a0f36904a3c51","family_id":"qf-triangle-explicit-validity","seed":20260943,"semantic_template":"qf-triangle-explicit-validity/{\"noncollinear\":true,\"operation\":\"validity\",\"vertices\":[\"I\",\"K\",\"M\"]}"},"fields":{"title":"Triangle Validity from Explicit Conditions","stem":"The three points in order are I, K, M; the prompt explicitly states that they are noncollinear. Using only the distinctness and noncollinearity conditions, do they form a nondegenerate triangle?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"The three vertices are distinct and noncollinear, so they form a nondegenerate triangle."},"skills":["distinct vertices","noncollinearity"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260925-triangle-explicit-validity-0019","batch_id":"batch-20260925-triangle-object-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"df5ba0efcd13d2a02d8ade6dd0fd3dd3526720f931493ae1940d907b333281ec","family_id":"qf-triangle-explicit-validity","seed":20260944,"semantic_template":"qf-triangle-explicit-validity/{\"noncollinear\":true,\"operation\":\"validity\",\"vertices\":[\"J\",\"L\",\"N\"]}"},"fields":{"title":"Triangle Validity from Explicit Conditions","stem":"The three points in order are J, L, N; the prompt explicitly states that they are noncollinear. Using only the distinctness and noncollinearity conditions, do they form a nondegenerate triangle?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"The three vertices are distinct and noncollinear, so they form a nondegenerate triangle."},"skills":["distinct vertices","noncollinearity"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260925-triangle-explicit-validity-0020","batch_id":"batch-20260925-triangle-object-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"eff21beb6478c8609aff37d57b5114e8f1f2db9be53ca512559fc08d75956626","family_id":"qf-triangle-explicit-validity","seed":20260945,"semantic_template":"qf-triangle-explicit-validity/{\"noncollinear\":true,\"operation\":\"validity\",\"vertices\":[\"K\",\"M\",\"O\"]}"},"fields":{"title":"Triangle Validity from Explicit Conditions","stem":"The three points in order are K, M, O; the prompt explicitly states that they are noncollinear. Using only the distinctness and noncollinearity conditions, do they form a nondegenerate triangle?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"The three vertices are distinct and noncollinear, so they form a nondegenerate triangle."},"skills":["distinct vertices","noncollinearity"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260925-triangle-explicit-validity-0021","batch_id":"batch-20260925-triangle-object-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"3884803cb15eb598774e6eb9c159c6d6da118b711f16280f56baba04a6fd0d4f","family_id":"qf-triangle-explicit-validity","seed":20260946,"semantic_template":"qf-triangle-explicit-validity/{\"noncollinear\":false,\"operation\":\"validity\",\"vertices\":[\"L\",\"L\",\"P\"]}"},"fields":{"title":"Triangle Validity from Explicit Conditions","stem":"The three points in order are L, L, P; the prompt explicitly states that they are collinear. Using only the distinctness and noncollinearity conditions, do they form a nondegenerate triangle?","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"The vertices are not all distinct, so they do not form the nondegenerate triangle of this entry."},"skills":["distinct vertices","noncollinearity"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260925-triangle-explicit-validity-0022","batch_id":"batch-20260925-triangle-object-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"12566f2ed58abf0d43aa7c8c2b366494cbf12679ce96cc5f88f59badfccda4a1","family_id":"qf-triangle-explicit-validity","seed":20260947,"semantic_template":"qf-triangle-explicit-validity/{\"noncollinear\":true,\"operation\":\"validity\",\"vertices\":[\"M\",\"O\",\"Q\"]}"},"fields":{"title":"Triangle Validity from Explicit Conditions","stem":"The three points in order are M, O, Q; the prompt explicitly states that they are noncollinear. Using only the distinctness and noncollinearity conditions, do they form a nondegenerate triangle?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"The three vertices are distinct and noncollinear, so they form a nondegenerate triangle."},"skills":["distinct vertices","noncollinearity"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260925-triangle-explicit-validity-0023","batch_id":"batch-20260925-triangle-object-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"e6a76e5e0f12584e202d9fff7889624f7ea959759976592f7f7087af7f69bb3f","family_id":"qf-triangle-explicit-validity","seed":20260948,"semantic_template":"qf-triangle-explicit-validity/{\"noncollinear\":true,\"operation\":\"validity\",\"vertices\":[\"N\",\"P\",\"R\"]}"},"fields":{"title":"Triangle Validity from Explicit Conditions","stem":"The three points in order are N, P, R; the prompt explicitly states that they are noncollinear. Using only the distinctness and noncollinearity conditions, do they form a nondegenerate triangle?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"The three vertices are distinct and noncollinear, so they form a nondegenerate triangle."},"skills":["distinct vertices","noncollinearity"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260925-triangle-explicit-validity-0024","batch_id":"batch-20260925-triangle-object-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"f6b3c18a4e4fb50a53b7b899f523be1f35e3f54959d2190aa65ba9080d3d2700","family_id":"qf-triangle-explicit-validity","seed":20260949,"semantic_template":"qf-triangle-explicit-validity/{\"noncollinear\":true,\"operation\":\"validity\",\"vertices\":[\"O\",\"Q\",\"S\"]}"},"fields":{"title":"Triangle Validity from Explicit Conditions","stem":"The three points in order are O, Q, S; the prompt explicitly states that they are noncollinear. Using only the distinctness and noncollinearity conditions, do they form a nondegenerate triangle?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"The three vertices are distinct and noncollinear, so they form a nondegenerate triangle."},"skills":["distinct vertices","noncollinearity"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260925-triangle-explicit-validity-0025","batch_id":"batch-20260925-triangle-object-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"01a250467eb246b00c8c25c36962f58b3d3572cce94a05eea0bb86b1cce1e5f8","family_id":"qf-triangle-explicit-validity","seed":20260950,"semantic_template":"qf-triangle-explicit-validity/{\"noncollinear\":false,\"operation\":\"validity\",\"vertices\":[\"P\",\"P\",\"T\"]}"},"fields":{"title":"Triangle Validity from Explicit Conditions","stem":"The three points in order are P, P, T; the prompt explicitly states that they are collinear. Using only the distinctness and noncollinearity conditions, do they form a nondegenerate triangle?","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"The vertices are not all distinct, so they do not form the nondegenerate triangle of this entry."},"skills":["distinct vertices","noncollinearity"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260925-triangle-vertex-set-0001","batch_id":"batch-20260925-triangle-object-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"c8fa53ef73b864c8f52d41f50bf2deca48a7b2a79b859600c7c63e6e9bc6cf9a","family_id":"qf-triangle-vertex-set","seed":20261026,"semantic_template":"qf-triangle-vertex-set/{\"noncollinear\":true,\"operation\":\"vertex_set\",\"vertices\":[\"A\",\"B\",\"C\"]}"},"fields":{"title":"Vertex Set of a Triangle","stem":"Triangle ABC has explicitly distinct noncollinear vertices. Write its vertex set in canonical order.","answer":{"kind":"short_text","value":"{A, B, C}","explanation":"Taking the three labels and sorting them canonically gives {A, B, C}."},"skills":["vertex sets","canonical ordering"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260925-triangle-vertex-set-0002","batch_id":"batch-20260925-triangle-object-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"de8b36443dd9ccb742f8c2d495a2356a761612f46000869e92dcde1e65ab980f","family_id":"qf-triangle-vertex-set","seed":20261027,"semantic_template":"qf-triangle-vertex-set/{\"noncollinear\":true,\"operation\":\"vertex_set\",\"vertices\":[\"D\",\"E\",\"F\"]}"},"fields":{"title":"Vertex Set of a Triangle","stem":"Triangle DEF has explicitly distinct noncollinear vertices. Write its vertex set in canonical order.","answer":{"kind":"short_text","value":"{D, E, F}","explanation":"Taking the three labels and sorting them canonically gives {D, E, F}."