{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r04-optimization-problem-0001","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"cb0097e32a0ce4249ed2d94d480fa1268f73b27930e36092e633d2b0b298daa0","family_id":"qf-app20-optimization-feasible-filter","seed":202610204001,"semantic_template":"qf-app20-optimization-feasible-filter/{\"feasible\":[true,true,false,true],\"values\":[-10,-8,12,0]}"},"fields":{"title":"Feasible Original Indices before Objective Comparison","stem":"Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. values=[-10, -8, 12, 0], feasible=[true, true, false, true]. Give (all values, feasible mask, every feasible original index).","answer":{"kind":"expression","value":"([-10, -8, 12, 0], [Yes, Yes, No, Yes], [0, 1, 3])","explanation":"Filter by declared eligibility without selecting an infeasible point that has a better objective value. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([-10, -8, 12, 0], [Yes, Yes, No, Yes], [0, 1, 3])."},"skills":["Feasible Original Indices before Objective Comparison"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r04-optimization-problem-0002","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"34756758006ceb33f09de8124b9576d8e76fdb885baeae15014885fc8c77a4e9","family_id":"qf-app20-optimization-feasible-filter","seed":202610204002,"semantic_template":"qf-app20-optimization-feasible-filter/{\"feasible\":[true,false,true,true],\"values\":[-9,-5,11,1]}"},"fields":{"title":"Feasible Original Indices before Objective Comparison","stem":"Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. values=[-9, -5, 11, 1], feasible=[true, false, true, true]. Give (all values, feasible mask, every feasible original index).","answer":{"kind":"expression","value":"([-9, -5, 11, 1], [Yes, No, Yes, Yes], [0, 2, 3])","explanation":"Filter by declared eligibility without selecting an infeasible point that has a better objective value. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([-9, -5, 11, 1], [Yes, No, Yes, Yes], [0, 2, 3])."},"skills":["Feasible Original Indices before Objective Comparison"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r04-optimization-problem-0003","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"df91498fd94fb0b281b6c95a47ed1a7a64edc9617551c877c7d0f77b796b6ef7","family_id":"qf-app20-optimization-feasible-filter","seed":202610204003,"semantic_template":"qf-app20-optimization-feasible-filter/{\"feasible\":[true,true,true,true],\"values\":[-8,-2,10,2]}"},"fields":{"title":"Feasible Original Indices before Objective Comparison","stem":"Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. values=[-8, -2, 10, 2], feasible=[true, true, true, true]. Give (all values, feasible mask, every feasible original index).","answer":{"kind":"expression","value":"([-8, -2, 10, 2], [Yes, Yes, Yes, Yes], [0, 1, 2, 3])","explanation":"Filter by declared eligibility without selecting an infeasible point that has a better objective value. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([-8, -2, 10, 2], [Yes, Yes, Yes, Yes], [0, 1, 2, 3])."},"skills":["Feasible Original Indices before Objective Comparison"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r04-optimization-problem-0004","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"4767365c4711d7b031e809b92305dc53adbdf98b6432f03f9b07e9a95351542d","family_id":"qf-app20-optimization-feasible-filter","seed":202610204004,"semantic_template":"qf-app20-optimization-feasible-filter/{\"feasible\":[true,false,false,true],\"values\":[-7,1,9,3]}"},"fields":{"title":"Feasible Original Indices before Objective Comparison","stem":"Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. values=[-7, 1, 9, 3], feasible=[true, false, false, true]. Give (all values, feasible mask, every feasible original index).","answer":{"kind":"expression","value":"([-7, 1, 9, 3], [Yes, No, No, Yes], [0, 3])","explanation":"Filter by declared eligibility without selecting an infeasible point that has a better objective value. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([-7, 1, 9, 3], [Yes, No, No, Yes], [0, 3])."},"skills":["Feasible Original Indices before Objective Comparison"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r04-optimization-problem-0005","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"50d111387cc32ddd6c1971b0e7411aa606fa2c7c8fe8508cc01224b5fdbf68e2","family_id":"qf-app20-optimization-feasible-filter","seed":202610204005,"semantic_template":"qf-app20-optimization-feasible-filter/{\"feasible\":[true,true,true,true],\"values\":[-6,4,8,4]}"},"fields":{"title":"Feasible Original Indices before Objective Comparison","stem":"Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. values=[-6, 4, 8, 4], feasible=[true, true, true, true]. Give (all values, feasible mask, every feasible original index).","answer":{"kind":"expression","value":"([-6, 4, 8, 4], [Yes, Yes, Yes, Yes], [0, 1, 2, 3])","explanation":"Filter by declared eligibility without selecting an infeasible point that has a better objective value. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([-6, 4, 8, 4], [Yes, Yes, Yes, Yes], [0, 1, 2, 3])."},"skills":["Feasible Original Indices before Objective Comparison"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r04-optimization-problem-0006","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"03f4311ed2ceb077d548c436f403b9426714f19c22f3820f00431baa1f34c00c","family_id":"qf-app20-optimization-feasible-filter","seed":202610204006,"semantic_template":"qf-app20-optimization-feasible-filter/{\"feasible\":[true,false,true,true],\"values\":[-5,7,7,0]}"},"fields":{"title":"Feasible Original Indices before Objective Comparison","stem":"Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. values=[-5, 7, 7, 0], feasible=[true, false, true, true]. Give (all values, feasible mask, every feasible original index).","answer":{"kind":"expression","value":"([-5, 7, 7, 0], [Yes, No, Yes, Yes], [0, 2, 3])","explanation":"Filter by declared eligibility without selecting an infeasible point that has a better objective value. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([-5, 7, 7, 0], [Yes, No, Yes, Yes], [0, 2, 3])."},"skills":["Feasible Original Indices before Objective Comparison"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r04-optimization-problem-0007","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"d51f513a277fa86951fec9730c4e3d41ed032e9ba7a2cd8972ba9cd4d249d86c","family_id":"qf-app20-optimization-feasible-filter","seed":202610204007,"semantic_template":"qf-app20-optimization-feasible-filter/{\"feasible\":[true,true,false,true],\"values\":[-4,-7,6,1]}"},"fields":{"title":"Feasible Original Indices before Objective Comparison","stem":"Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. values=[-4, -7, 6, 1], feasible=[true, true, false, true]. Give (all values, feasible mask, every feasible original index).","answer":{"kind":"expression","value":"([-4, -7, 6, 1], [Yes, Yes, No, Yes], [0, 1, 3])","explanation":"Filter by declared eligibility without selecting an infeasible point that has a better objective value. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([-4, -7, 6, 1], [Yes, Yes, No, Yes], [0, 1, 3])."},"skills":["Feasible Original Indices before Objective Comparison"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r04-optimization-problem-0008","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"7872234aeb0aeaa23e40478d5abb1a646d3a6a4ba4b6ca154692928f9112a585","family_id":"qf-app20-optimization-feasible-filter","seed":202610204008,"semantic_template":"qf-app20-optimization-feasible-filter/{\"feasible\":[true,false,true,true],\"values\":[-3,-4,5,2]}"},"fields":{"title":"Feasible Original Indices before Objective Comparison","stem":"Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. values=[-3, -4, 5, 2], feasible=[true, false, true, true]. Give (all values, feasible mask, every feasible original index).","answer":{"kind":"expression","value":"([-3, -4, 5, 2], [Yes, No, Yes, Yes], [0, 2, 3])","explanation":"Filter by declared eligibility without selecting an infeasible point that has a better objective value. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([-3, -4, 5, 2], [Yes, No, Yes, Yes], [0, 2, 3])."},"skills":["Feasible Original Indices before Objective Comparison"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r04-optimization-problem-0009","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"7e0f72989814c6d99df4b472eb32e523f75bbc2bc95c924173fcda1fea6239f5","family_id":"qf-app20-optimization-feasible-filter","seed":202610204009,"semantic_template":"qf-app20-optimization-feasible-filter/{\"feasible\":[true,true,true,true],\"values\":[-2,-1,4,3]}"},"fields":{"title":"Feasible Original Indices before Objective Comparison","stem":"Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. values=[-2, -1, 4, 3], feasible=[true, true, true, true]. Give (all values, feasible mask, every feasible original index).","answer":{"kind":"expression","value":"([-2, -1, 4, 3], [Yes, Yes, Yes, Yes], [0, 1, 2, 3])","explanation":"Filter by declared eligibility without selecting an infeasible point that has a better objective value. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([-2, -1, 4, 3], [Yes, Yes, Yes, Yes], [0, 1, 2, 3])."},"skills":["Feasible Original Indices before Objective Comparison"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r04-optimization-problem-0010","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"3cd896ddb5b387ca1e98071943d4f039c9708f8d881a53b86b69a5f07b06537c","family_id":"qf-app20-optimization-feasible-filter","seed":202610204010,"semantic_template":"qf-app20-optimization-feasible-filter/{\"feasible\":[true,false,false,true],\"values\":[-1,2,3,4]}"},"fields":{"title":"Feasible Original Indices before Objective Comparison","stem":"Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. values=[-1, 2, 3, 4], feasible=[true, false, false, true]. Give (all values, feasible mask, every feasible original index).","answer":{"kind":"expression","value":"([-1, 2, 3, 4], [Yes, No, No, Yes], [0, 3])","explanation":"Filter by declared eligibility without selecting an infeasible point that has a better objective value. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([-1, 2, 3, 4], [Yes, No, No, Yes], [0, 3])."},"skills":["Feasible Original Indices before Objective Comparison"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r04-optimization-problem-0011","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"84522b59eaf3110e181d4c2109fffc998c21a4d725c0c855866880254cc26d57","family_id":"qf-app20-optimization-feasible-filter","seed":202610204011,"semantic_template":"qf-app20-optimization-feasible-filter/{\"feasible\":[true,true,true,true],\"values\":[0,5,2,0]}"},"fields":{"title":"Feasible Original Indices before Objective Comparison","stem":"Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. values=[0, 5, 2, 0], feasible=[true, true, true, true]. Give (all values, feasible mask, every feasible original index).","answer":{"kind":"expression","value":"([0, 5, 2, 0], [Yes, Yes, Yes, Yes], [0, 1, 2, 3])","explanation":"Filter by declared eligibility without selecting an infeasible point that has a better objective value. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([0, 5, 2, 0], [Yes, Yes, Yes, Yes], [0, 1, 2, 3])."},"skills":["Feasible Original Indices before Objective Comparison"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r04-optimization-problem-0012","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"a16678886aba5c8d4f8c4843715206569d3324abf66fa493b2f0598abdd6d0e1","family_id":"qf-app20-optimization-feasible-filter","seed":202610204012,"semantic_template":"qf-app20-optimization-feasible-filter/{\"feasible\":[true,false,true,true],\"values\":[1,8,1,1]}"},"fields":{"title":"Feasible Original Indices before Objective Comparison","stem":"Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. values=[1, 8, 1, 1], feasible=[true, false, true, true]. Give (all values, feasible mask, every feasible original index).","answer":{"kind":"expression","value":"([1, 8, 1, 1], [Yes, No, Yes, Yes], [0, 2, 3])","explanation":"Filter by declared eligibility without selecting an infeasible point that has a better objective value. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([1, 8, 1, 1], [Yes, No, Yes, Yes], [0, 2, 3])."},"skills":["Feasible Original Indices before Objective Comparison"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r04-optimization-problem-0013","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"7ee07286f6aa2f97c1c99497222cf701353b493d2ecb6179639d5de0ebe2aa38","family_id":"qf-app20-optimization-feasible-filter","seed":202610204013,"semantic_template":"qf-app20-optimization-feasible-filter/{\"feasible\":[true,true,false,true],\"values\":[2,-6,0,2]}"},"fields":{"title":"Feasible Original Indices before Objective Comparison","stem":"Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. values=[2, -6, 0, 2], feasible=[true, true, false, true]. Give (all values, feasible mask, every feasible original index).","answer":{"kind":"expression","value":"([2, -6, 0, 2], [Yes, Yes, No, Yes], [0, 1, 3])","explanation":"Filter by declared eligibility without selecting an infeasible point that has a better objective value. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([2, -6, 0, 2], [Yes, Yes, No, Yes], [0, 1, 3])."},"skills":["Feasible Original Indices before Objective Comparison"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r04-optimization-problem-0014","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"183626068cc07da417b8dc5326a504a45e3e516556b0ad481c4ba6540db1cc9c","family_id":"qf-app20-optimization-feasible-filter","seed":202610204014,"semantic_template":"qf-app20-optimization-feasible-filter/{\"feasible\":[true,false,true,true],\"values\":[3,-3,-1,3]}"},"fields":{"title":"Feasible Original Indices before Objective Comparison","stem":"Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. values=[3, -3, -1, 3], feasible=[true, false, true, true]. Give (all values, feasible mask, every feasible original index).","answer":{"kind":"expression","value":"([3, -3, -1, 3], [Yes, No, Yes, Yes], [0, 2, 3])","explanation":"Filter by declared eligibility without selecting an infeasible point that has a better objective value. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([3, -3, -1, 3], [Yes, No, Yes, Yes], [0, 2, 3])."},"skills":["Feasible Original Indices before Objective Comparison"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r04-optimization-problem-0015","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"7109b9dd0f1be561da8bdf605f149376f8cc9957542d920f4cc8a670a97a8743","family_id":"qf-app20-optimization-feasible-filter","seed":202610204015,"semantic_template":"qf-app20-optimization-feasible-filter/{\"feasible\":[true,true,true,true],\"values\":[4,0,-2,4]}"},"fields":{"title":"Feasible Original Indices before Objective Comparison","stem":"Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. values=[4, 0, -2, 4], feasible=[true, true, true, true]. Give (all values, feasible mask, every feasible original index).","answer":{"kind":"expression","value":"([4, 0, -2, 4], [Yes, Yes, Yes, Yes], [0, 1, 2, 3])","explanation":"Filter by declared eligibility without selecting an infeasible point that has a better objective value. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([4, 0, -2, 4], [Yes, Yes, Yes, Yes], [0, 1, 2, 3])."},"skills":["Feasible Original Indices before Objective Comparison"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r04-optimization-problem-0016","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"13d2443a6918699dba90ecc792d1587141d2278dab5b61e465ee94061bec83d9","family_id":"qf-app20-optimization-feasible-filter","seed":202610204016,"semantic_template":"qf-app20-optimization-feasible-filter/{\"feasible\":[true,false,false,true],\"values\":[5,3,-3,0]}"},"fields":{"title":"Feasible Original Indices before Objective Comparison","stem":"Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. values=[5, 3, -3, 0], feasible=[true, false, false, true]. Give (all values, feasible mask, every feasible original index).","answer":{"kind":"expression","value":"([5, 3, -3, 0], [Yes, No, No, Yes], [0, 3])","explanation":"Filter by declared eligibility without selecting an infeasible point that has a better objective value. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([5, 3, -3, 0], [Yes, No, No, Yes], [0, 3])."},"skills":["Feasible Original Indices before Objective Comparison"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r04-optimization-problem-0017","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"2671cb2bb07a11e6dcebfe3ce535c602cf9ac366622f92be8ffc80b6e48a1ddb","family_id":"qf-app20-optimization-feasible-filter","seed":202610204017,"semantic_template":"qf-app20-optimization-feasible-filter/{\"feasible\":[true,true,true,true],\"values\":[6,6,-4,1]}"},"fields":{"title":"Feasible Original Indices before Objective Comparison","stem":"Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. values=[6, 6, -4, 1], feasible=[true, true, true, true]. Give (all values, feasible mask, every feasible original index).","answer":{"kind":"expression","value":"([6, 6, -4, 1], [Yes, Yes, Yes, Yes], [0, 1, 2, 3])","explanation":"Filter by declared eligibility without selecting an infeasible point that has a better objective value. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([6, 6, -4, 1], [Yes, Yes, Yes, Yes], [0, 1, 2, 3])."},"skills":["Feasible Original Indices before Objective Comparison"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r04-optimization-problem-0018","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"cf585dae8a540def36f99533459c66c69176e171da69b1c62e4da13d957dcacf","family_id":"qf-app20-optimization-feasible-filter","seed":202610204018,"semantic_template":"qf-app20-optimization-feasible-filter/{\"feasible\":[true,false,true,true],\"values\":[7,-8,-5,2]}"},"fields":{"title":"Feasible Original Indices before Objective Comparison","stem":"Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. values=[7, -8, -5, 2], feasible=[true, false, true, true]. Give (all values, feasible mask, every feasible original index).","answer":{"kind":"expression","value":"([7, -8, -5, 2], [Yes, No, Yes, Yes], [0, 2, 3])","explanation":"Filter by declared eligibility without selecting an infeasible point that has a better objective value. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([7, -8, -5, 2], [Yes, No, Yes, Yes], [0, 2, 3])."},"skills":["Feasible Original Indices before Objective Comparison"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r04-optimization-problem-0019","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"6e037480336fe9a9953770eafa4ff39abb99d4657ba29164813fed0b56f593dd","family_id":"qf-app20-optimization-feasible-filter","seed":202610204019,"semantic_template":"qf-app20-optimization-feasible-filter/{\"feasible\":[true,true,false,true],\"values\":[8,-5,-6,3]}"},"fields":{"title":"Feasible Original Indices before Objective Comparison","stem":"Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. values=[8, -5, -6, 3], feasible=[true, true, false, true]. Give (all values, feasible mask, every feasible original index).","answer":{"kind":"expression","value":"([8, -5, -6, 3], [Yes, Yes, No, Yes], [0, 1, 3])","explanation":"Filter by declared eligibility without selecting an infeasible point that has a better objective value. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([8, -5, -6, 3], [Yes, Yes, No, Yes], [0, 1, 3])."},"skills":["Feasible Original Indices before Objective Comparison"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r04-optimization-problem-0020","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"1ec39985129de2b17631b9cb960b6b9b27b32d3454499250a74a7532c8ef9d80","family_id":"qf-app20-optimization-feasible-filter","seed":202610204020,"semantic_template":"qf-app20-optimization-feasible-filter/{\"feasible\":[true,false,true,true],\"values\":[9,-2,-7,4]}"},"fields":{"title":"Feasible Original Indices before Objective Comparison","stem":"Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. values=[9, -2, -7, 4], feasible=[true, false, true, true]. Give (all values, feasible mask, every feasible original index).","answer":{"kind":"expression","value":"([9, -2, -7, 4], [Yes, No, Yes, Yes], [0, 2, 3])","explanation":"Filter by declared eligibility without selecting an infeasible point that has a better objective value. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([9, -2, -7, 4], [Yes, No, Yes, Yes], [0, 2, 3])."},"skills":["Feasible Original Indices before Objective Comparison"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r04-optimization-problem-0021","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"98e6643f93150fea5944ec30c57a3019fa552c7b275b361555b0aa3a132db9bb","family_id":"qf-app20-optimization-feasible-filter","seed":202610204021,"semantic_template":"qf-app20-optimization-feasible-filter/{\"feasible\":[true,true,true,true],\"values\":[10,1,-8,0]}"},"fields":{"title":"Feasible Original Indices before Objective Comparison","stem":"Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. values=[10, 1, -8, 0], feasible=[true, true, true, true]. Give (all values, feasible mask, every feasible original index).","answer":{"kind":"expression","value":"([10, 1, -8, 0], [Yes, Yes, Yes, Yes], [0, 1, 2, 3])","explanation":"Filter by declared eligibility without selecting an infeasible point that has a better objective value. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([10, 1, -8, 0], [Yes, Yes, Yes, Yes], [0, 1, 2, 3])."},"skills":["Feasible Original Indices before Objective Comparison"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r04-optimization-problem-0022","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"7beb9dfcb37782cb4c151f8760983e1ad975c770603a73bfbfef965206f47380","family_id":"qf-app20-optimization-feasible-filter","seed":202610204022,"semantic_template":"qf-app20-optimization-feasible-filter/{\"feasible\":[true,false,false,true],\"values\":[11,4,-9,1]}"},"fields":{"title":"Feasible Original Indices before Objective Comparison","stem":"Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. values=[11, 4, -9, 1], feasible=[true, false, false, true]. Give (all values, feasible mask, every feasible original index).","answer":{"kind":"expression","value":"([11, 4, -9, 1], [Yes, No, No, Yes], [0, 3])","explanation":"Filter by declared eligibility without selecting an infeasible point that has a better objective value. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([11, 4, -9, 1], [Yes, No, No, Yes], [0, 3])."},"skills":["Feasible Original Indices before Objective Comparison"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r04-optimization-problem-0023","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"ecba82ff0ff84b40cea4a1ef709b3e1fcfe97f7ca807afad09bca46e0e80b871","family_id":"qf-app20-optimization-feasible-filter","seed":202610204023,"semantic_template":"qf-app20-optimization-feasible-filter/{\"feasible\":[true,true,true,true],\"values\":[12,7,-10,2]}"},"fields":{"title":"Feasible Original Indices before Objective Comparison","stem":"Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. values=[12, 7, -10, 2], feasible=[true, true, true, true]. Give (all values, feasible mask, every feasible original index).","answer":{"kind":"expression","value":"([12, 7, -10, 2], [Yes, Yes, Yes, Yes], [0, 1, 2, 3])","explanation":"Filter by declared eligibility without selecting an infeasible point that has a better objective value. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([12, 7, -10, 2], [Yes, Yes, Yes, Yes], [0, 1, 2, 3])."},"skills":["Feasible Original Indices before Objective Comparison"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r04-optimization-problem-0024","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"c9c844e7cf5e2221e787a60d0c24a724b08454d4b3196d423f661928488bc0eb","family_id":"qf-app20-optimization-feasible-filter","seed":202610204024,"semantic_template":"qf-app20-optimization-feasible-filter/{\"feasible\":[true,false,true,true],\"values\":[13,-7,-11,3]}"},"fields":{"title":"Feasible Original Indices before Objective Comparison","stem":"Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. values=[13, -7, -11, 3], feasible=[true, false, true, true]. Give (all values, feasible mask, every feasible original index).","answer":{"kind":"expression","value":"([13, -7, -11, 3], [Yes, No, Yes, Yes], [0, 2, 3])","explanation":"Filter by declared eligibility without selecting an infeasible point that has a better objective value. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([13, -7, -11, 3], [Yes, No, Yes, Yes], [0, 2, 3])."},"skills":["Feasible Original Indices before Objective Comparison"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r04-optimization-problem-0025","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"c2821ea01291bb8a220bfe1d10883850cbf1925e23f8149bed79a051a2512680","family_id":"qf-app20-optimization-feasible-filter","seed":202610204025,"semantic_template":"qf-app20-optimization-feasible-filter/{\"feasible\":[true,true,false,true],\"values\":[14,-4,-12,4]}"},"fields":{"title":"Feasible Original Indices before Objective Comparison","stem":"Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. values=[14, -4, -12, 4], feasible=[true, true, false, true]. Give (all values, feasible mask, every feasible original index).","answer":{"kind":"expression","value":"([14, -4, -12, 4], [Yes, Yes, No, Yes], [0, 1, 3])","explanation":"Filter by declared eligibility without selecting an infeasible point that has a better objective value. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([14, -4, -12, 4], [Yes, Yes, No, Yes], [0, 1, 3])."},"skills":["Feasible Original Indices before Objective Comparison"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r04-optimization-problem-0026","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"7737d24377c3fb051e5475557ef0b741fa57d1dff92990c1c55b83229c4933dd","family_id":"qf-app20-optimization-argmin","seed":202610204026,"semantic_template":"qf-app20-optimization-argmin/{\"feasible\":[true,true,false,true],\"values\":[-10,-8,12,0]}"},"fields":{"title":"Finite Minimum Value and Every Original Minimizer Index","stem":"Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. values=[-10, -8, 12, 0], feasible=[true, true, false, true]. Give (values, mask, min, minimum feasible value, all minimizing original indices).","answer":{"kind":"expression","value":"([-10, -8, 12, 0], [Yes, Yes, No, Yes], min, -10, [0])","explanation":"Separate the optimal numerical value from the complete tied argmin set. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([-10, -8, 12, 0], [Yes, Yes, No, Yes], min, -10, [0])."},"skills":["Finite Minimum Value and Every Original Minimizer Index"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r04-optimization-problem-0027","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"8cba82f9c063a7286cb1ea87e88d71babd0a962b3c7542face4b32578b3b0ff2","family_id":"qf-app20-optimization-argmin","seed":202610204027,"semantic_template":"qf-app20-optimization-argmin/{\"feasible\":[true,false,true,true],\"values\":[-9,-5,11,1]}"},"fields":{"title":"Finite Minimum Value and Every Original Minimizer Index","stem":"Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. values=[-9, -5, 11, 1], feasible=[true, false, true, true]. Give (values, mask, min, minimum feasible value, all minimizing original indices).","answer":{"kind":"expression","value":"([-9, -5, 11, 1], [Yes, No, Yes, Yes], min, -9, [0])","explanation":"Separate the optimal numerical value from the complete tied argmin set. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([-9, -5, 11, 1], [Yes, No, Yes, Yes], min, -9, [0])."},"skills":["Finite Minimum Value and Every Original Minimizer Index"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r04-optimization-problem-0028","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"02a661d31a6e85022b97e0562535638d08d1591dd79f71361c159a23edd56180","family_id":"qf-app20-optimization-argmin","seed":202610204028,"semantic_template":"qf-app20-optimization-argmin/{\"feasible\":[true,true,true,true],\"values\":[-8,-2,10,2]}"},"fields":{"title":"Finite Minimum Value and Every Original Minimizer Index","stem":"Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. values=[-8, -2, 10, 2], feasible=[true, true, true, true]. Give (values, mask, min, minimum feasible value, all minimizing original indices).","answer":{"kind":"expression","value":"([-8, -2, 10, 2], [Yes, Yes, Yes, Yes], min, -8, [0])","explanation":"Separate the optimal numerical value from the complete tied argmin set. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([-8, -2, 10, 2], [Yes, Yes, Yes, Yes], min, -8, [0])."},"skills":["Finite Minimum Value and Every Original Minimizer Index"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r04-optimization-problem-0029","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"bc895dffbc10e36207ec9435808ee60f24661c14c8a1d1a958935384b0f0d273","family_id":"qf-app20-optimization-argmin","seed":202610204029,"semantic_template":"qf-app20-optimization-argmin/{\"feasible\":[true,false,false,true],\"values\":[-7,1,9,3]}"},"fields":{"title":"Finite Minimum Value and Every Original Minimizer Index","stem":"Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. values=[-7, 1, 9, 3], feasible=[true, false, false, true]. Give (values, mask, min, minimum feasible value, all minimizing original indices).","answer":{"kind":"expression","value":"([-7, 1, 9, 3], [Yes, No, No, Yes], min, -7, [0])","explanation":"Separate the optimal numerical value from the complete tied argmin set. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([-7, 1, 9, 3], [Yes, No, No, Yes], min, -7, [0])."},"skills":["Finite Minimum Value and Every Original Minimizer Index"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r04-optimization-problem-0030","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"db78f6ee9edaac99d0029a2bd20ff9130a1062f14c703504d4da9925c43f6250","family_id":"qf-app20-optimization-argmin","seed":202610204030,"semantic_template":"qf-app20-optimization-argmin/{\"feasible\":[true,true,true,true],\"values\":[-6,4,8,4]}"},"fields":{"title":"Finite Minimum Value and Every Original Minimizer Index","stem":"Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. values=[-6, 4, 8, 4], feasible=[true, true, true, true]. Give (values, mask, min, minimum feasible value, all minimizing original indices).","answer":{"kind":"expression","value":"([-6, 4, 8, 4], [Yes, Yes, Yes, Yes], min, -6, [0])","explanation":"Separate the optimal numerical value from the complete tied argmin set. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([-6, 4, 8, 4], [Yes, Yes, Yes, Yes], min, -6, [0])."},"skills":["Finite Minimum Value and Every Original Minimizer Index"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r04-optimization-problem-0031","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"eba2b93bce047fe5782b8b221df5bcb49cb55769bb937e318492c65900802118","family_id":"qf-app20-optimization-argmin","seed":202610204031,"semantic_template":"qf-app20-optimization-argmin/{\"feasible\":[true,false,true,true],\"values\":[-5,7,7,0]}"},"fields":{"title":"Finite Minimum Value and Every Original Minimizer Index","stem":"Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. values=[-5, 7, 7, 0], feasible=[true, false, true, true]. Give (values, mask, min, minimum feasible value, all minimizing original indices).","answer":{"kind":"expression","value":"([-5, 7, 7, 0], [Yes, No, Yes, Yes], min, -5, [0])","explanation":"Separate the optimal numerical value from the complete tied argmin set. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([-5, 7, 7, 0], [Yes, No, Yes, Yes], min, -5, [0])."},"skills":["Finite Minimum Value and Every Original Minimizer Index"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r04-optimization-problem-0032","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"6e1498d9b87adedd0887aa1d70d150b3fb5486cfda4569854ee14883e57e3643","family_id":"qf-app20-optimization-argmin","seed":202610204032,"semantic_template":"qf-app20-optimization-argmin/{\"feasible\":[true,true,false,true],\"values\":[-4,-7,6,1]}"},"fields":{"title":"Finite Minimum Value and Every Original Minimizer Index","stem":"Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. values=[-4, -7, 6, 1], feasible=[true, true, false, true]. Give (values, mask, min, minimum feasible value, all minimizing original indices).","answer":{"kind":"expression","value":"([-4, -7, 6, 1], [Yes, Yes, No, Yes], min, -7, [1])","explanation":"Separate the optimal numerical value from the complete tied argmin set. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([-4, -7, 6, 1], [Yes, Yes, No, Yes], min, -7, [1])."},"skills":["Finite Minimum Value and Every Original Minimizer Index"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r04-optimization-problem-0033","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"2be37492b6ab98388da494901592142c3709366f5b2d61ab9a37f95243e7f2c8","family_id":"qf-app20-optimization-argmin","seed":202610204033,"semantic_template":"qf-app20-optimization-argmin/{\"feasible\":[true,false,true,true],\"values\":[-3,-4,5,2]}"},"fields":{"title":"Finite Minimum Value and Every Original Minimizer Index","stem":"Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. values=[-3, -4, 5, 2], feasible=[true, false, true, true]. Give (values, mask, min, minimum feasible value, all minimizing original indices).","answer":{"kind":"expression","value":"([-3, -4, 5, 2], [Yes, No, Yes, Yes], min, -3, [0])","explanation":"Separate the optimal numerical value from the complete tied argmin set. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([-3, -4, 5, 2], [Yes, No, Yes, Yes], min, -3, [0])."},"skills":["Finite Minimum Value and Every Original Minimizer Index"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r04-optimization-problem-0034","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"a4c19c355a6a6cd39dc21439814a7f2b7187b67ad2b2b45ac84f8d124a0ad067","family_id":"qf-app20-optimization-argmin","seed":202610204034,"semantic_template":"qf-app20-optimization-argmin/{\"feasible\":[true,true,true,true],\"values\":[-2,-1,4,3]}"},"fields":{"title":"Finite Minimum Value and Every Original Minimizer Index","stem":"Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. values=[-2, -1, 4, 3], feasible=[true, true, true, true]. Give (values, mask, min, minimum feasible value, all minimizing original indices).","answer":{"kind":"expression","value":"([-2, -1, 4, 3], [Yes, Yes, Yes, Yes], min, -2, [0])","explanation":"Separate the optimal numerical value from the complete tied argmin set. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([-2, -1, 4, 3], [Yes, Yes, Yes, Yes], min, -2, [0])."},"skills":["Finite Minimum Value and Every Original Minimizer Index"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r04-optimization-problem-0035","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"b83bb25f25509bd6a0f86300dc839b37b66c0f3ee32fbc17eea0e4674ebbf685","family_id":"qf-app20-optimization-argmin","seed":202610204035,"semantic_template":"qf-app20-optimization-argmin/{\"feasible\":[true,false,false,true],\"values\":[-1,2,3,4]}"},"fields":{"title":"Finite Minimum Value and Every Original Minimizer Index","stem":"Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. values=[-1, 2, 3, 4], feasible=[true, false, false, true]. Give (values, mask, min, minimum feasible value, all minimizing original indices).","answer":{"kind":"expression","value":"([-1, 2, 3, 4], [Yes, No, No, Yes], min, -1, [0])","explanation":"Separate the optimal numerical value from the complete tied argmin set. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([-1, 2, 3, 4], [Yes, No, No, Yes], min, -1, [0])."},"skills":["Finite Minimum Value and Every Original Minimizer Index"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r04-optimization-problem-0036","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"da66ceee307740bbc4093dd9fe2b72b25e44b0dbfdced1adff333ea916f5d57b","family_id":"qf-app20-optimization-argmin","seed":202610204036,"semantic_template":"qf-app20-optimization-argmin/{\"feasible\":[true,true,true,true],\"values\":[0,5,2,0]}"},"fields":{"title":"Finite Minimum Value and Every Original Minimizer Index","stem":"Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. values=[0, 5, 2, 0], feasible=[true, true, true, true]. Give (values, mask, min, minimum feasible value, all minimizing original indices).","answer":{"kind":"expression","value":"([0, 5, 2, 0], [Yes, Yes, Yes, Yes], min, 0, [0, 3])","explanation":"Separate the optimal numerical value from the complete tied argmin set. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([0, 5, 2, 0], [Yes, Yes, Yes, Yes], min, 0, [0, 3])."},"skills":["Finite Minimum Value and Every Original Minimizer Index"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r04-optimization-problem-0037","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"2421e8f33b6a6a3ab2b12d526611f74b241eb9a7745c9cfb76ae51750c88bffc","family_id":"qf-app20-optimization-argmin","seed":202610204037,"semantic_template":"qf-app20-optimization-argmin/{\"feasible\":[true,false,true,true],\"values\":[1,8,1,1]}"},"fields":{"title":"Finite Minimum Value and Every Original Minimizer Index","stem":"Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. values=[1, 8, 1, 1], feasible=[true, false, true, true]. Give (values, mask, min, minimum feasible value, all minimizing original indices).","answer":{"kind":"expression","value":"([1, 8, 1, 1], [Yes, No, Yes, Yes], min, 1, [0, 2, 3])","explanation":"Separate the optimal numerical value from the complete tied argmin set. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([1, 8, 1, 1], [Yes, No, Yes, Yes], min, 1, [0, 2, 3])."},"skills":["Finite Minimum Value and Every Original Minimizer Index"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r04-optimization-problem-0038","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"bbe0ad1218f7e92bffc7f969d22c0dc9608477b6e5b307076d6c9f17cf403a06","family_id":"qf-app20-optimization-argmin","seed":202610204038,"semantic_template":"qf-app20-optimization-argmin/{\"feasible\":[true,true,false,true],\"values\":[2,-6,0,2]}"},"fields":{"title":"Finite Minimum Value and Every Original Minimizer Index","stem":"Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. values=[2, -6, 0, 2], feasible=[true, true, false, true]. Give (values, mask, min, minimum feasible value, all minimizing original indices).","answer":{"kind":"expression","value":"([2, -6, 0, 2], [Yes, Yes, No, Yes], min, -6, [1])","explanation":"Separate the optimal numerical value from the complete tied argmin set. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([2, -6, 0, 2], [Yes, Yes, No, Yes], min, -6, [1])."},"skills":["Finite Minimum Value and Every Original Minimizer Index"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r04-optimization-problem-0039","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"0065b45020a5ce35eef25c90be09911e137d65dcffe4273de22980392a1267fd","family_id":"qf-app20-optimization-argmin","seed":202610204039,"semantic_template":"qf-app20-optimization-argmin/{\"feasible\":[true,false,true,true],\"values\":[3,-3,-1,3]}"},"fields":{"title":"Finite Minimum Value and Every Original Minimizer Index","stem":"Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. values=[3, -3, -1, 3], feasible=[true, false, true, true]. Give (values, mask, min, minimum feasible value, all minimizing original indices).","answer":{"kind":"expression","value":"([3, -3, -1, 3], [Yes, No, Yes, Yes], min, -1, [2])","explanation":"Separate the optimal numerical value from the complete tied argmin set. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([3, -3, -1, 3], [Yes, No, Yes, Yes], min, -1, [2])."},"skills":["Finite Minimum Value and Every Original Minimizer Index"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r04-optimization-problem-0040","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"1067a8e5ea195db66d96701d87c600d249a31e423fae4c8e4561c03326df810b","family_id":"qf-app20-optimization-argmin","seed":202610204040,"semantic_template":"qf-app20-optimization-argmin/{\"feasible\":[true,true,true,true],\"values\":[4,0,-2,4]}"},"fields":{"title":"Finite Minimum Value and Every Original Minimizer Index","stem":"Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. values=[4, 0, -2, 4], feasible=[true, true, true, true]. Give (values, mask, min, minimum feasible value, all minimizing original indices).","answer":{"kind":"expression","value":"([4, 0, -2, 4], [Yes, Yes, Yes, Yes], min, -2, [2])","explanation":"Separate the optimal numerical value from the complete tied argmin set. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([4, 0, -2, 4], [Yes, Yes, Yes, Yes], min, -2, [2])."},"skills":["Finite Minimum Value and Every Original Minimizer Index"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r04-optimization-problem-0041","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"9ee78fd5fb9ae6eaf58e959d79fd91cc22c0efcc75381f14373ad1b28116ac6a","family_id":"qf-app20-optimization-argmin","seed":202610204041,"semantic_template":"qf-app20-optimization-argmin/{\"feasible\":[true,false,false,true],\"values\":[5,3,-3,0]}"},"fields":{"title":"Finite Minimum Value and Every Original Minimizer Index","stem":"Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. values=[5, 3, -3, 0], feasible=[true, false, false, true]. Give (values, mask, min, minimum feasible value, all minimizing original indices).","answer":{"kind":"expression","value":"([5, 3, -3, 0], [Yes, No, No, Yes], min, 0, [3])","explanation":"Separate the optimal numerical value from the complete tied argmin set. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([5, 3, -3, 0], [Yes, No, No, Yes], min, 0, [3])."},"skills":["Finite Minimum Value and Every Original Minimizer Index"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r04-optimization-problem-0042","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"1af0df720f3fe7a54c56add883d11a38ff03fbff44a17d5fff20881414567066","family_id":"qf-app20-optimization-argmin","seed":202610204042,"semantic_template":"qf-app20-optimization-argmin/{\"feasible\":[true,true,true,true],\"values\":[6,6,-4,1]}"},"fields":{"title":"Finite Minimum Value and Every Original Minimizer Index","stem":"Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. values=[6, 6, -4, 1], feasible=[true, true, true, true]. Give (values, mask, min, minimum feasible value, all minimizing original indices).","answer":{"kind":"expression","value":"([6, 6, -4, 1], [Yes, Yes, Yes, Yes], min, -4, [2])","explanation":"Separate the optimal numerical value from the complete tied argmin set. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([6, 6, -4, 1], [Yes, Yes, Yes, Yes], min, -4, [2])."},"skills":["Finite Minimum Value and Every Original Minimizer Index"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r04-optimization-problem-0043","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"8153123dd47ed3609385c00267ad3d38d28295a31b5cdb335b5f3d67c53047a3","family_id":"qf-app20-optimization-argmin","seed":202610204043,"semantic_template":"qf-app20-optimization-argmin/{\"feasible\":[true,false,true,true],\"values\":[7,-8,-5,2]}"},"fields":{"title":"Finite Minimum Value and Every Original Minimizer Index","stem":"Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. values=[7, -8, -5, 2], feasible=[true, false, true, true]. Give (values, mask, min, minimum feasible value, all minimizing original indices).","answer":{"kind":"expression","value":"([7, -8, -5, 2], [Yes, No, Yes, Yes], min, -5, [2])","explanation":"Separate the optimal numerical value from the complete tied argmin set. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([7, -8, -5, 2], [Yes, No, Yes, Yes], min, -5, [2])."},"skills":["Finite Minimum Value and Every Original Minimizer Index"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r04-optimization-problem-0044","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"ee91ccb45e58fa92b9acf2152402bc9b0a1d944b8ac23321a4ca693795c76ac7","family_id":"qf-app20-optimization-argmin","seed":202610204044,"semantic_template":"qf-app20-optimization-argmin/{\"feasible\":[true,true,false,true],\"values\":[8,-5,-6,3]}"},"fields":{"title":"Finite Minimum Value and Every Original Minimizer Index","stem":"Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. values=[8, -5, -6, 3], feasible=[true, true, false, true]. Give (values, mask, min, minimum feasible value, all minimizing original indices).","answer":{"kind":"expression","value":"([8, -5, -6, 3], [Yes, Yes, No, Yes], min, -5, [1])","explanation":"Separate the optimal numerical value from the complete tied argmin set. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([8, -5, -6, 3], [Yes, Yes, No, Yes], min, -5, [1])."},"skills":["Finite Minimum Value and Every Original Minimizer Index"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r04-optimization-problem-0045","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"c5ef6d054d5ec47926349ae47227a91608b3e6f14eaf668f06cdc2671a4b47e7","family_id":"qf-app20-optimization-argmin","seed":202610204045,"semantic_template":"qf-app20-optimization-argmin/{\"feasible\":[true,false,true,true],\"values\":[9,-2,-7,4]}"},"fields":{"title":"Finite Minimum Value and Every Original Minimizer Index","stem":"Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. values=[9, -2, -7, 4], feasible=[true, false, true, true]. Give (values, mask, min, minimum feasible value, all minimizing original indices).","answer":{"kind":"expression","value":"([9, -2, -7, 4], [Yes, No, Yes, Yes], min, -7, [2])","explanation":"Separate the optimal numerical value from the complete tied argmin set. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([9, -2, -7, 4], [Yes, No, Yes, Yes], min, -7, [2])."},"skills":["Finite Minimum Value and Every Original Minimizer Index"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r04-optimization-problem-0046","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"4766c24e4937bc015cf026c815973b2047fa64e41ee1f3f32ccba100091f65d3","family_id":"qf-app20-optimization-argmin","seed":202610204046,"semantic_template":"qf-app20-optimization-argmin/{\"feasible\":[true,true,true,true],\"values\":[10,1,-8,0]}"},"fields":{"title":"Finite Minimum Value and Every Original Minimizer Index","stem":"Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. values=[10, 1, -8, 0], feasible=[true, true, true, true]. Give (values, mask, min, minimum feasible value, all minimizing original indices).","answer":{"kind":"expression","value":"([10, 1, -8, 0], [Yes, Yes, Yes, Yes], min, -8, [2])","explanation":"Separate the optimal numerical value from the complete tied argmin set. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([10, 1, -8, 0], [Yes, Yes, Yes, Yes], min, -8, [2])."},"skills":["Finite Minimum Value and Every Original Minimizer Index"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r04-optimization-problem-0047","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"a16b9043fbd20be73ed6eea3fd5dd46641684b40468f77d1a6d91909883db9ce","family_id":"qf-app20-optimization-argmin","seed":202610204047,"semantic_template":"qf-app20-optimization-argmin/{\"feasible\":[true,false,false,true],\"values\":[11,4,-9,1]}"},"fields":{"title":"Finite Minimum Value and Every Original Minimizer Index","stem":"Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. values=[11, 4, -9, 1], feasible=[true, false, false, true]. Give (values, mask, min, minimum feasible value, all minimizing original indices).","answer":{"kind":"expression","value":"([11, 4, -9, 1], [Yes, No, No, Yes], min, 1, [3])","explanation":"Separate the optimal numerical value from the complete tied argmin set. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([11, 4, -9, 1], [Yes, No, No, Yes], min, 1, [3])."},"skills":["Finite Minimum Value and Every Original Minimizer Index"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r04-optimization-problem-0048","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"4166d30d96b2ac89baffe46c1fde3e5910c52c09c30d9fe48f3fff49d0ef9cf4","family_id":"qf-app20-optimization-argmin","seed":202610204048,"semantic_template":"qf-app20-optimization-argmin/{\"feasible\":[true,true,true,true],\"values\":[12,7,-10,2]}"},"fields":{"title":"Finite Minimum Value and Every Original Minimizer Index","stem":"Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. values=[12, 7, -10, 2], feasible=[true, true, true, true]. Give (values, mask, min, minimum feasible value, all minimizing original indices).","answer":{"kind":"expression","value":"([12, 7, -10, 2], [Yes, Yes, Yes, Yes], min, -10, [2])","explanation":"Separate the optimal numerical value from the complete tied argmin set. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([12, 7, -10, 2], [Yes, Yes, Yes, Yes], min, -10, [2])."},"skills":["Finite Minimum Value and Every Original Minimizer Index"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r04-optimization-problem-0049","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"6a8c2ffa7e674baac9914b284b236441155f705273bdd2a67b85eec3e1107ca9","family_id":"qf-app20-optimization-argmin","seed":202610204049,"semantic_template":"qf-app20-optimization-argmin/{\"feasible\":[true,false,true,true],\"values\":[13,-7,-11,3]}"},"fields":{"title":"Finite Minimum Value and Every Original Minimizer Index","stem":"Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. values=[13, -7, -11, 3], feasible=[true, false, true, true]. Give (values, mask, min, minimum feasible value, all minimizing original indices).","answer":{"kind":"expression","value":"([13, -7, -11, 3], [Yes, No, Yes, Yes], min, -11, [2])","explanation":"Separate the optimal numerical value from the complete tied argmin set. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([13, -7, -11, 3], [Yes, No, Yes, Yes], min, -11, [2])."},"skills":["Finite Minimum Value and Every Original Minimizer Index"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r04-optimization-problem-0050","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"35598ee6e3835acab466168a0df165936258d1c4bc165191ac2318f376d12361","family_id":"qf-app20-optimization-argmin","seed":202610204050,"semantic_template":"qf-app20-optimization-argmin/{\"feasible\":[true,true,false,true],\"values\":[14,-4,-12,4]}"},"fields":{"title":"Finite Minimum Value and Every Original Minimizer Index","stem":"Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. values=[14, -4, -12, 4], feasible=[true, true, false, true]. Give (values, mask, min, minimum feasible value, all minimizing original indices).","answer":{"kind":"expression","value":"([14, -4, -12, 4], [Yes, Yes, No, Yes], min, -4, [1])","explanation":"Separate the optimal numerical value from the complete tied argmin set. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([14, -4, -12, 4], [Yes, Yes, No, Yes], min, -4, [1])."},"skills":["Finite Minimum Value and Every Original Minimizer Index"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r04-optimization-problem-0051","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"92d93c36e72599fd0c2db5a16fc9141db86384e3a4366e2a096a32ba67332287","family_id":"qf-app20-optimization-argmax","seed":202610204051,"semantic_template":"qf-app20-optimization-argmax/{\"feasible\":[true,true,false,true],\"values\":[-10,-8,12,0]}"},"fields":{"title":"Finite Maximum Value and Every Original Maximizer Index","stem":"Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. values=[-10, -8, 12, 0], feasible=[true, true, false, true]. Give (values, mask, max, maximum feasible value, all maximizing original indices).","answer":{"kind":"expression","value":"([-10, -8, 12, 0], [Yes, Yes, No, Yes], max, 0, [3])","explanation":"Compare only feasible candidates and retain all tied indices, not a claim of uniqueness. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([-10, -8, 12, 0], [Yes, Yes, No, Yes], max, 0, [3])."},"skills":["Finite Maximum Value and Every Original Maximizer Index"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r04-optimization-problem-0052","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"0812a989c248ba540f4096806388ddc33acbe499f8e632c9d23b69847e4e4fad","family_id":"qf-app20-optimization-argmax","seed":202610204052,"semantic_template":"qf-app20-optimization-argmax/{\"feasible\":[true,false,true,true],\"values\":[-9,-5,11,1]}"},"fields":{"title":"Finite Maximum Value and Every Original Maximizer Index","stem":"Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. values=[-9, -5, 11, 1], feasible=[true, false, true, true]. Give (values, mask, max, maximum feasible value, all maximizing original indices).","answer":{"kind":"expression","value":"([-9, -5, 11, 1], [Yes, No, Yes, Yes], max, 11, [2])","explanation":"Compare only feasible candidates and retain all tied indices, not a claim of uniqueness. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([-9, -5, 11, 1], [Yes, No, Yes, Yes], max, 11, [2])."},"skills":["Finite Maximum Value and Every Original Maximizer Index"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r04-optimization-problem-0053","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"3011fb211432d360e09dee6529c8d82356cddcb46a3f103d510d579c141064d2","family_id":"qf-app20-optimization-argmax","seed":202610204053,"semantic_template":"qf-app20-optimization-argmax/{\"feasible\":[true,true,true,true],\"values\":[-8,-2,10,2]}"},"fields":{"title":"Finite Maximum Value and Every Original Maximizer Index","stem":"Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. values=[-8, -2, 10, 2], feasible=[true, true, true, true]. Give (values, mask, max, maximum feasible value, all maximizing original indices).","answer":{"kind":"expression","value":"([-8, -2, 10, 2], [Yes, Yes, Yes, Yes], max, 10, [2])","explanation":"Compare only feasible candidates and retain all tied indices, not a claim of uniqueness. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([-8, -2, 10, 2], [Yes, Yes, Yes, Yes], max, 10, [2])."},"skills":["Finite Maximum Value and Every Original Maximizer Index"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r04-optimization-problem-0054","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"ada34a3e0e89b36d9004f926d8441a0c6a9635f7474b30f75329c3f31df3ad07","family_id":"qf-app20-optimization-argmax","seed":202610204054,"semantic_template":"qf-app20-optimization-argmax/{\"feasible\":[true,false,false,true],\"values\":[-7,1,9,3]}"},"fields":{"title":"Finite Maximum Value and Every Original Maximizer Index","stem":"Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. values=[-7, 1, 9, 3], feasible=[true, false, false, true]. Give (values, mask, max, maximum feasible value, all maximizing original indices).","answer":{"kind":"expression","value":"([-7, 1, 9, 3], [Yes, No, No, Yes], max, 3, [3])","explanation":"Compare only feasible candidates and retain all tied indices, not a claim of uniqueness. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([-7, 1, 9, 3], [Yes, No, No, Yes], max, 3, [3])."},"skills":["Finite Maximum Value and Every Original Maximizer Index"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r04-optimization-problem-0055","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"9a4c259028dafdd188876862111adc372dc39941047b82c1fc70e1ef244468e3","family_id":"qf-app20-optimization-argmax","seed":202610204055,"semantic_template":"qf-app20-optimization-argmax/{\"feasible\":[true,true,true,true],\"values\":[-6,4,8,4]}"},"fields":{"title":"Finite Maximum Value and Every Original Maximizer Index","stem":"Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. values=[-6, 4, 8, 4], feasible=[true, true, true, true]. Give (values, mask, max, maximum feasible value, all maximizing original indices).","answer":{"kind":"expression","value":"([-6, 4, 8, 4], [Yes, Yes, Yes, Yes], max, 8, [2])","explanation":"Compare only feasible candidates and retain all tied indices, not a claim of uniqueness. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([-6, 4, 8, 4], [Yes, Yes, Yes, Yes], max, 8, [2])."},"skills":["Finite Maximum Value and Every Original Maximizer Index"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r04-optimization-problem-0056","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"dcc266aec6b9090431e9c37cd037d2554151b7a073528c0093a8124e1c89cd2f","family_id":"qf-app20-optimization-argmax","seed":202610204056,"semantic_template":"qf-app20-optimization-argmax/{\"feasible\":[true,false,true,true],\"values\":[-5,7,7,0]}"},"fields":{"title":"Finite Maximum Value and Every Original Maximizer Index","stem":"Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. values=[-5, 7, 7, 0], feasible=[true, false, true, true]. Give (values, mask, max, maximum feasible value, all maximizing original indices).","answer":{"kind":"expression","value":"([-5, 7, 7, 0], [Yes, No, Yes, Yes], max, 7, [2])","explanation":"Compare only feasible candidates and retain all tied indices, not a claim of uniqueness. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([-5, 7, 7, 0], [Yes, No, Yes, Yes], max, 7, [2])."},"skills":["Finite Maximum Value and Every Original Maximizer Index"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r04-optimization-problem-0057","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"1052bcdf6b75e9b52581fc5d0c4211bdd92e6ff1a38ce441a5c87104d90f9be4","family_id":"qf-app20-optimization-argmax","seed":202610204057,"semantic_template":"qf-app20-optimization-argmax/{\"feasible\":[true,true,false,true],\"values\":[-4,-7,6,1]}"},"fields":{"title":"Finite Maximum Value and Every Original Maximizer Index","stem":"Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. values=[-4, -7, 6, 1], feasible=[true, true, false, true]. Give (values, mask, max, maximum feasible value, all maximizing original indices).","answer":{"kind":"expression","value":"([-4, -7, 6, 1], [Yes, Yes, No, Yes], max, 1, [3])","explanation":"Compare only feasible candidates and retain all tied indices, not a claim of uniqueness. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([-4, -7, 6, 1], [Yes, Yes, No, Yes], max, 1, [3])."},"skills":["Finite Maximum Value and Every Original Maximizer Index"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r04-optimization-problem-0058","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"9053863298f3146f4643b026b229b6f9f403e5286876cfff90db5253a6b7ef44","family_id":"qf-app20-optimization-argmax","seed":202610204058,"semantic_template":"qf-app20-optimization-argmax/{\"feasible\":[true,false,true,true],\"values\":[-3,-4,5,2]}"},"fields":{"title":"Finite Maximum Value and Every Original Maximizer Index","stem":"Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. values=[-3, -4, 5, 2], feasible=[true, false, true, true]. Give (values, mask, max, maximum feasible value, all maximizing original indices).","answer":{"kind":"expression","value":"([-3, -4, 5, 2], [Yes, No, Yes, Yes], max, 5, [2])","explanation":"Compare only feasible candidates and retain all tied indices, not a claim of uniqueness. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([-3, -4, 5, 2], [Yes, No, Yes, Yes], max, 5, [2])."},"skills":["Finite Maximum Value and Every Original Maximizer Index"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r04-optimization-problem-0059","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"9d6c7dcdb204e49917b7d186b7f56eb2b0d10b2cde91c4ac1195bcc43b9c1cd6","family_id":"qf-app20-optimization-argmax","seed":202610204059,"semantic_template":"qf-app20-optimization-argmax/{\"feasible\":[true,true,true,true],\"values\":[-2,-1,4,3]}"},"fields":{"title":"Finite Maximum Value and Every Original Maximizer Index","stem":"Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. values=[-2, -1, 4, 3], feasible=[true, true, true, true]. Give (values, mask, max, maximum feasible value, all maximizing original indices).","answer":{"kind":"expression","value":"([-2, -1, 4, 3], [Yes, Yes, Yes, Yes], max, 4, [2])","explanation":"Compare only feasible candidates and retain all tied indices, not a claim of uniqueness. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([-2, -1, 4, 3], [Yes, Yes, Yes, Yes], max, 4, [2])."},"skills":["Finite Maximum Value and Every Original Maximizer Index"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r04-optimization-problem-0060","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"52069719c1f3a58feeabf5909f758d9df46bc506b41be1364cc0a1588b95fcc9","family_id":"qf-app20-optimization-argmax","seed":202610204060,"semantic_template":"qf-app20-optimization-argmax/{\"feasible\":[true,false,false,true],\"values\":[-1,2,3,4]}"},"fields":{"title":"Finite Maximum Value and Every Original Maximizer Index","stem":"Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. values=[-1, 2, 3, 4], feasible=[true, false, false, true]. Give (values, mask, max, maximum feasible value, all maximizing original indices).","answer":{"kind":"expression","value":"([-1, 2, 3, 4], [Yes, No, No, Yes], max, 4, [3])","explanation":"Compare only feasible candidates and retain all tied indices, not a claim of uniqueness. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([-1, 2, 3, 4], [Yes, No, No, Yes], max, 4, [3])."},"skills":["Finite Maximum Value and Every Original Maximizer Index"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r04-optimization-problem-0061","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"19b7f89c582573f77117d2df28e7bf210093b6173b4a5565c8cba4e7062fe8b3","family_id":"qf-app20-optimization-argmax","seed":202610204061,"semantic_template":"qf-app20-optimization-argmax/{\"feasible\":[true,true,true,true],\"values\":[0,5,2,0]}"},"fields":{"title":"Finite Maximum Value and Every Original Maximizer Index","stem":"Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. values=[0, 5, 2, 0], feasible=[true, true, true, true]. Give (values, mask, max, maximum feasible value, all maximizing original indices).","answer":{"kind":"expression","value":"([0, 5, 2, 0], [Yes, Yes, Yes, Yes], max, 5, [1])","explanation":"Compare only feasible candidates and retain all tied indices, not a claim of uniqueness. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([0, 5, 2, 0], [Yes, Yes, Yes, Yes], max, 5, [1])."},"skills":["Finite Maximum Value and Every Original Maximizer Index"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r04-optimization-problem-0062","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"f9ad5011f66fc9aa14aba398effe2e0651e478955131b495349360e8509c484e","family_id":"qf-app20-optimization-argmax","seed":202610204062,"semantic_template":"qf-app20-optimization-argmax/{\"feasible\":[true,false,true,true],\"values\":[1,8,1,1]}"},"fields":{"title":"Finite Maximum Value and Every Original Maximizer Index","stem":"Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. values=[1, 8, 1, 1], feasible=[true, false, true, true]. Give (values, mask, max, maximum feasible value, all maximizing original indices).","answer":{"kind":"expression","value":"([1, 8, 1, 1], [Yes, No, Yes, Yes], max, 1, [0, 2, 3])","explanation":"Compare only feasible candidates and retain all tied indices, not a claim of uniqueness. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([1, 8, 1, 1], [Yes, No, Yes, Yes], max, 1, [0, 2, 3])."},"skills":["Finite Maximum Value and Every Original Maximizer Index"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r04-optimization-problem-0063","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"f7adf837c49955cf73eb31be0840d7e388b0b6f5552964fa6aaa421aea1b022d","family_id":"qf-app20-optimization-argmax","seed":202610204063,"semantic_template":"qf-app20-optimization-argmax/{\"feasible\":[true,true,false,true],\"values\":[2,-6,0,2]}"},"fields":{"title":"Finite Maximum Value and Every Original Maximizer Index","stem":"Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. values=[2, -6, 0, 2], feasible=[true, true, false, true]. Give (values, mask, max, maximum feasible value, all maximizing original indices).","answer":{"kind":"expression","value":"([2, -6, 0, 2], [Yes, Yes, No, Yes], max, 2, [0, 3])","explanation":"Compare only feasible candidates and retain all tied indices, not a claim of uniqueness. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([2, -6, 0, 2], [Yes, Yes, No, Yes], max, 2, [0, 3])."},"skills":["Finite Maximum Value and Every Original Maximizer Index"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r04-optimization-problem-0064","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"e283d1d797b1b5b88d67d970ceba59aa5641fc82bdf850662bd6daa307e66687","family_id":"qf-app20-optimization-argmax","seed":202610204064,"semantic_template":"qf-app20-optimization-argmax/{\"feasible\":[true,false,true,true],\"values\":[3,-3,-1,3]}"},"fields":{"title":"Finite Maximum Value and Every Original Maximizer Index","stem":"Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. values=[3, -3, -1, 3], feasible=[true, false, true, true]. Give (values, mask, max, maximum feasible value, all maximizing original indices).","answer":{"kind":"expression","value":"([3, -3, -1, 3], [Yes, No, Yes, Yes], max, 3, [0, 3])","explanation":"Compare only feasible candidates and retain all tied indices, not a claim of uniqueness. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([3, -3, -1, 3], [Yes, No, Yes, Yes], max, 3, [0, 3])."},"skills":["Finite Maximum Value and Every Original Maximizer Index"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r04-optimization-problem-0065","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"0e7a535c113e42e039dbc09416304aeb1efe55e75390aff3c455e22072d73824","family_id":"qf-app20-optimization-argmax","seed":202610204065,"semantic_template":"qf-app20-optimization-argmax/{\"feasible\":[true,true,true,true],\"values\":[4,0,-2,4]}"},"fields":{"title":"Finite Maximum Value and Every Original Maximizer Index","stem":"Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. values=[4, 0, -2, 4], feasible=[true, true, true, true]. Give (values, mask, max, maximum feasible value, all maximizing original indices).","answer":{"kind":"expression","value":"([4, 0, -2, 4], [Yes, Yes, Yes, Yes], max, 4, [0, 3])","explanation":"Compare only feasible candidates and retain all tied indices, not a claim of uniqueness. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([4, 0, -2, 4], [Yes, Yes, Yes, Yes], max, 4, [0, 3])."},"skills":["Finite Maximum Value and Every Original Maximizer Index"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r04-optimization-problem-0066","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"3538dc93b3583d5d6cdc4cc83503664357df80da2c83a7b46ea812af6ba9c9fa","family_id":"qf-app20-optimization-argmax","seed":202610204066,"semantic_template":"qf-app20-optimization-argmax/{\"feasible\":[true,false,false,true],\"values\":[5,3,-3,0]}"},"fields":{"title":"Finite Maximum Value and Every Original Maximizer Index","stem":"Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. values=[5, 3, -3, 0], feasible=[true, false, false, true]. Give (values, mask, max, maximum feasible value, all maximizing original indices).","answer":{"kind":"expression","value":"([5, 3, -3, 0], [Yes, No, No, Yes], max, 5, [0])","explanation":"Compare only feasible candidates and retain all tied indices, not a claim of uniqueness. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([5, 3, -3, 0], [Yes, No, No, Yes], max, 5, [0])."},"skills":["Finite Maximum Value and Every Original Maximizer Index"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r04-optimization-problem-0067","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"193b42701a093e5e33cf3ca8823a9920d99a4874cfcf1d8fccf95be56505afe8","family_id":"qf-app20-optimization-argmax","seed":202610204067,"semantic_template":"qf-app20-optimization-argmax/{\"feasible\":[true,true,true,true],\"values\":[6,6,-4,1]}"},"fields":{"title":"Finite Maximum Value and Every Original Maximizer Index","stem":"Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. values=[6, 6, -4, 1], feasible=[true, true, true, true]. Give (values, mask, max, maximum feasible value, all maximizing original indices).","answer":{"kind":"expression","value":"([6, 6, -4, 1], [Yes, Yes, Yes, Yes], max, 6, [0, 1])","explanation":"Compare only feasible candidates and retain all tied indices, not a claim of uniqueness. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([6, 6, -4, 1], [Yes, Yes, Yes, Yes], max, 6, [0, 1])."},"skills":["Finite Maximum Value and Every Original Maximizer Index"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r04-optimization-problem-0068","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"41246ba869d3be5228a2875a4cf2ea480aac36583942cf7ab30993e6693131e4","family_id":"qf-app20-optimization-argmax","seed":202610204068,"semantic_template":"qf-app20-optimization-argmax/{\"feasible\":[true,false,true,true],\"values\":[7,-8,-5,2]}"},"fields":{"title":"Finite Maximum Value and Every Original Maximizer Index","stem":"Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. values=[7, -8, -5, 2], feasible=[true, false, true, true]. Give (values, mask, max, maximum feasible value, all maximizing original indices).","answer":{"kind":"expression","value":"([7, -8, -5, 2], [Yes, No, Yes, Yes], max, 7, [0])","explanation":"Compare only feasible candidates and retain all tied indices, not a claim of uniqueness. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([7, -8, -5, 2], [Yes, No, Yes, Yes], max, 7, [0])."},"skills":["Finite Maximum Value and Every Original Maximizer Index"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r04-optimization-problem-0069","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"2cc953030075256b9ac5392df184a325b273c6a79e5122fbee7beca004b74315","family_id":"qf-app20-optimization-argmax","seed":202610204069,"semantic_template":"qf-app20-optimization-argmax/{\"feasible\":[true,true,false,true],\"values\":[8,-5,-6,3]}"},"fields":{"title":"Finite Maximum Value and Every Original Maximizer Index","stem":"Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. values=[8, -5, -6, 3], feasible=[true, true, false, true]. Give (values, mask, max, maximum feasible value, all maximizing original indices).","answer":{"kind":"expression","value":"([8, -5, -6, 3], [Yes, Yes, No, Yes], max, 8, [0])","explanation":"Compare only feasible candidates and retain all tied indices, not a claim of uniqueness. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([8, -5, -6, 3], [Yes, Yes, No, Yes], max, 8, [0])."},"skills":["Finite Maximum Value and Every Original Maximizer Index"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r04-optimization-problem-0070","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"3fac7681f8f99c1b43cfcb68013960ea95bb99c506829dc434688307c70d6d96","family_id":"qf-app20-optimization-argmax","seed":202610204070,"semantic_template":"qf-app20-optimization-argmax/{\"feasible\":[true,false,true,true],\"values\":[9,-2,-7,4]}"},"fields":{"title":"Finite Maximum Value and Every Original Maximizer Index","stem":"Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. values=[9, -2, -7, 4], feasible=[true, false, true, true]. Give (values, mask, max, maximum feasible value, all maximizing original indices).","answer":{"kind":"expression","value":"([9, -2, -7, 4], [Yes, No, Yes, Yes], max, 9, [0])","explanation":"Compare only feasible candidates and retain all tied indices, not a claim of uniqueness. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([9, -2, -7, 4], [Yes, No, Yes, Yes], max, 9, [0])."},"skills":["Finite Maximum Value and Every Original Maximizer Index"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r04-optimization-problem-0071","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"bcd420d691c70cd5500eecb94a1f168b8011ba1524f347e22f50f6a45c22f815","family_id":"qf-app20-optimization-argmax","seed":202610204071,"semantic_template":"qf-app20-optimization-argmax/{\"feasible\":[true,true,true,true],\"values\":[10,1,-8,0]}"},"fields":{"title":"Finite Maximum Value and Every Original Maximizer Index","stem":"Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. values=[10, 1, -8, 0], feasible=[true, true, true, true]. Give (values, mask, max, maximum feasible value, all maximizing original indices).","answer":{"kind":"expression","value":"([10, 1, -8, 0], [Yes, Yes, Yes, Yes], max, 10, [0])","explanation":"Compare only feasible candidates and retain all tied indices, not a claim of uniqueness. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([10, 1, -8, 0], [Yes, Yes, Yes, Yes], max, 10, [0])."},"skills":["Finite Maximum Value and Every Original Maximizer Index"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r04-optimization-problem-0072","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"a524064c27832c64ae8568e37587e607814ae38be99d74f1ebc387da1f232bed","family_id":"qf-app20-optimization-argmax","seed":202610204072,"semantic_template":"qf-app20-optimization-argmax/{\"feasible\":[true,false,false,true],\"values\":[11,4,-9,1]}"},"fields":{"title":"Finite Maximum Value and Every Original Maximizer Index","stem":"Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. values=[11, 4, -9, 1], feasible=[true, false, false, true]. Give (values, mask, max, maximum feasible value, all maximizing original indices).","answer":{"kind":"expression","value":"([11, 4, -9, 1], [Yes, No, No, Yes], max, 11, [0])","explanation":"Compare only feasible candidates and retain all tied indices, not a claim of uniqueness. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([11, 4, -9, 1], [Yes, No, No, Yes], max, 11, [0])."},"skills":["Finite Maximum Value and Every Original Maximizer Index"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r04-optimization-problem-0073","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"c411898d87c5e7f905befa8daa3049e18d4529b23342170927aaab9b045a06f4","family_id":"qf-app20-optimization-argmax","seed":202610204073,"semantic_template":"qf-app20-optimization-argmax/{\"feasible\":[true,true,true,true],\"values\":[12,7,-10,2]}"},"fields":{"title":"Finite Maximum Value and Every Original Maximizer Index","stem":"Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. values=[12, 7, -10, 2], feasible=[true, true, true, true]. Give (values, mask, max, maximum feasible value, all maximizing original indices).","answer":{"kind":"expression","value":"([12, 7, -10, 2], [Yes, Yes, Yes, Yes], max, 12, [0])","explanation":"Compare only feasible candidates and retain all tied indices, not a claim of uniqueness. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([12, 7, -10, 2], [Yes, Yes, Yes, Yes], max, 12, [0])."},"skills":["Finite Maximum Value and Every Original Maximizer Index"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r04-optimization-problem-0074","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"a6f0e36f2340b9208870f9a77abfdedb98e76d2f01359af4d6a293ea797b8501","family_id":"qf-app20-optimization-argmax","seed":202610204074,"semantic_template":"qf-app20-optimization-argmax/{\"feasible\":[true,false,true,true],\"values\":[13,-7,-11,3]}"},"fields":{"title":"Finite Maximum Value and Every Original Maximizer Index","stem":"Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. values=[13, -7, -11, 3], feasible=[true, false, true, true]. Give (values, mask, max, maximum feasible value, all maximizing original indices).","answer":{"kind":"expression","value":"([13, -7, -11, 3], [Yes, No, Yes, Yes], max, 13, [0])","explanation":"Compare only feasible candidates and retain all tied indices, not a claim of uniqueness. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([13, -7, -11, 3], [Yes, No, Yes, Yes], max, 13, [0])."},"skills":["Finite Maximum Value and Every Original Maximizer Index"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r04-optimization-problem-0075","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"f97261057c8ccb9579fc533685280816988191ea4fd53247a81f27efec895f32","family_id":"qf-app20-optimization-argmax","seed":202610204075,"semantic_template":"qf-app20-optimization-argmax/{\"feasible\":[true,true,false,true],\"values\":[14,-4,-12,4]}"},"fields":{"title":"Finite Maximum Value and Every Original Maximizer Index","stem":"Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. values=[14, -4, -12, 4], feasible=[true, true, false, true]. Give (values, mask, max, maximum feasible value, all maximizing original indices).","answer":{"kind":"expression","value":"([14, -4, -12, 4], [Yes, Yes, No, Yes], max, 14, [0])","explanation":"Compare only feasible candidates and retain all tied indices, not a claim of uniqueness. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([14, -4, -12, 4], [Yes, Yes, No, Yes], max, 14, [0])."},"skills":["Finite Maximum Value and Every Original Maximizer Index"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r04-optimization-problem-0076","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"f408080840e994468b0fadf16f852c49c9ef07962009624966e6bb59aab069fb","family_id":"qf-app20-optimization-linear-constraint-audit","seed":202610204076,"semantic_template":"qf-app20-optimization-linear-constraint-audit/{\"constraint\":[1,1,5],\"direction\":\"max\",\"objective\":[-2,2],\"points\":[[0,0],[1,0],[2,0],[3,0]]}"},"fields":{"title":"A Linear Constraint on a Complete Ordered Finite Point List","stem":"Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. Original points=[[0, 0], [1, 0], [2, 0], [3, 0]], constraint [A,B,c]=[1, 1, 5] means A*x+B*y≤c, objective [u,v]=[-2, 2] means u*x+v*y, direction=max. Give (constraint, objective, direction, every [original index,x,y,feasible?,objective value] row, best feasible value, all optimal indices). Preserve input point order and repeated points.","answer":{"kind":"expression","value":"([1, 1, 5], [-2, 2], max, [[0, 0, 0, Yes, 0], [1, 1, 0, Yes, -2], [2, 2, 0, Yes, -4], [3, 3, 0, Yes, -6]], 0, [0])","explanation":"Evaluate every row but optimize only over feasible rows; the result concerns this explicit list, not the whole continuous half-plane. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([1, 1, 5], [-2, 2], max, [[0, 0, 0, Yes, 0], [1, 1, 0, Yes, -2], [2, 2, 0, Yes, -4], [3, 3, 0, Yes, -6]], 0, [0])."},"skills":["A Linear Constraint on a Complete Ordered Finite Point List"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r04-optimization-problem-0077","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"73f29cec972d44de4e69ea49a605748b8545c87b43b6d5917c64b1794ad86988","family_id":"qf-app20-optimization-linear-constraint-audit","seed":202610204077,"semantic_template":"qf-app20-optimization-linear-constraint-audit/{\"constraint\":[2,1,6],\"direction\":\"min\",\"objective\":[-1,2],\"points\":[[0,0],[1,1],[2,2],[3,1]]}"},"fields":{"title":"A Linear Constraint on a Complete Ordered Finite Point List","stem":"Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. Original points=[[0, 0], [1, 1], [2, 2], [3, 1]], constraint [A,B,c]=[2, 1, 6] means A*x+B*y≤c, objective [u,v]=[-1, 2] means u*x+v*y, direction=min. Give (constraint, objective, direction, every [original index,x,y,feasible?,objective value] row, best feasible value, all optimal indices). Preserve input point order and repeated points.","answer":{"kind":"expression","value":"([2, 1, 6], [-1, 2], min, [[0, 0, 0, Yes, 0], [1, 1, 1, Yes, 1], [2, 2, 2, Yes, 2], [3, 3, 1, No, -1]], 0, [0])","explanation":"Evaluate every row but optimize only over feasible rows; the result concerns this explicit list, not the whole continuous half-plane. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([2, 1, 6], [-1, 2], min, [[0, 0, 0, Yes, 0], [1, 1, 1, Yes, 1], [2, 2, 2, Yes, 2], [3, 3, 1, No, -1]], 0, [0])."},"skills":["A Linear Constraint on a Complete Ordered Finite Point List"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r04-optimization-problem-0078","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"b0010952a442b8c847697754e520d06124c22e6b382a09834978740ff4bbe554","family_id":"qf-app20-optimization-linear-constraint-audit","seed":202610204078,"semantic_template":"qf-app20-optimization-linear-constraint-audit/{\"constraint\":[3,1,7],\"direction\":\"max\",\"objective\":[0,2],\"points\":[[0,0],[1,2],[2,4],[3,2]]}"},"fields":{"title":"A Linear Constraint on a Complete Ordered Finite Point List","stem":"Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. Original points=[[0, 0], [1, 2], [2, 4], [3, 2]], constraint [A,B,c]=[3, 1, 7] means A*x+B*y≤c, objective [u,v]=[0, 2] means u*x+v*y, direction=max. Give (constraint, objective, direction, every [original index,x,y,feasible?,objective value] row, best feasible value, all optimal indices). Preserve input point order and repeated points.","answer":{"kind":"expression","value":"([3, 1, 7], [0, 2], max, [[0, 0, 0, Yes, 0], [1, 1, 2, Yes, 4], [2, 2, 4, No, 8], [3, 3, 2, No, 4]], 4, [1])","explanation":"Evaluate every row but optimize only over feasible rows; the result concerns this explicit list, not the whole continuous half-plane. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([3, 1, 7], [0, 2], max, [[0, 0, 0, Yes, 0], [1, 1, 2, Yes, 4], [2, 2, 4, No, 8], [3, 3, 2, No, 4]], 4, [1])."},"skills":["A Linear Constraint on a Complete Ordered Finite Point List"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r04-optimization-problem-0079","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"0d2aeb3356c3b5e915c895c7691ae333e4a3d2264a0b4cdd1de8405d5e7f55d8","family_id":"qf-app20-optimization-linear-constraint-audit","seed":202610204079,"semantic_template":"qf-app20-optimization-linear-constraint-audit/{\"constraint\":[1,1,8],\"direction\":\"min\",\"objective\":[1,2],\"points\":[[0,0],[1,3],[2,6],[3,3]]}"},"fields":{"title":"A Linear Constraint on a Complete Ordered Finite Point List","stem":"Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. Original points=[[0, 0], [1, 3], [2, 6], [3, 3]], constraint [A,B,c]=[1, 1, 8] means A*x+B*y≤c, objective [u,v]=[1, 2] means u*x+v*y, direction=min. Give (constraint, objective, direction, every [original index,x,y,feasible?,objective value] row, best feasible value, all optimal indices). Preserve input point order and repeated points.","answer":{"kind":"expression","value":"([1, 1, 8], [1, 2], min, [[0, 0, 0, Yes, 0], [1, 1, 3, Yes, 7], [2, 2, 6, Yes, 14], [3, 3, 3, Yes, 9]], 0, [0])","explanation":"Evaluate every row but optimize only over feasible rows; the result concerns this explicit list, not the whole continuous half-plane. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([1, 1, 8], [1, 2], min, [[0, 0, 0, Yes, 0], [1, 1, 3, Yes, 7], [2, 2, 6, Yes, 14], [3, 3, 3, Yes, 9]], 0, [0])."},"skills":["A Linear Constraint on a Complete Ordered Finite Point List"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r04-optimization-problem-0080","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"ade8a48d6f84452f00b72ef89b5b4c0f155a8c58240d217de7c1baa425787f0d","family_id":"qf-app20-optimization-linear-constraint-audit","seed":202610204080,"semantic_template":"qf-app20-optimization-linear-constraint-audit/{\"constraint\":[2,1,9],\"direction\":\"max\",\"objective\":[2,2],\"points\":[[0,0],[1,4],[2,1],[3,0]]}"},"fields":{"title":"A Linear Constraint on a Complete Ordered Finite Point List","stem":"Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. Original points=[[0, 0], [1, 4], [2, 1], [3, 0]], constraint [A,B,c]=[2, 1, 9] means A*x+B*y≤c, objective [u,v]=[2, 2] means u*x+v*y, direction=max. Give (constraint, objective, direction, every [original index,x,y,feasible?,objective value] row, best feasible value, all optimal indices). Preserve input point order and repeated points.","answer":{"kind":"expression","value":"([2, 1, 9], [2, 2], max, [[0, 0, 0, Yes, 0], [1, 1, 4, Yes, 10], [2, 2, 1, Yes, 6], [3, 3, 0, Yes, 6]], 10, [1])","explanation":"Evaluate every row but optimize only over feasible rows; the result concerns this explicit list, not the whole continuous half-plane. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([2, 1, 9], [2, 2], max, [[0, 0, 0, Yes, 0], [1, 1, 4, Yes, 10], [2, 2, 1, Yes, 6], [3, 3, 0, Yes, 6]], 10, [1])."},"skills":["A Linear Constraint on a Complete Ordered Finite Point List"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r04-optimization-problem-0081","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"5b352b248abbbe5b0560b8cfdb6ffda02036e6dd8f50a9193296343319f454c2","family_id":"qf-app20-optimization-linear-constraint-audit","seed":202610204081,"semantic_template":"qf-app20-optimization-linear-constraint-audit/{\"constraint\":[3,1,10],\"direction\":\"min\",\"objective\":[-2,2],\"points\":[[0,0],[1,0],[2,3],[3,1]]}"},"fields":{"title":"A Linear Constraint on a Complete Ordered Finite Point List","stem":"Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. Original points=[[0, 0], [1, 0], [2, 3], [3, 1]], constraint [A,B,c]=[3, 1, 10] means A*x+B*y≤c, objective [u,v]=[-2, 2] means u*x+v*y, direction=min. Give (constraint, objective, direction, every [original index,x,y,feasible?,objective value] row, best feasible value, all optimal indices). Preserve input point order and repeated points.","answer":{"kind":"expression","value":"([3, 1, 10], [-2, 2], min, [[0, 0, 0, Yes, 0], [1, 1, 0, Yes, -2], [2, 2, 3, Yes, 2], [3, 3, 1, Yes, -4]], -4, [3])","explanation":"Evaluate every row but optimize only over feasible rows; the result concerns this explicit list, not the whole continuous half-plane. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([3, 1, 10], [-2, 2], min, [[0, 0, 0, Yes, 0], [1, 1, 0, Yes, -2], [2, 2, 3, Yes, 2], [3, 3, 1, Yes, -4]], -4, [3])."