},"skills":["vertex sets","canonical ordering"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260925-triangle-vertex-set-0003","batch_id":"batch-20260925-triangle-object-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"f64a4086415e3465a962eb7066a06f1615861d0d5de81469a652569a58169bf0","family_id":"qf-triangle-vertex-set","seed":20261028,"semantic_template":"qf-triangle-vertex-set/{\"noncollinear\":true,\"operation\":\"vertex_set\",\"vertices\":[\"G\",\"H\",\"I\"]}"},"fields":{"title":"Vertex Set of a Triangle","stem":"Triangle GHI has explicitly distinct noncollinear vertices. Write its vertex set in canonical order.","answer":{"kind":"short_text","value":"{G, H, I}","explanation":"Taking the three labels and sorting them canonically gives {G, H, I}."},"skills":["vertex sets","canonical ordering"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260925-triangle-vertex-set-0004","batch_id":"batch-20260925-triangle-object-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"9cc179b436d0fef8b45646a2b21c3e118d67328726007f133691ecc6e846bccf","family_id":"qf-triangle-vertex-set","seed":20261029,"semantic_template":"qf-triangle-vertex-set/{\"noncollinear\":true,\"operation\":\"vertex_set\",\"vertices\":[\"J\",\"K\",\"L\"]}"},"fields":{"title":"Vertex Set of a Triangle","stem":"Triangle JKL has explicitly distinct noncollinear vertices. Write its vertex set in canonical order.","answer":{"kind":"short_text","value":"{J, K, L}","explanation":"Taking the three labels and sorting them canonically gives {J, K, L}."},"skills":["vertex sets","canonical ordering"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260925-triangle-vertex-set-0005","batch_id":"batch-20260925-triangle-object-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"3aef0677cb796ef37d37012e3dc9d34ca7bcc9505af5322dec077d0085287c14","family_id":"qf-triangle-vertex-set","seed":20261030,"semantic_template":"qf-triangle-vertex-set/{\"noncollinear\":true,\"operation\":\"vertex_set\",\"vertices\":[\"M\",\"N\",\"P\"]}"},"fields":{"title":"Vertex Set of a Triangle","stem":"Triangle MNP has explicitly distinct noncollinear vertices. Write its vertex set in canonical order.","answer":{"kind":"short_text","value":"{M, N, P}","explanation":"Taking the three labels and sorting them canonically gives {M, N, P}."},"skills":["vertex sets","canonical ordering"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260925-triangle-vertex-set-0006","batch_id":"batch-20260925-triangle-object-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"3b4415a27b8131ed09a333458f9bf863b45170f64972ffe98293a70d6151d295","family_id":"qf-triangle-vertex-set","seed":20261031,"semantic_template":"qf-triangle-vertex-set/{\"noncollinear\":true,\"operation\":\"vertex_set\",\"vertices\":[\"Q\",\"R\",\"S\"]}"},"fields":{"title":"Vertex Set of a Triangle","stem":"Triangle QRS has explicitly distinct noncollinear vertices. Write its vertex set in canonical order.","answer":{"kind":"short_text","value":"{Q, R, S}","explanation":"Taking the three labels and sorting them canonically gives {Q, R, S}."},"skills":["vertex sets","canonical ordering"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260925-triangle-vertex-set-0007","batch_id":"batch-20260925-triangle-object-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"b377b989636189c51c0fa951971b16e417938f6e3b2ff0e5f5b905c2f4184439","family_id":"qf-triangle-vertex-set","seed":20261032,"semantic_template":"qf-triangle-vertex-set/{\"noncollinear\":true,\"operation\":\"vertex_set\",\"vertices\":[\"T\",\"U\",\"V\"]}"},"fields":{"title":"Vertex Set of a Triangle","stem":"Triangle TUV has explicitly distinct noncollinear vertices. Write its vertex set in canonical order.","answer":{"kind":"short_text","value":"{T, U, V}","explanation":"Taking the three labels and sorting them canonically gives {T, U, V}."},"skills":["vertex sets","canonical ordering"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260925-triangle-vertex-set-0008","batch_id":"batch-20260925-triangle-object-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"15e9e6d3c7b2f2a069c1bcf71e9ef1453394c2904b8e3ba6ef73684f03366e18","family_id":"qf-triangle-vertex-set","seed":20261033,"semantic_template":"qf-triangle-vertex-set/{\"noncollinear\":true,\"operation\":\"vertex_set\",\"vertices\":[\"W\",\"X\",\"Y\"]}"},"fields":{"title":"Vertex Set of a Triangle","stem":"Triangle WXY has explicitly distinct noncollinear vertices. Write its vertex set in canonical order.","answer":{"kind":"short_text","value":"{W, X, Y}","explanation":"Taking the three labels and sorting them canonically gives {W, X, Y}."},"skills":["vertex sets","canonical ordering"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260925-triangle-vertex-set-0009","batch_id":"batch-20260925-triangle-object-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"07e25aed34b7999106f3037e0d4a2cba488562b096174313e434f81f35cf5ecf","family_id":"qf-triangle-vertex-set","seed":20261034,"semantic_template":"qf-triangle-vertex-set/{\"noncollinear\":true,\"operation\":\"vertex_set\",\"vertices\":[\"A\",\"B\",\"D\"]}"},"fields":{"title":"Vertex Set of a Triangle","stem":"Triangle ABD has explicitly distinct noncollinear vertices. Write its vertex set in canonical order.","answer":{"kind":"short_text","value":"{A, B, D}","explanation":"Taking the three labels and sorting them canonically gives {A, B, D}."},"skills":["vertex sets","canonical ordering"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260925-triangle-vertex-set-0010","batch_id":"batch-20260925-triangle-object-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"76a8ce4e2fb3b1af2f9f8b564b38cebd40a71df01b3533c4bba013c0ee2ce933","family_id":"qf-triangle-vertex-set","seed":20261035,"semantic_template":"qf-triangle-vertex-set/{\"noncollinear\":true,\"operation\":\"vertex_set\",\"vertices\":[\"A\",\"C\",\"E\"]}"},"fields":{"title":"Vertex Set of a Triangle","stem":"Triangle ACE has explicitly distinct noncollinear vertices. Write its vertex set in canonical order.","answer":{"kind":"short_text","value":"{A, C, E}","explanation":"Taking the three labels and sorting them canonically gives {A, C, E}."},"skills":["vertex sets","canonical ordering"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260925-triangle-vertex-set-0011","batch_id":"batch-20260925-triangle-object-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"154a4ab38963ed24caafa9858a6041a59da89ceee0776e58980aeb24d2832bd7","family_id":"qf-triangle-vertex-set","seed":20261036,"semantic_template":"qf-triangle-vertex-set/{\"noncollinear\":true,\"operation\":\"vertex_set\",\"vertices\":[\"B\",\"D\",\"F\"]}"},"fields":{"title":"Vertex Set of a Triangle","stem":"Triangle BDF has explicitly distinct noncollinear vertices. Write its vertex set in canonical order.","answer":{"kind":"short_text","value":"{B, D, F}","explanation":"Taking the three labels and sorting them canonically gives {B, D, F}."},"skills":["vertex sets","canonical ordering"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260925-triangle-vertex-set-0012","batch_id":"batch-20260925-triangle-object-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"45f59a959af00a7761be78293274df8918d59608c0e9be69e454920f6333c981","family_id":"qf-triangle-vertex-set","seed":20261037,"semantic_template":"qf-triangle-vertex-set/{\"noncollinear\":true,\"operation\":\"vertex_set\",\"vertices\":[\"C\",\"E\",\"G\"]}"},"fields":{"title":"Vertex Set of a Triangle","stem":"Triangle CEG has explicitly distinct noncollinear vertices. Write its vertex set in canonical order.","answer":{"kind":"short_text","value":"{C, E, G}","explanation":"Taking the three labels and sorting them canonically gives {C, E, G}."},"skills":["vertex sets","canonical ordering"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260925-triangle-vertex-set-0013","batch_id":"batch-20260925-triangle-object-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"8e7defd362d46db4b377dca6bac817c30af47a9fb08ddd3d91e9b1610fb261ce","family_id":"qf-triangle-vertex-set","seed":20261038,"semantic_template":"qf-triangle-vertex-set/{\"noncollinear\":true,\"operation\":\"vertex_set\",\"vertices\":[\"D\",\"F\",\"H\"]}"},"fields":{"title":"Vertex Set of a Triangle","stem":"Triangle DFH has explicitly distinct noncollinear vertices. Write its vertex set in canonical order.","answer":{"kind":"short_text","value":"{D, F, H}","explanation":"Taking the three labels and sorting them canonically gives {D, F, H}."},"skills":["vertex sets","canonical ordering"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260925-triangle-vertex-set-0014","batch_id":"batch-20260925-triangle-object-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"e202d2e2eed570c8c2eeedbf89a01da7d82f21e23b8ca84570ca1375ea935277","family_id":"qf-triangle-vertex-set","seed":20261039,"semantic_template":"qf-triangle-vertex-set/{\"noncollinear\":true,\"operation\":\"vertex_set\",\"vertices\":[\"E\",\"G\",\"I\"]}"},"fields":{"title":"Vertex Set of a Triangle","stem":"Triangle EGI has explicitly distinct noncollinear vertices. Write its vertex set in canonical order.","answer":{"kind":"short_text","value":"{E, G, I}","explanation":"Taking the three labels and sorting them canonically gives {E, G, I}."},"skills":["vertex sets","canonical ordering"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260925-triangle-vertex-set-0015","batch_id":"batch-20260925-triangle-object-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"8de46da6e64b39dc39fc9572e59bd32cdec4c962bf72627579690c690342e7f6","family_id":"qf-triangle-vertex-set","seed":20261040,"semantic_template":"qf-triangle-vertex-set/{\"noncollinear\":true,\"operation\":\"vertex_set\",\"vertices\":[\"F\",\"H\",\"J\"]}"},"fields":{"title":"Vertex Set of a Triangle","stem":"Triangle FHJ has explicitly distinct noncollinear vertices. Write its vertex set in canonical order.","answer":{"kind":"short_text","value":"{F, H, J}","explanation":"Taking the three labels and sorting them canonically gives {F, H, J}."},"skills":["vertex sets","canonical ordering"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260925-triangle-vertex-set-0016","batch_id":"batch-20260925-triangle-object-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"f4c1a2841e83ec872f2768c5a0484614c928cc1bee40d2e88980bceea9f69ce1","family_id":"qf-triangle-vertex-set","seed":20261041,"semantic_template":"qf-triangle-vertex-set/{\"noncollinear\":true,\"operation\":\"vertex_set\",\"vertices\":[\"G\",\"I\",\"K\"]}"},"fields":{"title":"Vertex Set of a Triangle","stem":"Triangle GIK has explicitly distinct noncollinear vertices. Write its vertex set in canonical order.","answer":{"kind":"short_text","value":"{G, I, K}","explanation":"Taking the three labels and sorting them canonically gives {G, I, K}."},"skills":["vertex sets","canonical ordering"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260925-triangle-vertex-set-0017","batch_id":"batch-20260925-triangle-object-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"f09a1d8e3f4cb8387c3a165dc69050f56914c3735dbbc315990b39fbb812fcdf","family_id":"qf-triangle-vertex-set","seed":20261042,"semantic_template":"qf-triangle-vertex-set/{\"noncollinear\":true,\"operation\":\"vertex_set\",\"vertices\":[\"H\",\"J\",\"L\"]}"},"fields":{"title":"Vertex Set of a Triangle","stem":"Triangle HJL has explicitly distinct noncollinear vertices. Write its vertex set in canonical order.","answer":{"kind":"short_text","value":"{H, J, L}","explanation":"Taking the three labels and sorting them canonically gives {H, J, L}."},"skills":["vertex sets","canonical ordering"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260925-triangle-vertex-set-0018","batch_id":"batch-20260925-triangle-object-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"5f1518ff55f900a4593a0edc19785f2c144194078596fcb854a1efff8d1b8e5a","family_id":"qf-triangle-vertex-set","seed":20261043,"semantic_template":"qf-triangle-vertex-set/{\"noncollinear\":true,\"operation\":\"vertex_set\",\"vertices\":[\"I\",\"K\",\"M\"]}"},"fields":{"title":"Vertex Set of a Triangle","stem":"Triangle IKM has explicitly distinct noncollinear vertices. Write its vertex set in canonical order.","answer":{"kind":"short_text","value":"{I, K, M}","explanation":"Taking the three labels and sorting them canonically gives {I, K, M}."},"skills":["vertex sets","canonical ordering"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260925-triangle-vertex-set-0019","batch_id":"batch-20260925-triangle-object-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"a9962582f27a104249642afa8d6439d1845dcf478506ac2d966797260bf636a7","family_id":"qf-triangle-vertex-set","seed":20261044,"semantic_template":"qf-triangle-vertex-set/{\"noncollinear\":true,\"operation\":\"vertex_set\",\"vertices\":[\"J\",\"L\",\"N\"]}"},"fields":{"title":"Vertex Set of a Triangle","stem":"Triangle JLN has explicitly distinct noncollinear vertices. Write its vertex set in canonical order.","answer":{"kind":"short_text","value":"{J, L, N}","explanation":"Taking the three labels and sorting them canonically gives {J, L, N}."},"skills":["vertex sets","canonical ordering"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260925-triangle-vertex-set-0020","batch_id":"batch-20260925-triangle-object-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"f0f41431f47ca83d115fe2b75cdca440d16781b97417ff1597a81076f6fc9a93","family_id":"qf-triangle-vertex-set","seed":20261045,"semantic_template":"qf-triangle-vertex-set/{\"noncollinear\":true,\"operation\":\"vertex_set\",\"vertices\":[\"K\",\"M\",\"O\"]}"},"fields":{"title":"Vertex Set of a Triangle","stem":"Triangle KMO has explicitly distinct noncollinear vertices. Write its vertex set in canonical order.","answer":{"kind":"short_text","value":"{K, M, O}","explanation":"Taking the three labels and sorting them canonically gives {K, M, O}."},"skills":["vertex sets","canonical ordering"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260925-triangle-vertex-set-0021","batch_id":"batch-20260925-triangle-object-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"25ec3e674547553bd9515e7a00b31800d454c069773f72dc1f6b244d3d0beacf","family_id":"qf-triangle-vertex-set","seed":20261046,"semantic_template":"qf-triangle-vertex-set/{\"noncollinear\":true,\"operation\":\"vertex_set\",\"vertices\":[\"L\",\"N\",\"P\"]}"},"fields":{"title":"Vertex Set of a Triangle","stem":"Triangle LNP has explicitly distinct noncollinear vertices. Write its vertex set in canonical order.","answer":{"kind":"short_text","value":"{L, N, P}","explanation":"Taking the three labels and sorting them canonically gives {L, N, P}."},"skills":["vertex sets","canonical ordering"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260925-triangle-vertex-set-0022","batch_id":"batch-20260925-triangle-object-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"b2d97fc13e5323082eec427bef62dec78689fd046726d36127331b020ea23528","family_id":"qf-triangle-vertex-set","seed":20261047,"semantic_template":"qf-triangle-vertex-set/{\"noncollinear\":true,\"operation\":\"vertex_set\",\"vertices\":[\"M\",\"O\",\"Q\"]}"},"fields":{"title":"Vertex Set of a Triangle","stem":"Triangle MOQ has explicitly distinct noncollinear vertices. Write its vertex set in canonical order.","answer":{"kind":"short_text","value":"{M, O, Q}","explanation":"Taking the three labels and sorting them canonically gives {M, O, Q}."},"skills":["vertex sets","canonical ordering"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260925-triangle-vertex-set-0023","batch_id":"batch-20260925-triangle-object-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"b4138ff1b2feb7a025c06d8c04c54e064335c631ba08dfff9d70b9d646ede908","family_id":"qf-triangle-vertex-set","seed":20261048,"semantic_template":"qf-triangle-vertex-set/{\"noncollinear\":true,\"operation\":\"vertex_set\",\"vertices\":[\"N\",\"P\",\"R\"]}"},"fields":{"title":"Vertex Set of a Triangle","stem":"Triangle NPR has explicitly distinct noncollinear vertices. Write its vertex set in canonical order.","answer":{"kind":"short_text","value":"{N, P, R}","explanation":"Taking the three labels and sorting them canonically gives {N, P, R}."