},"skills":["A Linear Constraint on a Complete Ordered Finite Point List"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r04-optimization-problem-0082","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"b533e70000da791c0a26be38567ba3bfb9dac1cf322501072b46691e48b1dd9f","family_id":"qf-app20-optimization-linear-constraint-audit","seed":202610204082,"semantic_template":"qf-app20-optimization-linear-constraint-audit/{\"constraint\":[1,1,11],\"direction\":\"max\",\"objective\":[-1,2],\"points\":[[0,0],[1,1],[2,5],[3,2]]}"},"fields":{"title":"A Linear Constraint on a Complete Ordered Finite Point List","stem":"Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. Original points=[[0, 0], [1, 1], [2, 5], [3, 2]], constraint [A,B,c]=[1, 1, 11] means A*x+B*y≤c, objective [u,v]=[-1, 2] means u*x+v*y, direction=max. Give (constraint, objective, direction, every [original index,x,y,feasible?,objective value] row, best feasible value, all optimal indices). Preserve input point order and repeated points.","answer":{"kind":"expression","value":"([1, 1, 11], [-1, 2], max, [[0, 0, 0, Yes, 0], [1, 1, 1, Yes, 1], [2, 2, 5, Yes, 8], [3, 3, 2, Yes, 1]], 8, [2])","explanation":"Evaluate every row but optimize only over feasible rows; the result concerns this explicit list, not the whole continuous half-plane. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([1, 1, 11], [-1, 2], max, [[0, 0, 0, Yes, 0], [1, 1, 1, Yes, 1], [2, 2, 5, Yes, 8], [3, 3, 2, Yes, 1]], 8, [2])."},"skills":["A Linear Constraint on a Complete Ordered Finite Point List"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r04-optimization-problem-0083","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"d37d79de1fc861e55dddca1687768525d95f5f74c33ce021849d0f73ddb752dd","family_id":"qf-app20-optimization-linear-constraint-audit","seed":202610204083,"semantic_template":"qf-app20-optimization-linear-constraint-audit/{\"constraint\":[2,1,12],\"direction\":\"min\",\"objective\":[0,2],\"points\":[[0,0],[1,2],[2,0],[3,3]]}"},"fields":{"title":"A Linear Constraint on a Complete Ordered Finite Point List","stem":"Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. Original points=[[0, 0], [1, 2], [2, 0], [3, 3]], constraint [A,B,c]=[2, 1, 12] means A*x+B*y≤c, objective [u,v]=[0, 2] means u*x+v*y, direction=min. Give (constraint, objective, direction, every [original index,x,y,feasible?,objective value] row, best feasible value, all optimal indices). Preserve input point order and repeated points.","answer":{"kind":"expression","value":"([2, 1, 12], [0, 2], min, [[0, 0, 0, Yes, 0], [1, 1, 2, Yes, 4], [2, 2, 0, Yes, 0], [3, 3, 3, Yes, 6]], 0, [0, 2])","explanation":"Evaluate every row but optimize only over feasible rows; the result concerns this explicit list, not the whole continuous half-plane. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([2, 1, 12], [0, 2], min, [[0, 0, 0, Yes, 0], [1, 1, 2, Yes, 4], [2, 2, 0, Yes, 0], [3, 3, 3, Yes, 6]], 0, [0, 2])."},"skills":["A Linear Constraint on a Complete Ordered Finite Point List"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r04-optimization-problem-0084","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"ec1e571265882e7b8fd4e75bac7e150235347b657006b3daf141fc1ccefc700c","family_id":"qf-app20-optimization-linear-constraint-audit","seed":202610204084,"semantic_template":"qf-app20-optimization-linear-constraint-audit/{\"constraint\":[3,1,5],\"direction\":\"max\",\"objective\":[1,2],\"points\":[[0,0],[1,3],[2,2],[3,0]]}"},"fields":{"title":"A Linear Constraint on a Complete Ordered Finite Point List","stem":"Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. Original points=[[0, 0], [1, 3], [2, 2], [3, 0]], constraint [A,B,c]=[3, 1, 5] means A*x+B*y≤c, objective [u,v]=[1, 2] means u*x+v*y, direction=max. Give (constraint, objective, direction, every [original index,x,y,feasible?,objective value] row, best feasible value, all optimal indices). Preserve input point order and repeated points.","answer":{"kind":"expression","value":"([3, 1, 5], [1, 2], max, [[0, 0, 0, Yes, 0], [1, 1, 3, No, 7], [2, 2, 2, No, 6], [3, 3, 0, No, 3]], 0, [0])","explanation":"Evaluate every row but optimize only over feasible rows; the result concerns this explicit list, not the whole continuous half-plane. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([3, 1, 5], [1, 2], max, [[0, 0, 0, Yes, 0], [1, 1, 3, No, 7], [2, 2, 2, No, 6], [3, 3, 0, No, 3]], 0, [0])."},"skills":["A Linear Constraint on a Complete Ordered Finite Point List"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r04-optimization-problem-0085","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"58dde0c1a9b9a611eec9192dde0ac11c4ea98bc9c95e36b8771a5c50f19081af","family_id":"qf-app20-optimization-linear-constraint-audit","seed":202610204085,"semantic_template":"qf-app20-optimization-linear-constraint-audit/{\"constraint\":[1,1,6],\"direction\":\"min\",\"objective\":[2,2],\"points\":[[0,0],[1,4],[2,4],[3,1]]}"},"fields":{"title":"A Linear Constraint on a Complete Ordered Finite Point List","stem":"Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. Original points=[[0, 0], [1, 4], [2, 4], [3, 1]], constraint [A,B,c]=[1, 1, 6] means A*x+B*y≤c, objective [u,v]=[2, 2] means u*x+v*y, direction=min. Give (constraint, objective, direction, every [original index,x,y,feasible?,objective value] row, best feasible value, all optimal indices). Preserve input point order and repeated points.","answer":{"kind":"expression","value":"([1, 1, 6], [2, 2], min, [[0, 0, 0, Yes, 0], [1, 1, 4, Yes, 10], [2, 2, 4, Yes, 12], [3, 3, 1, Yes, 8]], 0, [0])","explanation":"Evaluate every row but optimize only over feasible rows; the result concerns this explicit list, not the whole continuous half-plane. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([1, 1, 6], [2, 2], min, [[0, 0, 0, Yes, 0], [1, 1, 4, Yes, 10], [2, 2, 4, Yes, 12], [3, 3, 1, Yes, 8]], 0, [0])."},"skills":["A Linear Constraint on a Complete Ordered Finite Point List"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r04-optimization-problem-0086","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"def506a418ffd242f5e803ccc4a887671447decc336dc92e7abb9dd81cb5ed2d","family_id":"qf-app20-optimization-linear-constraint-audit","seed":202610204086,"semantic_template":"qf-app20-optimization-linear-constraint-audit/{\"constraint\":[2,1,7],\"direction\":\"max\",\"objective\":[-2,2],\"points\":[[0,0],[1,0],[2,6],[3,2]]}"},"fields":{"title":"A Linear Constraint on a Complete Ordered Finite Point List","stem":"Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. Original points=[[0, 0], [1, 0], [2, 6], [3, 2]], constraint [A,B,c]=[2, 1, 7] means A*x+B*y≤c, objective [u,v]=[-2, 2] means u*x+v*y, direction=max. Give (constraint, objective, direction, every [original index,x,y,feasible?,objective value] row, best feasible value, all optimal indices). Preserve input point order and repeated points.","answer":{"kind":"expression","value":"([2, 1, 7], [-2, 2], max, [[0, 0, 0, Yes, 0], [1, 1, 0, Yes, -2], [2, 2, 6, No, 8], [3, 3, 2, No, -2]], 0, [0])","explanation":"Evaluate every row but optimize only over feasible rows; the result concerns this explicit list, not the whole continuous half-plane. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([2, 1, 7], [-2, 2], max, [[0, 0, 0, Yes, 0], [1, 1, 0, Yes, -2], [2, 2, 6, No, 8], [3, 3, 2, No, -2]], 0, [0])."},"skills":["A Linear Constraint on a Complete Ordered Finite Point List"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r04-optimization-problem-0087","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"8a40777cdb778fb938094574d43601274d055f42571bf33133ac9fee16ac8c92","family_id":"qf-app20-optimization-linear-constraint-audit","seed":202610204087,"semantic_template":"qf-app20-optimization-linear-constraint-audit/{\"constraint\":[3,1,8],\"direction\":\"min\",\"objective\":[-1,2],\"points\":[[0,0],[1,1],[2,1],[3,3]]}"},"fields":{"title":"A Linear Constraint on a Complete Ordered Finite Point List","stem":"Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. Original points=[[0, 0], [1, 1], [2, 1], [3, 3]], constraint [A,B,c]=[3, 1, 8] means A*x+B*y≤c, objective [u,v]=[-1, 2] means u*x+v*y, direction=min. Give (constraint, objective, direction, every [original index,x,y,feasible?,objective value] row, best feasible value, all optimal indices). Preserve input point order and repeated points.","answer":{"kind":"expression","value":"([3, 1, 8], [-1, 2], min, [[0, 0, 0, Yes, 0], [1, 1, 1, Yes, 1], [2, 2, 1, Yes, 0], [3, 3, 3, No, 3]], 0, [0, 2])","explanation":"Evaluate every row but optimize only over feasible rows; the result concerns this explicit list, not the whole continuous half-plane. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([3, 1, 8], [-1, 2], min, [[0, 0, 0, Yes, 0], [1, 1, 1, Yes, 1], [2, 2, 1, Yes, 0], [3, 3, 3, No, 3]], 0, [0, 2])."},"skills":["A Linear Constraint on a Complete Ordered Finite Point List"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r04-optimization-problem-0088","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"8728675278b26f62f78f17276bcd70665e1a0e886c05057a6b9e103ca412fff4","family_id":"qf-app20-optimization-linear-constraint-audit","seed":202610204088,"semantic_template":"qf-app20-optimization-linear-constraint-audit/{\"constraint\":[1,1,9],\"direction\":\"max\",\"objective\":[0,2],\"points\":[[0,0],[1,2],[2,3],[3,0]]}"},"fields":{"title":"A Linear Constraint on a Complete Ordered Finite Point List","stem":"Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. Original points=[[0, 0], [1, 2], [2, 3], [3, 0]], constraint [A,B,c]=[1, 1, 9] means A*x+B*y≤c, objective [u,v]=[0, 2] means u*x+v*y, direction=max. Give (constraint, objective, direction, every [original index,x,y,feasible?,objective value] row, best feasible value, all optimal indices). Preserve input point order and repeated points.","answer":{"kind":"expression","value":"([1, 1, 9], [0, 2], max, [[0, 0, 0, Yes, 0], [1, 1, 2, Yes, 4], [2, 2, 3, Yes, 6], [3, 3, 0, Yes, 0]], 6, [2])","explanation":"Evaluate every row but optimize only over feasible rows; the result concerns this explicit list, not the whole continuous half-plane. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([1, 1, 9], [0, 2], max, [[0, 0, 0, Yes, 0], [1, 1, 2, Yes, 4], [2, 2, 3, Yes, 6], [3, 3, 0, Yes, 0]], 6, [2])."},"skills":["A Linear Constraint on a Complete Ordered Finite Point List"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r04-optimization-problem-0089","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"3780ab8ce270a589bb22dd888a7bd40d5130ffb5944a705d5ed9fffc60c9fb6d","family_id":"qf-app20-optimization-linear-constraint-audit","seed":202610204089,"semantic_template":"qf-app20-optimization-linear-constraint-audit/{\"constraint\":[2,1,10],\"direction\":\"min\",\"objective\":[1,2],\"points\":[[0,0],[1,3],[2,5],[3,1]]}"},"fields":{"title":"A Linear Constraint on a Complete Ordered Finite Point List","stem":"Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. Original points=[[0, 0], [1, 3], [2, 5], [3, 1]], constraint [A,B,c]=[2, 1, 10] means A*x+B*y≤c, objective [u,v]=[1, 2] means u*x+v*y, direction=min. Give (constraint, objective, direction, every [original index,x,y,feasible?,objective value] row, best feasible value, all optimal indices). Preserve input point order and repeated points.","answer":{"kind":"expression","value":"([2, 1, 10], [1, 2], min, [[0, 0, 0, Yes, 0], [1, 1, 3, Yes, 7], [2, 2, 5, Yes, 12], [3, 3, 1, Yes, 5]], 0, [0])","explanation":"Evaluate every row but optimize only over feasible rows; the result concerns this explicit list, not the whole continuous half-plane. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([2, 1, 10], [1, 2], min, [[0, 0, 0, Yes, 0], [1, 1, 3, Yes, 7], [2, 2, 5, Yes, 12], [3, 3, 1, Yes, 5]], 0, [0])."},"skills":["A Linear Constraint on a Complete Ordered Finite Point List"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r04-optimization-problem-0090","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"f30bb90fde84d8eeb86555991f527785490c1a98dfa1bb4605eabaf5f9c621f1","family_id":"qf-app20-optimization-linear-constraint-audit","seed":202610204090,"semantic_template":"qf-app20-optimization-linear-constraint-audit/{\"constraint\":[3,1,11],\"direction\":\"max\",\"objective\":[2,2],\"points\":[[0,0],[1,4],[2,0],[3,2]]}"},"fields":{"title":"A Linear Constraint on a Complete Ordered Finite Point List","stem":"Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. Original points=[[0, 0], [1, 4], [2, 0], [3, 2]], constraint [A,B,c]=[3, 1, 11] means A*x+B*y≤c, objective [u,v]=[2, 2] means u*x+v*y, direction=max. Give (constraint, objective, direction, every [original index,x,y,feasible?,objective value] row, best feasible value, all optimal indices). Preserve input point order and repeated points.","answer":{"kind":"expression","value":"([3, 1, 11], [2, 2], max, [[0, 0, 0, Yes, 0], [1, 1, 4, Yes, 10], [2, 2, 0, Yes, 4], [3, 3, 2, Yes, 10]], 10, [1, 3])","explanation":"Evaluate every row but optimize only over feasible rows; the result concerns this explicit list, not the whole continuous half-plane. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([3, 1, 11], [2, 2], max, [[0, 0, 0, Yes, 0], [1, 1, 4, Yes, 10], [2, 2, 0, Yes, 4], [3, 3, 2, Yes, 10]], 10, [1, 3])."},"skills":["A Linear Constraint on a Complete Ordered Finite Point List"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r04-optimization-problem-0091","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"3f9f5c85f817d370f2b15471b5f1dc37842ec1cdc2441d9b13f1df9c673373ef","family_id":"qf-app20-optimization-linear-constraint-audit","seed":202610204091,"semantic_template":"qf-app20-optimization-linear-constraint-audit/{\"constraint\":[1,1,12],\"direction\":\"min\",\"objective\":[-2,2],\"points\":[[0,0],[1,0],[2,2],[3,3]]}"},"fields":{"title":"A Linear Constraint on a Complete Ordered Finite Point List","stem":"Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. Original points=[[0, 0], [1, 0], [2, 2], [3, 3]], constraint [A,B,c]=[1, 1, 12] means A*x+B*y≤c, objective [u,v]=[-2, 2] means u*x+v*y, direction=min. Give (constraint, objective, direction, every [original index,x,y,feasible?,objective value] row, best feasible value, all optimal indices). Preserve input point order and repeated points.","answer":{"kind":"expression","value":"([1, 1, 12], [-2, 2], min, [[0, 0, 0, Yes, 0], [1, 1, 0, Yes, -2], [2, 2, 2, Yes, 0], [3, 3, 3, Yes, 0]], -2, [1])","explanation":"Evaluate every row but optimize only over feasible rows; the result concerns this explicit list, not the whole continuous half-plane. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([1, 1, 12], [-2, 2], min, [[0, 0, 0, Yes, 0], [1, 1, 0, Yes, -2], [2, 2, 2, Yes, 0], [3, 3, 3, Yes, 0]], -2, [1])."},"skills":["A Linear Constraint on a Complete Ordered Finite Point List"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r04-optimization-problem-0092","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"ecb1218d74f0d45146f7749846e5ddb2d017487cafce40bd186b74b9b496b682","family_id":"qf-app20-optimization-linear-constraint-audit","seed":202610204092,"semantic_template":"qf-app20-optimization-linear-constraint-audit/{\"constraint\":[2,1,5],\"direction\":\"max\",\"objective\":[-1,2],\"points\":[[0,0],[1,1],[2,4],[3,0]]}"},"fields":{"title":"A Linear Constraint on a Complete Ordered Finite Point List","stem":"Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. Original points=[[0, 0], [1, 1], [2, 4], [3, 0]], constraint [A,B,c]=[2, 1, 5] means A*x+B*y≤c, objective [u,v]=[-1, 2] means u*x+v*y, direction=max. Give (constraint, objective, direction, every [original index,x,y,feasible?,objective value] row, best feasible value, all optimal indices). Preserve input point order and repeated points.","answer":{"kind":"expression","value":"([2, 1, 5], [-1, 2], max, [[0, 0, 0, Yes, 0], [1, 1, 1, Yes, 1], [2, 2, 4, No, 6], [3, 3, 0, No, -3]], 1, [1])","explanation":"Evaluate every row but optimize only over feasible rows; the result concerns this explicit list, not the whole continuous half-plane. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([2, 1, 5], [-1, 2], max, [[0, 0, 0, Yes, 0], [1, 1, 1, Yes, 1], [2, 2, 4, No, 6], [3, 3, 0, No, -3]], 1, [1])."},"skills":["A Linear Constraint on a Complete Ordered Finite Point List"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r04-optimization-problem-0093","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"300f0e022a88be1f08e408cf3a72e267cd149b0c3e182fcdc4dca77e20091a34","family_id":"qf-app20-optimization-linear-constraint-audit","seed":202610204093,"semantic_template":"qf-app20-optimization-linear-constraint-audit/{\"constraint\":[3,1,6],\"direction\":\"min\",\"objective\":[0,2],\"points\":[[0,0],[1,2],[2,6],[3,1]]}"},"fields":{"title":"A Linear Constraint on a Complete Ordered Finite Point List","stem":"Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. Original points=[[0, 0], [1, 2], [2, 6], [3, 1]], constraint [A,B,c]=[3, 1, 6] means A*x+B*y≤c, objective [u,v]=[0, 2] means u*x+v*y, direction=min. Give (constraint, objective, direction, every [original index,x,y,feasible?,objective value] row, best feasible value, all optimal indices). Preserve input point order and repeated points.","answer":{"kind":"expression","value":"([3, 1, 6], [0, 2], min, [[0, 0, 0, Yes, 0], [1, 1, 2, Yes, 4], [2, 2, 6, No, 12], [3, 3, 1, No, 2]], 0, [0])","explanation":"Evaluate every row but optimize only over feasible rows; the result concerns this explicit list, not the whole continuous half-plane. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([3, 1, 6], [0, 2], min, [[0, 0, 0, Yes, 0], [1, 1, 2, Yes, 4], [2, 2, 6, No, 12], [3, 3, 1, No, 2]], 0, [0])."},"skills":["A Linear Constraint on a Complete Ordered Finite Point List"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r04-optimization-problem-0094","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"8e2a299339552066864e668825e127ee51b38d41c732e1cc3f9729de1a1c8cac","family_id":"qf-app20-optimization-linear-constraint-audit","seed":202610204094,"semantic_template":"qf-app20-optimization-linear-constraint-audit/{\"constraint\":[1,1,7],\"direction\":\"max\",\"objective\":[1,2],\"points\":[[0,0],[1,3],[2,1],[3,2]]}"},"fields":{"title":"A Linear Constraint on a Complete Ordered Finite Point List","stem":"Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. Original points=[[0, 0], [1, 3], [2, 1], [3, 2]], constraint [A,B,c]=[1, 1, 7] means A*x+B*y≤c, objective [u,v]=[1, 2] means u*x+v*y, direction=max. Give (constraint, objective, direction, every [original index,x,y,feasible?,objective value] row, best feasible value, all optimal indices). Preserve input point order and repeated points.","answer":{"kind":"expression","value":"([1, 1, 7], [1, 2], max, [[0, 0, 0, Yes, 0], [1, 1, 3, Yes, 7], [2, 2, 1, Yes, 4], [3, 3, 2, Yes, 7]], 7, [1, 3])","explanation":"Evaluate every row but optimize only over feasible rows; the result concerns this explicit list, not the whole continuous half-plane. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([1, 1, 7], [1, 2], max, [[0, 0, 0, Yes, 0], [1, 1, 3, Yes, 7], [2, 2, 1, Yes, 4], [3, 3, 2, Yes, 7]], 7, [1, 3])."},"skills":["A Linear Constraint on a Complete Ordered Finite Point List"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r04-optimization-problem-0095","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"ded8579f99a8908bcf35cc6172692a9fd0102cf1fa69d4cf6fb24affd78cdc3b","family_id":"qf-app20-optimization-linear-constraint-audit","seed":202610204095,"semantic_template":"qf-app20-optimization-linear-constraint-audit/{\"constraint\":[2,1,8],\"direction\":\"min\",\"objective\":[2,2],\"points\":[[0,0],[1,4],[2,3],[3,3]]}"},"fields":{"title":"A Linear Constraint on a Complete Ordered Finite Point List","stem":"Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. Original points=[[0, 0], [1, 4], [2, 3], [3, 3]], constraint [A,B,c]=[2, 1, 8] means A*x+B*y≤c, objective [u,v]=[2, 2] means u*x+v*y, direction=min. Give (constraint, objective, direction, every [original index,x,y,feasible?,objective value] row, best feasible value, all optimal indices). Preserve input point order and repeated points.","answer":{"kind":"expression","value":"([2, 1, 8], [2, 2], min, [[0, 0, 0, Yes, 0], [1, 1, 4, Yes, 10], [2, 2, 3, Yes, 10], [3, 3, 3, No, 12]], 0, [0])","explanation":"Evaluate every row but optimize only over feasible rows; the result concerns this explicit list, not the whole continuous half-plane. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([2, 1, 8], [2, 2], min, [[0, 0, 0, Yes, 0], [1, 1, 4, Yes, 10], [2, 2, 3, Yes, 10], [3, 3, 3, No, 12]], 0, [0])."},"skills":["A Linear Constraint on a Complete Ordered Finite Point List"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r04-optimization-problem-0096","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"d9fa524558c599ca6f8ada0479fcf9cfb6ea0ca7def45b90352cefffe74d18a6","family_id":"qf-app20-optimization-linear-constraint-audit","seed":202610204096,"semantic_template":"qf-app20-optimization-linear-constraint-audit/{\"constraint\":[3,1,9],\"direction\":\"max\",\"objective\":[-2,2],\"points\":[[0,0],[1,0],[2,5],[3,0]]}"},"fields":{"title":"A Linear Constraint on a Complete Ordered Finite Point List","stem":"Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. Original points=[[0, 0], [1, 0], [2, 5], [3, 0]], constraint [A,B,c]=[3, 1, 9] means A*x+B*y≤c, objective [u,v]=[-2, 2] means u*x+v*y, direction=max. Give (constraint, objective, direction, every [original index,x,y,feasible?,objective value] row, best feasible value, all optimal indices). Preserve input point order and repeated points.","answer":{"kind":"expression","value":"([3, 1, 9], [-2, 2], max, [[0, 0, 0, Yes, 0], [1, 1, 0, Yes, -2], [2, 2, 5, No, 6], [3, 3, 0, Yes, -6]], 0, [0])","explanation":"Evaluate every row but optimize only over feasible rows; the result concerns this explicit list, not the whole continuous half-plane. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([3, 1, 9], [-2, 2], max, [[0, 0, 0, Yes, 0], [1, 1, 0, Yes, -2], [2, 2, 5, No, 6], [3, 3, 0, Yes, -6]], 0, [0])."},"skills":["A Linear Constraint on a Complete Ordered Finite Point List"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r04-optimization-problem-0097","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"ef2d7363e3ce529189acf652687fc766fc40f73cf90a7e5603c2337dca6f6389","family_id":"qf-app20-optimization-linear-constraint-audit","seed":202610204097,"semantic_template":"qf-app20-optimization-linear-constraint-audit/{\"constraint\":[1,1,10],\"direction\":\"min\",\"objective\":[-1,2],\"points\":[[0,0],[1,1],[2,0],[3,1]]}"},"fields":{"title":"A Linear Constraint on a Complete Ordered Finite Point List","stem":"Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. Original points=[[0, 0], [1, 1], [2, 0], [3, 1]], constraint [A,B,c]=[1, 1, 10] means A*x+B*y≤c, objective [u,v]=[-1, 2] means u*x+v*y, direction=min. Give (constraint, objective, direction, every [original index,x,y,feasible?,objective value] row, best feasible value, all optimal indices). Preserve input point order and repeated points.","answer":{"kind":"expression","value":"([1, 1, 10], [-1, 2], min, [[0, 0, 0, Yes, 0], [1, 1, 1, Yes, 1], [2, 2, 0, Yes, -2], [3, 3, 1, Yes, -1]], -2, [2])","explanation":"Evaluate every row but optimize only over feasible rows; the result concerns this explicit list, not the whole continuous half-plane. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([1, 1, 10], [-1, 2], min, [[0, 0, 0, Yes, 0], [1, 1, 1, Yes, 1], [2, 2, 0, Yes, -2], [3, 3, 1, Yes, -1]], -2, [2])."},"skills":["A Linear Constraint on a Complete Ordered Finite Point List"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r04-optimization-problem-0098","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"03d98370c8b60f4046ece2557251b3aaf59e8406d0bd1dc56f0668aa14df1c67","family_id":"qf-app20-optimization-linear-constraint-audit","seed":202610204098,"semantic_template":"qf-app20-optimization-linear-constraint-audit/{\"constraint\":[2,1,11],\"direction\":\"max\",\"objective\":[0,2],\"points\":[[0,0],[1,2],[2,2],[3,2]]}"},"fields":{"title":"A Linear Constraint on a Complete Ordered Finite Point List","stem":"Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. Original points=[[0, 0], [1, 2], [2, 2], [3, 2]], constraint [A,B,c]=[2, 1, 11] means A*x+B*y≤c, objective [u,v]=[0, 2] means u*x+v*y, direction=max. Give (constraint, objective, direction, every [original index,x,y,feasible?,objective value] row, best feasible value, all optimal indices). Preserve input point order and repeated points.","answer":{"kind":"expression","value":"([2, 1, 11], [0, 2], max, [[0, 0, 0, Yes, 0], [1, 1, 2, Yes, 4], [2, 2, 2, Yes, 4], [3, 3, 2, Yes, 4]], 4, [1, 2, 3])","explanation":"Evaluate every row but optimize only over feasible rows; the result concerns this explicit list, not the whole continuous half-plane. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([2, 1, 11], [0, 2], max, [[0, 0, 0, Yes, 0], [1, 1, 2, Yes, 4], [2, 2, 2, Yes, 4], [3, 3, 2, Yes, 4]], 4, [1, 2, 3])."},"skills":["A Linear Constraint on a Complete Ordered Finite Point List"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r04-optimization-problem-0099","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"8cd2bc7893c007f8b2cf6eabbc2319d2e715e3f2aabc3b81a5081629826cb8aa","family_id":"qf-app20-optimization-linear-constraint-audit","seed":202610204099,"semantic_template":"qf-app20-optimization-linear-constraint-audit/{\"constraint\":[3,1,12],\"direction\":\"min\",\"objective\":[1,2],\"points\":[[0,0],[1,3],[2,4],[3,3]]}"},"fields":{"title":"A Linear Constraint on a Complete Ordered Finite Point List","stem":"Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. Original points=[[0, 0], [1, 3], [2, 4], [3, 3]], constraint [A,B,c]=[3, 1, 12] means A*x+B*y≤c, objective [u,v]=[1, 2] means u*x+v*y, direction=min. Give (constraint, objective, direction, every [original index,x,y,feasible?,objective value] row, best feasible value, all optimal indices). Preserve input point order and repeated points.","answer":{"kind":"expression","value":"([3, 1, 12], [1, 2], min, [[0, 0, 0, Yes, 0], [1, 1, 3, Yes, 7], [2, 2, 4, Yes, 10], [3, 3, 3, Yes, 9]], 0, [0])","explanation":"Evaluate every row but optimize only over feasible rows; the result concerns this explicit list, not the whole continuous half-plane. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([3, 1, 12], [1, 2], min, [[0, 0, 0, Yes, 0], [1, 1, 3, Yes, 7], [2, 2, 4, Yes, 10], [3, 3, 3, Yes, 9]], 0, [0])."},"skills":["A Linear Constraint on a Complete Ordered Finite Point List"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261013-advance-20261020-r04-optimization-problem-0100","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"e8643a4c5d08dffa067abe0c2f0d4f069c48a6d679c92e73c5e02ac877aa9620","family_id":"qf-app20-optimization-linear-constraint-audit","seed":202610204100,"semantic_template":"qf-app20-optimization-linear-constraint-audit/{\"constraint\":[1,1,5],\"direction\":\"max\",\"objective\":[2,2],\"points\":[[0,0],[1,4],[2,6],[3,0]]}"},"fields":{"title":"A Linear Constraint on a Complete Ordered Finite Point List","stem":"Use the complete explicitly declared finite candidate list and Boolean feasible mask, with at least one feasible candidate. Preserve original zero-based indices and every tie; no unlisted or continuous-domain optimum or general complexity claim is inferred. Original points=[[0, 0], [1, 4], [2, 6], [3, 0]], constraint [A,B,c]=[1, 1, 5] means A*x+B*y≤c, objective [u,v]=[2, 2] means u*x+v*y, direction=max. Give (constraint, objective, direction, every [original index,x,y,feasible?,objective value] row, best feasible value, all optimal indices). Preserve input point order and repeated points.","answer":{"kind":"expression","value":"([1, 1, 5], [2, 2], max, [[0, 0, 0, Yes, 0], [1, 1, 4, Yes, 10], [2, 2, 6, No, 16], [3, 3, 0, Yes, 6]], 10, [1])","explanation":"Evaluate every row but optimize only over feasible rows; the result concerns this explicit list, not the whole continuous half-plane. Exact finite model checks are not general theorems or empirical forecasts. The exact result, retaining the requested order, is ([1, 1, 5], [2, 2], max, [[0, 0, 0, Yes, 0], [1, 1, 4, Yes, 10], [2, 2, 6, No, 16], [3, 3, 0, Yes, 6]], 10, [1])."},"skills":["A Linear Constraint on a Complete Ordered Finite Point List"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}