},"skills":["vertex sets","canonical ordering"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260925-triangle-vertex-set-0024","batch_id":"batch-20260925-triangle-object-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"48cbbc9c51522ac9f13265a52d684f4d29e6a3c20af16a2ca86e94346bd7f091","family_id":"qf-triangle-vertex-set","seed":20261049,"semantic_template":"qf-triangle-vertex-set/{\"noncollinear\":true,\"operation\":\"vertex_set\",\"vertices\":[\"O\",\"Q\",\"S\"]}"},"fields":{"title":"Vertex Set of a Triangle","stem":"Triangle OQS has explicitly distinct noncollinear vertices. Write its vertex set in canonical order.","answer":{"kind":"short_text","value":"{O, Q, S}","explanation":"Taking the three labels and sorting them canonically gives {O, Q, S}."},"skills":["vertex sets","canonical ordering"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260925-triangle-vertex-set-0025","batch_id":"batch-20260925-triangle-object-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"a83cd09187f0af99f6d6ba41af868287faa6feedd08af187ab5c24444ca8da80","family_id":"qf-triangle-vertex-set","seed":20261050,"semantic_template":"qf-triangle-vertex-set/{\"noncollinear\":true,\"operation\":\"vertex_set\",\"vertices\":[\"P\",\"R\",\"T\"]}"},"fields":{"title":"Vertex Set of a Triangle","stem":"Triangle PRT has explicitly distinct noncollinear vertices. Write its vertex set in canonical order.","answer":{"kind":"short_text","value":"{P, R, T}","explanation":"Taking the three labels and sorting them canonically gives {P, R, T}."},"skills":["vertex sets","canonical ordering"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260925-triangle-side-set-0001","batch_id":"batch-20260925-triangle-object-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"dff290e50c839f01fec8281d85fbe1f57820d0aa9b7b3ebd88e23c8d6a8ffb29","family_id":"qf-triangle-side-set","seed":20261126,"semantic_template":"qf-triangle-side-set/{\"noncollinear\":true,\"operation\":\"side_set\",\"vertices\":[\"A\",\"B\",\"C\"]}"},"fields":{"title":"Undirected Side Set of a Triangle","stem":"Triangle ABC has explicitly distinct noncollinear vertices. List its three undirected sides in canonical order.","answer":{"kind":"short_text","value":"AB, AC, BC","explanation":"Pairwise connection of the vertices followed by canonical ordering gives AB, AC, BC."},"skills":["undirected edges","canonical ordering"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260925-triangle-side-set-0002","batch_id":"batch-20260925-triangle-object-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"78c901641b33761c0ea35e371edd24269df8ec7a9e19a61628a838bde91544ce","family_id":"qf-triangle-side-set","seed":20261127,"semantic_template":"qf-triangle-side-set/{\"noncollinear\":true,\"operation\":\"side_set\",\"vertices\":[\"D\",\"E\",\"F\"]}"},"fields":{"title":"Undirected Side Set of a Triangle","stem":"Triangle DEF has explicitly distinct noncollinear vertices. List its three undirected sides in canonical order.","answer":{"kind":"short_text","value":"DE, DF, EF","explanation":"Pairwise connection of the vertices followed by canonical ordering gives DE, DF, EF."},"skills":["undirected edges","canonical ordering"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260925-triangle-side-set-0003","batch_id":"batch-20260925-triangle-object-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"34c7b9bdde8e8cd779450088f5824a771cbd6c349c95b3a4c996cd2d376c0e80","family_id":"qf-triangle-side-set","seed":20261128,"semantic_template":"qf-triangle-side-set/{\"noncollinear\":true,\"operation\":\"side_set\",\"vertices\":[\"G\",\"H\",\"I\"]}"},"fields":{"title":"Undirected Side Set of a Triangle","stem":"Triangle GHI has explicitly distinct noncollinear vertices. List its three undirected sides in canonical order.","answer":{"kind":"short_text","value":"GH, GI, HI","explanation":"Pairwise connection of the vertices followed by canonical ordering gives GH, GI, HI."},"skills":["undirected edges","canonical ordering"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260925-triangle-side-set-0004","batch_id":"batch-20260925-triangle-object-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"076b851c649142a8b625e86d1614fdcd87d568313ea4dc757ad591ad2b976012","family_id":"qf-triangle-side-set","seed":20261129,"semantic_template":"qf-triangle-side-set/{\"noncollinear\":true,\"operation\":\"side_set\",\"vertices\":[\"J\",\"K\",\"L\"]}"},"fields":{"title":"Undirected Side Set of a Triangle","stem":"Triangle JKL has explicitly distinct noncollinear vertices. List its three undirected sides in canonical order.","answer":{"kind":"short_text","value":"JK, JL, KL","explanation":"Pairwise connection of the vertices followed by canonical ordering gives JK, JL, KL."},"skills":["undirected edges","canonical ordering"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260925-triangle-side-set-0005","batch_id":"batch-20260925-triangle-object-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"b2dc32dfc21a9b42aa12a620d0f221725e9764cd67ba3edd4c08b9372e5141fe","family_id":"qf-triangle-side-set","seed":20261130,"semantic_template":"qf-triangle-side-set/{\"noncollinear\":true,\"operation\":\"side_set\",\"vertices\":[\"M\",\"N\",\"P\"]}"},"fields":{"title":"Undirected Side Set of a Triangle","stem":"Triangle MNP has explicitly distinct noncollinear vertices. List its three undirected sides in canonical order.","answer":{"kind":"short_text","value":"MN, MP, NP","explanation":"Pairwise connection of the vertices followed by canonical ordering gives MN, MP, NP."},"skills":["undirected edges","canonical ordering"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260925-triangle-side-set-0006","batch_id":"batch-20260925-triangle-object-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"6507c2473b85db5db24e7ebbce468bdb8d0cfc9cfd47c7dbb6df039a3adb8b26","family_id":"qf-triangle-side-set","seed":20261131,"semantic_template":"qf-triangle-side-set/{\"noncollinear\":true,\"operation\":\"side_set\",\"vertices\":[\"Q\",\"R\",\"S\"]}"},"fields":{"title":"Undirected Side Set of a Triangle","stem":"Triangle QRS has explicitly distinct noncollinear vertices. List its three undirected sides in canonical order.","answer":{"kind":"short_text","value":"QR, QS, RS","explanation":"Pairwise connection of the vertices followed by canonical ordering gives QR, QS, RS."},"skills":["undirected edges","canonical ordering"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260925-triangle-side-set-0007","batch_id":"batch-20260925-triangle-object-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"6b0ca4d000b376e631a04697da3cf7aa31890b0484688e2e7b8eda03905aa9b4","family_id":"qf-triangle-side-set","seed":20261132,"semantic_template":"qf-triangle-side-set/{\"noncollinear\":true,\"operation\":\"side_set\",\"vertices\":[\"T\",\"U\",\"V\"]}"},"fields":{"title":"Undirected Side Set of a Triangle","stem":"Triangle TUV has explicitly distinct noncollinear vertices. List its three undirected sides in canonical order.","answer":{"kind":"short_text","value":"TU, TV, UV","explanation":"Pairwise connection of the vertices followed by canonical ordering gives TU, TV, UV."},"skills":["undirected edges","canonical ordering"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260925-triangle-side-set-0008","batch_id":"batch-20260925-triangle-object-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"d70168dffd9d840981a3b947dbb983fef5de454f8226df3faff0b0238421d8ee","family_id":"qf-triangle-side-set","seed":20261133,"semantic_template":"qf-triangle-side-set/{\"noncollinear\":true,\"operation\":\"side_set\",\"vertices\":[\"W\",\"X\",\"Y\"]}"},"fields":{"title":"Undirected Side Set of a Triangle","stem":"Triangle WXY has explicitly distinct noncollinear vertices. List its three undirected sides in canonical order.","answer":{"kind":"short_text","value":"WX, WY, XY","explanation":"Pairwise connection of the vertices followed by canonical ordering gives WX, WY, XY."},"skills":["undirected edges","canonical ordering"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260925-triangle-side-set-0009","batch_id":"batch-20260925-triangle-object-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"a007fbe0ee8288f1abc04348ff1cd416674f1be97bd8f769d2d756e70eec6905","family_id":"qf-triangle-side-set","seed":20261134,"semantic_template":"qf-triangle-side-set/{\"noncollinear\":true,\"operation\":\"side_set\",\"vertices\":[\"A\",\"B\",\"D\"]}"},"fields":{"title":"Undirected Side Set of a Triangle","stem":"Triangle ABD has explicitly distinct noncollinear vertices. List its three undirected sides in canonical order.","answer":{"kind":"short_text","value":"AB, AD, BD","explanation":"Pairwise connection of the vertices followed by canonical ordering gives AB, AD, BD."},"skills":["undirected edges","canonical ordering"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260925-triangle-side-set-0010","batch_id":"batch-20260925-triangle-object-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"d9cd4b2765acdeb76d399f4c4eff6aaf9839aabedf0355979a61e8441deba46b","family_id":"qf-triangle-side-set","seed":20261135,"semantic_template":"qf-triangle-side-set/{\"noncollinear\":true,\"operation\":\"side_set\",\"vertices\":[\"A\",\"C\",\"E\"]}"},"fields":{"title":"Undirected Side Set of a Triangle","stem":"Triangle ACE has explicitly distinct noncollinear vertices. List its three undirected sides in canonical order.","answer":{"kind":"short_text","value":"AC, AE, CE","explanation":"Pairwise connection of the vertices followed by canonical ordering gives AC, AE, CE."},"skills":["undirected edges","canonical ordering"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260925-triangle-side-set-0011","batch_id":"batch-20260925-triangle-object-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"d33aae3d36d1dcc8c68f521d3ed8d017d784f97dad1c59b924557b9f15fed698","family_id":"qf-triangle-side-set","seed":20261136,"semantic_template":"qf-triangle-side-set/{\"noncollinear\":true,\"operation\":\"side_set\",\"vertices\":[\"B\",\"D\",\"F\"]}"},"fields":{"title":"Undirected Side Set of a Triangle","stem":"Triangle BDF has explicitly distinct noncollinear vertices. List its three undirected sides in canonical order.","answer":{"kind":"short_text","value":"BD, BF, DF","explanation":"Pairwise connection of the vertices followed by canonical ordering gives BD, BF, DF."},"skills":["undirected edges","canonical ordering"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260925-triangle-side-set-0012","batch_id":"batch-20260925-triangle-object-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"408ac27f5970ab18cc3645d381585e5bfbe0eebea922e9f94c56ebc2f20d638f","family_id":"qf-triangle-side-set","seed":20261137,"semantic_template":"qf-triangle-side-set/{\"noncollinear\":true,\"operation\":\"side_set\",\"vertices\":[\"C\",\"E\",\"G\"]}"},"fields":{"title":"Undirected Side Set of a Triangle","stem":"Triangle CEG has explicitly distinct noncollinear vertices. List its three undirected sides in canonical order.","answer":{"kind":"short_text","value":"CE, CG, EG","explanation":"Pairwise connection of the vertices followed by canonical ordering gives CE, CG, EG."},"skills":["undirected edges","canonical ordering"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260925-triangle-side-set-0013","batch_id":"batch-20260925-triangle-object-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"7cef9396ebcc458954deca8aa871be8f93fa9803bc465f8c4a3fe33f0f1d1b31","family_id":"qf-triangle-side-set","seed":20261138,"semantic_template":"qf-triangle-side-set/{\"noncollinear\":true,\"operation\":\"side_set\",\"vertices\":[\"D\",\"F\",\"H\"]}"},"fields":{"title":"Undirected Side Set of a Triangle","stem":"Triangle DFH has explicitly distinct noncollinear vertices. List its three undirected sides in canonical order.","answer":{"kind":"short_text","value":"DF, DH, FH","explanation":"Pairwise connection of the vertices followed by canonical ordering gives DF, DH, FH."},"skills":["undirected edges","canonical ordering"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260925-triangle-side-set-0014","batch_id":"batch-20260925-triangle-object-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"ab694dbdb5778bcdb099366ac54b7b45ae558acd9756853be4fd914bed82686c","family_id":"qf-triangle-side-set","seed":20261139,"semantic_template":"qf-triangle-side-set/{\"noncollinear\":true,\"operation\":\"side_set\",\"vertices\":[\"E\",\"G\",\"I\"]}"},"fields":{"title":"Undirected Side Set of a Triangle","stem":"Triangle EGI has explicitly distinct noncollinear vertices. List its three undirected sides in canonical order.","answer":{"kind":"short_text","value":"EG, EI, GI","explanation":"Pairwise connection of the vertices followed by canonical ordering gives EG, EI, GI."},"skills":["undirected edges","canonical ordering"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260925-triangle-side-set-0015","batch_id":"batch-20260925-triangle-object-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"da965813824b485d59e71e45a91d98c010c5ba9cf7eb606ec0dbe69888d33cdc","family_id":"qf-triangle-side-set","seed":20261140,"semantic_template":"qf-triangle-side-set/{\"noncollinear\":true,\"operation\":\"side_set\",\"vertices\":[\"F\",\"H\",\"J\"]}"},"fields":{"title":"Undirected Side Set of a Triangle","stem":"Triangle FHJ has explicitly distinct noncollinear vertices. List its three undirected sides in canonical order.","answer":{"kind":"short_text","value":"FH, FJ, HJ","explanation":"Pairwise connection of the vertices followed by canonical ordering gives FH, FJ, HJ."},"skills":["undirected edges","canonical ordering"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260925-triangle-side-set-0016","batch_id":"batch-20260925-triangle-object-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"2e7cb910465ce4026e44eda32a976a35d90e0f1cc4bf89b69bb157d7a0e4fa6b","family_id":"qf-triangle-side-set","seed":20261141,"semantic_template":"qf-triangle-side-set/{\"noncollinear\":true,\"operation\":\"side_set\",\"vertices\":[\"G\",\"I\",\"K\"]}"},"fields":{"title":"Undirected Side Set of a Triangle","stem":"Triangle GIK has explicitly distinct noncollinear vertices. List its three undirected sides in canonical order.","answer":{"kind":"short_text","value":"GI, GK, IK","explanation":"Pairwise connection of the vertices followed by canonical ordering gives GI, GK, IK."},"skills":["undirected edges","canonical ordering"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260925-triangle-side-set-0017","batch_id":"batch-20260925-triangle-object-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"58f27999fc28e6fefdb6c70d3d8c64ad770d6f1e8c518aac7d9a7061aa134307","family_id":"qf-triangle-side-set","seed":20261142,"semantic_template":"qf-triangle-side-set/{\"noncollinear\":true,\"operation\":\"side_set\",\"vertices\":[\"H\",\"J\",\"L\"]}"},"fields":{"title":"Undirected Side Set of a Triangle","stem":"Triangle HJL has explicitly distinct noncollinear vertices. List its three undirected sides in canonical order.","answer":{"kind":"short_text","value":"HJ, HL, JL","explanation":"Pairwise connection of the vertices followed by canonical ordering gives HJ, HL, JL."},"skills":["undirected edges","canonical ordering"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260925-triangle-side-set-0018","batch_id":"batch-20260925-triangle-object-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"fb760a3fac5a7bf6e53eb716575000684c3b08ecc2dab34d1fac19f2b0fbae04","family_id":"qf-triangle-side-set","seed":20261143,"semantic_template":"qf-triangle-side-set/{\"noncollinear\":true,\"operation\":\"side_set\",\"vertices\":[\"I\",\"K\",\"M\"]}"},"fields":{"title":"Undirected Side Set of a Triangle","stem":"Triangle IKM has explicitly distinct noncollinear vertices. List its three undirected sides in canonical order.","answer":{"kind":"short_text","value":"IK, IM, KM","explanation":"Pairwise connection of the vertices followed by canonical ordering gives IK, IM, KM."},"skills":["undirected edges","canonical ordering"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260925-triangle-side-set-0019","batch_id":"batch-20260925-triangle-object-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"cede3924b4427343e6cb454e50626e642d374bd68874d8cec2f0770dac9d38c0","family_id":"qf-triangle-side-set","seed":20261144,"semantic_template":"qf-triangle-side-set/{\"noncollinear\":true,\"operation\":\"side_set\",\"vertices\":[\"J\",\"L\",\"N\"]}"},"fields":{"title":"Undirected Side Set of a Triangle","stem":"Triangle JLN has explicitly distinct noncollinear vertices. List its three undirected sides in canonical order.","answer":{"kind":"short_text","value":"JL, JN, LN","explanation":"Pairwise connection of the vertices followed by canonical ordering gives JL, JN, LN."},"skills":["undirected edges","canonical ordering"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260925-triangle-side-set-0020","batch_id":"batch-20260925-triangle-object-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"83d946b926631e38dfa58da32bde4ff761be850ba9104b78c96b48cbdc4c488a","family_id":"qf-triangle-side-set","seed":20261145,"semantic_template":"qf-triangle-side-set/{\"noncollinear\":true,\"operation\":\"side_set\",\"vertices\":[\"K\",\"M\",\"O\"]}"},"fields":{"title":"Undirected Side Set of a Triangle","stem":"Triangle KMO has explicitly distinct noncollinear vertices. List its three undirected sides in canonical order.","answer":{"kind":"short_text","value":"KM, KO, MO","explanation":"Pairwise connection of the vertices followed by canonical ordering gives KM, KO, MO."},"skills":["undirected edges","canonical ordering"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260925-triangle-side-set-0021","batch_id":"batch-20260925-triangle-object-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"76993f6533e6f4637202be5624a1b3a65ee4e4238d0e77ec85a8004103144668","family_id":"qf-triangle-side-set","seed":20261146,"semantic_template":"qf-triangle-side-set/{\"noncollinear\":true,\"operation\":\"side_set\",\"vertices\":[\"L\",\"N\",\"P\"]}"},"fields":{"title":"Undirected Side Set of a Triangle","stem":"Triangle LNP has explicitly distinct noncollinear vertices. List its three undirected sides in canonical order.","answer":{"kind":"short_text","value":"LN, LP, NP","explanation":"Pairwise connection of the vertices followed by canonical ordering gives LN, LP, NP."},"skills":["undirected edges","canonical ordering"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260925-triangle-side-set-0022","batch_id":"batch-20260925-triangle-object-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"f173cd95b42e2db065ea52b42f130481ef07bff20fef650c2c25b3a74fae3b51","family_id":"qf-triangle-side-set","seed":20261147,"semantic_template":"qf-triangle-side-set/{\"noncollinear\":true,\"operation\":\"side_set\",\"vertices\":[\"M\",\"O\",\"Q\"]}"},"fields":{"title":"Undirected Side Set of a Triangle","stem":"Triangle MOQ has explicitly distinct noncollinear vertices. List its three undirected sides in canonical order.","answer":{"kind":"short_text","value":"MO, MQ, OQ","explanation":"Pairwise connection of the vertices followed by canonical ordering gives MO, MQ, OQ."},"skills":["undirected edges","canonical ordering"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260925-triangle-side-set-0023","batch_id":"batch-20260925-triangle-object-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"c3361e52d684e5b2749cd9c4ee08e0ad00b0ca83a72deae62e736f7cc7c9ebd8","family_id":"qf-triangle-side-set","seed":20261148,"semantic_template":"qf-triangle-side-set/{\"noncollinear\":true,\"operation\":\"side_set\",\"vertices\":[\"N\",\"P\",\"R\"]}"},"fields":{"title":"Undirected Side Set of a Triangle","stem":"Triangle NPR has explicitly distinct noncollinear vertices. List its three undirected sides in canonical order.","answer":{"kind":"short_text","value":"NP, NR, PR","explanation":"Pairwise connection of the vertices followed by canonical ordering gives NP, NR, PR."},"skills":["undirected edges","canonical ordering"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260925-triangle-side-set-0024","batch_id":"batch-20260925-triangle-object-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"71d0ea19bd2aca9987b5205c3d8d4efb8e3b394f361cae08b6ef59d9fb222944","family_id":"qf-triangle-side-set","seed":20261149,"semantic_template":"qf-triangle-side-set/{\"noncollinear\":true,\"operation\":\"side_set\",\"vertices\":[\"O\",\"Q\",\"S\"]}"},"fields":{"title":"Undirected Side Set of a Triangle","stem":"Triangle OQS has explicitly distinct noncollinear vertices. List its three undirected sides in canonical order.","answer":{"kind":"short_text","value":"OQ, OS, QS","explanation":"Pairwise connection of the vertices followed by canonical ordering gives OQ, OS, QS."},"skills":["undirected edges","canonical ordering"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260925-triangle-side-set-0025","batch_id":"batch-20260925-triangle-object-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"5aca2b249ed2b8fd7a43a9eb0be165bf64d914cc565449283223c8337c667ee7","family_id":"qf-triangle-side-set","seed":20261150,"semantic_template":"qf-triangle-side-set/{\"noncollinear\":true,\"operation\":\"side_set\",\"vertices\":[\"P\",\"R\",\"T\"]}"},"fields":{"title":"Undirected Side Set of a Triangle","stem":"Triangle PRT has explicitly distinct noncollinear vertices. List its three undirected sides in canonical order.","answer":{"kind":"short_text","value":"PR, PT, RT","explanation":"Pairwise connection of the vertices followed by canonical ordering gives PR, PT, RT."},"skills":["undirected edges","canonical ordering"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260925-triangle-opposite-side-0001","batch_id":"batch-20260925-triangle-object-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"ee55d6f1632e18a7add3ae238a41369c4d7f1b12db6a2f628e779e9bae36761b","family_id":"qf-triangle-opposite-side","seed":20261226,"semantic_template":"qf-triangle-opposite-side/{\"noncollinear\":true,\"operation\":\"opposite_side\",\"vertex\":\"A\",\"vertices\":[\"A\",\"B\",\"C\"]}"},"fields":{"title":"Side Opposite a Vertex","stem":"Triangle ABC has explicitly distinct noncollinear vertices. Which undirected side is opposite vertex A?","answer":{"kind":"short_text","value":"BC","explanation":"Removing vertex A leaves the other two vertices, which form side BC."},"skills":["vertices","opposite side"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260925-triangle-opposite-side-0002","batch_id":"batch-20260925-triangle-object-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"ddfa9e9a6428cbd130f4f6e74301832bf384756b8733a329ecf4ec1d9250c493","family_id":"qf-triangle-opposite-side","seed":20261227,"semantic_template":"qf-triangle-opposite-side/{\"noncollinear\":true,\"operation\":\"opposite_side\",\"vertex\":\"E\",\"vertices\":[\"D\",\"E\",\"F\"]}"},"fields":{"title":"Side Opposite a Vertex","stem":"Triangle DEF has explicitly distinct noncollinear vertices. Which undirected side is opposite vertex E?","answer":{"kind":"short_text","value":"DF","explanation":"Removing vertex E leaves the other two vertices, which form side DF."},"skills":["vertices","opposite side"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260925-triangle-opposite-side-0003","batch_id":"batch-20260925-triangle-object-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"b2e004136a66a556b0e9c89e82404b5dbc8c0f5f62dc26f94f6a8a71d3140c6b","family_id":"qf-triangle-opposite-side","seed":20261228,"semantic_template":"qf-triangle-opposite-side/{\"noncollinear\":true,\"operation\":\"opposite_side\",\"vertex\":\"I\",\"vertices\":[\"G\",\"H\",\"I\"]}"},"fields":{"title":"Side Opposite a Vertex","stem":"Triangle GHI has explicitly distinct noncollinear vertices. Which undirected side is opposite vertex I?","answer":{"kind":"short_text","value":"GH","explanation":"Removing vertex I leaves the other two vertices, which form side GH."},"skills":["vertices","opposite side"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260925-triangle-opposite-side-0004","batch_id":"batch-20260925-triangle-object-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"c129713449517ffc47538d24066efdad0ab65c72e667e368b142d943b4edf03c","family_id":"qf-triangle-opposite-side","seed":20261229,"semantic_template":"qf-triangle-opposite-side/{\"noncollinear\":true,\"operation\":\"opposite_side\",\"vertex\":\"J\",\"vertices\":[\"J\",\"K\",\"L\"]}"},"fields":{"title":"Side Opposite a Vertex","stem":"Triangle JKL has explicitly distinct noncollinear vertices. Which undirected side is opposite vertex J?","answer":{"kind":"short_text","value":"KL","explanation":"Removing vertex J leaves the other two vertices, which form side KL."},"skills":["vertices","opposite side"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260925-triangle-opposite-side-0005","batch_id":"batch-20260925-triangle-object-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"868bf9b1ed8c7956d383cbf7c17ad62ac7abdfb3fc4848e2f9993b1f0dd83851","family_id":"qf-triangle-opposite-side","seed":20261230,"semantic_template":"qf-triangle-opposite-side/{\"noncollinear\":true,\"operation\":\"opposite_side\",\"vertex\":\"N\",\"vertices\":[\"M\",\"N\",\"P\"]}"},"fields":{"title":"Side Opposite a Vertex","stem":"Triangle MNP has explicitly distinct noncollinear vertices. Which undirected side is opposite vertex N?","answer":{"kind":"short_text","value":"MP","explanation":"Removing vertex N leaves the other two vertices, which form side MP."},"skills":["vertices","opposite side"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260925-triangle-opposite-side-0006","batch_id":"batch-20260925-triangle-object-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"65ad7209be5f2356c9e04f9f9b057e7e3f5b4b4206b86b4461ec0e5bf614f0c8","family_id":"qf-triangle-opposite-side","seed":20261231,"semantic_template":"qf-triangle-opposite-side/{\"noncollinear\":true,\"operation\":\"opposite_side\",\"vertex\":\"S\",\"vertices\":[\"Q\",\"R\",\"S\"]}"},"fields":{"title":"Side Opposite a Vertex","stem":"Triangle QRS has explicitly distinct noncollinear vertices. Which undirected side is opposite vertex S?","answer":{"kind":"short_text","value":"QR","explanation":"Removing vertex S leaves the other two vertices, which form side QR."},"skills":["vertices","opposite side"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260925-triangle-opposite-side-0007","batch_id":"batch-20260925-triangle-object-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"df11bc98b29b2ce4ea7d6ab014a94f8afffebc8de924245bc2c46500879510ff","family_id":"qf-triangle-opposite-side","seed":20261232,"semantic_template":"qf-triangle-opposite-side/{\"noncollinear\":true,\"operation\":\"opposite_side\",\"vertex\":\"T\",\"vertices\":[\"T\",\"U\",\"V\"]}"},"fields":{"title":"Side Opposite a Vertex","stem":"Triangle TUV has explicitly distinct noncollinear vertices. Which undirected side is opposite vertex T?","answer":{"kind":"short_text","value":"UV","explanation":"Removing vertex T leaves the other two vertices, which form side UV."},"skills":["vertices","opposite side"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260925-triangle-opposite-side-0008","batch_id":"batch-20260925-triangle-object-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"9e089f30062fc1288c9011ab1949784c9c453091e1a6a4994fd2912dd3e30eb3","family_id":"qf-triangle-opposite-side","seed":20261233,"semantic_template":"qf-triangle-opposite-side/{\"noncollinear\":true,\"operation\":\"opposite_side\",\"vertex\":\"X\",\"vertices\":[\"W\",\"X\",\"Y\"]}"},"fields":{"title":"Side Opposite a Vertex","stem":"Triangle WXY has explicitly distinct noncollinear vertices. Which undirected side is opposite vertex X?","answer":{"kind":"short_text","value":"WY","explanation":"Removing vertex X leaves the other two vertices, which form side WY."},"skills":["vertices","opposite side"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260925-triangle-opposite-side-0009","batch_id":"batch-20260925-triangle-object-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"18be74e310ca3d5ee6bd96c9fe35ca79755d3c6b8f88890e6f8bc980951049ce","family_id":"qf-triangle-opposite-side","seed":20261234,"semantic_template":"qf-triangle-opposite-side/{\"noncollinear\":true,\"operation\":\"opposite_side\",\"vertex\":\"D\",\"vertices\":[\"A\",\"B\",\"D\"]}"},"fields":{"title":"Side Opposite a Vertex","stem":"Triangle ABD has explicitly distinct noncollinear vertices. Which undirected side is opposite vertex D?","answer":{"kind":"short_text","value":"AB","explanation":"Removing vertex D leaves the other two vertices, which form side AB."},"skills":["vertices","opposite side"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260925-triangle-opposite-side-0010","batch_id":"batch-20260925-triangle-object-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"abbbbd68e0dc4d3037a29b661edd8c66f1178a69988eaeba94335f6351430f74","family_id":"qf-triangle-opposite-side","seed":20261235,"semantic_template":"qf-triangle-opposite-side/{\"noncollinear\":true,\"operation\":\"opposite_side\",\"vertex\":\"A\",\"vertices\":[\"A\",\"C\",\"E\"]}"},"fields":{"title":"Side Opposite a Vertex","stem":"Triangle ACE has explicitly distinct noncollinear vertices. Which undirected side is opposite vertex A?","answer":{"kind":"short_text","value":"CE","explanation":"Removing vertex A leaves the other two vertices, which form side CE."},"skills":["vertices","opposite side"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260925-triangle-opposite-side-0011","batch_id":"batch-20260925-triangle-object-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"8b8391f97452d5cd5746488e9857f93996a876bbceaacbef7e1e47addecb616c","family_id":"qf-triangle-opposite-side","seed":20261236,"semantic_template":"qf-triangle-opposite-side/{\"noncollinear\":true,\"operation\":\"opposite_side\",\"vertex\":\"D\",\"vertices\":[\"B\",\"D\",\"F\"]}"},"fields":{"title":"Side Opposite a Vertex","stem":"Triangle BDF has explicitly distinct noncollinear vertices. Which undirected side is opposite vertex D?","answer":{"kind":"short_text","value":"BF","explanation":"Removing vertex D leaves the other two vertices, which form side BF."},"skills":["vertices","opposite side"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260925-triangle-opposite-side-0012","batch_id":"batch-20260925-triangle-object-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"fed289342f9eb3211b05cab495f9b3c26585f99a461849e136432e21b54f20f9","family_id":"qf-triangle-opposite-side","seed":20261237,"semantic_template":"qf-triangle-opposite-side/{\"noncollinear\":true,\"operation\":\"opposite_side\",\"vertex\":\"G\",\"vertices\":[\"C\",\"E\",\"G\"]}"},"fields":{"title":"Side Opposite a Vertex","stem":"Triangle CEG has explicitly distinct noncollinear vertices. Which undirected side is opposite vertex G?","answer":{"kind":"short_text","value":"CE","explanation":"Removing vertex G leaves the other two vertices, which form side CE."},"skills":["vertices","opposite side"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260925-triangle-opposite-side-0013","batch_id":"batch-20260925-triangle-object-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"fcecd88242829fa1ed5ac3de7e2a2e9a99d843671be13dc570eac0c6e86e5f1b","family_id":"qf-triangle-opposite-side","seed":20261238,"semantic_template":"qf-triangle-opposite-side/{\"noncollinear\":true,\"operation\":\"opposite_side\",\"vertex\":\"D\",\"vertices\":[\"D\",\"F\",\"H\"]}"},"fields":{"title":"Side Opposite a Vertex","stem":"Triangle DFH has explicitly distinct noncollinear vertices. Which undirected side is opposite vertex D?","answer":{"kind":"short_text","value":"FH","explanation":"Removing vertex D leaves the other two vertices, which form side FH."},"skills":["vertices","opposite side"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260925-triangle-opposite-side-0014","batch_id":"batch-20260925-triangle-object-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"faf832267cb0b9282c3efe73772ab4a22acb1e346cf910186d461c486076d961","family_id":"qf-triangle-opposite-side","seed":20261239,"semantic_template":"qf-triangle-opposite-side/{\"noncollinear\":true,\"operation\":\"opposite_side\",\"vertex\":\"G\",\"vertices\":[\"E\",\"G\",\"I\"]}"},"fields":{"title":"Side Opposite a Vertex","stem":"Triangle EGI has explicitly distinct noncollinear vertices. Which undirected side is opposite vertex G?","answer":{"kind":"short_text","value":"EI","explanation":"Removing vertex G leaves the other two vertices, which form side EI."},"skills":["vertices","opposite side"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260925-triangle-opposite-side-0015","batch_id":"batch-20260925-triangle-object-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"0fdc1d7026687bc14764f52795097a3d3627324f00c2c203ee8172eb79819079","family_id":"qf-triangle-opposite-side","seed":20261240,"semantic_template":"qf-triangle-opposite-side/{\"noncollinear\":true,\"operation\":\"opposite_side\",\"vertex\":\"J\",\"vertices\":[\"F\",\"H\",\"J\"]}"},"fields":{"title":"Side Opposite a Vertex","stem":"Triangle FHJ has explicitly distinct noncollinear vertices. Which undirected side is opposite vertex J?","answer":{"kind":"short_text","value":"FH","explanation":"Removing vertex J leaves the other two vertices, which form side FH."},"skills":["vertices","opposite side"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260925-triangle-opposite-side-0016","batch_id":"batch-20260925-triangle-object-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"74a567eb6a008af3a78d3cd6f78b4903564f56f89f3a4929f9b2d4f7e372f025","family_id":"qf-triangle-opposite-side","seed":20261241,"semantic_template":"qf-triangle-opposite-side/{\"noncollinear\":true,\"operation\":\"opposite_side\",\"vertex\":\"G\",\"vertices\":[\"G\",\"I\",\"K\"]}"},"fields":{"title":"Side Opposite a Vertex","stem":"Triangle GIK has explicitly distinct noncollinear vertices. Which undirected side is opposite vertex G?","answer":{"kind":"short_text","value":"IK","explanation":"Removing vertex G leaves the other two vertices, which form side IK."},"skills":["vertices","opposite side"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260925-triangle-opposite-side-0017","batch_id":"batch-20260925-triangle-object-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"c991b83993f451fc6d21933ce960383d259593cfd97d91af20e87f7bf0bf5e38","family_id":"qf-triangle-opposite-side","seed":20261242,"semantic_template":"qf-triangle-opposite-side/{\"noncollinear\":true,\"operation\":\"opposite_side\",\"vertex\":\"J\",\"vertices\":[\"H\",\"J\",\"L\"]}"},"fields":{"title":"Side Opposite a Vertex","stem":"Triangle HJL has explicitly distinct noncollinear vertices. Which undirected side is opposite vertex J?","answer":{"kind":"short_text","value":"HL","explanation":"Removing vertex J leaves the other two vertices, which form side HL."},"skills":["vertices","opposite side"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260925-triangle-opposite-side-0018","batch_id":"batch-20260925-triangle-object-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"49a57ea7f9abf0c25ffd8777425d5d45fe3f1a300f081e8ddd5c71d5aadc6a59","family_id":"qf-triangle-opposite-side","seed":20261243,"semantic_template":"qf-triangle-opposite-side/{\"noncollinear\":true,\"operation\":\"opposite_side\",\"vertex\":\"M\",\"vertices\":[\"I\",\"K\",\"M\"]}"},"fields":{"title":"Side Opposite a Vertex","stem":"Triangle IKM has explicitly distinct noncollinear vertices. Which undirected side is opposite vertex M?","answer":{"kind":"short_text","value":"IK","explanation":"Removing vertex M leaves the other two vertices, which form side IK."},"skills":["vertices","opposite side"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260925-triangle-opposite-side-0019","batch_id":"batch-20260925-triangle-object-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"258e4e89bb757d341b5d8efda953d2f4af13a333906f8d48add02de840115fce","family_id":"qf-triangle-opposite-side","seed":20261244,"semantic_template":"qf-triangle-opposite-side/{\"noncollinear\":true,\"operation\":\"opposite_side\",\"vertex\":\"J\",\"vertices\":[\"J\",\"L\",\"N\"]}"},"fields":{"title":"Side Opposite a Vertex","stem":"Triangle JLN has explicitly distinct noncollinear vertices. Which undirected side is opposite vertex J?","answer":{"kind":"short_text","value":"LN","explanation":"Removing vertex J leaves the other two vertices, which form side LN."},"skills":["vertices","opposite side"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260925-triangle-opposite-side-0020","batch_id":"batch-20260925-triangle-object-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"0cf8daf465e3930b21555db6d25518bab8e9168c1f6b0393c39c49f00f7e9c62","family_id":"qf-triangle-opposite-side","seed":20261245,"semantic_template":"qf-triangle-opposite-side/{\"noncollinear\":true,\"operation\":\"opposite_side\",\"vertex\":\"M\",\"vertices\":[\"K\",\"M\",\"O\"]}"},"fields":{"title":"Side Opposite a Vertex","stem":"Triangle KMO has explicitly distinct noncollinear vertices. Which undirected side is opposite vertex M?","answer":{"kind":"short_text","value":"KO","explanation":"Removing vertex M leaves the other two vertices, which form side KO."},"skills":["vertices","opposite side"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260925-triangle-opposite-side-0021","batch_id":"batch-20260925-triangle-object-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"afa13a4c1f7d8961172ffb4d56f7c3fce2ea041c671901954eb55857979bacaa","family_id":"qf-triangle-opposite-side","seed":20261246,"semantic_template":"qf-triangle-opposite-side/{\"noncollinear\":true,\"operation\":\"opposite_side\",\"vertex\":\"P\",\"vertices\":[\"L\",\"N\",\"P\"]}"},"fields":{"title":"Side Opposite a Vertex","stem":"Triangle LNP has explicitly distinct noncollinear vertices. Which undirected side is opposite vertex P?","answer":{"kind":"short_text","value":"LN","explanation":"Removing vertex P leaves the other two vertices, which form side LN."},"skills":["vertices","opposite side"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260925-triangle-opposite-side-0022","batch_id":"batch-20260925-triangle-object-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"384a768f3ec2b7b12ed25e085c2d3522a79d89c8d42ed4c55c3ac602679bdfd6","family_id":"qf-triangle-opposite-side","seed":20261247,"semantic_template":"qf-triangle-opposite-side/{\"noncollinear\":true,\"operation\":\"opposite_side\",\"vertex\":\"M\",\"vertices\":[\"M\",\"O\",\"Q\"]}"},"fields":{"title":"Side Opposite a Vertex","stem":"Triangle MOQ has explicitly distinct noncollinear vertices. Which undirected side is opposite vertex M?","answer":{"kind":"short_text","value":"OQ","explanation":"Removing vertex M leaves the other two vertices, which form side OQ."},"skills":["vertices","opposite side"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260925-triangle-opposite-side-0023","batch_id":"batch-20260925-triangle-object-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"30964ed1c5c71aa5832624c7cd1f374502f296b7e14ebf8fce3b8a2093ded245","family_id":"qf-triangle-opposite-side","seed":20261248,"semantic_template":"qf-triangle-opposite-side/{\"noncollinear\":true,\"operation\":\"opposite_side\",\"vertex\":\"P\",\"vertices\":[\"N\",\"P\",\"R\"]}"},"fields":{"title":"Side Opposite a Vertex","stem":"Triangle NPR has explicitly distinct noncollinear vertices. Which undirected side is opposite vertex P?","answer":{"kind":"short_text","value":"NR","explanation":"Removing vertex P leaves the other two vertices, which form side NR."},"skills":["vertices","opposite side"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260925-triangle-opposite-side-0024","batch_id":"batch-20260925-triangle-object-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"7ca8bd8b6622b2ead6beb575b8f72c336e08399108429491d9c9c3117623c28b","family_id":"qf-triangle-opposite-side","seed":20261249,"semantic_template":"qf-triangle-opposite-side/{\"noncollinear\":true,\"operation\":\"opposite_side\",\"vertex\":\"S\",\"vertices\":[\"O\",\"Q\",\"S\"]}"},"fields":{"title":"Side Opposite a Vertex","stem":"Triangle OQS has explicitly distinct noncollinear vertices. Which undirected side is opposite vertex S?","answer":{"kind":"short_text","value":"OQ","explanation":"Removing vertex S leaves the other two vertices, which form side OQ."},"skills":["vertices","opposite side"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260925-triangle-opposite-side-0025","batch_id":"batch-20260925-triangle-object-language","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"c136144bb4460c14ecaf9f455a63e5044b89725f9d6a2aabad62de02a9b0f214","family_id":"qf-triangle-opposite-side","seed":20261250,"semantic_template":"qf-triangle-opposite-side/{\"noncollinear\":true,\"operation\":\"opposite_side\",\"vertex\":\"P\",\"vertices\":[\"P\",\"R\",\"T\"]}"},"fields":{"title":"Side Opposite a Vertex","stem":"Triangle PRT has explicitly distinct noncollinear vertices. Which undirected side is opposite vertex P?","answer":{"kind":"short_text","value":"RT","explanation":"Removing vertex P leaves the other two vertices, which form side RT."},"skills":["vertices","opposite side"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}